Session R1: Geophysical Flows: General II

Evolution of shallow, horizontal shear layers with a horizontal density contrast

Shallow coastal ocean flows frequently involve strong horizontal shear layers in combination with a horizontal density gradient. In the absence of the density contrast, the flow undergoes the classic Rayleigh instability leading to the roll-up of the shear layer into vertical vortices. The density contrast results in a transverse gravity-driven tilting of the interface resembling a lock-exchange. The evolution of this rapid buoyancy-induced tilting of horizontal shear is explored with laboratory experiments performed in a new open-channel flume with a flapping, splitter-plate entrance. Measurements of the downstream evolution are made with co-incident PIV and LIF in horizontal planes at several vertical locations spanning the water column. The measurements show vortex roll-up and tilting and the subsequent emergence of horizontal Kelvin-Helmholtz billows that form on the interface and interact with the primary vortices. The characteristics of flow are discussed, including phase averaged and mean velocity, vorticity and density fields as a function of a scaling parameter that quantifies the relative effects of lateral shear and buoyancy adjustment. The experiments compare favorably with three-dimensional, implicit-LES, numerical model solutions for the experimental configuration and parameters.   

Self-similar structure of a corner wave at short times

We study theoretically the flow near the corner of a vertical flat plate partially submerged across an uniform stream. When the Froude number is large enough, a three dimensional wave forms at the corner of the plate which evolves downstream in a similar way as a time-evolving two dimensional plunging wave. We have performed pressure-impulse asymptotic analysis of the flow near the origin of the corner wave to describe the initial evolution of the wave and to clarify the physical mechanism that leads to its formation. The analysis shows that the wave crest exhibits a self similar behavior at short times. After this self-similar stage, the wave crest detaches plunges following a nearly ballistic trajectory. The results improve our computational modeling of the flow near the stern of a high-speed surface ship, providing the initial condition needed for CFD simulations to properly capture the behavior of these stern waves.   

Breaking Wave Impact on a Partially Submerged Rigid Cube in Deep Water

The impact of a plunging breaking wave on a partially submerged cube is studied experimentally. The experiments are performed in a wave tank that is 14.8~m long, 1.15~m wide and 2.2~m high with a water depth of 0.91~m. A single repeatable plunging breaker is generated from a dispersively focused wave packet (average frequency of 1.4~Hz) that is created with a programmable wave maker. The rigid ($L = 30.5$~cm) cube is centered in the width of the tank and mounted from above with one face oriented normal to the oncoming wave. The position of the center of the front face of the cube is varied from the breaker location ($x_b \approx 6.35$~m) to $x_b +0.05$~m in the streamwise direction and from $-0.25L$ to $0.25L$ vertically relative to the mean water level. A high-speed digital camera is used to record both white-light and laser-induced fluorescence (LIF) movies of the free surface shape in front of the cube before and after the wave impact. When the wave hits the cube just as the plunging jet is formed, a high-velocity vertical jet is created and the trajectory and maximum height of the jet are strongly influenced by the vertical position of the cube.   

Simulation-based study of wind load on surface-piercing body and its dependency on waves

The wind load acting on surface ships and offshore structures are important for their operation and safety. In this study, we simulate the flow fields of wind and wave past a surface-piercing structure using a multi-scale modeling strategy. At large scales, the turbulent wind is simulated using large-eddy simulation on boundary-fitted grid coupled with nonlinear wavefield simulation using a high-order spectral method. The large-scale simulation provides environmental inputs for the local-scale simulation around the body. At local scales, the air and water flows are simulated by a coupled level-set and volume-of-fluid method. An immersed boundary method is used to represent the body. From the simulation, the statistics and structure of the wind and wave fields around the body are elucidated, and the loads on the body are quantified. A variety of developing and fully developed wave spectra at different sea states are considered. Swells and their interactions with the local wind-waves are included in the simulation. It is found that the mean wind loads are highly dependent on the wave conditions, and the instantaneous wind forcing varies with the wave phase.   

Simulation of flow past a sphere in a stratified fluid

Direct numerical simulation is used to simulate spatially-evolving flow past a sphere in a stratified fluid. The immersed boundary method is used to treat the sphere inside the domain. The main objective of this study is to characterize the near wake region. Statistics of interest include the drag coefficient, separation angle, Strouhal number, and the spatial evolution of the velocity fluctuations and the defect velocity. In addition to quantitative statistics, visualizations of the vortex structures in the wake will also be provided and discussed. Results are compared and contrasted with previous experimental and numerical data for unstratified and stratified flow past a sphere.   

Falling bodies through sharply stratified fluids: theory and experiments

The motion of bodies and fluids moving through a stratified background fluid arises naturally in the context of carbon (marine snow) settling in the ocean, as well as less naturally in the context of the DWH Gulf oil spill. The details of the settling rates may affect the ocean contribution to the earth's carbon cycle. We look at phenomena associated with many falling spheres in stratified fluids, as well as behavior of multiphase buoyant plumes penetrating strong stratification. We present careful measurements critical heights for fully miscible jets and companion analytical prediction. In turn, we examine cases involving clouds of sinking particulate and rising buoyant oil emulsions and associated plume trapping behaviors.   

Vortex rings passing through sharp density transitions

In this presentation the various behaviors of a dense miscible vortex ring descending through a sharp stratification are explored. By varying experimental parameters it is found the ring dynamics can transition from those which pass through the interface to those which can become totally entrapped within the density transition, even though in all cases the ring is the most dense fluid in the system. Experimental results will outline these various behaviors and quantify this transition with an experimental phase diagram. A scaling law will be derived from dimensional considerations to predict this transition in behavior. Numerical simulations will also be presented and compared to the previous experimental results.   

A comparison between laboratory and numerical simulations of gravity-driven coastal currents with a geostrophic theory

Laboratory and numerical simulations of buoyant, gravity-driven coastal currents are summarized and compared to the inviscid geostrophic theory of Thomas \& Linden 2007.\footnote{Thomas, P. J. and Linden, P.F. 2007. Rotating gravity currents: small-scale and large-scale laboratory experiments and a geostrophic model. \textit{J. Fluid Mech.} \textbf{578}, 35-65.} The lengths, widths and velocities of the buoyant currents are studied. Agreement between the laboratory and numerical experiments and the geostrophic theory is found to depend on two non-dimensional parameters which characterize, respectively, the steepness of the plumes isopycnal interface and the strength of horizontal viscous forces (quantified by the horizontal Ekman number). The best agreement between experiments (both laboratory and numerical) and the geostrophic theory are found for the least viscous flows. At elevated values of the horizontal Ekman number, laboratory and numerical experiments depart more significantly from theory.   

Session R2: Granular Flows IV

Correlating Grain and Slider Dynamics in a Stick-Slip Experiment

We describe an experiment to characterize the stick-slip nature of sliding friction. In the experiment a solid slider is pulled by a spring moving at constant velocity across a 2D granular bed of bidisperse photoelastic discs confined to a vertical channel. A force sensor attached to the spring measures the pulling force on the slider, while two accelerometers on the slider provide angle and acceleration data. Synchronous photoelastic images of the granular bed acquired by a camera moving along with the slider allow us to correlate all features of the slider and granular dynamics. We particularly focus on the correlation of the slider acceleration and changes in the granular force network. This experiment can help us better understand both atomic scale friction experiments, and stick-slip at the geophysical scale.   

Flowing layer thickness in a granular tumbler

The thickness of the flowing layer in a tumbler varies substantially depending on flow conditions, but no predictive approach is available. We have studied monodisperse granular flows in air, water, and glycerine in a quasi-2D tumbler, focusing on the rolling regime to highlight common features and differences between dry and wet granular flows. For dry granular flows, the flowing layer thickness measured in units of particle diameter scales with a dimensionless flow rate based on the tumbler rotational speed and radius as well as the particle diameter. Using appropriate characteristic time scales, the data for the dry and liquid experiments also collapse fairly well. The Stokes number is a key dimensionless parameter to characterize the flow of granular material in liquids.   

Anatomy of flow and jam of a two dimensional granular flow in a hopper

We seek an understanding of the physics of jamming for hopper flow using high speed spatio-temporal video data for photoelastic disks flowing through a two-dimensional hopper. We have found experimental support for the hypothesis that jamming events of granular flow in a hopper occur as a Poisson process. Through measuring the density field and stress distribution, we demonstrate that ``dome-structured'' stress chains affect the density and velocity fields, leading to the mean flow profile in the hopper. We also measure how jamming statistics depend on the orifice sizes and the wall angles of a hopper. By calculating stress fluctuations, we conclude that instead of the density field, the formation of localized force chain arches controls the jamming transition of granular flow in a hopper. These data are part of an IFPRI-NSF Collaboratory for comparing physical data and simulations.   

Anisotropic surface friction

Contrary to the literature, we find that altering the surface roughness has a large effect on intruder drag in the quasi-static regime. Moreover we pattern the surface with a sawtooth texture and observe anisotropic drag: when the texture is comparable in size to the bead diameter the frictional force is 1/3rd greater for the flow directed against the sawtooth versus the opposite flow. We present a systematic study showing the dependence of the anisotropy on the texture's orientation.   

Microstructural theory for colloidal suspensions in active microrheology

The active microrheology problem where a probe particle is pulled through a bath of colloidal particles with a constant external force $F^{ext}$ is studied using a theoretical framework based on the Smoluchowski equation, with emphasis on concentrated colloidal suspensions far from equilibrium. The probability distribution of bath particles with respect to the probe, $g(r)$, is determined from an integro-differential equation solved by iterative numerical methods at different set of $Pe$ (ratio of external to Brownian forces) and volume fractions. The role of inter-particle interactions on microstructure is studied by using different types of pair potentials with the intention to model systems ranging from hard-spheres to soft colloids. The obtained distribution is then used to compute the apparent shear viscosity. The predictions of microstructure and rheology are compared with our Accelerated Stokesian Dynamics simulations and available experimental results.   

Effect of particle devolatilization on bed dynamics during biomass thermochemical conversion

Fluidization is a technique of choice for the thermochemical conversion of biomass. At conversion temperatures however, the amount of gases released by the biomass is large enough to impact the mixing of the reactive particles with the inert sand, and modify the bubbling frequency and intensity. This, in turn, may significantly affect the chemical processes and the final product distribution. In this context, optimizing reactor design and operating conditions requires a better understanding of the actual bed dynamics in the presence of reactive particles. In this work, two- and three-dimensional simulations of biomass conversion in a lab-scale fluidized bed reactor are conducted using a Lagrangian approach to handle the solid phase. The biomass devolatilization chemistry is described using a commonly used global model taking into account each constituent of the biomass. Statistical analysis of the particles and velocity fields is conducted and results are compared to non-reactive cases to quantify the effect of devolatilization on particle mixing, especially segregation, and on the bubbling pattern of the bed.   

Surface Chemistry Effects in Submerged Granular Flows of Hydrophobic Grains

We experimentally investigate submerged granular flows of hydrophobic and hydrophilic grains in a rotating drum. While slurry and suspension flows are common in nature and industry, effects of surface chemistry on flow behavior have received relatively little attention. The experiment consists of a cylindrical drum containing various concentrations of hydrophobic and hydrophilic grains of sand submerged in water rotated at a constant angular velocity. Sequential images of the resulting avalanches are taken and analyzed. While it is known that at slow speeds, submerged avalanches appear qualitatively similar to dry flows, our results suggest that the surface properties of the grains affect underwater flow significantly. High concentrations of hydrophobic grains result in an effectively cohesive interaction between the grains forming aggregates. We present data on the size of the aggregates, slope, and avalanche statistics with changes in concentration. The formation and nature of the aggregates depends significantly on the presence of air in the system. At concentrations larger than 75{\%} hydrophobic sand, the avalanches do not behave in a manner which is typical for sand, but as the concentration decreases, the aggregates are smaller, the angle of repose decreases, and the grains start showing rheological properties similar to those in regular sand.   

Percolation theory applied to the force field in granular material

We analyze the structure of the force field in slowly compressed granular system by the means of discrete element simulations. Using the tools of percolation theory, we compute the quantities describing the force field and discuss their dependence on polydispersity and frictional properties of the granular particles. Then, we correlate the results to the ones obtained using topological approach based on Betti numbers which measure the number of clusters as a function of force thresholds.   

Material point method simulation of dense granular material

Accurate modeling and simulation of granular flow or deformation require a numerical method with Lagrangian description to account for history dependence of the material. However, large deformation or flow of the material requires an Eulerian description. Numerically, different descriptions of the material result in different codes and applications. Unsatisfactory results have been reported by many modelers using both methods. For instance, element deletion scheme is used in the finite element method, a Lagrangian description, to eliminate the highly distorted elements, which results in artificial reduction of inertia from the problem. In codes using the finite volume method, an Eulerian descriptions, how to advect brittle damage of the material is a significant issue. To address these issues we use the material point method, which uses Lagrangian material points and Eulerian mesh simultaneously. Improvements are made to the original material point method for our applications. It is found that the improvements are critically important to granular flows results from brittle damage of the material, while it is marginally important to ductile materials.   

Couette and Fourier planar ows for a low density granular gas

We study in this work steady laminar flows in a low density granular gas. Our system is excited by shear and temperature sources at the boundaries (two infinite parallel walls). We describe previously unreported types of non-Newtonian granular flows. We obtain also their corresponding rheologic and hydrodynamic transport coefficients, following three independent methods: 1) an analytical solution, obtained from Grad's method applied to the inelastic Boltzmann equation, 2) a numerical solution of the inelastic Boltzmann equation, obtained by means of the Direct Simulation Monte Carlo method, and 3) molecular dynamics simulations. We show that the three procedures yield the same general classification of planar Fourier and Couette flows for the granular gas.   

Session R3: Bubbles IV

Velocimetry in cavitating flows by X-ray imaging

A promising method to measure velocity fields in a cavitating flow is presented. Dynamics of the liquid phase and of the bubbles are both investigated. The measurements are based on ultra fast X-ray imaging performed at the APS (Advanced Photon Source) of the Argonne National Laboratory. The experimental device consists of a millimetric Venturi test section associated with a transportable hydraulic loop. Various configurations of velocity, pressure, and temperature have been investigated. The slip velocity between vapor and liquid is calculated everywhere both velocities can be obtained. Reynolds stresses are also calculated, and compared with the ones obtained in non-cavitating conditions.   

Influence of Vortex Cavitation on Vortex Breakdown

Cavitation inception and development was observed in the vortices created by an $\Lambda $ = 70$^{\circ}$ delta wing over a range of attack angles and cavitation numbers. The location of cavitation inception, bubble size, growth rate, and the effect of cavitation on the location of vortex breakdown were studied. From the observations a rationale that governs the observed inception location, growth of incepted nucleus into a given shape is proposed. It is based on the alterations of the vortical core flow that an elongating bubble will cause. The minimizing potential theory of \textit{Rusak et al}\footnote{``The evolution of a perturbed vortex in a pipe to axisymmetric vortex breakdown,'' Rusak, Z., Wang. S., Whiting. C. H., \textit{Journal of fluid mechanics}, 1998, Vol 336, pp 211-237} is used to identify the constraints on the bubble growth which in turn helps us to understand the bubble shape and growth rate.   

High-speed microjet generation using laser-induced vapor bubbles

The generation and evolution of microjets are studied both experimentally and numerically. The jets are generated by focusing a laser pulse into a microscopic capillary tube ($\sim$50 $\mu$m) filled with water-based red dye. A vapor bubble is created instantly after shooting the laser ($<$1 $\mu$s), sending out a shockwave towards the curved free surface at which the high-speed microjet forms. The process of jet formation is captured using high-speed recordings at 1.0 $\times$ $10^6$ fps. The velocity of the microjets can reach speeds of $\sim$850 m/s while maintaining a very sharp geometry. The high-speed recordings enable us to study the effect of several parameters on the jet velocity, e.g. the absorbed energy and the distance between the laser spot and the free surface.The results show a clear dependence on these variables, even for supersonic speeds. Comparisons with numerical simulations confirm the nature of these dependencies.   

Bubbles in drops: from cavitation to exploding stars

We performed an experiment to generate single cavitation bubbles inside centimetric quasi-spherical water drops. To produce such drops, our experiment was realized under microgravity conditions (42nd ESA parabolic flight campaign). The ultra-fast recording of the bubble collapse and ensuing dynamics revealed consequences of the unique geometry of the drop's free surface. We obtained the first visualizations of a jet pair escaping the drop after the collapse of eccentrically-placed bubbles. The high quality of the images also disclosed some features of the inner drop dynamics. Due to their confinement within the isolated drop volume, shock waves emitted at the bubble collapse bounce back and forth thereby exciting gas nuclei into sub-millimetric bubbles. When located beneath the free surface, the collapse of these bubbles gives rise to narrow ``hair-like'' jets on the surface. Here we briefly describe the physics underlying these observations while discussing possible analogies with various astrophysical processes from the Sun (spicules) to asymmetric supernovae.   

Homogeneous cavitation in microfluidics: a record high dynamic tensile threshold

An experimental technique is presented which allows one to measure the rupture strength of water using a microfluidic approach. A transparent microfluidic channel is filled with clean water, partially leaving an air-water interface. A focused infrared laser pulse within the liquid creates a spherical shock wave near the interface. The shock reflects, due to acoustic impedance mismatch, as a strong tension wave with high negative pressures. The liquid becomes stretched and at the homogeneous cavitation threshold ruptures with the nucleation of vapor bubbles. These bubbles are captured using an optical delay and very short exposure times. Reproducible observations of the bubble nucleation are obtained, supporting our claim of homogeneous bubble nucleation. Multicomponent Euler flow simulation estimates a tensile stress threshold of -60 MPa, which is the largest reported tension for dynamic measurements.   

Understanding Cavitation Intensity through Pitting and Pressure Pulse Analysis

Cavitation erosion is of interest to the designers of ship propulsion devices because of its detrimental effects. One of the difficulties of predicting cavitation erosion is that the intensity of cavitation is not well predicted or defined. In this work we attempt to define the intensity of a cavitation erosion field through analysis of cavitation induced erosion pits and pressure pulses. In the pitting tests, material samples were subjected to cavitation field for a short duration of time selected within the test sample's incubation period, so that the test sample undergoes plastic deformation only. The sample material reacts to these cavitation events by undergoing localized permanent deformation, called pits. The resulting pitted sample surfaces were then optically scanned and analyzed. The pressure signals under cavitating jets and ultrasonic horns, for different conditions, were experimentally recorded using high frequency response pressure transducers. From the analysis of the pitting data and recorded pressure signals, we propose a model that describes the statistics, which in the future can be used to define the cavitation field intensity. Support for this work was provided by Office of Naval Research (ONR) under contract number N00014-08-C-0450, monitored by Dr. Ki-Han Kim.   

Vapor bubble evolution on a heated surface containing open microchannels

Power electronics require cooling technologies capable of high heat fluxes at or below the operating temperatures of these devices. Boiling heat transfer is an effective choice for such cooling, but it is limited by the critical heat flux (CHF), which is typically near 125 W/cm$^2$ for pool boiling of water on a flat plate at standard pressure and gravity. One method of increasing CHF is to incorporate an array of microchannels into the heated surface. Microchannels have been experimentally shown to improve CHF, and the goal of this study is to determine the primary mechanisms associated with the microchannels that allow for the increased CHF. While the use of various microstructures is not new, the emphasis of previous work has been on heat transfer aspects, as opposed to the fluid dynamics inside and in the vicinity of the microchannels. This work considers the non-isothermal fluid motion during bubble growth and departure by varying channel geometry, spacing, and heat flux input using a level-set method including vaporization and condensation. These results and the study of the underlying mechanisms will aid in the design optimization of microchannel-based cooling devices.   

Acoustically enhanced boiling heat transfer on a heated surface containing open microchannels

Acoustic actuation is used to enhance boiling heat transfer on a submerged heated surface containing an array of open microchannels by controlling the formation and evolution of vapor bubbles and inhibiting the instability that leads to film boiling at the critical heat flux. The effect of actuation at millimeter and micrometer scales is investigated with emphasis on the behavior of bubble nucleation, growth, contact-line motion, condensation, and detachment. The results show that microchannels control the location of boiling and reduce the mean surface superheat. In addition, acoustic actuation increases the heat flux at a given surface temperature and leads to a significant increase in the critical heat flux, a reduction of the vapor mass above the surface, and the breakup of low-frequency vapor slug formation.   

The most spherical cavitation bubble

Focusing a high energy pulsed laser into water is a widely used method to generate a single cavitation bubble. Such a bubble is generally assumed to collapse spherically. However, the precision of the focusing system and the effect of gravity, most often neglected, break the spherical symmetry of the collapse. In the experiment presented here, we generated the ``most spherical'' cavitation bubbles in a series of experiments by (1) running the experiments in microgravity (during the 52nd ESA Parabolic Flight Campaign), and (2) using an optimized laser focusing system. The collapse and the rebound of the bubbles were then investigated to experimentally determine the fraction of potential energy of the bubble transformed into the rebound bubble and into the shock wave at the collapse. We found that the transfer of the energy into both channels can be well predicted using a single non-dimensional parameter. A theoretical model is developed and shows good agreement with the experimental results.   

Drops levitated by an air cushion: asymptotic analysis and stability

Liquid drops can be kept from touching a plane solid surface by a gas stream entering from underneath, as observed for example for Leidenfrost drops. We discuss the limit of small flow rates, for which the gap between the drop and the substrate becomes very small, to obtain a full analytical description of the drop shapes and their stability. It is found that above a critical drop radius no stationary drops can exist and that unstable drops develop a gas ``chimney'' that breaks the drop in its middle. We point out similarities with the breakup of drops in a microfluidic T- junctions.   

Session R4: Drops X: Interaction with Heterogeneous Surfaces

Lattice Boltzmann Simulations of Drop Impact on Heterogeneous Surfaces

The dynamics of drop impact on heterogeneous substrates is important to understand from a materials research-application perspective. The phenomenon occurs in many situations, from ink-jet printing to fuel injection processes. Since drop impact is a physically complicated process, difficult to understand through experiments and theory alone, it is important to develop methods to study such a process numerically. The impact process poses many computational difficulties as well. Some of these difficulties include the tracking of a liquid-gas interface that undergoes extreme deformation in a short time period, accurately including the effects of surface tension, and realistically resolving the dynamic liquid-gas-solid contact line. Due to its kinetic nature, the Lattice Boltzmann Method(LBM) can incorporate mesoscopic physics into its formulation to resolve these difficulties, which otherwise pose significant problems for traditional continuum solvers. In our simulations, the interface is captured, instead of tracked, by keeping account of an order parameter in the fluid as in the phase field method. Here we discuss our numerical method and report results describing impact on a superhydrophobic surface for drops of large density ratio.   

Droplet Dynamics on Heterogeneous Substrates

Describing the dynamics of contact lines on heterogeneous substrates is important in fields ranging from coating technologies over microfluidics to enhanced oil recovery. The vast majority of studies on contact line dynamics considers the case of ideal, homogeneous substrates. Modelling chemically heterogeneous surfaces by introducing periodic variations in the wettability, we investigate the depinning and subsequent motion of 2D droplets driven by a body force. To this end, we study the time evolution of a sharp interface using Stokes dynamics together with Navier slip condition at the substrate, employing a boundary element formalism. The heterogeneity is represented by a position dependent microscopic contact angle. This allows us to quantify the modified droplet mobility, the spectrum of pinned and depinned solutions, and their dependence on periodicity and strength of the heterogeneity. Understanding the emergence of dynamic contact angles on heterogeneous substrates may open a new perspective on the relation of molecular and hydrodynamic models of contact line motion.   

Modelling of contact angle hysteresis on rough, non-uniform and superhydrophobic surfaces with lattice Boltzmann method

Contact Angle Hysteresis (CAH) is usually attributed to surface heterogeneity, contact line pinning, adsorption or interdiffusion. A model of CAH developed recently by Kubiak \& Wilson is demonstrated using the lattice Boltzmann method. The model is based on the dynamic surface heterogeneity, reorientation of surface molecules under wetting liquid, physical roughness, chemical heterogeneity and liquid adhesion and evaporation. Once the surface is wetted, the local static contact angle (CA) changes from its advancing value to match the receding static CA over time Ta. When the contact line retracts, the surface recovers its initial properties corresponding to the advancing static CA over time period Te, which corresponds to the physical evaporation. Further development of the model to include surface roughness and chemical heterogeneity is presented. The model shows good agreement with experimental results for several practical configurations i.e. droplet impact and coalescence, drops on tilted surface, and drops on superhydrophobic and non-uniform surfaces etc. The extended model exhibits great potential for predictive modelling using the lattice Boltzmann method, but can be also implemented in other schemes.   

A computational study of the impact of molten drops onto textured surfaces

We used an in-house, three-dimensional computational tool to study the impact and spreading of molten drops onto substrates with various surface patterns. The computational tool is GPU-accelerated and solves the mass, momentum and energy equations in the liquid phase and the conduction equation in the substrate. The drop, 40 $\mu m$ in diameter, is molten alumina, which is widely used in the thermal spray coatings. The surface patterns are created by positioning cuboid obstacles that their side dimension is at least 3 $\mu m$. We investigated the effects of obstacle height, aspect ratio and spacing as well the impact velocity on the spreading dynamics and the final geometry of the drop. In our study, the impact velocity was varied from 40 to 90 $m/s$, the obstacle height from 1 to 5 $\mu m$, and the obstacle spacing from 2 to 26 $\mu m$. The results show that the flattened drop has a disk-shape geometry when the obstacle spacing is either smallest or largest, and that significant deformations and fingering occur at the intermediate spacings. A quantitative relation was developed between the obstacle spacing and the final spread diameter of the drop. The results show the collapse of the final spread diameter normalized by the obstacle spacing when plotted against the spacing at different impact velocity and obstacle height.   

Two dimensional droplet spreading over chemically heterogeneous substrates

We investigate the spreading dynamics of a partially wetting two-dimensional droplet over chemically heterogeneous substrates. The contact line singularity is removed by assuming slip at the liquid-solid interface. Assuming small contact angles and strong surface tension effects, a long-wave expansion of the Stokes equations yields a single evolution equation for the droplet thickness. The chemical nature of the substrate is incorporated through local variations in the microscopic contact angle, which appear as boundary conditions in the governing equation. By asymptotically matching the flow in the bulk of the droplet with the flow in the vicinity of the contact lines, we obtain a set of coupled ordinary differential equations for the locations of the two droplet fronts. We verify the validity of our matching procedure by comparing the solutions of the ordinary differential equations with solutions of the full governing equation. A number of interesting features that are not present in chemically homogeneous substrates are found, such as the existence of multiple equilibria, the pinning of the droplet fronts at localized chemical features and the possibility for the droplet fronts to exhibit a stick-slip-like behavior.   

Three-dimensional contact line dynamics on heterogeneous substrates

Three-dimensional contact line dynamics on heterogeneous substrates is examined theoretically by using the motion of a viscous, partially wetting droplet over a horizontal and chemically heterogeneous substrate as a model system. We utilize a long-wave model for the evolution of the droplet thickness, whereby inertial and gravitational effects are neglected and the contact angles are assumed to be everywhere small. Noteworthy is that the present formalism does not depend on an imposed, Cox-Voinov-type relation between the apparent contact angle and the contact line speed. Instead, the contact line speed is found as part of the solution, facilitated by mapping the free-boundary problem to a fixed, circular domain. Analytical progress can be made by considering perturbations from a circular contact line and asymptotically matching the flow in the two-dimensional boundary layer around the contact line with the flow in the bulk of the droplet. This matching procedure eventually leads to a set of differential equations for the Fourier coefficients of the contact line. The derived equations are solved for a few representative substrate configurations.   

Destiny of a drop on a fiber: from barrel to clamshell and back

Drops on cylindrical fibers are a familiar sight, for instance in the form of dew drops on spider webs. They can exist in two competing morphologies, a cylindrically symmetric barrel state completely engulfing the fiber and an asymmetric clamshell state, in which the drop sits on the side of the fiber. Despite their omnipresence and their practical relevance the physical mechanisms governing the stability of the two morphologies remained elusive. Using electrowetting-functionalized fibers we determined of the stability limits of both morphologies as a function of the two relevant control parameters, the contact angle and the liquid volume. While clamshells are found to prevail for large contact angles and small volumes, and barrels prevail for small angles and large volumes, there is also a wide range of intermediate parameter values, for which both morphologies are mechanically stable. Mapping out the energy landscape of the system by numerical minimization of the free energy we find that the barrel state is easily deformed by non-axisymmetric perturbations. From a general perspective, the demonstration of electrowetting-based reversible switching of liquid morphologies on fibers opens up opportunities for designing functional textiles and porous materials.   

Modes of Contact Line motion on topographic substrates

The link between the geometry of a regular topographic pattern, the material Contact Angle and the macroscopic Contact Angle Hysteresis is still poorly understood. Employing the apparent contact angle as a control parameter, we numerically determine the shape of a liquid interface on patterns consisting of square arrays of pillars with different cross section. Both hydrophilic and hydrophobic substrates are considered. The increase of the apparent contact angle leads to a sequence stable morphologies which may belong to different interface topologies. Eventually, the interface becomes unstable, defining the Advancing Angle. Abrupt changes of the Advancing Angle, while varying the spacing, aspect ratio and material Contact Angle of the pillars, correspond to transitions to different Advancing Modes. With the same procedure we calculate Receding Angles, and consequently the Contact Angle Hysteresis. Finally, we discuss similarities and differences among pillars with either circular and square cross sections.   

Investigation of Contact Angle Behavior and Stability of Drops to Airflow Forcing on Rough Surfaces

A method for measuring full-field, instantaneous drop interface profiles on rough surfaces has been implemented to study contact angles and stability to wind forcing on metallic surfaces with micron-scale roughness. Wind tunnel experiments are conducted to produce criteria for runback of drops and set these thresholds for measured water drops spanning a range of Bond numbers from $Bo = 0.5$ to $5$ on roughness in the range of $R_A=0.8$ to $4.9$ with drop based Reynolds numbers spanning an order of magnitude. More importantly, these stability limits are tested with particular care taken to observe their relation to the behavior of both the contact line and contact angle distribution as the drop adjusts its configuration to find a stable condition until it is no longer able to do so and is blown downstream. Results such as critical shear rates and contact angles are discussed and compared with previous numerical studies in the literature such as Dimitrakopoulos [J.Fluid.Mech. 580, 2007] and Ding and Spelt [J.Coll.Sci. 599, 2008] along with experimental results such as Milne [Langmuir 25:24, 2009].   

Interplay of surface roughness and air pressure in splash suppression

Surface roughness has generally been found to increase the splashing of drops impacting on a solid surface [1]. However, we have recently found [2] that the effect of roughness is considerably more complex: it does promote the prompt splashing associated with rough surfaces, but also inhibits the splashing that occurs through the formation of a thin sheet. Consequently, as roughness is varied, the drop can splash through one or both of these mechanisms. Surprisingly, for sufficiently high viscosities there is a region where increasing roughness eliminates splashing entirely. We show that this result is robust and holds for a variety of liquids impinging on surfaces of different materials and geometries. The mechanism through which roughness causes splashing is intimately connected with the ambient gas. We find, as in the case of thin-sheet splashing [3], that the removal of the surrounding air suppresses prompt splashing. As the gas pressure decreases, fewer droplets are ejected until the drop completely ceases to splash. This threshold pressure increases with liquid viscosity and decreases with surface roughness and impact velocity. [1] K. Range, F. Feuillebois, \textit{J. Colloid Interface Sci}. \textbf{203}, 16 (1998); [2] A. Strandburg-Peshkin, M. M. Driscoll, S. R. Nagel, \textit{BAPS}. DFD.AH.7 (2009). [3] L. Xu, W. W. Zhang, S. R. Nagel,\textit{ Phys. Rev. Lett. }\textbf{94}, 184505 (2005); L. Xu, \textit{Phys. Rev. E} ~\textbf{75}, 056316 (2007); M. M. Driscoll, C. S. Stevens, S. R. Nagel, \textit{Phys. Rev. E} \textbf{82}, 036302 (2010).   

Session R5: CFD VII: Immersed Boundary Methods

An implicit ghost-cell immersed boundary method with mass source and sink for simulations of moving-body problems with control of spurious pressure oscillations

For moving body problems where the conventional immersed-boundary methods are employed, the simulation results are often contaminated by spurious pressure oscillations. The spurious pressure oscillations are known to be produced by the violation of mass conservation across interfaces between fluid and moving bodies and to be a function of mainly the grid spacing and time-step size. In the present work, we develop a new immersed boundary method which can control and significantly reduce the spurious pressure oscillations. A ghost-cell immersed boundary method is coupled with a mass source and sink algorithm to better conserve mass around boundary interfaces. A fully-implicit time integration scheme is employed for enhanced control of the time- step size thereby allowing better control of the spurious force oscillations on given mesh resolution. A novel method for treating multiple fresh and dead cells due to the use of a large time-step size is also developed. The present fully-implicit ghost-cell immersed boundary method coupled with a mass source/sink algorithm is demonstrated to significantly reduce spurious pressure oscillations thereby providing accurate and stable solutions for moving body problems.   

A volume penalization method for incompressible flows and scalar advection-di usion with moving obstacles

A volume penalization method for imposing homogeneous Neumann boundary conditions in advection-diffusion equations is presented. Thus complex geometries which even may vary in time can be treated efficiently using discretizations on a Cartesian grid. A mathematical analysis of the method is conducted first for the one-dimensional heat equation which yields estimates of the penalization error. The results are then confirmed numerically in one and two space dimensions. Simulations of two-dimensional incompressible flows with passive scalars using a classical Fourier pseudo-spectral method validate the approach for moving obstacles. The potential of the method for real world applications is illustrated by simulating a simplified dynamical mixer where for the fluid flow and the scalar transport no-slip and no-flux boundary conditions are imposed, respectively.   

A hybrid Pseudo-spectral Immersed-Boundary Method for Applications to Aquatic Locomotion

A hybrid pseudo-spectral immersed boundary method is developed for application in marine locomotion. Spatial derivatives are calculated using pseudo-spectral method while a 2nd-order Runge-Kutta scheme is used for time integration. The singular force applied on the immersed boundary is obtained using a direct forcing method. To avoid Gibb's phenomenon in the spectral method, we regularize the force by smoothing it over several grid cells. This method has the advantage of spectral accuracy and the flexibility to model irregular, moving boundaries on a Cartesian coordinate without complex mesh generation. The method is applied to examine locomotion of jellyfish for both jetting and paddling jellyfish.   

Wall-models for immersed-boundary methods

Immersed boundary (IB) methods, where the requirement for the computational grid to conform to solid boundaries is relaxed, have been widely used in a variety of applications. In the majority of cases IB methods are usually coupled to Cartesian solvers, and tackle low to moderate Reynolds number problems. Applications at high Reynolds numbers are prohibitively expensive since an increase in the wall-normal resolution can only be achieved by refining the computational grid in all coordinate directions. A solution to this problem is the development of wall-models for IB methods that can compensate for the luck of resolution in both laminar and turbulent regimes. In the present study we propose novel wall treatment based on a two-layer zonal approach, where the solution of a simplified set of equations is solved near the wall for the purpose of providing an accurate estimate of the near wall flow using information form the coarse underlying Navier-Stokes grid. Various models based on different levels approximation will be presented. Results will be shown for canonical cases such as the flow around a smooth cylinder and around a sphere at various Reynolds numbers.   

Fluid-Structure Interaction for Flapping Flexible Wings with Large Mass Ratio

A strong-coupling approach has been successfully used in our previous study for the fluid-structure interaction of flapping flexible wings. However, when the mass ratio of wing and fluid is considered, we are facing a problem to solve Poisson equation with discontinuous coefficients. As the mass ratio increases, normal algorithm for solving the above equation becomes costly and unstable. In this work, we applied the Black Box Multigrid Conjugate Gradient Preconditioned Method (Box-MGPCG) and a smoothing function to overcome the problem. The new algorithm shows consistent efficiency for mass ratio up to 1000. Therefore, it allows us to study the effect of large mass ratio to the performance of flapping flexible wings. Simulation results are also presented here.   

Simulation of flow over a sphere in a boundary layer using a GPU accelerated IB-LBM

Numerical simulations of flow over a sphere embedded in a laminar boundary layer are conducted for characterizing the effects of wall proximity on the drag and lift forces acting on the sphere. The wall proximity is defined as the distance from the wall to the center of sphere. We utilize an immersed boundary-lattice Boltzmann method (IB-LBM) with a multi-direct forcing technique (Suzuki \& Inamuro, Computers \& Fluids 2011) and combine the present method with a multi-block method (Yu et al., IJNMF 2002) for refining lattices near the sphere. We implement the present IB-LBM into a Graphical Processing Unit (GPU) using a PGI CUDA Fortran programming environment for accelerating the computations. We perform benchmark tests based on simulations of flow over a sphere in a free-stream for validations of the present IB-LBM and evaluations of the performance of the GPU implementation. The results of the drag and lift forces on the sphere according to the wall proximity will be shown in the final presentation.   

Gust effects on a freely falling plate

Depending on the Reynolds number and the Froude number, a freely falling plate usually performs one of the following four types of motion, flutter, tumble, steady or chaos fall. It is interesting to know that if and how a gust changes the falling status of a plate. In this work, Direct Numerical Simulations (DNS) will be conducted to study the effects of gust on the freely falling plate by varying the gust amplitude, frequency, and phase relative to the falling plate. Especially, for a plate lies in the chaotic (transitional) region, how its motion be affected as a response to the gust will be discussed.   

Three-dimensional simulations of the compressible, low-Reynolds number, flow around a hohlraum in a fusion chamber

Three-dimensional immersed interface simulations of the flow around a hohlraum in a fusion chamber will be presented. The high injection velocity of the hohlraum results in important compressibility effects while the Reynolds number is quite low due to the high temperature in the chamber (up to 8000K); still well within the continuum limit. A stable recirculation region forms behind the object. In addition, the hohlraum surface temperature is very low to preserve the hydrogen pellet at cryogenic conditions. These conditions are not commonly encountered in flows around blunt objects since high Mach number usually implies high Reynolds number. We study the effects of spin rate at different angles of attack and free flight dynamics. The formation of near surface secondary flow patterns is discussed as well as the distribution of the heat flux.   

A Hybrid Immersed Boundary-Immersed Interface Method for Cell Tracking in Microdevices

The manipulation of cells in microfluidic devices has become routine for biomedical applications such as cell sorting and trapping. To date most of the designs used for cell manipulation are based on experimental trial and error. A fast and accurate numerical algorithm can provide important insight into the design of these devices. In this study, a hybrid immersed boundary-immersed interface method is developed to study the complex behavior of cells in liquid. The immersed boundary method provides an accurate prediction of particle motion in a fluid while the immersed interface method gives second-order accurate solutions for the ion concentrations and electrostatic potential in the presence of moving cells. Both methods employ a fixed computational grid without the need for remeshing at each time step. Cells of different size, shape and charge are allowed to move under both hydrodynamic and electrokinetic forces. Moreover different channel geometries are considered to obtain the best trapping and separation performance. The present immersed boundary-immersed interface model is particularly suitable for bioMEMS devices as this method can accurately predict viscous and electrostatic forces as well as particle velocity, location, and particle membrane deflection.   

Large Eddy Simulation of Motion-Induced Contaminant Transports in Room Compartments

Large eddy simulation (LES) of contaminant transports due to complex human and door motions is conducted for characterizing the effect of the motion-induced wakes on the contaminant transports in room compartments where a contaminated and clean room are connected by a vestibule. We utilize a LES technique with an immersed-boundary method for moving objects (Choi et al., JCP 2007; Choi and Edwards, Indoor Air 2008) and extend the technique to include Eulerian descriptions of gas-phase contaminant transport as well as thermal energy transfer. We demonstrate details of contaminant transport due to human- and door-motion induced wake development during a short-duration event involving the movement of a person (or persons) from a contaminated room, through a vestibule, into a clean room. Parametric studies that capture the effects of human walking pattern, door operation, over-pressure level, and vestibule size are systematically conducted. The results of parameteric studies will be shown in the final presentation.   

Session R6: Focus Session: Evaporative Self-Assembly of Micro-and Nano-Particles

Drying of complex fluids at a moving contact line

We study the pattern formation induced by drying colloidal suspensions in a vertical Hele-Shaw cell immersed in a reservoir [1]. The contact line velocity can be well controlled by pumping out the solution from the reservoir. At low capillary number, we observe stick-slip motion and periodic strip deposition [2]. We measured the pinning force variation and the wavelength. We systematically vary the following parameters: receding velocity, evaporation rate, concentration, particle size, and pH of the suspension. Results allow determining the power law governing the pinning force variation. The pH, which has no effect on the pinning force variation, changes the deposition morphology significantly. Finally, we present a detailed comparison between colloidal suspensions and polymer solutions. \\[4pt] [1] H. Bodiguel, F. Doumenc, B. Guerrier EPJ-ST 166, 29-32 (2009) \\[0pt] [2] H. Bodiguel, F. Doumenc, B. Guerrier Langmuir, 13, 10758-10763 (2010)   

Dynamics of freely moving plates connected by a shallow liquid bridge

We study the dynamics of freely moving solid bodies connected by a shallow liquid bridge via analytic and experimental methods. The gap between the solid bodies is used as a small parameter within a lubrication approximation, reducing the problem to an Abel equation of the second kind. Analysis of the governing differential equation yields two novel physical phenomena: (1) An impulse-like peak in the force applied by the liquid bridge on the solid bodies, obtained from a uniform asymptotic solution for small Capillary numbers. (2) Both linear and non-linear oscillations of the system for the case of surfaces with low wettability, obtained from small perturbations of the system around the equilibrium point. An experimental setup examining the motion of freely moving solid bodies was constructed, yielding experimental data which compared favorably with the analytic results and specifically displayed the predicted oscillations and impulse-like peak of the applied force. The application of the current analysis to the micro-manipulation of solid bodies and possible future research directions are discussed.   

Real Time Electron Microscope Imaging of Nanoparticle Motion Induced by a Moving Contact Line

With the high resolution of the electron microscope, we imaged the interactions between receding and advancing contact lines and surface-bound nanoparticles. The experiments were carried out with a custom-made liquid cell, dubbed the nanoaquarium. The nanoaquarium seals a thin liquid layer between two thin, electron-transparent membranes, and allows one to image processes in liquid media with electrons. We observe that the nanoparticles are ejected in the wake of the receding contact line, and pushed by the advancing contact line. A simple mathematical model that accounts for surface tension and disjoining~pressure effects is constructed to interpret this curious phenomenon.   

Field-directed assembly of nanoparticles

The use of external fields to direct the assembly of colloidal suspensions, combined with new particle shape symmetries that couple strongly to such fields, is a powerful means for creating and tailoring materials with unique mechanical, optical and electronic properties [1]. I will present the evaporative assembly of nanostructured thin films from ellipsoidal titania nanoparticles. The deposition process is directed by an electric field. As the evaporation front recedes, a uniform film with thicknesses of 1-10 $\mu$m is deposited on the substrate. The films exhibit a large birefringence and high packing fraction due to the orientation of the particles. When the frequency is lowered, the particle orientation undergoes a parallel-random-perpendicular transition with respect to the field direction. The orientation dependence on field frequency and strength is explained by the polarizability of ellipsoidal particles. Particle orientation in the films also leads to anisotropic mechanical properties, which are manifested in their cracking patterns. In all, field-directed assembly of anisotropic particles provides a powerful means for tailoring nanoparticle film properties {\it in situ} during the deposition process. \\[4pt] [1] Grzelczak et al. Directed Self-Assembly of Nanoparticles. ACS Nano 4, 3591-3605 (2010).   

Suppressing the coffee stain effect: how to control colloidal self-assembly in evaporating drops using electrowetting

We study the influence of electrowetting on the evaporative self-assembly and formation of undesired solute residues, so-called coffee stains, during the evaporation of a drop containing non-volatile solvents. Electrowetting is found to suppress coffee stains of both colloidal particles of various sizes and DNA solutions at alternating (AC) frequencies ranging from a few Hertz to a few tens of kHz. Two main effects are shown to contribute to the suppression: (i) the time-dependent electrostatic force prevents pinning of the three phase contact line and (ii) internal flow fields generated by AC electrowetting counteract the evaporation driven flux and thereby prevent the accumulation of solutes along the contact line Please see the link below for a short presentation and movies: http://www.youtube.com/watch?v=xwipCVZnN4E   

Vibration Assisted Convective Deposition

A novel strategy for improving a convective deposition of aqueous binary suspensions of colloidal microspheres and nanoparticles was experimentally examined and reported. By adding a substrate vibration, an enhancement in deposited film qualities was observed. Moreover, by using this technique, it was easier and faster to obtain monolayer structures. In this experiment, we varied the amplitudes of substrate vibration between 0-330 $\mu $m. The quality of thin films was characterized by using a confocal laser scanning microscope and an image analysis. The motion of an interfacial liquid surface and the change in an evaporate rate due to a substrate vibration played an important role in an improvement of the deposition process. The monolayer structures formed from this rapid process can be used in a variety of optical, chemical, and biochemical sensing applications such as a LEDs device, a membrane separation and a cell capturing.   

Interaction of bi-dispersed particles with contact line in inkjet-printed evaporating colloidal drops

The deposition behavior of inkjet-printed aqueous colloidal mixture of micro and nanoparticles onto a glass substrate with systematically varied wettability has been investigated using fluorescence microscopy. Real-time bottom-view images show that particles inside an evaporating drop rearrange themselves near the drop contact line according to their sizes, where smaller particles tend to deposit closer to the contact line compared to the larger ones. By increasing substrate wettability, particles in the bi-dispersed mixture can be further separated compared to those on substrates of poor wettability. This is primarily because during different stages of evaporation, the interplay of surface tension, drag due to evaporative flow, and particle-substrate interactions, rearrange particles inside a colloidal drop near the contact line region. Forces acting on particles determine the extent to which particles enhance contact line pinning, which ultimately determines the final deposition morphology of particles from a bi-dispersed colloidal mixture. The effects of particle size contrast, particle volume fraction, and substrate surface energy on particle separation are examined in detail.   

Fast Evaporation of Spreading Droplets of Colloidal Suspensions

When a coffee droplet dries on a countertop, a dark ring of coffee solute is left behind, a phenomenon often referred to as ``the coffee-ring effect.'' A closely related yet less-well-explored phenomenon is the formation of a layer of particles, or skin, at the surface of the droplet. In this work, we explore the behavior of a mathematical model that can qualitatively describe both phenomena. We consider a thin axisymmetric droplet of a colloidal suspension on a horizontal substrate undergoing spreading and rapid evaporation. The lubrication approximation is applied to simplify the mass and momentum conservation equations, and the colloidal particles are allowed to influence droplet rheology through their effect on the viscosity. By describing the transport of the colloidal particles with the full convection-diffusion equation, we are able to capture depthwise gradients in particle concentration and thus describe skin formation, a feature neglected in prior models of droplet evaporation. Whereas capillarity creates a flow that drives particles to the contact line to produce a coffee-ring, Marangoni flows can compete with this and promote skin formation. Increases in viscosity due to particle concentration slow down droplet dynamics, and can lead to a significant reduction in the spreading rate.   

Capillary-Driven Convective Assembly of Colloidal Monolayers

Convective self-assembly is a powerful method for the deposition of particle thin films. We investigate the coupling between suspension properties and the deposition process during convective deposition of unary colloidal silica microspheres as well as the use of nanoparticles as packing aids. We can tune suspension and deposition properties to deposit submonolayer, monolayer, or multilayer morphologies. Thin films are analyzed via high speed confocal and scanning electron microscopy in order to generate local dynamic data describing the deposition process as well as the long-range structure of deposited thin films.   

Session R7: Turbulent Boundary Layers VIII: Geophysical

Disruption of bottom log-layer in LES of Langmuir circulation in shallow seas

We report on disruption of the log-layer in the resolved bottom boundary layer in large- eddy simulations (LES) of full-depth Langmuir circulation (LC) in a wind-driven shear current in neutrally-stratified shallow water. LC consists of parallel counter rotating vortices that are aligned roughly in the direction of the wind and are generated by the interaction of the wind-driven shear with the Stokes drift velocity induced by surface gravity waves. The disruption is analyzed in terms of mean velocity, budgets of turbulent kinetic energy (TKE) and budgets of TKE components. For example, in terms of mean velocity, the mixing due to LC induces a large wake region eroding the classical log- law profile within the range 90 $<$ z+ $<$ 200. The dependence of this disruption on wind and wave forcing conditions is investigated. Results indicate that the amount of disruption is primarily determined by the wavelength of the surface waves generating LC. These results have important implications on turbulence parameterizations for Reynolds-averaged Navier-Stokes simulations (RANSS) of the coastal ocean. Preliminary simulations highlight the need for turbulence models taking into account log-layer disruption by LC, as RANSS with the k-epsilon model is unable to capture this disruption.   

Dispersion length scales within the urban canopy

We discuss the results of lab experiments on three model urban canopies with small, medium and large building aspect ratios to examine the physics of dispersion within the urban canopy from a near-ground continuous point source of passive scalar. The model urban canopies had aspect ratios of building height to width (H/w) = 0.25, 1, 3. Measurements were taken of the turbulent velocity and scalar fields. Plume spreads, concentrations and distance from the source were non-dimensionalized using urban canopy length, time and velocity scales based on the geometry of the buildings. The scaling collapses the data for all three aspect ratios. A model to describe the results is developed. The model is based on a simple Gaussian formulation where the diffusion coefficients are determined by the theories of Taylor (1921) in the horizontal plane, and Hunt and Weber (1979) to account for the vertically inhomogeneous turbulence.   

Scale separation effects in turbulent boundary layers

The velocity and vorticity field interactions that underlie the mean mechanism of turbulent inertia and the wall-normal variation of turbulence kinetic energy are investigated over a wide variation in Reynolds number. Existing well-resolved laboratory data, $\delta^+=375$, $970$ \& $1500$, and data from the atmospheric surface layer over Utah's west desert, $\delta^+=890,000$, are used to establish the relevant statistical and spectral properties. The influences of scale- separation, as well as the scale selection phenomena first observed by Priyadarshana et al. (\textit{J. Fluid Mech.} \textbf{570}, 2007) are of interest. Scale-separation is quantified using both the difference and ratio of the peak frequencies of the relevant velocity and vorticity components. The scale selection phenomena is clarified by examining the relative behavior of the spectra and associated co-spectra as a function of both $y^+$ and $\delta^+$. Near the wall, scale- separation is due to the rapid spatial confinement of the vortical motions, while the scale selection correlates with the vorticity spectra. Away from the wall, scale-separation is due to the spatial dispersion of the vortical motions, and the scale selection correlates with the velocity spectra.   

On the distribution of the streamwise fluctuation velocity in wall bounded flows

The streamwise velocity fluctuations in wall-bounded flows has recently received renewed interest. Measurements and simulations at low Reynolds numbers ($Re$), as well as high $Re$ wind tunnel studies and data from the atmospheric boundary layer (ABL) are at hand but show sometime conflicting trends with $Re$. However, high $Re$ data often have some uncertainties associated with them, such as poor spatial resolution for laboratory data or other uncertainties associated with ABL experiments. Several models for the wall normal distribution of $u_{rms}$ have recently been proposed, based on various physical ideas together with empirical inputs. Here we propose a new model based on two observations: a) $u_{rms}$ normalized with the local velocity $U$ decreases linearly with respect to $U/U_\infty$ in the outer part of the flow, b) in the inner region $u_{rms}/U$ deviates from the linear trend at a specific value of $U/u_\tau(\approx 17)$, where $u_\tau$ is the friction velocity. Using this information it is possible to formulate a composite description of $u_{rms}$ in the wall normal direction for all Reynolds numbers. This shows two important results, namely the increase in $u_{rms}/u_\tau$ with $Re$ as well as a prediction of a second ``outer'' maximum when $Re$ is high enough, a debated feature that has been observed in ABL experiments as well as in some laboratory experiments at high $Re$.   

The effect of atmospheric stability on the energetic contribution of the large scale structures in turbulent boundary layers

Turbulent boundary layer measurements in wind tunnels and in the near neutral atmospheric surface layer outlined a significant contribution of the large scale motions to turbulent kinetic energy and Reynolds stresses for a wide range of Reynolds number, providing evidence of complex scale interactions across the wall region. In order to understand the effect of the large scales on the near wall turbulence and extend the predictive models of amplitude modulation to more realistic atmospheric conditions, different thermal stability conditions must be explored. In this study, experiments are performed in the atmospheric wind tunnel of the St. Anthony Falls Laboratory independently controlling air flow and floor temperatures. Measurements of fluctuating temperature simultaneously with the streamwise and wall normal velocity components are obtained with an ad hoc calibrated and customized triple-wire sensor. Scaling quantities and the dominant terms in the turbulent kinetic energy and temperature variance budget equations are estimated and discussed. A comparative analysis of the weakly stable, convective and neutral conditions based on the power spectra of the streamwise, wall normal and Reynolds stress contributions is presented. Appreciable differences in the energetic contributions of the large scales were observed.   

Cyclic instabilities, turbulence and heat transfer in rotating channel flow simulations

Fully developed turbulent channel flow subject to spanwise rotation including a passive scalar is studied by direct numerical simulations. The Reynolds number based on the bulk velocity and channel half width is up to 30000 and the rotation rate covers a broad range. At moderate rotation rates the flow partly relaminarizes on the stable side of the channel and in some cases turbulent spots or oblique laminar and turbulent bands can be identified. The turbulent Prandtl number is close to one in non-rotating channel flow, but is it much smaller if the flow is rotating. At high rotation rates and sufficiently high Reynolds numbers cyclic instabilities are observed. The time scale of the instabilities is much longer than any turbulent time scale. Further analysis show that these instabilities are caused by exponentially growing Tollmien-Schlichting (TS) waves which can develop due to the weak turbulence in rapidly rotating channel flow. When the amplitude is large these TS waves become unstable and break down into intense turbulence which decays because of the rotation. After some time the TS waves start growing again when the turbulence is sufficiently weak and the whole process repeats itself. The cyclic instabilities lead to intense bursts of turbulence, strong wall shear stresses and high heat transfer rates.   

The role of stability in modulating the structure and transport efficiency of turbulence in the atmospheric surface layer

A vast body of literature has emerged over the last few decades on the topology, dynamics, and role of coherent structures in turbulent boundary layer flows. The applicability of this knowledge to geophysical flows is problematic due to the often-dominant role of buoyancy. Here we aim to investigate the effect of buoyancy on coherent turbulent structures, with a focus on the ties between these structures and turbulent transport. The results confirm that the topology of the coherent structures is very sensitive to stability. The findings point to a gradual transformation of the structures from hairpin vortices (or horizontal rolls) to thermals, as the upward buoyancy flux increases. More importantly, this change induces a decorrelation of the momentum and scalar fluxes in the surface layer and significant change in the relative efficiencies of momentum and scalar transport. Scalars are transported much more efficiently under unstable conditions. These findings provide a better framework for including the effect of stability in turbulent transport models and open the way for more advanced models based on a better understanding of turbulent scale-interactions under different stabilities.   

Viscous boundary layers in turbulent Rayleigh-B\'{e}nard convection

Thermal convection at high Rayleigh number is a basic and important ingredient for the motion of air or the flow of water in the atmosphere and in the ocean. However, particularly in case of highly turbulent flows the knowledge about the temperature and the velocity field is still limited. Highly resolved 3d-Laser Doppler Velocimetry measurements in a large-scale Rayleigh-B\'{e}nard experiment with air at Rayleigh numbers up to 10$^{10}$ have been carried out and presented by our group on 2010's APS conference. All three velocity components have been measured simultaneously in the vicinity of the cooling plate in the central axis of the cylindrical sample. We found that the profile of the mean wall-normal velocity tends to zero. In the contribution of this year we will enhance the understanding of the heat transport by presenting the fluctuations of the wall-normal velocity component and the temperature. Again, we estimate the profile of the local heat flux from the independently measured velocity and temperature data.   

Reynolds and swirl number effects on turbulent pipe flow in a 90 degree pipe bend

Flows in pipe bends have been studied extensively over the last decades due to their occurrence both in the human respiratory and blood systems as well as in many technical applications. The centrifugal effect of the bend may give rise to Dean vortices and the behaviour of these has been of particular interest. While their motion has nicely been illustrated in laminar flows, the picture of their motion in turbulent flows remains rather blurred. Within the framework of the present work, fully developed turbulent pipe flow from a 100 diameter ($D$) long pipe is fed to a $90^\circ$ bend and the flow field at $0.5D$ downstream the bend has been studied by means of Time-Resolved Stereoscopic Particle Image Velocimetry, covering a Reynolds number range from 7000 to 34000 based on bulk velocity ($U_b$) and $D$. Additionally, a well defined swirl profile could be introduced by rotating the $100 D$ long straight pipe along its axis, yielding a variation in swirl number ($S$), defined as the ratio between the azimuthal velocity of the pipe wall and $U_b$, from 0 (the non-rotating case) to 1.2. The three-dimensional time-averaged and instantaneous flow field illustrating the symmetrical Dean vortices for $S=0$ and the influence by the swirling motion for $S\neq0$, the so-called ``swirl-switching phenomenon,'' as well as the large-scale structures will be presented and discussed.   

Session R8: Non-Newtonian Flows III

The effects of long-chain polymers on tip vortex flow and cavitation inception

Experiments have shown that propeller/hydrofoil tip vortex cavitation can be suppressed by properly injecting dilute polymer solutions at the tip. However, the mechanisms for this phenomenon are not well understood yet. To understand better the underlying flow physics the tip vortex flow generated by a rotating propeller in water and a dilute polymer solution (FENE-P model) was numerically simulated. It is found that the vortex flow structure is changed by the non-Newtonian features of polymers. Phenomenally the vortical rotation in a polymer solution is slower and the vortex center pressure is higher than in water. The non-Newtonian stress is much stronger than the Newtonian stresses in water. To further understand the non-Newtonian stresses contribution, the FENE-P model is also applied to a simplified quasi-cylindrical vortex. It is found analytically that in addition to the three normal stresses that are expected to be quadratic in the shear rate, one of the shear components is also quadratic. We also studied polymer effects on the dynamics of a bubble nucleus in the tip vortex. The bubble was found to grow to an elongated large cavity in water while it collapses in the polymer solution for the same cavitation number. This work was supported by the Office of Naval Research, Contract N00014-04-C-0110, monitored by Dr. Ki-Han Kim.   

Modeling Vortex Cavitation Inception Delay in a Swirl Chamber by Polymer Injection

Experimental studies have shown tip vortex cavitation can be delayed with injection of drag reducing dilute polymer solutions. We present here numerical simulations conducted to understand the mechanisms responsible for cavitation suppression with local polymer injection. A canonical flow in a linear vortex chamber was simulated by using the NS solver, \textsc{3DynaFS-Vis}$^{\copyright }$, equipped with a FENE-P viscoelastic model for the polymer solution and a transport equation to track its concentration. The simulation showed that injection of dilute polymer can delay cavitation inception at a much lower injection flow rate than needed with massive injection of water or a higher viscosity liquid. Injection of polymer increases the pressure along the vortex axis and a much earlier vortex breakdown created by the elasticity of the polymers appears to be responsible for the strong modification of the flow character. This results in a fast reduction of the rotational velocity, increase of the pressure, and delay of cavitation inception. The dependency of polymer effects on the injection flow rate and polymer concentration was also investigated, finding good consistency with experimental observations.   

Viscoelastic instabilities in a 3D Stokes-Oldroyd-B fluid

The consequences of three-dimensional viscoelastic instabilities are examined numerically using the Oldroyd-B model in the low Reynolds number (Stokes) regime. The fluid is driven by a simple time-independent forcing that, in the absence of viscoelastic stresses, creates a four-roll mill in (x,y) which is constant in z. It is now known that such forcing will force the 2d version of this system into symmetry breaking and flow mixing. Here we find that at sufficiently large, but O(1), Weissenberg number, 3d perturbations grow exponentially and lead to complex three-dimensional flow dynamics which can differ markedly from the 2d case.   

Study of the behavior of rising bubbles in a Boger-type fluid

Particle aggregation is a common phenomenon observed in viscoelastic multiphase flows. In this work a new effect has been observed to occur in monodispersed bubbly flows in a Boger-type fluid. It was found that the dispersion of bubble changes dramatically depending on the bubble size: if the diameter of the bubbles is small, large vertical clusters are formed; on the other hand, the bubble assembly rises in a dispersed manner if the bubble size is increased. To understand the condition for which agglomeration occurs two additional experiments were conducted: the interaction of two side-by-side bubble chains was analyzed; and, the unsteady behavior of the first normal stress difference was studied in a rheometric flow. These analyses suggest that there is a process of accumulation of elastic stress; when the accumulated elastic stress surpasses the viscous repulsive stress, aggregation can occur even at supercritical speeds. Interestingly, the two bubble diameters tested in the bubbly flow experiments are above and below the critical diameter for which the velocity of an isolated bubble becomes discontinuous, the so-called bubble velocity discontinuity. This suggests that the bubble dispersion improvement could result from the modification of the gas-liquid interface.   

Pertrurbation theory for dynamic behavior of a sphere settling in a viscoelastic fluid

We present a new perturbation theory for the motion of a rigid sphere settling in a viscoelastic Oldroyd-B fluid that can be generalized to other scenarios of viscoelastic fluid-structure interaction. In contrast to previous perturbation theories, the perturbative expansion variable is not the Weissenberg number, but instead it is a parameter measuring the feedback of the viscoelastic stress into the fluid momentum. This allows for accurate calculations at large Weissenberg numbers. Previous experiments, including our own, have documented that a sphere overshoots its terminal velocity on a transient timescale comparable to the fluid relaxation time. Our theory predicts this behavior as well as a non-trivial dependence of the drag on the Weissenberg number. I will also discuss experiments in which periodic forcing is applied to a body moving through a viscoelastic fluid, and the perturbation theory is used as a predictive tool.   

Phase syncronization of swimming infinite sheets in viscoelastic fluids

A Navier-Stokes/Oldroyd-B immersed boundary algorithm is used to examine the interaction of swimming infinite sheets with a viscoelastic fluid. In particular, we examine the spatial and temporal evolution of the polymer stress field. The effects of the bulk viscoelasticity on hydrodynamic synchronization of swimming sheets and sheets swimming next to solid walls is analyzed.   

Effects of viscoelasticity on the migration of a viscous drop in a shear flow near a wall

Dynamics of a drop migrating in a shear flow of a viscoelastic liquid (FENE-CR) near a wall is numerically investigated. Viscoelasticity hinders migration, and it is explained by investigating the viscoelastic forces around the drop. The orientation angle and the lateral migration velocities both decrease linearly with increasing viscoelasticity (Deborah number and amount of polymer viscosity). The enhanced curvature of the streamlines above the drop adds to this effect, it being more prominent for smaller deformation at lower capillary numbers. The slip velocity of the drop decreases with increasing Deborah number. For viscosity matched systems, the initial position does not influence the migration for the low values of Deborah number considered. However, at higher viscosity ratios, initial position plays a role. Increasing the viscosity ratio lowers the migration velocity and addition of viscoelasticity decreases it further. For very high viscosity ratio, viscoelasticity can induce drop migration towards the wall.   

Significance of viscoelastic effects on the rising of a bubble and bubble-to-bubble interaction

Numerical results for the rising of a bubble and the interaction between two bubbles in non-Newtonian fluids will be discussed. The computations are carried out using a multiscale method combining front-tracking with Brownian dynamics simulations. The evaluation of the material properties for the non-Newtonian fluid will be discussed firstly. The results from the computations of a single bubble show how elastic effects modify the deformation and rising of the bubble by pulling the tail of it. The relationship between the strength of the elastic forces and the discontinuity in the bubble terminal velocity, when plotted versus bubble volume, is also observed in the computations. The bubble-to-bubble interaction is dominated not only by elastic effects but also by the shear-thinning caused by the leading bubble, which leads the trailing bubble to accelerate faster and coalesce with the leading bubble.   

Viscoelastic droplet deformation in complex flow: application of the extended finite element

Deformation of a viscoelastic drop in a Newtonian matrix under Stokes flow is simulated using a eXtended finite element method (XFEM). We consider the matrix inside a continuous mixer (like twin screw extruder), where shear and elongational flows are presents. Surface tension is included in the traction vector across the interface between the droplet and the matrix. The governing balance equations~ are solved once over entire domain (droplet and matrix). The surface of droplet is described by a discretized mesh and its position is updated by tracking the nodal positions in time. For XFEM integration, the position of the surface is determined explicitly by a numerical level set. To couple the velocity between droplet and matrix, a constrain is applied on balance equations. Constraints are enforced using a Lagrangian multiplier and also using weak interface conditions. Results are discussed for different viscosity ratio's and different Weissenberg numbers.   

Session R10: General Fluid Dynamics III

An Investigation of Length Scales in Active Grid Generated Turbulence

A novel active grid design is used to generate high Reynolds number homogeneous, isotropic turbulence. Typically, active grids consist of square wings mounted on a bi- planar mesh of rods. Each rod of the mesh is controlled independently by a stepper motor, which receives randomly varied signals defining its period and speed of rotation. The present design consists of two bi-planar rod meshes. Wing placement alternates between the forward and aft meshes, allowing for the motion of adjacent wings to be decoupled by mounting them on independently rotating rods. By changing the degree of correlation between the motion of wings, the length scales of the output turbulence may be influenced while the turbulence itself remains approximately homogeneous and isotropic. Furthermore, the structure of the turbulence may be dependent on the wing geometry. As such, alternative wing geometries (e.g. circular) are also investigated. The primary focus of this study is to investigate the effect of initial conditions on the length scales of turbulence in the context of active grid generated turbulence.   

Identification and manipulation of dynamic modes in nematic liquid crystals

We present work identifying and manipulating patterns formed in an electroconvecting nematic liquid crystal. The existence of coherent, temporally and spatially correlated, structures are found in a wide range of driven systems. The development of new experimental and analytical techniques has enabled the identification of these structures and is beginning to elucidate their role in establishing macroscopic behavior. Here we describe an algorithm used to identify and track these structures, and report on the effects of local and global stimulation on their creation and evolution.   

Power consumption and dynamic structure in electroconvecting liquid crystals

A wide range of driven systems display complex, but correlated, dynamics as well as large fluctuations in energy injection, storage, and dissipation. We use an electroconvecting nematic liquid crystal as a model system to investigate the relationship between dynamical structure and energy flow. We use a dimensionality-reduction algorithm to identify the creation, evolution and annihilation of patterns of defects in a weakly-driven electroconvective state. By simultaneously measuring the electrical power drawn by the sample we are able to determine correlations between energy injection and defect dynamics. We will discuss these correlations as well as the interplay between energy flow and dynamic structures in this system.   

Hot balls splash and sink fast

When a heated sphere is immersed in a liquid, we induce an inverted Leidenfrost effect whereby the sphere is wrapped in a vapour jacket which protects it from physical contact with the liquid and, when released to fall freely in the liquid, the sphere's terminal velocity can increase dramatically compared to a cold ball. This Leidenfrost-induced vapour layer can lead to significant drag reduction by up to 85\% which appears to be the limiting case for drag reduction techniques based on gas layer injection. In a related experiment, when the heated sphere is released from above the surface, the dynamics of the entry are significantly different from the cold case, resulting in a prompt splash and cavity formation. We propose that this experiment is the ultimate non-wetting scenario during water-entry problems.   

Spatial characterization of underwater turbine wakes using Three-dimensional three-component (3D3C) velocity measurements

A growing interest in underwater turbines (using tidal, river, and marine currents among others) has been observed during the last few years. A fundamental understanding of the turbulent flow around underwater turbines is crucial to predicting the potential effects of these structures on the local morphology, water flow, and power available in the current. The flow structure downstream of a turbine are inherently complex in that it is both unsteady and three dimensional. For this reason, a measurement technique that captures the full volumetric three-dimensional velocity field is advantageous for analyzing the complexity of the flow. In this study, a miniature horizontal axis 3-blade underwater turbine, aligned in the direction of the mean flow, was placed in a water flume at the St. Anthony Falls Laboratory at the University of Minnesota. Three-dimensional three-component (3D3C) velocity measurements were made in the flow downstream of the miniature underwater turbine. Wake evolution, turbulence characteristics and primary three-dimensional flow features were identified in the instantaneous and ensemble-averaged flows at different locations downstream of the turbine.   

Physics of badminton shuttlecock. Part 2 : Turn around

We study experimentally shuttlecocks dynamics. In this part we show how the shuttlecock shape is optimized for badminton play. The shuttlecock always flies the nose forehead. After the impact it has thus to return. Actually it returns, oscillates and then stabilizes. We try to understand these damping oscillations and draw an analogy with the dandelions achenes and parachutists.   

Laminar jet injection in a pipe with co-flow

Particle Tracking Velocimetry (PTV) was used to investigate confined injection from a generic end-hole catheter within an axial co-flow environment. PTV was carried out in an iterative fashion where an approximate field was calculated from several time instances, and subsequently used as an estimator for hybrid tracking. The influence of momentum ratio on jet expansion, transport, and flow patterns was studied for several velocity ratios (VR = V$_{jet}$/V$_{out})$ between 0 and 10. The Reynolds number of the outer flow was 150 and that of the inner flow varied from 0 to 260. Flow patterns behind the catheter were dependent upon VR with recirculation regions present for low ratios. A separation bubble was observed behind the catheter for velocity ratios below 0.5 and two counter-rotating vortices were seen for VR = 0. As VR increased, asymmetry in the outer flow resulted in a single vortex behind the catheter with its position skewed toward the low flow side of the vessel and larger entrainment was present on the high flow side of the vessel. As VR increased above 0.5, recirculation was not observed and at VR = 1.0 the jet velocities were mainly in the streamwise direction.   

Effects of Exhaust Gas Recirculation on SI Engines at Wide Open Throttle

Exhaust gas recirculation, a charge dilution technique, has proven to be an effective method of reducing NOx emissions and fuel consumption of spark ignition engines. Wide open throttle operation also increases overall engine efficiency by reducing the pumping losses caused by throttling. In this study, the emissions and fuel economy benefits of exhaust gas recirculation (EGR) at wide open throttle conditions were quantified using a 2.4L port-injected engine. Engine performance and emissions data were recorded as the percentage of EGR in the intake charge was increased from zero to just above thirty percent (the EGR limit). This EGR percentage, in-cylinder pressure measurements, and the temperatures and pressures of the intake and exhaust were all recorded to ensure stable operating conditions. These tests were performed with a stoichiometric air-fuel ratio at a constant speed of 2000 rpm at wide open throttle. The variation of brake specific fuel consumption and emissions (in particular NOx) with increasing EGR percentages was analyzed.   

Pressure-velocity correlations in a flow upstream of a forward-facing step

The 2-dimensional velocity field upstream of a forward step was determined experimentally using Particle Image Velocimetry. A total of 4 seconds of data was acquired at $8000\rm{Hz}$. The flow velocity was $10\rm{ms^{-1}}$ with an $\rm{Re}_h$ of 20000, where $h=0.03\rm{m}$ is the step height. The boundary layer thickness relative to step height was $\delta/h=1.6$. The upstream surface pressure fluctuations were simultaneously measured using an array of 9 microphones embedded in tunnel floor. These pressure fluctuations are shown to have a direct linear correlation to the velocity perturbations. The correlation has a maximum of approximately 0.3 at upstream stations $x/h>2$ and reduces toward background noise levels as the flow approaches separation at $0.5 [Preview Abstract]

Session R11: Turbulence: Shear Layers II

Scaling Law for the Onset of Turbulence in Channel Flow

We are presenting experiments about the onset of turbulence in channel flow. We perturbed the base plane Poiseuille flow with continuous injection of water normally to the flow. We performed Particle Image Velocimetry experiments to measure the mean velocity profile with respect to the Reynolds number, $Re$ and the amplitude of the perturbation $u_{jet} /u_{cl}$. Due to the unstable nature of the flow with respect to finite amplitude perturbation, it should exist a minimal amplitude $\varepsilon $, which trigger the transition to the turbulence. In order to find this critical value, we define a new experimental criterion using the value of $\tilde {u}=\bar {u}_{cl} /\bar {u}_{cl,unperturbed}$, giving the deformation of the mean velocity profile. We found a power law for the onset of turbulence $\varepsilon =O(Re^{-3/2})$ and compared it with different models and previous experiments.   

Experimental Evolution of Local and Global Variables in the Subcritical Transition in Channel Flow

We perform experiments on the subcritical transition to the turbulence in a water channel with plane Poiseuille flow, perturbed by controlled injection of water normally to the wall. For different values of Reynolds number $Re$ and different amplitude of the perturbation $u_{jet} /u_{cl} $, we observed different states from laminar to turbulent. Using Particle Image Velocimetry, we study the dynamics of a local variable of the velocity field as the transverse magnitude and simultaneously we follows a global one, as the deformation of the mean velocity profile $\tilde {u}=\bar {u}_{cl} /\bar {u}_{cl,unperturbed} $. We discuss the evolution in the phase space of those variables as a function of the strength of the perturbation, and compare it with predictions made from low dimensional models.   

The low-frequency undulation mechanism in a open cavity shear layer flow

The unsteady flow and pressure field in an open cavity shear layer has been investigated using time resolved PIV measurements. Here, we focus on the closed-loop feedback mechanism that causes low-frequency undulation in the location of the shear layer relative to the cavity trailing corner. It is found that impingement of high momentum fluid on the forward-facing surface of this corner, when the shear layer is low, periodically increases the pressure there, and the inward flow along this wall. The latter re-circulates back to the leading corner of the cavity, increasing the pressure there, and imposing adverse pressure-gradients on the boundary layer upstream of the cavity. The resulting increase in boundary layer thickness starts an upward shift in the elevation of the shear layer, which reduces the momentum, pressure and jetting into the cavity at the downstream corner. This reduced backflow decreases the pressure at the inlet corner and the incoming boundary layer thickness, causing a downward shift in elevation of the shear layer. This low-frequency undulation has substantial impact on the turbulence and noise generations by the cavity corner.   

Simultaneous measurement of pipe flow downstream and upstream of 90 degrees bend by using stereo PIV

We measured velocity vector distribution in cross sections of a fully developed turbulent pipe flow upstream and downstream of a 90 degrees bend by using stereo PIV and single camera PIV simultaneously. Reynolds number was $Re$=27,000, and ratio of inner diameter $d$ (=50mm) of the pipe and radius of the centerline of the bend was 1.0. Instantaneous flow field downstream of the bend represented the unsteady motion of the anti-symmetric counter-rotating Dean vortices. Stagnation point, which was created by the flow induced by the two vortices, was observed at both inner and outer side of the bend. The stagnation point moves unsteadily within roughly 30 degree above and below the symmetry plane. In order to clarify the origin of such unsteady motion of the stagnation point, conditional average of the upstream velocity vector field conditioned by the azimuthal location of the stagnation point downstream the bend was computed. Under condition where the inner side stagnation point stays above (below) the symmetry plane, the conditional streamwise velocity upstream the bend exhibited a positive peak below (above) the plane on the outer side.   

The turbulent wake of a submarine model at varying pitch and yaw angle

The objective of the present study is to understand how the pitch and yaw angle affect the mean flow and turbulence in the wake of an axisymmetric submarine model (DARPA SUBOFF model). Measurements in the wake were performed at a Reynolds number based on the length of 2.37 $\times$ 10$^{6}$. Mean velocity and two-component turbulence measurements were performed using Pitot probes and hot wires in the span-wise plane at three different downstream positions: 5, 7.5 and 10 diameters downstream of the trailing edge. The range of measured angles of attack and yaw angles were limited to between 0 and 10\r{ } in part to avoid wind tunnel interference effects. Work supported by ONR Grant N00014-09-1-0263.   

Mixing length and scale-to-scale kinetic energy transfer in the wake of a fractal tree

To study the dynamics of turbulence interacting with multi-scale objects, we measure turbulence structure in the wake of a fractal tree-like object in a water channel, using PIV. The eddy viscosity is obtained from the correlation of mean shear and Reynolds shear stress distributions across the wake. We address the question whether a mixing length-scale can be identified in this flow, and if so, how it relates to the geometric length-scales in the pre-fractal object. One approach is based on spectral distributions. Another more practical approach is based on length-scale distributions evaluated using fractal geometry tools. These models agree well with the measured mixing length indicating that information about multi-scale clustering of branches has to be taken into account. To explore the energy transfer at different scales, data are spatially filtered at various scales and the subgrid-scale flux among scales is evaluated. In contrast to regions characterized by a single length scale (bottom of the tree) where a classical inertial range cascade behavior is observed with scale-independent flux, at heights where multiple branch generations interact with the flow, we find that the energy flux depends strongly on the filter size, increasing with smaller filter sizes. The results can be explained by production at multiple-scales.   

Heated Jets Emitting From a Rectangular Stack into a Cross Wind

A detailed analysis of jets in cross-flow is performed where jets heated to a centerline temperature $T_\circ = 425$\,K emit from a rectangular stack ($AR = 3.76$) into $T_{\infty} = 300 $\,K cross-wind at area-averaged momentum flux ratio $r = 3.3$. Cross-flow and jet centerline velocities are $U_{\infty} = 10$\,m/s and $V_\circ = 50$\,m/s, respectively. Injection is normal to the bounding wall from a raised stack such that the initial incidence of jet interaction with cross-flow occurs well outside of the boundary layer. Rake-mounted thermocouple measurements of mean temperature and cross-plane stereoscopic PIV measurements of the turbulent flow field are performed at multiple stations downstream of the stack in spanwise--wall- normal regions of interest. Stack yaw angles of $0^{\circ}$, $45^{\circ}$, and $90^{\circ}$ comprise a set of key orientations from which inferences can be made of real-world heated jet in cross-flow behavior where cross-flow directionality may vary under shifting mean wind direction. From the measurements made under each of these stack orientations, the downstream dispersion of the heated jet fluid is characterized as is the downstream evolution of the turbulence and associated vortical structures.   

Turbulent structures of impinging circular jet

Turbulent impinging jets are used in various engineering applications due to their ability to provide superior heat and mass transfer. In hydraulic engineering, impinging jet flows have a detrimental effect due to their ability to scour and erode sand beds. In order to gain a better insight into the mean flow, turbulence and coherent structures in impinging jet flows, we performed high resolution particle image velocimetry (PIV) measurements of a round normally impinging jet issuing from a nozzle with diameter d = 0.01 m at Reynolds number Re =20 000 and at the jet-to-plate distance H = 20d. This configuration was chosen to match previously reported experiments and to verify results obtained from numerical simulations in which several phenomena have been noted, but the underlying turbulence dynamics remained obscure. PIV velocity fields are measured in the streamwise - spanwise (x-z) planes in the free jet and stagnation regions while streamwise - wall normal (x-y) planes are probed in the radial wall jet region in the immediate proximity of the impinging plate. The focus of this study is to investigate in details mean velocities, various turbulent quantities and vorticity. Analysis of the coherent structures is also documented through the analysis of swirling strength and proper orthogonal decomposition (POD).   

Half-loop and full-loop shedding in the wake of wall-mounted square cylinders due to boundary layer-wake interaction

The vortical flow in the finite wall-mounted obstacle wakes can be important in heat transfer devices, turbomachinery components, and flame stabilizer devices, and is of fundamental importance since it displays fully three-dimensional states of K\'{a}rm\'{a}n vortex streets that are found in 2D bluff body wakes. The turbulent state of the wake of a finite square cylinder (height-to-width ratio $h/w$=8) has been found to be sensitive to the conditions of the approach boundary layer. The energetic quasi-periodic vortical structure topology is found to change between two topological states. Boundary layer thicknesses $\delta/d$=0.7 and 1.6 yield half-loop and full-loop structures, respectively. This modification of the structure topology has significant consequences for modifying the mixing, momentum transfer, turbulence production, and Reynolds stresses in the wake. Using synchronized particle image velocimetry (PIV) and surface pressure measurements for these two boundary layers, the coherent structures in the wake of the cylinder are reconstructed and analyzed. Vortical connector strands which tie together subsequently shed structures lead to high incoherent Reynolds stresses, streamwise vorticity, vortex stretching, and turbulence production in their neighbourhood, but do not appear in the lower regions of the wake for the half-loop topology.   

Session R13: Multiphase Flow VII

Modeling of Sulfuric Acid Condensation on Heat Exchanger Cooling Fins

Sulfuric acid corrosion on metallic heat exchanger cooling fins can cause serious blockage problem and stop the normal operation of heat exchangers. Corrosion rates are strongly dependent on surface film pH value. Therefore, a multi-physics computational framework was developed to predict the liquid film formed on solid surface and the pH distribution. Such a model can be used for better understanding of acid condensation from multi-species system. In this work, first, from S to H$_{2}$SO$_{4}$, formation of sulfuric acid in gas phase during combustion and cooling process was investigated with detailed chemistry mechanisms. The amount of SO$_{2}$ and SO$_{3}$ that plays important role in acid condensation process was calculated. Then, multi-component condensation process was modeled to produce a liquid film of acid and water solution condensed on solid surface that has low temperature. pH value was obtained based on the concentration of the acid. The above work provides critical information for corrosion analysis for heat exchangers.   

Reduced model for multi-component condensation

An extremely efficient reduced model for multi-component condensation is presented. The Becker-D\"oring (BD) equations are approximated by the General Dynamic Equation (GDE) in the supercritical region. The subcritical and critical regions are replaced by a source point that injects clusters into the supercritical region. The location and strength of the source point are determined from local estimates of the Gibbs free energy function, and the diffusion term in a corresponding Fokker-Planck equation. The result is a curve in composition space with Dirac delta function character in planes perpendicular to the curve. Integral properties of the GDE and BD solutions compare well for a typical two-component nucleation pulse experiment and computational effort is reduced by five orders of magnitude.   

Modeling of moving contact lines on electrically charged heated surfaces

Local fluid flow and heat transfer near moving contact lines on heated surfaces is usually described by mathematical models incorporating the effects of evaporation, surface tension, thermocapillarity, and disjoining pressure due to London-van der Waals forces. However, this description is not accurate for the cases when electric charges in the liquid and on the heated surface are present, which is usually the case in applications involving water and liquid metals. We develop a model which incorporates the electrostatic effects into the standard lubrication-type model of a contact line on a heated surface. The gas phase above the liquid is assumed to be pure vapor and the macroscopically dry region of the solid is covered with an adsorbed film. The local liquid-vapor interface shapes and the apparent contact angle are described as functions of the temperature and the charge density at the solid surface.   

Sustained inertial-capillary oscillations and jet formation in displacement flow in a tube

We study inertial effects in the displacement of a fluid in a capillary by a more viscous fluid using a level-set method. Various flow regimes are identified with a Reynolds and a capillary number as the main parameters. At relatively low Reynolds number, the meniscus forms a steady shape, and the interfacial curvature at the tube centre could change from being concave to convex upon increasing the Reynolds number. Beyond a critical Reynolds number, a quasi-steady solution is no longer found for sufficiently small contact angle values (less than 80 degrees): instead, the interface undergoes non-dampened periodic oscillations and, at even larger values of the Reynolds number, quasi-periodically, and the interface evolves from simple wavy shapes to complex shapes with multiple wavy units. Beyond a second critical Reynolds number, the liquid forms a jet and the meniscus advances with a nearly constant speed which decreases with Re. This is also observed at large contact angle values. In a developing jet, however, the interface shape remains partially quasi-steady, near the contact line region and the tube centre. The flow behaviour is shown to be robust over a range of other governing parameters, including the capillary number and the slip length.   

Bubbles in an isotropic homogeneous turbulent flow

Bubbly turbulent flow plays an important role in many engineering applications and natural phenomena. In this kind of flows the bubbles are dispersed in a turbulent flow and they interact with the turbulent structures. The present study focuses on the motion and hydrodynamic interaction of a single bubble in a turbulent environment. In most previous studies, the effect of bubbles on the carrier fluid was analyzed, under the assumption that the bubble size was significantly smaller that the smallest turbulence length scale. An experimental study of the effect of an isotropic and homogeneous turbulent flow on the bubble shape and motion was conducted. Experiments were performed in an isotropic turbulent chamber with nearly zero mean flow, in which a single bubble was injected. The fluid velocity was measured using the Particle Image Velocimetry (PIV) technique. The bubble deformation was determined by video processing of high-speed movies. The fluid disturbances on the bubble shape were studied for bubbles with different sizes. We will present experimental data obtained and discuss the differences among these results to try to understand the bubble - turbulence interaction mechanisms.   

Response of floating grains on a capillary Faraday wave in the dense limit

When macroscopic grains float on a water-air interface, they aggregate into a static cluster due to attractive gravity-induced capillary interaction between the grains. Here we study what happens when the grains in the cluster are excited using capillary Faraday waves with a wavelength comparable to the grain size. The grains are found to exhibit cooperative motion in domains which tend to become larger as the particle concentration $\phi$ increases towards the jamming point. We measure the average grain velocity and the velocity-velocity correlations of the grains in space and time as a function of $\phi$ and the driving amplitude $a$.   

Breakup of particle clumps on liquid surfaces

In this talk we describe the mechanism by which clumps of some powdered materials breakup and disperse on a liquid surface to form a monolayer of particles. We show that a clump breaks up because when particles on its outer periphery come in contact with the liquid surface they are pulled into the interface by the vertical component of capillary force overcoming the cohesive forces which keep them attached, and then these particles move away from the clump. In some cases, the clump itself is broken into smaller pieces and then these smaller pieces break apart by the aforementioned mechanism. The newly-adsorbed particles move away from the clump, and each other, because when particles are adsorbed on a liquid surface they cause a flow on the interface away from themselves. This flow may also cause particles newly-exposed on the outer periphery of the clump to break away. Since millimeter-sized clumps can breakup and spread on a liquid surface within a few seconds, their behavior appears to be similar to that of some liquid drops which can spontaneously disperse on solid surfaces.   

Surface shear viscosity effects on the damping of oscillations in millimetric liquid bridges

The damping rate of the small free oscillations in a non-cylindrical, axi-symmetric liquid bridge between two circular disks is calculated and compared with some previous experimental measurements using hexadecane in a millimetric liquid bridge. Current theories, accounting for viscous damping in both the boundary layers attached to the disks and the bulk, underestimated the measured damping by a $O$(1) quantity. Calculations based on the full Navier-Stokes equations are also in disagreement with the experimental results. These discrepancies are essentially eliminated in this work considering the effect of the surface shear viscosity (whose value results from empirical fitness), which could be due to the presence of a contaminating monolayer. Some conclusions are extracted in connection with surface wave damping in micro-fluidic devices.   

Optimized evaporation from a microchannel heat sink

Two-phase heat transfer devices, benefiting the unique thermal capacities of phase- change, are considered as the top choice for a wide range of applications involving cooling and temperature control. Evaporation and condensation in these devices usually take place on porous structures. It is widely accepted that they improve the evaporation rates and the overall performance of the device. The liquid menisci formed on the pores of a porous material can be viewed as the active sites of evaporation. Therefore, quantifying the rate of evaporation from a single pore can be used to calculate the total evaporation taking place in the evaporator given the density and the average size of the pores. A microchannel heat sink can be viewed as an structured porous material. In this work, an analytical model is developed to predict the evaporation rate from a liquid meniscus enclosed in a microchannel. The effects of the wall superheat and the width of the channel on the evaporation profile through the meniscus are studied. The results suggest that there is an optimum size for the width of the channel in order to maximize the thermal energy absorbed by the unit area of the heat sink as an array of microchannels.   

Numerical simulation of heat transfer provided by an impinging droplet train

A detailed investigation of the parameters that affect cooling within the thermal boundary layer created by a stream of impinging HFE-7100 droplets striking a pre-wetted and heated surface is performed. After the initial transient has ended, the flow enters a quasi-steady state in which the liquid crown formed during continuous droplet impact remains nearly stationary. Factors including initial film thickness, surface tension, droplet velocity, volumetric flow-rate and droplet frequency are categorized as either contributing to changing the thickness of the thermal boundary layer or as non-contributing parameters. Additionally, an analytical solution for the growth of the thermal boundary layer is proposed, using a crown propagation model, to describe the flow within the boundary layer. The analytical model shows good agreement with numerical results and incorporates the influence of the previously identified parameters.   

Session R14: Experimental Techniques V

Velocity measurements in a thermoacoustic refrigerator using Time-Resolved Particle Image Velocimetry

A standing-wave thermoacoustic refrigerator consists of a stack of plates placed in an acoustic resonator with two heat exchangers located at each end of the stack. The full understanding of the heat transfer between the stack and the heat exchangers of thermoacoustic systems is a key issue to improve the global efficiency of such devices. The aim of this work is to investigate the generation of vortices near the ends of the stack, which affects heat transfer. The aerodynamic field in the gap between the stack and the heat exchanger is characterized using a time-resolved particle image velocimetry technique. Measurements are performed in a standing-wave refrigerator operating at a frequency of 200 Hz. Instantaneous velocity fields are recorded at a frequency of 3125 Hz (i.e. 15 velocity fields per acoustic period). Measurements show that vortex shedding occurs at high pressure levels, when the nonlinear acoustic regime prevails and they validate previous experiments [Berson {\&} Blanc-Benon, J. Acoust. Soc. Am., 2007, 122(4), EL122-127]. The increased viscous dissipation generates additional heating and a loss of efficiency.   

Error Reduction in Molecular Tagging Velocimetry (MTV) Processing Using Image Filtering

Prior work has shown that the error level in MTV measurements is closely tied to the image SN level. In practice the SN ratio will depend on experimental conditions such as attenuation, Field of View, laser power, camera, etc.; however, there is a minimum SN level that can be achieved for any given experiment. Experience has shown that MTV images typically have a SN=2-8. It is therefore desirable to be able to lower image noise after the images are acquired to reduce measurement error. In this work post processing MTV images using image filtering schemes such as Gaussian Blur, FFT (band pass), median filtering etc. was investigated using synthetic MTV images with added random noise. The synthetic images were filtered and then processed using a direct correlation technique. The results showed that for very noisy images (i.e. SN$<$4) the all filtering techniques improved the displacement error by 10-40{\%}. As the SN increased filtering because less effective in decreasing error and in some cases increased the measurement error. The FFT band pass filter was most effective and improved measurement error for all SN levels.   

Determining the Shock Hugoniot of Transparent Materials with Hydrodynamic Pressure Loading

The shock Hugoniot is a fundamental relationship between pressure, volume, and energy for a given material. Accurate knowledge of the Hugoniot for a material is critical in order to determine its response to blast waves and ballistic impacts. Traditionally, the shock Hugoniot is measured on a point-by-point basis through an extensive series of high-velocity impact experiments. Observations are confined to pointwise pressure or velocity measurements at the free surfaces of the sample. In this work a new technique is presented, one which allows multiple points of the shock Hugoniot to be determined in a single experiment. A gram-scale explosive charge is detonated to produce an unsteady shock wave in the transparent material sample. Pressure between the charge and sample is initially high, but is rapidly reduced by expansion of the explosive product gases. This loading produces an initially strong shock wave, which attenuates to near the bulk sound speed as it transits the sample. Using a high-speed shadowgraph technique, multiple shock and particle velocity combinations are observed in a single experiment. This allows the measurement of a shock Hugoniot in fewer experiments than by traditional methods. This technique produces data in agreement with published Hugoniot results for polyurethane. It can be easily extended to measure the Hugoniot of any transparent solid, liquid, or gas.   

Toward an automated background oriented schlieren (BOS) system

The background oriented schlieren (BOS) technique is a useful method for visualizing refractive disturbances in a wide range of experimental settings. The technique visualizes refractive disturbances via their distortion of a distant background pattern (typically a speckle pattern). A cross-correlation computer algorithm is typically used to identify and measure distortions of the background pattern, thus revealing the refractive disturbance changes between images and producing a schlieren image. The cross-correlation algorithm, however, can be time-consuming and prevents an instantaneous schlieren image from being observed, thus hampering some potential BOS applications. Here a novel background patterning approach is presented which eliminates the need for the cross-correlation algorithm. Results are presented showing the sensitivity of the new background pattern and its potential application for providing instantaneous BOS images. Background pattern characteristics are explored for high- and low-speed fluid-dynamic applications.   

Molecular candidates of MTV in air

In molecular tagging velocimetry (MTV), the molecules of a gas are used as flow tracers. These tracers can be produced at will by illumination with a laser which promotes molecules to a long- lived excited state, fuses N$_2$ and N$_2$ to NO, or makes molecules phosphoresce. A while later these tagged molecules can be visualized by laser-induced fluorescence, or by just watching them while they phosphoresce. Candidates for MTV in turbulence research must be arranged in structures narrower than the Kolmogorov scale, which remain narrow as time progresses, and must live longer than the Kolmogorov time. These requirements invalidate many candidates, candidates once deemed successful. They do so in various surprising manners that involve a combination of fluid flow and molecular dynamics. Rather than velocimetry in turbulence, MTV techniques offer a unique view on basic dispersion processes at the smallest scales of turbulence. In this way we have measured the spreading of clouds whose size is a few times the Kolmogorov length and the Batchelor dispersion of objects whose size is inside the inertial range.   

Constant Current Plasma Anemometer

An improved design for a plasma anemometer that provides mega-Hertz bandwidth velocity measurements over a range of Mach numbers from subsonic to hypersonic, is presented. The anemometer uses a small volume of ionized air as the sensor. The ionized air is formed between two electrodes that are powered by a high-frequency AC voltage source. Resistance and capacitance elements in the AC power circuit that simulate a dielectric-barrier, have been added to prevent transient filament formation. This resulted in a 300-times reduction in the anemometer EMI of previous designs. In addition, a closed-loop feedback control has been added to maintain a constant current through the sensor. With constant current operation, the voltage drop across the ionized air between the electrodes varies linearly with air velocity (or mass-flux in a compressible flow). This is demonstrated through mean velocity calibrations of the anemometer for a range of velocities and feedback parameters. The dynamic response and other capabilities of the sensor will also be demonstrated.   

In-situ shear stress indicator using heated strain gages at the flow boundary

This work borrows the concept of hot-wire anemometry and sketch a technique that uses local heat transfer to infer the flow field and the corresponding stress. Conventional strain gages were mounted at the flow solid boundary as the heat source and acrylic boundary was chosen for its low thermal conductivity ensuring heat accumulation when a gage is energized. The gage would now work in slightly overheated state and its self-heating leads to an additional thermal strain. When exposed to a flow field, heat is brought away by local forced convection, resulting in deviations in gage signal from that developed in quiescent liquid. We have developed a facility to achieve synchronous gage measurements at different locations on a solid boundary. Three steady flow motions were considered: circular Couette flow, rectilinear uniform flow, and rectilinear oscillating flow. Preliminary tests show the gage reading does respond to the imposed flow through thermal effects and greater deviation was measured in flows of higher shear strain rates. The correlation between the gage signals and the imposed flow field is further examined by theoretical analysis. We also introduced a second solid boundary to the vicinity of the gage in the two rectilinear flows. The gage readings demonstrate rises in its magnitudes indicating wall amplification effect on the local shear strain, agreeing to the drag augmentation by a second solid boundary reported in many multiphase flow literatures.   

Assessment of the Derivative-Moment Transformation method for unsteady-load estimation

It is often difficult, if not impossible, to measure the aerodynamic or hydrodynamic forces on a moving body. For this reason, a classical control-volume technique is typically applied to extract the unsteady forces instead. However, measuring the acceleration term within the volume of interest using PIV can be limited by optical access, reflections as well as shadows. Therefore in this study an alternative approach, termed the Derivative-Moment Transformation (DMT) method, is introduced and tested on a synthetic data set produced using numerical simulations. The test case involves the unsteady loading of a flat plate in a two-dimensional, laminar periodic gust. The results suggest that the DMT method can accurately predict the acceleration term so long as appropriate spatial and temporal resolutions are maintained. The major deficiency was found to be the determination of pressure in the wake. The effect of control-volume size was investigated suggesting that smaller domains work best by minimizing the associated error with the pressure field. When increasing the control-volume size, the number of calculations necessary for the pressure-gradient integration increases, in turn substantially increasing the error propagation.   

Session R16: Porous Media III

Mathematical modelling of membrane separation

Membrane separation is commonly used in chemistry and chemical engineering, where the separation of one or several species of molecules is of interest. This presentation will presents mathematical modelling of the dynamic interplay between the transport equations through the membrane and the transport equations within the bulk solution. Thus, resulting in a system of PDE's with time varying boundary conditions. The model is used for predicting optimal parameters for separation processes.   

Reynolds number dependent flow regime characteristics for flow in porous media

The flow characteristics of distinct flow regimes in porous media and the evolution with Reynolds number is poorly understood at high Reynolds numbers. Typical means of measurement are MRI imaging, PTV and PIV, the latter two require refractive index matching. This study presents PIV measurements in a porous bed of spherical beads, for pore Reynolds numbers from 100 to 1500 resulting in flow in the inertial, unsteady inertial and turbulent flow regimes. The bed is a cube with five bead diameters on a side, with 15 mm beads. Measurements are based on two dimensional slices (five along the optical axis) using two fields of view; the first is four beads by four beads, and the second is of individual pores to provide highly spatial resolution. Fluorescent dye studies are presented. Velocity data are analyzed based on statistical results of two dimensional time series vector fields with emphasis on (i) identification of Reynolds number dependent flow structures (spatial and temporal), (ii) delineation of flow regime transitions, (iii) establishing pore-based fluctuation energy budgets and (iv) illustration of local dispersion characteristics. The goal is to provide statistical flow structure characteristics at the pore level for high Reynolds number flows to better understand dispersion characteristics.   

Pressure driven flow in porous tubular membranes

We consider the steady laminar flow of a Newtonian incompressible fluid in a porous tubular membrane with pressure-driven transmembrane flow. Due to its fundamental importance to membrane filtration systems, this flow has been studied extensively both analytically and numerically, yet a robust analytic solution has not been found. The problem is challenging due to the coupling between the transmembrane pressure and velocity with the simultaneous coupling between the axial pressure gradient and the axial velocity. We present a robust analytical solution which incorporates Darcy's law on the membrane surface. The solution is in the form of an asymptotic expansion about a small parameter related to the membrane permeability. We verify the analytical solution with comparison to 2-D spectral direct numerical simulations of ultrafiltration and microfiltration systems with typical operating conditions, as well as extreme cases of cross-flow reversal and axial flow exhaustion. In all cases, the agreement between the analytical and numerical results is excellent. Finally, we use the analytical and numerical results to provide guidelines about when common simplifying assumptions about the permeate flow may be made. Specifically, the assumptions of a parabolic axial velocity profile and uniform transmembrane velocity are valid only for small permeabilities.   

The Effect of Inlet Swirler Design on Passive Control of Combustion Noise and Instability

The use of porous inert media (PIM) in the reaction zone of a swirl-stabilized lean-premixed combustor provides a passive method of controlling combustion noise and instability. Swirl-stabilized combustors use an inlet swirler that imparts a swirling motion to the reactant flow and stabilizes the flame. In this study, the effect of swirler design and swirl number on combustion without and with PIM has been investigated experimentally, using a methane-fueled quartz combustor at atmospheric pressure. Swirler vane angle was varied to obtain swirl numbers of 0.45, 0.78, and 1.10. Swiler location was varied to obtain recess depth in the premixer tube of 0, 2.5, and 5 cm. Experiments were conducted at a constant air flow rate of 300 SLPM and equivalence ratios of 0.7, 0.75, and 0.8. PIM geometries with increasing and decreasing flow cross-sectional area were tested. The performance of each test case is compared by measuring sound pressure levels (SPL) with a microphone probe and observing the flame behavior. Results indicate that PIM can be effective in reducing noise and instability over a wide range of operating conditions. Total SPL reductions of up to 7.6 dBA were observed with PIM.   

How to Model the Lift Generation in a Highly Compressible Porous Media

Lift generation in highly compressible porous media under rapid compression continues to be an important topic in porous media flow for its superior potential in soft lubrication and squeeze damping. Although significant progress has been made in the study of the lift generation experimentally and theoretically (Wu et al., Journal of Fluid Mechanics 542, 281, 2005; Barabadi, et al., Journal of Heat Transfer, 131(10), 101006, 2009), how to theoretically characterize lifting forces remains unclear. In this paper the permeability of the porous media was measured using a permeater, and then dynamically compacted in a porous-walled cylinder piston apparatus. The obtained pore pressure generation was compared to two different theoretical models, a plug flow model and a consolidation model used in Wu et al. (2005) and Barabadi, et al. (2009). It shows that the consolidation model is appropriate. Furthermore, a viscoelastic model, containing a nonlinear spring in conjunction with a linear viscoelastic Generalized Maxwell mechanical module, is developed to characterize the solid phase lifting force, showing excellent agreement with experimental data. The paper presented herein, conclusively demonstrates the validity of the theoretical approach developed by Wu et al. (2005) and provides a meaningful approach in characterizing forces that contribute to lift generation in soft porous media under rapid compression.   

From Red Cells to Soft Porous Lubrication

Feng and Weinbaum (\textit{J. Fluid. Mech}., \textbf{422}, 282, 2000), inspired by the enhanced lift phenomena in downhill skiing, developed a new lubrication theory for highly compressible porous media where significantly increased lifting force was predicted as a planing surface glided over a soft porous layer; suggesting superior potential use of porous media for soft lubrication. In this study, we experimentally examine the lift generation phenomena by developing a novel soft porous bearing that consists of a running conveyer belt covered with a soft, 100{\%} polyester, porous sheet, and a stationary, fully instrumented, inclined, planar, upper board. Pore pressure was generated as the upper boundary glides over the soft porous bearing and was measured by pressure sensors. One observed that the pore pressure distribution is consistent with predictions by Feng and Weinbaum (2000), and is a function of the relative velocity between the planing surface and the running belt, the mechanical properties (e.g. porosity, permeability and stiffness) and thickness of the porous layer, as well as the compression ratios at the leading and trailing edges. A load cell is used to characterize the performance of the porous bearing, by comparing pore pressure to total lifting forces. The study presented herein significantly improves our understanding of the behavior of highly compressible porous media under fast compression.   

Probing the permeability of porous media by NMR measurement of stochastic dispersion dynamics

A generalized short-time expansion of hydrodynamic dispersion is derived using non-linear response theory. The result is in accordance with the well-known reduced cases of shear flow in ducts and pipes. In terms of viscous dominated (low Reynolds number) flow in porous media the generalized expansion facilitates the measurement of permeability by PGSE-NMR measurement of time dependent molecular displacement dynamics. To be more precise, for porous media characterized by a homogeneous permeability coefficient along the direction of flow $K$, and fluid volume fraction $\varepsilon $, the effective dispersion coefficient $D(t)=\langle \vert $\textbf{R}-$\langle $\textbf{R}$\rangle \vert ^{2}\rangle $/6$t$ of molecular displacements \textbf{R} due to flow and diffusion for a saturating fluid of molecular diffusivity $\kappa $ in viscous dominated flow is shown to be partially governed by the coefficient of permeability at short times. The short-time expansion is shown to be in agreement with pulsed field gradient spin echo NMR measurement of $D(t)$ in a random sphere pack media and analogous pore-scale random-walk particle tracking transport simulation.   

Instability of methane hydrate stability zone in permafrost deposits

As a part of a broad study of the dynamics of natural deposits of methane hydrates, we analyze the instability of the interface between the hydrate-bearing zone and the underlying gas-saturated layer. Conditions of Arctic permafrost with temperature below the ice melting point are considered. The physical model includes the Darcy filtration of gas, conduction and convection heat transfer, and the dynamic boundary conditions including the hydrate dissociation at the interface. The method of linear stability analysis is used. It is found that the system is stable and, thus, can exist only at relatively small thicknesses of both layers and at low-to-moderate permeability of the sediments. At larger thicknesses and higher permeability, the interface between the two layers is unstable to monotonic perturbations. The results do not support the hypothesis that the interface instability may lead to accelerating self-sustained dissociation of natural methane hydrates in the conditions of increasing global temperature.   

Direct simulation of the flow over a porous layer of large porosity

In this talk we report on direct numerical simulations of constant-density flow over and through a layer of a porous medium with large porosity. Initially the fluid is at rest and the flow is driven by a constant pressure gradient. Periodic boundary conditions are used along the streamwise direction, whereas no-slip conditions are specified on the bottom boundary which also coincides with the lower end of the porous strip. Further, outflow conditions are imposed on the top boundary of the computational domain, which is located sufficiently far from the porous medium. As the flow evolves, a boundary layer is formed on the lower end of the porous strip and an additional transition zone is formed right above its upper end. Due to the steep velocity gradients across this zone, a Kelvin-Helmholtz instability is onset which leads to the formation of a mixing layer. We present and analyze the characteristics of vortex pairing and growth rate of this mixing layer. Finally, we discuss the results of a parametric study with respect to the porosity of the medium.   

Micro-scale flow simulation and colloid transport modeling in saturated porous media

Adequate understanding of the mechanisms governing colloid retention by soil porous media is essential to the prediction and monitoring of the transport of contaminants through groundwater in the subsurface environment. In this talk, we focus on the representation of micro-scale flow and colloid-grain surface interactions in a computational approach. First, micro-scale viscous flows in a model porous media with different domain sizes and geometric configurations are simulated by the mesoscopic lattice Boltzmann method. A Lagrangian colloid tracking model is then used to study the dynamics of colloidal particles under the action of Brownian force, hydrodynamic forces, and physicochemical forces. The modeling and analysis of colloid transport will incorporate the effects of flow speed, solution ionic strength, collector surface roughness, and blocking effect, etc. Simulation results are used to study the unique nature of retention by the secondary energy minimum. Comparisons are made with parallel experimental results obtained from confocal microscopy. To speed up our colloid tracking modeling, parallel implementation using Message Passing Interface (MPI) is performed and the related scalability results will also be presented.   

Session R17: Microfluids Mixing

Measuring Convective and Diffusive Mixing in Inertial Droplet-Pair Collisions

Complete mixing, dilution, and sample homogenization are essential processes in modern Lab on a Chip and Micro Total Analysis Systems and these seemingly simple tasks remain a major obstacle. A new mixing technique has been proposed that accelerates mixing rates in droplets through controlled, high speed droplet-pair collisions. The collisions take place inside a confined microchannel and the droplet generation and entrainment processes are provided by an inertial gaseous flow. The fast time scales, small length scales, and highly Lagrangian nature of discrete droplet collisions makes optical diagnostics the obvious choice for understanding, characterizing, and quantifying mixing processes. Presented here is a simple and robust visualization and measurement technique that captures convective and diffusive mixing inside droplets using differential fluorescence. High speed digital imagery, custom image processing, and fluorescent intensity statistical analysis are employed to examine the contribution of convective rearrangement and tracer diffusion to droplet mixing following inertial droplet-pair collisions.   

Mixing in Three Dimensional Linear Spiral Microchannels

Since its introduction a decade ago, soft lithography has drastically changed our understanding of fluid physics under confinement by enabling rapid production of microchannels and microdevices. Despite its popularity however, soft lithography has some limitations, including fabrication of thoroughly three dimensional passages without using multiple layers. In this talk, we first introduce the fabrication of a simple three dimensional linear spiral microchannel in a polydimethylsiloxane (PDMS) mold. In two dimensional planar spiral microchannels, Dean number increases or decreases with each consecutive rotation as the radius of curvature decreases or increases, respectively. In our three dimensional spiral microchannel, however, the radius of curvature is constant and as a result the Dean number assumes a constant value. The mixing performance of two miscible fluids in this microchannel is characterized using digital image processing techniques. The influence of flow rate as well as the length of the spiral pitch on the mixing performance is studied. Other possible applications are also discussed.   

Optimal Blinking-Flow Microfluidic Mixers

The performance of blinking-flow microfluidic mixers is explored in order to identify optimal mixer designs. A two-dimensional lid-driven flow model is defined that approximates the cross-channel flow in three-dimensional grooved mixers. On either side of a specified separatrix location on the channel floor, the model imposes two different transverse velocities that generate a pair of counter-rotating vorticies of differing sizes. Blinking-flow mixers are then defined by alternating two such fields with the separatrix location for each field chosen independently. An exhaustive search of this design space demonstrates that the best blinking flow mixers are not symmetric, i.e., the second velocity field is not the mirror image of the first. The best mixers combine a field with the separatrix near the channel centerline with a field with separatrix near one of the side walls. Results are compared to comparable three-dimensional grooved channel mixers, and implications of these results for optimizing general mixer designs are discussed.   

Use of Eulerian Indicators to Predict Best Mixing Configurations for a Blinking 2D Lid-Driven Flow

The 2D lid driven model with an alternating flow between two double gyres whose relative size differs is used as the basis of a study to determine the predictive capabilities of two Eulerian Indicators (EI), dubbed the ``transversality'' and ``mobility'' with respect to the degree of mixing achieved. The ``transversality'' EI measures the angular difference between the two alternating velocity vectors at a given position in the flows domain. Experiments have indicated that streamline crossing between two alternating flows is associated with regions of good mixing. The ``mobility'' EI measures the percentage of the flows domain that contributes the most to particle transport. In the parameter space under study, the product of the two EI's is shown to correlate well with the variance of concentration for the fluid, calculated as a Lagrangian metric. The computational efficiency gained by calculating Eulerian Indicators compared to Lagrangian metrics allows for a more efficient search through this systems parameter space, suggesting configurations which are better suited to mix well, effectively cutting the design time for optimizing new mixing designs.   

Fluid Mixing from Viscous Fingering

Fluid mixing is an important and complex phenomenon. It plays a fundamental role in natural processes, including groundwater flows in heterogeneous media, reactive flows, mantle convection, debris gravity currents, and bacterial locomotion. Mixing at low Reynolds numbers is a notoriously difficult problem because it cannot rely on turbulence. Mixing efficiency at low Reynolds numbers can be enhanced by exploiting hydrodynamic instabilities that induce heterogeneity and disorder in the flow. The unstable displacement of fluids with different viscosities, or viscous fingering, provides a powerful mechanism to increase fluid-fluid interfacial area and enhance mixing. Here we describe the dissipative structure of miscible viscous fingering, and propose a two-equation model for the scalar variance and its dissipation rate. Our analysis predicts the optimum range of viscosity contrasts that, for a given P\'eclet number, maximizes interfacial area and minimizes mixing time. In the spirit of turbulence modeling, the proposed two-equation model permits upscaling dissipation due to fingering at unresolved scales.   

Experimental investigation of periodic lines in 3D lid-driven cylindrical cavity flows

Mixing of mass and heat by laminar flows occurs in many natural systems and industrial processes. Understanding of the basic mechanisms to enhance mixing efficiency is mostly based on mathematical analysis and numerical studies of prototype cases. Three-dimensional (3D) experiments, however, remain largely unexplored. The present investigation employs 3D Particle Tracking Velocimetry (3D-PTV) to investigate a few of these concepts in realistic experimental configurations. We focus on the observability of periodic lines in periodically lid-driven cylindrical cavity flows. Periodic lines play a central role in the transport properties. The fluid is set in motion via a time-periodic forcing protocol (piece-wise steady translations of one of the endwalls of the cylinder), 3D-PTV measurements have been performed to obtain the web of tracer paths. Experimental results confirm key features from theoretical analysis and numerical studies on the location and shape of the periodic lines. A hybrid method (numerical tracking of particles in an Eulerian flow field determined by experimental measurements) is used to extend the forcing to situations inaccessible by direct particle tracking via 3D-PTV.   

Reaction-diffusion in microdroplets: Theory \& Experiments

We study the dynamics of the reaction front that forms as two initially separated reactants meet. The reactants are initially contained in two different nanoliter droplets confined in a microfluidic device. Guiding and trapping the drops is performed using the \textit{rails} and \textit{anchors} technique. A laser pulse then triggers the chemical reaction by coalescing the drops and we monitor the integral of the reaction product. An asymptotic analysis (Trevelyan, Phys. Rev. E, 80, 2009) identifies two phases for this process. The production rate of the reaction is determined by diffusion in both. Initially the two reactants occupy different regions and have to diffuse to react. The product concentration integral then varies as $t^{3/2}$ with a prefactor that depends on the reaction kinetics. At large times, the reaction rate becomes limited by the diffusive supply of reactants which must travel over longer distances. The product concentration integral then increases as $t^{1/2}$ with a different prefactor containing the same physical ingredients. Confronting theory and experiment allows the measurement of physical and chemical constants.   

Exploiting numerical diffusion to study transport and chaotic mixing for extremely large P\'eclet values

We show that the purely convective mapping matrix approach provides an extremely versatile tool to study advection-diffusion processes for extremely large P\'eclet values ($\sim$108 and higher). This is made possible due to the coarse-grained approximation that introduces numerical diffusion, the intensity of which depends in a simple way on grid resolution. This observation permits to address fundamental physical issues associated with chaotic mixing in the presence of diffusion. Specifically, we show that in partially chaotic flows, the dominant decay exponent of the advection diffusion propagator will eventually decay as Pe-1 in the presence of quasiperiodic regions of finite measure, no matter how small they are. Examples of 2d and 3d partially chaotic flows are discussed.   

Visualizing millisecond chaotic mixing in droplets moving through a serpentine microchannel

We have developed a two-photon excitation fluorescence lifetime imaging technique to accurately and quantitatively measure mixing of two fluorescence dyes inside microdroplets. The line scanning along the microfluidic channel is passively achieved via the droplets flowing through the excitation focal point. Because the periodically generated droplets are identical, we scan multiple droplets and sum up the line signals of each droplet by cross/autocorrelation to obtain the line signal with a high signal-to-noise ratio. The droplets are scanned line by line by moving the focal point across the channel using a translation stage. The cross-sectional image of the droplet is then formed by aligning the scanning lines across the channel. A non-fitting method based on the ratio of fluorescence signals in lifetime decay is used for mixing ratio calibration. With this new imaging technique, we visualize millisecond chaotic mixing dynamics in microdroplets with 5 microsecond time resolution. The mapped chaotic mixing patterns match well with the 2D numerical simulation, performed based on the coupled Laminar two-phase flow level set model and transport of diluted species model, and also validate the characteristics of the alternative asymmetric vortex flow in droplets moving through a serpentine channel.   

Session R18: Acoustics II: Internal and External Flows

A simple sound source for temporally-developing mixing layers

Applying Lighthill's acoustic analogy equation to temporally-developing mixing layers, we derived a direct relation between the near-field work by pressure fluctuation and the far-field sound. The sound radiation predicted by the new model was compared to the direct numerical simulation, and the results agreed well for the sound radiation from different vortex dynamics in mixing layers: roll-up, pairing (or tearing), merging, saturation, and viscous damping. Using the new formulation, we explained the mechanism for sound generation from the considered flow, and depicted general topological structures for the distribution of sound sources.   

Large-amplitude acoustic streaming

A mechanism for the generation of large amplitude acoustically-driven streaming flows is proposed. Motivated by streaming observed in high-intensity discharge (HID) lamps, two-dimensional flow of an ideal gas in a channel geometry is analyzed in the asymptotic limit of high frequency forcing. Predictions of streaming flow magnitudes based on classical arguments invoking Reynolds stress divergences originating in viscous boundary layers are orders of magnitude too small to account for the observed mean flows. Moreover, classical ``Rayleigh streaming" theory cannot account for the direction of the cellular mean flows often observed in HID lamps. In contrast, the inviscid mechanism proposed here, which invokes fluctuating baroclinic torques away from viscous and thermal boundary layers, can account both for the magnitude and the orientation of the observed streaming flows.   

Control of Acoustic Reflections in a Closed-Circuit Wind Tunnel

Closed return wind tunnels, such as the Klebanoff--Saric Wind Tunnel (KSWT) at Texas A\&M University, can provide low-disturbance flows that are required to study boundary layer receptivity. Receptivity is the process through which environmental disturbances become the initial condition for boundary layer instabilities. One instability mechanism, Tollmien--Schlicting waves, is especially receptive to freestream sound. The receptivity of these waves is studied by introducing downstream-traveling planar sound waves that interact with the leading edge of a flat plate; however, changes in wind tunnel area create reflected waves that complicate the experiment. Reflections are mitigated using a secondary speaker located downstream of the test section that eliminates upstream- traveling reflections. The secondary speaker is controlled using a finite impulse response (FIR) filter. Microphone measurements are used to document the wave cancellation at multiple locations in the test section.   

Non-Linear High Amplitude Oscillations in Wave-shaped Resonators

A numerical and experimental study of non-linear, high amplitude standing waves in ``wave-shaped'' resonators is reported here. These waves are shock-less and can generate peak acoustic overpressures that can exceed the ambient pressure by three/four times its nominal value. A high fidelity compressible axisymmetric computational fluid dynamic model is used to simulate the phenomena in cylindrical and arbitrarily shaped axisymmetric resonators. Working fluids (Helium, Nitrogen and R-134a) at various operating pressures are studied. The experiments are performed in a constant cross-section cylindrical resonator in atmospheric pressure nitrogen and helium to provide model validation. The high amplitude non-linear oscillations demonstrated can be used as a prime mover in a variety of applications including thermoacoustic cryocooling.   

Rijke tube with flexible walls

Sound is excited spontaneously in a Rijke tube because the small temperature perturbations in an acoustic field interact with heat transfer from a heat source in the tube. The air particles near the heat source undergo a thermodynamic cyle converting heat to mechanical energy, which is heard as the sound emanating from the Rijke tube. This principle of energy conversion is used in thermoacoustic engines, and the main objective of this study is to improve their performance. The acoustic oscillations in the Rijke tube regulate the thermodynamic cycle, just as in conventional engines the cycle is controlled by the motion of a piston and the action of inlet and exit valves. The acoustic regulation in the Rijke tube, however, does not allow arbitrary control of the cycle in thermodynamic phase space. In this presentation, we introduce a new way of overcoming this limitation, one by using Rijke tubes with flexible walls. We will discuss how this modification allows for more general thermodynamic cycles to be executed by the air particles in the tube. This possibility, when used in thermoacoustic engines, opens a channel for further improving the engine performance.   

Computational study of flow noise from small gaps in turbulent boundary layers

The noise induced by small gaps underneath low-Mach-number turbulent boundary layers is studied using large-eddy simulation and Lighthill's equation. The latter is solved by employing an acoustically compact Green's function for the gap and by a boundary-element method. The gap leading-edge height is $13\%$ of the boundary-layer thickness, and the gap width and trailing-edge height are varied to investigate their effect on sound generation. The radiated acoustic field is dominated by the forward-facing step in the gap and resembles forward-step noise for wide gaps and/or asymmetric gaps with the trailing edge higher than the leading edge. For narrow and symmetric gaps, destructive interference of the sound from leading and trailing edges causes a significant decline in the low-frequency spectral content and thereby creates a broad spectral peak in the mid-frequency range. The effect of acoustic noncompactness of gaps is investigated by comparing solutions based on a compact Green's function and those from a boundary-element calculation. Excellent agreement is observed at low frequencies and away from the wall-normal direction. At higher frequencies, the sound field deviates from that of a compact streamwise dipole. The elevated level of surface pressure fluctuations induced by gaps and their recovery to equilibrium conditions are also examined.   

Investigation of a tone in flap tip noise

In this paper, we investigate numerically the noise generated by the flow around a high-lift configuration. The case studied is the noise generated by the flap tip of the MDA-30P30N high-lift geometry. We propose a cavity model as a simplification for the flap cove flow near the flap tip. The idea of representing the flap cove as a cavity is due to a tone in the spectrum from the numerical simulations of the full high lift geometry MDA-30P30N without spanwise gap between extended flap and the stowed flap. A high peak around 900Hz to 1000Hz was not expected and its source is not clear. The effort here is to investigate the source of frequencies around this value. There is a possibility of noise tones generated from the flap cove with frequencies around 900Hz according to the Rossiter model for the cavity. This mechanism of noise generation seems to be associated to the peak in the spectrum. Snapshot of instantaneous vorticity field near the flap tip supports that a mechanism of noise generation resembles the cavity mechanism. Further corroboration is presented through the Koopman modes (dynamic mode decomposition) of the pressure fields.   

Unsteady Lift and Radiated Sound Generated by a 2-D Airfoil in an Intermittent Flow

The spanwise correlation length scale of lateral velocity and the gust response function are the quantities of interest in predicting the sound production from an airfoil. Typically, these quantities are taken to be a correlation length scale model based on isotropic turbulence and Sears' gust response function, respectively. The present study is an experimental investigation of the accuracy of these selections when the turbulent approach flow is intermittently irrotational. Acoustic measurements of a flat-plate airfoil placed at three lateral locations in a single-stream shear layer are presented. The acoustic measurements are compared to radiated sound predictions based on detailed velocity field measurements.   

Investigation of noise production from a turbulent cylinder

We investigate noise production by a cylinder in turbulent flow (Re=10,000 and M=0.2), using the Ffowcs-Williams and Hawkings acoustic analogy, where the sound sources are computed from a compressible direct numerical simulation. It has been shown that vortices passing through a data surface generate spurious noise if the quadrupole term is neglected. Our implementation of the acoustic analogy, hence, uses porous data surfaces as well as the volume term. We compare our solution to available results, examine the effect of the placement of the data surface on the noise calculation by using multiple surfaces, and the effect of different proposed correction schemes that try to compensate for neglecting the quadrupole noise.   

Acoustic Scattering from Interaction of Dual Frequency Incident Fields

The pressure field produced by the spatial interaction of two high frequency incident plane waves in a three-dimensional scattering object is investigated. Of particular interest is the field produced in response to the difference-frequency component generated from the non-linear interaction of the two harmonically time varying acoustic beams in a high contrast medium. The scattered pressure at the difference frequency field has been shown to enhance the identification of abnormal biological tissue in recent medical ultrasound experiments. This work presents a computational study of the scattered pressure that results from the Reynolds stress in a fluid scatterer. Using Pade approximants, it is shown that the stress tensor can be computed using a uniform expansion in the contrast gauge for the scattered pressure. This allows one to investigate scattering volumes characterized by high compressibility contrast.   

Session R19: Instability General II

Liquid-Bridge Breaking Limits

Wet adhesion by liquid bridges in large arrays shows promise for use in lightweight, controllable on-demand devices. Applications include grab/release of wafer substrates, transport of micron-sized tiles for use in 3D printing and micro-dosing of personalized pharmaceutical drugs. By wetting and spreading, a drop can form a bridge and thereby ``grab'' a nearby solid substrate. By volume decrease or extension, the bridge can break. The breaking limit corresponds to bridge instability which can be predicted, knowing the static mechanical response of the bridge. Mechanical behaviors include force-volume (FV), pressure-volume (pV) and force-length (FL) responses. Instability crucially depends on the mode of failure -- failure under constant-force or constant length are typical cases. We study single bridge equilibria for their breaking limits. FV diagrams for the pin-pin equal and pin-pin unequal radii boundary conditions for different bridge heights are measured in the laboratory. The FL response in the case of pin-pin equal radii is also measured. Results are compared to predictions of static theory. Static results are then used to compare to dynamical sequences where volume is driven quasistatically by syringe or an electro-osmotic pump. As the breaking limit is approached, the shape deformation accelerates leading to non-equilibrium shapes not captured by the static analysis.   

Scenarios on a rotating two-fluid interface with a density contrast - the morphology and the transitions

We study experimentally an oil-water interface maintained in a cylindrical container with its upper boundary rotating at constant speeds. The interface exhibits intriguing morphology as the rotation speeds up, making transitions from a smooth hump that presumably compensates the centrifugal-force induced pressure dip, to more fascinating geometries such as a spinning flap top (a plateau) or a mound with distinct spatial steps. The available scenarios can be controlled by varying the depths of two fluids as well. Increasing the rotation rates also tends to induce wavy patterns that break the axial symmetry of those base shapes, while a violent collapse of the oil-water interface occurs at sufficiently fast rotations. We attempt to give partial explanations for the different scenarios.   

Role of intrinsic flame instability in the excitation of combustion chamber instability

While considerable progress was made on understanding the various modes of flame instability at the fundamental level, and substantial empirical information and phenomenological descriptions was also accumulated on combustion instability within combustion chambers such as those of rocket engines, few attempts were made to explore the possible macro-scale excitation of the latter through the micro-scale manifestation of the former. Here we present an initial attempt towards identifying such a possibility and the associated coupling mechanisms. We shall incorporate the flame parameters into the classical theories of liquid-propellant rocket engines, and then implement the rocket dynamics into the analyses of premixed and diffusion flame segments. The analyses are conducted for the various instability modes, including the diffusional-thermal, Darrieus-Landau, and Rayleigh-Taylor (body-force) instabilities for premixed flames, and the Kelvin-Helmholtz and body-force instabilities for diffusion flames. The role of chamber-generated sound on stabilizing the inherent flame instabilities and triggering the parametric instability is also considered.   

Experiments on the Mode Selection in Faraday Instability

The resonance of a fluid interface with an oscillating acceleration field is studied for liquid-liquid systems in small aspect ratio cylindrical and rectangular containers. The resonant phenomenon, known as Faraday waves, is more typically studied in large aspect ratio systems at high frequencies where multiple modes are excited simultaneously and the associated nonlinear interactions give way to a variety of patterns. In this work the low excitation frequency allows for the selection of individual cell modes and their dynamics are considered. The onset threshold for instability is compared to the predictions of this model. It is seen for the cell modes that frequency bands are well predicted by the model and the amplitudes are very close, with deviation attributable to interfacial pinning and sidewall stresses. Supercritical and subcritical bifurctions are observed, along with other nonlinear phenomena such as co-dimension2 points and wave breaking.   

Spatially localized patterns in 2D and 3D doubly diffusive convection

Doubly diffusive convection, that is, convection driven by a combination of concentration and temperature gradients, is known to display a wealth of dynamical behavior whose properties depend on the gradients. In the present work, we first investigate spatially localized states in two-dimensional horizontal thermosolutal convection with no-slip boundary conditions at top and bottom and vertical gradients of temperature and concentration. Numerical continuation demonstrates the formation of stationary convectons in the form of 1-pulse and 2-pulse states of both odd and even parity while time integration reveals the presence of stable time dependent spatially localized states. We next turn to large scale three-dimensional vertical enclosures placed in horizontal thermal and solutal gradients. Different types of spatially localized states are computed and the results related to the presence of homoclinic snaking.   

Modulation instability of space-periodic oscillatory patterns

Pattern selection and stability of regular (periodic in space) regimes is a classical problem with a number of applications in fluid dynamics. For steady bifurcations both competition of perfect periodic patterns and their stability with respect to slow modulations in space (e.g. Eckhaus or zigzag instabilities) are well studied. In contrast, in the case of Hopf bifurcation, usually only selection of patterns that possess a certain symmetry was analyzed (Silber \& Knobloch, Nonlinearity, 1991; Roberts et al, Contemp. Math, 1986), whereas the set of Ginzburg-Landau equations was studied only in the one-dimensional case (rolls). Dealing with a wide class of problems, where the longwave oscillatory instability takes place, we consider a stability of regular oscillatory patterns that belong to either square or hexagonal lattices with respect to spatial modulations. By means of the multiple scale expansion, we derive instability criteria valid near the stability threshold. Useful classification of possible perturbations of a regular structure is introduced. As an example, the theory is applied to Marangoni convection in a layer of a binary mixture with the Soret effect. Domains of stability of space-periodic patterns are obtained.   

Break of the symmetry in a two-lid driven cavity

The lid driven cavity has applications in crystal growth as well as in the coating industry. We study the problem of a driven cavity with two parallel walls moving at the same speed and in the same direction. Time marching calculations using Chebyshev-spectral method were done with different aspect ratios. As the Reynolds number increases, the onset of the instability is characterized by the break of the symmetry which is described and explained. The critical Reynolds number depends on the aspect ratio. This dependence is explained.   

Transition to turbulence in a quasi-2D Kolmogorov flow

We describe a combined experimental and numerical study of quasi-2D flows to search for unstable, exact solutions to Navier-Stokes known as Exact Coherent Structures (ECS), which may provide a foundation for a simplified dynamical description of turbulence. We focus on a system that closely approximates Kolmogorov flow by inducing shear in a thin fluid layer using electromagnetic forces. PIV is used to obtain time series of velocity fields from images of the visualized flows in the lab; time series of velocity fields are calculated numerically for flows with forcing similar to that in the experiments. Discrepancies arising from differences in lateral boundary conditions between experiments (no slip) and simulations (periodic) are addressed in two separate ways: (1) experimentally studying a large system to approximate the effects of periodic boundary conditions and (2) adding padding regions in the simulations to mimic finite system size. We describe in detail the sequences of bifurcation leading to turbulence in both experiments and simulations.   

Session R21: Vortex Dynamics VII

How leakage flow influences the hydrodynamic damping of a vibrating blade

The hydrodynamic damping of a structure is of particular importance in many engineering applications. In the case of axial turbines, the presence of a gap between the rotor tip and the shroud induces a leakage flow creating a tip vortex whose roll up process is highly dependent on the clearance size. The blade response to an excitation in the presence of this flow is however poorly characterized. In the present study, the hydrodynamic damping of a Naca hydrofoil in a water tunnel is investigated with respect to the gap width. An innovative device was designed to excite the hydrofoil in non-intrusive way: an underwater electric discharge creates a fast growing and collapsing bubble which generates strong shockwaves. The structural response is monitored with a Laser Vibrometer. Assuming a single degree of freedom system, the hydrodynamic damping for the first two eigen modes (bending and torsion) is identified for different values of upstream velocity, incidence angle and tip clearance size.   

Counter rotating open rotor flow field investigation using stereoscopic Particle Image Velocimetry

Counter rotating open rotor (CROR) propulsive systems are again considered as fuel efficient alternatives to conventional propulsion systems. In the present paper details of dedicated experiments on a generic CROR model are studied using stereoscopic Particle Image Velocimetry. The CROR model has 10 front blades and 8 aft blades, with blade design similar to modern propellers for high disk loadings. Recent progress in Particle Image Velocimetry applications to propeller flow analysis is used to further develop the technique for application to CROR systems. Stereoscopic Particle Image Velocimetry (SPIV) has been applied for the flow field investigation behind a counter rotating open rotor (CROR) model in order to enable experimental insight in the complex flow phenomena of multiple vortex structures. The paper discusses a dedicated triggering strategy for the determination of the phase positions of both propellers using the phase delays and revolution periods. Results of the PIV measurements are presented and the topological events of the rotor-interactions are discussed.   

A comparison between the growth of leading-edge and tip vortices on a low aspect ratio plate using 3D-PTV

The vortex formation process on an impulsively started flat plate at 45 degree incidence is studied using both direct force measurements as well as 3D-PTV. The focus of this experiment has been to study the competing evolution of leading-edge and tip vortices for a range of start-up motions. The 3D-PTV measurement volume, located in the tip region of the plate, provides detailed insight into the roll-up of the shear layers at early stages of the motion. By quantifying the evolution of circulation at various spanwise and tip locations, we are able to relate the unsteady generation of force to the instantaneous vortex topology present around the plate.   

Influence of outlet geometry on the swirling flow in a simplified model of a large two-stroke marine diesel engine

We present Stereoscopic particle image velocimetry measurements of the effect of a dummy-valve on the in-cylinder swirling flow in a simplified scale model of a large two-stroke marine diesel engine cylinder using air at room temperature and pressure as the working fluid and Reynolds number 19500. The static model has stroke-to-bore ratio of 4, is rotationally symmetric and the in-cylinder swirling flow is enforced by angled ports at the inlet. We consider a case analogous to engine when the piston is at bottom-dead-center. In absence of an exhaust valve the overall axial velocity profile is wake-like and flow reversal is observed on the cylinder axis, close to the inlet. Downstream, the flow reversal disappears and instead a localized jet develops. The corresponding tangential velocity profiles show a concentrated vortex with decreasing width along the downstream direction. By placing a concentric dummy-valve at the cylinder outlet, the magnitude of reverse flow at the inlet increases, the strong swirl is diminished and the axial jet disappears. We compare these findings with previous measurements in vortex chambers and discuss the relevance of these results with respect to development of marine engines.   

The effect of non-zero radial velocity on the impulse and circulation of starting jets

Vortex ring formation dynamics are generally studied using two basic types of vortex generators. Piston cylinder vortex generators eject fluid through a long tube which ensures a purely axial jet; whereas, vortex ring generators which expel fluid through a flat plate with a circular orifice produce 2-D jets (non-zero radial velocity). At the nozzle exit plane of the orifice type vortex generator the radial component of velocity is linearly proportional to the radial distance from the axis of symmetry, reaching a maximum at the edge of the orifice with a magnitude around 10 \% of the piston velocity (the ratio of the volume flux and the nozzle area). As the jet advances downstream the radial velocity quickly dissipates, and becomes purely axial less than a diameter away from the nozzle exit plane. The radial velocity gradient in the axial direction plays a key role in the rate at which circulation and impulse are ejected from the vortex generator. Though the radial component of velocity is small compared to the axial velocity, it has a significant effect on both the circulation and impulse of the starting jet because of this gradient. The extent of circulation and impulse enhancement is investigated through experimental DPIV data showing that the orifice device produces nearly double both circulation and energy (with identical piston velocity and stroke ratios).   

Effects of ground plane topology on vortex-ground interactions in a forced impinging jet

The phenomenon of a three-dimensionally unstable vortex-ground interaction is studied, motivated by the problem of sediment suspension by vortex-wall interactions from landing rotorcraft. In the current work, the downwash of a rotorcraft is simplified using a prototype flow consisting of an acoustically forced impinging jet. The goal of the current investigation is to quantify the effects of disturbances to the ground-plane boundary layer on the three-dimensional development of the vortex ring as it interacts with the ground plane. A small radial fence is employed to perturb the natural evolution of the secondary vortex, which typically exhibits azimuthal instabilities as it is wrapped around the primary vortex. The fence is observed to localize and intensify the azimuthal development, dramatically altering the mean flow in this region and generating corresponding azimuthal variations in the turbulent near-wall stresses. Multi-plane ensemble-averaged stereo PIV is employed to obtain volumetric, phase averaged data sets that are subjected to a triple decomposition to fully quantify turbulence effects. The effects of the radial fence are examined at both a high and low Reynolds number flows (Re = $\Gamma/\nu$ = 50,000 and 10,000, respectively), and the data is analyzed in the context of structures leading to significant sediment mobilization.   

Mach Number Effect on the Characteristics of a Free Pulsed Jet

An experimental study was carried out on a free pulsed jet over a Mach number range of 0.3 to 0.8. The data was obtained using Particle Image Velocimetry (PIV). The global flow field of the pulsed jet showed that over the range of Mach numbers considered, the centerline velocity decay, jet spreading and the normalized mass flow rate for a given Strouhal number (St = fd/Uj; where f is the frequency of pulsation, d is the nozzle exit diameter and Uj is the time-averaged axial velocity at the nozzle exit) are only weakly dependent on the nozzle exit Mach number. The phase-averaged results show that the vortex ring circulation is also weakly dependent on the nozzle exit Mach number for a given Strouhal number. The vortex ring pinch-off was found to be independent of the nozzle exit Mach number but dependent on the pulsing frequency.   

High-speed schlieren videography of vortex-ring impact on a wall

Ring vortices of approximately 20 cm diameter are generated through the use of an Airzooka toy. To make the vortex visible, it is seeded with difluoroethane gas, producing a refractive-index difference with the air. A 1-meter-diameter, single-mirror, double-pass schlieren system is used to visualize the ring-vortex motion, and also to provide the wall with which the vortex collides. High-speed imaging is provided by a Photron SA-1 digital video camera. The Airzooka is fired toward the mirror almost along the optical axis of the schlieren system, so that the view of the vortex-mirror collision is normal to the path of vortex motion. Vortex-wall interactions similar to those first observed by Walker et al. (JFM 181, 1987) are recorded at high speed. The presentation will consist of a screening and discussion of these video results.   

Session R23: Flow Control VI

Advanced Fluid Research On Drag reduction In Turbulence Experiments -- AFRODITE

A hot topic in today's debate on global warming is drag reduction in aeronautics. The most beneficial concept for drag reduction is to maintain the major portion of the airfoil laminar. Estimations show that the potential drag reduction can be as much as 15\%, which would give a significant reduction of NOx and CO emissions in the atmosphere considering that the number of aircraft take offs, only in the EU, is over 19 million per year. In previous tuned wind tunnel measurements it has been shown that roughness elements can be used to sensibly delay transition to turbulence$\footnote{Fransson et al. 2006 {\emph{Phys. Rev. Lett.}} {\bf{96}}, 064501.}$. The result is revolutionary, since the common belief has been that surface roughness causes earlier transition and in turn increases the drag, and is a proof of concept of the passive control method per se. The beauty with a passive control technique is that no external energy has to be added to the flow system in order to perform the control, instead one uses the existing energy in the flow. Within the research programme AFRODITE, funded by ERC, we will take this passive control method to the next level by making it twofold, more persistent and more robust.   

Closed-Loop Aerodynamic Flow Control of a Maneuvering Airfoil

The unsteady interaction between trailing edge aerodynamic flow control and airfoil motion in pitch and plunge is investigated in wind tunnel experiments using a 2-DOF traverse which enables application of time-dependent external torque and forces by servo motors. The global aerodynamic forces and moments are regulated by controlling vorticity generation and accumulation near the surface using hybrid synthetic jet actuators. The dynamic coupling between the actuation and the time-dependent flow field is characterized using simultaneous force and velocity measurements that are taken phase-locked to the commanded actuation waveform. The effect of the unsteady motion on the model-embedded flow control is assessed in unsteady several maneuvers. Circulation time history that is estimated from a PIV wake survey shows that the entire flow over the airfoil readjusts within about 1.5 TCONV, which is about two orders of magnitude shorter than the characteristic time associated with the controlled maneuver of the wind tunnel model. This illustrates that flow-control actuation can be typically effected on time scales that are commensurate with the flow's convective time scale, and that the maneuver response is primarily limited by the inertia of the platform.   

A Method to Control Compliance of Blades and Flaps

Compliant plates experience lower drag forces than rigid plates primarily due to reconfiguration. From this concept it follows that through modifying the compliance of a plate, the aerodynamic forces can be controlled. To achieve this control, the concept of hydroskeletons -- which are fluid filled cavities that resist deformation through the pressure of an internal fluid -- were used. Using this notion a compliant structure with an internal chamber was developed. Shape change was detected when filling the chamber with fluid and controlling the pressure. Preliminary testing involved simple internal geometries filled with water and pressurized up to 20 psi. Using this method a plate was built with several internal chambers, each with individual pressure control. The plate was attached to a force balance perpendicularly in a wind tunnel. Drag and lift forces were modified through changing the internal pressure both globally and locally.   

Manipulation of Laminar Separation Utilizing Dynamic Roughness at the Leading Edge of an Idealized Airfoil

Low Reynolds number flow over a symmetric, idealized airfoil with a reasonably constant laminar separation point was manipulated using a leading edge roughness element with small, time-dependent amplitude. At a fixed height and low Reynolds number the roughness element was able to reduce the extent of laminar separation over the airfoil as compared to a smooth airfoil. Further reduction of the separation was achieved by dynamically oscillating the roughness element in an appropriate range of actuation frequencies. Proper orthogonal decomposition performed upon the flow over the airfoil for both the baseline and active open loop case shows the introduction of persistent structures within the flow due to the oscillating roughness element. The coupling of this small input perturbation with the flow and the resultant manipulation of the separation bubble will be discussed for a range of flow and roughness conditions. The support of NSF CAREER award {\#}0747672 is gratefully acknowledged.   

Vortex shedding response of streamwise driven cylinders

Bluff body cylinders exhibit a range of responses when externally forced. This study experimentally investigated the modes of response and trends in shedding frequency of square and circular cylinders undergoing inline forced oscillations in a steady flow. Experiments were conducted in a free surface water channel over a range of Reynolds numbers from 1500 to 6300. With the driving frequency held constant at the natural unperturbed shedding frequency, the forcing amplitude was varied and the response examined. Frequency analysis of velocity, lift and drag forces showed that for low amplitude oscillation the shedding frequency decreases as amplitude increases, displaying a quadratic relationship. As amplitude increases further a region of possible mode competition exists until a critical amplitude is reached where the shedding locks to a period-doubled subharmonic of the forcing frequency. The region of mode competition is brief with an abrupt lock for the circular cylinder, while the square cylinder exhibits a gradual transition to the subharmonic over a larger range of amplitudes.   

Transition delay by means of base flow modulations

Recent experimental investigations have shown that spanwise modulations of the base flow may delay transition to turbulence.\footnote{Fransson et al. 2006 {\emph{Phys. Rev. Lett.}} {\bf{96}}, 064501.} In this study we explore the possibility to generate streaks of much larger amplitude than previously reported by using a row of miniature vortex generators (MVGs). Here, we present the first boundary layer experiment where streak amplitudes exceeding 30\% have been produced without having any secondary instability acting on them. Furthermore, the induced skin-friction drag due to the streaky base flow is quantified and it is demonstrated that the streaks can be reinforced by placing a second array of MVGs downstream of the first one. In this way it is possible to make the control more persistent in the downstream direction. We conclude that the specially designed set of MVGs, as a boundary layer modulator, is a promising candidate for successfully setting up robust and persistent streamwise streaks, which is a prerequisite for a successful flow control. This work is carried out within the AFRODITE programme funded by ERC.   

Electroactive Polymer based flow control at Low Reynolds Numbers

Electroactive polymers (EAPs) are used to achieve distributed, conformal actuation on aerodynamic surfaces, promote transition in places where laminar separation occurs, and maintain laminar flow where there is no separation. In this work, the feasibility of the EAPs in mitigating a laminar separation bubble on a flat plate was examined. First, the performance of the EAPs was evaluated using a Laser vibrometer and a high-speed camera to quantify the response of the EAP to input voltage and driving frequency and to better understand the physics of the actuator itself. Then, measurements using Stereoscopic particle image velocimetry were conducted in the vicinity of the EAP. Several parameters, such as the driving frequency, the input voltage, and the dimple size, were tested. Preliminary data show promising results, where the size of the separation bubble was significantly reduced when the EAPs were driven at the appropriate voltages and frequencies.   

Experimental Evaluation of Control Algorithms for a Supercavitating Vehicle

High speed supercavitating vehicles offer significant challenges regarding control. Vehicles with actuated control surfaces, such as cavitators and fins, are of considerable interest for maneuverability and control. To study the interaction of control surfaces and the body dynamics of the vehicle, a new hardware and software infrastructure has been developed at Saint Anthony Falls Laboratory (SAFL-U of Minn). In addition, a new vehicle prototype that utilizes a cavitator disk and fins for control, a 6 degree-of-freedom force balance to measure forces and moments, and a ventilation system to insure a fully developed supercavity was designed and tested in the high-speed water tunnel at SAFL. Based on experiments in presence of a supercavity surrounding the vehicle, mathematical models that map cavitator and fins angles to pitch moment, drag force and lift force are obtained. These mathematical models and the new platform enable the use of closed-loop control to significantly reduce pitch moment oscillations induced by a gust flow. This achievement shows a promising path towards the experimental validation of control algorithms for high-speed supercavitating vehicles. The platform architecture, experimental design, mathematical models, and validation process are presented here.   

Bubble Gate for In-Plane Flow Control

The ability to control fluid flow is of key importance for microfluidic devices. While a large number of sophisticated solutions have been demonstrated, there is still a great amount of interest in developing simple strategies that do not require complex fabrication steps and electrical connections. A small footprint, compatibility with different substrate materials, working fluids and temperatures are amongst other desirable characteristics. We demonstrate a bubble gate strategy that meets all the above. In this strategy, flow control is achieved using a controlled gas stream that intercepts a liquid stream at a T-junction, forming a gas-liquid interface (i.e. bubble). Closely positioned micropillars are employed to limit the bubble motion to a single degree of freedom. The bubble breaks into the liquid stream and occupies the entire liquid cross-section, when the gas pressure is continued. Hence, the bubble movement is able to stop or manipulate the liquid flow. Several control operations are discussed herein, including, but not limited to, valves, liquid metering and peristaltic pumping. PIV measurements are employed to investigate the transient flow structure.   

Vertical Fence Wake Manipulation Using Periodic Variation of Upstream Flow

The effect of periodic variation of upstream flow on the separated shear flows behind the vertical fence was experimentally investigated. Upstream flow was modified using small obstacles and this device made the periodic change of streamwise velocities in front of the fence. The experiments were performed in a circulating water channel. The Reynolds number based on the height of fence and freestream velocity was varied from 2000 to 6000. The vertical fence was submerged in the turbulent boundary layer. Stereoscopic-PIV method was used to measure the instantaneous velocity fields around a vertical fence. 800 instantaneous velocity fields were acquired in each experimental condition and the mean properties were calculated using the ensemble average method. The obtained results were compared with those of uncontrolled fence flow. The results showed the vertical fence under the upstream flow change has the local downwash flow behind the fence and this flow suppressed the separation bubble and made the smaller recirculation region compared with uncontrolled fence wake.   

Session R25: Instability in Jets and Wakes II

Mixing in Long Cylinder by a Stratified Jet: Laboratory Modeling and Theory

The evolution of buoyant turbulent jets released into a low aspect ratio (width/height) cavity filled with a homogeneous fluid was investigated experimentally. The motivation was to understand mixing process in U.S. Strategic Petroleum Reserves (SPR), where crude oil is stored in salt caverns of aspect ratio approximately 0.1. During maintenance, degassed oil is introduced as a jet from the top of the caverns while denser gas-laden crude oil is pumped out from the bottom. The focus was on mixing, formation and development of density layer as well as the time for replenishing oil in the container to an acceptable level of vapor pressure (gas concentration). Basing on the results of experiments a theoretical model was advanced which permits to calculate the vertical density distributions in cavern as a function of time and other external parameters. Satisfactory agreement between theory and measurements was demonstrated. The results obtained could be extrapolated to SPR flow mixing situations and help to improve the efficiency of expensive oil cavern refilling.   

The visualization of the acoustic feedback loop in impinging underexpanded supersonic jet flows using ultra-high frame rate Schlieren

An acoustic feedback model for supersonic jet impingement has been proposed in past literature. Due to the inherent difficulty in measuring highly transient phenomena, models of the feedback process have mostly relied on inference, and comparison to similar subsonic flows. Through the use of ultra-high speed cameras operating at one million frames per second, it has been possible to directly visualize the acoustic feedback loop for the first time. Time resolved Schlieren and shadowgraph image sequences capture the interaction of upstream travelling acoustic waves with the shear layer at the nozzle lip and shock structures within the jet core. The acoustic forcing at the nozzle lip produces a sinusoid like perturbation in the shear layer that is highly transient both temporally and spatially. This perturbation grows rapidly into a Kelvin-Helmholtz like vortex ring. These time resolved measurements offer new insights into the fundamental physical mechanisms governing the acoustic feedback loop in supersonic jet impingement.   

The Effect of Orifice Eccentricity on Instability of Liquid Jets

The hydrodynamic instability of inviscid jets issuing from elliptic orifices is studied. A linear stability analysis is presented for liquid jets that includes the effect of the surrounding gas and an explicit dispersion equation is derived for waves on an infinite uniform jet column. Elliptic configuration has two extreme cases; round jet when ratio of minor to major axis is unity and plane sheet when this ratio approaches zero. Dispersion equation of elliptic jet is approximated for large and small aspect ratios considering asymptotic of the dispersion equation. In case of aspect ratio equal to one, the dispersion equation is analogous to one of the circular jets derived by Yang [1]. In case of aspect ratio approaches zero, the behavior of waves is qualitatively similar to that of long waves on a two dimensional liquid jets and the varicose and sinuous modes are predicted [2]. The growth rate of initial disturbances for various azimuthal modes has been presented in a wide range of disturbances. \\[4pt] [1]. Yang, H. Q. 1992 Asymmetric instability of a liquid jet. Phys. Fluids \textbf{4}, 681-689. \\[0pt] [2]. Hagerty, W. W., Shea, J. F. 1955 A study of the stability of plane fluid sheets. J. Appl. Mech. \textbf{22}, 509-514.   

The vortex breakdown of a variable property jet with swirling flow.

The vortex breakdown of a coaxial variable property jet with swirling flow has been experimentally investigated in this work, focusing on how the swirl of the inner and outer jets affect the formation of a stagnation point in the swirling jet. In the case of the CO$_{2}$ jet, the stagnation point flow is more easily formed compared to the air jet, and the stagnation point location was lower than that of the air jet. Stagnation point flow is also formed easier with the introduction of the swirl of the outer jet, and its location is also lower compared to the nonswirling case. The lowering of the stagnation point location of the swirling inner jet with density and viscosity differences due to the swirl of the inner and outer jets will be physically explained in this presentation by considering the theoretical equation obtained by analytically solving a simplified Navier-Stokes equation, (S. Matsubara, H. Gotoda, A. Adzlan, T. Ueda, Experiments in Fluids, 2011 (In press)) which has not been reported in previous research on fluid dynamics.   

Hydrodynamic Instabilities in Round Liquid Jets in Gaseous Crossflow

Water jets in the presence of uniform perpendicular air crossflow were investigated theoretically and experimentally using high speed imaging for gaseous Weber numbers (We) below 30, small liquid jet Ohnesorge numbers, and large liquid and gaseous Reynolds numbers. Previously, a bag instability has been reported for We between 4 and 30. Jets first deform into curved sheets due to aerodynamic drag, followed by the formation of partial bubbles (bags) along the jet streamwise direction that expand and ultimately burst. Single bags were present at each streamwise position along the liquid jets in prior experiments featuring liquid jet nozzle diameters less than the capillary length of water. We have found that at larger nozzle diameters it is possible to observe multiple bags at the same streamwise jet position because single bags of such large sizes would be unstable. Theoretical predictions for individual bag expansion diameter over time agree with experimental measurements.   

Scalar and Velocity Field Measurements in Variable Density Jets in Crossflow

This experimental study explores both unforced and acoustically forced behavior of variable density transverse jets via simultaneous acetone PLIF and PIV measurements. Jets composed of mixtures of helium and nitrogen are injected normally from a converging nozzle into an air crossflow. The jet-to-crossflow density ratio $S$ is varied among test cases by changing the proportions of nitrogen and helium as well as the fraction of seeded acetone. A recent study\footnote{Getsinger, et al., AIAA Paper 2011-0040, 2011} determined that transverse jets (of Reynolds number $Re_{j}=1800$) likely transition to global instability in response to sufficient lowering of the jet-to-crossflow density ratio $S$ (below 0.45-0.40) and/or momentum flux ratio $J$ (below 10). This transition is characterized by weak shear layer instabilities that are easily overcome by external forcing for the convectively unstable (high $S$ and $J$) case, and strong pure-tone oscillations resistant to external forcing for the globally unstable (low $S$ and $J$) case. The effect of this instability transition on jet dynamics and mixing is examined here, as are alterations in the velocity field that may be associated with the behavior of the instabilities.   

Analysis of nonlinear interactions among instability mechanisms in a jet in crossflow

We undertake an analysis of datasets from direct numerical simulation of a jet in crossflow, using the method of Dynamic Mode Decomposition (DMD). The procedure reveals coherent structures in the flow known as Koopman modes, which oscillate at frequencies that are also computed by the method. Both the crossflow and the jet inflow profile are laminar. As the jet-to-crossflow velocity $R$ is increased, we observe the breakdown of hairpin vortices characteristic for low values of $R$. Near-wall structures corresponding to low-frequency oscillations are revealed above $R=1.5$ by the DMD analysis, and their interaction with modes on the jet trajectory results in complex flow patterns, which however retain spanwise symmetry. At $R=2.5$ and higher, spanwise symmetry is broken, and the flow exhibits the complex dynamics typically observed in literature. Furthermore, we study the effects of crossflow unsteadiness on jets at low $R$, showing that the hairpin vortices are able to persist under noise of moderate amplitude introduced upstream of the jet orifice.   

Linear forcing response of subsonic jets

The linear stability of spatially developing subsonic jets is investigated. A parametric base flow model is employed that matches experimental data for turbulent mean flows and that includes a solid nozzle. Temporal eigenmodes are computed using a newly developed ``shift-relax'' method. All eigenmodes are found to be stable in an isothermal setting. While this observation is in agreement with classical local stability results, a stable eigenmode spectrum seems inappropriate for the description of the convective instability dynamics of jets, which are known to be highly receptive to external perturbations. Instead, we propose to characterize jet instability in terms of the linear global flow response to sustained low-level forcing. External perturbations inside the nozzle duct are identified that give rise to the most amplified flow response at a prescribed frequency. Results will be discussed both for incompressible and compressible settings.   

Instability of low viscosity elliptic jets with varying aspect ratio

In this work an analytical description of capillary instability of liquid elliptic jets with varying aspect ratio is presented. Linear stability analysis in the long wave approximation with negligible gravitational effects is employed. Elliptic cylindrical coordinate system is used and perturbation velocity potential substituted in the Laplace equation to yield Mathieu and Modified Mathieu differential equations. The dispersion relation for elliptical orifices of any aspect ratio is derived and validated for axisymmetric disturbances with $m = $0, in the limit of aspect ratio, $\mu = 1$, i.e. the case of a circular jet. As Mathieu functions and Modified Mathieu function solutions converge to Bessel's functions in this limit the Rayleigh-Plateau instability criterion is met. Also, stability of solutions corresponding to asymmetric disturbances for the kink mode, $m = 1$ and flute modes corresponding to $m \geq 2$ is discussed. Experimental data from earlier works is used to compare observations made for elliptical orifices with $\mu \ne 1$. This novel approach aims at generalizing the results pertaining to cylindrical jets with circular cross section leading to better understanding of breakup in liquid jets of various geometries.   

Local absolute instability in the near field of hot and light round jets

We present a numerical investigation of the viscous spatiotemporal stability properties of low-density round jets emerging from circular nozzles or tubes. The two particular cases typically studied in experiments, namely a hot gas jet discharging into a quiescent cold ambient of the same species, and an isothermal jet consisting of a mixture between two gases with different molecular weight, discharging into a stagnant ambient of the heavier species, are treated separately. We use a realistic representation of the base velocity and density profiles based on boundary layer theory, taking into account the effect of variable transport properties. Our results show significant quantitative differences with respect to previous studies that use parametric presumed-shape base profiles, and reveal that hot jets are generically more unstable than light jets. In addition, the downstream evolution of the local stability properties of the jet is analyzed, revealing that, whereas a localized pocket of absolute instability can take place in the jet, for the combination of jet-to-ambient density ratio, Reynolds number, and initial momentum thickness used in experiments available in the literature, the absolutely unstable region in the jet is bounded by the jet outlet. The global transition observed in these experiments is demonstrated to take place when the absolutely unstable domain becomes sufficiently large.   

Session R26: Nanofluids IV

Electroosmosis in a nanofilm of chloride-aqueous solution with counter-charged surface patches

We study Electroosmotic flow (EOF) by conducting Non-Equilibrium MD Simulations (NEMDS) of water and chloride on a silica substrate. The system response is studied as axial electric fields (AEF) are imposed and as the surface charge (SC) is modified by implementing counter-charged patches (CP). The density profiles reveal that the CP result in an ionic depletion in bulk solvent and in a higher hydrophilicity than on regular silica. We compute lower velocities for the cases with higher SC on the CP. Our velocities are in agreement to results from previous MD studies. Density and velocity profiles reveal a stationary chloride layer and a stagnant water region on the CP. This stationary layer grows as CP with higher charges are settled and as weaker AEF are imposed. We infer that ionic accumulation on the CP and hydrophilicity are responsible for the EOF velocity changes for systems with different CP and the same AEF imposed. We perform continuum calculations and the EOF velocities agree with the results obtained from NEMDS. We show that by modifying SC on a substrate, systematic changes can be induced in EOF at the nanoscale.   

Electrokinetics of Correlated Electrolytes and Ionic Liquids

Perhaps the most basic assumption of classical electrokinetic theory is the mean-field approximation, where the each ion feels only the electric field produced by the mean charge density (via Poisson's equation) rather than the fluctuating Coulomb forces with individual neighbors. Here, we present a simple continuum model for electrostatic correlations between finite-sized ions, which leads to a 4th order modified Poisson equation, convenient for the analysis of electrokinetic phenomena. When the mean-field approximation breaks down, e.g. due to large ion concentrations, large ion valences, and/or nanoscale confinement, the zeta potential loses its significance, and the model predicts that electro-osmotic flows are typically reduced - or even reversed - by correlation effects, compared to the prediction of the Helmholtz-Smoluchowski formula. This may help to explain the over-prediction of induced-charge electro-osmotic flows by classical models. An interesting limit of the model describes electro-osmosis in solvent-free ionic liquids and molten salts, which may be important in energy storage and electroactuation applications.   

Characterization of Electrical Properties of Nanowires by Electro-orientation

We investigate the electro-orientation of large-aspect-ratio particles in liquid suspension as a possible technique to determine the particles' electrical conductivity and/or permittivity, which are often poorly known and difficult to measure directly. With the application of a spatially uniform AC electric field, ellipsoidal particles in suspension will rotate into alignment with their longest axis along the field. In the low frequency limit, the alignment rate itself does not distinguish between equally sized particles of different properties. However, it is possible to characterize the particle's electrical properties by measuring the crossover frequency at which its alignment rate transitions from conductivity-dominated to permittivity-dominated behavior. Moreover, the crossover frequency is insensitive to the particle aspect ratio for large aspect ratios, making the electro-orientation technique suitable even for nanowires, whose precise length is difficult to resolve optically. We present experimental results obtained by optical microscopy on the alignment rate of nano- and micro- wires under applied fields of different frequency. Experiments are conducted with particles of different type and size to determine how the electro-orientation crossover frequency varies with particle conductivity and aspect ratio. We compare our experimental results with theoretically obtained values, and assess electro-orientation as a nanowire-characterization technique.   

Examining Permittivity Effects in Electric Double Layers using Molecular Dynamics and Atomistic-to-Continuum Modeling

Charged surfaces exposed to an ionic solution attract an electric double layer: stratifications of solvent and solute molecules significantly deviating from their bulk concentrations. The double layer screens the charges in solution from those at the surface, but due to the anisotropy in the near-wall fluid, characterizing the precise mechanics by which this happens has proven difficult. Molecular dynamics (MD) simulations are capable of explicitly resolving the complex layering effects in the vicinity of the charged interface, but much work remains to analyze the results and improve the understanding of these phenomena. In this work, we use atomistic-to-continuum methods to analyze the spatially-varying electrical permittivity in these layers at different potentials and ion concentrations, focusing on salt water solutions. The permittivity is a particularly relevant quantity because it determines the capacitance of the different ionic layers. We will present a mathematical formalism for extracting this quantity from an MD realization and provide examples of how this coarse-grained quantity varies with a simulation. It will then be demonstrated how the resolved permittivity informs the realized voltage drop across the various parts of the double layer.   

Atomistic simulations of nanoscale electrokinetic transport

An efficient and accurate algorithm for atomistic simulations of nanoscale electrokinetic transport will be described. The long-range interactions between charged molecules are treated using the Particle-Particle Particle-Mesh method and the Poisson equation for the electric potential is solved using an efficient multi-grid method in physical space. Using this method, we investigate two important applications in electrokinetic transport: electroosmotic flow in rough channels and electowetting on dielectric (EWOD). Simulations of electroosmotic and pressure driven flow in exactly the same geometries show that surface roughness has a much more pronounced effect on electroosmotic flow. Analysis of local quantities shows that this is because the driving force in electroosmotic flow is localized near the wall where the charge density is high. In atomistic simulations of EWOD, we find the contact angle follows the continuum theory at low voltages and always saturates at high voltages. Based on our results, a new mechanism for saturation is identified and possible techniques for controlling saturation are proposed.   

Molecular Dynamics Models of the Electric Double Layer for Large Zeta Potentials

The Classical Poisson-Boltzmann (PB) theory for the electric double layer (EDL) breaks down at the nanoscale as zeta potential increases. The ability to accurately model the EDL for large potentials is important for engineering high energy storage devices. To better understand behavior at large potentials, various molecular dynamics (MD) models were developed. MD models range from an idealized Lennard-Jones ionic fluid between unstructured walls to a salt water solution between solid substrates. All models feature a bulk fluid region in order to obtain a reference state. Models are compared using charge density profiles, solvent and solute concentration profiles, and zeta potentials as metrics. Local polarization structure can be obtained from the salt water MD models. Despite its inability to capture these effects, the idealized model similarly deviates from PB theory at large potentials. Ion concentration and surface charge density are varied in a parametric study using the idealized model.   

Characterization of the Velocity and Power Consumption of Electroosmotic Flow in Nanochannels Using Numerical Simulations

A numerical simulation of the electroosmotic flow in a nanochannel is performed. The study focuses on characterizing the velocity behavior when changes are applied to the zeta potential in the electrical double layer and the electric field. Similarly, the characteristics of power consumption are indentified by the ratio of convection to conduction current, which changes with flow velocity and ion concentration. In the 2D numerical simulations the electrostatic potential is obtained by the Poisson Boltzmann dilute solution theory which is solved in its nonlinear form and is validated from published work. Aqueous solutions of 1:1 electrolytes at bulk ion concentrations from 1-100 mM are considered. The viscous-driven nature of the flow outside the electric double layer causes an adverse pressure gradient along the center of the channel which is examined in detail. Pressure effects at the inlet and outlet are also considered. The need for higher inlet pressure increases with velocity, which is proportional to the applied electric field. Increasing the bulk ion concentration causes minimal change in average velocity under conditions of zero slip at the channel walls. In the case when a slip length is imposed at the walls, the flow velocity increases significantly with ion concentration. The increase in slip length also increases the ratio of convection to conduction current.   

Lattice Boltzmann simulation of electrostatic double layer interaction force for nanoparticles

Modeling the transport and retention of nanoparticles (NPs) through soil porous media requires an accurate description of the electrostatic interaction force between a nanoparticle and soil grain. In this study, we apply the lattice Boltzmann method to directly solve the nonlinear Poisson Boltzmann (PB) equation for several geometric configurations including plate-plate, NP-plate, and NP-NP interactions, for any surface potentials and interaction distances and for different boundary conditions. Interaction energy and force are then derived from the simulations. For the case of plate-plate interaction, the simulation results are compared to the exact solution of the nonlinear PB equation. It is shown that the linear PB solution is valid when the nondimensional surface potential is less than one, and that the linear PB solution over-predicts the interaction force for intermediate gap distances but under-predicts the force for small gap distances. For NP-plate and NP-NP interactions, an axisymmetric lattice Boltzmann formulation is developed to solve the governing equations. The results will be compared to the classic approximate expressions of interaction force to evaluate their validity and to study the effect of nanoparticle size.   

The effects of external electric field on the structure of water inside and outside single-walled carbon nanotubes

In the present work, all-atom molecular dynamics (MD) simulations are utilized to examine the structure of water inside and outside the armchair SWCNT in the presence of external electric field parallel or perpendicular to the tube axis. Extensive MD simulations have been performed in wide ranges of $E$ (0-3V/nm) at room conditions (300 K and 1 bar). The dependence of liquid density profile, orientation of dipole moment and hydrogen bonds profiles are discussed on the electric fields. With the parallel electric field, the structure of water outside the SWCNT changes slightly while inside the SWCNT the water structure is found to be more ordered. With the perpendicular electric field, the structure of water both inside and outside the SWCNT has changed dramatically. When the strength of field is above 1V/nm, the chains or the layers structures inside the SWCNT are broken and even the isolated water molecule is found. Outside the SWCNT, liquid density profiles, orientation of dipole moment and hydrogen bonds profiles are found to be the non-axisymmetric. This work may be helpful in understanding the physics of the confined water and in the design of future nanofluidic devices.   

Modeling of Ion Transport in Nanochannels

Transport of ions in fluidic environment is a basis for many biological processes. Microchannel ions flow is characterized by formation of electric double layer (EDL) near the solid wall. In nanochannel, however, the formation of EDL can be prevented by the constrained geometry leading to the creation of a single ion layer and resulting in the selective movement of ions. The confinement effects can be controlled by the wall charges providing a controlability to the nanoscale diffusion (pumping effect). This study will present model and molecular dynamics simulations of three-dimensional nanochannel flow of charged fluid. The various concentration of ions in solution was studied as well as the influence of the external force.   

Session R27: Biofluids: General II: Microbubbles and Droplets

The Acoustic Atomization of Droplets within a Bubble

The process of vaporizing liquid microdroplets using ultrasound is known as acoustic droplet vaporization (ADV). Gas embolotherapy is a proposed cancer therapy that uses the ADV process to selectively generate microbubbles, which can then lodge in the microvasculature to occlude blood flow and starve the tumor. We have observed that continued ultrasound exposure to microbubbles adhering to a wall induces in a droplet atomization process. The atomization process originates at the gas-liquid interface and produces a spray of liquid droplet within the microbubble along the axis of the acoustic beam. Single pulses with 30 cycles from 3.5 and 7.5 MHz single element focused transducers operating at peak negative pressures ranging from 4 to 8 MPa were used to generate atomization. The atomization process was observed in microbubbles ranged from 30 $\mu $m to 1 mm in diameter. The extent of the atomization had a direct relationship with acoustic pressure.   

Bubble Transport and Splitting in a Symmetric Bifurcation

Transport and splitting of gas bubbles through a geometrically symmetric bifurcation is investigated numerically as a model of cardiovascular gas bubble transport in air embolism and Gas Embolotherapy. An interface capturing Volume of Fluid Method on an Eulerian fixed grid is used to compute the bubble splitting at the symmetric bifurcation. Bubble transport and splitting is investigated for a range of roll angles, capillary numbers, Reynolds numbers and Bond numbers. Results indicate that splitting is observed to be more homogenous at higher capillary numbers and lower roll angles. It is observed that at nonzero roll angles and small bubble lengths, there is a critical value of the capillary number below which the bubbles do not split and are transported entirely into the upper branch. The value of the critical capillary number increases with roll angle and the bubble length. Shear stress distribution at the bifurcation carina increases several folds as the bubble tip reaches the carina. These findings suggest that, in large vessels, gas emboli tend to be transported upward unless flow is unusually strong. In smaller vessels more even splitting of bubbles is predicted. The endothelial cells at a vessel bifurcation would be potentially exposed to higher stress levels, which might induce bioeffects.   

Frequency dependent subharmonic threshold for contrast microbubbles

We numerically investigate the predictions from several contrast microbubble models to determine the excitation threshold for subharmonic generation. All models are transformed into a common interfacial rheological form, where encapsulation is represented by two radius dependent surface properties---effective surface tension and surface dilatational viscosity. In contrast to the classical perturbative result, the minimum threshold for subharmonic generation is not always obtained near twice the resonance frequency; instead it can occur over a range of frequency from resonance to twice the resonance frequency. The quantitative variation of the threshold with frequency depends on the model, bubble radius and encapsulation properties. Some models incorporate an upper limit on effective surface tension (resulting from strain softening or rupture of the encapsulation during expansion). Without this upper limit, the threshold is extremely large especially near the resonance frequency and there is a global minimum near twice the resonance frequency. On the other hand, having zero surface tension in the buckled state (the lower limit) increases the threshold especially near twice the resonance frequency which in presence of the upper limit results in a possible shift of the minimum threshold towards resonance.   

The fluid mechanics of nutrient transport within biofilms

Bacterial biofilms are interface-associated colonies of bacteria embedded in an extracellular matrix that is composed primarily of polymers and proteins. During the growth of a biofilm, nutrient is taken up by the surface of the biofilm, and contained by cells in the bulk. A critical problem is that above a critical size there is necessarily a growth bottleneck, in which the biofilm cannot take up enough nutrients to feed all of the cells within it. We discuss, through theory and experiments, several strategies that are employed by biofilms of Bacillus subtilus to avoid this growth bottleneck. These include clever use and control of osmotic pressure (through the expression of polymeric extracellular matrix); the excretion of surfactants and the use of associated marangoni stresses; and the distribution of flagella (used as mixers) within the bulk of the biofilm. Some speculations about other potential mechanisms (for which there is no current experimental support) will also be presented.   

Modeling and 3-D Simulation of Biofilm Dynamics in Aqueous Environment

We present a complex fluid model for biofilms growing in an aqueous environment. The modeling approach represents a new paradigm to develop models for biofilm-environment interaction that can be used to systematically incorporate refined chemical and physiological mechanisms. Special solutions of the model are presented and analyzed. 3-D numerical simulations in aqueous environment with emphasis on biofilm- ambient fluid interaction will be discussed in detail.   

Variation of flow-induced stresses within scaffolds used in bone tissue engineering

Bone tissue engineering is often based on seeding adult stem cells on porous scaffolds and subsequently placing these scaffolds in flow perfusion bioreactors to stimulate cell differentiation and cell growth. In the present study, the distribution of stresses in structured porous scaffolds under flow is investigated by calculating the probability density function of flow-induced stresses in different scaffold geometries with simulations. The physical reason for the development of particular stress distributions is further explored, and it is found that the direction of flow relative to the internal architecture of the porous scaffold is important for stress distributions. When the flow direction is random relative to the configuration of the geometric elements making up the scaffold, it is found that a common distribution, such as the one suggested by Voronov et al. (Appl. Phys. Let., 2010, 97:024101), can be used to describe the stress distribution.   

From thermodynamics to fluid mechanics: Enhancing the 2-D protein crystallization process

The leading method to determine protein structure is to perform X-ray diffraction on protein crystals. However, crystallizing protein is a challenging task which is usually met with limited success. 2-D protein crystals at the air/water interface are commonly obtained under quiescent conditions. Recently, the formation of such crystals was shown to be enhanced by the presence of flow. Here, we examine both the kinetics of the process, including the detrimental effects of protein aggregation, as well as the fluid dynamics associated with successful crystallization events. The deep-channel surface viscometer geometry is utilized which consists of the annular flow between two stationary cylinders and a rotating floor. For a particular protein surface concentration, a Reynolds number threshold has been identified above which crystals grow and below which they do not. This flow system also allows for the determination of the surface shear viscosity, which provides an indication of the mesoscale interactions associated with protein crystals.   

Constrained droplets for high resolution microscopy of protein fibrillization

The use of constrained droplets (droplets with pinned contact lines on solid surfaces) is proposed here as a method for sample support in optical microscopy studies. Capillarity acts to contain the liquid sample, allowing access for observations in the bulk and at the gas/liquid interface. At the capillary length scale, surface tension forms stable interfaces, virtually immune to gravity and with curvatures that can be adjusted. This is particularly useful when studying the gas/liquid interface and its vicinity under high resolution optical microscopy. Such observations are normally performed using oil immersion objectives which must be positioned within distances only tens of microns from the region of interest. Constrained droplets can also be used at small scales, requiring minute volumes of analyte. The use of the constrained droplet method is demonstrated by studying the aggregation of insulin into amyloid fibrils in the solution and at the gas/liquid interface, where proteins are prone to denaturation and subsequent fibrillization. Such an aggregation process is associated with many neurodegenerative diseases, including Alzhemier's.   

Material characterization of poly-lactic acid shelled ultrasound contrast agent and their dynamics

Micron-size gas bubbles encapsulated with lipids and proteins are used as contrast enhancing agents for ultrasound imaging. Biodegradable polymer poly-lactic acid (PLA) has recently been suggested as a possible means of encapsulation. Here, we report \textit{in vitro} measurement of attenuation and scattering of ultrasound through an emulsion of PLA agent as well as theoretical modeling of the encapsulated bubble dynamics. The attenuation measured with three different transducers of central frequencies 2.25, 3.5 and 5 MHz, shows a peak around 2-3 MHz. These bubbles also show themselves to possess excellent scattering characteristics including strong non-linear response that can be used for harmonic and sub-harmonic contrast imaging. Our recently developed interfacial rheological models are applied to describe the dynamics of these bubbles; rheological model properties are estimated using measured attenuation data. The model is then applied to predict nonlinear scattered response, and the prediction is compared against experimental observation.   

Blood Flow through an Open-Celled Foam

The Hazen-Dupuit-Darcy (HDD) equation is commonly used in engineering applications to model the pressure gradient of flow through a porous media. One major advantage of this equation is that it simplifies the complex geometric details of the porous media into two coefficients: the permeability, K, and form factor, C. However through this simplification, the flow details within the porous media are no longer accessible, making it difficult to study the phenomena that contribute to changes in K and C due to clotting of blood flow. To obtain a more detailed understanding of blood flow through a porous media, a direct assessment of the complex interstitial geometry and flow is required. In this study, we solve the Navier-Stokes equations for Newtonian and non-Newtonian blood flow through an open-celled foam geometry obtained from a micro-CT scan. The nominal strut size of the foam sample is of $O$(10e-5) m and the corresponding Reynolds number based upon this length ranges up to $O$(10). Fitting the pressure gradient vs. Darcy velocity data with the HDD equation demonstrates that both viscous and inertial forces play an important role in the flow through the foam at these Reynolds numbers. Recirculation zones are observed to form in the wake of the pore struts, producing regions of flow characterized by both low shear rates and long fluid residence times, factors of which have been shown in previous studies to promote blood clotting.   

Session R28: Flapping Flight

Time-resolved measurements of the velocity field over the wing of bats during flight

Particle Image Velocimetry (PIV) has become a well-established tool to study flows associated with flying animals. The wake shed by flying bats as it is seen in the Trefftz plane is by now well described for several bat species. However, to complete the understanding of the three-dimensional wake structures, additional views are necessary. To meet this need, bats were trained to fly at a stationary position in the wind tunnel at wind speeds between 2 m/s and 6 m/s. Aligning the laser light sheet parallel to the free stream, we measured, using time-resolved PIV (200 Hz), the air flow in the region of the left wing of the animals. Three high-speed cameras (400 Hz) were used to capture the position and movement of the bat and to reconstruct the wing kinematics. Characteristic flow structures were observed consistently at different spanwise positions, including the starting and stopping vortices at the beginning and end of the downstroke, as well as other vortex and wake features.   

Inertial and Fluid Forces during Bat Flight Maneuvers

Flying animals generate forces to move through the air with the coordinated movement of their wings. Bats have evolved a particularly impressive capacity in flight control. With more than 24 wing joints bats are able to manipulate wing area, angle of attack, and camber to control their flight through altering aerodynamic forces on their wings. Here we use a model-based tracking framework to reconstruct the highly articulated wing and body kinematics of maneuvering bats from high-speed video. Using this data, we extract a simplified wing geometry and kinematics during various flight maneuvers. The time-dependent fluid flow and resultant forces on the wing are computed with CFD using a direct numerical simulation, and then used in a low-order model of the bat dynamics. This reconstruction identifies the relative importance of both inertial and aerodynamic forces during flight maneuvers.   

Large-Eddy Simulations of Flapping-Induced Lift Enhancement

This work isolates the heaving motion of flapping flight in order to numerically investigate the fluid-structure interaction at Reynolds numbers relevant to birds and bats. Although there has been much focus on insect flight, larger vertebrates fly at a higher Reynolds number, which leads to different dynamics in terms of flow separation, reattachment, and high-lift mechanisms. In this work, an incompressible large-eddy simulation is used to simulate the periodic heaving of a flat plate at various angles of attack. It is found that the heaving motion can increase the average lift when compared with the steady flow, more so than is expected from the relative angle of attack. The additional lift is attributed to the vortex dynamics at the leading edge. The lift enhancement and flow features are compared with experimental results.   

Lift force enhancement and fluid-structure interactions on a self-excited flapping wing model

We present data from a mechanical model that we have used to explore a physical mechanism that may have aided transition from gliding to flapping flight over fifty million years ago. The model is composed of a cantilevered flat plate with a hinged trailing flap and is tested in a low-speed wind tunnel. For slow wind speeds the model is stationary, but above a critical wind speed the wing starts to oscillate due to an aeroelastic instability. A positive angle of attack on the wing results in a positive lift force. However, this lift force is significantly enhanced once the wing starts to oscillate. We used particle image velocimetry (PIV) to understand the unsteady aerodynamics of the self-excited flapping wing, and to identify and characterize the mechanisms that generate the enhanced lift force. We also discuss the implications of our results on the evolution of powered biological flight.   

Fluid-structure interactions on compliant membrane wings

Membrane wings are characteristic of flying animals such as bats, as well as low Reynolds number Micro Air Vehicles. These wings exhibit interesting features such as self-cambering, soft stall, and good performance at large angles of incidence. The interaction between the membrane and the vortical structures over the wing play an important role in the wing's performance. Vortices shed from the leading edge and tip interact with the membrane to select vibration modes, which depend on the details of the wing loading. However, the vibration modes are sensitive to the boundary conditions of the membrane. Here, we present results using force and membrane displacement measurements as well as Particle Image Velocimetry (PIV) from wind tunnel experiments on rectangular membrane wings with identical planform, but with different kinds of perimeter support. The different boundary conditions on the membrane affect the wing shape, support different vibration modes at different frequencies, and affect aerodynamic performance.   

A bi-directional leading-edge vortex in slow-flying bats

A leading-edge vortex (LEV) is crucial to bat afloat, since a LEV could generate high lift which could not be predicted by the conventional aerodynamics theories. The LEV usually exhibits an intensive spiral vortex of a unidirectional axial flow on the top surface of wing. In this study, we numerically simulate a slowing-flying bat using immersed boundary method. The morphology and kinematics of bat are taken from experimental measurements. It is observed from our simulation that the stretching and collapse motions of wing could induce a bi-directional axial flow. The bi-directional axial flows stabilize the LEV and enhance its intensity. The observation is further investigated by using a simple model: the flows around a spanwise oscillating plate. The spanwise oscillation could enhance the LEV and make its more stable. This result implies a link of bat kinematics with its unusual aerodynamic performances.   

Force estimation and turbulence in the wake of a freely flying European Starling

Flapping wings are one of the most complex yet widespread propulsion method found in nature. Although aeronautical technology has advanced rapidly over the past 100 years, natural flyers, which have evolved over millions of years, still feature higher efficiency and represent one of nature's finest locomotion methods. One of the key questions is the role of the unsteady motion in the flow due to the wing flapping and its contribution to the forces acting on a bird during downstroke and upstroke. The wake of a freely flying European Starling is investigated as a case study of unsteady wing aerodynamics. Measurements of the near wake have been taken using long duration high-speed PIV in the wake behind a freely flying bird in a specially designed avian wind tunnel. The wake has been characterized by means of velocity and vorticity fields. The measured flow field is decomposed based on the wing position phases. Drag and lift have been estimated using the mean velocity deficit and the circulation at the wake region. In addition, kinematic analysis of the wing motion and the body has been performed using additional high-speed cameras that recorded the bird movement simultaneously with the PIV. Correlations between the wing kinematics and the flow field characteristics are presented as well as the time evolution of the velocity, vorticity and additional turbulence parameters.   

Characterization and Scaling of Vortex Shedding from a Plunging Plate

Leading-edge and trailing-edge vortices (LEV and TEV) are investigated for a plunging flat plate airfoil at a chord Reynolds number of 10,000 while varying plunge amplitude and Strouhal number. Digital Particle Image Velocimetry is used to examine the strength and dynamics of shed vortices. Vortex strength, timing, pinch-off and trajectory are examined. By tracking the development of both the LEV and TEV in phase-locked measurements throughout the cycle and extracting the respective vortex circulation, the dimensionless circulation of both the LEV and TEV at each phase in the cycle could be determined. Guided by theoretical considerations for vorticity generation and aerodynamic theory, we will discuss the role of kinematic parameters on vortex shedding and the applicability of a scaling factor for the circulation of the shed vortex structures. Whereas a scaling parameter based on plate kinematics effectively collapses the circulation values of the shed leading-edge vortices with variation in Strouhal number, plunge amplitude, and angle of attack, it is found that the strength of the trailing-edge structures vary little with variation in plunge amplitude and angle of attack.   

Optimization of Flapping Based Locomotion

Locomotion at the macro-scale is important in biology and industrial applications, such as for understanding the fundamentals of flight to enable design of artificial locomotors. We present results on optimal actuation profiles for locomotion of a rigid, flapping body at intermediate Reynolds number. The actuation consists of a vertical velocity control attached to a pivot point of an ellongated rigid body, which is allowed to rotate and is affected by a torsional spring; the spring acts as an elastic recoil. No a priori assumption is made on the form of the vertical actuation, except for smoothness. Thus, we pose an infinite dimensional time-varying, PDE-constrained optimization problem (with additional constraints on the vertical control) and solve it by variational methods. We explore the effects of parameter variations on the optimal locomotion profile, such as the torsional spring constant, relative mass density of body to fluid, and discuss the effects on locomotion strategies.   

Spontaneous motion of flapping wings driven by hydrodynamic instability

Recent experimental [1] and numerical [2] studies have examined the dynamics of rigid symmetric wings flapping vertically in a quiescent fluid and free to move in the horizontal direction. It has been observed that above a critical flapping frequency the flow loses its symmetry while the wing starts to move horizontally and eventually reaches a quasi constant horizontal speed. The present work reconsiders this problem from an hydrodynamics instability point of view. The basic flow is periodic and symmetric, the periodicity being imposed by the vertical forcing frequency while the symmetry of the velocity field ensures no motion in the horizontal direction. The linear stability is examined using the Floquet theory, with the assumption of asymmetric perturbations to explain the onset of horizontal forces. Numerical results of the stability problem will be shown. The cases of wings fixed or free to move will be analyzed and compared.\\[4pt] [1] Vandenberghe N., Zhang J. {\&} Childress S., ``A symmetry-breaking leads to forward flapping'', Journal of Fluid Mechanics, 506, 147 (2004)\\[0pt] [2] Alben S. {\&} Shelley M. ``Coherent locomotion as an attracting state for a free flapping body``, Proc. Natl. Acad. Sci., U.S.A., 102, 11163 (2005)   

Session R29: Suspension Swimming

Out-of-Equilibrium effects in suspensions of light-activated artificial microwimmers

We present a new type of colloidal artificial swimmers propelled by the decomposition of hydrogen peroxide and activated by light. The effect is reversible and allows external control of the swimming/non swimming behavior of the particles. Moreover the bulk synthesis makes possible the study of very concentrated assemblies of monodisperse and identical microswimmers. These active agents are used to explore fancy effects of out-of-equilibrium systems, e.g. clustering, ``tugboat'' effect...   

Laboratory studies of ocean mixing by microorganisms

Ocean mixing plays a major role in nutrient and energy transport and is an important input to climate models. Recent studies suggest that the contribution of fluid transport by swimming microorganisms to ocean mixing may be of the same order of magnitude as winds and tides. An experimental setup has been designed in order to study the mixing efficiency of vertical migration of plankton. To this end, a stratified water column is created to model the ocean's density gradient. The vertical migration of Artemia Salina (brine shrimp) within the water column is controlled via luminescent signals on the top and bottom of the column. By fluorescently labelling portions of the water column, the stirring of the density gradient by the animals is visualized and quantified. Preliminary results show that the vertical movement of these organisms produces enhanced mixing relative to control cases in which only buoyancy forces and diffusion are present.   

A kinetic model for concentrated active suspensions

We study the dynamics in concentrated suspensions of active self-propelled particles using a kinetic model and three-dimensional continuum simulations.In a previous model for semi-dilute active suspensions (Saintillan and Shelley 2008), we have revealed the existence of hydrodynamic instabilities and complex correlated motions with pattern formation in suspensions of pushers, while suspensions of pullers undergo no such dynamics. Here, we modify this previous kinetic model by including an additional nematic alignment torque proportional to the local concentration in the equation for the rotational velocity of the particles, causing them to align locally with their neighbors (Doi and Edwards 1986). Linear stability analyses in the isotropic and aligned states show that in the presence of such a torque both pusher and puller suspensions are unstable to random fluctuations. Large-scale three-dimensional simulations of the kinetic equations are also performed and confirm the existence of these instabilities, which lead to the formation of nematic-like structures at high concentrations. Detailed measures are defined to quantify the degree and direction of alignment, and the effects of steric interactions on pattern formation are discussed in detail.   

Instabilities and global order in concentrated suspensions of spherical microswimmers

We use numerical simulations to probe the dynamics of concentrated suspensions of spherical microswimmers interacting hydrodynamically. Previous work in the dilute limit predicted instabilities of aligned suspensions for both pusher and puller swimmers, which we confirm computationally. Unlike previous work, we show that isotropic suspensions of spherical swimmers are also always unstable. Both types of initial conditions develop long-time polar order, of a nature which depends on the hydrodynamic signature of the swimmer but very weakly on the volume fraction up to very high volume fractions.   

Transverse swimming in a dilute suspension of active swimmer under an oscillating shear flow

Simulations of a dilute suspension of pusher swimmers under an oscillating shear flow show that a large fraction of them swim preferentially in the vortex and flow direction, perpendicular to the gradient direction. These two directions alternate in a collective way among all the swimmers. Experiments of a suspension of E.Coli in a Hele-Shaw cell under an oscillating flow manifest the same behavior.   

Effect of viscoelasticity on the collective behavior of swimming microorganisms

Hydrodynamic interactions of swimming microorganisms can lead to coordinated behaviors of large groups. Previous theoretical work has shown that in mean-field theories the interactions give rise to a linear instability of the uniform isotropic state if the organisms push themselves forward. However, that work is done with the organisms suspended in a Newtonian fluid, while many organisms exist in a non-Newtonian medium. Using a mean-field theory and the Oldroyd-B constitutive equation, we show how viscoelasticity of the suspending fluid alters the hydrodynamic interactions and therefore the ability of the group to coordinate. We quantify the ability to coordinate by the initial growth rate of a small disturbance from the uniform isotropic state. For small wavenumbers the response is qualitatively similar to a Newtonian fluid but the Deborah number determines the effective viscosity of the suspension. At higher wavenumber, the response of the fluid to small amplitude oscillatory shear flow leads to a maximal growth rate at a particular wavelength. This is in stark contrast to the Newtonian result.   

Shaken, but not stirred: how vortical flow drives small-scale aggregations of gyrotactic phytoplankton

Coastal ocean observations reveal that motile phytoplankton form aggregations at the Kolmogorov scale (mm-cm), whereas non-motile cells do not. We propose a new mechanism for the formation of this small-scale patchiness based on the interplay of turbulence and gyrotactic motility. Counterintuitively, turbulence does not stir a plankton suspension to homogeneity but drives aggregations instead. Through controlled laboratory experiments we show that the alga \textit{Heterosigma akashiwo} rapidly forms aggregations in a cavity-driven vortical flow that approximates Kolmogorov eddies. Gyrotactic motility is found to be the key ingredient for aggregation, as non-motile cells remain randomly distributed. Observations are in remarkable agreement with a 3D model, and the validity of this mechanism for generating patchiness has been extended to realistic turbulent flows using Direct Numerical Simulations. Because small-scale patchiness influences rates of predation, sexual reproduction, infection, and nutrient competition, this result indicates that gyrotactic motility can profoundly affect phytoplankton ecology.   

Enhancement of biomixing by swimming cells in 2D films

Fluid mixing in active suspensions of microorganisms is important to ecological phenomena and shows surprising statistical behavior. We investigate the mixing produced by swimming unicellular algal cells (Chlamydomonas) in quasi-2D films by tracking the motions of cells and of microscopic passive tracer particles advected by the fluid. The reduced spatial dimension of the system leads to long-range flows and a surprisingly strong dependence of tracer transport on the swimmer concentration. The mean square displacements are well described by a stochastic Langevin model, with an effective diffusion coefficient D growing as the 3/2 power of the swimmer concentration, due to the interaction of tracer particles with multiple swimmers. We also discuss the anomalous probability distributions of tracer displacements, which become Gaussian at high concentration, but show strong power-law tails at low concentration.\footnote {H. Kurtuldu et al., Proc. Nat. Acad. Sci. 108, 10391 (2011)}   

Active stress driven convection in a suspension of chemotactic bacteria

We examine the linear stability of a suspension of swimming bacteria producing dipolar hydrodynamic disturbances confined in a channel subjected to a linear chemo-attractant gradient across the channel. At the continuum level swimming bacteria exert an ``active'' stress on the fluid which is a function of the bacterial concentration and orientation fields. In the base-state without any fluid flow, the fluxes from the chemotactic and diffusive motion of the bacteria balance to yield exponential number density and active stress profiles across the channel. We show that such a base-state is unstable to perturbations in the number density parallel to the channel walls if the bacterial concentration exceeds a critical value determined by a Peclet number measuring the strength of chemotaxis relative to diffusion. Active stress gradients resulting from the perturbation in the number density drive convective fluid flow, which transports bacteria into the regions of highest perturbed bacteria concentration reinforcing the original perturbation.   

Energy Transport in a Concentrated Suspension of Bacteria

Coherent structures appear in a concentrated suspension of swimming bacteria. While transport phenomena in a suspension have been studied extensively, how energy is transported from the individual cell scale to the larger meso-scale remains unclear. In this study, we carry out the first successful measurement of the three-dimensional velocity field in a dense suspension of bacteria. The results show that most of the energy generated by individual bacteria dissipates on the cellular scale. Only a small amount of energy is transported to the meso-scale, but the gain in swimming velocity and mass transport due to meso-scale coherent structures is enormous. These results indicate that collective swimming of bacteria is efficient in terms of energy. This study sheds light on how energy can be transported toward smaller wave numbers in the Stokes flow regime.   

Session R30: Microfluids: General VII

Tracking the Growth Rate of Nanopillar Formations Caused by Large Thermocapillary Forces

Viscous nanofilms are known to deform spontaneously into periodic arrays of nanopillars when exposed to a strong transverse thermal gradient. Comparison of the characteristic pillar spacing in experiment with predictions of linear instability analysis suggests that thermocapillary forces, and not acoustic phonon pressure or electrostatic image charge, are likely the dominant destabilizing mechanism [1]. Examination of the dynamical shapes and growth rates of emerging peaks provides an even more stringent test of the physical mechanism underlying the deformation process. Here we report measurements based on white light interferometry in which the reflected intensity from individual color channels is used to monitor the growth and shape of 3D formations in molten polymer nanofilms. Numerous experiments were conducted to isolate the influence of various operating parameters. These measurements exhibit an extended regime characterized by exponential growth which persists well beyond small amplitude deformations. The corresponding growth rates agree well with predictions of linear stability theory based on thermocapillary flow; however, the inferred film viscosities are systematically larger than bulk values. \\[4pt] [1] E. McLeod, Y. Liu, and S. M. Troian, Phys. Rev. Lett. 106, 175501(2011)   

Dynamics of flexible molecules in thinning fluid filaments

Newtonian liquids that contain small amounts ($\sim $ppm) of flexible polymers can exhibit viscoelastic behavior in extensional flows. In this talk, we report the results of experiments on the thinning and breakup of polymeric fluids in a simple microfluidic device. We aim to understand the stretching dynamics of flexible polymers by direct visualization of fluorescent DNA molecules, a model polymer. A Boger fluid, composed of 100 ppm polyacrylamide and 85{\%} w/w glycerol, is seeded with stained lambda---DNA molecules ( $<$ 10{\%} v/v) imaged by high speed epifluorescence microscopy. We observe that the strong flow in the thinning fluid threads provide sufficient forces to stretch the DNA molecules away from their equilibrium coiled state. The distribution of stretch lengths, however, is very heterogeneous due to molecular individualism and initial conditions. Once the molecules are stretched to their full length and aligned with the flow, they translate along the fluid thread as rigid rods until the point of pinch off. After pinch off, both the fluid and molecules return to a relaxed state.   

Optimum Transport in Flat Heat Pipes

In this study we investigate wetting behavior of the wick structure and the maximum theoretical heat transfer rate of a 40 cm titanium flat heat pipe. Large scale flat heat pipes are designed for high performance electronics cooling. Wick designs in flat heat pipes are typically limited by viscous drag and capillary pressure, and do not transport fluids as sufficient rates to meet practical cooling requirements. An analytical model is used to describe flow through wick structure with array of pillars. The capillary pressure and viscous drag are obtained by surface energy calculation and numerical simulations, respectively. To verify the model, we conducted wetting tests on the wick samples with different pillar dimensions. The model agrees qualitatively with the experiments, but under predicts the viscous drag. We extend the model to calculate the pressure drop for liquid and vapor flows, which predicts the upper limit for heat transport in flat heat pipes. Pillar parameters are optimized for maximum heat transfer rate, which approaches several hundred of Watts.   

Validation of CFD models for microscale nanoprecipitation reactor using $\mu$-PIV and confocal $\mu$-LIF

Over the past a few decades, computational fluid dynamics (CFD) models have become more and more important in the process of reactor design in chemical engineering. Compared to experimental methods, they can provide comprehensive information on the flow field as well as other fields, such as concentration. However, they also need to be validated against experimental data to ensure the accuracy. In this work, the micro-scale particle image velocimetry ($\mu$-PIV) is employed in conjunction with the confocal-base micro-scale laser induced fluorescence ($\mu$-LIF) to specifically validate CFD models for use in microscale nanoprecipitation reactor. The former is for the velocity field measurement and the latter gives us the mixture fraction information. Both RANS and LES are used to simulate the field flow. For RANS, a DQMOM-IEM micromixing model is used to predict the mixture fraction field while only a scalar transport equation is solved in the LES simulations. Comparisons between simulation results and experimental data show that RANS might not be the right tool for such reactors. LES, on the other hand, gives reasonably satisfactory predictions.   

Thermophoresis of a temperature responsive polymer

Thermophoresis, the migration of a species due to a temperature gradient, has been shown to be a possible mechanism for manipulating molecules in microfluidic devices. The mechanism governing thermophoresis is complex making its dependence on different physical factors hard to predict. We experimentally investigate thermophoresis of a polymer which exhibits inverse temperature dependence of its solubility in water. For sufficiently high average temperatures, two forms of the molecule are present. We measure the Soret coefficient of both and find that one has positive S$_{T}$ and the other negative. We investigate the cause of this sign change using a Lattice Boltzmann based simulation. We find that the conformation of the polymer can influence its migration in a temperature gradient.   

Microscale heat transfer enhancement using spinodal decomposition

In many cases, miniaturization is limited by our ability to quickly remove heat; current state-of-the-art cooling approaches have significant limitations, particularly for high heat flux applications. Recent studies have shown that phase separation of a binary liquid-liquid mixture quenched to a temperature below the spinodal curve can be used to enhance heat transfer in small-scale devices. In particular, it has been shown that the self propulsion of single droplets formed during the intermediate stage of spinodal decomposition can produce considerable agitation and, as a result, enhanced heat transport. Spinodal phase separation dynamics can be described by the coupled Cahn-Hilliard/Navier-Stokes equations; unfortunately, simulation of these equations at the device scale is computationally costly due to the mulltiscale nature of spinodal decomposition, which requires resolution of the phase interface between the two fluids which is of atomistic size. In this talk we discuss possible approaches for reducing this computational cost by calculating the resulting transport from synthetic fluctuating fields that simulate the effect of spinodal decomposition but are generated stochastically without solving the Cahn-Hilliard equation at close-to-atomistic resolution.   

Improved theory on AC electrothermal flows

We compare simulations from new theory to experimental measurements on AC eletrothermal flows (ACET) for micromixing application on 96 microwell (10 $\mu$L) plate for high conductivity physiological solutions. This application leads to certain design constraints (electrode sizes, voltage range, conductivity). Beneath each microwell filled with saline solution ($\sigma$=0.02 mS/cm, to 16 mS/cm.), a sinusoidal voltage (0 to 40Vpp, 1MHz) is applied between 3 interdigitated gold electrodes 35 $\mu m$ thick, separated by a 150$\mu m$ gap. Due to this design, the ACET flows, measured by $\mu PIV$, doesn't follow the present theory. Similarly to natural convection, a bifurcation like behaviour is observed : the flows appear only above a critical voltage. The velocities scale as $V^p$ with $p\geq4$ with $p$ increasing with conductivities. We analyse the validity conditions of the weak temperature gradient approximations. Accordingly we propose a thermal-electrical strong coupling model, which is traditionally neglected. We also study the competition between ACET and natural convection appearing in this configuration.   

Controlling the trajectories of bubble trains at a microfluidic junction

The increasing number of applications facilitated by digital microfluidic flows has resulted in a sustained interest in not only understanding the diverse, interesting and often complex dynamics associated with such flows in microchannel networks but also in developing facile strategies to control them. We find that there are readily accessible flow speeds wherein resistance to flow in microchannels decreases with an increase in the number of confined bubbles present, and exploit this intriguing phenomenon to sort all bubble of a train exclusively into one of the arms of a nominally symmetric microfluidic loop. We also demonstrate how the arm into which the train filters into can be chosen by applying a \textit{temporary} external stimulus by means of an additional flow of the continuous liquid into one the arms of the loop. Furthermore, we show how by tuning the magnitude and period of this temporary stimulus we can switch controllably, the traffic of bubbles between both arms of the loop even when the loop is \textit{asymmetric}. The results of this work should aid in developing viable methods to regulate traffic of digital flows in microfluidic networks.   

Measurement of charge of a droplet induced by contact electrification

The contact electrification is the charge transfer between two surfaces by contact and separation. We have developed the experimental method to measure the amount of charge of a droplet induced by contact electrification. In the method, the uniform electric field is applied to a droplet suspended in dielectric oil. The horizontal movement of a droplet is determined by the balance between electric and drag force. The drag force exerted on a droplet has been calculated by Hadamard-Rybczinski solution. The effects of a droplet size, electrolyte concentration of an aqueous droplet on the amount of charge have been examined.