Session LA: Poster Session (3:15-5:00PM)

Oscillatory Behavior of an Arc Airfoil in Low-Speed Airflow

A computational investigation is conducted to study the oscillatory behavior of an arc airfoil situated in low-speed airflow. The present work is relevant to situations where the conventional rigid airfoils do not apply, such as the flight of bats. The outcome of this study is also beneficial in the design of micro air vehicles with flexible wings. The computations are performed using a deforming mesh to accommodate the airfoil oscillations. An unsteady, spatially second-order algorithm is employed to capture the time-variations of the lift and drag coefficients. A key feature of the present work is the flow response to airfoil oscillations. Fast Fourier Transform was applied to various parameters of the flow. For certain values of angle of attack for the non-oscillating airfoil, the flow has a dominant frequency and a well-defined vortex shedding. For other values of angle of attack, the flow around the non-oscillating airfoil contains many frequencies and has complex vortical structures. However, the oscillating airfoil in all cases makes the flow field periodic with well-defined patterns of vortex shedding. In this work, the flux of vorticity from the airfoil surface into the airflow is computed and compared with the pressure gradient along the surface of the airfoil. Effects of oscillations on magnitude and behavior of aerodynamic forces are also studied.   

A universal law of the elasticity of multilamellar lipid membranes under compression

Multilamellar lipid membranes play critical roles in the mechanics and chemistry of cells, lung and biolubrication of articular joints. One of their most interesting mechanical properties is their elasticity than enable them to resist anisotropic compression where the pressure in the direction normal to the membrane is larger than in other directions. This resistance to compression is strongly dependent on hydration, or the number of water molecules confined between two adjacent lipid membranes. Using coarse-grained molecular dynamics, we show that the elastic behavior or multilamellar membranes is in fact universal over a large range of hydration. A universal law is derived from considerations of intermolecular forces and volume vacancy between lipid molecules. The ability of the proposed law to predict the increase of the membrane surface area as a function of the compression rate and hydration is expected to help the modeling of multilamellar membranes at the continuum level.   

Designing self-propelling micro-swimmers using responsive gels

We use computational modeling to design a synthetic micro-swimmer that not only self-propels but also navigates in highly viscous environments. Our simple swimmer consists of a cubic gel body with two rectangular stiff flaps attached to its opposite sides and a stimuli-sensitive flexible flap at the body front. The responsive gel undergoes periodic expansion and contraction that can be induced by certain external stimuli such as temperature, light, magnetic or electric fields. The periodic changes in the volume of the body lead to asymmetric beating motion of the propulsion flaps which propel the micro-swimmer through the inertialess fluid. We study the effect of body elasticity on the locomotion of our swimmer and show how the elasticity of the body can be harnessed to induce forward and backward swimming motion. We also demonstrate that our swimmer can successfully turn in the desired direction following the bending of the responsive steering flap. In this scenario, the steering flap bends and creates flow asymmetry which results in the swimmer rotation.   

Flexible Wing Pitch-up and Pitch-down in Free Steam Flows

The direct simulations of the pitch-up and pitch-down of flexible and rigid wings in a free stream are conducted at the Reynolds number of $Re=100$ by using the lattice Boltzmann flexible particle method. The effect of bending flexibility in span-wise direction on unsteady aerodynamics are investigated. It is found that when the reduced frequency is large, the lift and drag forces increase nonlinearly upto a maximum as the flexibility increases, then falls down as the flexibility becomes excessively large. The maximum value in both lift and drag forces are significantly larger for a flexible wing than for a rigid wing. However, when the reduced frequency is small, no obvious lift maximum is observed. It seems that flexibility can be used to enhance the lift force at a high reduced frequency. The power efficiency, or lift force per input power, has a similar behavior to the lift, indicating the flexibility could benefit the power efficiency. Surprisingly flexibility improves lift only during pitch-down motion while the flexibility has a negative impact on lift during pitch-up motion, indicating that the pitch-down motion dominates the lift improvement due to flexibility. In a maneuver case a small and adequate deformation may largely enhances the wake capture, results in large LEV and TEV and reduces the flow separation. The wake capture is a main mechanism for a flexible wing to improve the lift.   

Simplified physical models of the flow around flexible insect wings at low Reynolds numbers

Some of the smallest insects fly at Reynolds numbers in the range of 5-100. We built a dynamically scaled physical model of a flexible insect wing and measured the resulting wing deformations and flow fields. The wing models were submerged in diluted corn syrup and rotated about the root of the wing for Reynolds numbers ranging from 1-100. Spatially resolved flow fields were obtained using particle image velocimetry (PIV). Deformations of the wing were tracked using DLTdv software to determine the motion and induced curvature of the wing.   

Particle Deposition During Airway Closure

Inhaled aerosol particles deposit in the lung and may be from environmental, toxic, or medical therapy sources. While much research focuses on inspiratory deposition, primarily at airway bifurcations due to inertial impaction, there are other mechanisms that allow the particles to reach the airway surface, such as gravitational settling and diffusion depending on particle size. We introduce a new mechanism not previously studied, i.e. aerosol deposition from airway closure. The airways are lined with a liquid layer. Due to the surface tension driven instability, a liquid plug can form from this layer which blocks the airway. This process of airway closure tends to occur toward the end of expiration. In this study, the efficiency of the impaction of the particles during airway closure will be investigated. The particles will be released from the upstream of the airway and convected by the air flow and deposited onto the closing liquid layer. We solve the governing equations using a finite volume approach in conjunction with a sharp interface method for the interfaces. Once the velocity field of the gas flow is obtained, the path of the particles will be calculated and the efficiency of the deposition can be estimated.   

Transient motion of mucus plugs in respiratory airways

Airway closure occurs in lung diseases such as asthma, cystic fibrosis, or emphysema which have an excess of mucus that forms plugs. The reopening process involves displacement of mucus plugs in the airways by the airflow of respiration. Mucus is a non-Newtonian fluid with a yield stress; therefore its behavior can be approximated by a Bingham fluid constitutive equation. In this work the reopening process is approximated by simulation of a transient Bingham fluid plug in a 2D channel. The governing equations are solved by an Arbitrary Lagrangian Eulerian (ALE) finite element method through an in-house code. The constitutive equation for the Bingham fluid is implemented through a regularization method. The effects of the yield stress on the flow features and wall stresses are discussed with applications to potential injuries to the airway epithelial cells which form the wall. The minimum driving pressure for the initiation of the motion is computed and its value is related to the mucus properties and the plug shape.   

Mucus Rupture in A Collapsed airway: An Experimental Study

Mucus plugs can completely obstruct an airway. Difficulty in mucus clearance results in lost gas exchange and inflammation. Non-Newtonian properties of mucus, yielding stress and shear-thinning, play significant roles in mucus clearance. We use aqueous carbopol 940 as a mucus stimulant to study clearance of a mucus plug with properties of yielding stress and shear-thinning in a bench-top experiment. A collapsed airway of the 12$^{th}$ generation in a human lung is simulated in a two-dimensional PDMS channel. A stable pressure drop is set along the plug to drive rupture. A micro-PIV technique is used to acquire velocity fields during the rupture process. A yielding pressure drop (initiating plug yielding) is nearly independent of initial plug length. Plug rupture can occur by focused deformation along the centerline or by total plug propagation where the trailing film is thicker than the precursor film. Maximum velocity appears at the rupture moment, and increases at higher pressure drop or smaller plug length. The wall shear gradient can undergo a rapid reversal when rupture occurs, possibly an injurious event to underlying airway epithelial cells.   

Microbubble array under ultrasound excitation and its application in cell capture

In this paper, we studied the fluid flow and particle motion induced by a microbubble array exited under ultrasound. A circulation vortex generated in spaces between microbubble array could be controlled by the spacing of the array, the amplitude and frequency of the ultrasound. We observed that particles/cells of particular size could be trapped near the microbubble surface. The microbubble array is used to enrich bimolecular concentration locally as well as capture cells. Such active attraction mechanism has advantages over traditional passive capture methods.   

Dynamic behavior of lean swirling premixed flame generated by change in gravitational orientation -Nonlinear forecasting based on the complex network theory

We experimentally investigated the deterministic nature in the dynamic behavior of a lean swirling premixed flame generated by a change in gravitational orientation from the viewpoint of nonlinear forecasting based on the complex network theory. When the gravitational direction is changed relative to the flame front, i.e., in inverted gravity, an unstable flame is formed in a limited domain of equivalence ratio and swirl number (Gotoda. H et al., PRE, vol. 81, 026211, 2010). A radial basis function network, which quantifies the predictability of time variations in flame front fluctuations of the unstable flames, is applied as a sophisticated nonlinear forecasting method in this work. A nonlinear forecasting approach based on the complex network theory clearly demonstrates that the dynamic behavior of flame front fluctuations represents low-dimensional deterministic chaos. The deterministic nature in the dynamic behavior of flame front fluctuations revealed using the radial basis function network has not yet been reported in previous research on the flame front instability.   

Analysis and Development of a Quick Acting Diaphragm-less Shock Tube Driver

This work discusses the construction and performance characteristics of a diaphragmless shock tube driver. Shock waves play integral roles in many industrial, medical and scientific environments, consequently it is important to observe the behaviour of these waves and how they interact with their surroundings. The diaphragmless shock tube provides a quick and effective means of producing shock waves in gases. The major advantages compared to conventional diaphragms include, minimal downtime between repeated experiments, opening times comparable to those of conventional diaphragms and infinitely adjustable opening pressure without the use of various diaphragm thicknesses. Moreover, the diaphragmless design also eliminates fragments that are carried downstream of the shock tube once the conventional diaphragm is ruptured. The design utilized in this work is built on that of Downey et al. [M.S. Downey, T.J. Cloete, A.D.B.Yates, Shock Waves 21(4): 315-319, 2011] and is improved in order to obtain faster opening times leading to stronger shock formation. Furthermore in depth numerical analysis using the commercial CFD package Fluent is carried out to validate experimental data for driven pressures and opening times as a function of driver pressure.   

Calibration of the k-$\epsilon$ model constants for use in CFD applications

The k-$\epsilon$ turbulence model is a popular choice in CFD modelling due to its robust nature and the fact that it has been well validated. However it has been noted in previous research that the k-$\epsilon$ model has problems predicting flow separation as well as unconfined and transient flows. The model contains five empirical model constants whose values were found through data fitting for a wide range of flows (Launder 1972) but ad-hoc adjustments are often made to these values depending on the situation being modeled. Here we use the example of flow within a regular street canyon to perform a Bayesian calibration of the model constants against wind tunnel data. This allows us to assess the sensitivity of the CFD model to changes in these constants, find the most suitable values for the constants as well as quantifying the uncertainty related to the constants and the CFD model as a whole.   

Control of Polymer Electrodes Shape via Microflow Control in a Drying Droplet

We demonstrated a simple patterning method for the deposition of polymer electrodes such as poly(3,4- ethylenedioxythiophene)/poly(styrenesulfonate) (PEDOT/PSS). We made use of the difference in wettability between hydrophobic surfaces and hydrophilic surfaces to make the patterns. However, the patterns made with our patterning method created undesirable ring-like stains, which were caused by the outward flow of the solute within the PEDOT/PSS solution drop. To achieve homogenous device performance, we proposed a simple process for removing this ring-like stain by making the surface tension gradient in the PEDOT/PSS solution drop. Because this surface tension gradient causes the inward flow of the solute within the PEDOT/PSS solution drop, the ring-like stain is removed. Finally, we confirmed the potential of our patterning method for polymer electrodes such as the PEDOT/PSS by fabricating pentacene thin-film transistors (TFTs) and measuring the electrical properties of the pentacene TFTs.   

Experimental investigation of free falling thin disks. Part II: Onset of three dimensional motion from zigzag to spiral

The free falling motion of thin disk with small dimensionless moment of inertia was investigated experimentally. Transition from two dimensional zigzag motions to three dimensional spiral motions takes place as a consequence of breakup of planar symmetry flow structures. The counter-rotating vortices behind the disk became asymmetry induced by the instability of three dimensional disturbances, one of the separation location moves from the edge to the disk broad surface which induced a new upright vortex. The oscillation in the direction normal to zigzag plane increases with the development of instability. Meanwhile, the oscillation of nutation angle vanishes and reaches a constant value. In addition, we have shown that small moment of inertia is responsible for growth of disturbances in the third dimension by means of generalized Kirchhoff equations.   

Experimental study on thermocapillary motion of isolated drop and coalescence problems of drops

Thermocapillay migrations of drops under temperature gradient were studied through ground-based experiment, experiment using drop tower and space experiment in microgravity. The motion of isolated drop at moderate to large Marangoni numbers (Ma) and the interaction of drops were investigated. Experimental data show that the scaled migration velocity of isolated drop, V/V$_{YGB}$, appears an obvious decrease trend with the increase of Maragoni number up to 5500. This result does not agree with some theoretical predictions. Interferometry was applied in our space experiment to visualize the whole temperature field and to get detailed informations of temperature variation around a moving drop and the thermal wake behind it. Interferometric images indicate that drop's migration very sensitively follows the direction of temperature gradient because of slow migration velocity and microgravity condition. The temperature disturbance around a leading drop and the thermal wake behind it would exist for a quite long time in the real case. The variation of temperature field would substantially affect the migration velocity of a trailing drop in both direction and value, and this would bring about coalescence problems of two or multiple drops.   

Droplet Breakup Mechanisms in Air-blast Atomizers

Atomization processes are encountered in many natural and man-made phenomena. Examples are pollen release by plants, human cough or sneeze, engine fuel injectors, spray paint and many more. The physics governing the atomization of liquids is important in understanding and utilizing atomization processes in both natural and industrial processes. We have observed the governing physics of droplet breakup in an air-blast water atomizer using a high magnification, high speed, and high resolution LASER imaging technique. The droplet breakup mechanisms are investigated in three major categories. First, the liquid drops are flattened to form an oblate ellipsoid (lenticular deformation). Subsequent deformation depends on the magnitude of the internal forces relative to external forces. The ellipsoid is converted into a torus that becomes stretched and disintegrates into smaller drops. Second, the drops become elongated to form a long cylindrical thread or ligament that break up into smaller drops (Cigar-shaped deformation). Third, local deformation on the drop surface creates bulges and protuberances that eventually detach themselves from the parent drop to form smaller drops.   

Development of Anodized-Aluminum Temperature-Sensitive Paint for Flow Field Measurements

Anodized-aluminum temperature-sensitive paint (AA-TSP) is developed to capture the flow fields related to the temperature. Instead of using conventional polymer type TSP, the anodized-aluminum coating can hold material properties from cryogenic to high temperatures limited by its melting point of $\sim$ 930 K. We studied various luminophores onto this coating as a global temperature sensor. Six different quantum dots, which varied the luminescent peak wavelengths, are applied onto this coating. Rhodamine-B, pyronin B, pyronin Y, and europium complex are studied, which are also good candidates as the temperature sensing probes. The temperature calibrations of the developed AA-TSP are shown. The temperature is varied from 100 to 500 K. The temperature sensitivities of the developed AA-TSPs are related to the temperature range calibrated. Comparisons of the AA-TSPs related to the sensitive temperature range are included. A global temperature measurement in a hypersonic wind tunnel is shown as a demonstration of the developed AA-TSPs.   

Dual luminescence imaging applied for capturing the temperature distribution of a super-cooled droplet in collision icing

Dual luminescence image is applied to capture the temperature distribution of a super-cooled droplet in icing when the droplet collides onto a plate. The imaging technique captures the temperature-sensitive luminescence and the temperature-insensitive luminescence, which are spectrally separated. These images are captured by a hi-speed color camera. The icing process from super-cooled condition to ice gives insight into further understandings of the icing in flights, power cables, architectures, etc. The icing formation is shown by time steps by using the hi-speed camera. The formation is discussed from the images captured. The plates are coated with icephobic coatings to understand their effects on the collision icing.   

Influence of local parameters on the dispersion of traffic-related pollutants within street canyons

Ventilation within urban cities and street canyons and the associated air quality is a problem of increasing interest in the last decades. It is important for to minimise exposure of the population to traffic-related pollutants at street level. The residence time of pollutants within the street canyons depends on the meteorological conditions such as wind speed and direction, geometry layout and local parameters (position of traffic lane within the street). An experimental study was carried out to investigate the influence of traffic lane position on the dispersion of traffic-related pollutants within different street canyons geometries: symmetrical (equal building heights on both sides of the street), non-symmetrical (uniform building heights but lower on one side of the street) and heterogeneous (non-uniform building heights on both sides of the street) under constant meteorological conditions. Laboratory experiments were carried out within a water channel and simultaneous measurements of velocity field and concentration scalar levels within and above the street canyons using PIV and PLIF techniques. Traffic -related emissions were simulated using a line emission source. Two positions were examined for all street geometries: line emission source was placed in the centre of the street canyon; line emission source was placed off the centre of the street.   

Wake Structure of Oscillating Cylinders

We studied the vortex-induced oscillations of a tethered cylinder in a flow tank. The cylinder shows various changes (steady, periodic, autorotation) in its orientation as a function of Reynolds number and particle aspect ratio. In particular, we examine a new metric- namely, the distance from the cylinder to the vortex as a function of the Reynolds number. This simple metric proves to be very helpful in characterizing the changes in vortex structure and serves as a useful marker for the various bifurcations in the flow. It is implied through data visualization that this critical point (which indicates a change in wake structure) is present regardless of the lengths of the cylinders. We examined Reynolds numbers in the range of about Re = 550 to Re = 4800, based on the cylinder's length. We also examined relationships between Strouhal number for the particle and associated vortex as a function of Reynolds number and particle aspect ratio.   

The mass, energy, space and time systemic theory- Black hole will take the dark comet to impact our earth

Our solar system has a companion black hole-``Tyche.'' A black hole have many dark planets (dark comets) like that Sun have many planets. The companion black hole could take its dark comets to go into our solar system, So there are a lot of dark comet near the orbit of Jupiter. The companion black hole go near our solar system every 25-27 million years. It could take its dark comets to impact our earth and could trigger the Mass Extinction. The black hole is the space-time center like a dark gas ball. So it absorb the space-time to go to its center like that Sun absorb the mass of matter by the gravity. Because it can absorb the space-time, when the companion black hole go near our solar system, it can cause the expand of space-time of solar system and the red-shift of our observation. The new idea will instead of the ``cosmic inflation''. The black hole and sun build up a system together. When the black hole inbreak our solar system in 20 years, not only it will break our environment, but aslo it will change the systemic genetical code of our life and thing. So it will kill many lives and will produce new life. So it could trigger the Mass Extinction.   

The mass, energy, space and time systemic theory-MEST

The displacement and period of the orbit of the motion are the space-time; the probability of them are the quantum space-time. Both of the energy-momentum tensor and metric tensor belong to the gravitational field. It can direct the space-time. The black hole has a space-time center as a origin of a mass-energy coordinate system and a binding energy of space-time like that sun has a mass-energy center and the nuclear energy. And it has a dark matter field around. There is a balance energy equation between sun and black hole. \begin{equation} E=h\nu=mc^2 \end{equation} Among it, E: the energy of wave of sun, m: the mass of wave, c: the velocity of wave, $\nu$: the frequence of wave, h: the Planck constant. \begin{equation} E'{\psi}=i{\hbar}\frac{\partial{\psi}}{{\partial}t} \end{equation} \begin{equation} m'{\psi}=-i{\hbar}\frac{{\partial}{\psi}{\partial}t} {{(\partial}x)^2} \end{equation} Among it, $E'\psi$: the energy of dark wave of black hole, $m'\psi$: the mass of dark wave, c$'$: the velocity of dark wave, ${\psi}$: the Wave Functions. \begin{equation} h\nu+E'{\psi}=mc^2+m'{\psi}c'^2, (c'^2=-\frac{({\partial}x)^2} {({\partial}t)^2}) \end{equation}   

Axially asymmetric rotating tank experiments for thermally forced stationary waves in geophysical fluids

Fluid dynamical experiments using a rotating tank with an imposed radial temperature gradient provide classical examples of the realization of large-scale atmospheric circulation in a laboratory setting. The last decade has seen a revival of such experiments for research and education. Classical rotating tank experiments have adopted axially symmetric boundary conditions to maintain a zonally uniform ``pole-to-equator'' temperature gradient. Symmetry breaking arises from internal dynamics of baroclinic instability. A notable exception is the class of experiments for topographic effects, in which an isolated obstacle is added to the bottom boundary. This study explores a new type of experiments that are axially asymmetric due to an imposed, zonally non-uniform, temperature in the lateral boundary. This mimics the contrast of warm pool versus cold tongue in the tropical Pacific Ocean. The experiments produced thermally forced quasi-stationary waves with their wavelength comparable to the scale of the localized thermal boundary forcing. The applications of this new type of experiments to understanding Earth's climate will be discussed.   

Possible Electrostatic Precursors to Granular Slip Events

For at least the past 40 years, reports have repeatedly appeared of atmospheric lightning and related effects preceding major earthquakes. Many of these reports are anecdotal and of uncertain reliability, while others appear to have been substantiated by more recent scientific electric field measurements. In this work, we describe laboratory experiments that appear to exhibit sporadic, but statistically significant, electrical precursors to granular slip events. The cause of this phenomenon is unclear: the materials used are neither piezoelectric nor triboluminescent. We speculate that the electrical signals may be related to other electrical phenomena known to be associated with material failures in other contexts, for example in crack formation and in tape peeling.   

The formation of bulges and coastal currents from buoyant outflows

Buoyant outflows exiting (e.g. from an estuary or a sea strait) to the coastal ocean may form large bulges and coastal currents which propagate downshelf. Laboratory experiments show that the effect of the earth's rotation is to deflect the trajectory of the buoyant outflow into an inertial circle so that the buoyant outflow impacts the coastline further downshelf at an impact angle $\phi$. Bulges form if $\phi$ is larger than 60$^{\circ}$. Bulges store a significant fraction of the buoyant outflow; this attenuates the scales of the downshelf coastal current. The characteristics of the coastal current also depend on the ambient depth parameter, h/H, and the bottom slope parameter R/y$_{B}$. The width of the outflow also influences whether or not bulges form; bulge formation is described by a two-parameter space comprising the ambient depth parameter h/H and the Kelvin number K. Comparisons are made with oceanic observations.   

Lattice Boltzmann inverse modeling of water flows in the Everglades National Park

Knowledge of water flow in the Everglades National Park is vital for ecosystem restoration efforts. Of interest here is the planned rehabilitation of ``ridge-and-slough'' habitats, characterized by numerous adjacent sawgrass ridges aligned parallel to the flow direction. In many areas, reduced water flow due to water management systems has resulted in the conversion of ridge-and-slough landscapes into dense sawgrass stands. Previous studies of water flow have included tracer experiments, typically performed at several points in the region, with measurements taken over several days. Here we report initial results of inverse modeling of data from the EverTREx series of experiments using the parameter estimation code PEST coupled with a Lattice Boltzmann code. We perform two-component simulations in two dimensions, using satellite imagery to model the presence of vegetation in analogy with a porous medium. The final goals of this project are to reduce or remove the need for on-the-ground experiments for determining water flow characteristics in the Everglades, and to predict the effect of changes in water management systems on the flow.   

Effective Interactions Between Intruders in Vibrated Granular Materials

Despite the strong fluctuations in a rapidly moving granular material, dissipation and correlations in collisions can lead to long range forces in granular materials. In this experiment, we study the long-range attraction between two objects when immersed in a vibrated granular system. Depending on the strength of vibration, a granular system can take the form of a gas or be fluidized. We place two large intruders in each of these systems to track the effective interactions between the intruders, varying frequency, amplitude, size of grains, and the shape of the intruder. In particular, we study the interaction of spheres in a granular gas and the effective force between plates in a granular fluid. Using image processing, we track the separation of the intruders over time. We find that parallel plates attract if they are separated by less than approximately 15 particle diameters and reach a final position in which one ordered layer of grains is between them. Granular gas experiments suggest a long-range interaction, but observed effects in the mean position are much weaker than the fluctuations. Ongoing work focuses on varying the vibration parameters (amplitude, frequency, {\&} waveform) and increasing statistics.   

Effects of Shear Thickening Properties in Oscillating Non-Newtonian Fluids

We study the behavior of a shear-thickening, non-Newtonian fluid when shaken at a variety of accelerational amplitudes and frequencies. Mixing corn starch with water, using cesium chloride to match density and prevent separation, produces a fluid with shear thickening properties. When a thin layer of this fluid is vertically oscillated, it can produce Faraday waves as well as other phenomena that are characteristic of non-Newtonian fluids, such as stable holes and time-dependent, delocalized regions that grow from small initial disturbances in the fluid layer. We investigate how the concentration of corn starch (and as a result the shear-thickening properties of the fluid) affects which phenomena are observed, and we demonstrate that this concentration does have a significant effect on the fluid behavior.   

Pulsed laser induced self-assembly of nanoparticle arrays: Competing liquid phase instabilities

Thin film copper rings were synthesized on silicon dioxide thin films with various radii, thicknesses and widths and were subsequently liquefied via a nanosecond pulse laser treatment. During the nanoscale liquid lifetimes, the rings experience competing retraction dynamics and thin film and/or Rayleigh-Plateau type of instability, which lead to arrays of ordered nanodroplets. Ultimately, the original geometry dictates the instability pathway, which for narrow rings obeys the Rayleigh-Plateau type of instability, while for wider rings is influenced by the thin film instability. Hydrodynamic simulations describe well the observed time and length scales as well as the observed radial and circumferential instabilities which lead to different nanodroplet ensembles.   

Effect of viscosity ratio on liquid-liquid jets subjected to radial/axial electric field

Linear stability analysis for viscous liquid-liquid electrified jets subjected to axisymmetric (m=0) and asymmetric (m=1) perturbations has been performed. Both radial and axial electric field configurations are considered and the importance of viscosity ratio ($\lambda $= viscosity of surrounding fluid/Viscosity of inside fluid) is studied. $\lambda $ is shown to have a damping effect on both the modes of perturbation. However the effect is more pronounced for the m=1 mode as compared to m=0 mode in the presence of electric fields. Viscosity ratio, along with electric field can control the dominance of individual modes. While m = 1 mode can only be realized in the lower $\lambda $ limit when radial field is on, it is always possible to realize m = 1 mode under axial fields provided the threshold field is applied. A phase diagram showing predominance of the two modes at any given value of electric field and viscosity ratio is generated for both axial and radial electric field setups. This phase diagram can serve as a guideline for the required set of operating parameters in order to suppress/realize any desired mode of instability.   

Kinetic approach to Kaluza's magnetohydrodynamics

Ten years ago we presented a formalism by means of which the basic tenets of relativistic magnetohydrodynamics were derived using Kaluza's ideas about unifying fields in terms of the corresponding space time curvature for a given metric.\footnote{A. Sandoval-Villalbazo and L.S. Garcia-Colin; Phys. of Plasmas 7, 4823 (2000).} In this work we present an attempt to obtain the thermodynamic properties of a charged fluid using using Boltzmann's equation for a dilute system adapted to kaluza's formalism. The main results that we obtain are analytical expressions for the main currents and corresponding forces, within the formalism of linear irreversible thermodynamics. We also indicate how transport coefficients can be calculated. Other relevant results are also mentioned.   

Effect of electrode geometry on charging of a water droplet in a dielectric liquid

Electrophoresis of a charged droplet (ECD) in a dielectric liquid can be used as a droplet manipulation method without complicated electrode or circuit design. For further utilization of its advantages, we need thorough understanding on the charging mechanism and the electrode geometry effect. We have investigated the effect of electrode geometry on the amount of charging experimentally and numerically. In the experiments, we have checked the difference of charge amount between the pin type and the plate type electrodes. A high speed camera and an electrometer are used for the measurement simultaneously. We also have calculated the charge amounts for both cases numerically. The charge amounts predicted from the simulation show good agreement with those of the experiments. In both cases, a droplet gets more charges on the pin type electrode. This result can be used for better design in the microfluidic applications using electric charging method.   

A microfluidic platform for impedance analysis and characterization of human umbilical vein endothelial cells

The characterization of endothelium morphology and permeability under fluid shear stress can provide essential information regarding the onset of different pathological conditions, as well as, the uptake of drugs and biomolecules. Real-time assessment of the integrity of cell monolayers and cell motility has been accomplished by implementing electrical impedance analysis. In this study, we report a micro-electrode array biosensor incorporated into a microfluidic platform for the impedance spectroscopy of Human Umbilical Vein Endothelial Cells (HUVECs) under physiological fluid shear stress. The biosensor consists of two adjacent and identical microfluidic channels which allows for simultaneous assessment of the electrical properties of a HUVEC monolayer and that of the cell culture media alone. Additionally, the biosensor is attached to a custom designed electronic system that simplifies the data acquisition and analysis of time-dependent multiplexed measurements for the different electrodes. The impedance spectrum (40 Hz to 10 MHz) was collected for HUVECs before and under different physiological fluid shear stress forces to yield insight to flow induced changes in HUVEC morphology, permeability, and relevant electrical parameters. This biosensor can be used as an \textit{in vitro} model of the endothelium for new drug discovery, as well as, part of biochemical assays for cell mechanism studies.   

Non-Newtonian behavior of magnetized ferrofluids as revealed by high speed x-ray phase contrast imaging

Objects moving through a magnetized ferrofluid experience enhanced drag as a result of the presence of magnetic particles and magnetic particle agglomerations which form due to magnetic attractive forces. The precise impact of an agglomeration on an object depends on the characteristics of the agglomeration, the relative sizes of the object and agglomeration, as well as other control parameters. In this study, high speed phase contrast imaging was used to directly image the impact of long thread-like magnetic particle agglomerations on the rheological properties of ferrofluids. Particularly, numerous types of interactions between these threads and translating objects, including free-falling 500 micron sized solid glass spheres and intermittently rising vapor bubbles were quantified. At these scales, objects may bind to particle threads resulting in momentary re-direction or arrest of the object's trajectory, alluding to a form of yield stress. Therefore, there is a macro-viscosity property in flows of this type, which has a potentially significant impact of the use of ferrofluids in micro-fluidics and drug delivery.   

DNA Size Segragation at a Convergent Stagnation Point

We investigate using counter-rotating vortices and a convergent stagnation point to segregate different sizes of DNA using a lattice Boltzmann based simulation with a bead-spring model for the polymer. We find that longer DNA molecules are left rotating in the fluid while shorter molecules aggregate at the stagnation point. The separation of the polymers depends on the fluid flow rate and a non-specific attractive force with the channel walls. We report on the robustness of this technique.   

Falling ball viscometry of magnetized ferrofluids

Falling spheres of 500 $\mu$m were used to perform viscometric experiments on magnetized ferrofluids. The role of the angle of orientation of an applied unifom field relative to the direction of fall has been examined with high speed phase contrast imaging using the Advanced Photon Source. The magnetized ferrofluid exhibits an anisotropic viscosity that we can quantify in terms of a tensorial viscosity coefficient. We find that the effective drag is greater when the fall occurs normal to the applied field rather than parallel to it, a result that is opposite to what is predicted by many ferrofluid magnetoviscosity models, but consistent with the properties of electro- and magneto-rheological fluid, liquid crystal, and polymer fluid rheology models. Finally, we discuss the dispersion of these results in terms of thread-like aggregations of magnetic particles observed in the experiments.   

Ink transfer mechanism for gravure-offset printing by using flow visualization

We investigated ink transfer mechanism for gravure-offset printing by monitoring ink transfer process. For convenient visualization of ink transfer, cantilever-type roll-to-plate gravure offset printing system is designed. We visualized ink transfer process from patterned plate to rolling blanket roller. Serial images were captured by using high-speed CMOS camera and long range microscope, and analyzed by image process. We investigated the rotational effect of blanket roller on ink transfer mechanism by comparing the ink transfer process with different pattern angle and printing speed.   

Enhanced evaporation from surfaces of width comparable to that of the mass boundary layer thickness

We investigate the optimal distribution of spacing and size of stomata on a leaf, which enhances net evaporation rate. Although evaporation flux is known to be maximal at contact lines, is diffusion of the vapor also enhanced by the accompanying increase in the total perimeter when the contact lines are adjacent? The evaporation rate from the stomata is analyzed using a 1-D model for stomata distributions on a leaf and a 2-D convection-diffusion equation in the surrounding space. A universal behavior is observed as a function of the Peclet number Pe and stomata size. For stomata much wider than the mass boundary layer thickness, evaporation rate increases as the stomata are made smaller; but below a critical size, the evaporation rate saturates to a constant value. This transition occurs when stomata size is comparable to the mass boundary layer thickness. We experimentally tested this behavior with liquid evaporating from micro-channels of varying channel widths in a wind tunnel providing a range of Pe.   

Effects of Microstructural Parameters on Permeability of Fibrous Materials to Non-Newtonian Fluids

In this work, a series of numerical simulations has been devised to relate the non-Newtonian permeability constant of a fibrous medium to its Newtonian counterpart. Developing virtual 3-D geometries that resemble the internal microstructure of a fibrous material, we studied the effects of fiber diameter, fiber in-plane and through-plane orientations, and media's porosity on the media's permeability to Non-Newtonian fluids such as blood. The results of our digital experiments are used in conjunction with available analytical relations, derived to predict the non-Newtonian permeability constants of granular beds, to develop new empirical correlations for fibrous materials.   

Time resolved measurements of particle lift off from the wall in a turbulent water channel flow

Time-Resolved Particle Image Velocimetry (TR-PIV) and digital holography measurements were carried out in a dilute particle-laden flow tracking both Polystyrene Spheres (PS, $\sim $0.583 mm, $d^{+}\sim $10) as well as resolving the instantaneous velocity field of the turbulent flow. Measurements were performed in a closed loop, transparent, square channel facility (50x50 mm$^{2})$ at 127.5cm from the inlet with bulk water velocity 0.3 m/s (Re$_{h}$ = 7353) and friction velocity 0.0174 m/s. Data were captured at 1~kHz, corresponding to a time scale 5x smaller than the flow's viscous scale. Single view digital holographic cinematography was used to track the 3D PS motion inside the VOI (17x17x50 mm$^{3})$ including the wall bottom. TR-PIV in a vertical plane (29.3x29.3 mm$^{2})$ oriented along the channel's centerline imaged PS together with flow tracers. Discrimination was based on their size difference. Instantaneous sequences of PS plotted on the spatial velocity, vorticity and swirling strength maps showed the effect of turbulent flow structures and resulting particle movement. Results are presented for particles that lift off from the bottom wall as a result of complex interaction with ejection and sweep motions.   

Lagrangian particle tracking in strained and buoyant flows

We present experimental particle tracking results in two turbulent flow configurations, straining flow and buoyant flow. Our focus is on the influence of large scale structure of such flows on the motions of passive and inertial particles, in particular acceleration statistics, Lagrangian structure functions, and two point statistics. The results are contrasted with previous work, and our results from approximately isotropic flows. The Eulerian structure of the underlying flow field is measured by applying the PIV method.   

Pore-scale Analysis of the effects of Contact Angle Hysteresis on Blob Mobilization in a Pore Doublet

The mobilization of residual oil blobs in porous media is of major interest to the petroleum industry. We studied the Jamin effect, which hampers the blob mobilization, experimentally in a pore doublet model and explain the Jamin effect through contact angle hysteresis. A liquid blob was trapped in one of the tubes of the pore doublet model and then subjected to different pressure gradients. We measured the contact angles (in 2D and 3D) as well as the mean curvatures of the blob. Due to gravity effects and hysteresis, the contact angles of the blob were initially (zero pressure gradient) non-uniform and exhibited a pronounced altitude dependence. As the pressure gradient was increased, the contact angles became more uniform and the altitude dependence of the contact angle decreased. At the same time, the mean curvature of the drainage interface increased, and the mean curvature of the imbibition interface decreased. The pressure drops across the pore model, which we inferred with our theory from the measured contact angles and mean curvatures, were in line with the directly measured pressure data. We not only show that a trapped blob can sustain a finite pressure gradient but also develop methods to measure the contact angles and mean curvatures in 3D.   

Effect on Turbulence Radiation Interaction in Particle Laden Flow

The effects of Turbulence Radiation Interactions (TRI) in particulate laden flows can significantly influence thermal radiation fields and corresponding material heating. Most combustion problems contain strong heterogeneities which can be treated stochastically. In pulverized coal combustion these heterogeneities include particulate such as coal, fly-ash, and char. This work expands upon a simplified test case, developed by Deshmukh et al. (Proc. Comb. Inst., 2009), to highlight the effects of fuel particulate on TRI phenomena. This includes the decaying isotropic turbulence with a single-step reaction in the presence of solid particulates. Three different test cases were studied: a simplified gas-phase combustion problem without particulate, non-reacting particulate in the gas-phase combustion, a solid-fuel/gas-oxidizer combustion model. Sensitivity of TRI uncertainties such as thermal radiation fields and thermal emission to the presence fuel particulates is investigated in this test problem using direct numerical simulation for the gas-phase and Monte-Carlo approach for the radiative heat transfer.   

Shooting inertial wave packets into rotating turbulence

We experimentally study the effect of localized fluctuations in energy injection rate on existing rotating turbulent flow. We show that such fluctuations generate packets of inertial waves, propagating along the axis of rotation. Close to the energy source the propagating pulses leave the steady turbulent field unaffected. Energy is transferred from the pulses into the steady turbulent field only at height h above the injection plane. This height is determined by equating the propagation time of an inertial wave to h, with the time for nonlinear interaction between the wave and the turbulent field. This mechanism, which allows ``shooting'' turbulence to selected heights, is expected to be important in rapidly rotating geophysical flows.   

Flow Instability in Channel Flow with a Streamwise-periodic Array of Circular Cylinders

A parametric study has been carried out to elucidate the characteristics of flow instability in laminar channel flow with a streamwise-periodic array of circular cylinders. This flow configuration is relevant to heat exchanger applications. The presence of cylinders in channel flow causes the attached wall boundary layer to separate, leading to a significant change in flow instability. There exist two kinds of instability; flow undergoes a primary instability (Hopf bifurcation) at a low Reynolds number, and the resulting time-periodic two-dimensional flow subsequently becomes unstable to three-dimensional disturbances at a higher Reynolds number (secondary instability). We report here the dependencies of the primary instability as well as the flow characteristics of the subsequent time-periodic 2D flow, including flow-induced forces and Strouhal number of vortex shedding, on the distance between the cylinders and the channel wall. We also present a Floquet stability analysis on the time-periodic 2D flows to identify the onset of the secondary instability leading to 3D flow.   

Non-linear stability and transition analysis in reactive hypersonic shear-layers

Carbon chemistry and the endothermic reactions it supports were previously shown to delay hypersonic boundary layer instability and transition. The present analysis addresses the analogous problem in free shear-layers and arrives to the conclusion that the lack of the acoustic trapping mechanism implies that endothermic chemistry can lead to stabilization or destabilization of the shear-layer depending on the free-stream temperature. This study identifies three mechanism by which carbon chemistry affects instability and transition. The first is rooted in the changes to the inflectional profiles caused by the visco- chemical interaction. The second is due to damping of the perturbation by finite rate chemistry. The third is linked to streamwise relaxation which delays the onset of secondary instability of vortical structures generated by a saturated primary instability wave. Linear analysis predicts changes in growth rate lower than 30\% for Mach numbers below 5. Nonlinear parabolized stability analysis predicts significantly larger differences, depending on whether the primary or secondary instability trigger the transition onset.   

Dispersion of capillary waves in elliptical cylindrical jets

In this work motion of a low speed liquid jet issuing from an elliptic orifice through the air is studied. Mathematical solution of viscous free-surface flow for this asymmetric geometry is simplified by using one-dimensional Cosserat (directed curve) equations which can be assumed as a low order form of Navier-Stokes equations for slender jets. Linear solution is performed and temporal and spatial dispersion equations are derived. Growth rate and phase speed of unstable and stable modes under various conditions are presented. The possibility of instability of asymmetric disturbances is studied too. With distance down the jet, major and minor axes are altered and finally jet breaks up due to capillary instability. The effect of jet velocity and viscosity and also orifice ellipticity on axis-switching and breakup is investigated.   

Influence of confinement by smooth and rough walls on particle dynamics in dense hard-sphere suspensions

We used video microscopy and particle tracking to study the dynamics of confined hard-sphere suspensions. Our fluids consisted of 1.1-$\mu $m-diameter silica spheres suspended at volume fractions of 0.33--0.42 in water-dimethyl sulfoxide. Suspensions were confined in a quasiparallel geometry between two glass surfaces. First, as the separation distance (H) is decreased from 18 to 1 particle diameter, a transition takes place from a subdiffusive behavior (as in bulk) at large H, to completely caged particle dynamics at small H. These changes are accompanied by a strong decrease in the amplitude of the mean-square displacement (MSD) in the horizontal plane parallel to the confining surfaces. In contrast, the global volume fraction essentially remains constant when H is decreased. Second, measuring the MSD as a function of distance from the confining walls, we found that the MSD is not spatially uniform but smaller close to the walls.. Although confinement also induces local variations in volume fraction, the spatial variations in MSD can be attributed only partially to this effect. The changes in MSD are predominantly a direct effect of the confining surfaces. Hence, both the wall roughness and the separation distance (H) influence the dynamics in confined geometries.   

Large-scale structures of the turbulent boundary layer in wall-normal/spanwise plane

Coherent wall-normal structures in turbulent boundary layer (TBL) have been investigated by scrutinizing the direct numerical simulation (DNS) dataset with \textit{Re}$_{\theta }$=2500. The spatial signatures of hairpin vortex legs were frequently observed in the vector fields of the wall-normal/spanwise (\textit{yz}) plane and it was found that groups of such hairpin legs induce wall-normal-aligned elongated structures with a large Reynolds shear stress; this result strongly supports the typical hairpin packet model. The two-point correlation of the velocity fluctuations showed that the wall-normal length scales vary linearly with the distance from the wall and the two-point correlations between the signed swirling motions showed that interactions between counter-rotating vortices are predominant throughout the boundary layer and especially frequent in the near-wall region.   

Observations of Anisotropy in Atmospheric Turbulence by Means of Moir\'{e} Deflectometry

We report observations of strong anisotropy in the statistical properties of atmospheric turbulence, using a method based on moir\'{e} deflectometry. By combining use of a telescope with moir\'{e} deflectometry we achieve a high sensitivity to fluctuations in the wave-front phase, which are, in turn, related to fluctuations in the fluid density. As phase fluctuations of the wave front in the aperature of the telescope are imaged on the first grating of the moir\'{e} deflectometer, a high spatial resolution is achieved. Experimentally, we measure covariance of angle of arrival (AA) between pairs of points displaced spatially on the telescope aperature and find significant differences between scaling exponents derived for covariances in the longitunal and transverse directions. We note that the method does not require the use of the Taylor hypothesis and has the advantage of being relatively simple and inexpensive.   

Large Eddy Simulation of Turbulent Flow in a Ribbed Pipe

Turbulent flow in a pipe with periodically wall-mounted ribs has been investigated by large eddy simulation with a dynamic subgrid-scale model. The value of Re considered is 98,000, based on hydraulic diameter and mean bulk velocity. An immersed boundary method was employed to implement the ribs in the computational domain. The spacing of the ribs is the key parameter to produce the d-type, intermediate and k-type roughness flows. The mean velocity profiles and turbulent intensities obtained from the present LES are in good agreement with the experimental measurements currently available. Turbulence statistics, including budgets of the Reynolds stresses, were computed, and analyzed to elucidate turbulence structures, especially around the ribs. In particular, effects of the ribs are identified by comparing the turbulence structures with those of smooth pipe flow. The present investigation is relevant to the erosion/corrosion that often occurs around a protruding roughness in a pipe system.   

Simulation of Colliding Vortex Rings and Parallel Performance of Lattice Boltzmann Method

Vortex motion or flow with vorticity plays an essential role in almost all kinds of fluid motion of interest. In order to investigate the mechanisms of vortex reconnection, numerical simulation of collision of two vortex rings in three dimensions was carried out using lattice Boltzmann method. We have studied several runs with different initial angles and positions of the ring planes, i.e., head-on collision, inclined collision and off-side collision, keeping the other parameters fixed. However, in order to achieve high resolution on vortex reconnection and its coherent structures, hundreds million of lattices are often necessary in a three dimensional domain, parallel implementations are adopted to attend the demand of an expressive memory amount and processing power of the method. Two vortex collisions have been used as case study to evaluate our implementation, and very good parallel performance was achieved up to thousands of CPUs in a distributed computer system. The lattice Boltzmann method has proved to be an important technique for the numerical solution of partial differential equations because it has nearly ideal scalability on parallel computers for many applications.   

Nonlinear pulsations of a Hamiltonian system of the fourth order by a nonlinear trigonometric series

Dynamics of Hamiltonian systems is the key issue of solitary waves since the initial-value problems on free surfaces and interfaces are reduced to Hamiltonian problems in the reference frame moving with the wave. The Hamiltonian approach covers applications at high Reynolds numbers, which range from the famous irrotational Boussinesq-Rayleigh solitary wave to the rotational waves with a uniform vorticity. The Hamiltonian system with a polynomial potential of the fourth order is studied in the asymmetric case of subcritical periodic pulsations by using a nonlinear trigonometric series in even powers of cosine. The series solutions are computed symbolically and compared with the numerical solution using the Fehlberg fourth-fifth order Runge-Kutta method with degree four interpolant. It is shown that the series solutions with uniform convergence are superior to the numeric solutions with local convergence. The qualitative comparison of the theoretical solutions with the experimental profiles of the Geminga pulsar is also provided.   

Thermophoresis of a thermally responsive polymer

Thermophoresis is the migration of a species in response to a temperature gradient. This mechanism can be used to manipulate molecules in microfluidic channels. We experimentally investigate thermophoresis of a synthetic polymer. The polymer is thermally responsive and changes conformation in aqueous solution at the cloud point temperature. Two forms of the polymer are present in the temperature gradient at an average temperature near the cloud point, with one conformation migrating to the hot side of the channel and the other to the cold. We also investigate the polymer's migratory dependence on dissolved ionic species, specifically NaCl, which changes the cloud point temperature. We examine the effect of the conformation change on thermophoresis using a lattice-Boltzmann- based simulation.   

An experimental investigation of the multiphase flows in a photobioreactor for algae cultivation

Algal biomass is a promising feedstock for biofuels production, with photobioreactors being one of the major cultivation systems for algal cells. Light absorption, fluid dynamics, and algal metabolism are three key factors in determining the overall performance of a photobioreactor. The behavior of the multiphase flow (i.e., liquid phase -- water, gas phase -- CO$_{2}$ and O$_{2}$, and solid phase -- algal cells) and turbulent mixing inside the reactor are the core connecting the three factors together. One of the major challenges in the optimal design of photobioreactors for algae cultivation is the lack of in-depth understanding of the characteristics of the multiphase flows and turbulent mixing. In this study, we present a comprehensive experimental study to investigate the effects of turbulent mixing in photobioreactors on the performance of a photobioreactor for algae cultivation. A high-resolution particle image velocity (PIV) system is used to achieve time-resolved, in-situ flow field measurements to quantify the turbulent mixing of the multiphase flows inside the bioreactor, while algal cultures are also grown in the same reactor with the same experimental settings. The mixing characteristics of the multiphase flow are correlated with the algal growth performance in the bioreactors to elucidate the underlying physics to explore/optimize design paradigms for the optimization of photobioreactor designs for algae cultivation.   

Session L1: Geophysical Flows: Oceanography IV

Quantifying Parametric Uncertainty in Ocean General Circulation Models: A Sparse Quadrature Approach

We use Polynomial Chaos (PC) expansions to quantify propagation of parametric uncertainties in Ocean General Circulation Models (OGCMs). We focus on short-time, high-resolution simulations in Gulf of Mexico with wind stresses corresponding to hurricane Ivan. A non-intrusive sparse quadrature approach is used to determine the PC coefficients providing a detailed representation of the stochastic model response. The quality of the PC representation is examined through a systematic refinement of the number of resolution levels. The resulting PC representation is then utilized in computing distributions of model variables and analyzing local and global sensitivity of the solution to uncertain parameters.   

Large-eddy simulation of large-scale convection cells in unstably stratified open channel flow

Results are presented from large-eddy simulation of unstably stratified open channel flow driven by a pressure gradient with zero surface shear stress and a no-slip bottom. Unstable stratification is imposed by a constant cooling flux at the surface and an adiabatic bottom wall. Under neutrally stratified conditions, the flow is characterized by weak full-depth streamwise cells similar to Couette cells in plane Couette flow. Surface cooling leads to stronger full-depth convection cells of larger spanwise scale. Surface cooling increases vertical and spanwise velocity fluctuations in the upper half of the channel, while increasing mixing throughout the water column. Similarities and differences between the flow with full-depth convection cells and a second flow with full-depth Langmuir cells generated via surface wave-current interaction will be highlighted. Comparison between flows is based on visualizations and diagnostics including (i) profiles of mean velocity, (ii) profiles of resolved Reynolds stress components, (iii) invariants of the resolved Reynolds stress anisotropy tensor and (v) balances of the transport equations for mean resolved turbulent kinetic energy.   

Approximate deconvolution large eddy simulation of a barotropic ocean circulation model

We investigate a new large eddy simulation closure modeling strategy for two-dimensional turbulent geophysical flows. This closure modeling approach utilizes approximate deconvolution, which is based solely on mathematical approximations and does not employ additional phenomenological arguments. The new approximate deconvolution model is tested in the numerical simulation of the wind-driven circulation in a shallow ocean basin, a standard prototype of more realistic ocean dynamics. The model employs the barotropic vorticity equation driven by a symmetric double-gyre wind forcing, which yields a four-gyre circulation in the time mean. The approximate deconvolution model yields the correct four-gyre circulation structure predicted by a direct numerical simulation, but on a coarser mesh and at a fraction of the computational cost. This first step in the numerical assessment of the new model shows that approximate deconvolution could be a viable tool for under-resolved computations in the large eddy simulation of more realistic turbulent geophysical flows.   

Mesoscale- and submesoscale-resolving simulations with an anisotropic Smagorinsky subgrid model

The oceanic submesoscales are motions of scale O(100m-1km) that lie between the large, O(100km), mesoscales and the smaller, O(10m), three dimensional eddies. Past studies showed submesoscales are critical to the evolution of fronts in the ocean and to the ecological cycle. This study discusses results from submesoscale-resolving simulations with a nonhydrostatic ocean model employing an anisotropic Smagorinsky subgrid model. Our simulated domain is O(100km) in the horizontal and O(100m) in the vertical with highly anisotropic grid resolutions, O(500-1000m) and O(10m), respectively. The domain resolves both mesoscale and submesoscale eddies. Past studies with similar domains have achieved horizontal subgrid mixing either through constant eddy-viscosities or implicitly through the underlying numerical algorithm. We present results from simulations with and without surface winds. Intense submesoscale activity occurs near the fronts and is associated with O(1) Rossby numbers. With winds, the subgrid dissipation of resolved kinetic energy is strongest in regions with negative potential vorticity and the vertical buoyancy flux is enhanced in the presence of baroclinicity below the mixed layer. Without winds, the subgrid dissi pation and vertical velocity are smaller than in the wind-driven case.   

Turbulence, mixing, and blooms at ocean fronts

Regions with large horizontal density gradients, or fronts, are ubiquitous features of the upper ocean. As locations where density surfaces outcrop from the ocean interior, fronts serve as conduits for transport of fluid properties, linking the deep ocean and the atmosphere. Although fronts are under-resolved in most global ocean models, recent work has shown that they strongly affect the large-scale circulation and biology of the ocean. This talk will describe results from recent studies based on large-eddy simulations (LES), which find that turbulent mixing is strongly affected by fronts and is subject to two competing effects: turbulence is generated from the available potential energy associated with the front, but vertical mixing is inhibited by the stable stratification that develops as the front slumps. By coupling a simple biological model with the LES, we find that reduced vertical mixing at fronts can trigger phytoplankton blooms in light-limited conditions. These results help explain satellite-based observations of unexpected mid-ocean blooms at high latitudes.   

A Variable Resolution Global Ocean Model

The Model for Prediction Across Scales (MPAS) is a new software framework for the rapid development of climate model components on unstructured grids. The grids may be quasi-uniform or variable density, on a sphere or rectangular domain, and may use quadrilateral cells, triangle cells, or Voronoi tessellations. MPAS variable density grids are particularly well suited to regional climate simulations. MPAS is developed cooperatively by NCAR MMM and the LANL COSIM team. The MPAS-Ocean component now includes most of the features of a full ocean-climate model. High resolution global simulations with full bathymetry have been run for hundreds of simulated years and produce realistic currents and eddying behavior. MPAS-Ocean may be run with z-level or isopycnal vertical coordinates, and includes high-order horizontal and vertical advection and implicit vertical mixing. Current efforts focus on split barotropic/baroclinic timestepping and improving performance.   

Evaluation and Improvement of RANS models for Stably Stratified Turbulence

The focus of this study is to account for the effects of buoyancy forces in RANS models for stratified turbulence. To this end, changes to the stratification parameters that account for buoyancy effects in RANS models are proposed. DNS data of stably stratified turbulence are used to study the parameters in two equation turbulence models such as the buoyancy parameter $C_{\epsilon3}$, and the turbulent Prandtl number $Pr_t$ in the $k$-$\epsilon$ model. Both the gradient Richardson number $Ri = N^2/S^2$, where $N$ is the buoyancy frequency and $S=d\overline{u}/dz$ is the mean shear rate, and the turbulent Froude number $Fr_k=\epsilon/(Nk)$, are used as correlating parameters to characterize stratification in the $k$-$\epsilon$ model. We show that it may be more appropriate to use $Fr_k$ as the parameter of choice for modeling the stratification parameters in the $k$-$\epsilon$ model since it is based on the local properties of the turbulence as opposed to $Ri$, which is a mean property of the flow. The proposed modifications were implemented in a 1-D water column model called the General Ocean Turbulence Model (GOTM) and used to simulate stably stratified channel flows. The results from numerical simulations using the modified $k$-$\epsilon$ model are compared to DNS data of stably stratified channel flow to assess its efficacy. This modified formulation is also compared with other stability functions in GOTM.   

Energy Cascade in the Regime of Realistic Ocean Circulation

Ocean circulation is forced at the large scales and the instability of the resulting large-scale flow gives rise to intermediate-scale eddies. The large-scale flow and the resultant eddies are both in approximate geostrophic balance; such balance results in an inverse cascade of energy. Consequently, small scale dissipation becomes ineffective and dissipation is limited to interactions of the larger and intermediate scale flow structures with solid boundaries. We consider the modification of this asymptotic behavior in the presence of a range of scales over which unbalanced motions are possible.   

Examination of the Turbulent Kinetic Energy Budgets in the Mid-Water Column of the Chesapeake Bay Estuary

A local turbulent kinetic energy (TKE) balance is examined from measurements obtained during two-week long field experiment in the Chesapeake Bay near Kent Island, MD, under low to moderate wind conditions. Velocity data were collected with two vertically separated Acoustic Doppler Velocimeters and an upward looking pulse coherent profiler covering 0.8 to 2.5 m above bottom in approximately 5 m of water. Additionally, upward oriented AWAC mounted on a separate frame was used to obtain water column tidal current vertical profiles and overlying wave directional system. Stratification is monitored using two vertically separated CT sondes and estimated Ozmidov scale ranges from very small values up to 5m. Occurrences of large TKE dissipation rates coincide with times of maximum bottom boundary layer shear production with consistently larger values during ebb flows. In general dissipation rate exceeds shear production minus buoyancy flux in the mid-water column. Potential sources of enhanced levels of dissipation are examined including vertical turbulent transport, wind driven shear production and presence of surface gravity waves.   

Session L2: Instability in Boundary Layers II

Transition to Turbulence and Heat-Transfer Overshoot in an Adverse Pressure Gradient High-Speed Boundary Layer

Spatial direct numerical simulations (DNS) of transitional high-speed boundary layers with zero and adverse pressure gradients and an isothermal wall are presented for different transition scenarios. The maximum momentum thickness Reynolds numbers vary between 2500 and 5500 and the edge Mach numbers vary between 6 and 4.8 for the different cases presented. Disturbances are introduced into the initially laminar boundary layer through suction and blowing at the wall. Different transition scenarios including first mode oblique breakdown and second mode fundamental resonance are explored. The presence of an adverse pressure gradient accelerates the transition process. Comparisons of the nonlinear modal growth and breakdown for the different initial forcing scenarios will be shown. First mode oblique breakdown is shown to lead to an overshoot in heat transfer and the most rapid development to a turbulent state.   

Effect of Surface Curvature on Crossflow Instability in Swept-Wing Boundary Layers

A three-dimensional boundary layer is subject to crossflow instability that manifests itself in the form of stationary or traveling disturbances. Stationary disturbances are induced by surface roughness while free stream turbulence induces traveling disturbances. It is known that convex surface curvature tends to stabilize crossflow instability while the mean flow non-parallel effect is generally destabilizing, with the net effect being mildly stabilizing when compared to the results obtained using quasi-parallel linear stability theory. Here, an analysis is performed for two swept airfoils using parabolized stability equations that account for both the surface curvature and the non-parallel effect. One airfoil has larger convex curvature than the other, where the convex surface curvature is scaled by defining a Gortler number. The net decrease in the stationary crossflow N factor is about 6 for the airfoil with stronger curvature. The analysis suggests that, if transition is induced by stationary crossflow disturbances, then surface curvature could be used as a control parameter for natural laminar flow design. The strong effect of surface curvature on stationary disturbances highlights the importance of investigating the receptivity of stationary and traveling disturbances since the latter are much less influenced by surface curvature resulting in much higher relative N factors for traveling disturbances.   

Secondary instability analysis of pre-transitional streaks in boundary layers

In the presence of free-stream vortical disturbances, laminar boundary layers develop streamwise-elongated perturbations of high amplitude, commonly known as Klebanoff streaks. The regions of shear surrounding these primary structures provide the potential for the growth of secondary instabilities which ultimately initiate bypass transition. By means of linear analysis, we examine the secondary instability which precedes the formation of turbulent spots. The base state is extracted from direct numerical simulations of the bypass process. The simulation setup is similar to the work of Jacobs \& Durbin (2001), where transition is triggered by broadband free-stream vortical forcing. The velocity field therefore includes a spectrum of streaks with different structures and amplitudes. The stability analysis can nevertheless identify the streaks which indeed develop secondary instabilities and break down to turbulence. The predictions of linear theory, in particular the instability wavelength and phase speed, are compared to the streak instabilities recorded in the DNS of the full bypass process.   

Conditional Sampling of Bypass Transition in Pressure Gradient Boundary Layers

Conditional sampling of velocity fields from Direct Numerical Simulations (DNS) of bypass transition is performed with discrimination between laminar and turbulent events. Individual positive and negative streaks are isolated and an extreme value analysis of their amplitudes is performed. A more detailed view of the growth of positive and negative streaks is obtained than is typical by simply measuring the root mean square perturbations. The resulting velocity distributions are compared with the amplitudes of streaks which undergo secondary instability, and breakdown into turbulent spots. A range of pressure gradients is considered and the rates of turbulent spot production and propagation are investigated. While the spot production rate increases significantly with adverse pressure gradient, it is found that the spot propagation rate is unaffected. By considering the spot spreading angle others have shown a pressure gradient dependence of the propagation parameter. The current work eschews the spreading angle, opting instead to directly track the growth of the spot volume.   

Attachment-Line Heating in a Compressible Flow

The attachment-line boundary layer on a swept wing can be subject to either an instability or contamination by wing-root turbulence. A model of the attachment-line boundary layer is first developed including compressibility and wall heating in a Falkner-Skan-Cooke class of 3-D boundary layers with Hartree parameter of 1.0. For cases otherwise subcritical to either contamination or instability, the destabilizing effect of leading-edge heating under a variety of sweep angles and flight conditions is demonstrated. The results correlate with the attachment-line Reynolds number. Because the required heating levels are reasonable and achievable to trip the flow over the wing to turbulent, one possible application of this work is in the establishing of a baseline turbulent flow (on demand) for the calibration of a laminar-flow-control health monitoring system. **Portion based on work under Framework Agreement between Airbus Americas and NIA, and opinions, findings, conclusions do not necessarily reflect views of Airbus or NIA. **Support from AFOSR/NASA National Center for Hypersonic Research in Laminar-Turbulent Transition through Grant FA9550-09-1-0341 gratefully acknowledged.   

Transition prediction for oblique breakdown in supersonic boundary layers with uncertain disturbance spectrum

Prediction of laminar-turbulent transition is important for the design of heat shields for planetary (re)-entry vehicles. The heat load may increase significantly if a previously laminar boundary layer on the vehicle surface becomes turbulent. Transition-prediction methods based on linear stability theory, such as the $e^N$-method, offer an attractive compromise between simplicity and accuracy. However, non-linear stages of disturbance evolution as well as the receptivity stage are neglected, hampering the general use of these methods. Here we perform an investigation of the oblique breakdown scenario. In this scenario, a pair of oblique waves is convectively amplified and quickly leads to turbulence once these waves reach an amplitude of approximately two percent. This knowledge allows us to define a simple breakdown criterion as a model for the non-linear stage. The receptivity process, whose outcome provides the initial disturbance amplitudes, may not be as easily modeled. Flow physics of the receptivity process are neglected here. Instead, we assume an uncertain disturbance spectrum, which depends on the disturbance frequency and spanwise wave number. Using stochastic collocation, linear stability theory is then employed to yield a probabilistic transition prediction.   

The pre-cursor of Kelvin-Helmholtz instabilities in wake-perturbed separated boundary layers

The interaction of large-scale wake disturbances with a pressure-induced separation bubble on a flat plate is studied by direct numerical simulation. The space-time development of the separated region shows roll-up vortices in the separated shear layer. Their appearance is closely associated with the receptivity of the upstream attached boundary layer. The wake-passing excites a linear normal mode of the boundary layer. This mode, which is initially very small, appears in the form of two-dimensional wave-trains upstream of the separation point, but becomes unstable and transforms into the Kelvin-Helmholtz mode as the profile separates. Studies based on varying the frequency or modifying the shape of the forcing further support this scenario of the initial development of the rolls in the separated shear layer, and show that the influence of the wakes is not to directly force the Kelvin-Helmholtz instability of the separation bubble, but to induce perturbations upstream in the attached boundary that eventually seed the instability of the separated shear layer.   

Stability of unsteady flow in a rotating torus

We consider the temporal evolution of a viscous incompressible fluid in a torus of finite curvature; a problem first investigated experimentally by Madden and Mullin (1994), herein referred to as MM. The system is initially in a state of rigid-body rotation (about the axis of rotational symmetry) and the container's rotation rate is then changed impulsively. We describe the transient flow that is induced at small values of the Ekman number, over a time scale that is comparable to one complete rotation of the container. We show that (rotationally symmetric) eruptive singularities (of the boundary layer) occur at the inner or outer bend of the pipe for a decrease or an increase in rotation rate respectively. Moreover, there is a ratio of initial-to-final rotation frequencies for which eruptive singularities can occur at both the inner and outer bend simultaneously. We also demonstrate that the flow is susceptible to non-axisymmetric inflectional instabilities. The inflectional instability arises as a consequence of the developing eruption and is shown to be in qualitative agreement with the experimental observations of MM. Detailed quantitative comparisons are made between asymptotic predictions and finite (but small) Ekman number Navier-Stokes computations using a finite-element method.   

Session L3: Dynamical Systems and Chaos II

Burning invariant manifolds for propagating fronts in a chain of vortices

We present experimental studies of the behavior of reaction fronts in a chain of alternating vortices. The flow is produced by a magnetohydrodynamic forcing technique, and the fronts are produced by the ferroin-catalyzed Belousov-Zhabotinsky chemical reaction. We introduce {\em burning invariant manifolds} (BIMs) which act as barriers to front propagation, similar to the role played by invariant manifolds as barriers to passive transport in two-dimensional flows. Unlike manifolds for passive transport, though, BIMs are one-sided barriers, passing either left- or right-going fronts but blocking the other. We show how the BIMs can be measured experimentally for both time-independent and time-periodic flows. The experimental results are compared to simulations based on a simplified numerical model of the flow.   

Lobe dynamics and front propagation in advection-reaction-diffusion systems

We consider the addition of reaction-diffusion dynamics to systems undergoing chaotic advection. This can be viewed as a simplified model of diverse systems such as combustion dynamics in a chaotic flow, microfluidic chemical reactors, and blooms of phytoplankton and algae. Recently, we have proposed that front propagation in these systems is strongly influenced by burning invariant manifolds (BIMs)---geometric structures analogous to traditional invariant manifolds for passive transport. Additionally, BIMs may be used to define tangle-like structures that support a version of lobe dynamics for front propagation. In this talk, we discuss the theory and structure of BIMs and demonstrate the modified lobe-dynamics. We also present a potential application of the lobe dynamics to the control of reactive flows.   

The geometry of mode-locked fronts in periodically driven advection-reaction-diffusion systems

We consider reaction-diffusion dynamics within a periodically driven fluid forming a linear chain of alternating vortices. Prior theoretical and experimental work on this system has demonstrated rich structure in the dynamics of the reaction front; for certain parameter values, the front will be mode locked to the external driving. Using dynamical systems theory, we relate the mode-locking behavior to the existence of relative periodic orbits (RPOs), and we show that the mode-locked front itself follows the profile of a ``burning invariant manifold'' (BIM)---a generalization of traditional invariant manifolds for passive transport, which incorporates the dynamics of front propagation. Together, the RPOs and BIMs provide clear criteria for the emergence and destruction of mode locking as well as an explanation of the front geometry.   

Barriers to reaction front propagation in a spatially random, time-independent flow

We present experimental studies of barriers, called {\em burning invariant manifolds} (BIMs), to front propagation in a spatially random, time-independent flow. We generate the flow with a magnetohydrodynamic technique that uses a DC current and a disordered pattern of permanent magnets. The velocity field is determined from this flow using particle tracking velocimetry, and reaction fronts are produced using the Ferroin-catalyzed Belousov-Zhabotinsky (BZ) chemical reaction. We use the experimental velocity field and a three-dimensional set of ODEs to predict from theory the location and orientation of BIMs. These predicted BIMs are found to match up well with the propagation barriers observed experimentally in the same flow using the BZ reaction. We explore the nature of BIMs as one-sided barriers, in contrast to invariant manifolds that act as barriers for passive transport in all directions. We also explore the role of projection singularities in the theory and how these singularities affect front behavior.   

Computation of Lagrangian Coherent Structures from their Variational Theory

We describe a computational algorithm for detecting hyperbolic Lagrangian Coherent Structures (LCS) from a recently developed variational theory [1]. In contrast to earlier approaches to LCS, our algorithm is based on exact mathematical theorems that render LCS as smooth parametrized curves, i.e., trajectories of an associated ordinary differential equation. The algorithm also filters out LCS candidates that are pure artifacts of high shear. We demonstrate the algorithm on two-dimensional flow models and on an experimentally measured turbulent velocity field.\\[4pt] [1] G. Haller, A variational theory of hyperbolic Lagrangian Coherent Structures,\emph{\ Physica D} \textbf{240} (2011) 574-598   

Geodesic Theory of Transport Barriers in Unsteady Flows

We introduce a unified approach to detecting finite-time Lagrangian transport barriers in two-dimensional unsteady flows with general time dependence. Seeking transport barriers as least deforming material lines, we obtain a variational formulation for such barriers. This variational problem turns out to be well-posed only for three types of transport barriers: hyperbolic barriers (generalized stable and unstable manifolds), elliptic barriers (generalized KAM curves or eddy boundaries), and parabolic barriers (generalized shear jets). Such barriers then coincide with minimal geodesics under an appropriate metric induced by the Cauchy-Green strain tensor on the initial configuration of the flow. The geodesics are obtained as a solution of an ordinary differential equation, and hence are available in a smooth, parametrized form. We show how these new results reveal previously unknown transport barriers in complex model flows and geophysical data sets.   

Noise induced state transitions, intermittency and universality in the noisy Kuramoto-Sivashinsky equation

The Kuramoto-Sivashinsky (KS) equation is a paradigmatic model for a wide spectrum of systems exhibiting spatio-temporal chaos, such as a thin-liquid film falling down a vertical substrate. Here we deal with the noisy KS eqiation which can be derived for the falling film problem with a topographically random substrate. We examine the effects of additive noise in a regime close to the instability onset. We show that when the noise is highly degenerate, in the sense that it acts only on the first stable mode, the solution of the KS equation undergoes several transitions between different states, including a critical on-off intermittent state that is eventually stabilized as the noise strength is increased. Similar results are obtained with the Burgers equation, which has often been used as a prototype of one-dimensional turbulence. Such noise-induced transitions can be completely characterized through critical exponents, obtaining that both equations belong to the same universality class. The results of our numerical investigations are explained rigorously using multiscale techniques.   

A new mode reduction strategy applied to the generalized Kuramoto-Sivashinsky equation

The generalized Kuramoto-Sivashinsky (gKS) equation is one of the simplest prototypes modeling nonlinear active media with energy supply, energy dissipation and dispersion. Not surprisingly, it has been reported for a wide variety of physical settings, from reaction-diffusion systems, e.g. propagation of concentration waves and flame-front instabilities, to fluid dynamics, e.g. a viscous film flowing down an inclined plane. We undertake a combined theoretical-numerical study of the gKS equation. We first approximate it with a renormalization group equation. This approximation forms the basis for a non-standard stochastic mode reduction that guarantees optimality in the sense of maximal information entropy. Herewith, noise is rigorously defined in the reduced gKS equation and hence provides an analytical explanation for its origin. These derivations allow us to develop reliable numerical approximations to the gKS equation and a rigorous methodology on how to add noise. Interestingly, noise becomes increasingly important by decreasing the degrees of freedom in the discretization strategy.   

Torus Streamlines in the 3D Steady Lid-driven Cavity Flows

Streamlines of the incompressible vortical flows in three-dimensional rectangular cavities with different aspect ratios are numerically studied for several Reynolds numbers by using a combined compact finite difference (CCD) scheme with high accuracy and high resolution. The flow is driven by a lid moving tangentially with constant speed. Non-dimensional geometrical parameters of the cavity are the depth-to-width aspect ratio $\Gamma $ and the span-to-width aspect ratio $\Lambda $. The flow parameter is the Reynolds number Re. We study the flow structures in the square cavity ($\Gamma $=1) with the spanwise aspect ratios $\Lambda $=1 and 6.55 for Re from 100 to 400. Torus streamlines are obtained from the velocity field of the steady incompressible flow. Several other streamlines show chaotic behavior. They are equivalent to a non-autonomous Hamiltonian system of one-degree-of-freedom. In order to examine the features of the flow pattern with different parameters, we analyze the Poincare sections in the cross sections of cavities.   

Topological chaos in a lid driven cavity flow at finite Reynolds number

Topological chaos, or chaos that is guaranteed to exist in a system due to sufficiently complex motion of a few periodic orbits, has been demonstrated for creeping flow in a lid driven cavity. Nearly-periodic systems can by analyzed in a similar way based on the presence of Almost Invariant Sets (AIS) with similarly complex space-time trajectories. We extend this analysis to finite Reynolds number flows in a lid driven cavity using a 2D Fourier-Chebyshev spectral algorithm for the streamfunction-vorticity formulation, which enables accurate particle tracking that can resolve the exponential stretching of material lines in the flow. Simply extending the Stokes' flow parameters to stirring at finite Reynolds number leads to a decrease in system performance, but tuning the system based on the topological analysis can lead to enhanced stirring.   

Session L4: Drops VII: Impact and Interactions

Particle-drop Impact in Midair

For the first time the impact of a drop and particle in the mid-air is studied, which is a fundamental physical phenomenon relevant to many applications involving a fluidized bed and a liquid jet, e.g. drug particle coating, and upgrading of heavy oil. To date it has not been clear what happens when a particle and drop collide in midair. An apparatus was build to allow deterministic impact of a particle and drop to occur in midair. Using high speed imaging the impact of three different particles with water drops is studied at different relative velocities. Possible collision outcomes are elucidated in terms of particle-drop diameter ratio, Weber number, and particle wettability. Three distinct regimes of bonding, ripping and coating, and shattering are identified and discussed in this novel study. The differences between on-axis versus off-axis impact is also briefly discussed.   

Gravitational Collisions of Spherical Drops at Finite Stokes Numbers and Low Reynolds Numbers

Collision efficiencies are calculated by a trajectory analysis for two sedimenting spherical drops with exact methods for determining the hydrodynamic forces at finite Stokes number and low Reynolds number. When the Reynolds number is small, fluid inertia is negligible, and the hydrodynamic forces are linear functions of the translational velocities of the drops. However, at nonzero Stokes numbers, drop inertia must be taken into account, and the hydrodynamic forces do not balance the applied forces. For drops in close approach, lubrication forces and attractive molecular forces are considered. Comparison is made between the effects of unretarded and retarded van der Waals forces and Maxwell slip on collision efficiencies. An important application is to raindrop growth for drop radii between 10 and 30 $\mu$m. The collision efficiency goes through a minimum and then approaches the Smoluchowski limit of no hydrodynamic interactions as the drop size and Stokes number become increasingly large. Theoretical predictions are required in this range of drop sizes because experiments are difficult.   

Bouncing Jets

Contrary to common intuition, free jets of fluid can ``bounce'' off each other on collision in mid-air, through the effect of a lubricating air film that separates the jets. We have developed a simple experimental setup to stably demonstrate and study the non-coalescence of jets on collision. We present the results of an experimental investigation of oblique collision between two silicone oil jets, supported by a simple analytical explanation. Our focus is on elucidating the role of various physical forces at play such as viscous stresses, capillary force and inertia. A parametric study conducted by varying the nozzle diameter, jet velocity, angle of inclination and fluid viscosity reveals the scaling laws for the quantities involved such as contact time. We observed a transition from bouncing to coalescence with an increase in jet velocity and inclination angle. We propose that a balance between the contact time of jets and the time required for drainage of the trapped air film can provide a criterion for transition from non-coalescence to coalescence.   

Bubble entrapment by droplet-meniscus collision

The impact of a sessile droplet with a meniscus, close to a moving contact line, is studied experimentally with high-speed imaging. Above a certain velocity and impacting droplet size, bubbles are entrained into the liquid during the process of coalescence. By looking through the liquid we can resolve the formation of an air sheet that is trapped between the drop and the meniscus. This sheet breaks up into a single or multiple bubbles, depending on the experimental conditions. We characterize the various mechanisms for entrainment and identify scaling relations for the size of the entrained bubbles in terms of impacting droplet size and velocity.   

The Effect of Gas Properties on Mesler Bubble Entrainment

Mesler entrainment involves the generation of hundreds of micron size bubbles, frequently distributed in a chandelier- like pattern following the impact of a liquid drop with a bulk surface of the same fluid. To date, research on Mesler entrainment has taken place in air at atmospheric pressure and has therefore neglected to test the influence of gas properties. The results of drop impact studies are presented where a controlled environment was employed consisting of air- helium and air-carbon dioxide mixtures. The dynamic viscosity of pure air at STP is $1.85 \times 10^{-5}$ Pa.s and the kinematic viscosity is $1.6 \times 10^{-5}$ $m^2/s$. By using air-helium and air-carbon dioxide mixtures, kinematic viscosities ranging from 0.5 to 7 times that of air were attained, with dynamic viscosities ranging 0.8 to 1.0 times that of air. The frequency of occurrence of Mesler entrainment is noted for methanol in these environments and is compared with results gathered in air. The effect of the gas phase viscosities and the Capillary number are discussed.   

Jetting from impact of a spherical drop with a deep layer

We performed an experimental study of jets during the impact of a spherical drop with a deep layer of same liquid. Using high speed optical and X-ray imaging, we observe two types of jets: the so-called ejecta sheet which emerges almost immediately after impact and the lamella which emerges later. For high Reynolds number the two jets are distinct, while for low Reynolds number the two jets combine into a single continuous jet. We also measured the emergence time, speed, and position of the ejecta sheet and found simple scaling relations for these quantities.   

``Effervescent'' Atomization in two dimensions

A planar \emph{Savart} water sheet uniformly seeded with small air bubbles in large surface concentration is studied as a model experiment of the so-called ``effervescent'' atomization process. This two-dimensional setup allows for a quantitative observation of all the steps of the sheet disintegration into a collection of disjointed droplets. The bubbles are heterogeneous nucleation sites which puncture the sheet forming growing holes. The dynamics of the holes opening competes with the simultaneous nucleation rate of new holes in a statistically stationary fashion. The liquid constitutive of the sheet is then transitorily concentrated into a web of ligaments of various lengths and diameters, at the junction between adjacent holes. Their break-up produces the final spray. We provide a complete description of the ligaments web statistics in the case where nucleation is synchronous, and show that the drop size dispersion from the breakup of a single ligament is responsible for the shape of the resulting overall spray drop size distribution.   

Dynamics of a drop trapped inside a circular hydraulic jump

We investigate the dynamics of a drop trapped inside a circular hydraulic jump : in our experiment, a circular hydraulic jump is formed by a viscous jet impacting a horizontal glass disk. A drop of the same liquid, deposited in the jump does not coalesce, and remains trapped at its periphery, because of the air entrainment linked to the high drop rotation speed. Depending on the flow rate, the drop can exhibit complex dynamics, from regular rotation along the jump to ``chaotic'' behaviour. We also studied in detail hydrodynamics of the liquid drop and its interaction with the jump. Our investigations show that hydrodynamics of the jump is still not fixed.   

Session L5: CFD V: Numerical Methods II

On the accuracy of difference formulas at block interfaces in Structured Adaptive Mesh Refinement (S-AMR) methods

S-AMR is a cost/efficient strategy to solve a variety of complex problems in laminar and turbulent incompressible flows. The computational grid consists of a number of nested grid blocks at different resolution levels. The coarsest grid blocks always cover the entire computational domain, and local refinement is achieved by the bisection of selected blocks in every coordinate direction. This generates coarse-fine interfaces between blocks whose treatment affects the accuracy and conservation properties of solver. In the present study we will focus on the effects of different interpolation strategies on the properties of finite-differences taken at block boundaries or cells neighboring the boundaries. Looking into a set of model problems we found that for a variety of popular interpolation schemes (both low and high order) the symmetry properties of central difference operators are lost and dissipation and phase errors are added to the errors of the difference formulas. Recurring interpolation, in particular, degrades the quality of formulas as more coarse and fine point values are introduced in an asymmetric manner. Solution strategies based on the minimization of the modified wavenumber error will be presented.   

A Method of Adaptive Mesh Refinement on Cartesian Unstructured Meshes

A general method for a dynamic meshing library with built-in localized adaptive mesh refinement (AMR) routines for hexahedral meshes is presented. Current block-based AMR methods apply stacked nested finer grids to regions of the computational domain, solve the governing equations of the flow within the fine grid, and then interpolate the fine grid values to the coarse grid. Unlike existing libraries, the proposed method is designed to generate fully unstructured grids that may be refined and coarsened on-the-fly up to an arbitrary level. This approach allows for \emph{h}-refinement without the memory and computational expense of calculating masked coarse grid cells, as is done in block-based AMR. The hexahedral nature of the meshes simplifies the finite-volume algorithms, reducing the computational expense of refinement when compared with arbitrary tetrahedral-mesh solvers. Complex surfaces can be quickly modeled by successive refinement of control volumes while retaining numerical stability and minimizing the size of the grid.   

A fully conservative finite-volume method for incompressible Navier-Stokes equations on locally refined nested Cartesian grids

A second-order-accurate finite-volume method is developed for the solution of incompressible Navier-Stokes equations on locally refined nested Cartesian grids. Numerical accuracy and stability on locally refined nested Cartesian grids are achieved using a finite-volume discretization of the incompressible Navier-Stokes equations based on higher- order conservation principles - {\it i.e.}, in addition to mass and momentum conservation, kinetic energy conservation in the inviscid limit is used to guide the selection of the discrete operators and solution algorithm. Hanging nodes at the interface are {\it implicitly} slanted to improve the pressure-velocity projection, while the other parts of the grid maintain an orthogonal Cartesian grid topology. The present method is found to significantly improve the computational efficiency while it is straightforward to implement. The present method shows superior conservation of mass, momentum, and kinetic energy compared to the conventional methods employing interpolation at the interface between coarse and fine grids in simulations of Taylor vortex, lid-driven cavity flow, and flow over a square cylinder.   

A Space/Time Dynamically Adaptive Method for Multiscale Problems

Systems of partial differential equations (PDEs) describing problems that are multiscale in space and time are computationally very expensive to solve. In order to overcome the challenges related to both thin spatial layers and temporal stiffness we propose the use of a wavelet adaptive multilevel representation (WAMR) in space and an adaptive model reduction method (G-Scheme) in time. The multilevel structure of the algorithm provides a simple way to adapt computational refinements to local demands of the solution. High resolution computations are performed only in spatial regions where sharp transitions occur, while the G-Scheme is an explicit solver developed for stiff problems which is built upon a local decomposition of the dynamics in three subspaces involving slow, active and fast time scales. Only the modes in the active subspace are integrated numerically, the others are approximated asymptotically. Subsequently, the original problem not only becomes substantially smaller, but more importantly non-stiff. Combining the WAMR technique with the G-Scheme yields a time accurate solution of a prescribed accuracy with a much smaller number of space- time degrees of freedom. While the computational scheme can be used to solve a wide class of stiff PDE problems, we will illustrate its use in the solution of the Navier Stokes equations in reactive flows.   

Parallel Adaptive Wavelet Collocation Method for PDEs

A parallel adaptive wavelet collocation method for solving a large class of Partial Differential Equations is presented. The parallelization is achieved by developing an asynchronous parallel wavelet transform, which allows to perform wavelet transform and derivative calculations on each processor without additional data synchronization on each level of resolution. The data are stored using tree-like structure with tree roots starting at sufficiently large level of resolution to shorten tree traversing path and to minimize the size of trees for data migration. Both static and dynamic domain partitioning approaches are developed. For the dynamic domain partitioning, trees are considered to be the minimum quantum of data to be migrated between the processors. This allows fully automated and efficient handling of non-simply connected partitioning of a computational domain. Dynamic load balancing is achieved via domain repartitioning during grid adaptation step and reassigning tree data structure nodes to the appropriate processors to ensure approximately the same number of nodes on each processor. The parallel efficiency of the approach is discussed based on parallel Coherent Vortex Simulations of homogenous turbulence with linear forcing at effective non-adaptive resolutions up to $2048^3$ using as many as $1024$ CPU cores.   

A Hybrid Grid Compressible Flow Solver for Large-Scale Supersonic Jet Noise Simulations on Multi-GPU Clusters

A compressible flow solver for multi-GPU clusters has been developed for performing large-scale supersonic jet noise and other high-speed compressible flow simulations over hybrid grids. While supersonic jet noise simulations require the accurate representation of complex nozzle geometry and thus the use of unstructured grids, much of the domain geometry can be represented sufficiently with structured grids, which drastically reduces memory bandwidth consumption and storage. Therefore, hybrid grids are employed, which combine an unstructured grid representation in the vicinity of the nozzle with a structured grid representation in the wake region of the flow field. Performance benchmarks are drawn from large-scale runs performed using this solver, including a jet nozzle with chevrons and multi-species flows involving jet engine exhaust.   

Numerical study on the onset of electro-convection between planar electrodes caused by unipolar charge injection

Two-dimensional electrohydrodynamic (EHD) convection in a dielectric liquid between a pair of planar electrodes has been studied numerically considering autonomous unipolar charge injection from the bottom electrode. The steep gradient in the charge-density distribution and its time evolution can be resolved successfully using upwind schemes for the convective terms in the charge conservation equation. The Navier-Stokes equations coupled with the charge conservation equation and the Poisson equation for the potential are solved using the SIMPLE algorithm. We also apply a perturbation method to study the linear stability problem to derive more accurate critical parameter values for the onset of electro-convection. In particular, we are interested in the effect of injection strength and the horizontal length of the domain on the stability characteristics. Our two-dimensional numerical solutions are compared with the linear stability analysis for the validation of the code.   

Vorticity confinement technique for drag prediction

This work couples wake-integral drag prediction and vorticity confinement technique (VC) for the improved prediction of drag from CFD simulations. Induced drag computations of a thin wing are shown to be more accurate than the more widespread method of surface pressure integration when compared to theoretical lifting-line value. Furthermore, the VC method improves trailing vortex preservation and counteracts the shift from induced drag to numerical entropy drag with increasing distance of Trefftz plane downstream of the wing. Accurate induced drag prediction via the surface integration of pressure barring a sufficiently refined surface grid and increased computation time. Furthermore, the alternative wake-integral technique for drag prediction suffers from numerical dissipation. VC is shown to control the numerical dissipation with very modest computational overhead. The 2-D research code is used to test specific formulations of the VC body force terms and illustrate the computational efficiency of the method compared to a ``brute force'' reduction in spatial step size. For the 3-D wing simulation, ANSYS FLUENT is employed with the VC body force terms added to the solver with user-defined functions (UDFs). VC is successfully implemented to highly unsteady flows typical for Micro Air Vehicles (MAV) producing oscillative drag force either by natural vortex shedding at high angles of attack or by flapping wing motion.   

Computational and experimental study of airflow around a fan powered UVGI lamp

The quality of indoor air environment is very important for improving the health of occupants and reducing personal exposure to hazardous pollutants. An effective way of controlling air quality is by eliminating the airborne bacteria and viruses or by reducing their emissions. Ultraviolet Germicidal Irradiation (UVGI) lamps can effectively reduce these bio-contaminants in an indoor environment, but the efficiency of these systems depends on airflow in and around the device. UVGI lamps would not be as effective in stagnant environments as they would be when the moving air brings the bio-contaminant in their irradiation region. Introducing a fan into the UVGI system would augment the efficiency of the system's kill rate. Airflows in ventilated spaces are quite complex due to the vast range of length and velocity scales. The purpose of this research is to study these complex airflows using CFD techniques and validate computational model with airflow measurements around the device using Particle Image Velocimetry measurements. The experimental results including mean velocities, length scales and RMS values of fluctuating velocities are used in the CFD validation. Comparison of these data at different locations around the device with the CFD model predictions are performed and good agreement was observed.   

Integration Techniques for Stokes Boundary Integrals

Stokes flow is often approached through a boundary integral formulation. The integrals involved are singular or nearly singular and therefore are not resolved well through standard quadrature methods. Various techniques to improve the accuracy of such integrals exist. We will present a brief survey of methods for singular and nearly singular Stokes integrals for both 2D and 3D flows.   

Session L6: Drops VIII: Complex Phenomena

Foliar disease transmission: insights from fluid dynamics

Rainfalls are suspected to trigger the spread of a multitude of foliar diseases that could be devastating for agricultural and forestry outputs and balance. A wealth of key fluid mechanics phenomena arise from the impact of drops on plant leaves. We present the results of a combined experimental and modelling investigation shading light on the modes of precipitation-induced foliar disease transmission.   

Sliding motion of an oscillating drop driven by ac electrowetting on inclined plane

When a drop is placed on an inclined solid plane, the drop can stick to or slide along the solid surface due to an opposition between the gravitational force and the pinning force from contact angle hysteresis. Here we demonstrate that sessile drops of sizes below the capillary length can be mobilized through drop oscillation induced by ac electrowetting at low frequency on a low inclined solid plane. The effects of ac frequency on the sliding condition and terminal sliding velocity are investigated. At resonant frequency, drops reach maximum terminal sliding velocities. Varying the applied voltage at a fixed frequency, we find the threshold voltage for a sliding drop and the empirical relationship between the applied voltage and terminal sliding velocity. Using the relationship between drop size and frequency, we can selectively slide drops of a specific size along an inclined plane.   

Droplet dynamics in microfluidic stratifications

We experimentally study the dynamic response of viscous droplets to external microflows. A segmented flow of droplets is injected into a stratified flow of miscible fluids using a square microchannel with two focusing sections. This method enables us to locally manipulate the capillary number of the continuous phase and examine the hydrodynamic coupling between droplets and a variety of flow fields in confined geometries. Focus is on the behavior of droplets entering a region with parallel streams having different interfacial tensions and viscosities. A general phase-diagram is proposed and droplet behavior is investigated in relation with dynamic wetting properties. This study shows methods for modifying the physicochemical environment of microfluidic droplets.   

Scaling laws for electrospraying

When stressed by strong electric fields, fluid menisci develop conical structures called Taylor cones which emit from their tips fine jets that in turn break up to form a mist of charged droplets. This phenomenon, known as electrohydrodynamic tip-streaming, cone-jetting, or electrospraying finds application in a number of industrially and scientifically important processes, including mass spectrometry, particle synthesis, and cloud physics. Here, this phenomenon is analyzed using the leaky-dielectric model developed by Taylor and Melcher for the situation in which an initially spherical free drop of an incompressible Newtonian fluid surrounded by a gas is subjected to an electric field. The resulting initial-boundary-value-problem is solved using the finite element method with elliptic mesh generation and adaptive, implicit time integration. The simulation results and simple scaling arguments are then used to infer the universal scaling laws governing the sizes and charges of the small electrospray drops.   

Transient Reduction of the Drag Coefficient of Charged Droplets via the Convective Reversal of Stagnant Caps

Droplets are frequently observed to move as if they were solid rather than liquid, i.e. with no slip at the liquid-liquid interface. This behavior is usually explained in terms of the so-called ``stagnant cap'' model, in which surfactants accumulate at the trailing edge of the droplet, immobilizing the surface and increasing the observed drag coefficient. Here we show that the drag coefficient for charged droplets is temporarily reduced by reversing the direction of an electric driving force. Using high speed video we simultaneously track the velocity and relative interfacial velocity of individual aqueous droplets moving electrophoretically through oil. The observed surface behavior is highly sensitive to the surfactant concentration. For sufficiently low or sufficiently high surfactant concentrations, upon reversal of the electric field the droplet rapidly accelerates in the opposite direction but then decelerates, concurrent with a transient rearrangement of tracer particles on the droplet surface. In contrast, droplets with intermediate surfactant concentrations exhibit no deceleration nor tracer particle rearrangement. We interpret these observations in terms of convectively dominated rearrangement of the stagnant cap, and we discuss the implications for precise electrophoretic control of droplet motion in lab-on-a-chip devices as well as droplet charge estimation through velocimetry.   

Electromagnetic liquid pistons for capillarity-based pumping

Two adjoining ferrofluid droplets can behave as an electronically-controlled oscillator or switch by an appropriate balance of magnetic, capillary, and inertial forces. Their motion can be exploited to displace a surrounding liquid, forming electromagnetic liquid pistons. Such ferrofluid pistons can pump a precise volume of liquid via finely tunable amplitudes or resonant frequencies with no solid moving parts. Here we demonstrate the use of these liquid pistons in capillarity-dominated systems for variable focal distance liquid lenses with nearly perfect spherical interfaces. These liquid/liquid lenses feature many promising qualities not previously realized together in a liquid lens, including large apertures, immunity to evaporation, invariance to orientation relative to gravity, and low driving voltages. The dynamics of these liquid pistons is examined, with experimental measurements showing good agreement with a spherical cap model. A centimeter-scale lens was shown to respond in excess of 30 Hz, with resonant frequencies over 1 kHz predicted for scaled down systems.   

Negative radiation forces and the asymmetry of scattered radiation: spheres in Bessel beams

The discovery that acoustical [1] and optical [2,3] radiation forces computed on spheres placed on the axis of acoustical and optical Bessel beams may be opposite the direction of beam propagation makes it appropriate to reexamine the relationship between radiation forces and the asymmetry of the scattered radiation. For all of the previously identified acoustical cases in which the force was negative and the scattering pattern was also computed, it was found that the backscattering was suppressed and the forward scattering relatively enhanced (see e.g. [1]). In the present research the acoustic radiation force on an arbitrary isotropic sphere is related to the asymmetry in the scattering and the extinction introduced by the sphere for the case of a helical Bessel beam of arbitrary order [4]. The analysis confirms that conditions are more favorable for generating negative forces when the asymmetry is such that the backscattering is suppressed relative to the forward scattering. It is also found, however, that absorption of power by the sphere gives rise to a positive force contribution, a term which has been neglected in the corresponding optical analysis [2].\\[0pt] [1] P. L. Marston, J. Acoust. Soc. Am 120, 3518 (2006). [2] J. Chen et al., Nature Photonics (2011). [3] A. Novitsky \& C.-W. Qiu, arXiv:1102.5285v1 (2011). [4] L. K. Zhang \& P. L. Marston (submitted).   

Pulsating Electrohydrodynamic Cone-Jets: from Choked Jet to Oscillating Cone

Pulsating cone-jets occur in a variety of electrostatic spraying and printing systems. We report an experimental study of the pulsation frequency to reconcile two models based on a choked jet and an oscillating cone, respectively. The two regimes are demarcated by the ratio of the supplied flow rate ($Q_s$) to the minimum flow rate ($Q_m$) required for a steady Taylor cone-jet. When $Q_s < Q_m$, the electrohydrodynamic flow is choked at the nozzle because the intermittent jet, when on, emits mass at the minimum flow rate; the pulsation frequency in the choked jet regime is proportional to $Q_s/Q_m$. When $Q_s > Q_m$, the Taylor cone anchored at the nozzle experiences a capillary oscillation analogous to the Rayleigh mode of a free drop; the pulsation frequency in the oscillating cone regime plateaus to the capillary oscillation frequency which is independent of $Q_s/Q_m$.   

Electrohydrodynamic drop deformation by a strong electric field

Using matched asymptotic expansions within the Taylor-Melcher leaky-dielectric model, we analyze the strong deformation of a drop by a strong electric field. As is common in slender-body analyses, the small drop slenderness is used as the expansion parameter. This parameter however is not a priori specified in the problem formulation, and must be found throughout the course of the asymptotic solution. Sherwood's scaling for dielectric liquids, inverse with the 6/7-power of the electric field, applied here. Slender shapes are possible only for low drop viscosities. We identify a new inequality, in terms of material-property ratios, necessary for the evolution to a slender shape, which is independent of Taylor discriminating inequality, necessary for initial deviation to prolate shapes.   

Desiccation of a Sessile Drop of Blood: Cracks Formation and Delamination

The evaporation of drops of biological fluids has been studied since few years du to several applications in medical fields such as medical tests, drug screening, biostabilization... The evaporation of a drop of whole blood leads to the formation of final typical pattern of cracks. Flow motion, adhesion, gelation and fracturation all occur during the evaporation of this complex matter. During the drying, a sol-gel transition develops [1]. The drying kinetics is explained by a simple model of evaporation taking account of the evolution of the gelation front. The system solidifies and when stresses are too important, cracks nucleate. The cracks formation and the structure of the crack pattern are investigated. The initial crack spacing is found in good agreement with the implementation in open geometry of the model of cracks formation induced by evaporation proposed by Allain and Limat [2]. Finally, the drop is still drying after the end of the formation of cracks which leads, like in the situation of colloid suspensions [3], to the observation of a delamination phenomenon.\\[0pt] [1] B. Sobac and D. Brutin, Structural and Evaporative Evolutions in Desiccating Sessile Drops of Blood, Phys. Rev. E 84, 011603, 2011. [2] C. Allain and L. Limat, Phys. Rev. Lett. 74, 2981 (1995). [3] L. Pauchard, B. Abou, K. Sekimoto, Infuence of Mechanical Properties of Nanoparticles on Macrocrack Formation, Langmuir, 25(12), 6672-6677, 2009.   

Session L7: Turbulent Boundary Layers VI

Three-dimensional structure of momentum transfer in turbulent channels

The three-dimensional structures of the intense tangential Reynolds stress in plane turbulent channels (Qs) are studied by quadrant analysis, with emphasis on the logarithmic and outer layers. Wall-detached Qs are isotropically oriented background stress fluctuations, common to most turbulent flows, and do not contribute to the mean stress. Most of the stress is carried by a self-similar family of larger attached Qs, increasingly complex away from the wall, with fractal dimensions $D\approx 2$. They are ``sponges of flakes,'' while vortex clusters are ``sponges of strings.'' Although their number decays away from the wall, the fraction of the stress that they carry is independent of their heights, and a substantial part resides in a few objects extending beyond the centreline, reminiscent of the VLSM of several authors. The predominant logarithmic-layer structures are side-by-side Q4-Q2 pairs of sweeps and ejections, with an associated cluster, with dimensions and stresses similar to Townsend's conjectured attached eddies. They align themselves streamwise, but not strongly enough to explain the very long structures in the channel centre.   

Hairpin vortices in the transitional and developed turbulence of a flat-plate boundary layer

Using Vortex lines to reveal vortical structures in turbulent flows has been in disfavor for some time. They are field lines that can be drawn wherever the flow is rotational, regardless of whether a true vortex exists there or not. However, their virtues are that the vortices they can reveal do not depend on setting a detection threshold, unlike all the vortex identifiers based on the velocity gradient tensor or based on a low pressure criterion, and they can isolate individual vortices. Such individual hairpin vortices have been identified in the transition region near $Re_\theta = 500$ of a recent flat-plate boundary layer and in the developed turbulence near $Re_\theta = 1950$. The vortices in these two regions emerge out of sheets of unorganized vorticity in the viscous sublayer and have quite similar characteristics. An octant analysis based on the combinations of signs of the velocity and temperature fluctuations, $u$, $v$ and $\theta$, shows that the momentum and heat fluxes in both the transitional and developed regions are predominantly of the mean gradient type. The fluxes appear to be closely associated with wall layer vortices that transport momentum and heat toward and away from the wall.   

The structure of the vorticity field in the near-wall region of turbulent channel flow at high-Reynolds number

The structure of the vorticity field in turbulent channel flow is studied by using direct numerical simulations of the incompressible Navier-Stokes equations with up to $2048\times 1536\times 2048$ grid points; the maximum friction Reynolds number is $Re_\tau=2560$. Instantaneous vortex-line plots show the presence of $\Omega$-shaped hairpin vortices in the near-wall region of turbulent channel flow. The $\Omega$-shaped hairpin vortices in the near-wall region are well displayed by a bundle of vortex lines starting from points along a line near $y^+=10$ parallel to the mean stream. They suggest that the hairpin vortices are formed by instabilities and roll-ups of sheets of spanwise vorticity in the buffer layer of turbulent channel flow. The three-dimensional structure of the low-speed region of the streamwise velocity near the wall ($y^+<100$) is discussed in view of these vortex lines starting from the buffer layer.   

Flow Visualization of Artificially Generated Hairpin Vortices

To investigate the potential mechanisms for hairpin packet formation in fully turbulent boundary layers, a flow visualization study of artificially generated hairpin vortices in an otherwise laminar boundary layer is performed. The experiments are conducted in a recently constructed free surface water channel at Lafayette College. A new method to artificially generate individual hairpin vortices is employed which utilizes a flexible membrane which is inflated to create transient hemispherical protrusions on a flat plate, zero pressure gradient laminar boundary layer. By controlling the duration of time the membrane protrudes above the wall, a single vortex can be reliably generated. This technique avoids the need for fluid injection in order to ensure uniform particle seeding for subsequent PIV measurements. Multiple generation sites are placed at different streamwise locations to allow hairpins of different maturity to interact. The characteristics of single hairpin vortices will be compared to those described in the literature along with a qualitative analysis of the interaction of two hairpin vortices.   

Dynamical Properties of Vortex Furrows in Transitioning Boundary Layers

A vortex filament simulation of the spatially growing transitional boundary layer reveals the presence of low speed streaks underlying furrow-like streamwise oriented folds in the surface vorticity layer (AIAA J. Vol. 48, 2010; Proc. ETC13, 2011). The putative hairpin vortices and packets widely observed in boundary layers are found to be an illusion created by assigning the status of structure to the visualized form of regions of rotational motion created by the vortex furrows. Thus, at best, hairpins roughly describe the shape taken by that part of the vorticity within the furrows that directly causes rotation while ignoring the ``invisible'' and considerable non-rotational part. The life history of the furrows is discussed here including a description of how they grow and the dynamics of the vorticity field within them. Long lived furrows represent ``factories'' within which initially spanwise vorticity progresses from arch to either one or two-lobed mushroom-like structures in a continuous stream. Furrows grow by this same process. At the heart of the furrow phenomenon is a self-reinforcing process by which streamwise vorticity begets more streamwise vorticity.   

Evolution of Reynolds stresses in a turbulent boundary layer

Understanding Reynolds shear-stress events in a turbulent boundary layer is of crucial importance for modelling and controlling turbulent wall-flows. In this study, we examine the evolution in time and space of these shear-stress events by performing time-resolved PIV measurements in a stream-wise wall-normal plane of a turbulent boundary layer at $Re_\tau\approx2500$. The conditions are similar to the experiment by Dennis \& Nickels (J. Fluid Mech. 2011, vol. 673), who performed measurements at $Re_\theta=4700$. Four high-speed cameras positioned next to each other, 4-5 m downstream of a glass rod trip, captured a region of flow spanning approximately $2\delta$ in stream-wise and $0.5\delta$ in wall-normal direction. This zoomed-in field-of-view enables high spatial, $l^+\approx20$, and temporal resolution, $\Delta t^+\approx 1$ which will allow us to describe the evolution of shear-stress events in time and space. In the talk, detailed analyses including instantaneous tracking of Reynolds shear-stress events, quadrant decomposition and spectra of the stream-wise, wall-normal and Reynolds shear-stress fluctuations will be presented.   

The topology of the footprints of wall-turbulence

When studying the topology of turbulent flows, the three invariants of the velocity gradient tensor are often used. For incompressible flow the first invariant $P$ is zero and the topology of the flow structures can be investigated in terms of the second and third invariants, $Q$ and $R$ respectively. For example, isosurfaces of $Q$ above a certain threshold are often used in an attempt to identify vortical structures in the flow. In wall-turbulence, however, these invariants are zero on a no slip wall. Therefore, analysis tools relying on these invariants cannot be used to topologically study the footprint of turbulence on the wall. In this paper, it is proposed that the ``flow'' field on a wall can be described by a no slip Taylor-series expansion. This provides a new tensor relating skin friction to streamwise and spanwise coordinate. Like the velocity gradient tensor, it is possible to define invariants $\mathcal{P}$, $\mathcal{Q}$ and $\mathcal{R}$ of the so-called ``no slip'' tensor. It will also be shown that it may be possible to investigate the topology of the flow field on a no slip wall in terms of these invariants.   

Space-Time Correlation of Large-Scale Structures in a Turbulent Boundary Layer

Taylor's hypothesis is often used to project temporal data into the spatial domain and has been used in the past to show the presence of large-scale structures ($>10\delta$) in the log and lower wake region of the turbulent boundary layer (TBL). To investigate the spatial and temporal evolution of such large-scale structures, the present study employs time-resolved Particle Image Velocimetry (PIV) in several streamwise-spanwise planes in the log-layer of a TBL ($Re_\theta=2,000$). In order to capture the full extent of these structures, four high-speed, high-resolution PIV systems are combined to span a region of approximately $3\delta \times 12\delta$ and a continuous time sequences of $\approx 50\delta/U$. Such data sets are currently unavailable from previous experimental investigations and reveal the existence of long and very long ($>8\delta$) low- and high-speed structures. Two-point space-time correlations are employed to examine the temporal extent and meandering nature of these structures with respect to their size and spacing in the log-layer. Furthermore, the validity of Taylor's hypothesis is tested for such long projection distances.   

High spatial resolution measurements of large-scale three-dimensional structures in a turbulent boundary layer

Large-scale three-dimensional (3D) structures in a turbulent boundary layer at Re$_\theta$ = 2000 are examined via the streamwise extrapolation of time-resolved stereo particle image velocimetry (SPIV) measurements in a wall-normal spanwise plane using Taylor's hypothesis. Two overlapping SPIV systems are used to provide a field of view similar to that of direct numerical simulations (DNS) on the order of $50\delta \times 1.5\delta \times 3.0\delta$ in the streamwise, wall-normal and spanwise directions, respectively, with an interrogation window size of $40^+ \times 20^+ \times 60^+$ wall units. Velocity power spectra are compared with DNS to examine the effective resolution of these measurements and two-point correlations are performed to investigate the integral length scales associated with coherent velocity and vorticity fluctuations. Individual coherent structures are detected to provide statistics on the 3D size, spacing, and angular orientation of large-scale structures, as well as their contribution to the total turbulent kinetic energy and Reynolds shear stress.   

Energy dissipating structures in turbulent boundary layers

We present numerical experiments of a dipole crashing into a wall, a generic event in two-dimensional incompressible flows with solid boundaries. The Reynolds number $Re$ is varied from $985$ to $7880$, and no-slip boundary conditions are approximated by Navier boundary conditions with a slip length proportional to $Re^{-1}$. Energy dissipation is shown to first set up within a vorticity sheet of thickness proportional to $Re^{-1}$ in the neighborhood of the wall, and to continue as this sheet rolls up into a spiral and detaches from the wall. The energy dissipation rate integrated over these regions appears to converge towards $Rey$-independent values, indicating the existence of energy dissipating structures that persist in the vanishing viscosity limit. Details can be found in Nguyen van yen, Farge and Schneider, PRL, {\bf 106}, 184502 (2011).   

Session L8: Compressible Flows II

Low-dissipation hybrid schemes for simulations of compressible multicomponent flows

In the present work an efficient hybrid scheme is proposed for numerical simulations of compressible multicomponent flows. The algorithm is based on a high-order accurate weighted essentially non-oscillatory (WENO) scheme for shock capturing and a non-dissipative central scheme in the split form for smooth regions. The central-difference method results in a reasonable speed up and exhibits better resolution properties for turbulence. The shock capturing is handled using the AUSM+up Riemann solver with a WENO reconstruction of the primitive variables. A new sensor based on the first norm of the difference of WENO weights from the ideal weights is used at the beginning of each Runge-Kutta step for a smooth transition between the central and WENO fluxes at interfaces. The scheme is shown to prevent spurious pressure oscillations at interfaces. The performance of the method is presented for a set of problems including the Sod shock tube problem, the Shu-Osher problem and the planar Richtmyer-Meshkov instability with particular emphasis on mixing at early and late times. This research was supported in part by the DOE NNSA under the Predictive Science Academic Alliance Program by grant DEFC52- 08NA28616.   

A Novel A Posteriori Investigation of Scalar Flux Models for Passive Scalar Dispersion in Compressible Boundary Layer Flows

A novel direct numerical simulation (DNS) based a posteriori technique has been developed to investigate scalar transport modeling error. The methodology is used to test Reynolds-averaged Navier-Stokes turbulent scalar flux models for compressible boundary layer flows. Time-averaged DNS velocity and turbulence fields provide the information necessary to evolve the time-averaged scalar transport equation without requiring the use of turbulence modeling. With this technique, passive dispersion of a scalar from a boundary layer surface in a supersonic flow is studied with scalar flux modeling error isolated from any flowfield modeling errors. Several different scalar flux models are used. It is seen that the simple gradient diffusion model overpredicts scalar dispersion, while anisotropic scalar flux models underpredict dispersion. Further, the use of more complex models does not necessarily guarantee an increase in predictive accuracy, indicating that key physics is missing from existing models. Using comparisons of both a priori and a posteriori scalar flux evaluations with DNS data, the main modeling shortcomings are identified. Results will be presented for different boundary layer conditions.   

The conservative cascade of kinetic energy in compressible turbulence

We use a coarse-graining approach to analyze inter-scale transfer of kinetic energy in compressible turbulence. We present the first direct evidence that mean kinetic energy cascades conservatively beyond a transitional ``conversion'' scale-range despite not being an invariant of the compressible flow dynamics. We use high-resolution three-dimensional simulations of compressible hydrodynamic turbulence on $512^3$ and $1024^3$ grids. We probe regimes of forced steady-state isothermal flows and of unforced decaying ideal gas flows. The key quantity we measure is pressure dilatation cospectrum, $E^{PD}(k)$, where we provide the first numerical evidence that it decays at a rate faster than $k^{-1}$ as a function of wavenumber. This is sufficient to imply that mean pressure dilatation acts primarily at large-scales and that kinetic and internal energy budgets statistically decouple beyond a transitional scale-range. Our analysis establishes the existence of an ensuing inertial range over which mean SGS kinetic energy flux becomes constant, independent of scale. Over this inertial range, mean kinetic energy cascades locally and in a conservative fashion despite not being an invariant.   

Energy-Pressure-Velocity-Scalar Filtered Mass Density Function

The ``Energy-Pressure-Velocity-Scalar Filtered Mass Density Function'' (EPVS-FMDF) is a new subgrid scale (SGS) model developed for large eddy simulation of high speed turbulent flows. This is an extension of the previously developed ``velocity-scalar filtered mass density function'' method [1] in low speed flows. In the EPVS-FMDF formulation, compressibility effects are accounted for by including two additional thermodynamic variables: the pressure and the internal energy. This is the most general form of the FDF for high speed flow simulations. The EPVS-FMDF is obtained by solving its transport equation, in which the effects of convection for velocity and scalar field appear in a closed form. The unclosed terms are modeled in a fashion similar to that in RANS-PDF methods. The modeled EPVS-FMDF transport equation is solved by a Lagrangian Monte Carlo method and is employed for LES of a temporally developing mixing layer at several values of the convective Mach number. The predicted results are assessed by comparison with direct numerical simulation (DNS) data.\\[4pt] [1] Sheikhi, M. R. H., Givi, P., and Pope, S. B., Velocity-Scalar Filtered Mass Density Function for Large Eddy Simulation of Turbulent Reacting Flows, Phys. Fluids, 19(9): 095196 1-21 (2007)   

Small-scale intermittency in compressible turbulence

While the effects of compressibility on low-order quantities such as the mean turbulent kinetic energy and dissipation in decaying turbulence have been extensively investigated, little is known about the scaling of fine intermittent structures and how they scale with Reynolds and turbulent Mach numbers. It is thus unclear how the intermittent behavior of energy dissipation rate, for example, in compressible flows compares with its incompressible counterpart. Massive direct numerical simulations of isotropic compressible turbulence at finer-than-usual grid resolutions were conducted to investigate the scaling of small-scale intermittency at a range of Reynolds and turbulent Mach numbers. Large-scale forcing is applied to attain a stationary state which permits better statistical sampling of intermittent activity and, at the same time, provides results independent of initial conditions. Scaling exponents for energy dissipation rate are computed and compared to theoretical models. While low-order moments of dissipation show weak dependence on compressibility levels and thus possess scaling exponents similar to the incompressible case, high-order moments depend on the turbulent Mach number. Differences in the scaling of solenoidal and dilatational components are related to the structure of the most intense events for each type of motion. The consequences of the finidings are discussed in the context of high Reynolds number flows.   

A numerical method for DNS/LES of high--enthalpy turbulent flows

A numerical method is developed for simulation of high-- enthalpy turbulent flows. A non-dissipative algorithm is used for accurate flux reconstruction at the cell faces. The method is combined with a predictor corrector based shock capturing scheme to simulate strong shock waves encountered in high-- enthalpy flows. A non--linear limiter is used to limit the application of shock capturing only to the vicinity of the shock wave to minimize dissipation. The Navier-Stokes equations are suitably modified to represent various thermo--chemical processes occurring in high--enthalpy flows. A five species model for air is considered. To account for finite rate chemical reactions, individual mass conservation equations are solved for every species. An equation for conservation of vibrational energy is also solved to account for vibrational excitation. Species diffusion is modeled through Fick's law. Transport properties are computed taking high temperature effects into account. The numerical method is evaluated using test problems.   

Modeling Compressed Turbulence with BHR

Turbulence undergoing compression or expansion occurs in systems ranging from internal combustion engines to supernovae. One common feature in many of these systems is the presence of multiple reacting species. Direct numerical simulation data is available for the single-fluid, low turbulent Mach number case. Wu, et al. (1985) compared their DNS results to several Reynolds-averaged Navier-Stokes models. They also proposed a three-equation $k-\varepsilon-\tau$ model, in conjunction with a Reynolds-stress model. Subsequent researchers have proposed alternative corrections to the standard $k-\varepsilon$ formulation. Here we investigate three variants of the BHR model (Besnard, 1992). BHR is a model for multi-species variable-density turbulence. The three variants are the linear eddy-viscosity, algebraic-stress, and full Reynolds-stress formulations. We then examine the predictions of the model for the fluctuating density field for the case of variable-density turbulence.   

Differential Reynolds stress closure modeling of compressible shear flows

The most important difference between turbulence in high and low Mach number flows stems from the changing role and action of pressure at different speed regimes. In the rapidly distorted turbulence regime, this effect is well captured by rapid distortion theory (RDT) which shows that gradient Mach number characterizes the role/action of pressure very accurately. Thus motivated, we develop a new rapid pressure-strain correlation model for high-speed compressible shear flows in which the closure coefficients are functions of the local gradient Mach number. The functional dependence of the model coefficients on the Mach number is obtained by comparison against RDT data. This closure naturally leads to a pressure-dilatation closure model. Further analysis reveals that a modification of the dissipation equation is also mandatory to accommodate the pressure-dilatation closure physics. Full differential Reynolds stress closure calculations of plane supersonic mixing layers are performed and comparison with the experimental data of Goebel and Dutton shows that the model exhibits good overall agreement without any further model calibration.   

{\it A Priori} Assessment of the FDF Sub-Closures in Compressible Turbulence

Results are presented of {\it a priori} assessment of some of the sub-closures required in LES via FDF in compressible turbulent flows. This is done via assessment of DNS of several turbulent flow configurations at varying compressibility levels and Reynolds numbers. Optimum model parameters are calculated by maximizing the correlation coefficients between the SGS exact and modelled terms. The effects of the filter width are also assessed for some of the sub-closures.   

Application of gradient limiters for computation of viscous fluxes in an unstructured compressible flow solver

HYDRA, an unstructured finite-volume CFD code used internally by Rolls--Royce LLC, evaluates viscous fluxes using a characteristic-based scheme in which the characteristic variables are modified with a pseudo-Laplacian smoothing introduced in the doctoral dissertation of Moinier (Oxford University, 1999). Since the pseudo-Laplacian scheme is inadequate for removing numerical oscillations in a variety of situations, a replacement scheme is proposed and implemented with characteristic variables approximated using a smoothed flux limiter based on a traditional minmod scheme. Formally, the method retains second-order accuracy except near oscillations. Convergence plots and comparisons with data demonstrate that the limiter technique provides improvement compared with baseline simulations. Convergence plot comparisons show improved mass flow conservation, removal of oscillations, and the capability of converging to machine zero without sacrificing overall accuracy. Besides this specific application to shock capturing in compressible flows, similar flux limiters may also be appropriate for use in implicit LES for incompressible flows where other limiters and/or filters are currently used in a similar pseudo-Laplacian manner, and also for compressible LES.   

Session L9: Flow Control IV

Unsteady Aerodynamic Flow Control of a Suspended Axisymmetric Moving Platform

The aerodynamic forces on an axisymmetric wind tunnel model are altered by fluidic interaction of an azimuthal array of integrated synthetic jet actuators with the cross flow. Four-quadrant actuators are integrated into a Coanda surface on the aft section of the body, and the jets emanate from narrow, azimuthally segmented slots equally distributed around the model's perimeter. The model is suspended in the tunnel using eight wires each comprising miniature in-line force sensors and shape-memory-alloy (SMA) strands that are used to control the instantaneous forces and moments on the model and its orientation. The interaction of the actuation jets with the flow over the moving model is investigated using PIV and time-resolved force measurements to assess the transitory aerodynamic loading effected by coupling between the induced motion of the aerodynamic surface and the fluid dynamics that is driven by the actuation. It is shown that these interactions can lead to effective control of the aerodynamic forces and moments, and thereby of the model's motion.   

Experimental Study of Plasma Control of an Unstarting Supersonic Flow

Experimental studies of the control of unstarting supersonic model inlet flows using Dielectric Barrier Discharges (DBD) is demonstrated at Mach 4.7 flow conditions and a static temperature of $\sim $60K and static pressure of $\sim $1kPa. Planar Laser Rayleigh Scattering (PLRS) is used to visualize important flow features, such as boundary layers and shockwaves. Supersonic flow unstart is initiated by injecting mass into model inlet flows of either laminar or tripped turbulent boundary layer flow conditions. DBD discharge actuation of the tripped turbulent flow delays the unstart process, shifting the unstart dynamics closer to what is seen for the laminar boundary layer case. In all studies, a single DBD actuator pair is used, oriented parallel to the freestream flow, generating spanwise disturbances. It is proposed that strong suction flow which brings high momentum freestream flow near exposed electrode can be a mechanism of this actuation. PLRS reveals that this actuation is spatially confined to the regions close to the actuator electrodes, greatly limiting their performance.   

High Mach Number Leading-edge Flow Separation Control using AC DBD Plasma Actuators

Wind tunnel experiments were conducted to quantify the effectiveness of alternating current dielectric barrier discharge flow control actuators to suppress leading-edge stall on a NASA energy efficient transport airfoil at compressible freestream speeds. The objective of this research was to increase lift, reduce drag, and improve the stall characteristics of the supercritical airfoil near stall by flow reattachment at relatively high Mach and Reynolds numbers. In addition, the effect of unsteady (or duty cycle) operation on these aerodynamic quantities was also investigated. The experiments were conducted for a range of Mach numbers between 0.1 and 0.4. corresponding to a Reynolds number range of 560,000 through 2,260,000. Lift, drag, quarter chord moment, and suction side pressures were measured near stall for baseline, steady actuation, and a scan of nondimensional duty cycle frequencies. The results show that the plasma actuators were effective at reattaching the leading-edge separated flow as evidenced by the increase in maximum lift coefficient and stall angle (as much as 2.5 degrees). The experiment also showed that lift was increased the most when the plasma actuator was operated unsteady with a nondimensional frequency of unity.   

Interaction of Finite-span Synthetic-jets with a Cross-flow over a Swept Wing

The formation of secondary flow structures due to the interaction of three finite span synthetic jets with a cross-flow was investigated experimentally over a finite sweptback wing (cross-sectional profile of the NACA 4421) at a Reynolds number of 100,000. Stereoscopic PIV data were collected across the three jets in the wing's mid-span section, where the effect of the jets' location, and their blowing ratio were analyzed based on the three-dimensional flow field using time-averaged and phase-averaged statistics. The arrangement of synthetic jets was investigated through the use of varying actuation combinations in order to fully understand the interaction of the three jets with the cross flow. In the present study, an angle of attack of 13.5deg was chosen for the model, in which the boundary layer was attached in the vicinity of the middle synthetic jet and partially separated in the vicinity of the jet closer to the wing tip. The present work confirmed the previous findings of the presence of secondary tilted flow structures.   

Reduction of vortex shedding intensity from a cylinder using semi-active flow control

Experiments were performed in the open water channel at the Waterpower Laboratory, NTNU, Norway, with the aim of reducing vortex shedding intensity by semi-active flow control. The test rig consisted of a perforated steel tube lined by a rubber bellows. The holes (d/D=0.6) formed a line at the leading edge, one tube diameter apart. Two flow control modes were attainable; (1) lining being flush with the cylinder wall, and (2) pressurized lining creating leading edge bumps. Upstream flow conditions were monitored, and used as input for the control loop governing the pressure of the lining. A flat metal rod, onto which strain gauges were glued, was positioned in the wake. It was assumed that the motion of the rod corresponded to the velocity components normal to the main flow direction. Thus the motion of the rod described the vortex shedding from the tube. Strouhal numbers were found to be approximately 0.3. It was the assumption that the bumps would disrupt vortex formation and reduce the vortex intensity. Tests showed that the assumption was plausible, with observed intensity reductions of 15-30{\%} for Re$_{D} \quad \sim $ [20000 to 50000]. Plots also appear to show a breakdown of organization in the wake when the tube is in activated mode. It was shown that semi-active control of vortex shedding behind a cylinder is achievable.   

Lift and Drag on a NACA0015 Airfoil With Duty Cycle Active Flow Control

Active flow control experiments were carried out over a NACA 0015 airfoil with a trailing edge flap. Two arrays of synthetic jet actuators were mounted in the airfoil with one on near the leading edge (0.1c) and the other on the main wing body near the wing/flap interface (0.65c). Characterization of the SJA's showed they produced their highest exit velocities at a frequency of 1100 Hz, which was near the natural frequency of the piezo membranes. When actuated at frequencies corresponding to the flow natural frequencies (10-100Hz) the jets produced no jet velocity. In order to control the flow using a frequency near the flow's natural shedding frequency the synthetic jets were actuated using a forcing frequency near the piezo natural frequency with a duty cycle frequency of 10-1000Hz. Force balance results showed that for a 0\r{ } flap deflection the active flow control delayed stall and lowered drag regardless of the duty cycle frequency. At flap deflections of 20\r{ } and 40\r{ } differences were observed between the continuously forced and duty cycles cases. For these cases continuous forcing increased the stall angle and reduced drag. Duty cycle forcing also delayed stall however it significantly increased drag near the stall AOA even compared to the no forcing case.   

Manipulating forces by interactive separation and circulation control

Steady, unsteady and intermittent suction and blowing from localized or distributed slots are used to reveal the physical mechanisms and their interaction in order to manipulate (enhance or reduce) the forces on various aerodynamic bodies and surfaces. Performance under ideal inviscid conditions is used as a standard of performance to compare the outcomes to. While high-lift airfoils were part of the focus, flow over humps which lead to large separation zones was also investigated. Surface pressure measurements, wake surveys and surface visualization were utilized over a wide range of operating conditions in the NDF at IIT. Velocities ranged from $20$ to $110$ m/s ($0.06 < M < 0.31$), corresponding to chord Reynolds numbers from $500,000$ to $3,700,000$, and included a full range of airfoil angles of attack with flap deflections from $10$ to $55$ degrees and various leading edge configurations. Steady suction control was more effective at eliminating the large separation bubble created by the model, requiring a pressure ratio between the applied force and inviscid force of approximately unity, whereas blowing required a two to one ratio. Pulsed suction was superior and enhanced by the operating frequency or duty cycle. Separation control (SC) was modified by the presence of circulation control (CC). Steady-blowing SC near the leading edge reduced the effect of blown-flap CC, whereas steady-suction SC increased the performance gain.   

Improvement for efficiency of frictional drag reduction by repetitive bubble injection

Repetitive bubble injection was examined for promoting frictional drag reduction by bubbles based on idea of ``resource allocation'' and voidage waves formed in a horizontal bubbly channel. Gain factor, which is defined as the ratio of degree of the drag reduction by the mean void fraction of bubbles, $\alpha$, showed dramatic improvement on the efficiency of the drag reduction in comparison with continuous bubble injection at the same $\alpha$. This improvement is prominent at small void fractions at which the continuous bubble injections enhance the frictional drag. Simultaneous recording of advecting bubbles with measurements of shear stress profiles at the channel wall indicated that preceding large bubbles provide great drag reduction and following small, low concentration bubbles don't affect the frictional drag. Namely the bubbles as a limited resource are efficiently used for the drag reduction in the repetitive bubble injection.   

Transitory Aerodynamic Control of Unsteady Separation

The dynamics of the controlled three-dimensional attachment of transitory stall over an airfoil oscillating in pitch is investigated in wind tunnel experiments using a partial spanwise array of surface-integrated pulsed jet actuators. The actuation has a characteristic time scale that is an order of magnitude shorter than the convective time scale of the base flow. It is shown that the control authority of the single pulse is highly-dependent on the oscillation cycle phase due to the timed interactions between the actuation jets and the evolution of the dynamic stall vortex on the suction surface. The transitory effects of the actuation can be extended and exploited for significant suppression of the dynamic stall by using successive pulsed actuation strategically staged during the cycle. High-resolution phase-locked PIV measurements in the cross stream plane on the suction surface and in the near wake demonstrate that the pulsed actuation sequence can effectively regulate the accumulation (trapping) and shedding of vorticity. The time-modulation of the vorticity fluxes results in significant temporal changes in circulation, and consequently in the measured time-dependent aerodynamic forces and moments.   

Experimental Study of the Temporal Nature of an Actively Controlled Three Dimensional Turret Wake

Experimental measurements have been performed to characterize the actively controlled wake of a three-dimensional, non- conformal turret which is a bluff body commonly used for housing optical systems on airborne platforms. As a bluff body, turrets can generate strong turbulent flow fields that degrade the performance of the optical systems and the aircraft. Experiments were performed in a low-speed wind tunnel at Syracuse University using particle image velocimetry and dynamic pressure measurements with the objective of developing a better understanding of the spatial and temporal nature of the wake flow field. Active control was achieved using dynamic suction in the vicinity of the turret aperture and was found to have a significant impact on the structure of the wake as well as the temporal characteristics of the flow field. With a better understanding of the wake characteristics, closed-loop, active flow control systems will be developed to help reduce fluctuating loading and aero- optical distortions associated with the turbulent flow field.   

Session L10: General Fluid Dynamics I

The origin of the self-organization of the 2D Euler fluid flows

The 2D ideal incompressible fluid is usually described in terms of streamfunction, velocity and vorticity. An equivalent model consists of a discrete set of point-like vortices interacting in plane by a long-range potential. The essential property of the latter model is that it re-formulates the description in terms of matter, field and interaction. We first extend the model to reflect the parity-invariance and show that returning to continuum it leads to a field-theoretical formulation, with a Lagrangian density for a nonlinear scalar (matter) field, a gauge field and their minimal interaction. A fundamental property of the 2D Euler fluid is revealed in this way: the extremum of the action functional shows Self-Duality, a property known to generate coherent structures (almost all known solitons and instantons in the natural systems). We derive analytically the sinh-Poisson equation, governing the stationary states at relaxation.The presence of the Chern- Simons part in the Lagrangian explains why in 3D the fluid will never relax to a stationary coherent flow. Connections with 4D fermion systems (Nambu-Jona-Lasinio) and with surfaces of constant mean curvature (CMC) will be presented. Stability of certain regular flows results from the property of non-self- intersection of CMC surfaces embedded in 3D space.   

On Liouville's theorem in fluid mechanics

Since the early work of Burgers it has been known that discretizations of fluid models possess a version of Liouville's theorem on conservation of phase space volume. In fact, spectral representations of two-dimensional turbulence are known to have a detailed version of this theorem. The existence of such Liouville theorems led many (e.g.\ Burgers, Lee, Kraichnan and Montgomery) to consider various statistical mechanical approaches to turbulence. We show how this theorem arises naturally from the Hamiltonian structure of inviscid fluid equations.   

A ``reciprocal'' theorem for the prediction of loads on a body moving in an inhomogeneous flow at arbitrary Reynolds number

We derive a theorem paralleling Lorentz's reciprocal theorem and providing general expressions for the force and torque acting on a rigid body of arbitrary shape moving in an inhomogeneous incompressible flow at arbitrary Reynolds number. This theorem follows the approach initiated by Quartapelle and Napolitano (1983) by making use of auxiliary solenoidal irrotational velocity fields. It allows any component of the force and torque to be evaluated solely in terms of velocity and vorticity, irrespective of its orientation with respect to the relative velocity between the body and fluid. When the body moves in a time-dependent linear flow, this theorem reveals the various couplings between the body translation and rotation and the strain rate and vorticity of the carrying flow. We show that the predictions obtained with this approach encompass all those previously obtained in the inviscid limit. We also show how it can be used to evaluate explicitly the drag and lift components of the force acting on high-Reynolds-number bubbles moving in inhomogeneous flows.   

Spatiotemporal cascades of the Poiseuille-Hagen flow in invariant elliptic structures

Spatiotemporal cascades of the transitional Poiseuille-Hagen flow are considered in elliptic structures, which are invariant with respect to differential and nonlinear algebraic operations. Differentiation and algebra of the invariant structures and decomposition of smooth velocity profiles in the invariant structures are treated both theoretically and symbolically. Reduction of the invariant elliptic structures to invariant trigonometric structures and invariant hyperbolic structures is also considered. By using the invariant structures, the displayed and hidden perturbations of the basic Poiseuille-Hagen flow are represented as dual perturbations, while the series solution for the perturbed flow converges uniformly. The cascade solution for the Poiseuille-Hagen flow is constructed in a multiscale form, which explicitly shows the effect of various factors at multiple scales.   

An Exact Solution of the 3D Navier-Stokes Equation

We use a time evolution equation for the single particle distribution function (Muriel, Physica D, 1997) to generate the time evolution of the velocity fields. These velocity fields are then substituted into the Navier-Stokes equation to calculate the pressure gradients. The pressure gradients are then integrated over space to generate pressure tensors. In addition, we calculate the energy fields, showing that there is no blow up. The pressure tensors, and the velocity fields constitute an exact solution to the 3D Navier-Stokes equation for a compressible fluid (Muriel, Results in Physics, 2011). All calculated fields are smooth, producing no turbulence by any generous definition of turbulence. We raise the question: is the Navier-Stokes equation the correct problem definition for turbulence? (Muriel, The Quantum Nature of Turbulence, Nova Science Publishers, New York (2010). We will display the plots of the solution in a 3D toroid configuration. The solution found may be used to reformulate fluid dynamics using an initial value formulation.   

Adaptive Control of the Forced Generalized Korteweg-de Vries-Burgers Equation

The adaptive control problem of the forced generalized Korteweg-de Vries-Burgers (GKdVB) equation when the spatial domain is $[0,1]$ is considered. Three different adaptive control laws are designed for the forced GKdVB equation. The $L^2$-global exponential stability of the solutions of these equations is shown for each of the proposed control laws by using the Lyapunov theory. Numerical simulations based on the Finite Element method (FEM) are presented to validate the analytical developments.   

Phase space dynamical density functional theory for colloids with hydrodynamic interactions

We study the dynamics of a colloidal fluid in the full position- momentum phase space. These dynamics are modelled by stochastic equations of motion for a large number of identical spherical particles. We include the full hydrodynamic interactions, which strongly influence the non-equilibrium properties of the system. For large systems, the number of degrees of freedom prohibits a direct solution of the equations and a reduced model is necessary. Under certain assumptions, we derive a dynamical density functional theory (DDFT), i.e. a reduction to the dynamics of the reduced one-body distribution. Our formulation includes the case where the momentum distribution is not a local Maxwellian. Near equilibrium, it reduces to a Navier-Stokes-like equation with additional non-local terms. In the high friction limit, we show rigorously that it reduces to a previously-derived DDFT, describing only the position distribution, but with a novel definition of the diffusion tensor.   

Attitudes Towards Fluids: the Impact of Flow Visualization

Since 2003, a course on flow visualization has been offered to mixed teams of engineering and fine arts photography students at the University of Colorado. A survey instrument has been developed that explores student perceptions of and attitude towards fluid physics. It has been administered to students in the flow visualization course, in a traditional junior level fluid mechanics course, and in a course on design. Survey results indicate that the students in the flow visualization course, after a semester of making images for art's sake, emerge believing that fluid mechanics is more important to themselves as engineers and to society than the students in the traditional course which is packed with real-life engineering examples . The use of photography in improving student perceptions is being extended to a course on perception of design; preliminary results from a survey on attitudes towards design will be presented. Examples of student images from both courses will be presented as well.   

Applying the results of education research to help students learn more

Over the past 5 years, the physics faculty at the University of Colorado have worked to transform three core courses in our upper-division undergraduate physics curriculum: Classical Mechanics/Math Methods, Electricity and Magnetism and Quantum Mechanics. We discuss our transformations as a potential model for transformation of other upper-division courses, such as fluid mechanics. The goal of our transformations was to improve student learning and to develop materials and approaches that other faculty could adopt or adapt. This work began with faculty in the department meeting regularly to define explicit course learning goals, which then served as a foundation for the subsequent course transformations. The development of the curriculum was also guided by the results of observations, interviews, and analysis of student work. We applied the principles of active engagement and learning theory to transform many elements of the course. Reforms included ``clicker'' questions, tutorials, modified homeworks, and more. In this talk, we will outline the process, the reforms, and present evidence of the effectiveness of these reforms relative to traditional courses. Some research-based fluid mechanics instructional materials will also be discussed. Our curriculum materials are available at http://www.colorado.edu/sei/departments/physics.htm.   

Session L11: Turbulence Theory III

Effects of Outer Scales on Near-Wall Reynolds Stresses and Higher-Order Statistics

The classical view of wall-bounded turbulence suggests that the near-wall region should be scaled with characteristic scales that are closely related to that region. For the last decade, however, alternative concepts considering the influence of outer scales were proposed. Herein, we show that the near-wall Reynolds stresses as well as higher-order statistics in different geometries (e.g., zero-pressure-gradient boundary layers, and pipe and channel flows) collapse in single Reynolds-number-independent curve when scaled with an alternative mixed scaling based on $\bf{u_{\tau}^{3/2}u_{e}^{1/2}}$.   

Relevant length scales and time scales in shear flow turbulence

Shear flow turbulence has been the subject of fundamental research due to its ubiquitous presence in engineering and natural flows. In this study, we take a fresh approach using dimensional arguments tempered by physical reasoning to gain further insights on their phenomenology. Beginning with the four basic quantities: turbulent kinetic energy $k$, dissipation rate $\epsilon$, kinematic viscosity $\nu$ and mean shear $S$, we construct six length scales and two time scales that are most relevant to this classical problem and discuss their implications on phenomenology. Analysis of the variation of all six length scales and two timescales using high-resolution DNS data of turbulent channel flow and homogeneous shear flow are used to highlight important transitions in the flow dynamics and provide a framework to explain the energy cascade process.   

On the smallest sub-kolmogorov mean length scale and its implications on phenomenology

The smallest scale in turbulence has been predicted to be less than the Kolmogorov scale $\eta$ by a factor of Re$^{1/4}$ and attributed to the intermittency of the turbulent kinetic energy dissipation rate $\varepsilon$. We show through dimensional arguments that this smallest limit corresponds to a new mean length scale based on turbulent kinetic energy $k$ and kinematic viscosity $\nu$, given by ($\nu^{2}$/$k)^{1/2}$. The independence of this scale with $\varepsilon$ raises the issue of physical dependence of length scales and challenges classical phenomenology. Thus the notion that the smallest scales are set by the intermittent fluctuations of dissipation rate may be physically in-accurate. Given that $\varepsilon$ is also set independently by the large scale and the turbulent kinetic energy, the physical consequence is that the dissipative portion of energy cascade is constrained between $\eta$ and ($\nu ^{2}$/$k)^{1/2}$. Another important implication stems from the fact that ($\nu ^{2}$/$k)^{1/2}$ is a mean length scale. This alludes to the existence of even smaller scales of motion in the instantaneous field that are governed by the fluctuations in turbulent kinetic energy.   

Length scales in anisotropic turbulence

In isotropic turbulence, a single scalar function fully describes the velocity correlation tensor. The characteristic scales of this correlation function, the Taylor scale and the integral scale, then have an unambiguous interpretation. The integral scale, for example, is a measure of the most energetic scale of turbulence. Anisotropic turbulence is more complicated. We examined theoretically and experimentally the relationships between correlation functions measured in two directions in anisotropic turbulence. We found that the ratio of characteristic scales measured in the different directions was a function of the ratio of fluctuating velocities in the two directions. In the case of the integral scale, the inertial range scaling law controls the relationship. In other words, not only is the integral scale a measure of the large scale, but it is also connected to inertial range dynamics.   

Stirring turbulence with turbulence

We stir wind--tunnel turbulence with an active grid that consists of rods with attached vanes. The time--varying angle of these rods is controlled by random numbers. We study the response of turbulence on the statistical properties of these random numbers. The random numbers are generated by the Gledzer--Ohkitani--Yamada shell model, which is a simple dynamical model of turbulence that produces a velocity field displaying inertial--range scaling behavior. The range of scales can be adjusted by selection of shells. We find that the largest energy input and the smallest anisotropy are reached when the time scale of the random numbers matches that of the large eddies in the wind--tunnel turbulence. A large mismatch of these times creates a flow with interesting statistics, but it is not turbulence.   

PIV study of turbulence generated by fractal grids in a water tunnel

An experimental study of turbulence generated by low-blockage space-filling fractal square grids was performed using 2D Particle Image Velocimetry (PIV) in a water tunnel. In addition to the experimental technique (PIV) and the fact that it was carried out in water, this study has also the particularity of having considerable incoming free stream turbulence with an intensity, in the streamwise (u'/U) and spanwise (v'/U)~ directions, of 2.8 and 4.4 {\%} respectively. Results on turbulence intensity and Taylor microscale of the flow generated by our fractal grids are in good agreement with the previous wind tunnel study of Mazellier and Vassilicos [``Turbulence without the Richardson-Kolmogorov cascade,'' \textit{Phys. Fluids} \textbf{22}, 075101 (2010)] provided that a different normalization scale is used which takes into account the free stream turbulence characteristics. This normalisation scale is a good estimator of the turbulence peak downstream of not only fractal but also regular grids. Finally, local isotropy of fractal generated turbulence was checked based on the gradients estimated from the 2D velocity field and compared with the ones from regular grids.   

Extraction of nonequilibrium -7/3 energy spectrum in experimental measurement turbulence data

A perturbation expansion for the energy spectrum about a base Kolmogorov $k^{-\frac{5}{3}}$ steady state yields an additional $-7/3$ power component which is induced by the fluctuation of the dissipation rate $\varepsilon$ and represents a nonequilibrium state. DNS study revealed actual existence of $- 7/3$ spectrum in homogeneous shear flow at $Re_\lambda \approx 150$ (\textit{Phys. Fluids} \textbf{23}, 035107 (2011)). In this study, an attempt is made to extract the same spectrum in the data measured using the hot wire anemometer in the experiment of the driving mixing layer, in which nearly constant mean shear is established ($Re_\lambda \approx 468$, Y. Tsuji (2008)). The time series data are converted to the spatially evolving data employing the Taylor's hypothesis and $\varepsilon$ is obtained. To be in accordance with the statistical theory, the variations of $\varepsilon$ in the time scale comparable to the integral length scale are considered. Nonequilibrium component is extracted applying a conditional sampling on $d \varepsilon/dt$, and it is shown that the deviation from the base $-5/3$ spectrum fits the $-7/3$ power slope. The temporal development of the spectrum is divided into two regimes, Phases 1 and 2. Large energy contained in the low- wavenumber range in Phase 1 is cascaded to the small scales in Phase 2. This energy transfer is accomplished by the reversal in the sign of -7/3 power component. These results agree well with the DNS.   

Concentration dependence of the effects of polymer additives on bulk turbulence

We present an experimental study of the polymer concentration dependence of the effects of minute long chain polymer additives on bulk turbulent flow. It is found that the measured Eulerian structure function of the velocity field is strongly modified by the presence of the polymer additives. And there exists a critical concentration below which only small scales are modified while above which both small scales and large scales are modified. We found that the critical concentration depends on the energy dissipation rate of the flow, this dependence can be explained by de Gennes' elastic theory on turbulence of dilute polymeric solution.   

What correlations between velocity differences and velocity sums tell us about small scale universality

An ongoing question about turbulent flows is the degree to which the small scales are universal because they become independent of the details of the forcing at large scales. Recent work has explored these issues by measuring correlations between velocity differences over a distance r (whose variance is dominated by scales near r) and velocity sums over the same distance (whose variance is dominated by the large scales). Some correlations between velocity differences and sums are required by the Navier-Stokes equations (Hosokawa, Prog. Theor. Phys. Lett., 118:169, 2007.) This talk will look at experimental measurements of correlations between velocity differences and velocity sums from several flows. The correlations which are required by Navier-Stokes dynamics do not appear to violate the assumption of independence between the large and small scales. However, there are other correlations in the experimental data which can only be explained by dependence of the small scales on the details of the forcing of the flows. The variance of the velocity differences shows a strong conditional dependence on the velocity sum that is different in different flows. The anisotropy of the velocity differences also shows conditional dependence on the velocity sum.   

POD models for turbulent convection in rectangular cells

Two low-dimensional models (LDM) for turbulent convection in rectangular cells, based on the Galerkin projection of the Boussinesq equations onto a finite set of empirical eigenfunctions, are presented. The empirical eigenfunctions are obtained from a Proper Orthogonal Decomposition (POD) of the fields using the Snapshot Method. The first case is a three-dimensional cell in which a classical turbulent Rayleigh-B\'{e}nard flow evolves. The second case is based on two-dimensional DNS data of mixed convection in a cell with heated obstacles as well as in- and outlets of air. In both cases, a quadratic inhomogeneous coupled ODE system is obtained for the evolution of the modal amplitudes. The truncation to a finite number (a few hundred) of degrees of freedom, requires the additional implementation of an eddy viscosity-diffusivity to capture the missing dissipation of the small-scale modes. The magnitude of this additional dissipation mechanism is determined by requiring statistical stationarity and a total dissipation that corresponds with the original DNS data. We introduce a mode-dependent eddy viscosity-diffusivity, which turns out to reproduce the large-scale properties of the turbulent convection qualitatively well.   

Session L12: Turbulence: Mixing II

The Eddy-Diffusivity in Turbulent Two-Particle Dispersion

R. H. Kraichnan (1966) and T. S. Lundgren (1981) derived a formula for the eddy-diffusivity in Richardson's theory of turbulent 2-particle dispersion: $$\eta _{ij}({\bf r}, t)=\int ^{t}_{0} ds \langle(u_{i} ({\bf x} + {\bf r}, t) - u_{i} ({\bf x}, t)) (u_{i}({\bf x} + {\bf r}, t\vert s) - u_{j}({\bf x}, t \vert s)\rangle. $$ This formula involves the Lagrangian velocity field ${\bf u}({\bf x}, t \vert s)$ experienced at time $s < t$ by the fluid particle which is at point ${\bf x}$ at time t. Evaluating this formula requires tracking fluid particles backward in time, a difficult task with standard DNS. We compute the formula using the JHU Turbulence Database,\footnote{http://turbulence.pha.jhu.edu/} which stores the entire spacetime history of a 1024$^{3}$ DNS of homogeneous, isotropic turbulence at $Re_{\lambda }=433$. We average over particle pairs started at many different initial positions ${\bf x}$ with initial separations ${\bf r}$. We obtain a time-dependent eddy-diffusivity $\eta_{ij}({\bf r}, t)$ which has Batchelor scaling $(\varepsilon r)^{2/3}t$ for short time and Richardson scaling $\varepsilon^{1/3 }r^{4/3}$ for long time. Our resulting diffusion model describes both the Batchelor and Richardson regimes and also predicts new phenomena not yet seen in experiment or simulations.   

Passive Scalar in 2D Turbulence

We examined the behavior of a passive scalar in a 2D turbulent flow and confirm the so-called Batchelor scaling. For large r, the second order structure function S$_2$($r$) = $<(\theta(x+r) - \theta(x))^2>$ $\sim$ log($r$). For small r, S$_2$($r$) $\sim$ $r^2$. The logarithmic dependence of S$_2$($r$) is consistent with a power spectrum that goes as the inverse power of $k$, the wavenumber. These experiments are performed using a falling soap film as the 2D turbulent system and various colored dyes for the passive scalar, which is injected at a point. The decaying turbulence is generated using a comb oriented perpendicular to the film. It does not appear to matter whether the dye is injected above or below the comb. The measurements were made in the Eulerian frame at a single point. Time is then replaced by distance using the Taylor frozen turbulence hypothesis. The structure function is determined from the correlation function, which is calculated using a photon correlation scheme. The passive scalar measurements are compared with the behavior of thickness fluctuations in the soap film, which is another random variable.   

Encounter rates of Lagrangian particles in homogeneous isotropic turbulence

Contact rates of Lagrangian particles are investigated numerically by direct simulation of homogeneous isotropic turbulence. The flow Reynolds number, the number of particles, and the contact radius are systematically changed, and the effects on the contact rates are discussed. In the talk, results based on a kinematic simulation of turbulence by unsteady random Fourier modes will be also presented.   

Bounded Stochastic Shell Mixing Model: Further Development and Application to Inhomogeneous Scalar Mixing

\parindent 0pt Xia and Collins [\emph{Physics of Fluids} {\bf 23} (6):065107, 2011] developed the Bounded Stochastic Shell Mixing (BSSM) model that takes into account the multi-scale nature of the turbulent mixing process. They successfully applied the model to mixing of isotropic scalars with an initial double-delta probability density function (PDF). To enforce the scalar bounds, they introduced a novel ``zeroth mode'' that precisely cancels the inherently non-conservative random terms in the formulation. The extension of the model to the mixing of inhomogeneous scalar fields uses notional particles that move with a fluctuating velocity that is chosen to conform with the underlying turbulent energy spectrum. A consistency condition further requires the particle motion in the direction of the mean scalar gradient be carefully connected to the generation of the scalar fluctuation. The appropriate constraint has been derived and is enforced by the numerical algorithm. This new formulation has been applied to turbulent mixing of a scalar slab of specified thickness. (In the limit of zero thickness, this reduces to the classical ``line source'' problem.) We analyze multiple scalars so that differential diffusion can be considered as well as the effect of the thickness of the slab (relative to the turbulence length scales). The predictions of the BSSM model compare well with direct numerical simulations.   

Variations in scalar transport characteristics between forwards and backwards turbulent dispersion

Recent studies about backwards dispersion in time have shown differences with forwards turbulent dispersion, and have highlighted the importance of understanding these differences for practical applications. This work used a direct numerical simulation combined with a Lagrangian scalar tracking approach to obtain single particle and relative dispersion statistics for both forwards and backwards dispersion in an infinitely long turbulent channel flow. The computational domain was 4$\pi $h $\times $ 2h $\times $ 2$\pi $h in x, y, z (where h is the half channel height and h = 300 and h = 150). Results showed differences in the rates of forwards and backwards relative scalar dispersion. The variation in the rates of relative scalar dispersion for a variety of Prandtl numbers (Pr) from 0.1 to 50 was also investigated. The primary direction of heat transport was found to be oriented almost close to the direction perpendicular to the channel walls, for all regions of the channel and for Pr up to 1000. Higher and enduring rates of heat transport were observed for the case of backwards turbulent dispersion. In analogy with the physics of optics, a quantity named the ``turbulent dispersive ratio'' was introduced to indicate the differences between backwards and forwards dispersion.   

Passive Scalar Mixing in Compressible Isotropic Turbulence

Turbulent mixing of a passive scalar is studied through use of implicit large-eddy simulation (ILES) in the context of forced compressible, isotropic turbulence with a mean scalar gradient. The under-resolved prediction of mixing by an under-resolved turbulent velocity field is the problem that the ILES framework addresses without using any explicit model. Low wavenumber forcing is done separately for the solenoidal and dilatational components of the velocity in order for the flow field to achieve a statistically stationary state. The efficiency of ILES allows for the creation of large time-volume ensembles at relatively low computational cost. Effects of Mach number, grid resolution, and the forcing ratio of solenoidal to dilatational kinetic energy on the flow and subsequent scalar mixing will be presented.   

Stochastic transport models for mixing in variable-density turbulence

In variable-density (VD) turbulent mixing, where very-different- density materials coexist, the density fluctuations can be an order of magnitude larger than their mean. Density fluctuations are non-negligible in the inertia terms of the Navier-Stokes equation which has both quadratic and cubic nonlinearities. Very different mixing rates of different materials give rise to large differential accelerations and some fundamentally new physics that is not seen in constant-density turbulence. In VD flows material mixing is active in a sense far stronger than that applied in the Boussinesq approximation of buoyantly-driven flows: the mass fraction fluctuations are coupled to each other and to the fluid momentum. Statistical modeling of VD mixing requires accounting for basic constraints that are not important in the small-density-fluctuation passive-scalar-mixing approximation: the unit-sum of mass fractions, bounded sample space, and the highly skewed nature of the probability densities become essential. We derive a transport equation for the joint probability of mass fractions, equivalent to a system of stochastic differential equations, that is consistent with VD mixing in multi-component turbulence and consistently reduces to passive scalar mixing in constant-density flows.   

Consistency and realizability requirements for stochastic diffusion models for variable-density turbulent mixing

Rational turbulence model development has applied principles that ensure consistency with the physical conservation laws and statistical constraints. Examples are the principles of invariance and realizability (Lumley, Adv.\ Appl.\ Mech., 18, 1979, pp.\ 123--176), and linearity and independence of passive scalars in mixing (Pope, Phys.\ Fluids, 26, 1983, pp.\ 404--408). Models that violate these principles can produce unphysical results. We discuss modeling principles and constraints for variable-density multi-material turbulent mixing. We develop the consequences of the mass conservation law for multi-component mixtures for random-walk methods in variable- density turbulence. In such flows the density fluctuations can be larger than the mean density and several important constraints restrict the functional forms of mixing models. One consequence of the constraints developed is that the coefficient of the Wiener process (if nonzero) must be nonlinear and coupled to the other mass fractions to ensure consistency with mass conservation. Typical Langevin-type models for these processes violate these constraints peculiar to variable-density mixing.   

Modeling the subfilter scalar variance for large eddy simulation in forced isotropic turbulence

Static and dynamic model for the subfilter scalar variance in homogeneous isotropic turbulence are investigated using direct numerical simulations (DNS) of a lineary forced passive scalar field. First, we introduce a new scalar forcing technique conditioned only on the scalar field which allows the fluctuating scalar field to reach a statistically stationary state. Statistical properties, including 2nd and 3rd statistical moments, spectra, and probability density functions of the scalar field have been analyzed. Using this technique, we performed constant density and variable density DNS of scalar mixing in isotropic turbulence. The results are used in an a-priori study of scalar variance models. Emphasis is placed on further studying the dynamic model introduced by G. Balarac, H. Pitsch and V. Raman [ Phys. Fluids 20, (2008) ]. Scalar variance models based on Bedford and Yeo's expansion are accurate for small filter width but errors arise in the inertial subrange. Results suggest that a constant coefficient computed from an assumed Kolmogorov spectrum is often sufficient to predict the subfilter scalar variance.   

Effect of initial conditions on mixing within a turbulent channel flow

We analyze the mixing of a passive scalar (temperature) in a turbulent channel flow for different initial conditions by means of numerical simulations. The numerical domain is a channel delimited by two parallel and infinite flat walls, simulated using periodic boundary conditions in the streamwise and spanwise directions. We consider three initial distributions of temperature, where hot and cold fluids are separated by a sharp but continuous interface that subdivides the computational domain into two identical halves. The interface is taken parallel to the walls or perpendicular to them, oriented in the streamwise or spanwise directions. We perform a direct numerical simulation of the temperature field at $Re_{\tau} = 190$ when the flow is fully turbulent. The numerical scheme combines an advection diffusion solver, i.e, a third-order flux integral method based on UTOPIA (Leonard \emph{et al.}, Appl. Math. Modeling, 1995), with a Navier-Stokes solver, i.e, spectral code released by Prof. John Gibson, http://www.channelflow.org). We quantify the time-evolution of the mixing performance of the turbulent flow using different measures of the mixing, including a negative Sobolev norm -- a diagnostic currently used to asses the mixing performance of laminar flows. Finally, we discuss the influence of the initial conditions on the turbulent mixing. Funding was provided by NSERC (grants RGPIN217169 and RGPIN217184).   

Session L13: Multiphase Flow V: Numerical II

A second order Lagrangian Eulerian momentum bounded method for multiphase flows

A Lagrangian Eulerian framework relying on both Level Set and Volume of Fluid methods is presented in the context of multiphase flow computations. The resulting interface capturing scheme is shown to preserve planarity, and to conserve mass exactly for solenoidal and linear velocity fields. A novel fractional step approach for the incompressible Navier Stokes equation is also presented. The proposed scheme relies on a consistent transport of volume fraction and momentum fields, which also preserves velocity boundedness. A sharp interface projection step is derived accordingly. The algorithm is shown to conserve momentum exactly for solenoidal linear velocity, and to lead to robust computations.   

A GPU-accelerated flow solver for incompressible two-phase fluid flows

We present a numerical solver for incompressible, immiscible, two-phase fluid flows that is accelerated by using Graphics Processing Units (GPUs). The Navier-Stokes equations are solved by the projection method, which involves solving a pressure Poisson problem at each time step. A second-order discretization of the Poisson problem leads to a sparse matrix with five and seven diagonals for two- and three-dimensional simulations, respectively. Running a serial linear algebra solver on a single CPU can take 50-99.9\% of the total simulation time to solve the above system for pressure. To remove this bottleneck, we utilized the large parallelization capabilities of GPUs; we developed a linear algebra solver based on the conjugate gradient iterative method (CGIM) by using CUDA 4.0 libraries and compared its performance with CUSP, an open-source, GPU library for linear algebra. Compared to running the CGIM solver on a single CPU core, for a 2D case, our GPU solver yields speedups of up to 88x in solver time and 81x overall time on a single GPU card. In 3D cases, the speedups are up to 81x (solver) and 15x (overall). Speedup is faster at higher grid resolutions and our GPU solver outperforms CUSP. Current work examines the acceleration versus a parallel CGIM CPU solver.   

The Lagrangian filtered mass density function (LFMDF) or LES/PDF method for turbulent two-phase flows

In this talk, a new formalism for the filtered density function (FDF) approach is developed for the treatment of turbulent polydispersed two-phase flows in LES simulations. Contrary to the FDF used for turbulent reactive single-phase flows, the present formalism is based on Lagrangian quantities and, in particular, on the Lagrangian filtered mass density function (LFMDF) as the central concept. This framework allows modeling and simulation of particle flows for LES to be set in a rigorous context and various links with other approaches to be made. In particular, the relation between LES for particle simulations of single-phase flows and Smoothed Particle Hydrodynamics (SPH) is put forward. Then, the discussion and derivation of possible subgrid stochastic models used for Lagrangian models in two-phase flows can set in a clear probabilistic equivalence with the corresponding LFMDF. Finally, a first stochastic model will be proposed in this framework and numerical simulations will show the comparison of LES simulations against DNS.   

An extended quadrature method of moments for polydisperse multiphase flows

Polydisperse multiphase flows arise in many applications, and thus there has been considerable interest in the development of numerical methods to find solutions to the kinetic equation used to model such flows. Quadrature-based moment methods (QBMM) are an important class of methods for which the accuracy of solution can be improved in a controlled manner by increasing the number of nodes. However, when large numbers of nodes are required to achieve the desired accuracy, the moment-inversion problem can become ill-conditioned. In this work, a new generation of quadrature algorithms is introduced that uses an explicit form for the distribution function. This extended quadrature method of moments (EQMOM) approximates the distribution function by a sum of classical weight functions, which allow unclosed source terms to be computed with great accuracy by increasing the number of quadrature nodes independent of the number of transported moments. Here we use EQMOM to solve a kinetic equation with evaporation, aggregation and breakage terms and compare the results with analytical solutions.   

Realizable High-Order Finite-Volume Schemes for Diffusion in Quadrature-Based Moment Methods

Population balance equations (PBEs) can be reformulated in terms of the moments of the distribution function and a quadrature-based moment method (QBMM) can be used to solve them. The success of the QBMM is based on a moment-inversion algorithm that does not work if the moments are non-realizable. For convection terms, the authors have shown that when using a finite-volume approach, a moment-based cellwise reconstruction may lead to non-realizable schemes and hence a reconstruction based on weights and abscissas should be used instead. However, researchers working with diffusive PBEs have not reported realizability problems when using cellwise moment-based reconstruction. This work shows that when moment-based reconstruction with a $2^{nd}$-order finite-volume scheme is used, realizability is automatically guaranteed by the satisfaction of Courant-Friedrichs-Lewy (CFL) condition. However, for any high-order finite-volume schemes, a moment-based reconstruction may fail to guarantee realizability. We present high-order realizable schemes based on reconstruction of weights and abscissas. These new schemes give a better performance for a certain class of diffusive PBE problems. Realizability conditions are also presented for a general unstructured mesh.   

DNS of droplet-laden incompressible turbulence: surface tension in a VoF method

We investigated the continuous surface force (CSF) model to include the surface tension within a split-advection and mass-conserving volume of fluid (VoF) method for DNS of droplet-laden incompressible turbulence. The liquid-gas interface curvature is computed accurately using a variable-stencil height-function technique. Different implementations of the surface tension and pressure gradient terms within a projection method were tested, and their stability evaluated in terms of the magnitude of spurious currents for a droplet at rest in both two and three dimensions. The inherent asymmetry of the split-advection algorithm is reflected in the results of this test case. Our results show that a machine-accurate balance between pressure and surface tension forces can be achieved by enforcing symmetry of the VoF function. We have modified the sequence of the advection sweeps, and our results show that, in the case of non-zero Weber number, e.g.~when a mean droplet velocity is present, the algorithm is accurate and stable. We present DNS results of fully-resolved droplet-laden incompressible isotropic turbulence.   

A Multiscale Approach to Compute Mass Transfer in Bubbly Flows

Mass transfer in the liquid phase of gas-liquid multiphase flows usually takes place at a considerably slower rate than the transfer of momentum, so mass flux boundary layers are much thinner than momentum boundary layers. In Direct Numerical Simulations (DNS) the resolution requirement for flows where the Schmidt number (kinematic viscosity divided by mass diffusivity) is high are therefore significantly higher than for flow without mass transfer. While it is, in principle, possible to capture the mass transfer using adaptive grid refinement, the structure of the boundary layer is relatively simple and well understood. Here we develop a multi- scale approach to compute the mass transfer from buoyant bubbles, using a boundary-layer approximation next to the bubble and a relatively coarse grid for the rest of the flow. We show that the approach works well by comparing the results both with fully resolved simulations for modest Schmidt number and with empirical correlations for high Schmidt numbers.   

An improved connectivity-free point set method to simulate multiphase flow

An improved connectivity-free point set method is presented to simulate the multiphase flow. Similar to the front tracking method, the point-set method tracks the interface explicitly. However, it does not require any logical connectivity among interface markers, which provides the flexibility in modeling large morphological changes such as bubble merging and breaking up. The topology changes are handled automatically by proper interface reconstruction scheme and also conveniently ease the small interface undulation due to advection. A meshfree RKPM interpolation method is employed to improved the algorithm which can handle non-uniform meshes and provide boundary corrections for free surface flows in situations when interface markers end at walls. Great accuracy is achieved for both the unit normal and curvature calculation. The incompressible two-phase flow is simulated using stabilized finite element method. Several test cases are performed to validate the improved method and show its capability in simulating multiphase type of flows successfully.   

Session L14: Experimental Techniques III

An optimal arrangement of a three or four hot-wire sensor array to simultaneously measure velocity component statistics in turbulent wall flows

A highly resolved turbulent channel flow DNS with $Re_\tau =200$ has been used to investigate the ability of probes made up of arrays of three or four hot-wire sensors to simultaneously and accurately measure statistics of all three velocity components in turbulent wall flows. Such arrays have also been combined in probes to measure, in addition, velocity gradient based statistics. Various virtual sensor arrangements have been tested in order to study the effects of position, number of sensors and spatial resolution on the measurements. First, the effective cooling velocity was determined for each sensor of an idealized probe, where the influence of the velocity component tangential to the sensors and flow blockage by the presence of the probe are neglected. Then, simulating the response of the virtual probes to obtain the effective velocities cooling the sensors, velocity component statistics have been calculated neglecting the velocity gradients over the probe sensing area. A strong influence of both mean and fluctuation velocity gradients on measurement accuracy was found. A new three-sensor array configuration designed to minimize the influence of the velocity gradients is proposed, and its accuracy is compared to two-sensor X- and V-array configurations.   

An in-situ calibration technique for four-wire hot-wire probe in conjunction for atmospheric studies

There is an increasing need to resolve the small-scales of atmospheric turbulence in order to estimate the higher order statistics of the turbulent flow. Sonic anemometers are commonly used in atmospheric research; however their application can only provide data with low special and temporal resolution. Hot-wire (HW) probes are still the best tool to obtain turbulent statistics with high temporal and spatial resolution. But HW probes are rarely used for atmospheric measurement due to the intricacy and logistical difficulties associated with the calibration and applications of the required probes for this flow field. In the present study, an in-situ method of calibration of a four-wire hot-wire anemometer is proposed, which bypasses the need for prior calibration. A proper data reduction algorithm has been developed to be used in conjunction with the four-wire probe. The proposed methodology enables one to use the hot-wire anemometer for atmospheric measurement to obtain three dimensional velocity information, at high spatial and temporal resolution, without the necessity of going through extensive calibration procedure. The feasibility of this method has been tested in laboratory and Monte Carlo simulation has been used to establish the stability and sensitivity of the data reduction algorithm.   

New measurement technique for turbulent flow as a replacement for hot-wire anemometry

We present latest developments of the 2d-Laser Cantilever Anemometer (2d-LCA), a sensor, which has been developed for highly resolved measurements of turbulent flows. Its measuring principle allows for high temporal resolutions of beyond 50kHz at spatial scales in sub millimeter range. This performance is achieved by measuring the deformation of a tiny cantilever via laser pointer, which experiences drag forces caused by the flow. The cantilever features two deformation modes, i.e. bending and twisting, whereas the latter occurs only for oblique inflow. Thus the sensor is capable of measuring two velocity components. Latest developments focus on the design of the cantilever. For example, an additional structure for a better sensitivity towards cross winds and an improved reflection pad were realized. Further improvements concern the laser beam guiding within the sensor. Beside this we are in the process of setting up advanced electronics and new types of PSD-elements with the goal of increasing the sensitivity. Comparison measurements between the re-designed 2d-LCA and older versions were performed and showed improvements relating signal quality and reliability. Further measurements in turbulent flow with an x-wire as a reference confirmed the ability of the new sensor to carry out measurements at comparable high resolutions.   

Multi-color particle shadow accelerometry (cPSA)

We present an extension of multi-color particle shadow velocimetry (cPSV) to unsteady acceleration measurement. cPSV uses a multi-color, pulsed LED light source for illumination. Particle shadow images recorded by a digital color camera are color separated and inverted. Standard DPIV processing methods are then used to estimate 2-D displacement vector fields. Acceleration estimates are facilitated by acquisition of three sequential images (one per color) in each camera exposure. Here, we prove the technique by measuring the tangential acceleration of a moving solid body, and compare the results to accelerometer measurements. We also present preliminary acceleration measurements performed in a near-wall turbulent pipe flow.   

Development of an Acoustic Localization Method for Cavitation Experiments in Reverberant Environments

Cavitation is a major concern for the US Navy since it can cause ship damage and produce unwanted noise. The ability to precisely locate cavitation onset in laboratory scale experiments is essential for proper design that will minimize this undesired phenomenon. Measuring the cavitation onset is more accurately determined acoustically than visually. However, if other parts of the model begin to cavitate prior to the component of interest the acoustic data is contaminated with spurious noise. Consequently, cavitation onset is widely determined by optically locating the event of interest. The current research effort aims at developing an acoustic localization scheme for reverberant environments such as water tunnels. Currently cavitation bubbles are being induced in a static water tank with a laser, allowing the localization techniques to be refined with the bubble at a known location. The source is located with the use of acoustic data collected with hydrophones and analyzed using signal processing techniques. To verify the accuracy of the acoustic scheme, the events are simultaneously monitored visually with the use of a high speed camera. Once refined testing will be conducted in a water tunnel. This research was sponsored by the Naval Engineering Education Center (NEEC).   

MLM: Dust Explosion Potential Warning System

A quite large range of materials, when dispersed as a dust cloud in air, can support an explosion. Empirically derived minimum explosive concentration (MEC) values are typically in the range: 30-80 grams/m$^{3}$; that is, nominally 2.5-8.3{\%} of STP density. Currently, there is no field-deployable measurement system to determine the mass loading (grams/m$^{3})$ of airborne dust. Proof-of-concept measurements for the MSU Mass Loading Monitor (MLM) are reported. A charge of dusty air, ingested into a cylinder, is accelerated (a$_{p}$=ct) by a driving piston and partially ($\approx $8{\%}) discharged from the open end of the cylinder. The deformable control volume momentum equation can be integrated with respect to time to yield $\alpha _{( )}-\beta _{( )}=\gamma \rho _{( )}$ where ( ) will indicate with (w) or without (w/o) dust. The pressure integral ($\alpha )$ and the shear integral ($\beta )$ balance the momentum within the cylinder at the end of the smoke plus the integral of the momentum flux. The kinematic attributes of these terms are represented by $\gamma $. It will be shown how the mass loading ($\rho _{w}-\rho _{w/o})$ can be determined. A full length paper (The Mass Loading Monitor Fundamental Principles And Proof Of Concept) will be published in \textit{Meas. Sci. and Tech.}   

Comparing the sphere anemometer to standard sensors for 2D wind measurements

The cup anemometers commonly used for wind energy applications are fairly robust, but suffer from several drawbacks like their limited temporal resolution, a systematic overestimation of the wind speed in turbulent flows and the inability to measure the wind direction. While sonic anemometers can measure the wind vector at a higher temporal resolution, they are more fragile and significantly more expensive. Therefore, we propose the sphere anemometer as a robust and highly-resolving alternative to standard anemometers. Designed without wearing parts, the sphere anemometer provides simultaneous wind speed and direction measurements as needed for wind turbine operation especially under challenging conditions such as offshore installation. In our contribution, we introduce the setup of the sphere anemometer which is based on the velocity-dependent deflection of a flexible tube with a sphere mounted atop. The deflection is measured in two dimensions using a light pointer, which allows for the simultaneous determination of wind speed and direction via calibration. Experimental results from wind tunnel measurements with sonic anemometer and sphere anemometer are presented, as well as first comparative measurements from the operation on the nacelle of a near-shore wind turbine.   

Geometrical Optimization of a Cylindrical Plasma Lens

Previous work by the authors have demonstrated the concept of an AC ``plasma lens'' for optical path difference (OPD) control of laser wavefronts. Plasma lenses feature no moving parts and a high frequency response, both of which are highly favorable for adaptive optics. This work investigates the geometrical constraints the plasma lens design, particularly the influence of the diameter of electrodes and gap distance between electrodes. A simplified electrostatic model for the plasma lens is developed and compared with experimental results. A good agreement is found between the experiments and theory. In regard to plasma lens design, the findings indicate (1) that there exists a critical gap-distance-to-diameter ratio, and (2) that the spatial efficiency of the device depends highly on the gap-distance-to-diameter ratio.   

Time-resolved tomographic PIV measurements in swirling jets

The vortex dynamics of swirling jets at a Reynolds number of 1,000 is investigated by time-resolved tomographic Particle Image Velocimetry. Experiments are conducted at several values of the swirl number S from 0 to 0.8, therefore spanning the transition between weak and strong swirl regimes. Time resolved measurements are performed with the intention to shed more insight into the relation between shear layer instability at the outer side of the jet and the unsteady behaviour of the core region characterized by tumbling/precession motion. The average flow topology is addressed first in order to highlight the topological differences between weak and strong swirl flows. The three-dimensional topology of vortex structures is then visualized with Q criterion. Finally, the measured velocity and vorticity field is employed to estimate the terms of the vorticity equation, which enable to discuss on a more quantitative basis the effect on vortex dynamics and on the overall phenomenology of swirling jets.   

Session L16: Separated Flows II

Effect of wakes from moving upstream rods on boundary layer separation from a high lift airfoil

Highly loaded airfoils in turbines allow power generation using fewer airfoils. High loading, however, can cause boundary layer separation, resulting in reduced lift and increased aerodynamic loss. Separation is affected by the interaction between rotating blades and stationary vanes. Wakes from upstream vanes periodically impinge on downstream blades, and can reduce separation. The wakes include elevated turbulence, which can induce transition, and a velocity deficit, which results in an impinging flow on the blade surface known as a ``negative jet.'' In the present study, flow through a linear cascade of very high lift airfoils is studied experimentally. Wakes are produced with moving rods which cut through the flow upstream of the airfoils, simulating the effect of upstream vanes. Pressure and velocity fields are documented. Wake spacing and velocity are varied. At low Reynolds numbers without wakes, the boundary layer separates and does not reattach. At high wake passing frequencies separation is largely suppressed. At lower frequencies, ensemble averaged velocity results show intermittent separation and reattachment during the wake passing cycle.   

Experimental investigation of frequency lock-on in separated flow

Separated flow is a complex phenomenon comprised of several flow dynamics. Recent experimental and computational investigations propose that, depending on flow conditions, the nature of flow separation is governed by three dominant mechanisms: the shear layer, separation bubble, and wake instabilities. The nonlinear interactions of these instabilities provide potential for separation characterized by various lock-on states. This study provides an experimental investigation into the lock-on type dynamics for separated flows from various two-dimensional airfoil shapes, Reynolds numbers, and angles of attack. Two simultaneously sampled hot-wire probes are used to acquire velocity in two of the three regions of interest. The data quantify nonlinear coupling between the instabilities observed in the shear layer, the wake, and, in the case of mean flow reattachment, the separation bubble. The locations of these phenomena are determined with simple two-component particle image velocimetry. The coupling is assessed via higher-order spectral and moment analysis. Several of the cases that demonstrate resonant behavior are included for discussion.   

Wake Modes of Rotationally Oscillating Cylinders at low Re

Vortex shedding from bluff bodies is important in various engineering applications because the wake can have many effects, including exciting vibrations in structures and altering convective heat transfer. While vortex shedding from cylinders in cross-flow and cylinders undergoing transverse and in-line oscillations has been studied extensively, only limited data is available for rotational oscillations and is mainly limited to spectral analysis of the wake. Water tunnel experiments were carried out at Re = 150 to investigate the wake of a rotationally oscillating cylinder for oscillation frequencies from 0.67 to 3.5 times the natural shedding frequency and peak-to-peak oscillation amplitudes up to 320\r{ }. DPIV was used to study both the near and far wake within this parameter space. Well-defined patterns of wake vortices were observed in distinct regions of the parameter space, similar to the wake modes of transversely oscillating cylinders in cross-flow. In portions of the parameter space for which information exists in the literature the wake modes are well-related to spectral data. Variants of modes in previously unexplored regions are explained in terms of harmonics. The initial application of these results to understanding heat transfer enhancement from rotationally oscillating cylinders will also be addressed.   

Separation Control in a Centrifugal Bend Using Plasma Actuators

An experiment and CFD simulation are presented to examine the use of plasma actuators to control flow separation in a 2-D channel with a 135$^{\circ}$ inside-bend that is intended to represent a centrifugal bend in a gas turbine engine. The design inlet conditions are $P=330$\,psia., $T=1100^{\circ}$F, and $M=0.24$. For these conditions, the flow separates on the inside radius of the bend. A CFD simulation was used to determine the location of the flow separation, and the conditions (location and voltage) of a plasma actuator that was needed to keep the flow attached. The plasma actuator body force model used in the simulation was updated to include the effect of high-pressure operation. An experiment was used to validate the simulation and to further investigate the effect of inlet pressure and Mach number on the flow separation control. This involved a transient high-pressure blow-down facility. The flow field is documented using an array of static pressure taps in the channel outside-radius side wall, and a rake of total pressure probes at the exit of the bend. The results as well as the pressure effect on the plasma actuators are presented.   

An experimental study of flow past an oscillating cylinder

We present preliminary experimental results on flow past an oscillating cylinder at frequency ratios varying from 0 to 5 and oscillation amplitudes varying from $\pi /8$ to $\pi $. The experiments are conducted at Reynolds number of 185. The frequency ratio, f$_{R}$, is defined as the ratio of cylinder oscillation frequency to vortex shedding frequency from a non-oscillating cylinder. The diagnostic is done using hydrogen bubble technique for flow visualization in a plane. It is found that at one diameter downstream from the cylinder, vortex shedding frequency matches the forcing frequency (lock-on) at all f$_{R} \quad >$1 and all amplitudes; however, for f$_{R} \quad <$1 there is a window adjacent to f$_{R}$ = 1 where lock-on occurs and this depends on oscillation amplitude. In the far wake at nine diameters from the cylinder, the lock-on region is centered around f$_{R}$ = 1 and depends strongly on amplitude. The visualization of the vortical structures showed that near f$_{R}$ =1.0 the vortices became very compact and well formed in the visualization plane. Their size decreases considerably at much higher f$_{R}$'s in the near-wake. The motion pictures reveal interesting phenomenon of merger of vortices at certain f$_{R}$'s.   

Experimental Study of Wake Instabilities of a Blunt Trailing Edge Profiled Body at Intermediate Reynolds Numbers

The periodic shedding of von K\'arm\'an vortices is the primary instability in the wake of nominally 2D bluff bodies, beyond a critical Reynolds number around 45-49. When Reynolds number passes a second threshold, which can be as high as 700 depending on profile geometry, secondary instabilities emerge and accompany the von K\'arm\'an vortices. For most bluff bodies, these instabilities appear as pairs of counter-rotating streamwise vortices, and spanwise undulations of the von K\'arm\'an vortices. The mechanism and scale of these instabilities depend on the bluff body geometry and Reynolds number. The focus of the present study is to identify and characterize the dominant secondary instability in the wake of a blunt trailing edge profiled body at intermediate Reynolds numbers between 8,000 and 20,000 based on the body thickness. The experiments, which include PIV and hot-wire measurements in the wake, complement previous studies involving the same bluff body at higher and lower Reynolds numbers, and make it possible to determine the scale and mechanism of the secondary instability at intermediate Reynolds numbers.   

Comparison of turbulent separation over a smooth surface and mako shark skin on a NACA 4412 hydrofoil

Shark skin is being investigated as a means of passive flow separation control due to the flexibility and preferential flow direction of the scales covering the skin. In this study, the effect of the scales is observed in a tripped turbulent boundary layer by comparing the flow over a NACA 4412 hydrofoil with a smooth surface to that over the same hydrofoil with samples of mako shark skin affixed to its upper surface. These samples were taken from the flank area of the shark because the scales at that location have been shown to have the greatest angle of erection, and thus the best potential for separation control. All flow data in this study was obtained using Time-Resolved Digital Particle Image Velocimetry and recorded at multiple angles of attack (between 8 and 16 degrees) and two Reynolds numbers. The flow was primarily analyzed by means of the backflow coefficient (a value based on the percentage of time that flow in a region over the hydrofoil is reversed) and the time history of instantaneous flow velocity values at specific points in the boundary layer over the hydrofoil models.   

An Experimental Study of Flow Separation over 2D Transverse Grooves

A shark's scales help to reduce drag over its body by controlling boundary layer separation over its skin. It is theorized that the scales bristle when encountering a reversing flow, thereby trapping vortices between the scales, creating a partial slip condition over the surface and inducing turbulence augmentation in the boundary layer. In an attempt to replicate and study these effects, a spinning cylinder was used in a water tunnel to induce separation over a flat plate with 2 millimeter square 2D transverse grooves. The results were compared to separation occurring over a flat plate without grooves using DPIV. The angular speed of the cylinder was varied. The observed delays in separation, changes in separation bubble shedding frequency and other effects upon the boundary layer are discussed.   

Flow around the tip of a circular cylinder in proximity with a channel bottom wall

Measurement probes create a region of disturbed flow in the vicinity of the probe tip. The present investigation examined the disturbance due to an idealized probe (a circular cylinder) that penetrated the free surface of an open channel flow as well as potential interactions of the disturbance with the channel bottom. Stereoscopic particle image velocimetry (PIV) was used to measure the three components of velocity in the vertical plane of symmetry downstream the cylinder with the tip of the cylinder located zero to four diameters from the channel bottom. The disturbance characteristics (change in velocity and turbulence quantities), vertical distance to the extent of disturbance as measured from cylinder tip, and downstream distance to the point of maximum disturbance have been determined. The cylinder tip depth that caused interaction with the channel bottom leading to onset of scour was also investigated.   

Session L17: Reacting Flows III: Engines, Sprays, and Soot

The flow field in a rotating detonation-wave engine

Rotating detonation-wave engines (RDE) are a form of continuous detonation-wave engine. They potentially provide further gains than an intermittent or pulsed detonation--wave engine (PDE). However, significantly less work has been on this concept when compared to the PDE. In this talk, we present the detailed flow field in an idealized RDE, primarily consisting of two concentric cylinders. A premixed detonable mixture is injected into the annulus between the two concentric cylinders. Once a detonation is initiated, it keeps travelling around in the annulus as long as there is fresh detonable mixture ahead of it. Hence, the injection process is critically important to the stability and performance of the RDE. Furthermore, we show that the flow field is quite complex consisting of multiple shock waves and the outflow is primarily axial, although the detonation-wave is travelling around circumferentially.   

Fluid dynamics in a Rotating-Detonation-Engine with micro-injectors

Rotating detonation engines (RDE's) represent a natural extension of the extensively studied pulse detonation engines (PDE's) for obtaining propulsion from the high efficiency detonation cycle. RDE's require fuel and oxidizer under high pressure to be injected through micro-nozzles from one or two plenums (for premixed and non-premixed). This injection process is critically important to the stability and performance of the RDE. This paper studies the effect of this injection process on the detonation wave within the combustion chamber, with an emphasis on how the fluid dynamics are affected. Both two-dimensional and three-dimensional simulations are done using well proven numerical methods for both the combustion chamber and mixture plenums of an idealized RDE.   

LES Of A Model Aircraft Combustor: Spray Model Assumptions And Pollutant Formation

Large eddy simulations of NASA's Lean Direct Injection spray combustor are performed. Fuel spray is described using Lagrangian particles, and combustion is modeled using a multi-regime flamelet approach. Particular emphasis is placed on analyzing how spray model assumptions affect pollutant predictions. This analysis is performed by running a series of cases that employ different spray evaporation models, different spray cone angles, and different bulk air flow rates. Results demonstrate that both CO and NO are leading order sensitive to the details of the spray formulation. Temperature is also shown to be leading order sensitive to the spray formulation, while major species such as CO$_2$ and H$_2$O are less sensitive. These results highlight the difficulty of validating pollutant models with liquid fueled experiments that are subject to spray modeling uncertainty.   

Theory of vaporization and combustion of fuel sprays in strained laminar mixing layers

The vaporization and combustion of a monodisperse fuel spray in a laminar counterflow mixing layer is investigated under conditions such that the droplet Stokes number is smaller than 1/4, so that the droplets do not cross the stagnation plane, but instead tend to accumulate there because of their inertial slip motion. Vaporization is confined to the thin strained mixing layer separating the spray from the hot stream, which can be described with an Eulerian description for the liquid phase. The numerical integration of the resulting boundary-value problem provides the structure of the reactive mixing layer, including the standoff distance from the stagnation plane where droplets disappear and the flame location. Limiting asymptotic solutions for extreme values of the controlling parameters are also determined, and a generalized vaporization law for droplets in the presence of thermal gradients is derived. The results provide increased understanding of laminar spray flamelets.   

A multi-scalar PDF approach for LES of turbulent spray combustion

A comprehensive joint-scalar probability density function (PDF) approach is proposed for large eddy simulation (LES) of turbulent spray combustion and tests are conducted to analyze the validity and modeling requirements. The PDF method has the advantage that the chemical source term appears closed but requires models for the small scale mixing process. A stable and consistent numerical algorithm for the LES/PDF approach is presented. To understand the modeling issues in the PDF method, direct numerical simulation of a spray flame at three different fuel droplet Stokes numbers and an equivalent gaseous flame are carried out. Assumptions in closing the subfilter conditional diffusion term in the filtered PDF transport equation are evaluated for various model forms. In addition, the validity of evaporation rate models in high Stokes number flows is analyzed.   

DNS of aerosol evolution in a turbulent jet

The effects of turbulence on the evolution of aerosols are not well understood. In this work, the interaction of aerosol dynamics and turbulence are studied in a canonical flow configuration by numerical means. The configuration consists of a hot nitrogen stream saturated with dibutyl phthalate (DBP) vapor mixing with cool air in a shear layer. A direct numerical simulation (DNS) for the momentum and scalar fields is coupled with the direct quadrature method of moments (DQMOM) for the condensing liquid phase. The effects of turbulent mixing on aerosol processes (nucleation, condensation, and coagulation) are quantified by analyzing the statistics of number density and droplet sizes.   

Soot formation in unstrained diffusion flames

The formation of soot particles has been investigated in CH$_4$/O$_2$ diffusion flames using a burner which allows the creation of a nearly unstrained planar reaction sheet. The sooting limits, soot volume fraction and particle size were measured as a function of bulk flow across the flame mixture strength and transport properties of the reactants. Mass spectrometry was used to measure the effective mixture composition close to the flame and Laser Induced Incandescence (LII)for the soot volume fraction and particle size. The parameter space was mapped as follows: Starting from a stable non-sooting baseline flame, the mixture strength was progressively increased by raising the fuel volume fraction while keeping other parameters constant (bulk flow across the flame, oxidant and inert composition). As the mixture strength was increased, the soot volume fraction and particle size increased up to a point where very big soot particle aggregates became visible to the naked eye on the flame side of the sooting layer. The exact mechanism by which these super aggregates arise is unknown but it is postulated that the absence of strain in the flow field and the thermophoretic effect allows soot particles to remain in a region of the burning chamber suitable for growth for an extended period of time.   

Characterization of Mixing and Ignition Effects in Flow-Reactors Using a Particle Method

Recent investigations have indicated discrepancies between measurements and simulations of the ignition delay for syngas-mixtures at high-pressure/low- temperature conditions. While relevant sources for these discrepancies have been identified in the context of rapid compression machines and shock tubes, the underlying mechanisms and nonidealities in flow-reactor experiments have not yet been quantified. The objective of this investigation is to characterize effects of turbulence and flow-field inhomogeneities on the mixing and ignition-dynamics in flow-reactors. To this, an idealized flow-reactor is considered, in which the unsteady and three-dimensional flow-field is obtained from the solution of a large-eddy simulation. A particle method is used to describe the mixing, induction, and subsequent ignition of the reactants. Utilizing this model, parametric studies are performed to systematically quantify effects of initial mixture-preparation, flow-rate modulation, and turbulence-levels on the ignition-process over a range of practically relevant temperature and pressure conditions.   

Quantification of the uncertainties in the prediction of extinction of hydrogen-air diffusion flames

The study of the physical processes that lead to extinction of flames in gaseous hydrogen-air non-premixed combustion is of paramount importance for the reliable design of power plants and advanced propulsion systems in automobiles and hypersonic aircrafts. However, there remain several uncertainties in the experimental quantification of reaction rates of elementary steps in most of hydrogen-air mechanisms, which can produce hazards in hydrogen manipulation and engine malfunction. In this study, the effects of aleatory uncertainties in the chemical reaction-rate constants induced in hydrogen-air counterflow diffusion-flame extinction processes are addressed, with a probabilistic representation of the uncertain parameters sampled with a Markov-Chain Monte Carlo algorithm. Measurements of the reaction-rate constants and their associated uncertainty factors, reported earlier for the Stanford hydrogen-air detailed chemical mechanism, are used to study the propagation of uncertainties in the calculation of scalar dissipation rates at extinction. Non-intrusive methods are used to analyze the variablities, with the probability density function of the scalar dissipation rate being sampled around regions involving flame extinction and global sensitivity indices being computed by Monte Carlo sampling.   

Regression Rate Enhancement of Hybrid Rocket Motors using Mixed Hybrid Concept

Low regression rates have been a major problem for hybrid rocket motors. In the present study, the effect on regression rate by adding ammonium perchlorate (AP) in solid fuel is studied numerically. AP mixed with HTPB is used as solid fuel and gaseous oxygen (GOX) is used as oxidizer. Solid fuel compositions are chosen such that the rocket motor retains start-stop capability. A reduced three step mechanism proposed in the literature is utilized to simulate the combustion. In the combustion chamber, two distinct flame fronts are captured. AP decomposition reaction forms a premixed flame front near the fuel surface. The AP decomposed products also react with HTPB. Heat released in these reactions improves the heat transferred to solid fuel and the regression rate significantly. Un-burnt fuel in the products further reacts with GOX forming a diffusion flame front farther from fuel surface. The presence of premixed flame front thus overcomes the low-regressing nature of hybrid combustion. It is found that 50{\%} AP in solid fuel increases the regression rate by as much as 3 times.   

Session L18: Microfluids: Fluidic Devices I

Levitation, aggregation and separation of micro-sized particles in a Hydrodynamic Acoustic Sorter, HAS

Levitation, aggregation and separation of micron-sized particulate materials can be generated in a fluidic resonator by an ultrasonic standing wave field force. A piezoelectric transducer generates standing waves between the two walls of a parallel plate channel composing the resonator. The number of pressure nodes $n$ is given by the relationship: $w=n\lambda /2$ with $\lambda$ the wavelength. The primary radiation force generated by the standing wave generates levitation of micron-sized particles driving them toward the nodal planes. An equilibrium position is reached in the channel thickness where the acoustic force balances the gravity force. The equilibrium position is independent on particle size but it depends on the acoustic properties. Once particles reach the equilibrium position, transversal secondary forces generate aggregation. We shall present the levitation and aggregation process of latex particles and cancer cells in a 2MHz resonator. We demonstrate the possibility of separating particles under flow in a Hydrodynamic Acoustic Sorter HAS, in function of their acoustic impedance and in function of their size using a programming field force.   

Continuous Separation of Microparticles in a Microfluidic Channel via the Elasto-inertial Effect of Non-Newtonian Fluid

Pure separation and sorting of microparticles from complex fluids are essential for biochemical analyses and clinical diagnostics. In this study, we present a simple and label-free method to separate microparticles with high purity using the elasto-inertial characteristic of non-Newtonian fluid in microchannel flow. At the inlet, particle-containing sample flow was pushed toward the side walls by introducing sheath fluid from the center inlet. Particles of 1 $\mu $m and 5 $\mu $m diameter that were suspended in viscoelastic fluid were successfully separated in the outlet channels: larger particles were notably focused on the centerline of the channel at the outlet, while smaller particles kept flowing along the sidewalls with minimal lateral migration to centerline. The same technique was further applied to separate platelets from diluted whole blood. Through cytometric analysis, we found that the purity of collected platelets was close to 99.9{\%}. Conclusively, the technique of microparticle separation using elasto-inertial forces in non-Newtonian fluid is proven to be an effective method for separating and collecting microparticles based on size differences with high purity.   

Interactive tuning of flow geometry for size-sensitive sorting of microparticles

We show that sensitive selection, focusing, and sorting of microparticles by size is possible in microfluidic setups without the need for moving boundaries or external forces on the particles. The flow domain is flexibly and interactively shaped by the superposition of a transport flow and a microbubble-induced streaming flow. This method separates particles for which both the absolute size and the size differential are only a few micrometers, in a setup whose smallest geometric scale is about 100 microns. Size-dependent trapping, release, and focusing can be effected and used for switching and sorting [1]. Devices based on this novel concept are easy to fabricate and can be directly tailored to a variety of transported objects, including cells and vesicles. \\[4pt] [1] C. Wang, S. V. Jalikop and S. Hilgenfeldt, Applied Physics Letters {\bf 99}, 034101 (2011).   

Continuous size-based dielectrophoretic particle sorting in a microfluidic device

The dielectrophoresis~(DEP) force acting on a particle passing through a nonuniform electric field is proportional to its volume, making DEP well-suited for size-based particle sorting. Pinched flow fractionation uses the geometry constraints of a narrow segment of microchannel to effect size-based separation. We combine these two techniques in series to create a size-based microfluidic sorting device, using negative DEP to allow for continuous particle sorting. An interdigitated array of five L-shaped electrodes permits the sorting of up to five different particle sizes. For a given set of particle sizes ($\sim \!1$--$10 \textrm{ }\mu$m), this sorting process can be optimized by using the applied potentials on the electrodes as our optimization parameters. Through on-chip voltage control of the electrodes, we can achieve sorting for various sets of particle sizes with the same microfluidic device geometry. We compare the computational optimization solution to an analytical solution and with experimental results.   

Gravity driven separation based on lateral displacement in anisotropic microfluidic media

We designed an anisotropic periodic array of rectangular obstacles and directly measured the Brownian motion of particles in the absence of an external field. Earlier, we established that in the limit of small driving forces, particle-wall hydrodynamic interactions, coupled with geometric confinement, lead to non- linear effects in the mobility of rigid spherical particles in the periodic array. We further proposed that such anisotropic media could be used for continuous size-based separation of particles in microfluidic devices. Here, we show that such anisotropic systems could also lead to separation in the deterministic limit of high Peclet numbers. We use gravity as the driving force and investigate the effect of the orientation of the force with respect to the media. We observe directional locking in the motion of the particles, analogous to that observed in macroscopic systems and discuss the role of irreversible particle-obstacle interactions in the observed behavior. We report the average migration angles for different sizes of particles and confirm the utility of these anisotropic arrays to create microdevices for continuous particle sorting.   

Diamagnetic Particle Separation in Ferrofluid Microflows

Particle separation is important for a wide range of applications. A variety of force fields have been demonstrated to separate particles in microfluidic devices. Magnetic field-induced separation is simple, cheap, and free of fluid heating issues that accompany electric, acoustic, and optical methods. We develop a novel magnetic particle separation method in a curved microchannel with a nearby permanent magnet. This method is capable of separating both magnetic and nonmagnetic particles by size. It is based on the dependence of particle magnetophoresis on the particle size and the particle's distance from the magnet. We present in this talk a continuous separation of 3 $\mu $m- and 5 $\mu $m-diameter polystyrene particles in a ferrofluid flow without magnetic and fluorescent labeling. We also develop a numerical model to simulate the particle separation process.   

Continuous blood fractionation using an array of slanted grooves

Blood is a complex fluid having different specialized biological functions and containing a plethora of clinical information. The separation of different blood components is a crucial step in many research and clinical applications. In this work we take advantage of the flow characteristics in microfluidic devices in which the bottom surface is patterned with slanted rectangular grooves to continuously fractionate blood. We exploit the flow in the vicinity of the patterned surface when the dimensions of the grooves are much smaller than the dimensions of the main channel. In these devices, we observed that the grooves act as open channels guiding flow along them with the flow over them being in the direction of the main channel. We present experiments in which the different blood components are deflected laterally to a different extent by the flow along the grooves depending on their sedimentation velocity, which allows their continuous fractionation. In particular, the heavier red blood cells experience the largest deflection while the lighter white blood cells deflect the least, allowing their passive and minimally invasive isolation. In addition, this fluidic platform can also be used to separate magnetically labeled circulating cancer cells which can be retained in the flow along the grooves using a sufficiently strong magnetic force.   

Dielectrophoretic Separation of Live and Dead Yeast Cells in Microfluidic Reservoirs

Insulator-based dielectrophoresis (iDEP) is an emerging technology that has been widely used to manipulate particles and cells in microfluidic devices. Current iDEP devices use in-channel micro-obstacles such as hurdles, posts and ridges to create electric field fields, which may cause potential Joule heating problem due to the locally amplified electric field. In this talk we present a dielectrophoretic separation method in microfluidic reservoirs. Due to the significant size mismatch between a microchannel and its end-channel reservoirs, electric fields gradients are inherently produced at the microchannel-reservoir junction. The induced dielectrophoresis can be utilized to focus and trap cells and particles. We demonstrate a continuous concentration and a selective isolation of live yeast cells from dead yeast cells in a reservoir under DC-offset AC electric fields. The effects of AC to DC field ratio and AC field frequency on the separation performance are both examined. We also develop a numerical model to understand and predict the observed cell motions in microfluidic reservoirs.   

Surface Design for Efficient Capturing of Rare Cells in Microfluidic Device

This work aims to design, fabricate, and characterize a micro-patterned surface that will be integrated into microfluidic devices to enhance particle and rare cell capture efficiency. Capture of ultralow concentration of circulating tumor cells in a blood sample is of vital importance for early diagnostics of cancer diseases. Despite the significant progress achieved in development of cell capture techniques, the enhancement in capture efficiency is still limited and often accompanied with drawbacks such as low throughput, low selectivity, pre-diluting requirement, and cell viability issues. The goal of this work is to design a biomimetic surface that could significantly enhance particle/cell capture efficacy through computational modeling, surface patterning, and microfluidic integration and testing. A PDMS surface with microscale ripples is functionalized with epithelial cell adhesion molecule (EpCAM) to capture prostate cancer PC3 cells. Our microfluid chip with micropatterns has shown significantly higher cell capture efficiency and selectivity compared to the chips with plane surface or classical herringbone-grooves.   

Cascade and staggered dielectrophoretic cell sorters

We report experimental results of successful separation of different cancer cells (breast and prostate) from colorectal cancer cells in Dielectrophoresis (DEP) in continuous operation. Conductivity influence on DEP spectrum for each cell type has been investigated. Under optimized condition, different cell type can be separated from each other. Enrichment factor and cell purity are measured to characterize the performance of the DEP chip. AC voltage and frequency effect on the separation is measured. In practical lab-on-a-chip application highly purified cell and high flow rate are required. In order to increase the purity of the isolated cells, cascade DEP sorter is developed. To increase flow rate, staggered DEP sorter is developed. It is found that compared with single DEP sorter, adding cascade DEP sorter can significantly increase r the purity of the target cell. With the staggered chip, the flow rate can be increased without compromising enrichment factor.   

Session L19: Rayleigh Taylor Instability II

One-dimensional-turbulence simulations of reactive Rayleigh-Taylor turbulence

We consider the problem of reactive Rayleigh-Taylor turbulence in the Boussinesq framework, and model combustion with a reaction-progress-variable method, and a KPP reaction. The interesting feature of this problem is that the interface (flame) between heavy/cold reactants and light/hot products moves against gravity. Such problem is challenging because of the delicate interplay between turbulence, buoyancy, and reactions, and the wide separation between large and small scales. One model that has the capabilities to deal with these challenges is the one-dimensional-turbulence (ODT) model. In this talk, we discuss ODT results for non-reactive and reactive Rayleigh-Taylor turbulence, and compare them with those from direct numerical simulations (DNS). Here, the key advantage of ODT over DNS is that it can be used to explore larger parameter spaces.   

Late-time evolution of Rayleigh-Taylor instability in a domain of a finite size

For the first time a theoretical analysis was developed to systematically study the late-time evolution of Rayleigh-Taylor instability in a domain of a finite size. The nonlinear dynamics of fluids with similar and contrasting densities are considered for two-dimensional and three-dimensional flows driven by sustained or time-dependent acceleration. The flows are periodic in the plane normal to the direction of acceleration and have no external mass sources. Group theory analysis is applied to accurately account for the mode coupling. Asymptotic nonlinear solutions are found to describe the interface dynamics far from the boundaries and near the boundaries. The influence of the size of the domain on the diagnostic parameters of the flow is identified. In particular, it is shown that in a finite size the domain the flow is decelerating compared to spatially extended case. The theory outcomes for the numerical modeling and design of experiments on Rayleigh-Taylor instability are discussed.   

Reynolds--Averaged Navier--Stokes Modeling of Large Reynolds Number Mechanical and Scalar Rayleigh--Taylor Turbulent Mixing

A three- and four-equation, variable-density, incompressible Reynolds-averaged Navier--Stokes model incorporating mechanical and scalar turbulence is used to simulate Rayleigh--Taylor turbulent mixing with an Atwood number equal to one-half. Using both Reynolds number-dependent (optimal) and constant late-time model coefficients obtained by minimizing the $L^2$ norm between the model and the large Reynolds number $3072^3$ Cabot--Cook direct numerical simulation data, the predicted mixing layer evolution is compared with the averaged DNS data in a posteriori tests. The terms in the transport equation budgets are compared in detail to their profiles across the mixing layer predicted by the DNS. The capability of the model to predict the degree of molecular mixing is also assessed.   

Turbulent Rayleigh-Taylor flow driven by time-varying accelerations

We report on numerical simulations of turbulent Rayleigh-Taylor flow subject to variable acceleration histories. The acceleration profiles were inspired by experiments and theoretical studies, and include an impulsive acceleration, accel-decel profiles, as well as a constant drive as the baseline case. The simulations were performed using the MOBILE software, a variable-density, incompressible fluid flow code. The advection algorithm employs a 3$^{rd}$-order, monotonicity-preserving upwind scheme, allowing the definition of sharp interfaces in the flow, while pressure convergence is accelerated by the use of a multi-grid scheme. The simulations are initialized with two classes of perturbations: narrow-band, short-wavelength modes and broadband with long-wavelength modes. The effect of initial amplitudes on the perturbations is investigated under the variable drive conditions. The acceleration profiles are capable of producing stages of ``demixing,'' useful in validating turbulence models of RTI.   

Direct Numerical Simulations of Rayleigh-Taylor instability

The development of the Rayleigh-Taylor mixing layer is studied using data from an extensive new set of Direct Numerical Simulations (DNS). This includes a suite of simulations with grid size of $1024^2 \times 4608$ and Atwood number ranging from A=0.04 to 0.9, in order to examine small departures from the Boussinesq approximation as well as large Atwood number effects, and a high resolution simulation of grid size $4096^2 \times 4032$ and Atwood number of 0.75. After the layer width had developed substantially, additional branched simulations have been run under reversed and zero gravity conditions. The results presented address the role of the initial conditions on the mixing layer development and the discrepancy between the growth rates in various experiments and numerical simulations, as well as the changes in Rayleigh-Taylor turbulence properties at large density ratios.   

Simulations of Compressible Rayleigh-Taylor Instability Using the Adaptive Wavelet Collocation Method

Numerical simulations of the single-mode compressible Rayleigh-Taylor instability are performed on an adaptive mesh using the Adaptive Wavelet Collocation Method (AWCM). Due to the physics-based adaptivity and direct error control of the method, AWCM is ideal for resolving the wide range of scales present in the development of the instability. The problem is initialized consistent with the solutions from linear stability theory, with two diffusively mixed, stratified fluids of differing molar masses as the background state. Of interest are the compressibility effects on the departure time from the linear growth, the onset of strong non-linear interactions, and the late-time behavior of the fluid structures. The late time bubble and spike velocities are computed and compared to those obtained in the incompressible case.   

On Buoyancy and Shear Mixing

Combined Rayleigh Taylor and Kelvin Helmholtz instabilities play a significant role in a number of phenomena, most importantly inertial confinement fusion. Should the relationship between initial conditions and mixing be determined, then, in principle, the level of mixing could be controlled through the setting of specific conditions. To investigate this proposition, a Kelvin Helmholtz Rayleigh Taylor experiment with a low Atwood number, buoyancy- and velocity-driven mixing width was investigated. The experiment was modeled using an implicit large eddy simulation code which uses a finite volume technique to solve the three dimensional incompressible Euler equations. The number of modes and the magnitude of the perturbations were set to investigate the rate of development as well as the maximum growth reached of the mixing width. Preliminary results show a promising overall agreement for the mixed region when the number of modes is increased.   

Direct Numerical Simulation of Tilted Rayleigh-Taylor Instability

The tilted Rayleigh-Taylor instability, where the initial interface is not perpendicular to the driving acceleration, is investigated using Direct Numerical Simulations (DNS). In this configuration, the inclination of the initial interface results in a large-scale overturning motion in addition to the buoyancy driven instability. The DNS results are compared to the rocket-rig experiments of Smeeton and Youngs (AWE Report No. 35/87) at several Atwood numbers (A=0.267, 0.48, and 0.90). Since the initial conditions in these experiments are largely unknown, an extensive range of initial conditions have been explored to match the mixing layer growth between DNS and experiments. The evolution of the mixing layer was found to be strongly influenced, for the duration of the experiments, by the initial spectrum shape and peak location, as well as the perturbation amplitude. A set of initial conditions matching the experimental growth rates has been determined. Results are also presented on the interaction between shear and buoyancy, including the parameters influencing the overturning and mixing.   

Session L20: Interfacial/Thin Film Instability V

Linear Instability, Self-Similarity and Nonlinear Growth in Ultrathin Wetting Films Driven by Thermocapillary Flow

Nanoscale viscous films subject to very large thermocapillary stresses are susceptible to a linear instability resembling nanopillar arrays. The interstitial regions, which provide the fluid needed to grow these structures, are observed to undergo rapid depletion down to tens of nanometers in thickness. Previous analyses have neglected the role of van der Waals forces in these systems [1]. A linear stability analysis of ultrathin films in which the disjoining pressure is comparable to thermocapillary and capillary forces confirms that wetting van der Waals forces generate larger interpillar spacings. More importantly, however, growth beyond the linear regime is characterized by an ultra flat depletion zone. Using a combination of analytic work and finite element simulations, we have identified a self-similar regime in which finite-amplitude disturbances to this zone produce a significant non-linear response. The resulting waveform shape is indicative of a secondary growth process leading to nanopillar formation. We discuss the behavior of three distinct growth regimes characterizing initial pillar growth, depletion zone formation, and secondary pillar growth. [1] M. Dietzel and S. M. Troian, Phys. Rev. Lett. 103, 074501 (2009); J. Appl. Phys. 108, 074308 (2010)   

The onset of Marangoni convection for evaporating liquids with spherical interfaces and finite boundaries

We examine the stability of evaporating liquids with spherical interfaces bounded at one value of the polar angle for all azimuthal angles. A linear stability analysis is performed and the results are used to explain why a system with water evaporating from a funnel constructed of PMMA undergoes stable quiescent evaporation but a system with a funnel constructed of stainless steel experiences a transition from a quiescent state to a state with Marangoni convection. We develop the expression for a new stability parameter that provides a quantitative prediction of the transition to Marangoni convection, and find the predictions to be consistent with experiments.   

Coherence Resonance Behavior in Thermocapillary Lithography

Interest in alternative means of nanofilm lithographic patterning has focused attention on a number of thin film hydrodynamic instabilities which can spontaneously generate periodic arrays of 3D protrusions. The interface evolution equation, which results from a competition between stabilizing capillary forces and destabilizing external driving forces, are well described by a nonlinear, fourth order PDE rather sensitive to initial and boundary conditions. Even small levels of noise result in arrays prone to variations in array pitch and array height at levels currently unacceptable for commercial applications. In this talk, we focus on thin film patterning by thermocapillary forces. We demonstrate how an adjacent cooled template with a small sinusoidally roughened surface presented to the free surface of a molten nanofilm can be used to trigger very rapid and uniform array growth with a pitch even smaller than predicted by linear stability analysis. This behavior is reminiscent of coherence resonance phenomena in which a small amount of external noise can trigger resonant uniform growth. We quantify the behavior of waveforms generated in this way by a combination of weakly non-linear analysis and finite element simulations.   

Film falling on a porous substrate

Consider a two dimensional viscous incompressible liquid film falling on a saturated porous inclined plane. The interface between the liquid and porous medium is modeled using a one-domain approach for which the permeability and porosity varies continuously. A two-equation model is derived in terms of the flow rate $q(x,t)$ and total height $H(x,t)$ within the framework of boundary layer approximations using weighted residual techniques. Coefficients of the model are expressed in terms of combinations of the integrals of the base flow $f$ and weight function $w$ that are determined numerically to ensure consistency of the approach at first order in the film parameter. The influence of properties of the homogeneous porous substrate on the wave dynamics is investigated by constructing the nonlinear traveling wave solutions.   

How does a soap film burst during generation?

Foams are dispersions of bubbles in a liquid matrix in the presence of stabilizing surfactants. Even if foams are ubiquitous, the ability of a solution to create a certain foam quantity is still not fully understood. As a first step, we choose to work on a simplified system and studied the stability of a soap film during its generation. We have built an experiment, in which we determine simultaneously the velocity of a frame pulled out of a soapy solution and the entire shape of the liquid film. We found that the film is made of two parts: the bottom part is of uniform and stationary thickness, well described by the classical Frankel's law; in the top part, the film drains until a black film appears near the frame upper boundary frame, and then bursts. In this study, we characterize both part of the films and show that the Frankel law breaks down at high capillary number due to surfactants confinement. We also explain why films pulled at high velocity have a shorter lifetime than those pulled at low velocity.   

Modeling of the stability of free-falling liquid curtain flow

The physical mechanisms leading to the disintegration of a gravitational (non parallel) two-dimensional plane liquid curtain (sheet), occurring at low fluid flow rates, are not yet fully known. The problem is reconsidered here through the development of an unsteady inviscid mathematical model where the dependent variables are expressed by means of polynomial expansions in terms of powers of the local lateral distance from the centerline position. Surface tension effects are included, and the ambient pressure field may be either applied or induced by the compliant free interface. The linearization around the base flow allows the separation of sinuous and varicose responses. The global linear stability of such a model is analyzed by inspecting both modal and non-modal amplifications of disturbances energy. An equation of energy budget is also derived, which is used to estimate the contribution of the various physical effects evaluated via direct numerical simulations of the governing system of equations.   

Layer formation in particle-laden free-films

Solutions to a model of a particle-laden free-film that includes structural oscillatory forces in addition to van der Waals forces are presented. Examination of steady solutions to the equations reveals layer and bulge solutions. Fully nonlinear time-dependent numerical calculations reveal that at fixed concentration a uniform film evolves into a multi-layered film, the heights of which are given by the common tangent construction applied to the particle-film interaction free energy. If the interaction free energy curvature is negative there is no barrier to the formation of a layered film from the uniform film, whereas if the interaction free energy curvature is positive the uniform layer is metastable. This behavior is analogous to spinodal decomposition and nucleation and growth mechanisms observed in classical first order phase transformations. Phase diagrams for layer transitions are also presented and discussed.   

Interfacial instabilities of reactive fingering

We consider viscous flows in a Hele-Shaw cell in which two immiscible fluids chemically react and form a complex substance at the interface. The interface is modeled as an elastic membrane whose bending rigidity depends on the local curvature. A dispersion relation is derived using the energy variation method. Several types of instabilities are categorized and how various physical parameters affect the stability is investigated. Our model is able to explain the anomalous fingering instability from experimental observations reported by other authors.   

Thin film rupture on flat and structured surfaces with surface charge densities

We perform a linear and nonlinear stability analysis to determine the conditions at which a thin film of viscous liquid containing a small concentration of ions will rupture for different surface charge densities at the solid-liquid and gas-liquid interfaces. The rupture is driven by the combined action of the electrostatic component of the disjoining pressure and van der Waals forces. The evolution of the interface shape is described using the system of lubrication-type equations. By considering a small perturbation to the constant steady-state solution, we obtain the growth rate of the instability and find a wave number range where the perturbation decays. The nonlinear stability analysis is performed by solving the interface shape equation numerically for a range of parameters corresponding to different values of the initial film thickness, Debye length, and surface charge densities. We then discuss applications of the same mathematical framework to analyze film rupture on charged structured surfaces.   

Session L21: Vortex Dynamics V

Effects of Spanwise-Modulated Blowing on the Cylinder Near-Wake

Three-dimensional characteristics of the wake of a circular cylinder at Re=5\begin{math}\times10^{3}\end{math} were controlled using spanwise-modulated forcing from dielectric barrier discharge plasma actuators. Three-dimensional blowing profiles were created by varying the shape of the buried electrode in the spanwise direction. A sinusoidal voltage of 10 kVpp at 5 kHz was applied between the electrodes to create the plasma. Wake surveys conducted with a rake of x-wires were used to understand the impact of the actuation on the time-resolved wake development. Simultaneous transverse profiles at multiple spanwise positions reveal that the actuation has a substantial impact on the spanwise variation of frequency and phase of the K\'{a}rm\'{a}n shedding process, as well as on the mean and fluctuating properties of the wake profile. Cross-correlations indicate a loss of coherence between adjacent spanwise locations, and the amplitude of the dominant vortex shedding frequency was substantially attenuated due to forcing. Further studies were carried out by modulating the actuation with harmonics and sub harmonics of K\'{a}rm\'{a}n shedding and the shear layer instability, with the aim of introducing small-scale structures that enhance break-up of the wake coherence.   

A cantilevered flexible cylinder in cross-flow

Biological fluid-structure interactions of high aspect ratio bluff bodies are commonplace: flow around tall plants; flow through arrays of sensory vibrissae, antennae, and hairs. In this study, we seek insight to this class of problems by generalizing the flow configuration to uniform flow past a flexible cantilevered cylinder. Experiments were conducted for $Re_{D}$ = 100-500. Cylinders deflected with the flow and demonstrated multimodal oscillations in both the streamwise and transverse directions. Oscillation frequencies were correlated with vortex shedding frequencies, but low oscillation frequencies (sub-1 Hz), which were not apparently vortex- induced, were also present. Two $Re_{D}$ regimes were noted in which the vortex shedding frequency remained relatively constant with $Re_ {D}$,while the two regimes were separated by an intermediate transition region. This feature results in an apparently linear relationship between $St$ and $Re_{D}$ in each regime. Hydrogen bubble visualization showed strong three-dimensionality in the wake, as well as a diversity of wake structures varying with $Re_ {D}$.   

A Case Study of Horseshoe Vortex Dynamics at Laminar and Turbulent Juncture Flows

To better understand the impacts of oncoming boundary-layer characteristics on the horseshoe vortex dynamics forming at a cylinder-wall junction, a case study is conducted in a free-surface water channel involving cylinder-channel floor and cylinder-end plate junctions. Endplates had two different leading-edge geometries, namely a sharp and a super-elliptical shape. The Reynolds number was kept at 10,000, based on the cylinder diameter. Laminar boundary layer forms along the channel floor and on the endplate with the super-elliptical leading edge. The plate with a sharp leading edge, however, involves flow separation at the leading edge, followed by a reattachment then an early transition to turbulence. On this plate, turbulent boundary layer is achieved. Flow visualization was performed on the plane of symmetry via PIV. Vortex trajectories and the velocity spectra depict periodic nature of the laminar horseshoe vortices and a variation of the spatial and temporal characteristics of horseshoe systems with the boundary layer thickness. Turbulent approach boundary layer led to disorganized and complex horseshoe vortex formation.   

Self-Excited Fluidic Energy Harvesters with Finite-Length Cylinders

In this experimental work, we explore the possibility of using piezoelectric materials for harvesting electrical energy from fluid flow. Such harvesters may be used for powering small sensors and obviate the need for batteries and/or power lines. Piezoelectric harvesters behave as AC-coupled devices and need oscillatory motion to generate an electrical output. The harvester should be designed to be ``self-excited,'' i.e. capable of initiating and sustaining the necessary oscillations in steady and uniform flows. The present configuration consists of a piezoelectric cantilever beam with a cylindrical tip body which promotes aeroelastic vibrations induced by vortex shedding. The harvester was tested in a wind tunnel and it produced 0.1 mW of electrical power at a flow speed of about 1.19 m/s. Using strain measurements and a distributed parameter model, the harvested electrical power was predicted, and a reasonable agreement is obtained with the measurements. The magnitude and frequency of the driving aerodynamic forces were also estimated. Results were comparable with literature data on flow past oscillating cylinders. Finally, the effect of using various shapes of tip body is presented.   

Vortex Induced Vibration of an Inclined Cylinder in Flow

The Vortex Induced Vibration (VIV) of a cylinder inclined to the incoming flow is not studied as extensively as the normal-incidence case. For a rigid inclined cylinder, it is believed that the cylinder behaves similarly to a vertical one if the component of the flow velocity normal to the cylinder axis is considered. We investigate the extent to which this assumption is valid by conducting a series of experiments on a flexibly mounted cylinder placed inclined to the incoming flow with various angles of inclination in a Reynolds number range of 500 - 10,000. The cylinder, mounted on springs, is placed in the test section of a recirculating water tunnel, and for each angle of inclination, we increase the flow velocity gradually, and measure the displacement and frequency of the resulting vibrations. We examine how various angles of inclination result in various lock-in regions (large-amplitude vibrations) and we determine the critical angle of inclination beyond which the axial component of the flow velocity will have a non-negligible influence on the observed vibrations.   

Vortex dislocations in the wake of a circular cylinder

Cross flow over complex cylindrical geometries, such as cylinders with discontinuities in diameter, results in non-uniform wake vortex shedding with complex vortex interactions. In the present study, the development of vortex dislocations in the wake of a circular cylinder is investigated. A dual-step circular cylinder geometry is employed, which consists of a large-diameter cylinder placed at the midspan of a small-diameter cylinder. In a uniform flow, wake development depends primarily on the Reynolds number (Re$_{D})$, the ratio of the large cylinder diameter (D) to the small cylinder diameter (d), and the aspect ratio of the large cylinder (L/D). Experimental investigations are performed for Re$_{D}$=1080, D/d=2, and 0.2$\le $L/D$\le $2.0 in a water flume facility utilizing flow visualization, laser Doppler velocimetry, and particle image velocimetry. Also, direct numerical simulations are performed for a laminar vortex shedding regime, where, based on previous studies, interactions between large-scale vortical structures are expected to be similar to those observed in turbulent wakes. The results show that the large cylinder induces vortex dislocations that are manifested by half-loop vortex connections forming between consecutive small cylinder vortices. The remaining small cylinder vortices form vortex connections across the wake of the large cylinder. The dislocations occur at a distinct frequency, which decreases with decreasing L/D.   

Nonlinear restoring forces in vortex-induced vibration

When studying vortex-induced vibration of a rigid circular cylinder, almost all experimental and computational studies involve the cylinder being supported by linear springs. However, there are cases in which we may be interested in the VIV response of a cylinder supported by nonlinear springs. A system with nonlinearities in the restoring force has the potential to increase the amplitude response envelope, critical to the success of aero-vibrating energy harvesters. On the other hand, designing nonlinear restoring forces to decrease the amplitude response may lead to structures more able to withstand flow-induced vibration. In addition, adding nonlinear terms to the restoring force on a rigid cylinder might be used to simulate higher-order dynamics of long, elastic marine cables. To experimentally observe the effects of nonlinear springs on flow-induced vibration, we apply a novel approach that lets us parametrically control the nature of the springs and the strength of the nonlinearities. The technique, called Cyber-Physical Fluid Dynamics, uses a force-feedback control system to simulate arbitrary forces on a submerged body [the details of this system were shown in the APS presentation of Mackowski \& Williamson (2010)]. We present results using this technique to explore the amplitude response of a circular cylinder in a crossflow.   

The flow around the node to anti-node transition of an oscillating flexible cylinder

The vortex dynamics in the wake of cylinders is a topic of interest, for its implications in engineering since the forties. Most of the work has been done with stationary cylinders or with oscillating rigid cylinders when they are elastically mounted. If the cylinders are flexible, not only the structural dynamics become more complex, but the fluid dynamics around the cylinder are much more complicated. We study the flow around a flexible cylinder when oscillating in its first or second structural mode. An experimental set-up allows producing forced oscillations on the model, in a way that mode number, oscillating frequency and amplitude can be controlled. Experiments were conducted in a motorised towing tank, for a wide range of towing speeds, frequencies and amplitudes. Digital Particle Image Velocimetry (DPIV) was used to quantify the flow and to investigate the flow structures and vortex modes around the cylinder. The interest was given to the extreme amplitude regions and to the node to anti-node transitional regions.   

The Effect of Shape on the Wake of Low-Aspect-Ratio Wall-Mounted Obstacles

Wall-mounted bodies in boundary layer flows are ubiquitous in nature and engineering applications. We evaluate the role of shape on the wakes around three different low-aspect-ratio wall-mounted obstacles in shallow boundary-layer flow: semi-ellipsoids with the major axis of the base ellipse aligned in the transverse and streamwise directions, and a sphere. Despite their geometric simplicity, the obstacles create extremely complex, highly three-dimensional and unsteady flow fields for which the transport mechanisms of momentum and scalars are still not well-understood. All three obstacles have the same height and the aspect ratios considered are 0.67, 0.89 and 1, respectively. DPIV was used to interrogate the flow. Streamwise structures observed in the mean wake include tip, base, and horseshoe vortex pairs, which vary significantly in strength with changes in obstacle geometry. Significant variation in the strength of these structures with streamwise location suggests a complex connectivity with the mean spanwise arch structure in the near wake. The three-dimensional topology of the mean wake will be discussed.   

Session L23: Low Re Number Aerodynamics

Spanwise drag variation on low Re wings -- revisited

Aerodynamic performance measurement and prediction of airfoils and wings at chord Reynolds numbers below $10^5$ is both difficult and increasingly important in application to small-scale aircraft. Not only are the aerodynamics strongly affected by the dynamics of the unstable laminar boundary layer but the flow is decreasingly likely to be two-dimensional as Re decreases. The spanwise variation of the flow along a two-dimensional geometry is often held to be responsible for the large variations in measured profile drag coefficient. Here we measure local two-dimensional drag coefficients along a finite wing using non-intrusive PIV methods. Variations in $C_{d} (y)$ can be related to local flow variations on the wing itself. Integrated values can be compared with force balance data, and the proper description of drag components at low Re will be discussed.   

Exploration of the Relationship Between Wake Vortex Parameters and Thrust Force on Oscillating Airfoils Using a Vortex Array Model

Recently, we demonstrated the ability of a simple model, based on an array of finite-core Gaussian vortices, to accurately reproduce the unsteady velocity field in the wake of, and drag/thrust force acting on harmonically/non-harmonically pitching airfoils. In the present work, this model is employed to explore how the thrust force varies with wake vortex parameters; i.e. circulation, core radius and streamwise/cross-flow spacing of the vortices. Insight from this investigation will be helpful to draw links between trailing-edge flexibility and the detailed process of generation of wake vortices. Such links may have the potential for providing a path towards a rational, yet efficient, approach for tailoring trailing-edge flexibility to obtain desirable force characteristics for flapping-wings Micro Air Vehicles.   

Vortex arrangement in the wake of rigid and flexible rapidly pitching airfoils at low Reynolds number

An experimental investigation of the wake of an airfoil undergoing rapid pitch oscillation is conducted in a water tunnel at a chord Reynolds number of about 2000. ~Flow visualization is utilized to characterize the vortical patterns in the wake of the airfoil, which is constructed from a NACA 0036 profile fitted with an extended trailing edge with controllable flexibility. The spatial configuration of the vortices is extracted in terms of streamwise and cross-flow spacing over a range of pitching frequencies and amplitudes. We discuss how different levels of flexibility alter the vortex spacing parameters and the conditions under which the traditional Karman vortex pattern, corresponding to a wake profile, changes to the reverse Karman pattern associated with a jet profile.   

Effects of fluid behavior around low aspect ratio, low Reynolds number wings on aerodynamic stability

The innovation of micro aerial vehicles (MAVs) has brought to attention the unique flow regime associated with low aspect ratio (LAR), low Reynolds number fliers. The dominant effects of developing tip vortices and leading edge vortices create a fundamentally different flow regime than that of conventional aircraft. An improved knowledge of low aspect ratio, low Reynolds number aerodynamics can be greatly beneficial for future MAV design. A little investigated but vital aspect of LAR aerodynamics is the behavior of the fluid as the wing yaws. Flow visualization experiments undertaken in the group for the canonical case of varying AR flat plates indicate that the propagation of the tip vortex keeps the flow attached over the upstream portion of the wing, while the downstream vortex is convected away from the wing. This induces asymmetric, destabilizing loading on the wing which has been observed to adversely affect MAV flight. In addition, experimental load measurements indicate significant nonlinearities in forces and moments which can be attributed to the development and propagation of these vortical structures. A non-dimensional analysis of the rigid body equations of motion indicates that these nonlinearities create dependencies which dramatically change the conventional linearization process. These flow phenomena are investigated with intent to apply to future MAV design.   

The Effects of AR on Membrane Wing Performance in Low Re Flight

There is increased interest in the design of micro air vehicles (MAVs) due to their military reconnaissance and surveying capabilities. Research has shown that the use of membrane wings in low Reynolds number flight results in performance characteristics that, when compared to rigid wing counterparts of similar geometry, are beneficial. An experimental study was performed to determine if the benefits of membrane wings change when AR is decreased. The membrane wings used silicon rubber affixed to aluminum frames of repeated cell geometry. The wings tested employed 1, 3, 5 and 9 cells and had ARs of 0.9, 2.6, 4.1, and 4.33 respectively. Measurements of lift and drag at a Reynolds number of 49,000 were acquired over a range of angles of attack. Vibration frequencies of the membranes were obtained via high-speed imagery. Comparisons of lift and drag data for the flat plates and membrane wings showed that the membrane wings with ARs of 0.9 and 2.6 did not show the same performance benefits as the higher AR membrane wings.   

Volumetric Three-Component Measurements of the Flowfield around Periodically Cambered Plates

The small size and low speed of the micro aerial vehicles (MAVs) place them in the low Reynolds number (Re) regime. The performance of conventional airfoils severely deteriorates at low Reynolds numbers. Therefore, unconventional wing designs are necessary to meet the operational requirements of the MAVs. Periodically cambered plates with an aspect ratio of five (AR = 5) were constructed for flowfield and performance measurements. Three-dimensional three-component (3D3C) flowfield measurements were carried out at a Reynolds number of 28,000 at different angles of attack. The locations of separation, transition and reattachment are estimated based on the mean velocities and Reynolds shear and normal stresses in the streamwise, spanwise and wall-normal directions. The effects of the tip vortices on the three-dimensionality of the reattachment line are resolved by the 3C3C measurement technique. Additionally, the effects of the cell size on the separation and reattachment locations are investigated. The results also include details about the vorticity about the X, Y and Z axes.   

Dynamics of Spanwise Vorticity on a Rotating Flat Plate

Leading-edge vortex (LEV) structures were examined using phase-locking digital particle image velocimetry for two rotating flat plates with aspect ratios of 2 and 4. The plates were accelerated uniformly for approximately 45\r{ } to a constant rotational speed. Reynolds numbers of 4,000, 8,000, and 16,000 were investigated. The flow field was measured in chordwise planes at two spanwise positions, while varying angle of attack and azimuthal position of the plate. The results show a concentrated, stationary vortex structure at the leading-edge of the plate. The strength of the leading edge vortex (LEV) was found to vary with azimuthal position, Reynolds number, and angle of attack. The time variation in LEV strength is studied using a control volume analysis taking into account in-plane and out-of-plane vorticity fluxes as well as interactions with opposite-sign vorticity generated beneath the LEV on the plate surface.   

Vortex Shedding vs. Thrust Production for Free-to-Pivot Flat Plates

As an abstraction of flapping-wings, we consider flat plates in rectilinear motion, with the leading edge undergoing periodic oscillation, and the plate left free to pivot about its leading edge, between incidence angle limits of $\pm $45\r{ }. Measurements include thrust production and resistive force, with leading edge and trailing edge vortices visualized by dye injection, conducted in a water tunnel operated here as a towing tank. Imposed acceleration of the plate's leading edge produces a rotational motion followed by a translational phase at constant incidence angle, and a reverse rotation at the semi-stroke extremum. Varying aspect ratio from 3.4 to nominally 2D, neither thrust nor resistive force evince an aspect ratio dependency. Reynolds number does not effect flow development or force production across 5000 $<$ Re $<$ 25000. Investigating the conjecture that imposed acceleration stabilizes the leading edge vortex, we find no difference across a range of acceleration profiles. The dominant parameter affecting thrust production is the plate stroke to chord ratio, with values of $\sim $6 and above being most favorable. Further, as a simplification of aeroelastic effects conducted with otherwise rigid plates, we consider a plate sliced spanwise and thus forming two hinged plates. This produces both lower thrust and resistive force than in the single-plate case, resulting in no improvement in hovering figure of merit, which amongst all cases peaks at $\sim $ 0.3.   

Fluid Structure Interactions on an Electro-Elastomer Membrane Wing

Wing flexibility is an important aspect of many natural flyers that has been demonstrated to have several specific aerodynamic benefits. An engineering abstraction of flexibility in wings is to use an extensible membrane stretched over a rigid frame. A key aspect of a membrane wing's performance is its tension as that will dictate how far it can stretch and its natural vibrational frequency. In this work we use a dielectric elastomer membrane, whose ability to stretch is a function of a voltage applied across it. The membrane is adhered to an elliptical planform wing which was placed in the freestream of an open jet wind tunnel. Measurements of the aerodynamic performance, membrane shape and flow field over the wing have been acquired as a function of angle of attack and voltage across the elastomer independently as well as synchronously. These measurements demonstrate how the membrane's characteristics alter the flow over it and translate to the generation of aerodynamic forces. These characteristics are studied in terms of both the static deflection increasing the wings camber as well as the time dependent excitation through the membrane's vibrations.   

Fluid and Structure Dynamics of Flow over a Membrane Wing

The coupled effect of flow induced membrane deformations and their return influence on the flow are investigated. Multi-cell wings are made by adhering heated, thin Silicone membranes to 2.7 percent thick, rectangular aluminum frames with rigid leading edge and battens. Time-resolved flow and structure deformations are measured by synchronized acquisition of high-speed, two-component Particle Image Velocimetry (PIV) and stereoscopic Digital Image Correlation (DIC). Mean and instantaneous effects are studied at a chord based Reynolds number of 48,000, while metrics are compared for membrane cell size of aspect ratio 1 and 0.5. Two PIV measurement fields of view are employed to study flow over the membrane surface as well as that of the near wake. Power spectral density and correlation techniques will be utilized, along with analysis of membrane mean deformation and rms fluctuation behavior to better understand the fluid-structure interactions. The effects of membrane behavior on flow separation, shear layer size and location, along with vorticity will be analyzed in comparison to flow over a similar geometry flat plate.   

Falling Maple Seed: The mechanism for its spin

A maple seed falls in a characteristic downward spiral. One explanation of its spinning motion is the auto-rotational effect. As the seed falls, the aerodynamic torque on the feather will cause it to spin like a wind-mill. However, the film of a falling seed shows that its spinning motion precedes the steady descent. And surprisingly, the seed with little feather can also spin. We experimentally quantify the kinematics of falling seeds with different shapes. The analysis of the coupling between the rigid body dynamics and the aerodynamics offers a new explanation for the cause of the spin.   

Session L24: Biofluids: General I

Meshfree Computations for Flow Pumping in a Microchannel Inspired by Insect Physiological Systems

The present study is inspired by pumping mechanisms observed in physiological systems in insects that use multiple contractions to transport fluid. A meshfree computational method is used to solve for the 2D viscous flow in a microchannel at low Reynolds number. The channel is assumed to have a large aspect ratio and localized multiple contractions from the upper wall. These contractions are allowed to move with or without time (phase) lags with respect to each other. The flow development and structures induced by these wall contractions are obtained at various snapshots in the collapse cycle. The effect of the contraction amplitudes and time-lags between its individual prescribed motion protocols on the flow variables and on the time-averaged net flow over a complete cycle of wall motions is studied. The meshfree computational approach presented here is based on the method of fundamental solutions (MFS) which is considered to be an efficient numerical technique for solving elliptic boundary value problems (BVP) such as the Stokes equations. This class of numerical methods uses a set of singularized force elements (Stokeslets) which are distributed according to the method of collocations with unknown strengths. The Stokeslets' strengths are then calculated by imposing the appropriate boundary conditions and solving the resulting system of equations. The flow motions induced by these point forces are then computed by the principle of superposition.   

Butterfly proboscis: natural combination of a drinking straw with a nanosponge

The ability of Lepidoptera, or butterflies and moths, to drink liquids from rotting fruit and wet soil, as well as nectar from floral tubes, raises the question of whether the conventional view of the proboscis as a drinking straw can account for the withdrawal of fluids from porous substrates or of films and droplets from floral tubes. We discovered that the proboscis promotes capillary pull of liquids from diverse sources due to a hierarchical pore structure spanning nano- and microscales. X-ray phase-contrast imaging reveals that Plateau instability causes liquid bridges to form in the food canal, which are transported to the gut by the muscular sucking pump in the head. The dual functionality of the proboscis represents a key innovation for exploiting a vast range of nutritional sources. A transformative two-step model of capillary intake and suctioning can be applied not only to butterflies and moths but also potentially to vast numbers of other insects such as bees and flies.   

Bubbles of Metamorphosis

Metamorphosis presents a puzzling challenge where, triggered by a signal, an organism abruptly transforms its entire shape and form. Here I describe the role of physical fluid dynamic processes during pupal metamorphosis in flies. During early stages of pupation of third instar larvae into adult flies, a physical gas bubble nucleates at a precise temporal and spatial location, as part of the normal developmental program in Diptera. Although its existence has been known for the last 100 years, the origin and control of this ``cavitation'' event has remained completely mysterious. Where does the driving negative pressure for bubble nucleation come from? How is the location of the bubble nucleation site encoded in the pupae? How do molecular processes control such a physical event? What is the role of this bubble during development? Via developing in-vivo imaging techniques, direct bio-physical measurements in live insect pupal structures and physical modeling, here I elucidate the physical mechanism for appearance and disappearance of this bubble and predict the site of nucleation and its exact timing. This new physical insight into the process of metamorphosis also allows us to understand the inherent design of pupal shell architectures in various species of insects.   

Contraction driven flow in the extended vein networks of \textit{Physarum polycephalum}

The true slime mold \textit{Physarum polycephalum} is a basal organism that forms an extended network of veins to forage for food. \textit{P. polycephalum} is renown for its adaptive changes of vein structure and morphology in response to food sources. These rearrangements presumably occur to establish an efficient transport and mixing of resources throughout the networks thus presenting a prototype to design transport networks under the constraints of laminar flow. The physical flows of cytoplasmic fluid enclosed by the veins exhibit an oscillatory flow termed ``shuttle streaming.'' The flow exceed by far the volume required for growth at the margins suggesting that the additional energy cost for generating the flow is spent for efficient and/or targeted redistribution of resources. We show that the viscous shuttle flow is driven by the radial contractions of the veins that accompany the streaming. We present a model for the fluid flow and resource dispersion arising due to radial contractions. The transport and mixing properties of the flow are discussed.   

Fluid Flow of Vitrectomy

Vitrectomy is a microsurgical technique to remove the vitreous gel from the vitreous cavity. Due to the viscoelastic nature of the vitreous gel, its complex fluidic behavior during vitrectomy affects the outcome of the procedure. Therefore, the knowledge of such behavior is essential for better designing the vitrectomy devices, such as vitreous cutters, and tuning the system settings such as port and shaft diameters, infusion, vacuum, and cutting rate. We studied the viscoelastic properties of porcine vitreous humor using a stressed-control shear rheometer and obtained its relaxation time, retardation time, and shear-zero viscosity. We performed a computational study of the flow in a vitreous cutter using the viscoelastic parameters obtained from the rheology experiments. We found significant differences between the modeled vitreous gel and a Newtonian surrogate fluid in the flow behavior and performance of the vitreous cutter. Our results will help in understanding of the vitreous behavior during vitrectomy and providing guidelines for new vitreous cutter design.   

Leonardo's branching rule in trees: How self-similar structures resist wind

In his notebooks, Leonardo da Vinci observed that ``\emph{all the branches of a tree at every stage of its height when put together are equal in thickness to the trunk},'' which means that the total cross-sectional area of branches is conserved across branching nodes. The usual explanation for this rule involves vascular transport of sap, but this argument is questionable because the portion of wood devoted to transport varies across species and can be as low as 5\%. It is proposed here that Leonardo's rule is a consequence of the tree skeleton having a self-similar structure and the branch diameters being adjusted to resist wind-induced loads. To address this problem, a continuous model is first considered by neglecting the geometrical details of branching and wind incident angles. The robustness of this analytical model is then assessed with numerical simulations on tree skeletons generated with a simple branching rule producing self-similar structures.   

Aquatic vegetation in flow: To buoy or not to buoy

Previous studies show that the flexural stiffness and buoyancy of many species of aquatic vegetation change in response to hydrodynamic conditions. We present a theoretical and experimental study that describes the flow-induced reconfiguration of aquatic vegetation across the natural range of vegetation buoyancy and stiffness. We show how posture and drag depend on two dimensionless parameters that represent the relative magnitudes of the hydrodynamic forcing, and the restoring forces due to stiffness and buoyancy. Reconfiguration leads to a transition away from the classical quadratic drag law. We present scaling laws that describe the relationship between drag and velocity for both stiffness- and buoyancy-dominated reconfiguration. Our results may explain the morphological plasticity observed for aquatic vegetation.   

Modeling tumor growth in a complex evolving confinement using a diffuse domain approach

Understanding the spatiotemporal evolution of tumor growth represents an essential step towards engineering effective treatment for cancer patients. At the macroscopic scale, various biophysical models describing tumors as continuum fluids have been constructed, particularly on a Cartesian grid, where efficient numerical schemes are available to analyze the model for general tumor behaviors in a relatively unconfined space. For practical problems, however, tumors are often found in a confined sub-domain, which can even be dilated and distorted by the growing tumor within. To study such tumors, we adopt a novel diffuse domain approach that enables us to adapt a model to an evolving sub-domain and formulate the modified problem on a Cartesian grid to utilize existing numerical schemes. To demonstrate this approach, we adapt a diffuse-interface model presented in Wise et al. [2008, Three-dimensional multispecies nonlinear tumor growth - I Model and numerical method, J. Theor. Biol. 253, 524-543] to simulate lymphoma growth in a lymph node structure.   

The mechanics of pollination by wind: is anemophily aeroelastically optimized for reproduction?

Approximately 10 percent of plant species rely on wind for pollination (anemophily). These include many taxa of economic importance: e.g. cultigens such as wheat and maize; species like grasses and ragweed that trigger allergies; and the conifers, our most important species for the forest industry in the mid- latitudes. It has often been assumed that anemophily is an inefficient mechanism compared to animal pollination (zoophily), but very little is known about the forces and micromechanics that deliver pollen grains into wind streams. Here we ask a fundamental question: is anemophily optimized for pollen shedding? In this talk, we focus on an as-yet rudimentary theory of turbulence- initiated pollen shed that models the pollen-bearing stamen as an aeroelastic oscillator. Ongoing experiments with anemophilous and zoophilous flowers excited by shakers are analyzed to extract values of damping ratios, adhesion forces and flexural rigidities. Finally, the anatomical differences between anemophilous and zoophilous species are evaluated using a dimensionless number that measures the ratio of adhesion to aeroleastic forces.   

Universality of osmotically driven sap-flow in plants

Since Ernst M\"{u}nch in the 1920s proposed that sugar transport in the phloem vascular system of plants is driven by passive osmotic pressure gradients, it has been strongly debated whether this hypothesis can account even for long distance translocation. Recently, it was shown that theoretical optimization of the M\"{u}nch mechanism leads to surprisingly simple predictions for the dimensions of the phloem sieve elements in relation to those of the plants [Jensen et. al., J. Roy. Soc. Interface \textbf{8}, pp. 1155--1165 (2011)]. We show that the theoretical results are very insensitive to the details of the sugar-loading (in leaves) and unloading (in shoots or roots) and can even be obtained from a simple coupled resistor model. We have compiled anatomical data for a wide group of plants and find good agreement with theory, even for conifer trees, in which the sugar translocation is substantially slower than hardwood trees.   

Session L25: Particle-laden Flows IV

Simulated tornado debris tracks: implications for inferring corner flow structure

A large collection of three-dimensional large eddy simulations of tornadoes with fine debris have been recently been performed as part of a longstanding effort at West Virginia University to understand tornado corner flow structure and dynamics. Debris removal and deposition is accounted for at the surface, in effect simulating formation of tornado surface marks. Physical origins and properties of the most prominent marks will be presented, and the possibility of inferring tornado corner flow structure from real marks in the field will be discussed.   

Numerical simulation of a bidisperse turbidity current interacting with a Gaussian bump

We study a particle-laden lock-exchange current interacting with a Gaussian bump by means of DNS simulations. Our software package TURBINS employs an immersed boundary implementation of the Boussinesq Navier-Stokes equations for the fluid motion, coupled to transport equations for the particle concentration fields. The suspension includes two particle sizes with a settling velocity ratio of 10. As the current travels over the bottom topography, we record instantaneous deposit profiles and wall shear stress contours. As the current impinges on the obstacle, it becomes strongly three-dimensional. Comparison of the final deposit profiles near the Gaussian bump against the case of a flat surface shows a smaller influence of the topography on the fine particles than on the coarse ones. Due to lateral deflection, deposition generally decreases near the bump, while increasing away from it. Some distance downstream of the obstacle, the deposit profiles lose their memory of the bump and become nearly uniform again. Instantaneous wall shear stress profiles are employed in order to estimate the critical conditions at which bedload transport and/or particle resuspension can occur in various regions.   

Modelling Submarine Turbidity Currents

When a large scale pyroclastic flow enters the ocean it leads to the spreading of sediment across the deep ocean through particle laden flows known as turbidity currents. Turbidity currents are driven by gravitational forces associated with a density difference caused by the presence of suspended particles. This generates a flow which transports the suspended particles, but which progressively slows as they sediment to the underlying boundary. We adopt a shallow layer model in which vertical accelerations are neglected and employ a three equation system that expresses the conservation of fluid and particulate mass and formulates a balance of momentum for a current flowing down an incline. Importantly we include the effects of entrainment of surrounding fluid into the flow. Solutions are constructed using numerical means and they reveal the strong dependence of run out length on the rate of entrainment. Further, the prediction of the distribution of the deposit from the flow compares favourably with field data from the July 2003 event from Soufri\`{e}re Hills volcano, Montserrat.   

Convective instability in sedimentation

We investigate the convective sedimentation in a stably stratified saltwater using linear stability analysis and 3D direct numerical simulation. We consider sediment particle with grain diameter in the range of 1.5 to 60 $\mu$m. Equilibrium Eulerian approach and dilute flow assumption are adopted to simplify the governing equations of the two-phase system (Balachandar and Eaton 2009, Annul Rev. Fluid Mech.). A semi-empirical closure of particle diffusivity due to long-range interaction is adopted (Segre et al. 2007, Phys. Rev. Lett.). For a fixed salt diffusivity, the particle phase can act as either slow or fast diffusing agent in a double-diffusive system depending on the particle diameter. Additionally, the settling-driven mechanism can also trigger instability. Linear stability analysis is carried out as the guideline for 3D numerical simulation. Simulation results indicate different finger patterns for different particle settling velocity and sediment concentration. For fine particle, where the double-diffusive mechanism plays an important role, the instability is enhanced by the settling. The finger size is on centimeter scale and the finger pattern is more nonlinear and asymmetric. For large particle, the interfacial instability appears long after the particles pass the density interface induced by salt where Rayleigh-Taylor instability takes place and finger pattern is more symmetric. Fully nonlinear analysis with 3D direct numerical simulations will be presented in the meeting.   

Particle jet formation during explosive dispersal of solid particles

Previous experimental studies have shown that when a layer of solid particles is explosively dispersed, the particles often develop a non-uniform spatial distribution. The instabilities within the particle bed and at the particle layer interface likely form on the timescale of the shock propagation through the particles. The mesoscale perturbations are manifested at later times in experiments by the formation of coherent clusters of particles or jet-like particle structures, which are aerodynamically stable. Experiments have been carried out in spherical and cylindrical geometry to investigate the influence of particle diameter and density and the ratio of particle to high explosive mass on the relative tendency for instabilities to develop in the expanding particle cloud. The number of particle jets that form tends to scale with a particle compaction Reynolds number corresponding to the ratio of inertial to frictional forces of the particle system. Below a critical Reynolds number, the expanding particle cloud remains stable.   

Shear stress and particle removal measurements of a turbulent air jet impinging normally upon a surface

When a jet of air impinges normally upon a surface, it imposes a shear stress parallel to the wall in all directions from the impingement point. Particle removal from that surface is assumed to be mainly due to that imposed shear stress. ~But that shear stress has been difficult to measure and has, in the past, been inferred from particle removal rates.~ Here we make a basic measurement of mean shear stress imposed upon a planar wall by a normally-impinging turbulent air jet using the technique of oil-film interferometry. The resulting shear-stress distribution is then compared with the removal rates of latex microspheres from a planar glass surface as a function of the distance from jet impingement normalized by the height of the nozzle above the surface.~ The particle removal experiments are carried out with sparse (few particle collisions) particle distributions. These experiments show that the efficiency of particle removal is directly but not linearly related to the imposed shear stress. A distinct shear stress threshold was found, below which little or no particle removal occurred.   

Large-Scale Simulations of Realistic Fluidized Bed Reactors using Novel Numerical Methods

Turbulent particle-laden flows in the form of fluidized bed reactors display good mixing properties, low pressure drops, and a fairly uniform temperature distribution. Understanding and predicting the flow dynamics within the reactor is necessary for improving the efficiency, and providing technologies for large-scale industrialization. A numerical strategy based on an Eulerian representation of the gas phase and Lagrangian tracking of the particles is developed in the framework of NGA, a high- order fully conservative parallel code tailored for turbulent flows. The particles are accounted for using a point-particle assumption. Once the gas-phase quantities are mapped to the particle location a conservative, implicit diffusion operation smoothes the field. Normal and tangential collisions are handled via soft-sphere model, modified to allow the bed to reach close packing at rest. The pressure drop across the bed is compared with theory to accurately predict the minimum fluidization velocity. 3D simulations of the National Renewable Energy Lab's 4-inch reactor are then conducted. Tens of millions of particles are tracked. The reactor's geometry is modeled using an immersed boundary scheme. Statistics for volume fraction, velocities, bed expansion, and bubble characteristics are analyzed and compared with experimental data.   

Large-Scale Eulerian-Lagrangian Simulations of Turbulent Particle-Laden Riser Flows

Turbulent gas-particle flows play fundamental roles in a wide range of technical systems. Understanding and predicting particle-laden turbulent flows is key to ensuring optimal performance and improving the design of devices such as fluidized bed reactors. In this work, a Lagrangian description of the particles is combined with state-of-the-art schemes for high-fidelity turbulence simulations in order to enable predictive numerical modeling of particle cluster formation in turbulent riser flows. The simplified riser configuration of He et al is used to answer several key questions regarding meso-scale structures in risers, in particular regarding (1) the onset of instability, especially in the limit of low volume fractions, (2) the role played by the drag model formulation (in particular the dependence of the drag law on void fraction) and (3) the collision model in the formation and dynamics of particle structures. Simulation results are compared with experimental results in terms of cluster size and shape, as well as gas and particle statistics. Then, a wall-free fully periodic configuration is considered and differences in cluster statistics are discussed.   

Porosity-Permeability Relations in Granular, Fibrous and Tubular Porous Media

A Voronoi diagram-based stochastic geometry generator was developed to generate porous media models of granular, fibrous and tubular types. By adjusting geometry parameters such as number of random seeds and width of channels between grains or radius of fibers/tubes, homogenous and isotropic models of porous media with specified porosity can be accurately generated. The relation of porosity to geometry parameters was proven to be repeatable, and additional manipulations on geometries were built in, including creation of anisotropy and heterogeneity. A parallelized Lattice Boltzmann simulator with nearly ideal speedup was developed and employed to study porosity-permeability relations. Simulation data obtained in the porosity range of 0.01-0.4 revealed that properly normalized permeability in tubular porous media is higher than that in the granular type when porosity becomes greater than 0.1, which can be explained by its more efficient use of the pore space to conduct the flow. Simulation data obtained from fibrous media in solid volume fraction range of 0.01-0.4 agreed with published results, and showed a rapid change with solid volume fraction in the dilute limit.   

Modeling enduring contact in Direct Numerical Simulations of incipient motion of granular beds

A boundary integral method for fast Direct Numerical Simulations of particle-laden flow on Cartesian grids is used here to model the incipient motion of particle beds forced by a steady current. The particle hydrodynamic force is determined numerically by resolving the flow around individual particles. Analytical lubrication force corrections are added during collisions when the interstitial gap becomes smaller than the grid step. The mechanical force normal and tangential to the contact between particles is modeled by a linear elastic-plastic law and a history dependent friction law, respectively. Resolving fluid-structure interaction effects during collisions is numerically expensive because the collision time scale is two orders of magnitude smaller than the maximum time step for numerical stability of the viscous flow. We improve the numerical efficiency with an acceleration-based control of the time step so that the maximum time step is used for enduring contacts with low particle acceleration. Quantitative comparison for sediment motion initiation is made with laboratory data.   

Session L26: Minisymposium: Cardiac Fluid Dynamics: Translating Fundamental Insights into Clinical Practice

How the heart works when it fills: what every fluid mechanician needs to know

The two principles that govern the diastolic (filling) phase of all human hearts are: ``constant volume pump'' and ``suction pump.'' The $\approx$ 850 ml volume of the pericardial sack decreases by only $\approx$ 40 ml by end systole. This requires that atrial-ventricular volumes simultaneously reciprocate and it underscores the pressure pump (systolic) and volume pump (diastolic) roles of the chambers. Of the 4 heart chambers -- ONLY the left ventricle actually serves as a systolic pressure pump. When the normal left ventricle initiates filling after mitral valve opening, it generates only a small (4mmHg) maximum atrioventricular pressure gradient (LVP$<$ LAP) while its pressure continues to decrease for about 100 msec while its volume increases (dP/dV$<$ 0). Because the chamber recoils faster than it can fill it is a suction (volume) pump. The purpose of diastole is to fill the chamber (mass transfer) in the fraction of a second available in order to maintain cardiac output. The streamlines entering through the 5cm$^2$ mitral valve initially have a blunt velocity profile and because mitral valve plane alignment is off-center relative to LV long axis, blood rapidly forms an asymmetric toroidal vortex whose formation time has been shown to depend on LV chamber parameters of stiffness, relaxation and load. Recent Lagrangian coherent structure (LCS) analysis of vortex ring growth in the LV reveals nature's elegant fluid mechanics based solution to the diastolic mass transfer problem. The intraventricular vortex also ``rinses'' the trabeculated inner surface of the heart thereby preventing formation of blood clots and facilitates mitral leaflet coaptation to minimize mitral valve regurgitation.   

Hypertrophic Cardiomyopathy (HCM): How Flow Analysis May Drive Medical Management and Surgical Approach

Hypertrophic Cardiomyopathy (HCM) is the most common inherited heart disease and occurs in 1 in 500 persons worldwide regardless of race, age and gender. It is the most common cause of sudden death in the young and also causes heart failure and cardiac arrhythmias. The primary anatomic abnormality is thickening of certain walls, or sometimes global thickening of the left or right ventricle. The patterns of thickening along with increased ventricular stiffness lead to suboptimal ventricular filling and inefficient ejection of blood from the ventricle. Treatment for HCM can be medical or surgical. The choice of therapy is driven by the presence and severity of outflow obstruction. Flow analysis could provide sophisticated information about outflow and inflow ventricular dynamics. These flow dynamics features may enable better medical choices and provide information that would allow superior surgical planning.   

Vortices formed on the mitral valve tips aid normal left ventricular filling

For the left ventricle to function as an effective pump it must be able to fill from a low left atrial pressure. However, this ability is lost in patients with heart failure. We investigated the fluid dynamics of the left ventricle filling by imaging the blood flow in patients with healthy and impaired diastolic function, using 2D phase contrast magnetic resonance imaging and we quantified the intraventricular pressure gradients and the strength and location of the formed vortices. We found that during early filling in normal subjects, prior to the opening of the mitral valve the flow moves towards the apex and subsequently at the time of the opening of the valve the rapid movement of the mitral annulus away from the left ventricle apex enhances the formation of a vortex ring at the mitral valve tips. Instead of being a passive byproduct of the process as was previously believed, this vortex ring facilitates filling by reducing convective losses and enhancing the function of the left ventricle as a suction pump. Impairment of this mechanism contributes to diastolic dysfunction, with the left ventricle filling becoming dependent on left atrial pressure, and eventually leading to heart failure.   

Multiscale modeling and surgical planning for single ventricle heart patients

Single ventricle heart patients are among the most challenging for pediatric cardiologists to treat, and typically undergo a palliative course of three open-heart surgeries starting immediately after birth. We will present recent tools for modeling blood flow in single ventricle heart patients using a multiscale approach that couples a 3D Navier-Stokes domain to a 0D closed loop lumped parameter network comprised of circuit elements. This coupling allows us to capture the effect of changes in local geometry, such as shunt sizes, on global circulatory dynamics, such as cardiac output. A semi-implicit numerical method is formulated to solve the coupled system in which flow and pressure information is passed between the two domains at the inlets and outlets of the model. A finite element method with outflow stabilization is applied in the 3D Navier-Stokes domain, and the LPN system of ordinary differential equations is solved numerically using a Runge-Kutta method. These tools are coupled via automated scripts to a derivative-free optimization method. Optimization is used to systematically explore surgical designs using clinically relevant cost functions for two stages of single ventricle repair. First, we will present results from optimization of the first stage Blalock Taussig Shunt. Second, we will present results from optimization of a new Y-graft design for the third stage of single ventricle repair called the Fontan surgery. The Y-graft is shown, in simulations, to successfully improve hepatic flow distribution, a known clinical problem. Preliminary clinical experience with the Y-graft will be discussed.   

Cardiac Hemodynamics in the Pathogenesis of Congenital Heart Disease and Aortic Valve Calcification

An improved understanding of the roles of hemodynamic forces play in cardiac development and the pathogenesis of cardiac disease will have significant scientific and clinical impact. I will focus on the role of fluid dynamics in congenital heart disease and aortic valve calcification. Congenital heart defects are the most common form of birth defect. Aortic valve calcification/stenosis is the third leading cause of adult heart disease and the most common form of acquired valvular disease in developed countries. Given the high incidence of these diseases and their associated morbidity and mortality, the potential translational impact of an improved understanding of cardiac hemodynamic forces is very large.   

Session L27: Minisymposium: The Fluid Dynamics of Geological CO2 Sequestration

Fluid dynamics of CO$_2$ sequestration

A means of reducing environmental damage due to anthropogenic emissions of carbon dioxide (CO$_2$) is through geological storage in porous reservoir rocks until well past the end of the fossil fuel era. Here we discuss the propagation and form of the buoyancy-driven propagation of multiphase CO$_2$-brine plumes bounded by an impermeable barrier or cap rock. Long-term containment of CO$_2$ is important, and we will quantify some of the risks due to leakage in this system. Finally, stable sequestration through capillary forces or through dissolution of CO$_2$ into the brine is greatly enhanced by mixing, which is often dominated by layered stratigraphy. Here we describe injection into a two-layered porous medium, and show the sensitive dependence of propagation and mixing on the input flux, Q. For two-layered systems we find that above a critical flux, Q$_C$, fluid injected at the base of a relatively low permeability layer preferentially flows in the more permeable upper layer leading to an overriding current, thus enhancing mixing. Finally, we apply these ideas to examine the storage of CO$_2$ within the Sleipner field, where CO$_2$ has been injected since 1996. The talk will be illustrated by some desktop experiments.   

Monitoring pressure evolution during geological CO$_2$ storage

Pressure build-up near the injection well is a critical factor limiting injection rates during CO$_2$ storage and leads to measurable deformation at the surface above the injection site. The radial solutions for pressure and saturation in two-phase compressible flow are self-similar and they illustrate that the pressure outside the two- phase region is comparable to single-phase flow. However, pressure dissipation into ambient rocks reduces lateral pressure propagation significantly. Pressure build-up also leads to surface deformation and provides a monitoring tool to invert for reservoir parameters. We formulate an inverse problem to infer the permeability distribution in a quasi-static poroelastic model. Here, we neglect two-phase flow and focus on pressure dissipation into ambient formations. The misfit between model and observations is minimized under the constraint of the poroelastic equations. A numerical study of injection into a deep layer illustrates the possibilities and limitations of retrieving lateral permeability variations from a coupled inversion.   

CO$_2$ migration and sequestration by combined capillary and solubility trapping: theory, experiments, and capacity estimates at the basin scale

The large-scale injection and storage of carbon dioxide (CO$_2$) into deep saline aquifers is a promising tool for reducing atmospheric CO$_2$ emissions to mitigate climate change. Success of geologic sequestration relies on trapping the buoyant CO$_2$, to minimize the risk of leakage into shallower formations through pre- existing wells, fractures or faults. However, traditional reservoir-simulation tools are currently unable to resolve the impact of small-scale trapping processes on fluid flow at the scale of a geologic basin. Here, we formulate a sharp-interface mathematical model for the post-injection migration of a CO$_2$ plume driven by groundwater flow in a sloping aquifer, subject to both capillary trapping and CO$_2$ dissolution by convective mixing. We develop semi-analytical solutions that elucidate the nontrivial interplay between the two trapping mechanisms, and how their synergetic action controls plume migration. We validate the theory by means of laboratory experiments with analogue fluids to study how convective mixing arrests the buoyant current. We use our findings to estimate the dimensionless rate of solubility trapping for several large saline aquifers in the United States, and assess the importance of solubility trapping in practice.   

Multiphase, multicomponent simulations and experiments of reactive flow, relevant for combining geologic CO$_2$ sequestration with geothermal energy capture

Understanding the fluid dynamics of supercritical carbon dioxide (CO$_2$) in brine- filled porous media is important for predictions of CO$_2$ flow and brine displacement during geologic CO$_2$ sequestration and during geothermal energy capture using sequestered CO$_2$ as the subsurface heat extraction fluid. We investigate multiphase fluid flow in porous media employing particle image velocimetry experiments and lattice-Boltzmann fluid flow simulations at the pore scale. In particular, we are interested in the motion of a drop (representing a CO$_2$ bubble) through an orifice in a plate, representing a simplified porous medium. In addition, we study single-phase/multicomponent reactive transport experimentally by injecting water with dissolved CO$_2$ into rocks/sediments typically considered for CO$_2$ sequestration to investigate how resultant fluid-mineral reactions modify permeability fields. Finally, we investigate numerically subsurface CO$_2$ and heat transport at the geologic formation scale.   

Practical applications of CO$_2$ flow modeling in commercial scale sequestration projects

We review various challenges related to modeling of CO$_2$ flow through porous media, in the specific context of commercial scale sequestration projects of multiple millions of tons per year. Proper understanding and modeling of the physics of rock- CO$_2$ and rock-brine interactions have dramatic implications for CO$_2$ plume spread, and the final ``fate'' of the injected CO$_2$. We demonstrate the practical relevance of these concepts on specific geologic sites that are currently being developed for commercial scale sequestration in the United States.   

Session L29: Low Reynolds Number Swimming in Shear Flow

Statics and dynamics of planar shearable filaments in viscous fluid: A Cosserat rod approach

Cilia and flagella are ubiquitous in biology as a means of motility and constitute one of the most incredible engineering works of nature. Their inner core, namely the axoneme, consists of a remarkable phylogenetically conserved cytoskeletal structure formed by an assembly of semifexible filaments interconnected by crosslinking proteins. As a result, the flagellum or cilium is not only capable to flexure under the action of an external load, but also to shear. The latter is however a consequence from the intricate elastic crosslinking proteins which causes the elastic bending to couple with shearing deformations, modifying dramatically the effective mechanical response of these bundles of filamentous polymers. We consider deformations of nonlinearly elastic slender rods immersed in a fluid, and analyse the differences between the elastic cross-link shear response and pure material shear resistance under the action of viscous dissipation. We show that pure material shearing effects from Timoshenko's beam theory or, equivalently, Cosserat Rod Theory are fundamentally different from elastic crosslink induced shear found in filament bundles, such as the axoneme.   

Drag reduction of a hairy disk

We investigate experimentally the hydrodynamics of a hairy disk immersed in a two-dimensional flowing soap film. Drag force is measured as a function of hair length, density and coating area. An optimum combination of these parameters yields a drag reduction of 17\%, which confirms previous numerical predictions of 15\% by Favier et al (2009). Flow visualization indicates the primary mechanism for drag reduction is the bending, adhesion and reinforcement of hairs trailing the disk, which reduces wake width and traps ``dead water.'' Thus, the use of hairy coatings can substantially reduce an object's drag while negligibly increasing its weight.   

Low Reynolds number swimming in a stratified fluid

Significant progress has been made in analyzing low-Reynolds number locomotion in homogeneous fluids. Even though many aquatic environments are influenced by vertical variations in density, the effects of stratification on the hydrodynamics of swimming of small organisms are very poorly understood. In this article, by using a squirmer model, we show that motility, energy expenditure, and nutrient uptake of small organisms in a density stratified fluid can be largely influenced due to buoyancy effects. Not only does the stratification suppress the swimming velocity, but it also enhances the nutrient uptake and the energy required for a squirmer to swim across pycnoclines.   

Evaluating Satiated Copepod Behavioral Responses to Thin Layer Flow Structure

Zooplankton exploit a variety of chemical and fluid mechanical cues in foraging, mate-seeking, and habitat partitioning contexts. To examine the influence of environmental cues on zooplankton aggregations in coastal marine thin layers, a laboratory thin layer mimic was built. The apparatus uses a laminar, planar jet (the Bickley jet) to produce ecologically-relevant layers of chemical (beneficial and harmful phytoplankton) and fluid mechanical (shear strain rate) cues for zooplankton behavioral assays. Particle image velocimetry (PIV) and laser-induced fluorescence (LIF) were employed to fully quantify the spatial structure of the chemical and fluid mechanical cues, ensuring a close match to \textit{in situ} conditions and allowing for investigations into threshold cue levels responsible for inducing behavioral responses. Evaluating the effect of hunger level on behavioral responses is particularly important for producing accurate individual-based simulations of zooplankton population dynamics. Behavioral assays with the calanoid copepod \textit{Temora longicornis} have produced digitized trajectories and, subsequently, path kinematics. Observed behaviors include increased turn frequency and decreased relative swimming speed, which result in increased residence time in the free jet shear layer. Cue-induced individual behaviors have the potential to produce population-scale aggregations.   

Bacterial Rheotaxis

Rheotaxis is the directed movement of an organism resulting from fluid velocity gradients, long studied in fish, aquatic invertebrates and spermatozoa. Here we show that rheotaxis also occurs in bacteria. Using controlled microfluidic shear flows, we demonstrate and quantify rheotaxis in \textit{Bacillus subtilis}. A mathematical model of a bacterium swimming in a shear flow is in good agreement with observations and reveals that bacterial rheotaxis results from a subtle interplay between velocity gradients and the helical shape of flagella, which together generate a torque that reorients the cell, altering its swimming direction. The magnitude of the observed rheotactic velocity is comparable to typical chemotactic velocities, suggesting that rheotaxis can interfere with bacterial processes based on directed motility, such as foraging and infection.   

Bacterial motility and chemotaxis in shear

Bacteria often exhibit directed motility (``taxis'') in response to gradients of dissolved resources, like nutrients or oxygen. While we have a detailed understanding of chemotaxis in quiescent environments, it has been largely overlooked how this behavior is affected by fluid flow, despite the ubiquity of flow in bacterial habitats. Here we present experiments on aerotaxis (attraction to dissolved oxygen) of \textit{Bacillus subtilis} in controlled shear flows. Using novel microfluidic devices we expose bacterial suspensions to steady oxygen gradients, with independent control over shear rates. From single-cell trajectories and the spatial distribution of bacteria, we show that the cell rotation induced by shear reduces the aerotactic performance, demonstrating that hydrodynamic conditions affect bacterial fitness.   

Chemotactic Motility of Sperm in Shear

Chemical gradients are utilized by plants and animals in sexual reproduction to guide swimming sperm cells toward the egg. This process (``chemotaxis''), which can greatly increase the success of fertilization, is subject to interference by fluid flow, both in the bodily conduits of internal fertilizers (e.g. mammals) and in the aquatic environment of external fertilizers (e.g. benthic invertebrates). We studied the biomechanics of chemotaxing sea urchin spermatozoa using microfluidic devices, which allow for the precise and independent control of attractant gradients and fluid shear. We captured swimming trajectories and flagellar beat patterns using high-speed video-microscopy, to detect chemotactic responses and measure the effect of fluid forces on swimming. This work will ultimately help us to understand how swimming sperm cells actively navigate natural chemoattractant gradients for successful fertilization.   

Enhanced vertical mixing by grass shrimp (Palaemenets) in a linearly stratified fluid

Laboratory experiments investigated the vertical mixing generated by grass shrimp (Palaemenets) in a linearly stratified tank (50x50x70 cm). The linear stratification ($N$~=~0.19~s$^{-1})$ becomes homogeneous in approximately two days, much faster than if only molecular diffusion was at play. The density evolution in time agrees well with the solution of the diffusion equation for values of enhanced $k_{s}$ (2.0 10$^{-2 }$cm$^{2}$/s when 100 shrimp are present and $k_{s}$~=~1.0 10$^{-2 }$cm$^{2}$/s with 50 shrimp) when compared to the molecular diffusivity of salt $k_{s}$~=~1.3 10$^{-5}$ cm$^{2}$/s. Hence, the laboratory experiments suggest that the enhanced vertical mixing generated by the presence of grass shrimp in a linearly stratified ambient fluid has a diffusive behavior with a diffusivity enhanced by 3 orders of magnitude when compared to the molecular diffusivity of salt.   

Bacterial locomotion in a wall bounded shear flow

Statistically robust experimental observations on swimming characteristics of bacteria in a wall bounded shear flow are crucial for understanding cell attachment and detachment, interfacial rheology during the initial formation of a biofilm. We combined microfluidics and holography to measure 3-D trajectories of \textit{E. coli} (AW405), subjecting to a carefully controlled shear flow. Experiments are conducted in a straight micro-channel of 40x3x0.2 mm, latter being the depth, with the maximum shear rates up to 200 s$^{-1}$. Holographic microscopic movies recorded at 40X magnification and 15 fps are streamed in real time to a data acquisition computer for an extended period of time ($>$20 min) that allows us to examine long term shear responses. Three-dimensional locations and orientations of bacterial are extracted with a resolution of 0.185 $\mu $m in lateral directions and 0.5 $\mu $m in the wall normal direction. The 3-D trajectories are tracked by an in-house developed particle tracking algorithm. Over thousand 3-D trajectories over a sample volume of 380$\times $380$\times $200 $\mu $m have been obtained. On-going analysis focuses on the effects of flow on cell migration and attachment near a sheared surface.   

Bacteria Aggregation in a Steady Vortical Flow

The interaction between microorganisms and flow field is an important, yet complicated topic that affects the design of biological reactors, marine ecological processes, and biofilm formation in porous media. Vortical structures and secondary flows are inherently present in porous media despite small Reynolds numbers. Our experimental results show that bacteria in a steady vortical flow aggregate and subsequently form biofilm streamers in a microfluidic system. The combined effects of shape, motility and the vortical background flow contribute to this fast bacteria aggregation.