Session GA: Turbulent Boundary Layers: Experiments II

Measurements of spatio-temporal spectra in a zero-pressure gradient turbulent boundary layer

The structure of the velocity field in wall-parallel planes in a zero pressure gradient turbulent boundary layer is interrogated using time-resolved digital particle image velocimetry at moderate Reynolds number ($Re_{\tau}=500$). In order to investigate turbulent boundary layer structure in light of the emerging understanding of the nature of very large scale motions (VLSMs), two high speed cameras are placed side-by-side to recover streamwise structures over ten times the boundary layer thickness in length, while still resolving the dissipative scales. The simultaneous spatial (streamwise and spanwise) and temporal joint spectra and correlations are used to investigate the validity of Taylor's hypothesis as the wall is approached, in light of the known significant wall normal extent of the VLSMs and the associated range of convection velocities.   

Instantaneous shear stress distribution in a turbulent wall-bounded flow

Knowledge of wall shear stress is crucial for understanding of all wall-bounded turbulent flows and also for many technical applications. The aim of the present work is to develop a novel stress sensor which is capable of measuring surface shear stress over an extended region of the flow. This sensor as a direct method for measuring surface stresses consists of mounting a thin film made of a elastic polymer on the surface of the solid model. The geometry and mechanical properties of the elastomer are measured, particles acting as markers are applied on the film surface, and an optical technique is used to measure the film deformation caused by the flow. While the technique can be used in air or water, its sensitivity can be tuned for different flow conditions. The static and dynamic calibration of the sensor, and its application to a fully developed turbulent channel flow at moderately high Reynolds numbers will be addressed, and results will be compared with indirectly measured wall shear stress from PIV experiment.   

Time-resolved PIV in fully developed turbulent pipe flow

Stereoscopic particle image velocimetry was used to study the three component flowfield in both fully developed turbulent pipe flow and at several locations downstream of a horizontal $90^{\circ}$ bend. The data was acquired with a high speed camera, making it possible to resolve the flow field in time for Reynolds numbers up to $35'000$. The secondary motions downstream the bend appears to be governed by either a Dean type motion were two swirls with opposite signs coexists, one in the upper and one in the lower half of the pipe respectively. Or a motion where two swirls, as large as the pipe, with opposite sings are alternating between each other. Both motions are present at the same Reynolds numbers, but the unsteady behavior appears to be more common for higher Reynolds numbers.   

3-D Flow Visualization of a Turbulent Boundary Layer

A recently developed 3-D flow visualization technique is used to visualize large-scale structures in a turbulent boundary layer. The technique is based on the scanning of a laser light sheet through the flow field similar to that of Delo and Smits (1997). High-speeds are possible using a recently developed MHz rate pulse burst laser system, an ultra-high-speed camera capable of 500,000 fps and a galvanometric scanning mirror yielding a total acquisition time of 136 microseconds for a 220 x 220 x 68 voxel image. In these experiments, smoke is seeded into the boundary layer formed on the wall of a low-speed wind tunnel. The boundary layer is approximately 1.5'' thick at the imaging location with a free stream velocity of 24 ft/s yielding a Reynolds number of 18,000 based on boundary layer thickness. The 3-D image volume is approximately 4'' x 4'' x 4''. Preliminary results using 3-D iso-surface visualizations show a collection of elongated large-scale structures inclined in the streamwise direction. The spanwise width of the structures, which are located in the outer region, is on the order of 25 -- 50{\%} of the boundary layer thickness.   

Harvesting energy from turbulence in boundary layers by using piezoelectric generators

The availability of significant kinetic energy in fluid flows distributed over a number of temporal and spatial scales creates a unique opportunity to convert this energy into electrical output by using piezoelectric generators. The unsteadiness due to turbulence can produce mechanical strain energy in the piezoelectric material which in turn can generate a build up of charge that can be used to power electronic devices. In the present work, short length piezoelectric beams were placed in a zero pressure gradient two dimensional turbulent boundary layer at Reynolds numbers based on momentum thickness up to 6500 to evaluate their performance as energy generators. The piezoelectric beam was traversed across the boundary layer to determine the location where the output power is maximized. It was found that the location of maximum power is not close to the wall where most of the turbulent activities are high but further away from the wall. The work has shown that there is a three-way coupled interaction~between the fluid flow, the piezoelectric structure and its electromechanical field.   

Turbulent Coherent Structures in a Thermally Stable Boundary Layer

An experiment was conducted to examine the effect of thermal stability on turbulent coherent structures occurring in a flat plate boundary layer. The objective is to further characterize the turbulence in thermally stable atmospheric boundary layers, commonly found in the arctic regions, focusing on Reynolds number independent effects. This experiment was conducted in a 16 foot long, 4'x2' cross-section, open-return wind tunnel by replacing the upper surface with a heated half inch aluminum plate. The plate was maintained at an isothermal condition, the boundary layer along this surface was tripped and the tunnel run at the lowest speed possible, in order to maintain both a fully turbulent boundary layer and a large Richardson number. A wide range of stabilities were investigated, with Richardson numbers ranging from 0 to 0.5, covering both the weakly and strongly stable regimes. Using thermocouple temperature measurements and time resolved particle image velocimetry; an attempt was made to identify changes in coherent turbulent motions corresponding to changing flow stability. Additionally, an attempt was made to identify significant features of the turbulence that could be used to identify clearly delineating features of the weakly stable and strongly stable flow regimes.   

Buoyancy effects on large- and small-scale turbulent motions in the atmospheric surface layer during the transition through neutral stability

The present study examines how the transitory nature of the atmosphere, both on diurnal and meso timescales, affects the evolution of Very Large-Scale Motions in the Atmospheric Surface Layer (ASL) during the transition through neutral thermal stability. It is hypothesized that the finite time duration of the near-neutral period arrests the development of VLSMs in the ASL, compared to those expected in a canonical turbulent boundary layer having equivalent Reynolds number; and that, this, in turn, affects the structure of the small-scale turbulence by impeding inner-outer interactions. These scientific questions are addressed using simultaneously sampled hot-wire and sonic anemometry time series obtained during a field campaign in Utah's western desert. The pointwise data span a wall-normal distance between 1 mm and 30 m above the surface over a time period of several hours centered around neutral transition. Velocity spectra as a function of time (i.e., thermal stability) are shown as well as statistics associated with the turbulent bursting process. Results are compared against those obtained both at lower Reynolds number in the laboratory and in the neutral ASL.   

Turbulent structures in smooth and rough open channel flows

Turbulent flow in open channels is unique because it is bounded by the free surface and the flow is entirely dominated by the bed turbulence. Both experiments and simulations agree that the large-scale near-wall structures interact with the free surface without significant reduction of their strength. Still the link between bed and free-surface turbulence is not well understood and it is of a particular importance for the processes occurring at the surface in shallow geophysical flows. In this paper, high resolution particle image velocimetry (PIV) measurements in an open channel flow are presented. Velocity measurements were obtained in the streamwise - wall normal (x-y) plane and streamwise-spanwise (x-z) plane. Streamwise-spanwise (x-z) planes were acquired at various vertical locations. The focus of this study is to investigate the streamwise oriented vortices along the flow depth as documented through the analysis of swirling strength, conditional averaging and vortex statistics. Turbulence measurements in rough open channel flow are also presented and compared with those on the smooth wall.   

A turbulent boundary layer on a rough wall at hypersonic speeds

Previous experiments on hypersonic turbulent boundary layers have documented the general features of the mean flow behavior on a smooth plate, but virtually no data exist describing the boundary layer behavior on a rough wall for Mach numbers greater than about 5. Here, we report PIV measurements of the mean flow and two components of velocity fluctuations on a flat plate with three different roughness geometries: a square bar roughness, and two diamond roughness elements of different height. The boundary layer develops at Mach 7.2 in a perfect gas, at a Reynolds number based on momentum thickness of about 3600. The results are compared with DNS under identical flow conditions. Supported under NASA Grant NNX08AB46A, Program Manager Catherine McGinley.   

Session GB: Turbulence: Fundamentals I

The bottleneck effect and the Kolmogorov constant in three-dimensional turbulence

A large database generated from direct numerical simulations (DNS) of isotropic turbulence, including recent simulations at up to $4096^3$ resolution and Taylor microscale Reynolds numbers of up to about $1000$, is used to explore the bottleneck effect in three-dimensional energy spectrum and in second-order structure functions, and to determine the Kolmogorov constant, $C_K$. The difficulties in estimating $C_K$ at any finite Reynolds number are examined. Our data from well-resolved simulations show that the bottleneck effect decreases with the Reynolds number and that its behavior is independent of the nature of the forcing scheme and is insensitive to small-scale resolution. This trend is seen in both spectral and physical spaces, though the effect is less noticeable in the latter. An alternative to the usual procedure for determining $C_K$ is suggested. The proposal does not depend on a particular choice of fitting ranges or power-law behavior in the inertial range. Within the resolution of the numerical data, $C_K$ thus determined is constant in the Reynolds number. A simple model including non-local energy transfer is proposed to reproduce the observed scaling. Further implications of the findings are discussed.   

Split energy cascade in turbulent flows

Hydrodynamic turbulence exhibits a remarkable dependence on the space dimension. This property manifests for instance in the direction of the kinetic-energy cascade, which is direct in 3D and inverse in 2D. A passive scalar transported by a turbulent flow shows an analogous behavior. In isotropic flows, the variance of the scalar field cascades either downwards or upwards depending on the dimension, the degree of compressibility, and the scaling exponent of the carrier flow. We undertake a geometrical approach to investigate the dependence of turbulence and turbulent transport on the space dimensionality. We first consider a system that is fully under analytical control, i.e. a passive scalar transported by a Gaussian short-correlated flow on a cylindrical surface, where the radius can be inflated or collapsed at will. For any finite radius, the variance cascade splits into a direct branch and an inverse one. This behavior is intimately connected to the existence of a non-degenerate invariant measure for the fluid-particle separations. Direct numerical simulations of the Navier-Stokes equations show that also the kinetic-energy cascade splits when the aspect ratio of the flow is less than one.   

Controlling the Dual Cascade of Two-dimensional Turbulence

It has been established that monoscale forcing cannot produce the dual cascades of energy and enstrophy with the scaling laws predicted by Kraichnan--Leith--Batchelor (KLB) theory. However, we have been able to find forcings which do produce the KLB scalings: $E(k)\propto k^{-5/3}$ for the inverse energy cascade and $E(k)\propto k^{-3}$ for the forward enstrophy cascade. We find these forcings using a novel adjoint-equation-based optimal control technique. First, the control problem is formulated and a method for controlling the energy spectrum of solutions of the incompressible Navier--Stokes equations is proposed. The control process is validated by several test cases. Then, this control method is applied to a pseudo-spectral numerical computation of the 2-D incompressible Navier-Stokes equations with doubly periodic boundary conditions in order to find the forcing that reproduces the scaling laws of KLB theory. Finally, we demonstrate that the flows we obtain are indeed dynamically active by measuring directly the energy and enstrophy fluxes. We also compare our forcing and the resulting turbulence with results obtained using a linear forcing recently proposed by Lundgren (2003). The results presented here show that the choice of forcing can fundamentally alter the dynamics and spectral properties of the turbulence, and that the theoretically attractive choice of band-width limited forcing is actually inconsistent with KLB theory.   

Forward/Inverse Energy Cascade in 2D and QG Turbulence

We perform numerical simulations to study two-dimensional and quasi-geostrophic turbulence. In all runs, small scale forcing injects energy at wave number, $ k_f $, and the inverse energy cascade is halted at large scale by linear drag. A new decomposition of spectral energy flux into aggregated transfer function cascading up and down (hereafter ATFu and ATFd) is introduced instead of Kraichnan's classical approach. Both functions are positive, monotonically increasing in spectral space and have the same power-law dependency in the energy inertial range. Amazingly, the ATFd has discontinuity at $ k_f $ and the jump equals to energy injection rate $ \dot{E}_{in} $ while the ATFu is always continuous. This implies that the energy injected is transferred first to small scale and then cascade inversely but not directly to large scale. The QG turbulence resembles the 2D turbulence if $ \beta $ effect is too weak to create zonal flow. If zonal jets are spotted, the exponent of the power-law dependency and the magnitude of ATFs are smaller compared to that in 2D turbulence indicates that $ \beta $ inhibits the inverse energy cascade. The properties of ATFs are strongly dependent on $ \dot{E}_{in} $ and the drag loss but not $ k_f $.   

Inverse Cascades and Zonal Flows on a Beta Plane

We examine the role of forward and inverse cascades in 2D turbulence in creating zonal jets on a $\beta$-plane. The magnitude of the characteristic velocity and the characteristic width of a zonal jet are set by the balance of the two cascades. The widths of the jets are strongly dependent on the value of the local Rossby deformation radius $L_R$. Kinetic energy is dominated by potential energy at length scales greater than $2 \pi L_R$. We find that little energy inverse cascades to scales greater than $2 \pi L_R$, and there is a break in the slope of the kinetic energy spectrum at that scale. Forcing at small scales produces large-scale zonal flows that resemble the widths, but not the magnitudes, of jet streams of Jupiter and Saturn. The magnitudes of the large-scale velocities of the computed zonal flows are much smaller than on Jupiter or Saturn. The transfer of energy from small scales to large scales involves many more wave number triads on an $f$-plane than on a $\beta$- plane, so the equilibrium energy of the large scale zonal flows is determined by only a few triads.   

What is turbulence and which way does it cascade?

Turbulence is defined as an eddy-like state of fluid motion where the inertial vortex forces of the eddies are larger than any of the other forces that tend to damp the eddies out. Inertial vortex forces vxw are zero for irrotational flows, so irrotational flows are not turbulent by definition even though they may be random and induced by turbulence. Because the vorticity w is always produced at small scales, turbulence always cascades from small scales to large. Turbulence growth is limited by vertical buoyancy forces at the Ozmidov scale of fossilization and by horizontal Coriolis forces at the Hopfinger scale of fossilization. Fossil turbulence is defined as a perturbation in any hydrophysical field produced by turbulence that persists after the fluid is no longer turbulent at the scale of the perturbation. Most turbulent mixing in the ocean and atmosphere occurs in fossil turbulence patches where most of the turbulent kinetic energy of the patch has radiated near vertically as fossil turbulence waves. Vertical heat, mass, momentum and information transport in the ocean is dominated by an intermittent generic process termed beamed zombie turbulence maser action mixing chimneys (see http: //maeresearch.ucsd.edu /\~{}cgibson /Documents2007 /GibsonBB08Nov26\_Alist.htm).   

Scale-locality of the energy cascade in turbulence using Fourier Analysis

We investigate the scale-locality of non-linear interactions which drive the energy cascade in a turbulent flow. The main picture that emerges from our work is that the primary participants in the cascade process are triplets of ``eddies'' comprised of adjacent \emph{logarithmic bands} of Fourier modes. We disprove in particular an alternate picture of ``local transfer by nonlocal triads'' by showing that such triads, due to their restricted number, make a vanishingly small contribution to the energy flux in the inertial range. We rigorously prove that it is only the aggregate effect of a geometrically increasing number of local wavenumber triads which can sustain the energy cascade to small scales. Our analysis shows that the SGS definition of the flux is the proper measure of the cascading energy and that the sharp spectral filter has a firm theoretical basis for use in LES modeling. It also demonstrates the danger in the widespread notion that the elementary interactions in turbulence are those involving triads of single Fourier modes. We support our results with numerical data from a $512^3$ pseudo-spectral simulation of isotropic turbulence with phase-shift dealiasing.   

Quantifying the locality of nonlinear interactions in MHD turbulence

The locality functions introduced by Kraichnan give the fraction of the energy flux across a given cutoff wavenumber $k_c$ that is due to nonlinear interactions with wavenumbers $k$ smaller than the cutoff (the infrared locality function) or greater than the cutoff (the ultraviolet locality function). Previous analysis of DNS data for hydrodynamic turbulence confirmed the theoretical scaling exponent of $n=4/3$ in the wavenumber ratio and in the limit of the infinite inertial range. We have extended the analysis to DNS data for MHD turbulence. Out of four nonlinear terms contributing to the energy transfer, two dominant ones, $b \cdot \nabla b$ and $b \cdot \nabla u$, lead to the locality functions that exhibit behavior that can be characterized by scaling exponents in the infrared. The extend of the inertial range is insufficient to determine the exponents uniquely but the data are indicative of values between 1/2 and 2/3, i.e., much less than for hydrodynamic turbulence. Therefore, the nonlinear energy transfer is significantly more nonlocal in MHD turbulence, with potential implications for theory and modeling.   

Energy flux in non-equilibrium energy spectra in steady turbulence

The energy spectrum $E(k)$ and energy flux function $\Pi(k)$ in non-equilibrium state are obtained using the spectral energy equation based on the Kovasznay, Leith diffusion and Heisenberg hypothesis. The derived models are assessed using the DNS data for forced homogeneous isotropic turbulence. Three different forcing schemes are used and compared. In all these forcing schemes, the base spectrum obeys the Kolmogorov law $E(k) \propto k^{-5/3}$, and $\Pi(k)=$ const, but the temporal development of the the deviatoric spectrum and flux is divided into the three phases. In the period in which $d\varepsilon/dt \equiv \dot{\varepsilon} > 0$, $E(k) \propto k^{-7/3}$ and $\Pi (k) \propto k^{-2/3}$ in the inertial subrange (Phase 1), while $E(k) \propto -k^{-7/3}$ and $\Pi(k) \propto -k^{-2/3}$ when $\dot{\varepsilon} < 0$ (Phase 2), where $\varepsilon$ is the dissipation rate. In the transient period between Phase 1 and Phase 2, $\dot{\varepsilon} \approx 0$ and $\ddot{\varepsilon}$ is large, and $E(k) \propto k^{-9/3}$ and $\Pi(k) \propto k^{- 4/3}$ (Phase T). On average, the deviatric spectrum induces the forward scatter of the energy into the small scale in Phase 1, and the backward scatter of the small scale energy into the large scale in Phase 2. These results are overall consistent with the prediction obtained using the closure models, but the eddy-viscosity Heisenberg model does not yields $E(k) \propto k^ {-9/3}$ in Phase T. Due to the effect of the intermittency, the energy spectrum and flux exhibit a slight deviation in the exponents.   

Session GC: Turbulence Simulations IV

Study of local isotropy in a turbulent pipe flow using longitudinal and transverse structure functions

The scaling exponents of the longitudinal $\left\langle \Delta u_z^n\right\rangle$ and the two transverse structure functions, $\left\langle \Delta u_r^n\right\rangle$ and $\left\langle \Delta u_{\theta}^n\right\rangle$ with $n \leq 7$ are studied in a fully developed incompressible turbulent pipe flow at $Re_D = 24580$ and $50000$ using direct numerical simulation flow fields. The scaling exponents for $\left\langle \Delta u_r^n\right\rangle$ and for $\left\langle \Delta u_{\theta} ^n\right\rangle$ increase with the turbulent Reynolds number $R_ {\lambda}$. However, the scaling exponents for $\left\langle \Delta u_z^n\right\rangle$ remain nearly unchanged. The Kolmogorov universal constants in both of the dissipative range and inertial range for the longitudinal structure functions show a smaller increase with $R_{\lambda}$ than those for the transverse structure functions. The present results are compared with previous experimental and DNS data for channel and duct flows (Antonia \textit{et al.} (1997). Phys. Fluids, 9 (11), 3465)   

Tensor-based Lagrangian time correlations in DNS of isotropic turbulence

We study Lagrangian statistics of dynamically important tensors, such as velocity- gradient tensor, together with its symmetric and antisymmetric parts, through fluid particle tracking. The data, a $1024^4$ space-time DNS of forced isotropic turbulence, are accessed using the web-services of the JHU public database (http://turbulence.pha.jhu.edu). A Tensor-based time-correlation function is defined by the tensor product between variables at different times along the Lagrangian trajectory. Analyses in the literature had shown slightly longer correlation times for the square rotation rate as compared to the square strain-rate magnitude. However, here we show that the difference is much larger when considering the dynamically more relevant tensor-based correlation function. The question whether these trends are due mostly to vortical coherent structures (worms) is addressed using conditional averaging. Even with the exclusion of worms, rotation-rate remains significantly more correlated over time than the strain-rate. The analysis is done for the pressure Hessian tensor and significant differences are obtained for its trace and deviatoric parts.   

Pressure, acceleration and velocity structure functions in DNS at high Reynolds number and/or improved small-scale resolution

Evidence from both numerical simulation and experiment in the literature suggest the second-order structure function of pressure fluctuations requires higher Reynolds number than the pressure spectrum for inertial range scaling. We use a direct numerical simulation database for isotropic turbulence at resolution up to $4096^3$ to directly calculate the pressure structure function and pressure gradient two-point correlation. We examine the relationships between those statistics and those same quantities calculated from fourth-order velocity structure functions. Our results suggest that the longitudinal, mixed and transverse fourth-order velocity structure functions, usually denoted by $D_{LLLL}(r)$, $D_{LLNN}(r)$ and $D_{NNNN}(r)$, obey, to a good approximation, the same scalings for scale size $r$ in the inertial range. While mutual cancellations limit the accuracy with which these can be used to evaluate the pressure structure function the ambiguities clearly become smaller at higher Reynolds number. We also use new datasets of improved small-scale resolution albeit at lower Reynolds number to re-examine the nature of pressure gradient and viscous force correlations at small scale separations, more definitively than possible before.   

Multi-particle Lagrangian statistics of turbulent dispersion from simulations of isotropic turbulence at $R_{\lambda}\approx 1100$

Numerical simulations at up to \(4096^3\) grid resolution have been conducted on machines with very large processor counts to obtain the statistics of Lagrangian particle pairs and tetrads in turbulent relative dispersion. Richardson-Obukhov scaling for mean-square pair separation adjusted for initial conditions is observed for intermediate initial separations, in support of prior estimates of about 0.6 for Richardson's constant. Simulations at \(R_{\lambda} \approx 650\) have also been conducted for sufficient duration to obtain fully converged exit time statistics for independently moving particles at very large scales. The fact that all particle pairs reach such large scales of separation means the inertial subrange of exit times is also captured accurately. The results show Kolmogorov scaling for positive moments of exit time, but a strong dependence on initial separations for inverse moments. Inertial-range estimates of tetrad shape factors are reinforced by simulations at Taylor-scale Reynolds numbers up to about 1100. Tetrad shape parameters conditioned on cluster size are also examined in order to understand geometric features of turbulent dispersion in more detail.   

DNS of the thermal effects of laser energy deposition in isotropic turbulence

Laser energy deposition in isotropic turbulence is studied using DNS. A spectral numerical method is combined with shock-capturing and numerical challenges faced are discussed. A model problem involving energy deposition near a single vortex is studied as a first step. For the turbulent problem, $Re_{\lambda} = 30$ and $M_t = 0.001$ and $0.3$ are considered. Evolution of the mean flow is divided into shock formation, shock propagation and core roll up stages. For $M_t = 0.3$, the turbulence slows down shock formation and propagation and prevents core roll up. This behavior is not observed for $M_t = 0.001$. The turbulence intensities are enhanced due to compression from the shock wave and suppressed due to expansion in the core. Turbulent kinetic energy budgets are computed to explain this behavior. Effect of mean vorticity production on the turbulence is also studied. As an application, laser energy deposition near a wall is studied. Orientation of the laser axis and distance of the focal volume from the wall are found to affect the evolution of the resulting flow field.   

Decomposition of Fluid Acceleration by Rotational and Irrotational Motion in Isotropic Turbulence

It is well known that fluid acceleration in turbulence is highly intermittent. Source of the intermittency was found to be closely related to the rotational motion of coherent vortical structures. From the Poisson equation for pressure, $\frac{1}{\rho} \nabla^2 P=\Omega -\frac{\epsilon}{2 \nu}$, acceleration, which is mostly the negative of pressure gradient, can be expressed as a sum of acceleration-like terms, $-\nabla (\nabla^2)^{-1} \Omega + \nabla (\nabla^2 )^{-1} \frac {\epsilon}{2 \nu}$, each of which is named as $a^{\Omega}$ and $a^{\epsilon}$ . They are acceleration due to rotational motion of eddy and acceleration due to irrotational strain field, respectively. We investigated the statistical characteristics of those accelerations by using direct numerical simulation of isotropic turbulence. Flatness of acceleration is of order of 10 but flatness of $a^{\Omega}$ and $a^{\epsilon}$ are $3 \sim 5$ which represents less intermittency in the range of $Re_{\lambda} = 47 \sim 130$. Based on the cylinder vortex model, we show that probability density function of acceleration must have -5/3 slope and pdf's of $a^{\Omega}$ and $a^{\epsilon}$ must have -3 slope in log- log scale when the Reynolds number is infinite. Numerical and experimental results do not show clear slope since the Reynolds number is relatively low, but an asymptotic behavior is observed.   

Evolution of Compressible Decaying Isotropic Turbulence with Multi-temperature Non-equilibrium

Understanding and predicting of transition and turbulence under non-thermodynamical-equilibrium (NTE) conditions are important for hypersonic flight and other industrial applications. In NTE turbulence, the Kolmogorov paradigm, which forms the basis of most equilibrium turbulence models, may be invalid. Furthermore, under the NTE conditions, multiple temperatures often take place in diatomic gases even at room temperature due to the insufficient particle collisions. Therefore, the effect due to the internal degrees of freedom interactions on turbulence physics is essential in non-equilibrium flows. Here, we apply gas kinetic scheme for DNS of compressible decaying isotropic turbulence with multi-temperature non-equilibrium. Our results show that the rotational collision number in the rotational energy relaxation model and the initial energy ratio of rotational and translational modes can significantly affect the evolution of the decaying turbulence.   

Large-eddy simulation of compressible flow over a backward-facing step using a spectral multidomain method

Analysis of compressibility effects on separated curved shear layers in practical configurations has received little attention in the turbulence community. In this work, we perform large-eddy simulation (LES) of cold flow in an asymmetric dump-combustor with a spectral multi-domain method. The LES method combines a high-order multi-domain approximation with a dynamic sub-grid model and explicit interpolant-projection filtering to facilitate simulation at high Reynolds numbers. The inflow turbulence is modeled using a novel stochastic model, which is both efficient and general. We investigate the impact of the important physical parameters, such as the state of the boundary layer at separation, Reynolds number and Mach number as well as the interplay between them. One of the principal findings is the different responses of the transitional and turbulent shear layers with increase in compressibility. Increase in compressibility for the transitional flow causes a larger production of turbulent kinetic energy resulting in a faster growth of the shear layer. While for the turbulent shear layer, the growth rate is inhibited with increase in compressibility as a result of higher pressure-dilatation.   

The scaling of polymer drag reduction with polymer and flow parameters in turbulent channel flow

The scaling of polymer drag reduction with polymer and flow parameters is investigated using results from direct numerical simulations (DNS) of dilute, homogeneous polymer solutions in a turbulent channel flow performed at a base Reynolds number of $Re_{\tau_b} \approx 230$. The full range of drag reduction from onset to maximum drag reduction (MDR) is reproduced in DNS with realistic polymer parameters, with results in good agreement with available experimental data. Onset of drag reduction is found to be a function of both the polymer concentration and the Weissenberg number ($We_\tau$), in agreement with the predictions of DeGennes (1986). Saturation of drag reduction is achieved at a viscosity ratio of $\beta \approx 0.98$ at all $We_\tau$, with the magnitude of drag reduction at saturation being a strong function of $We_\tau$. A $We_{\tau_b} \sim O(Re_{\tau_b}/2)$ is needed to reach MDR. The presence of the polymer results in attenuation of turbulence at certain turbulent scales, determined by the Weissenberg number and the concentration. At saturation concentrations, the size of the largest attenuated eddy conforms to the predictions of Lumley (1969), while at concentrations below saturation, it conforms to a modified form of DeGennes (1986) theory. A mechanism of polymer drag reduction consistent with these observations will be presented.   

Turbulent Channel Flow With $\Lambda$ Shape Turbulators on One Wall

tudy of turbulent heat or mass transport is of special interest in engineering, especially for heat exchangers. For instance, roughness elements (turbulators) are usually placed on the walls of the internal channels of a turbine blade to enhance the heat transfer. In the present paper, DNSs are carried out for passive heat transport in a turbulent channel flow with $\Lambda $ shape square ribs for w/k = 1, 3, 7, 15 (w being the pitch, k the height of the ribs turbulators. The angle of inclination of the lambda shape turbulators is 45 degrees. Numerical results show that $\Lambda $ shape square ribs are more efficient than square ribs in maximizing the heat transfer. The configuration with w/k=3 presents the largest heat flux. The increase in the heat transfer is due to a secondary motion which is generated by the $\Lambda $ shape turbulators. Two counter rotating vortices above the square ribs transport the heat out of the wall into the center of the channel. The distribution of the heat flux coefficient is not uniform in the channel and leads to temperature gradients at the wall. The total drag of the $\Lambda $ shape turbulators is larger than that over a smooth wall due to an increase of form drag.   

Session GD: Flow Control IV

Effect of Dielectric Properties on Functional Relationship between Plasma Initiation and Ambient Pressure

A parameter study is conducted using Single Dielectric Barrier Discharge (SDBD) plasma actuators. An experimental setup is used to determine the plasma initiation voltage for a range of pressure, frequency, dielectric thickness, and dielectric material. An actuator is placed in a sealed chamber evacuated to a given negative gage pressure. Peak-to-peak voltage of an AC sine wave is then increased until plasma formation is verified by means of light intensity. The variation of this initiation voltage is determined as a function of ambient pressure for different combinations of thickness/material of the SDBD dielectric. The relationship is then presented so as to assess its collapsibility to a parameter describing the ratio of the dielectric coefficient to the dielectric thickness, which is central to lumped element models used in plasma modeling. Future work will examine the relationship at pressures above atmospheric.   

Effect of Actuation Parameters on Opposition Control of Transient Growth in a Blasius Boundary Layer Using Plasma Actuators

This work is concerned with investigating an actuation scheme, using plasma actuators, designed to negate the effect of the transient growth instability occurring in a Blasius boundary layer and, by this means, delaying the bypass transition process. The actuators investigated consists of a spanwise array of symmetric plasma actuators, which are capable of generating spanwise periodic counter-rotating vortices. The effectiveness of the actuator array was tested on disturbances introduced via an array of cylindrical roughness elements. Early investigations have demonstrated a reduction of the total disturbance energy produced by the roughness elements by up to 68\% depending on the actuator geometry. In the present study, the focus is on determining the effect that the excitation signal supplied to the actuator, such as waveform, frequency and amplitude, can have on the receptivity of the boundary layer to the plasma forcing. It is found that the excitation can change the modal content of the disturbance introduced inside the boundary layer by the actuator. The consequences of these results are discussed with respect to actuator modelling and issues related to eventual integration with a feedback control system for transition control.   

Preliminary numerical assessment of turbulent skin friction control with plasma actuators

Plasma actuators (PA) introduce a body force in the near-wall region of a fluid flow. This body force has already been successfully used for separation and transition flow control. We investigate the possibility of applying PAs to turbulent skin friction drag reduction by testing the effect of a modelled PA's body force in a numerically simulated turbulent channel flow. The body force is implemented into a control loop, which aims at impeding the spanwise velocity component near the wall surface. We assume to employ distributed sensors and actuators of finite size in order to investigate optimum actuator sizes for practical applications. Since the detailed physics of the body force generation by PAs and the resulting force distributions are still under study and a matter of discussion, we employ different models for the force distribution with the goal to identify the critical requirements for skin friction drag reduction with PAs.   

S-Duct Engine Inlet Flow Control Using SDBD Plasma Streamwise Vortex Generators

The results of a numerical simulation and experiment characterizing the performance of plasma streamwise vortex generators in controlling separation and secondary flow within a serpentine, diffusing duct are presented. A no flow control case is first run to check agreement of location of separation, development of secondary flow, and total pressure recovery between the experiment and numerical results. Upon validation, passive vane-type vortex generators and plasma streamwise vortex generators are implemented to increase total pressure recovery and reduce flow distortion at the aerodynamic interface plane: the exit of the S-duct. Total pressure recovery is found experimentally with a pitot probe rake assembly at the aerodynamic interface plane. Stagnation pressure distortion descriptors are also presented to show the performance increase with plasma streamwise vortex generators in comparison to the baseline no flow control case. These performance parameters show that streamwise plasma vortex generators are an effective alternative to vane-type vortex generators in total pressure recovery and total pressure distortion reduction in S-duct inlets.   

Development of plasma streamwise vortex generators for increased boundary layer control authority

This experimental study focuses on active boundary layer flow control utilizing streamwise vorticity produced by a single dielectric barrier discharge plasma actuator. A novel plasma streamwise vortex generator (PSVG) layout is presented that mimics the passive flow control characteristics of the trapezoidal vane vortex generator. The PSVG consists of a common insulated electrode and multiple, exposed streamwise oriented electrodes used to produce counter-rotating vortical structures. Smoke and oil surface visualization of boundary layer flow over a flat plate compare the characteristics of passive control techniques and different PSVG designs. Passive and active control over a generic wall-mounted hump model, Re$_c$ = 288,000-575,000, are compared through static wall pressure measurements along the model's centerline. Different geometric effects of the PSVG electrode configuration were investigated. PSVG's with triangular exposed electrodes outperformed ordinary PSVG's under certain circumstances. The electrode arrangement produced flow control mechanisms and effectiveness similar to the passive trapezoidal vane vortex generators.   

Plasma Enhanced Aerodynamics of Wind Turbine Blades

A series of computer simulations was conducted to determine the optimal method for reducing the chord length of large wind turbine blades while incorporating advanced flow control to offset the resulting loss in aerodynamic performance. The dominant building trend in the wind energy industry of turbines with progressively larger diameters provided the inspiration for this study. By reducing the chord along the inner region of the wind turbine blade, the total blade length could then be extended for the same mass of blade while limiting the additional costs and issues associated with increased blade length. In order to preserve certain geometric characteristics, the reduction in chord was achieved by scaling along the chord alone or by simply truncating the blade with a flat or circular cut. The aerodynamic requirements for the modified blade sections were to equal or better the total lift and the lift-to-drag ratio of the original blade sections. For this investigation, flow control consisted of plasma actuators located at a combination of the leading edge, maximum thickness, and trailing edge locations of the modified blade sections.   

Noise reduction in a heated Mach 1.3 jet using plasma actuators

Heating capabilities have recently been added to the free jet facility at the Gas Dynamics and Turbulence Laboratory (GDTL) of the Ohio State University using a storage-based off-line electric heater. This addition makes it possible to test the effectiveness of the localized arc filament plasma actuators (LAFPAs) for the purpose of either noise mitigation or mixing enhancement over a wide range of temperatures. These actuators have been used successfully at GDTL in high Reynolds number, high-speed unheated jets. The facility consists of an axisymmetric jet of exit diameter 2.54 cm with different nozzle blocks and variable jet temperature in an anechoic chamber. Previous work with a Mach 0.9 jet has shown significant increases in noise reduction effectiveness with increasing temperature. The next step is to determine if and how this trend continues in supersonic heated jets. A number of combinations of forcing azimuthal mode and temperature ratio at a wide range of forcing frequencies are experimented in a perfectly-expanded Mach 1.3 axisymmetric jet to examine LAFPAs effectiveness for far-field noise mitigation. The preliminary results to be presented indicate that the trends observed in the previous work continue in this supersonic jet.   

Low dimensional analysis of the flow over a three dimensional turret

The presence of turbulent flows in the path of a collimated beam produces degradation in its intensity hence abating its performance. A study of the flow physics around a cylindrical turret with the application of open-loop control has been performed. The evaluation of flow control performance is accomplished by analyzing the changes in the turbulent flow time/length scales across the turret surface for three cases. Even though these quantities are not direct measures of the aero-optics, literature suggest there is a strong relationship between them. Open-loop results demonstrate reductions in both RMS and Reynolds shear stress over the separated region. Results of the autocorrelations of the unsteady pressure sensors for the actuated low speed tests exhibit a more organized almost periodic behavior. We are interested in developing a low dimensional description of the flow field over a 3D turret through the use of velocity and unsteady surface pressure measurements. This will incorporate velocity/pressure correlations and mathematical tools such as Proper Orthogonal Decomposition and Modified Linear Stochastic Measurements to construct a low dimensional velocity-based closed-loop flow control model to estimate the flow states in real-time.   

Active Flow Control over a 3D Articulating Turret

An investigation of active flow control was conducted on an articulating 3D turret with a flat aperture using suction as the control input. Observability of the system was obtained by simultaneously sampled dynamic surface pressure at multiple locations around the aperture along with velocity flow field at the center plane of the turret. Both open loop and closed-loop control cases are examined for the purpose of reducing the turbulent fluctuations directly over the aperture. Open-loop control reduces the separation in the flow and decreases the levels of turbulence above the aperture. The large database of no control and open-loop control also provides a basis to develop closed-loop control. For closed-loop control, a simple proportional controller will feed back a low dimensional estimation of the flow based on dynamic surface pressure and velocity in an effort to improve upon the open-control cases.   

Active Flow Control Techniques for use on Three Dimensional Hemispherical Turrets

Hemispherical turrets have been a topic of considerable interest over the past several decades with studies focusing on airborne optical device applications. Highly three dimensional, turbulent flows develop in the wake of a turret, especially when a flat, optical aperture is in place on the hemisphere. Both open and closed-loop flow control have been successfully applied to this geometry to control the turbulent flow over the aperture, but control of large scale structures in the wake using open-loop flow control have been less effective. Fluctuating loads on the turret, which can induce undesired structural loading, have been attributed to strong, turbulent fluctuations in the velocity of the turret wake. The current work involves developing a more robust active control system (both open and closed-loop using suction based actuators) that will not only allow for the control of the flow over the aperture as Syracuse University is currently studying, but will also allow for control of the large scale flow structures that develop in the wake of a turret.   

Session GE: Biofluids V: Cardiac Flows

Unsteady flows modeling using Smoothed Particle Hydrodynamics

Cardiovascular diseases are the major cause of death in North America. Investigation of blood flow behavior in the cardiovascular system is, therefore, of great interest in biomedical engineering and cardiology. These kinds of flows are characterized by highly inertial pulsatile effects and deformable boundaries. The most important limitation of conventional numerical methods for simulating such flows is their main nature dependence on the process of mesh generation; distortion and remeshing that are numerically expensive. An alternative to overcome these limitations can be the new generation of numerical methods called meshfree methods. Smoothed Particle Hydrodynamics (SPH) is a Lagrangian meshfree method created originally to simulate astrophysical phenomena and later developed for applications in continuum solid and fluid mechanics. In this investigation, the potential of SPH method to model pulsating laminar flow in simplified (rigid) geometries found in the cardiovascular system such as left heart cavity and stenosed artery are examined. This work represents the first attempt to model internal pulsatile flows for a variety of Reynolds numbers using SPH. Although reaching physiological conditions still needs several improvements, SPH showed a good capability and could become a promising numerical method to simulate cardiovascular flows.   

Left ventricle of mammalian hearts optimzed for high hydrodynamic efficiency

Mammalian hearts have four chambers: two atria (left and right) and two ventricles (left and right). The left ventricle (LV) is the primary pumping engine that pumps blood to all end organs of the body. The energetic efficiency of LV is therefore crucial for life. An important factor that contributes to the overall LV pumping efficiency is the hydrodynamic cost of blood flow within the LV chamber. LV blood flow is created by the cyclical expansion/contraction motion of LV wall and its hydrodynamic cost is certainly affected by the geometry and motion of LV wall. In this work we investigated the relationship between the hydrodynamic cost of LV filling/ejecting and LV geometry/motion and showed that the geometry and motion of mammalian hearts were optimized to minimize the hydrodynamic cost of LV blood flow.   

Early embryonic intra-cardiac flow fields at three idealized ventricular morphologies

Pulsatile 3D multiple inlet/outlet flow within tiny (100-300$\mu $m dia) embryonic ventricles feature distinct intra-cardiac flow streams whose role in regulating the morphogenesis of spiral aorto-pulmonary septum has long been debated. The low Re number flow regimes limit mixing of these streams as replicated in our flow-visualization experiments with chick embryos. A state-of-the art high-resolution immersed boundary CFD solver which was developed for complex patient-specific cardiovascular internal flow problems is applied and optimized for this problem. Idealized tubular ventricles at 3 major embryonic stages (straight, C- and D- loops) are created by our sketch-based anatomical editing tool. CFD results are validated with PIV measurements acquired from a micro-fabricated C-loop stage replica and in vivo flow vis data from confocal microscopy. This model provided the inlet velocity profile for arterial models and flow fields at the inner curvature of embryonic hearts for different ventricular topologies are compared for off-design modes.   

Simulations of heart mechanics over the cardiac cycle

This study is concerned with the numerical simulation of blood flow and myocardium motion with fluid-structure interaction of the left ventricle (LV) of a canine heart over the entire cardiac cycle. The LV geometry is modeled as a series of nested prolate ellipsoids and is capped with cylindrical tubes representing the inflow and outflow tracts. The myocardium is modeled as a multi-layered, slightly compressible, transversely isotropic, hyperelastic material, with each layer having different principal directions to approximate the fibrous structure. Blood is modeled as a slightly compressible Newtonian fluid. Blood flow into and out of the LV is driven by left atrial and aortic pressures applied at the distal ends of the inflow and outflow tracts, respectively, along with changes in the stresses in the myocardium caused by time-dependent changes in its material properties, which simulate the cyclic contraction and relaxation of the muscle fibers. Numerical solutions are obtained with the use of a finite element code. The computed temporal and spatial variations of pressure and velocity in the blood and stresses and strains in the myocardium will be discussed and compared to physiological data. The variation of the LV cavity volume over the cardiac cycle will also be discussed.   

Fluid Structure Interaction simulation of heart prosthesis in patient-specific left-ventricle/aorta anatomies

In order to test and optimize heart valve prosthesis and enable virtual implantation of other biomedical devices it is essential to develop and validate high-resolution FSI-CFD codes for carrying out simulations in patient-specific geometries. We have developed a powerful numerical methodology for carrying out FSI simulations of cardiovascular flows based on the CURVIB approach (Borazjani, L. Ge, and F. Sotiropoulos, Journal of Computational physics, vol. 227, pp. 7587-7620 2008). We have extended our FSI method to overset grids to handle efficiently more complicated geometries e.g. simulating an MHV implanted in an anatomically realistic aorta and left-ventricle. A compliant, anatomic left-ventricle is modeled using prescribed motion in one domain. The mechanical heart valve is placed inside the second domain i.e. the body-fitted curvilinear mesh of the anatomic aorta. The simulations of an MHV with a left-ventricle model underscore the importance of inflow conditions and ventricular compliance for such simulations and demonstrate the potential of our method as a powerful tool for patient-specific simulations.   

Volumetric velocity measurements on flows through heart valves

Volumetric velocity fields inside two types of artificial heart valves were obtained experimentally through the use of volumetric 3-component velocimetry (V3V). Index matching was used to mitigate the effects of optical distortions due to interfaces between the fluid and curved walls. The steady flow downstream of a mechanical valve was measured and the results matched well with previously obtained 2D PIV results, such as those of Shipkowitz et al. (2002). Measurements upstream and downstream of a deformable silicone valve in a pulsatile flow were obtained and reveal significant three-dimensional features of the flow. Plots and movies will be shown, and a detailed discussion of the flow and various experimental considerations will be included. Reference: Shipkowitz, T, Ambrus J, Kurk J, Wickramasinghe K (2002) Evaluation technique for bileaflet mechanical valves. J. Heart Valve Disease. 11(2) pp. 275-282.   

Fluid dynamics of aortic valve stenosis

Aortic valve stenosis, which causes considerable constriction of the flow passage, is one of the most frequent cardiovascular diseases and is the most common cause of the valvular replacements which take place for around 100,000 per year in North America. Furthermore, it is considered as the most frequent cardiac disease after arterial hypertension and coronary artery disease. The objective of this study is to develop an analytical model considering the coupling effect between fluid flow and elastic deformation with reasonable boundary conditions to describe the effect of AS on the left ventricle and the aorta. The pulsatile and Newtonian blood flow through aortic stenosis with vascular wall deformability is analyzed and its effects are discussed in terms of flow parameters such as velocity, resistance to flow, shear stress distribution and pressure loss. Meanwhile we developed analytical expressions to improve the comprehension of the transvalvular hemodynamics and the aortic stenosis hemodynamics which is of great interest because of one main reason. To medical scientists, an accurate knowledge of the mechanical properties of whole blood flow in the aorta can suggest a new diagnostic tool.   

Dynamic Energy Loss Characteristics in the Native Aortic Valve

Aortic Valve (AV) stenosis if untreated leads to heart failure. From a mechanics standpoint, heart failure implies failure to generate sufficient mechanical power to overcome energy losses in the circulation. Thus energy efficiency-based measures are direct measures of AV disease severity, which unfortunately is not used in current clinical measures of stenosis severity. We present an analysis of the dynamic rate of energy dissipation through the AV from direct high temporal resolution measurements of flow and pressure drop across the AV in a pulsatile left heart setup. Porcine AV was used and measurements at various conditions were acquired: varying stroke volumes; heart rates; and stenosis levels. Energy dissipation waveform has a distinctive pattern of being skewed towards late systole, attributed to the explosive growth of flow instabilities from adverse pressure gradient. Increasing heart rate and stroke volume increases energy dissipation, but does not alter the normalized shape of the dissipation temporal profile. Stenosis increases energy dissipation and also alters the normalized shape of dissipation waveform with significantly more losses during late acceleration phase. Since stenosis produces a departure from the signature dissipation waveform shape, dynamic energy dissipation analysis can be extended into a clinical tool for AV evaluation.   

Fluid-structure interaction analysis of the flow through a stenotic aortic valve

In Europe and North America, aortic stenosis (AS) is the most frequent valvular heart disease and cardiovascular disease after systemic hypertension and coronary artery disease. Understanding blood flow through an aortic stenosis and developing new accurate non-invasive diagnostic parameters is, therefore, of primarily importance. However, simulating such flows is highly challenging. In this study, we considered the interaction between blood flow and the valve leaflets and compared the results obtained in healthy valves with stenotic ones. One effective method to model the interaction between the fluid and the structure is to use Arbitrary Lagrangian-Eulerian (ALE) approach. Our two-dimensional model includes appropriate nonlinear and anisotropic materials. It is loaded during the systolic phase by applying pressure curves to the fluid domain at the inflow. For modeling the calcified stenotic valve, calcium will be added on the aortic side of valve leaflets. Such simulations allow us to determine the effective orifice area of the valve, one of the main parameters used clinically to evaluate the severity of an AS, and to correlate it with changes in the structure of the leaflets.   

A study of the pulsatile flow and its interaction with rectangular leaflets

To avoid the complexity and limited understanding of the 3D pulsatile flow field through heart valves, a cardiac-like flow circuit and a test channel were designed to study the behavior of bidimensional leaflets made of hyperelastic materials. We study a simple 2D arrangement to understand the basic physics of the flow-leaflet interaction. Creating a periodic pressure gradient, measurements of leaflet deflection were obtained for different flow conditions, geometries and materials. Using PIV and Phase Locking techniques, we have obtained the leaflet motion and the time-dependent flow velocity fields. The results show that two dimensionless parameters determine the performance of a simple bi-dimensional valve, in accordance with the flow conditions applied: $\Pi _{1}$=f(sw)$^{1/2}$(E/$\rho )^{1/2}$ and $\Pi _{2}$=V/(2slw), where f is the pulsation frequency, V is the stroke volume, s, w and l are the dimensions on the leaftlet and E and $\rho $ are the elastic modulus and density of the material, respectively. Furthermore, we have identified the conditions for which the fluid stresses can be minimized. With these results we propose a new set of parameters to improve the performance of prosthetic heart valves and, in consequence, to reduce blood damage.   

Session GF: Microfluidics: Electric Fields and Particles

Electro-hydrodynamic particle levitation on electrodes

When colloidal particles deposit electro-phoretically onto a planar electrode, they slowly aggregate, eventually forming planar 2D crystalline structures. The attractive particle-particle interaction is due to electrokinetic flows associated with the particle Debye layer as well as the induced Debye layer surrounding the electrode. A common feature in the experimental observations is the small thickness of the particle-electrode gap separation, which was indeed reflected in the numerical figures employed hitherto in the existing numerical analyses. Here, we exploit it using singular perturbation methods. Thus, the fluid domain is separated into an ``inner'' gap region, where the electric field and flow strain rate are intensive, and an ``outer'' domain, consisting of the remaining fluid domain, where they are moderate. The inner region is analyzed using standard lubrication approximation, and the outer region is investigated using tangent-spheres coordinates. This method provides an analytic approximation for the hydrodynamic force that keeps the particle levitating against the action of gravity, as well as far-field approximations for the velocity decay, which agree with existing numerical simulations.   

Near-contact electrokinetic interactions between ideally polarizable particles

When a zero-net-charge spherical particle is exposed to a uniformly applied electric field it polarizes, giving rise to an induced zeta potential distribution and a concomitant electro-osmotic flow field. Due to symmetry, the particle does not experience any electrophoretic motion. This symmetry is disturbed when an adjacent boundary (e.g. another particle or a channel wall) is introduced. This gives rise to boundary-driven particle motion, which is nonlinear in the applied field, approximately quadratic in it when it is weak. Using matched asymptotic expansions, we analyze electrokinetic interactions between a pair of ideally polarizable particles at small gap separations. When the field is applied perpendicular to their line of center, it tends to repel the particles away from each other. This repulsion is dominated by the pressure field within the gap, animated by the intense electric field there. The resulting pair interaction weakly diverges as an irrational power of the gap thickness. When the field is applied in parallel to the line of center, the electric field within the gap is exponentially small, and the pair interaction is bounded.   

DC electrokinetic transport of a cylindrical particle in a rectangular microchannel

Electrokinetic transport of a cylindrical microparticle in a straight microchannel under direct current (DC) electric fields is numerically and experimentally investigated. DC dielectrophoresis (DEP) is taken into account in the proposed mathematical model, which is composed of the Navier-Stokes equations for the flow field and the Laplace equation for the electric field solved in an arbitrary Lagrangian-Eulerian (ALE) framework. Cylindrical particles experience an oscillatory motion under low electric fields. As the electric field increases, the induced DEP force acting on the particle gradually diminishes the oscillatory motion. Once the electric field is larger than a certain threshold value, the particle only translates with its axis parallel to the applied electric field after a short oscillatory motion. The numerical predictions are in good agreement with the experimental results.   

Modeling Electrophoresis of Microtubules in Microchannels

We simulate the electrophoretic motion of individual microtubules in microchannels in order to obtain their anisotropic mobility and compare with recent experimental results (van den Heuvel et al., PNAS, 2007). We include for comparison simulation results for a circular cylinder with a similar ``effective'' radius, in order to examine how the surface roughness of microtubules affects the electrical double layer, the externally applied field, and hence the electrophoretic mobility. The simulation method is based on the smoothed profile method (SPM) -- an immersive-boundary-like method --and spectral element discretization. The new method allows for arbitrary differences in the electrical conductivities between the charged surfaces and the ionized solution.   

Electrophoresis of deformable elastic particles

Electrophoretic motion of a deformable dielectric elastic particle, having a fixed zeta potential,placed in an external electric field, has been numerically simulated. The potential field is solved in the fluid external to the particle, to compute the applicable Helmholtz-Smoluchowski slip boundary conditions on the particle surface. A constitutive equation is constructed for an incompressible neo-Hookean elastic solid where the extra stress tensor is assumed to be linearly proportional to the $Almansi$ strain tensor, to govern the deformation of the particle. A monolithic finite element solver which uses an Arbitrary Lagrangian-Eulerian moving mesh technique is then used to solve the velocity, pressure and stress field in both the fluid and solid phases simultaneously. The particle is initially elliptical and is aligned perpendicular to the direction of the applied electric field. Elastic deformation is observed as the particle moves. Two cases of zero and finite Reynolds number are examined to delineate the effect of the inertial terms on the deformation of the particle. The stress and pressure distributions on the particle surface are also compared with some analytical solutions.   

Effects of Ion Sterics and Hydrodynamic Slip on Electrophoresis of a Colloidal Particle

The classical theory of a spherical colloids' electrophoretic mobility is founded on the Poisson-Nernst-Planck (PNP) equations and assumes the standard hydrodynamic no-slip boundary condition at the fluid/solid interface. In the (common) limit of thin double-layers, the mobility has long been known to exhibit a maximum at some zeta potential, then decrease and asymptote to a constant value. Dukhin, O'Brien, White and others showed this to result from the importance of excess ionic surface conductivity within the double-layer. The fundamental assumptions that underpin this result are, however, subject to challenge: in recent years, a finite liquid/solid slip has been measured over a variety of surfaces, and the PNP equations predict physically impossible ion concentrations precisely at the high zeta potentials where the mobility maximum occurs. Here, we discuss the dramatic effect that hydrodynamic slip and finite-ion-size steric effects in double-layers have upon the electrophoretic mobility of spherical colloids, and therefore upon the interpretation of electrophoretic mobility measurements.   

Electrokinetic Traveling Waves in Non-Dilute Colloidal Dispersions

The existence of electrokinetically-driven, traveling waves in colloidal dispersions is presented. A non-dilute colloidal dispersion of 2 micron polystyrene microspheres are exposed to an ac electric field. Traveling waves consist of alternating regions of compressed and rarefied particle volume fraction that propagate through the dispersion parallel to the applied field. Colloids under the application of these ac fields have no net displacement, yet the travelling waves propagate at speeds at a tenth of the RMS electrophoretic velocity of individual particles. The collective dynamics of the colloids are described by the one dimensional, inviscid Burgers' equation. The waves originate from the modification of the colloid velocity due to the mobility's dependence on the local volume fraction and the particle electrokinetic polarization dipole interactions. The Burgers' equation analysis is used to predict the wave speed of the traveling waves.   

Aggregation and Coalescence of Emulsion Droplets via Electrohydrodynamic Flows

Electrohydrodynamic (EHD) flows are known to cause rigid colloids to aggregate near electrodes [1]. Here we report that EHD flows also induce immiscible liquid droplets to aggregate and, for sufficiently strong electric fields, to coalesce. We measure the aggregation and coalescence rates of micron-scale olive oil droplets in water, and we interpret the coalescence rates in terms of a balance between EHD flow and repulsive colloidal scale (DLVO) forces. The results have broad implications for industrial processes in which trace amounts of immiscible oils need to be removed from aqueous solutions.\\[4pt] [1] Ristenpart, Aksay \& Saville, J. Fluid Mechanics 575, 83, (2007).   

Electric field induced self assembly of floating rectangular plates

We show that an external electric field normal to a fluid-fluid interface can be used to self assemble rectangular plates floating on the interface and that the lattice spacing of the monolayer thus formed can be varied by changing the electric field intensity. In our experiments, a rectangular plate floats so that the contact line is pinned at the upper edge. Plates experience lateral forces due to capillarity which cause them to cluster. In the presence of an electric field, plates are also subjected to the repulsive electrostatic forces which, together with the attractive capillary forces, determine the equilibrium spacing of the monolayer. The interface profile around the plates is also modified by the electric field.   

Brownian Dynamics modeling of electrophoretic dsDNA-molecule separation using nanofluidic devices

We present a Brownian Dynamics model of electrophoretic separation of short (up to 7 persistence lengths) dsDNA molecules in nanofluidic devices. Our formulation uses the Worm-Like-Chain model with hydrodynamic interactions. Our simulation results are in good agreement with the experimental results of Fu et al. [{\it Phys. Rev. Lett.}, {\bf 97}, 018103, 2006] for realistic values of all physical parameters. We also find good agreement between our simulation results and the theoretical model of Li et al. [{\it Anal. Bioanal. Chem.}, {\bf 394}, 427, 2009] who proposed an asymmetric separation device that operates under the effect of an alternating electric field.   

Session GG: Microfluidics: Mixing

Formation of coherent structures in 3D laminar mixing flows

Mixing under laminar flow conditions is key to a wide variety of industrial systems of size extending from microns to meters. Examples range from the traditional (and still very relevant) mixing of viscous fluids via compact processing equipment down to emerging micro-fluidics applications. Profound insight into laminar mixing mechanisms is imperative for further advancement of mixing technology (particularly for complex micro-fluidics systems) yet remains limited to date. The present study concentrates on a fundamental transport phenomenon of potential relevance to laminar mixing: the formation of coherent structures in the web of 3D fluid trajectories due to fluid inertia. Such coherent structures geometrically determine the transport properties of the flow and better understanding of their formation and characteristics may offer ways to control and manipulate the mixing properties of laminar flows. The formation of coherent structures and its impact upon 3D transport properties is demonstrated by way of examples.   

Streamlines and mixing patterns for drops in capillaries

We present a theoretical and numerical investigation of streamlines and mixing patterns within drops flowing in capillaries. We study theoretically the limit case of purely viscous flow around a small drop, and find that recirculating regions are always present at the front and back of such drops. Using two-dimensional simulations, we visualize streamlines for larger drops, showing that the extent of these recirculating torii increases with drop size and decreases with Reynolds number. We study the mixing within drops as they are subjected to time-dependent shear, thus modeling a sinusoidal channel, and find that while cross-stream mixing is efficient, streamwise mixing is hindered by the front and back recirculating regions.   

Chaotic mixing in a plane channel with rotating arc walls

The effect of chaotic advection on the advection-diffusion of passive species is investigated for a new type of open flow mixer. This mixer is of active type with a perturbation of the flow imposed by three rotating circular arc walls (RAW) in a two-dimensional plane channel flow. Different steady flow topologies can be obtained depending on the respective directions of the RAW. Efficient stirring protocols were designed by the combination of some steady streamline patterns giving rise to chaotic mixing. The dynamical behavior of the mixing induced by these protocols were compared and discussed for different control parameters.   

The Ranz Stretch model and its extensions applied to mixing and reversibility

Mixing and separation are central to several chemical systems and are often carried out using microfluidics. Flow in a microfluidic device is usually in the laminar or Stokes regime. So mixing - a combination of stirring and diffusion - is often performed using chaotic flows which stir much faster than non chaotic flows. For separation of solutes of different diffusivities, Heller proposed the principle of Separation by Diffusive Irreversibility (SDI) which combines the reversibility of stirring and irreversibility of diffusion. Fundamental to both mixing and SDI is the interplay of convection and diffusion which is difficult to understand because of the challenging nature of convective coupling of solute concentration and the flow in the governing convective diffusion equation. Our approach is to use the Ranz model which observes the evolution of a single strand of concentration in the local linear flow. While this model captures the qualitative behavior of the chaotic and non chaotic flows, it fails to quantitatively predict the scaling of mixing and separation characteristics. Our goal is to identify a set of parameters that quantify the effects of stretch history and distribution and the presence of islands on mixing and separation. I will present a study of these effects, and the extensions of Ranz model incorporating these effects. I will compare the results from the model to the numerical simulation. The model will improve our understanding of mixing and irreversibility in Stokes flows.   

Long-term description of chaotic mixing induced by resonance phenomena

We present a quantitative long-term theory of resonant mixing in 3-D near-integrable flows. We illustrate that such resonance phenomena as resonance and separatrix crossings accelerate mixing by causing the jumps of adiabatic invariants. The resulting mixing can be described in terms of a single diffusion-type equation. We show what modifications must be made to accommodate the effects of the boundaries of the domain and possible correlations between the successive jumps.   

Development of an optimal mixer: a conceptual study

We define as an optimal mixer a mixing device able to deliver a uniformly optimal mixing performance over a wide range of operating and initial conditions. We consider the conceptual problem of designing an optimal mixer starting from a reference mixing device, the sine flow. We show that the time-periodic sine flow performs poorly and erratically over most operating and initial conditions. In steps we modify the design of the reference mixer to obtain a mixing device whose performance, over the entire operating range, is as good as or better than the best performance of the sine flow. First, we optimize the time-sequence of the stirring velocity fields. The resulting mixer performs substantially better than the sine flow, but it is still suboptimal because the actuating system cannot control all the states. Second, we equip the sine flow with a new actuating system that allows optimized shifts of the stirring velocity fields in the cross-flow direction. This new actuating system is able to control all states. The resulting mixer delivers a suboptimal performance only at low operating conditions due to the use of a time-periodic stirring protocol. Finally, we obtain an optimal mixer by coupling the time and shift optimizations. We show that the resulting optimal mixer is able to deliver a nearly uniform optimal performance, insensitive to the geometry of the initial conditions, over the entire operating range.   

Effects of herringbone groove geometry on flow kinematics in a high aspect-ratio microchannel

Passive mixing is often achieved in laminar microscale flows by driving fluid through microchannels with geometries that produce secondary flows and/or by splitting and recombining the fluid multiple times. One very successful microscale mixer design is the staggered herringbone mixer introduced by Stroock et al. (Science 2002) In the presented work, we consider very high aspect ratio (62:1) microchannels with a repeated staggered herringbone pattern spanning the entire width of the microchannel. Herringbone geometries with three different interior angles of the herringbone pattern (45, 90, and 135 degrees) were investigated. The flowfields within the herringbone mixers were determined using microscopic particle image velocimetry (microPIV). Velocity fields were measured at the midplane of the microchannel and at the groove-channel interface for Reynolds numbers based on microchannel hydraulic diameter of 0.08, 0.8, and 8. These wide microchannels produce secondary flow patterns that effectively split the fluid into parallel streams without having to fabricate physically separate channels.   

Breaking Regular Islands for Improved Mixing in an Electro-osmotic Device

Two-dimensional electro-osmotic flow with strong spatial and weak temporal variations of the zeta potential is investigated theoretically for the purpose of enhancing mixing in a microchannel. The flow is a superposition of a primary component and a perturbation. The primary flow, generated by the spatially periodic zeta potential, consists of recirculating rolls, while the perturbation arises due to a small time periodic variation of the zeta potential distribution. In this work, we propose a method that allows us to identify the values of the parameters which produce complete mixing. The method is based on tracking the linear stability of the main periodic orbits corresponding to the recirculating rolls of the primary flow. Poincar\'{e} maps, Lyapunov exponents and a box counting measure are computed to corroborate our results.   

Experimental study of mixing in low gravity by vibrations

In the absence of external forces, the diffusion process leads to the mixing of species on long time scale. The application of vibrations to a fluid system with density gradient causes relative flows inside the fluid. The aim of this study is to analyze the physical mechanism, by which vibrations affect the mixing process of two stratified miscible fluids. The rectangular cavity (10mm x5 mm x 3mm) filled half-by-half with the two different miscible liquids is subjected to translational vibration. The direction of translational periodic vibrations with a constant frequency and amplitude is parallel to the interface between the two fluids. The system is kept at constant temperature. There is strong interplay between gravity and vibrational impact. To elucidate the vibrational mechanism the experiments were performed in parabolic flights organized by the European Space Agency. Parabolic flights provide repeated periods of approximately 20 seconds of reduced gravity preceded and followed by 20 seconds of hypergravity. The transient evolution of concentration field during microgravity time is investigated by optical digital interferometry. The analysis of the results shows that mixing and flow pattern in liquids depends not only on vibration stimuli but on the sharpness of the interface as well.   

Session GH: Drops IV: Breakup

Contraction of Asymmetric Newtonian Liquid Filaments

Understanding the dynamics of satellite drops is important in several industrial applications involving drop formation including inkjet printing, electrospraying and atomization. The precursor to these satellite drops is a slender liquid filament that connects an about-to-form drop to the rest of the liquid in the nozzle. Once a filament is formed, it either contracts into a single satellite or breaks into multiple satellites, due to surface tension. Our understanding of the contraction of Newtonian filaments in a passive ambient fluid has improved greatly over the past two decades thanks to the numerical analyses of Schulkes (1996) and Notz and Basaran (2004) who modeled the filaments as cylinders that are terminated by two identical spherical caps. However, in many situations, the filament shapes at the onset of formation may not be symmetric as in the aforementioned studies. To improve our understanding of the fluid mechanics of contraction of such asymmetric filaments, we study here the recoil of filaments whose initial shapes are sections of tapered axisymmetric cones that are terminated by two unequal spherical caps. The dynamics are studied by both a 2-D analysis and a 1-D slender-jet analysis, and the results are summarized by constructing phase diagrams involving the dimensionless groups governing the dynamics.   

Effect of initial shape on contraction dynamics of Newtonian filaments

Slender liquid filaments arise in a number of applications involving drop formation, atomization, and cloud physics. Under the action of surface tension, a filament either contracts into a single drop or breaks into multiple drops as it recoils. Our understanding of the contraction of Newtonian filaments in a passive ambient fluid has improved greatly over the past two decades thanks to the numerical analyses of Schulkes (1996) and Notz and Basaran (2004) who modeled the filaments as cylinders that are terminated by two identical hemispherical caps. However, in many situations, the initial shape of a filament may resemble more that of two unequal globular or spherical drops that are connected by a slender cylinder. The dynamics of contraction of such filaments are studied here by both a two-dimensional analysis and a one-dimensional slender-jet analysis, and the results are summarized by constructing phase diagrams involving the dimensionless groups governing the dynamics.   

Droplet formation from the breakup of micron-sized liquid jets

Droplet formation from the breakup of a liquid jet emerging from a micron-sized circular nozzle is investigated with ultra high-speed imaging at 1 million frames per second and within a lubrication approximation model [Eggers and Dupont, Phys. Rev. Lett. 262, 1994, 205-221]. The capillary time $\tau_c = \sqrt {\rho r^3 / \gamma}$ is extremely small -- of the order of $1\mu {}\mbox{s}$. In the analyzed low Reynolds number regime the jet breakup is driven by surface tension forces only. Rayleigh breakup is not influenced by the surrounding air. The high- speed imaging results and those from the model calculation perfectly agree for various liquid viscosities and jet velocities, confirming a universal scaling law also for diminutive Rayleigh jets.   

Scaling in two-fluid pinch-off

Two-fluid pinch-off is encountered when drops or bubbles of one fluid are ejected from a nozzle into another fluid or when a compound jet breaks. While the breakup of a drop in a passive environment and that of a passive bubble in a liquid are well understood, the physics of pinch-off when both the inner and outer fluids are dynamically active is inadequately understood. In this talk, the breakup of a compound jet whose core and shell are both incompressible Newtonian fluids is analyzed computationally by a method of lines ALE algorithm which uses finite elements with elliptic mesh generation for spatial discretization and adaptive finite differences for time integration. Pinch-off dynamics are investigated well beyond the limit of experiments set by the wavelength of visible light and that of various algorithms used in the literature. Simulations show that the minimum neck radius $r$ initially scales with time $\tau$ before breakup as $\tau^{\alpha}$ where $\alpha$ varies over a certain range. However, depending on the values of the governing dimensionless groups, this initial scaling regime may be transitory and, closer to pinch-off, the dynamics may transition to a final asymptotic regime for which $r \sim \tau^{\beta}$, where $\beta \neq \alpha$.   

Single drop fragmentation is the source of raindrops size distribution

Like many natural objects, raindrops are distributed in size. By extension of what is known to occur inside the clouds, where small droplets grow by accretion of vapor and coalescence, raindrops in the falling rain at the ground level are believed to result from a complex mutual interaction with their neighbors. We show that the raindrops polydispersity, generically represented according to Marshall-Palmer's law, is quantitatively understood from the fragmentation products of non interacting, isolated drops. Both the shape of the drops size distribution, and its parameters are related from first principles to the dynamics of a single drop deforming as it falls in air, ultimately breaking into a dispersion of smaller fragments containing the whole spectrum of sizes observed in rain. The transformation is accomplished within a timescale much shorter than the typical collision time between the drops.   

Droplet breakup past an obstacle

To investigate the transport of drops in a porous medium, we consider a model at the scale of an elementary event consisting of drop passing an obstacle in a microfluidic channel. We can thus observe the breakup process in a controlled way. We demonstrate that there exists an unstable situation for which a drop manages to pass the obstacle without breaking and define a critical value of the capillary number Ca* for which a drop will break. We also show that the obstruction dimensions play an important role in the breakup-non breakup transition. Finally we propose a model which describes the observed transition between breakup and non-breakup.   

Production of ultra-small ink jet drops using drop-on-demand (DOD) drop formation

The formation of drops having radii that are smaller than the radii of the nozzle from which they are ejected is an active area of research in drop-on-demand (DOD) ink jet printing. In the last decade, Chen and Basaran (Phys Fluids, 2002; US patent, 2003) showed experimentally and computationally that several fold reduction in drop radius R (an order of magnitude reduction in drop volume V) is possible by judicious use of waveform modulation in which one or more intrinsic time scales such as capillary time, time for vorticity diffusion, and time for piezo actuation are varied. In this paper, we report the results of a computational study through which we have uncovered a novel method for achieving a factor of 5-10 reduction in R (about two to three orders of magnitude reduction in V). Scaling arguments are also developed which yield a simple expression for the size of the ultra-small drops formed as a function of the governing dimensionless groups. Formation of such small drops using DOD technology may prove especially attractive in applications involving direct printing of flexible electronics and solar cells.   

Oscillations of a capillary switch used as a miniature opto-fluidic device

A capillary switch (CS) is a continuous volume of liquid consisting of a sessile and a pendant drop that are coupled through a liquid filled hole in a plate. When capillary force is much larger than body forces such as gravity, this simple, coupled interfacial system exhibits multiple equilibrium states beyond a critical volume. Owing to its extremely small size, and hence large curvature and highly spherical air-liquid interface, an oscillating CS can potentially be used as a variable focus liquid lens in MEMS devices. The dynamics of an oscillating CS are studied by solving the full 3D axi-symmetric or 2D Navier-Stokes equation using the Galerkin finite element method (G/FEM). Applying means of forcing such as oscillating the pressure in the gas surrounding the sessile (pendant) drop and vibrating the plate, modes of oscillation are identified from resonances observed during frequency sweeps. The shift in the frequencies of oscillation of lower modes due to changes in parameters such as liquid volume, plate thickness, and liquid viscosity and surface tension are also studied. Results are shown to agree well with experimental observations by Hirsa and coworkers.   

Effects of viscoelasticity on retraction of a sheared drop

The retraction of a sheared drop when either the drop or the matrix phase is Oldroyd B is investigated. The retraction is initially faster and later slower with increasing drop viscoelasticity. The initial faster relaxation of viscoelastic drops is due to inward pulling viscoelastic stresses at the drop tip and the later slowing down is due to the slowly relaxing viscoelastic stresses at the equator. The behavior is captured well by three model ODEs for two principal viscoelastic stresses (along the tip and equatorial directions) and the deformation. Matrix viscoelasticity slows the relaxation of a Newtonian drop right from the beginning because of the slow relaxation of stresses near the drop tip with increasing Deborah number. For drops sheared in supercritical conditions, when initially stretched beyond a certain length, relaxation leads to neck formation with two bulbous ends resulting in drop break-up, while for less stretching, it relaxes back to its spherical state.   

Dynamics of contracting viscoelastic filaments

Satellite drops are detrimental to many industrial applications involving the formation of viscoelastic drops including inkjet printing, DNA microarraying, and printing of flexible solar cells. The precursor to these satellite drops is a slender liquid filament that connects an about-to-form drop to the rest of the liquid in the nozzle.~ Once a filament is formed, it contracts due to surface tension. A filament may undergo further breakup during recoil. Whereas the contraction of Newtonian filaments in a passive ambient fluid is well understood (Schulkes 1996 and Notz and Basaran 2004), the contraction dynamics of viscoelastic filaments remains largely unexplored and is addressed in this presentation.~ Here the filament shape is idealized as an axisymmetric fluid cylinder terminated by hemispherical end-caps, and the conformation tensor formalism (Pasquali {\&} Scriven 2002) is used to model the viscoelasticity.~ The dynamics of contracting filaments are then analyzed by means of both a well-benchmarked two-dimensional finite element algorithm (Notz et al. 2001, Chen et al. 2002) and a one-dimensional slender-jet algorithm (Padgett et al. 1996).~ Regions of the parameter space are identified where recoiling filaments give rise to either a single satellite drop or multiple satellites.   

Session GJ: Bubbles IV: Microbubbles, Bubble Motion

Microbubbles transfer and segregation mechanisms in turbulent upward/downward channel flow.

The dispersion of microbubbles in a turbulent channel flow is studied by means of direct numerical simulation (DNS), both in upward and downward flow with a two-way coupling approach. Microbubbles dispersion shows a sharply distinct behavior in the two flow cases: in upward flow bubbles tend to accumulate and segregate near the walls, whereas in the downward flow they tend to segregate in the center of the channel. This different spatial distribution, which is due to the interplay between turbulent wall transfer mechanisms and the local fluid forces acting on bubbles (especially the lift force), is expected to have an influence on the flow field. In this work, we present detailed results from a systematic analysis on the effect of the different forces acting on bubbles and how the flow statistics are modified by the presence of bubbles.   

Study of dynamics of microbubble generation in microchannels

The novel technique to generate micrometer-order bubbles was developed by using a microchannel with a squeezed T-junction, and the mechanism of bubble generation was investigated by using a high-speed camera with 106 Hz and the microscopy. The experiments were conducted by using three kinds of channels with the different cross-section size, and pure water, ethanol and silicon oil were selected as the liquid phase to examine the effect of the cross-section size of the channels and the physicality of the liquid phase. The liquid velocity at the T-junction and the gas pressure were set at 0.1$\sim $3.0 m/s and 10$\sim $200 kPa, respectively. The experimental results indicate that the proposed technique realizes to generate 10$\sim $30 $\mu $m diameter bubbles, and the diameter of the generated bubble becomes smaller with an increase of the liquid velocity, until limit points of bubble generation. From the experiment near the bubble generated limit, liquid pressure balances with the gas pressure and the Laplace pressure under the bubble generated limit, and the bubble diameter is dominated by Weber number which is defined using an equivalent diameter of the cross-section of the channel and the mean velocity of the liquid phase.   

Numerical study on the behavior of a microbubble encapsulated by hyperelastic membrane in the ultrasound field

The surface stability problem of a microbubble encapsulated by a neo-Hookean hyperelastic membrane is numerically addressed. To predict this nonlinear behavior, the continuity equation and the Navier-Stokes equation are directly solved by means of the boundary-fitted finite-volume method on an orthogonal curvilinear coordinate system. The force balances of the membrane are derived from the traction jump condition, coupling with the in-plane tensions and transverse shear tension. The bubble is insonified by an ultrasound pulse at frequency of 1MHz and consisting of a burst of 10 cycles. The strain-softening features are presented referring to a linear model based on the Rayleigh-Plesset equation. For small acoustic amplitude, the result based on the neo-Hookean model is in good agreement with that on the linear model. With the increasing of oscillatory amplitude, the neo-Hookean membrane bubble shows an enhanced strain-softening effect -- larger expansion, smaller contraction and higher harmonics during contraction. In addition, the neo-Hookean membrane bubble presents second-order shape instability. At the same time, this second-order mode shows subharmonics characteristics, which is considered as a potential medical application for ultrasonic imaging.   

Effect of Ultrasound-Induced Bjerknes Force on the Dynamics of Microbubbles. Interaction with Saffman's lift

We will discuss results of experiments on the trajectories of Ultrasound Contrast Agents immersed in low Reynolds steady flow in a pipe. The microbubbles are subject to hydrodynamic forces, and are under the effect of external ultrasound forcing propagating normal to the flow direction. High speed visualization of the microbubbles trajectories shows significant deviations in the direction perpendicular to the flow. This displacement is due to the balance of the Bjerknes force and Saffman's lift. The dependency of the value and orientation of the microbubbles trajectories indicates a rich mechanism for the coupling between these two forces. In the absence of ultrasound excitation, Saffman's lift forces the microbubbles towards the wall. The volume oscillations induced on the microbubble by the propagating ultrasonic pressure waves significantly modify the lift, reversing its direction and making it away from the wall.   

Numerical Simulation of a Bubble Bouncing with a Free Surface

The paper presents a numerical study of a bubble-bouncing with a free surface using a three dimensional front-tracking method. According to our preliminary study, the bubble-free surface interaction is summarized as follows. The bubble becomes slightly oblate as it propels upward, and the bubble starts contacting at the side, rather than the top, to the elevated free surface. Then the liquid in film between the bubble and free surface is gradually drained until the bubble reaches the highest position. Finally, the bubble bounces back from the free surface due to the stored energy on the both of the surfaces and the self-induced flow field. We focus in the rebound depth, and duration time of bubble-free surface contact (contact time, hereafter). The contact time measured from the distance between the bubble center and free surface exhibits -0.5 power of surface tension coefficient, whereas the contact time based on the distance between the bubble top and free surface was found to be insensitive to surface tension coefficient. In the presentation, we also discuss the velocity field within the liquid film and the time-dependency of the film volume.   

Multiscale interactions of bubbles with free vortex flows

We simulate bubble and particle interactions with several types of free vortex flows using both a Discrete Element Model (DEM) and a fully resolved approach. In the DEM approach, DNS is used with Lagrangian particle tracking to compute the motion of a subgrid scale dispersed phase. The {\it volumetric} displacement of the fluid by the dispersed phase is modeled along with interphase momentum-exchange for more realistic coupling of the dispersed phase to the flow. In the fully resolved approach, a fictitious domain technique is used with refined grids to directly compute the motion of the dispersed phase to obtain high fidelity solutions. First, both approaches are used to simulate bubble entrainment into a stationary Gaussian vortex [Oweis et al. 2005]. Next, bubble entrainment and interaction with a traveling vortex tube [Sridhar \& Katz 1999] is simulated using the DEM approach. Finally, a viscous falling `blob' of particles is simulated [Walther \& Koumoutsakos 2001, Mitts 1995], where the dispersed phase generates and interacts with a 3D vortex ring. The results show that the less expensive DEM approach with volumetric coupling is able to capture clustering induced flow distortion, while the fully resolved approach gives insight into dispersed phase scale interactions with the flow.   

Power spectral density in mono-dispersed bubbly flows

An experimental study was carried out to determinate the power spectral density functions of mono-dispersed bubbly flows in a vertical channel using flying hot-film anemometry. To improve the phase discrimination technique, an optic fiber was attached to the hot-film sensor. In this manner, it was possible to clearly separate the erroneous signals caused by bubble collision with the sensor. A special array of capillaries was used to produce nearly mono-dispersed flow. Measurements were performed with gas fractions up to 6$\%$. The power spectral density distributions were found to have a good qualitative agreement with those obtained by other authors. Depending on the values of the Reynolds number and gas volume fraction a progressive change from a $-5/3$ to $-3$ decay was observed.   

Self propulsion of bubbles in wedge-shaped geometries

Self propulsion of bubbles and drops can be created by geometrically forcing capillary pressure gradients. We investigated such self propulsion experimentally by confining long bubbles in flat wedge-shaped geometries that have rectangular cross sections and are closed at both ends. The bubble moves from the narrow end toward the wider end with a speed that monotonically decreases in time. The fluid motion past the bubble occurs through the corners between the bubble and walls of the rectangular cross-section, so that the fluid flow is fully three dimensional. In order to quantitatively describe the motion of the bubble we introduce a one-dimensional model in the spirit of lubrication theory. The predictions of the model are in very good agreement with the experimental measurements and capture the variations with bubble size, wedge angle, and viscosity of the continuous phase.   

Change of \textit{Re} dependency of single bubble 3D motion by surface slip condition in surfactant solution

Path instability of single bubble in water is sensitive to surfactant. One of the key effects of surfactant is to decrease bubble rising velocity (i.e. increase drag) and change bubble slip condition from free-slip to no-slip. This phenomenon is described as Marangoni effect. However, the surfactant effect to path instability is not fully investigated. In this research, we measured bubble 3D trajectories and velocity in dilute surfactant solution to reveal the relation between 3D motion mode and slip condition. Experimental parameters are types of surfactants, concentrations and bubble sizes. Bubble motions categorized as straight, spiral or zigzag are plotted on two-dimensional field of bubble Reynolds number \textit{Re} and normalized drag coefficient $C_{D}^{\ast }$ which is strongly related to surface slip condition. Range of \textit{Re} is from 200 to 1000 and $C_{D}^{\ast }$ is from 0 to 1. Our results show that when $C_{D}^{\ast }$ equals 0 or 1 (free-slip condition or no-slip condition, respectively), bubble motion mode is changed by \textit{Re}. However when $C_{D}^{\ast }$ is 0.5, bubble motion is always spiral. It means that \textit{Re} dependency of bubble motions is strongly affected by slip condition. We will discuss its mechanism in detail in our presentation.   

Slowing down bubbles with sound

We present experimental evidence that a bubble moving in a fluid in which a well-chosen acoustic noise is superimposed can be significantly slowed down even for moderate acoustic pressure. Through mean velocity measurements, we show that a condition for this effect to occur is for the acoustic noise spectrum to match or overlap the bubble's fundamental resonant mode. We render the bubble's oscillations and translational movements using high speed video. We show that radial oscillations (Rayleigh-Plesset type) have no effect on the mean velocity, while above a critical pressure, a parametric type instability (Faraday waves) is triggered and gives rise to nonlinear surface oscillations. We evidence that these surface waves are subharmonic and responsible for the bubble's drag increase. When the acoustic intensity is increased, Faraday modes interact and the strongly nonlinear oscillations behave randomly, leading to a random behavior of the bubble's trajectory and consequently to a higher slow down. Our observations may suggest new strategies for bubbly flow control, or two-phase microfluidic devices. It might also be applicable to other elastic objects, such as globules, cells or vesicles, for medical applications such as elasticity-based sorting.   

Session GK: Multiphase Flows III

Multiscale modeling of non-homogenous flows with non-Newtonian properties

A new multiscale approach to modeling non-homogenous flows where non-Newtonian effects are significant will be discussed. The computations are carried out by combining an immersed-boundary-method, able to capture the response of non-homogenous systems, with Brownian Dynamics able to predict the local properties. The exchange of information between the continuum-based and Brownian Dynamics models, which capture the system properties at different scales, is done through the velocity gradient and stress state tensors. The stress-state tensor estimated with the Brownian Dynamics simulations is introduced in the solution of the front-tracking method, whereas the velocity gradient state is used to estimate the local properties. How to achieve an adequate computational cost will also be discussed. The methodology is validated for two different problems: (i) the deformation of a Newtonian drop immersed in a simple shear flow and suspended in a viscoelastic fluid; (ii) the buoyancy of air bubbles in a viscoelastic fluid.   

Single-equation versus multi-equation models in simulation of material flows

When considering interactions of two pieces of different materials, often a single momentum equation is used; and different materials are treated as two different species of a solid material. The stress in the momentum equation is calculated differently depending on the material occupying the point. This approach is limited when considering breakup of the materials into pieces with typical size smaller than numerical grid resolution. After the breakup, one would prefer to use a two-equation model to simulate the flow of the debris of the two solid materials. It is a significant issue when and how to switch from single-equation mode to the two-equation model. A different approach is to start with a two-equation model, and to treat the system as continuous two-phase system before the material breakup. When material breakup happens, the equation system has a smooth transition into disperse two-phase flows. The issue is then, how this two-equation approach compared with the single equation approach before the material breakup. What material interaction model is needed for such numerical calculation? The present paper tries to answer some of these questions using numerical examples.   

Multiscale Issues in DNS of Multiphase Flows

In spite of the enormous information and understanding that DNS are providing for relatively complex multiphase flows, real systems provide challenges that still limit the range of situations that can be simulated, even when we limit our studies to systems well described by continuum theories. The problem is, as one might expect, one of scale. Starting with simulations where the ``dominant small-scales'' are fully resolved, it is frequently found that multiphase flows also can generate features much smaller than the dominant flow scales, consisting of very thin films, filaments, and drops. Frequently there is a clear separation of scales between these ``features,'' usually inertia effects are relatively small for the local evolution, and in isolation these features are often well described by analytical models. Here we describe the use of a thin film model to account for unresolved features of the flow. By using a semi-analytical model for the flow in the film beneath a drop sliding down a sloping wall, we capture the evolution of films that are too thin to be accurately resolved using a relatively coarse grid that is sufficient to resolve the rest of the flow. Extensions of these ideas to flows with mass and heat transfer as well as phase change and chemical reactions are also discussed.   

Smoothed particle hydrodynamics applied to multiphase flows

Fully Lagrangian numerical simulations of multiphase flows are performed using a numerical approach that is a variation of smoothed particle hydrodynamics. The momentum conservation equation for the constant mass fluid elements is described using the Boltzmann transport equation and particle phase space probability density function. Analogous to the familiar forms of continuum fluid mechanics, the acceleration of a fluid element is due to the gradient of local kinetic stress, the constitutive terms of which are determined following expansion methods from kinetic theory of a dense gas. Including first-order terms, the acceleration of fluid elements is proportional to local particle density and relative velocity, and those elementary forces tend to drive the system towards an equilibrium state. The fundamental restoring and dissipative particle forces are shown to model familiar pressure, viscous, and surface tension effects at the macroscopic scale. The method is applied to test problems that include the wall- bounded flow of two nearly immiscible fluids, the rise of bubbles in an infinite quiescent liquid, and hard sphere sediment transport. Simulations are performed in both two and three dimensions, and the observations are compared to published results.   

A Comparison of Multiphase LBGK and MRT LBE Models

One undesirable feature of LBE methods as diffuse interface methods is the existence of parasitic currents. Recently, Lee and Fischer have shown that if the potential form of the intermolecular force is used, the parasitic currents can be eliminated. In their study, the LBGK collision model is used. As we know that multiple-relaxation-time (MRT) collision model has a number of advantages over the lattice Bhatnagar-Gross-Krook (LBGK) model. In this study, we will replace the LBGK with MRT collision model. We compared the stability and Galilean invariance of the two models. The test case is a circular bubble. We found that LBGK is very sensitive to the initial given density values. For the Galilean invariance property, we first get the converged equilibrium solution. Then we add an external velocity. We found that LBGK scheme diverges even a very small velocity is given. From these comparisons, we conclude that MRT is more stable and preserve Galilean invariance better than LBGK.   

Effects of confinement on a rotating sphere

The hydrodynamic force and couple acting on a rotating sphere in a quiescent fluid are modified by nearby boundaries with possible consequences on spin-up and spin-down times of particles uspended in a fluid, their wall deposition, entraiment and others. Up to now, the vast majority of papers dealing with these problems have considered the low-Reynolds-number regime. This paper focuses on the effect of inertia on the hydrodynamic interaction of a spinning sphere with nearby boundaries. Rotation axes parallel and perpendicular to a plane boundary as well as other situations are studied. Several steady and transient numerical results are presented and interptreted in terms of physical scaling arguments. The Navier-Stokes equations for an incompressible, constant-property Newtonian fluid are solved by the finite-difference PHYSALIS method. Among the noteworthy features of this method are the fact that the no-slip condition at the particle surface is satisfied exactly and that the force and torque on the sphere are obtained directly as a by-product of the computation. This feature avoids the need to integrate the stress over the particle surface, which with other methods is a step prone to numerical inaccuracies. A locally refined mesh surrounding the particle is used to enhance the resolution of boundary layers maintaining a manageable overall computational cost.   

A linear spatial stability analysis of liquid-gas rotating co-flowing jet

We present a linear spatial stability analysis of a liquid-gas rotating co-flowing jet. The parallel mean velocity is computed as a function of the radial coordinate by solving the coupled liquid-gas Navier-Stokes equations in a cylindrical coordinate system. A multi-domain Chebyshev spectral collocation method is applied to the perturbed Navier-Stokes equations (linearized about the mean parallel flow). Both axisymmetric and helical modes are considered. Numerical calculations are performed to obtain the growth rates and frequencies of the most unstable modes. The effect of density ratio, viscosity ratio and surface tension are discussed.   

Two Types of Equations for Nonlinear Wave Propagation in a Liquid Containing Microbubbles

Weakly nonlinear propagation of one-dimensional dispersive waves in mixtures of a liquid and a number of spherical gas bubbles are theoretically investigated based on two-fluid averaged equations derived by the present authors. A set of equations consists of the conservation laws of mass and momentum for gas and liquid phases, and Keller's bubble dynamics equation. The compressibility of liquid leads to the wave attenuation due to bubble oscillations. By using the appropriate scaling of physical parameters and the method of multiple scales, two types of equations for nonlinear wave propagation in long ranges are derived. In a moderately low frequency band, the behavior of weakly nonlinear waves is governed by the KdV-Burgers equation. On the other hand, in a moderately high frequency band, the nonlinear modulation of quasi-monochromatic wave train is governed by the nonlinear Schroedinger equation with an attenuation term.   

Fluctuations in number and volume fraction in granular and multiphase flows: implications for theory and modeling

Fluctuations in the number of particles, and consequently the fraction of volume occupied by them, are observed in experiments as well as simulations of granular and multiphase flows. The mathematical representation of these fluctuations is described, and compared with the standard average number density representation in kinetic theory of granular and gas-solid flow. Implications for the strong and weak forms of the conservation laws of hydrodynamic quantities are discussed, and this leads to possible approaches to model the effect of fluctuations. The manifestation of fluctuations in current closure models is examined using data from direct numerical simulation. Implications for the stability analysis of gas-solid flows, and the stability limits calculated from reduced statistical representations are discussed.   

Session GL: Particle Laden Flows II: Turbulence

Hybrid RANS/LES of particle-laden turbulent flows

One of the main issues in using large-eddy simulation (LES) for high Reynolds number flows in bounded domains is the requirement of very fine grid resolution near walls. We present a hybrid RANS/LES method in conjuction with a Lagrangian particle tracking algorithm, for the numerical prediction of particle-laden turbulent flows. The hybrid RANS/LES methodology aims to reduce the high computational effort of wall-resolved LES. This approach is based on the concept of dividing the simulation into a near-wall RANS part and an outer LES part, and allows the thickness of the near-wall RANS layer to be chosen freely. The near-wall layer is interfaced to the outer LES region using compatibility conditions for velocity and turbulent viscosity across the interface that are extracted dynamically as the simulation progresses. The influence of parameters such as particle shape and size, particle density and flow Reynolds number on the particle dispersion and total deposition is examined. Particles of fiber shape are more prone to deposition. Total particle deposition increases with the particle size, density and Reynolds number.   

Simulation of turbulent flow laden with finite-size spherical particles

Particle-laden turbulent flow is of importance to many engineering applications and natural phenomena. Most previous studies utilize the point particle approach to study the effects of particles on the carrier turbulence, under the assumptions that the particle size is significantly smaller than the smallest turbulence length scale and the particle volume fraction is low. The present study focuses on the motion and hydrodynamic interactions of finite-size freely moving particles in a turbulent background flow. A mesoscopic lattice Boltzmann approach is applied to simulate a homogeneous isotropic turbulence and to realize the no-slip boundary condition on the boundary of each moving particle. The short-range lubrication force not resolved by the simulation is represented by a model in terms of particle relative location and velocity. The change of energy spectrum compared with the particle-free turbulence is discussed, as well as the time evolution of the turbulent kinetic energy and the dissipation rate. The effects of varying particle size, volume fraction, and particle-to-fluid density ratio will also be examined.   

High-inertia particle acceleration statistics in a turbulent channel flow

Recent experiments in a turbulent boundary layer (Gerashchenko et al., 2008) have shown that the variance in the acceleration fluctuations of small, heavy particles in the near wall region increases with increasing inertia, contrary to the trend found for homogeneous and isotropic turbulence. In a previous study, we ran direct numerical simulations (DNS) of inertial particles in a channel flow to show how this phenomenon is related to the coupling of particle motion with shear and gravity. In this work, we extended the DNS to a much broader range of particle Stokes number (20, 40 and 100). The trend for the mean and variance of the particle-acceleration statistics at these much higher Stokes numbers are consistent with what previously was found for homogeneous and isotropic turbulence. We attribute this behavior to the inertial filtering by the particles of the underlying turbulent flow, as though at these higher Stokes numbers particles sample a more nearly isotropic flow field. The effect of gravity also has been considered and will be presented in detail.   

Direct Numerical Simulation of dense particle-laden turbulent flows using immersed boundaries

Dense particle-laden turbulent flows play an important role in many engineering applications, ranging from pharmaceutical coating and chemical synthesis to fluidized bed reactors. Because of the complexity of the physics involved in these flows, current computational models for gas-particle processes, such as drag and heat transfer, rely on empirical correlations and have been shown to lack accuracy. In this work, direct numerical simulations (DNS) of dense particle-laden flows are conducted, using immersed boundaries (IB) to resolve the flow around each particle. First, the accuracy of the proposed approach is tested on a range of 2D and 3D flows at various Reynolds numbers, and resolution requirements are discussed. Then, various particle arrangements and number densities are simulated, the impact on particle wake interaction is assessed, and existing drag models are evaluated in the case of fixed particles. In addition, the impact of the particles on turbulence dissipation is investigated. Finally, a strategy for handling moving and colliding particles is discussed.   

Experimental Investigation of Charged Inertial Particles in Turbulence

We report results from experiments aimed at studying the interactions of electrically charged inertial particles in homogeneous, isotropic turbulence. Conditions are selected to investigate the effects of mutual electrostatic repulsion of particles on their dynamics. We measure droplet clustering and relative velocities. The experiments are carried out in a laboratory chamber with nearly homogeneous, isotropic turbulence. The turbulence is characterized using LDV and 2-frame holographic particle tracking velocimetry. We seed the flow with charged particles and use digital holography to obtain 3D particle positions and velocities. From particle positions, we investigate the impact of mutual electrostatic repulsion on inertial clustering through the calculation of the radial distribution function (RDF). Specifically, repulsion overcomes inertial clustering below a shielding length as seen by a strong reduction in the RDF.   

Effect of filtering on inertial particle clustering in homogeneous isotropic turbulence

The use of large-eddy simulation (LES) to represent inertial particles in a turbulent flow field requires a model for the effect of the subfilter eddies on the particle motion. A particularly challenging aspect of this modeling is correctly capturing particle clustering, which is driven principally by the small-scale eddies that have been filtered in a LES. In this paper, we investigate this problem by performing direct numerical simulations of homogeneous isotropic turbulence with inertial particles and compare the results to particles moving through a low-pass filtered velocity field. The filtering is done in wavenumber space and is akin to a `perfect' LES in that there is no subgrid model. We look at the two-particle radial distribution function (RDF) and the relative velocity probability density function (PDF) at different separation distances. We find that both the RDF and relative velocity PDF change substantially in response to the filtering. In particular, the level of clustering can be suppressed or enhanced depending on the value of the Stokes number. The spatial scales of the clustering are also affected. The results suggest requirements that a subfilter model should satisfy to correctly reproduce the RDF and relative velocity PDF. Such information will assist the future development of a LES model for inertial particles.   

On the effects of Taylor-lengthscale size particles on isotropic turbulence

The effects of spherical particles of Taylor-lengthscale size ($ d \sim \lambda $) on isotropic turbulence are studied via DNS. A mesh of $256^3$ grid points is used with an initial microscale Reynolds number $Re_{\lambda 0}= 75 $. The flow around 6400 freely-moving particles is fully resolved using the Immersed Boundary method. The maximum volume fraction of the particles is $\phi_v = 0.1$. The maximum density ratio is $ \rho_p/\rho_f = 10 $ which corresponds to a mass fraction $\phi_m = 1.$ Our results show that particles with diameter $d \sim \lambda$ always reduce the turbulence kinetic energy (TKE), mostly by enhancing its dissipation rate, $\varepsilon(t)$. The augmented dissipation rate exceeds $\Psi_p(t)$, the rate of increase of TKE due to the two-way coupling force imparted by the particles on the surrounding fluid. The increased dissipation rate occurs close to the front of the particle surface due to the increased strain rates (both extensional and compressive) as the particles move through the surrounding turbulent eddies. For fixed volume fraction and diameter of the particles, the most pronounced effects on TKE, its dissipation rate and its rate of change due to two-way coupling occur by increasing the ratio $\rho_p/\rho_f$ which is directly proportional to the Stokes number, ($\tau_p/\tau_k$), and the particles mass fraction, $\phi_m $.   

Mixing of inertial particles at a turbulent - non turbulent interface

Motivated by the problem of entrainment of dry air into clouds, water droplets are sprayed into the high turbulence side of a shearless turbulence mixing layer: a layer in which there is a step in turbulence intensity across the interface but there is negligible change in the mean velocity (Veeravelli and Warhaft, JFM, 1989, 208, 191). Active and passive grids are used to form the mixing layer. A splitter plate is used to separate droplet-non droplet interface near the origin. Particle concentration, size and velocity are determined by Phase Doppler Particle Analyzer, the velocity field by hot wires, and the droplet accelerations by particle tracking. The results are compared with injecting the particles into one side of homogeneous turbulence. We show that the particle number density is approximately an order of magnitude smaller on the low turbulence side of the turbulent-non-turbulent interface compared with that of a turbulent- turbulent interface with the same initial distribution of inertial particles on one side. Stokes and Froude number effects are investigated. Sponsored by the U.S. NSF.   

Large scale accumulation of inertial particles in turbulent channel flow

Spatially inhomogeneous turbulent flows induce peculiar phenomena on the transport of a dispersed phase of inertial particles. In channel flows the most striking effect is the spatial segregation of particles that may achieve a concentration at the wall largely exceeding that in the bulk. Here we approach the issue by considering direct numerical simulations in a channel seeded with different populations of diluted, tiny particles. The simulations at Re$_{\tau}$=180 have been performed using the largest domain size so far. The structures found in the fully developed stage of the process show strong spanwise correlations more intense than those found in the corresponding elongated structures of low and high fluid speed. The extremely regular spanwise organization corresponds to a mean spacing of about 120 plus units. The turbulent simulations with an increased size of the numerical box highlight some significant differences in the correlation of particle concentrations. A possible explanation of this feature can be related to large-scale structures of the velocity field, which might carry a considerable amount of energy. Correlations between turbulent events, sweep and ejections, and the particle motion to and from the wall will be also presented.   

Self-similarity in particle laden flows at constant volume

We consider constant volume thin film slurries on an incline. Clear fluids in this geometry are known to have a front position that moves according to a $t^{1/3}$ scaling law, based on similarity solution analysis [Huppert, Nature, 1982]. We investigate the same dynamics for particle laden flow using a recently proposed lubrication model for the slurry and physical experiments. Our analysis includes the role of a precursor in the model. We conclude that in the lubrication model, the height of the precursor significantly influences the speed of the fluid front, independent of particles settling in the direction of flow. By comparing theory with experiments we conclude that the $t^{1/3}$ scaling law persists, to leading order, for slurry flows with particle settling. However additional physics is needed in the existing lubrication models to quantitatively explain departures from clear-fluid self-similarity due to particle settling.   

Session GM: Supersonic/Hypersonic I

Fluid-structure interaction of converging shocks in water

Numerical simulations of shock focusing in a convergent water-filled geometry with various types of elastic solids (rubber, plastic and metal) as the surrounding material have been performed. The fluid deforms the solid, generating elastic waves, which in turn affect the liquid; thus creating a coupled fluid-structure problem. Here, we use the Overture suit, a code for solving partial differential equations on curvilinear overlapping grids using adaptive mesh refinement. The Euler equations with a stiffened equation of state are used in the fluid domain and linear elasticity is assumed in the solid domain. Preliminary results indicate that the wave speed of the material has a significant influence on the behavior of the converging shock. Comparisons between numerical and experimental results are presented and have the potential to aid in the design of marine structures with convergent sections subjected to dynamic loading events.   

Mixing analysis of PLIF images in a multi-stream injection nozzle

We present quantitative analysis of image sequences of multi-stream injection nozzle flows with several different injection geometries. Image sequences were acquired by A.M. Ragheb and G.S. Elliott (UIUC) using planar laser-induced fluorescence (PLIF) in iodine to visualize flow mixing. The injection nozzle was comprised of a slot, ejector and injector block, with rows of ejector and injector holes along the slot length. The ejector flow exits in an underexpanded state so that upon expanding it forces the slot and injector flows together to enhance mixing. For this study, the diameter and geometry of ejector holes were varied to assess their effect on mixing. Two configurations of ejector holes were used, each with two different diameters for a total of 4 cases with data collected at downstream stations. We carried out a quantitative mixing analysis for these configurations, using two parameters to quantify the mixing. The first parameter, the mixing quality criterion, is assessed from the statistics of the PLIF image intensity histograms, which are bimodal for poorly-mixed flows and have a single peak in well-mixed flows. The second parameter is mixing interface length. Our analysis shows that one injection scheme significantly enhances mixing by stretching the mixing interface.   

Analysis of DNS database of canonical shock/turbulence interaction

A set of databases generated by direct numerical simulation of isotropic turbulence passing through a shock wave is analyzed. Averages conditioned on the local instantaneous shock strength are used to elucidate the structure of the shock/turbulence interaction through the strongest and weakest points on the shock. For sufficiently strong turbulence there exists completely smooth profiles through the shock-region. The unsteady shock-motion is analyzed and linked to the incoming turbulence.   

A Derivation of New Regularized Euler Equations from Basic Principles

Both turbulence and shock formation in inviscid flows are prone to high wave number mode generations. This continuous generation of high wavemodes results in energy cascade to ever smaller scales in turbulence and creation of shocks in compressible flows. This high wavenumber problem is often remedied by the addition of a viscous term in both compressible and incompressible flows. The author's group recently reported a regularization technique for the Burgers equation (Norgard and Mohseni 2008) which is now extended to one-dimensional compressible Euler equations (Norgard and Mohseni 2009). This investigation presents a formal derivation of these equations from basic principles. We will extend our previous results to multidimensional compressible and incompressible Euler equations. We expect this technique to simultaneously regularize shocks and turbulence. Numerical simulation demonstrating the shock regularization properties of these equations will be presented.   

A low-dissipation and dispersion finite volume method for large eddy simulation of compressible flow on arbitrary unstructured grids

One way to develop stable solvers for large eddy simulation with minimal numerical dissipation is to use so-called summation-by-parts (SBP) operators. These discrete operators mimic the integration-by-parts property of the continuous equations, leading to discrete stability by the energy method. Unfortunately, the application of large eddy simulation to compressible flows of engineering interest often involves complex geometries and consequently unstructured grids. In the present work, a method for constructing a fast, explicit compressible flow solver for large eddy simulation is presented that uses standard polynomial reconstruction techniques to build accurate finite volume operators, which are subsequently modified based on the extent to which they are not SBP. Because the SBP property is a property of the operators and not the solution, this can be performed as a pre-processing step in a large eddy simulation. Several examples will be presented demonstrating the robustness and accuracy of this compromise approach, including sound radiated from transonic and supersonic jets.   

High Resolution Direct Numerical Simulations of Compressible Isotropic Turbulence

We present results from a systematic study of Direct Numerical Simulations of forced compressible turbulence. The simulations explore the $M_t$--$\chi$ parameter space where $M_t$, the turbulent Mach number, varies from 0.02--0.6, and $\chi$, the ratio of dilatational to solenoidal energy, varies from 0.01--10, on up to $1024^3$ meshes, with maximum Taylor Reynolds numbers of $R_\lambda>300$. Thus, the study covers the weakly to moderate compressibility effects regime as reflected in the turbulent Mach number values, as well as the low to strong dilatational effects regime that may arise independently from the Mach number effects, e.g. due to exothermic reactions. The forcing method is designed to control the statistically stationary state values of the dissipation (thus the Kolmogorov scale) and the ratio of dilatational to solenoidal dissipation. This ensures that the simulations are both stable and well resolved. The DNS results are used to examine the spectral properties of the solenoidal and dilatational velocity fields and highlight changes in the turbulence properties due to compressibility and dilatational effects.   

Development of a numerical code for the study of a supersonic planar wake

The fully-developed supersonic planar wake represents a canonical high-speed flow occurring in many aeronautical applications. The goal of the current research program is to perform a high-quality direct numerical simulation in order to thoroughly compare the statistics with classical experimental data and gain a better understanding of the structures present in the far-field of a supersonic planar wake. In order to study this flow a code is under development using a very efficient modified MacCormack-type scheme to solve the governing equation set. The main drawback of this numerical method is the large dispersive errors occurring in regions of sharp gradients which can occur in as shocklets in highly compressible flow. To this effect, a study of the numerical properties of this scheme is done using classical one-dimensional test cases such as the Shu-Osher and the Sod problem. The scheme compares very favorably to typical compressible schemes such as the Pade and Roe solvers but shows a very significant advantage in terms of memory usage and speed.   

Effects of Turbulence on Taylor-Sedov Blast Waves in Radially-Symmetric Geometries

Progress in extending studies of the classical Taylor--Sedov blast wave problem by incorporating effects due to turbulence is reported. Investigations consist of the analytical development and initial numerical findings describing the evolution of large and instantaneous energy releases from point explosions (in radially-symmetric systems) while coupling turbulent instabilities. The closure of the Reynolds-Favre averaged mean flow equations is accomplished using a $K$-- $\epsilon$ model in the gradient diffusion approximation. To reduce the complexity of the problem, self-similar analysis is used to reduce the space-time dependent system of partial differential equations to coupled, nonlinear ordinary differential equations in the self-similarity variable. Preliminary approximations considered in the problem are also discussed.   

Session GN: Non-Newtonian Flows I

Analytical solution for creeping channel flow of non-Newtonian compressible fluid subject to wall slip

Creeping channel flows of compressible viscoplastic fluids subject to wall slip are important in many industries as well as presenting significant academic challenges. Here we present analytical solutions for pressure-driven steady flows of viscoplastic fluids within planar and circular channels. Herschel-Bulkley constitutive equation is employed in conjunction with constant or pressure dependent wall slip coefficients. Simplifications of the Hershel-Bulkley fluid provide other generalized Newtonian fluids including power law and Newtonian fluids. Under the assumption that pressure only changes in the flow direction and its gradient deviates slightly from a constant, explicit solutions are derived for distributions of pressure, velocity, and slip velocity within the channels. The analytical solutions are compared against numerical solutions as well as experimental data collected using rectangular slit dies. The effects of compressibility and wall slip on the flows are elucidated. A distinctive feature of such a flow is that, when the slip coefficient is considered to be inversely proportional to pressure, the slip velocity increases rapidly in the flow direction and the flow can evolve into a pure plug flow at the exit, removing the stress singularity that is presumed to exist in the transition from the channel flow into a free surface flow at the exit.   

Transient growth without inertia

We study transient growth in inertialess plane Couette and Poiseuille flows of viscoelastic fluids. For streamwise-constant 3D fluctuations, we demonstrate analytically the existence of initial conditions that lead to quadratic scaling of both the kinetic energy density and the elastic energy with the Weissenberg number, $We$. This shows that in strongly elastic channel flows, both velocity and polymer stress fluctuations can exhibit significant transient growth even in the absence of inertia. Our analysis identifies the spatial structure of the initial conditions (i.e., components of the polymer stress tensor at $t = 0$) responsible for this large transient growth. Furthermore, we show that the fluctuations in streamwise velocity and the streamwise component of the polymer stress tensor achieve $O(We)$ and $O(We^2)$ growth, respectively, over a time scale $O (We)$ before eventual asymptotic decay. We also demonstrate that the large transient responses originate from the stretching of polymer stress fluctuations by a background shear and draw parallels between streamwise-constant inertial flows of Newtonian fluids and streamwise-constant creeping flows of viscoelastic fluids. One of the main messages of this work is that, at the level of velocity fluctuation dynamics, polymer stretching and the Weissenberg number in elasticity-dominated flows effectively assume the role of vortex tilting and the Reynolds number in inertia-dominated flows of Newtonian fluids.   

Extensional dynamics of viscoplastic filaments

A one-dimensional slender-thread model is used to explore viscoplastic dripping under gravity and the controlled extension of a liquid bridge. We describe dynamics up to pinch-off and consider the possibility of using measurements in the two configurations (eg. drop volume) to infer rheological parameters. The model results are compared with experiments using aqueous solutions of Carbopol and kaolin suspensions.   

Multiscale simulation of polymer melt flows between parallel plates

The behaviors of polymer melt composed of short chains with ten beads in parallel plates are simulated by using a hybrid method of molecular dynamics and computational fluid dynamics. The creep motion under a constant shear stress and recovery after removing the stress, the pressure driven flows and the flows in rapidly oscillating plates are simulated. The flow profiles of polymer melt are quite different from those of the Newtonian fluid due to the elasticity or the shear thinning. The delayed elastic deformation and plug-like velocity profile are reproduced, respectively, in the creep and pressure driven flow. In the rapidly oscillating plates the viscous boundary layer of the melt is much thinner than that of the Newtonian fluid due to the shear thinning of the melt. Three different rheological regimes, i.e., the viscous fluid, viscoelastic liquid, and viscoelastic solid regimes, form over the oscillating plate according to the local Deborah numbers. The melt behaves as a viscous fluid in a region for $\omega\tau^R\la 1$, and the crossover between the liquid-like and solid-like regime takes place around $\omega\tau^{\alpha}\simeq 1$ (where $\omega$ is the angular frequency of the plate and $\tau^R$ and $\tau^{\alpha}$ are Rouse and $\alpha$ relaxation time, respectively).   

Experimental study of the hydrodynamic interaction between a pair of bubbles ascending in a non-Newtonian liquid

We present some experimental results about the interaction of a pair of bubbles ascending in non-Newtonian fluids. A high speed camera was used to follow in-line and off-line rising motion of two bubbles in a Newtonian fluid (a glycerin-water solution), a Boger fluid (aqueous polyacrylamide solution), and a shear-thinning fluid (aqueous xanthan solution). For the case of shear-thinning fluids, the power index, n, affects the tendency of the bubble pair to aggregate. Therefore, in addition to bubble separation, orientation and Reynolds number, the hydrodynamic force depends strongly on the shear-thinning nature of the fluid. Several examples will be shown. For elastic fluids, the Deborah number affects the hydrodynamic interaction. We found that the appearance of the negative wake changes the nature of the interaction substantially. Some examples and comparisons with numerical results will be presented.   

A numerical study of the hydrodynamic interaction of bubble pairs ascending in non-Newtonian liquids

This talk presents computational results on the interaction of a pair of bubbles immersed in non-Newtonian fluids. The Arbitrary Lagrangian-Eulerian (ALE) technique was used to simulate two bubbles rising in tandem or side by side in shear-thinning and Oldroyd-B fluids. In the shear-thinning fluid, the pairwise interaction is affected by the the Eotvos and Reynolds numbers as well as the initial orientation of two bubbles. In particular, two in-line bubbles will rise together and form a doublet as the trailing bubble catches up with the leading one. In a viscoelastic fluid, a negative wake may appear depending on the initial separation between the bubbles. The capillary number, which can be an indicator of the bubble deformability, seems to play a secondary role in the bubble interaction. The numerical simulations complement previous experiments done with bubble swarms by our group.   

Selective withdrawal of non-Newtonian fluids: surface deformation induced by a sink flow

This talk reports experiment and numerical studies of selective withdrawal in a fluid-gas system. Using visual observation and finite element simulations based on an Arbitrary Lagrangian-Eulerian scheme, we have explored the effects of viscoelasticity on the deformation of free surface when the fluid is polymer solution (experiment) or Giesekus fluid (simulation). In the experiments, we find a thin air jet emanating from the tip of the free surface for polymer solutions when the distance between the free surface and the sink is below a critical value. This does not occur for the free surface of Newtonian liquids, and is caused by the additional elongational stress due to the polymer. In the simulations, the effects of elasticity on the surface deformation have been captured. The balance between surface and viscoelastic forces may potential be used for measuring extensional viscosity.   

Active and hibernating turbulence in minimal channel flow of Newtonian and polymeric fluids

The experimental observation of minute amount of polymers reducing turbulent drag has been long established. In this study, we isolate the turbulent self-sustaining process by conducting direct numerical simulations (DNS) in minimal flow units (MFU). These solutions obtained at various polymer parameters recover all key transitions in viscoelastic turbulent flows reported previously in experiments at much higher Re, including the onset of drag reduction, low degree of DR (LDR), high degree of DR (HDR) and maximum drag reduction (MDR). At MDR, the mean velocity profile is insensitive to changing polymer parameters. The LDR-HDR transition is characterized by a sudden increase in the minimal box size of sustaining turbulence, which may correspond to a qualitative change in the self-sustaining mechanism. Dynamics of turbulence show intermittent appearance of ``hibernation'' periods, which are characterized by long-lasting flow structures with low instantaneous wall shear stress and low turbulence intensity. These periods appear both in Newtonian and viscoelastic fluids; however they are observed much more frequently in HDR and MDR stages, which contribute substantially to the relatively high level of DR. Instantaneous velocity profiles during hibernation periods resemble the Virk MDR profile, including the disappearance of the log-law layer and a comparable slope with the Virk MDR asymptote.   

Entangled chain dynamics of polymer knots in extensional flow

We formulate a coarse grained molecular dynamics model of polymer chains in solution that includes hydrodynamic interactions, thermal fluctuations, nonlinear elasticity, and topology-preserving solvent mediated excluded volume interactions. The latter involve a combination of potential forces with explicit geometric detection and tracking of chain entanglements. By solving this model with numerical and computational methods, we study the physics of polymer knots in strong extensional flow (Deborah number, $De=1.6$). We show that knots slow down the stretching of individual polymers by obstructing via entanglements the ``natural", unraveling, flow-induced chain motions. Moreover, the steady state polymer length and polymer-induced stress values are smaller in knotted chains than in topologically trivial chains. We indicate the molecular processes via which the rate of knot tightening affects the rheology of the solution.   

A Finite Volume Solver for Non-Newtonian flow on Unstructured Grid with Application in Blood Flow

In order to simulate blood flow in complex vessel, a finite volume solver for Casson fluid flow based on SIMPLE algorithm of Newtonian fluid on unstructured collocated grid is developed. For the discretization of convective fluxes and source term, it is similar with Newtonian fluid. For the discretization of diffusion fluxes, viscosity will take the value calculated from the flow field of previous iteration in order to avoid the complexity caused by the complicated viscosity expression as a function of shear rate. Then the discretization of momentum equation is similar with that of Newtonian fluid with variable viscosity and SIMPLE algorithm can be used to resolve the pressure-velocity coupling. Casson fluid flow through a symmetric sudden expansion channel is compared with literature and the good agreement between simulated velocity distributions with literature confirms the validation of present algorithm. Afterwards, blood flows in T-type bifurcation are simulated by our proposed algorithm. The simulation result of Casson fluid is more consistent with experiment than that of Newtonian fluid, which indicates that using Casson model to simulate on-Newtonian characteristics of blood is successful and necessary.   

Session GP: Instability: Jets & Wakes III

Visualization of Pulsating Low-Speed Flows from a Basic Annular Jet

Results of a study involving pulsating low-speed free jets issuing from an annular orifice into a quiescent medium are discussed. Transient flow behavior associated with pulsating jets is known to affect entrainment, mixing, and spread rate characteristics. Also, annular jet flows often provide a better description of the flow associated with nozzles used in engineering applications. However, the flow phenomena related to pulsating annular jets is still not fully understood. In this study, flow in the initial region of a pulsating low-speed annular water jet issuing into a quiescent water reservoir was visualized by means of a dye. The blocking ratio was fixed at 0.7. The Reynolds number was varied from 59 to 155 and the Strouhal number from 0.133 to 1.90. For the experimental conditions considered, two different flow regimes were observed. At high pulse frequencies, the flow field resembled that of the steady annular jet. As the frequency decreased, the flow transitions into a structure composed of a train of toroidal vortices, i.e. vortex rings. The frequency at which transition occurred was proportional to the Reynolds number.   

The stability of multiple tip vortices

The talk will present some new results on the viscous stability of multiple tip vortices. Using a BiGlobal stability approach we predict the critical Reynolds number for a variety of vortex configurations. Some discussion of the inviscid instability of these multiple vortex configurations will also be given.   

Evolution of turbulent jets in low aspect ratio containers

The evolution of homogeneous and buoyant turbulent jets released into a low aspect ratio (width/height) container was investigated experimentally using PIV, MSCT probing and digital imaging. The motivation was to understand mixing process occurring in U.S. Strategic Petroleum Reserves (SPR), where crude oil is stored in salt caverns of low aspect ratio. During maintenance or filling, oil is introduced as a jet from the top of the caverns. This study is focussed on mean and turbulent flow characteristics as well as global flow instability and periodic oscillations intrinsic to jets in low aspect ratio containers. Scaling arguments were advanced for salient flow parameters, which included the characteristic length (container width $D)$ and velocity (for homogeneous jets, $J^{1/2}D,$ where $J$ is the momentum flux at the jet exit) scales. For buoyant jets, the buoyancy flux $B$ needs to be introduced as an additional parameter. Such jet flows do not reach a steady state, but bifurcate periodically with a frequency scale $J^{1/2}/ D^{2}$ while enhancing global mixing.   

Controlling a liquid jet inside the regular breakup regime by applying a composite disturbance to the actuator

In this work, we control the breakup characteristics of a liquid jet by manipulating a piezoelectric actuator and thus the disturbance applied to the jet. We are thereby able to provide desirable droplet size patterns over a wide frequency range. The regular breakup regime refers to the frequency range where the breakup characteristics are repeatable. Thus, although the droplets may not be uniform in size, they pinch off the stream at a constant rate. The regular breakup regime for different jet velocities and diameters has been specified experimentally. The experiments show formation of secondary droplets between main droplets, mostly around the lower frequency range of the regular breakup regime. We remove these secondary droplets by sending a composite disturbance comprising of a fundamental disturbance at the principal driving frequency and another harmonic mode. The choice of the additional harmonics depends on the desired droplets size pattern. It is thus possible to relate initial input disturbance waveform to the droplet formation pattern.   

Three-dimensional radiative instabilities in a stratified plane jet

We investigate the three-dimensional stability of a stratified plane Bickley jet in the Boussinesq approximation framework. The angle $\theta$ between the shear plane and the direction of stratification and the Froud number $Fr$ are considered as a control parameters. Following the parallel flow approximation, the instability wave solution is sought in the form of a normal mode in two directions. We draw attention to a mechanism whereby Kelvin-Helmholtz mode may have a radiative structure and more generally how internal waves (or gravity waves) associated with unstable radiative modes may be spontaneously generated.   

Microphone-array measurements of the surface-pressure field produced by oblique and normal impinging jets

The sptio-temporal, wall-pressure fluctuation generated by an axi-symmetric jet impinging on a flat wall is measured using a 30-microphone array. The focus of the study is the influence of the impingement angle on the strength, spatial distribution and space-time characteristics of the unsteady wall-pressure field. The investigation is conducted at jet Reynolds number of approximately 13000, based on jet diameter and three impingement angles: 0, 15 and 30 degrees. The results show that the impingement angle has strong influence on the level of pressure fluctuations, leading to large increase on the side where the flow experiences less turning (relative to normal impingement), and vice versa. Substantial influences are also found on the spatial characteristics and convection velocity of the pressure-generating flow structures. These effects and others will be presented and discussed in this talk.   

Primary Breakup of a High Speed Liquid Jet

The primary breakup of a high speed jet is studied numerically in 2D and 3D using the front tracking method. We introduce an improved, robust, locally grid based method for reconstruction of tangled interfaces. This method improves the handling of topological change of the surface mesh in the 3D simulations, and is essential for the success of the simulations presented here. From the 2D axisymmetric simulations, we find agreement with experiment in regard to the tip velocity of the jet and its overall degree of breakup or spreading. Due to resolution restrictions, we observe in 3D breakup primarily in the jet tip region and somewhat larger droplets than expected from theory.   

Forming a fine jet in inkjet printing

The formation of fine jets during the piezoelectric drop-on-demand inkjet printing has been investigated using ultra-high-speed video imaging. The speed of the jet can exceed 80 m/s, which is much higher than the general drop velocity during inkjet printing. The diameters of the thinnest jets are of the order of a few microns. The generation of such fine jets has been studied over a wide range of viscosities, using 7 different concentrations of water-glycerin solutions. This jetting is associated with the collapse of an air-pocket which is sucked into the nozzle during the printing. This occurs for longer expansion times for the piezo-element. We have characterized the relationship between the speed of the fine-jet and other parameters like the diameter of the jet and the physical properties of the liquid.   

Saturation of the Magnetorotational Instability at Large Elssaser Number

The MRI is believed to play an important role in accretion disk physics in extracting angular momentum from the disk and allowing accretion to take place. The instability is investigated within the shearing box approximation under conditions of fundamental importance to astrophysical accretion disk theory. The shear is taken to be the dominant source of energy, but the instability itself requires the presence of a weaker vertical magnetic field. Dissipative effects are suffiently weak that the Elsasser number is large. Thus dissipative forces do not play a role in the leading order linear instability mechanism. However, they are sufficiently large to permit a nonlinear feedback mechanism whereby the turbulent stresses generated by the MRI act on and modify the local background shear in the angular velocity profile. To date this response has been omitted in shearing box simulations and is captured by a reduced pde model derived from the global MHD fluid equations using multiscale asymptotic perturbation theory. Results from simulations of the model indicate a linear phase of exponential growth followed by a nonlinear adjustment to algebraic growth and decay in the fluctuating quantities. Remarkably, the velocity and magnetic field correlations associated with these growth and decay laws conspire to achieve saturation of angular momentum transport.   

Session GQ: Instability: Interfacial and Thin-Film IV

Fingering Instability During Debonding: From a Viscous Liquid to a Soft Elastic Solid

We investigate the fingering instability during debonding of a confined viscoelastic layer in a circular lifted Hele-Shaw cell.\footnote{J. Nase, A. Lindner, C. Creton, PRL \textbf{101}, 074503 (2008)} We use PDMS with different degrees of crosslinking, ensuring a continuous transition from a viscous liquid to a soft elastic solid. During debonding, a fingering instability with characteristic initial wavelength $\lambda$ evolves. When going from a liquid to a solid, we observe a transition from bulk to interfacial mechanisms. We predict this transition from linear viscoelastic and surface properties. We show that for the interfacial mechanism, $\lambda$ depends solely on the film thickness, whereas for the bulk mechanism, $\lambda$ depends on the material parameters. $lambda$ is in both cases in quantitative agreement with linear stability analysis. For a Newtonian oil, we discuss in detail the coarsening of the pattern during debonding. Adapting a recent 3D technique, we visualize for the first time in situ the contact line between viscoelastic material and air in three dimensions, providing direct access to the boundary conditions.   

The effects of viscosity and pressure on the bursting of a drop in a Hele-Shaw cell

As one fluid is injected into another fluid of greater viscosity, instabilities occur in the form of fingers which extend radially from the injection point (Saffman \& Taylor, Proc. R. Soc. Lon. A, 1958). As the lower-viscosity fluid reaches the free surface it rapidly bursts through the higher- viscosity fluid (times are typically less that 50 ms for our system) and a pressure drop occurs. This pressure drop induces the shrinking of the non-bursting fingers. By varying the air pressure and water-glycerol viscosity we study this process by analyzing sequences of images prior and after the bursting event inside a Hele-Shaw cell with a gap spacing of between 10 and 500 micrometers. It has been shown that in a micro-scale environment the effects of gravity are negligible as fluid flow is dominated by capillary forces, thus such a setup would behave in space just as it does on Earth. Therefore it may then be possible to use hot air injected into a Hele-Shaw cell filled with water to generate steam in a microgravity environment.   

Two-phase hydrodynamic model for air entrainment at moving contact line

The moving contact line problems are challenging because they involve multiple length scales. One interesting case arises when an advancing liquid of high viscosity entrains the surrounding phase, such as air. In this presentation, we introduce a hydrodynamic model that generalizes the lubrication theory in order to take into account the velocity fields of the two phases. Assuming that the curvature of the interface is small we derive a differential equation for the interface profile at stationary state. We found that there is a critical capillary number above which no steady meniscus can exist and instability will occur. For example, air bubbles will be entrained into the liquid at the advancing contact line. However, we found no instability when neglecting the viscosity of the surrounding phase, illustrating the two-phase nature of the problem.   

Surfactant effect on the motion of long bubbles in capillary tubes

In this talk, we give a theoretical proof of the thickening effect of surfactant by considering a small concentration of surfactant $\Gamma$ and variable surface tension on a long bubble interface which is moving slowly and steadily in a capillary tube filled with a liquid of viscosity $\mu$. The contact angle is taken as zero at the walls and the gravitational effect is neglected. This problem was originally considered by Bretherton and later studied numerically by Park (1990) and Ratulowski and Chang (1991). The main result we obtain is a formula of the film thickness in terms of $M$ and $\Gamma$ where $M$ is the Marangoni number. A comparison with Bretherton's ``clean'' case shows the thickening effect of surfactant. This talk is partially based on an going work with Gelu Pasa.   

Stability of liquid sheet edges

Accelerating edges of thin liquid sheets are ubiquitous and are known to experience a longitudinal (along-the-edge) instability, which often leads to their break-up and atomization. The fundamental physical mechanisms of this instability are studied analytically in the form of a concise model. It is discovered that the classical Rayleigh-Taylor mechanism is substantially modified which leads to a stability picture different from that for flat interfaces, in part due to an interplay with Rayleigh-Plateau mechanisms. In particular, as the Bond number increases, first only one critical wave number is excited, but for higher values of the Bond number several critical wavenumbers can coexist with the same growth rates. This allows for the transition from the regular picture, in which one wavelength sets the pattern, to the frustrated picture, in which a few wavenumbers compete with each other.   

A Phase-field Model of Wetting in Porous Media -- Origin of Gravity Fingering During Infiltration

We present a new continuum mathematical model of wetting into dry soil. The inspiration for the new model is the flow of thin films (like water down a plane), which also displays fingering instability. The key idea is very simple: the macroscopic equations must reflect the presence of a macroscopic interface---the wetting front. We then cast the model in the rigorous framework of phase-field models and nonlocal thermodynamics. The new model is appealing. It is a simple extension of the traditional model---Richards' equation---with a new term (a fourth-order derivative in space) but without any new parameters. It reproduces the two key features of unsaturated flow: a nonmonotonic saturation profile, and gravity fingering. It explains why, when, and how, fingers form. It shows excellent quantitative agreement with experiments in terms of tip saturation, tip velocity and finger width. The most attractive aspect is, however, that the new model offers a starting point for fundamentally new formulations of multiphase flow in porous media.   

Transient numerical simulation of miscible channel flow with heat transfer and viscous heating

Pressure-driven miscible channel flow undergoing heat transfer and viscous heating, focusing on the displacement of a highly viscous fluid by a less viscous one, is studied by direct numerical simulations using the finite volume method. The flow dynamics are governed by the continuity and Navier-Stokes equations, coupled to an energy equation and a convective- diffusion equation for the concentration of the more viscous fluid through a concentration- and temperature- dependent viscosity. The effect of temperature difference, Nahme, Prandtl, and Schmidt numbers on the propagation of the front separating the two fluids and temporal evolution of the mass of the less viscous fluid is examined.   

Numerical simulations of two-fluid channel flow with wall deposition and ageing effects

We study the dynamics of two immiscible fluids with a high viscosity contrast in pressure-driven channel flow using direct numerical simulations at moderate Reynolds numbers. The equations of mass, momentum and energy conservation in both fluids are solved using a procedure based on the diffuse interface method. A Cahn-Hilliard equation is also solved for the volume fraction. Numerical solutions are obtained subject to no-slip and no-penetration conditions at the walls, and constant flow rate conditions at the channel inlet; outflow conditions are imposed at the outlet. This model accounts for a thermal instability in the bulk, through a chemical equilibrium model based on the Gibbs free energy, which leads to the formation of the highly viscous phase and its deposition at the channel walls. We also account for the evolution of the rheology of the deposited phase through ``ageing.'' We present results showing typical flow dynamics and the effect of system parameters on the average deposit thickness.   

Displacement flows between Newtonian fluids at moderate Reynolds numbers in rectangular channels

Displacement flows between two Newtonian fluids in rectangular channels is studied by numerical and analytical means. Two-stages are clearly seen in the displacement process: first, a core of the displaced fluid is removed by a finger of the displacing fluid with width less than the channel height; then, the film of the displaced fluid adjacent to the wall left behind is then removed via interfacial instabilities that grow spatio-temporally. The shape of the finger dictated by a meniscus in the front and a tail of nearly asymptotic height; the latter is a function of the viscosity and density ratios, Weber number and Reynolds number. This dependence is studied by means of highly resolved direct numerical simulations using the diffuse-interface method. The interface shapes obtained is compared with analytical steady state solutions of the meniscus shapes in the downstream region and the asymptotic film thickness in the upstream region.   

Effect of film thickness on EHD-driven instability of superimposed flows

This study aims to investigate the effect of fluid layer thickness on EHD-driven instability of superimposed fluids using Direct Numerical Simulations (DNS). The geometric setup consists of two fluids having different electrical properties confined between two horizontal electrods, where the lighter fluid is overlaid on top of the heavier one. A front tracking/finite difference scheme is used, in conjunction with Taylor's leaky dielectric model, to solve the governing electrohydrodynamics equations in both fluids at finite Reynolds numbers and the dynamics of the interface and incipience of instability is investigated as a function of the thickness of the lower layer.   

Session GR: Viscous Flows I

Low Reynolds Flow Visualization Revisited: Free-Surface and Wall Effects

Many of the seminal experimental flow visualizations at low Reynolds number can be attributed to the pioneering works of S. Taneda. These classic investigations are still considered today benchmark visualizations and are widely used as textbook examples (Van Dyke, \textit{An Album of Fluid Motion}, 1982). With the advent of modern quantitative flow visualization techniques, we are in a position to revisit in more detail some of the original questions posed by Taneda, including boundary effects on viscous flows surrounding objects (\textit{J Phys Soc Jpn}, 1964). In the present talk, we conduct experimental flow visualizations around three-dimensional objects at low Reynolds number (\textit{Re}=$O$(10$^{-3}$-10$^{-1}))$. Quantitative visualizations are implemented in a tow tank using velocimetry measurements (PIV); models including cubes and spheres are submerged in a highly viscous Newtonian fluid (silicon oil, 5000x viscosity of water). Here, we discuss wall effects on velocity profiles in the near- and far-field surrounding such objects. Moreover, we interrogate the influence of the free surface of the tank on the resulting viscous flow fields. The present experimental setup offers a versatile framework to investigate a wide range of fundamental fluid mechanical problems relating flows at low Reynolds number.   

Transition from Hele-Shaw Flow to 2-D Creeping Flow

In the Hele-Shaw experimental technique, liquid flows at very low Reynolds number through the narrow gap $b$ between parallel plates. When a body is inserted between the plates, and dye is introduced upstream, the streaklines appear nearly identical to streamlines of steady 2-D potential flow over a body of the same shape. For example, Hele-Shaw flow does not separate at sharp corners, just like potential flow. However, if the plates are very far apart (large $b$), the resulting creeping flow at the same low Reynolds number is observed to separate at sharp corners, unlike potential flow. Here, we investigate how the flow changes from Hele-Shaw flow (small $b$) to 2-D creeping flow (large $b$). Low Reynolds number CFD simulations of a fence of height $s$ along a wall in a channel reveal that the transition from Hele-Shaw flow to 2-D creeping flow is not sudden, but rather quite gradual as channel gap width is increased. Separation bubbles appear at small $b$/$s$, and grow in size as $b$/$s$ increases. The reattachment length reaches 1{\%} of the 2-D value at $b$/$s \approx 0.21$, but it does not reach 99{\%} of the 2-D value until $b$/$s \approx 150$. Furthermore, for all values of $b$/$s$ for which separation and reattachment are observed, even for large $b$/$s$ ($>$ 100), the reattachment length of the separation bubble is non-uniform across the span; it starts high, dips to a minimum, and then slowly rises, reaching 99{\%} of the center plane value beyond about 15$s$ to 20$s$ from the wall.   

Three-dimensional corner flows in microchannels

We study, by means of three-dimensional numerical simulations and analytical investigations, low Reynolds number fluid flows in rectangular micro-channels that present sharp angles, bends or curved boundaries. These flows are characterized by the generation of secondary streamwise vorticity, adjacent to the boundary, whose intensity is related to the rate of change of the curvature of the boundary (Balsa, 1998). We also study how this not well-known, yet relevant phenomenon affects the transport of scalar quantities at the boundary.   

Exchange flows in the low Reynolds number flow limit

We analyze the viscous gravity current that occurs when two fluids with different densities flow into each other in a two-dimensional channel. Assuming that the mixing between them and the surface tension at their interface are negligible, we study the flow within the lubrication approximation. For the general case of two fluids with different viscosities and in the presence of an imposed flow rate, the evolution of the current can be described by a single nonlinear PDE. When the mean flow rate is zero (closed channel) the model admits self-similar solutions for the thickness of the gravity current and solutions are obtained for different viscosity ratios. We also present numerical solutions for the gravity current in the cases of a non-zero imposed flow rate (open channel).   

Balancing a ball on a moving vertical wall covered in viscous fluid

We present the results of experimental investigations into balancing heavy balls and cylinders on a vertical moving wall using a thin layer of viscous fluid. It is found that balance can be achieved over a very narrow range of speeds and the critical speed for fixed point behavior scales with the surface area of the cylinders and spheres. Surprising data collapse is achieved using the density of the particles.   

Visualization of Internal Flows with Pressure Oscillation and Surface Modification

A Stirling engine's displacer piston causes motion in its working fluid that exposes the fluid to pressure oscillations that directly impact flow behavior. Stirling engines are highly efficient external combustion engines that are often used in renewable energy applications and have been identified for use on near space platforms as auxiliary power units. The goal of this study was to identify the basic structures of the transient flow field within the expansion cylinder of a Stirling engine without the added complications introduced by convective heat transfer. A two-dimensional representation of the flow within the expansion cylinder of a Stirling engine was produced using an optically-accessible piston-enclosure configuration. The transient flow field within the enclosure was visualized using a rheoscopic fluid. The Reynolds number, based on the frequency of the piston oscillation and the stroke length, was varied from 1.74 to 9.05. Several transient flow structures are identified and the impact that an array of triangular fins has on these flow structures will be discussed.   

Axisymmetric Ice Shelf Dynamics

West Antarctica is composed principally of marine ice sheets, in which the mainland (grounded) ice sheet extends over the coastline as a floating ice shelf. Fed by snowfall far upstream, these sheets transport ice from the grounded component, over the grounding line, where the ice shelf lifts off, and into the ice shelf, which ultimately calves and adds water to the ocean. An idealized two-dimensional ice shelf has no dynamical influence on the grounded ice sheet or the position of the grounding line. However, horizontal stresses within a three-dimensional ice shelf, caused for example by ice rises or the lateral walls of a bay, can help fix the grounding line and prevent it from receding. This study investigates theoretically and experimentally the dynamics of an idealized three-dimensional ice shelf which flows radially from a point source, to elucidate the controlling influence of circumferential stresses within the shelf.   

A fully 3D experimental and theoretical study of flow patterns and Lagrangian trajectories generated by spinning bent rods in viscous fluids

The fluid motion induced by spinning cilia is fundamental to many living organisms. Under some circumstances it is appropriate to approximate cilia as rigid bent rods. We study the effects of shape and orientation of these idealized cilia upon flow structures in a Stokes fluid. By utilizing slender body theory and image method, an asymptotic solution is constructed for a slender body attached to a no-slip flat plane and rotating about its base sweeping out a cone. Using 3D stereoscopic projection in a table-top experiment we explore the complex flow structures and present quantified comparisons with the theoretical predictions. Intriguing short, intermediate and long time phenomena of particle trajectories are documented, and the intricacies of their theoretical modeling reported.   

A higher-order Hele-Shaw approximation for micro-channel flows

The classic hydrodynamic Hele-Shaw problem is revisited in the context of evaluating the viscous resistance to low-Mach compressible gas flows through shallow non-uniform microfluidic configurations (whose depths are small in comparison with all other characteristic dimensions). Earlier calculations have demonstrated that failure to satisfy the no-slip condition at the channel lateral walls severely restricts the applicability of the resulting approximation. To overcome this we have extended the calculation to incorporate an inner solution in the vicinity of the side walls (which, in turn, allows for the characterization of the effects of non-rectangular channel cross sections) and its matching to an outer correction. Comparison with finite-element simulations demonstrates a remarkably improved accuracy relative to the leading-order Hele-Shaw approximation. This suggests the present scheme as a useful alternative for the rapid performance estimate of microfluidic devices.   

Acoustic Droplet Vaporization through PDMS

Acoustic droplet vaporization (ADV) involves the generation of bubbles from albumin-encapsulated perfluorocarbon (PFC) droplets that have been insonated with high intensity ultrasound (US). Gas embolotherapy, utilizing ADV, may facilitate occlusion of blood flow in the vasculature as bubbles undergo volume expansion of up to 125 times. Cancer therapy could benefit from such occlusions through starvation of the tumor. In order to visualize the detailed mechanics of vaporization and expansion process of the PFC droplets, idealized microvessels were constructed using polydimethylsiloxane (PDMS) channels. Microchannels (20 micron diameter) were fabricated using PDMS with polymer-crosslinker mixing ratios ranging from 5:1 to 20:1. Droplets were introduced into the channels and exposed to US for vaporization. Mixing ratios were observed to impact the impedance matching at the water-PDMS interface, which affected the threshold for ADV. The threshold was lowest for mixing ratios of 5:1 and 20:1, and greatest for 9:1. Final bubble volumes were compared with a computational model by Ye {\&} Bull and were found to be consistent. This work is supported by NIH grant R01EB006476.   

Session GS: Geophysical: Oceanographic II

Double Trouble: Internal Tide Attractors in Double Ridge Systems

A theoretical and experimental study is presented of the generation of internal tides by barotropic tidal flow over topography in the shape of a double ridge. A one-dimensional map is constructed that allows one to track the ray paths of waves reflecting between the ocean surface and topography, and this device is used to expedite the search for internal tide attractors between the ridges, these being attracting, closed ray paths. Calculations are then presented for the steady state scattering of internal tides from the barotropic tide. When attractors are present, these computations break down unless dissipation is also incorporated into the problem, in which case there is significantly enhanced energy conversion in the presence of attractors. We conclude with a direct comparison between theoretical predictions and the results of a laboratory experiment, as well as possible applications to geophysical locations.   

Low-mode internal tide generation by topography: an experimental and numerical investigation

We summarize recently published work (J.~Fluid Mech.) and analyze the low-mode structure of internal tides generated in laboratory experiments and numerical simulations by a two- dimensional ridge in a channel of finite depth. The height of the ridge is approximately half of the channel depth and the regimes considered span sub- to super-critical topography. For small tidal excursions, on the order of 1\% of the topographic width, our results agree well with linear theory. For larger tidal excursions, up to 15\% of the topographic width, we find that the scaled mode one conversion rate decreases by less than 15\%, in spite of nonlinear phenomena that break-down the familiar wave-beam structure and generate harmonics and inter- harmonics. Modes two and three, however, are more strongly affected. For this topographic configuration most of the linear baroclinic energy flux is associated with the mode-1 tide, so our experiments reveal that nonlinear behavior does not significantly affect the barotropic to baroclinic energy conversion in this regime, which is relevant to large scale ocean ridges. This may not be the case, however, for smaller scale ridges that generate a response dominated by higher modes.   

A numerical study of oscillatory two-layer stratified flow over three-dimensional topography

A fully-nonlinear numerical model of two-layer stratified flow over three-dimensional topography is used to investigate the generation and propagation of interfacial waves by steady as well as oscillatory flows. Quantitative comparisons of the simulation results are made with shallow-water and weakly nonlinear theories. Qualitative comparisons are made with laboratory experiments and ocean observations.   

Tidal flow over 3D topography generates out-of-forcing plane harmonics

About 1 TW of mixing energy in the ocean comes from internal waves generated by tidal flow over bottom topography [1]. The generation of these waves in three dimensions (3D) remains poorly understood. We use a 3D axisymmetric Gaussian mountain as a model topographic feature and obtain numerical and experimental results for the internal wave field generated by tidal flow. The experiments use a model mountain in a 200 L tank, and particle image velocimetry for imaging. The numerical methods are the same as those in [2], and utilize a finite volume scheme to evaluate the 3D internal wave field. The stratification and forcing frequency are chosen such that 2$\omega <$ N (N is the buoyancy frequency), allowing the propagation of second harmonics. Surprisingly, when the maximum topographic slope exceeds the slope of second harmonic wave propagation, strong second harmonics are generated in the direction perpendicular to the tidal forcing direction. At high forcing amplitude, these harmonic waves have higher amplitude than the in-forcing-plane harmonics. \\[4pt] [1] W. Munk and C. Wunsch, Deep-Sea Res. I \textbf{45}, 1977 (1998)\\[0pt] [2] B. King, H. P. Zhang, and H. L. Swinney. Submitted to Phys. Fluids   

The phase lead of shear stress in shallow-water flow over a perturbed bottom

Analysis of the flow over a slowly perturbed bottom (when perturbations have a typical length scale much larger than water height) is often based on the shallow-water (or Saint-Venant) equations, with the addition of a wall-friction term which is a local function of the mean velocity. By this choice small sinusoidal disturbances of wall stress and mean velocity are bound to be in phase with each other. In contrast, studies of shorter-scale disturbances have long established that a phase lead develops between wall stress and mean velocity, with a crucial destabilizing effect on sediment transport over an erodible bed. Our purpose here is to calculate the wall-stress phase lead under large-length-scale conditions, using asymptotic matching techniques for turbulent flow. This calculation provides significant corrections to the shallow-water model.   

Hydrodynamic instability and rip current generation

Rip currents are jet-like offshore flows which are part of the horizontal cell circulations originating inside the surf zone. It is generally acknowledged that alongshore variations in the wave field are essential to rip current generation, however, such a variability can arise from a variety of processes. We present here a linear instability analysis and show that the coupling of waves and evolving currents can lead to a positive feedback, generating rip currents in a system initially alongshore uniform. Preliminary results based on a simplified beach profile show that circulations with alongshore spacing of a few hundreds meters can be initiated by the instability on beaches of typical water depth. Qualitative agreements with observations of natural rip currents are obtained. Extension to complex beach bathymetry is made, and some results are discussed.   

Resonant forcing of nonlinear internal waves by a density current released into a two-layer fluid

The propagation of a density current released by a dam break into a fluid with two-layer stratification is a geophysical fluid dynamics problem relevant to the ocean and atmosphere. Analogous to topographic forcing, a transcritical resonance is observed when the speed of the density current falls within a range, $c_l [Preview Abstract]

Sediment wave formation by unstable internal waves in a turbidity current boundary layer

The bedform of sediment that is deposited from turbidity currents onto the ocean floor is often found to exhibit long-wavelength variations, with crest lines perpendicular to the flow direction (``sediment waves''). A temporal stability analysis, based on the 2D Navier--Stokes equations, reveals the presence of unstable internal waves in the bottom boundary layer of a turbidity current. Instability arises from the interaction between the current and the sediment bed, via the competing effects of particle deposition and erosion. Due to the velocity and density variations within the boundary layer, near-stationary internal waves near the bottom may exist under both sub- and supercritical outer flow conditions. Unstable internal waves display long wavelengths and are typically found to slowly travel upstream. Both features are in qualitative agreement with field observations on sediment waves.   

Critical Richardson Numbers in Breaking Internal Waves

The breaking of internal waves is known to be responsible for much of the vertical mixing observed in the ocean, large lakes, and the atmosphere. In order to both correctly model and correctly infer the mixing associated with breaking internal waves, a thorough understanding of the instability mechanism driving these turbulent events is crucial. In this study, a primary indicator of turbulence in stratified flows, the gradient Richardson number (Ri), is examined for internal waves on the verge of instability. We use simultaneous high-resolution scalar (Planar Laser-Induced Fluorescence, PLIF) and velocity (Digital Particle Image Velocimetry, DPIV) measurement techniques to infer the gradient Richardson number of breaking and near-breaking progressive internal waves in a laboratory channel. The results show important deviations from the oft-assumed canonical stability limit of Ri=1/4, which we attribute to the unsteadiness of the internal wave-generated shear driving the instability. Results are compared to inviscid theory based on the normal modes equation. These results have important implications for the diagnosis of turbulent mixing in stratified environments.   

Dissipation Mechanisms of Internal Solitary-like Waves in the Ocean

Internal solitary-like waves (ISWs) are ubiquitous, highly energetic features in the coastal ocean where they are predominately generated by tide-topography interaction. There are many unanswered questions about the generation and fate of these waves and a better understanding of these processes is necessary for developing parameterizations of their effects for use in large scale models. Several sets of observations have suggested that the mixing associated with ISW trains is important for setting the stratification in some regions of the coastal ocean (e.g, the Scotian Shelf and the Portuguese Shelf). This talk will begin with a discussion of the energetics of large amplitude internal waves. I will then discuss three dissipation mechanisms for ISWs and consequences for mixing: instabilities in the bottom boundary layer, the breaking of shoaling waves, and shear instabilities in the pycnocline. Results from 2D numerical simulations will be presented for all three mechanisms, with a focus on shear instabilities. 3D simulations of shear instabilities have recently been initiated. It is hoped that results from these simulations will also be presented.   

Session GT: Vortex Dynamics and Vortex Flows IV

Trajectory of an Elliptic Vortex Ring

An elliptic vortex ring is known to be unstable due to its oscillatory deformation while propagating. It oscillates periodically at low aspect ratios, but deforms and breaks up into two smaller rings at high aspect ratios. Although studies on elliptic vortex rings have been conducted before, certain aspects of the vortex ring behavior remain unclear; in particular the influence of Reynolds number on their trajectories. Moreover, most of the earlier experimental studies were conducted using flow visualization techniques, which provide only qualitative description on the motion of elliptic vortex rings and not their velocity and vorticity fields. In the present investigation, we focus our attention on the vorticity field during various stages of the vortex ring deformation; particularly the effect of Reynolds number and aspect ratio on the vortex ring trajectory. Experiments are conducted in a water tank using elliptic nozzles of aspect ratios 1, 2 and 3. Obviously, the nozzle aspect ratio of 1 represents a circular nozzle, and the results are included here for comparison. Preliminary results show that the trajectory of elliptic vortex ring of aspect ratio 2 is insensitive to changes in the Reynolds numbers, but this is not the case with the aspect ratio 3, where noticeable deviation of the trajectory at lower Reynolds numbers is observed. The cause of this deviation and its implication will be discussed.   

Vortex ring impacting on wall

Three dimensional vortex ring impacting a wall at different angles of incidence has been numerically investigated using the lattice Boltzmann model. The detailed flow behavior, vortex evolution, and pressure distribution on wall have been studied systematically with the Reynolds number of 100 $<$ Re $<$ 1000, and the impact angle of the range of 0\r{ } $< \quad \theta \quad <$ 60\r{ }. Our results show that only when Re $>$ 100, the interaction of the vortex ring with the wall can generates the secondary vortex rings. The evolution of vortex structure is also strongly influenced by $\theta $. The increase of $\theta $ will cause a wrap process of the secondary vortex ring and an obvious suppression of the tertiary vortex ring generation. Further more, the study identified new features of vortex structure and its interaction with wall, in particular, for the oblique impact scenarios. A simple model is adopted to describe the basic characteristics of pressure distribution on the wall along the symmetry vortex ring plane at low Reynolds number.   

Comparison of DNS Determination of the Dynamics of Vortex Rings in Viscous Fluids and Experiment

We have been studying vortex rings in water for some time [1] and recently became aware of an important paper studying vortex rings by direct numerical simulation (DNS) from Coleman's group at Southampton [2]. There is clearly much to be learned from a comparison of the results in [1] and [2]. The first insight is a comparison of slowing vortex rings, where we find quite similar decay rates at comparable Reynolds numbers. A second insight is gained by noting that they find a time t* needs to elapse before the core adjusts to its vorticity distribution. We find photographically that the ring needs to propagate at least one gun diameter before it adjusts its vorticity. A third insight is that the rings in Fig. 5(b) of [2] do not change much in radius, consistent with the results in Table 2 of our paper [1]. The talk will cover more recent comparisons of the two works including observations of the growth of vortex waves.\\[4pt] [1] I. S. Sullivan, J. J. Niemela, R. Hershberger, D. Bolster and R. J. Donnelly, J. Fluid Mech. 609 319 (2008).\\[0pt] [2] P. J. Archer, T. G. Thomas and G. N. Coleman, J. Fluid Mech.598 201 (2008).   

Interaction of the 2D vortex patch with the wall. Eruption of the boundary layer phenomenon.

The boundary layer eruption phenomenon caused by a 2D patch of vorticity moving above a wall was investigated. It was shown that eruption phenomenon depends on the viscosity (or Reynolds number, Re) of the fluid. There exists a threshold value of Re above which the eruption takes place. The initiation of the eruption goes through the creation of a small recirculation zone near the solid wall. For small Re numbers it disappears but for larger it is strongly stretched in the direction perpendicular to the wall. The terminal state is appearance of a saddle point on streamlines inside the recirculation zone. Next this zone is torn off and portion of the fluid particles from the near wall region are abruptly ejected into the other flow. Further increase of the Reynolds number causes more complex flow. One can observe that eruption is regenerative and that the vortex patch can produce a cascade of secondary vortices. The vortex-in-cell method was employed to investigate the eruption phenomenon.   

Local Stability Analysis of Fat Vortex Rings

The stability of fat vortex rings is studied by the geometrical optics method. It is found that Hill's vortex is subject not only to the elliptical instability but also to the curvature instability, which is due to the curvature of vortex tubes and first found for the vortex ring with thin core. A new type of instability is also found; it is a coupled mode of the elliptical and curvature instabilities. The strongest instability is the elliptical instability for a wide area of the vortex, while the coupled instability surpasses the elliptical instability near the surface. The effects of swirl on the instability are investigated. The maximal growth rate becomes small as the magnitude of swirl becomes large.   

DPIV Measurements of Vortex Ring Interaction with Multiple Permeable Screens

Flow visualization of the interaction of a vortex ring impinging on several parallel, transparent permeable screens was made previously for screens with 84{\%} open area ratio. The results indicated the vortex ring split into smaller vortical structures after its interaction with the first screen and exhibited a continuous break down into increasingly irregular flow after interaction with subsequent screens. The flow did not reorganize into a transmitted vortex ring as was observed with vortex rings impinging on a single permeable screen. The present work seeks to provide a more quantitative assessment of the flow through screens using DPIV. DPIV measurements were made using an aqueous solution that was refractive index matched to the transparent screens. Measurements were made for vortex rings interacting with screens with variable spacing and open area ratios of 58{\%}-84{\%}. The vortex rings were generated with a piston-cylinder vortex ring generator using piston stroke-to-diameter ratios of 2-4 and jet Reynolds numbers of 1000-2000. Preliminary results show splitting and decay of the flow vorticity in agreement with the flow visualization.   

Stability of relative equilibria of three vortices

Three point vortices on the unbounded plane have relative equilibria wherein the vortices either form an equilateral triangle or are collinear. While the stability analysis of the equilateral triangle configurations is straightforward, that of the collinear relative equilibria is considerably more involved. The only comprehensive analysis available in the literature, by Tavantzis \& Ting [{\it Phys. Fluids}, {\bf 31}, 1392 (1988)], is not easy to follow nor is it very physically intuitive. The symmetry between the three vortices is lost in this analysis. A different analysis is given based on explicit formulae for the three eigenvalues determining the stability, including a new formula for the angular velocity of rotation of a collinear relative equilibrium. A graphical representation of the space of vortex circulations is introduced, and the resultants between various polynomials that enter the problem are used. This approach adds considerable transparency to the solution of the stability problem and provides more physical understanding. The main results are summarized in a diagram that gives both the stability or instability of the various collinear relative equilibria and their sense of rotation.   

Remarks on Continuation of Inviscid Vortex Flows in the Presence of the Kutta Condition

Our investigation concerns solutions of the steady--state Euler equations in two dimensions featuring finite--area regions with constant vorticity embedded in a potential flow. Using elementary methods of the functional analysis we derive precise conditions under which such solutions can be uniquely continued with respect to their parameters, valid also in the presence of the Kutta condition concerning a fixed separation point. Our approach is based on the Implicit Function Theorem and perturbation equations derived using shape--differentiation methods. These theoretical results are illustrated with careful numerical computations carried out using the Steklov--Poincar\'e method which show the existence of a global manifold of solutions connecting the point vortex and the Prandtl--Batchelor solution, each of which satisfies the Kutta condition.   

Reynolds number effects on the dynamics of the turbulent horseshoe vortex: High resolution experiments and numerical simulations

Turbulent flows past wall-mounted obstacles are dominated by dynamically rich, slowly evolving coherent structures producing most of the turbulence in the junction region. Numerical simulations [Paik et al., \textit{Phys. of Fluids} 2007] elucidated the large-scale instabilities but important questions still remain unexplored. One such question is with regard to the effect of the Reynolds number on the dynamics of the turbulent horseshoe vortex (THV). We carry out high-resolution laboratory experiments for the flow past a wall mounted cylinder in a laboratory water tunnel for Re$_{D}$= 26000, 48000 and 117000. We employ the Time-Resolved Particle Image Velocimetry technique to resolve the dynamics of the flow at the symmetry plane of the cylinder and analyze the instantaneous velocity fields using the Proper Orthogonal Decomposition technique. The experimental study is integrated with coherent-structure-resolving numerical simulations providing the first comprehensive investigation of Reynolds number effects on the dynamics of the THV.   

Session GU: Granular IV

Collective dynamics of floaters on a Faraday wave

The dynamics of particles floating on a standing Faraday wave is studied experimentally. For low particle concentration it was shown [G. Falkovich et al. Nature 435, 1045 (2005)] that non-wetting particles accumulate at the antinodes of the standing wave. This was found to be a single particle effect. Here, we study what happens when the particle concentration is increased: Surprisingly, we observe that the same particles that cluster at the antinodes for low particle concentration move to the nodes for high concentrations. The explanation of this effect lies in the collective, attractive capillary interaction among particles which counteracts the tendency of the particles to move toward the antinodes. The transition between the two regimes is studied as a function of the concentration and is found to exhibit extremely long transients.   

Coarsening of Faraday Heaps: Experiment, Simulation, and Theory

When a layer of granular material is vertically shaken, the surface spontaneously breaks up in a landscape of small Faraday heaps that merge into larger ones on an ever increasing timescale. This coarsening process is studied in a linear setup, for which the average lifetime of the transient state with $N$ Faraday heaps is shown to scale as $N^{-3}$. We describe this process by a set of differential equations for the peak positions; the calculated evolution of the landscape is in excellent agreement with both the experiments and simulations. The same model explains the observational fact that the number of heaps towards the end of the process decreases approximately as $N(t) \propto t^{-1/2}$.   

Granular compaction under confinement

We report on experiments that explore the impact of confinement on a compacting granular system. When a granular pack is subjected to successive vertical vibrations it undergoes a slow compaction process as individual grains rearrange and pack more closely together. We control the position and applied force of a confining boundary at the top surface of the granular system during these vibrations. This confinement limits the amount of dilation that occurs during the vibrations and significantly reduces the rate of compaction in comparison to the same system with a free top surface.   

Shocks and Patterns in Continuum Simulations of Oscillated Granular Layers

We study interactions between shocks and standing wave patterns in continuum simulations of vertically oscillated granular layers. Layers of grains atop a plate with sinusoidal oscillations in the vertical direction leave the plate at some time during the cycle if the accelerational amplitude of oscillation is greater than the acceleration of gravity. Above a critical acceleration, standing waves form stripe patterns. In these same shaken layers, shocks are produced when layers collide with the plate after leaving the plate earlier in the cycle. We simulate vertically shaken layers using numerical solutions of continuum equations to Navier-Stokes order to find number density, average velocity, and granular temperature as functions of time and location within the cell. We compare shocks and standing waves coexisting in this system; pressure gradients produced by shocks play a significant role in the formation of standing wave patterns.   

Measurement of Density Fluctuations in a Vertically Oscillated Granular Bed at the Onset of Vibrofluidization

The transition from solid- to liquid-like behavior in vertically oscillated granular media is probed through measurements of density fluctuations near the point of vibrofluidization. The intracycle dynamics are used to define the critical vibration acceleration required for vibrofluidization in deep beds. Clear successive shock waves are formed, and the resulting density fluctuations initiated near the free surface propagate downward with increasing energy. When ``heating'' the bed by vibration, ``melting'' begins at the free surface.   

Comparison of two quadrature-based moment methods for simulating dilute granular gases

A dilute non-isothermal inelastic granular gas between two stationary Maxwellian walls is studied by means of numerical simulations of the Boltzmann kinetic equation with a hard-sphere collision kernel for mono-dispersed particles. Two types of quadrature-based moment methods with different orders of accuracy in terms of the moments of the distribution function are used with four different inelastic collision models. The models differ in the manner with which the moment equations are closed and in the number of moments that can be controlled for a given number of quadrature points. Results from the kinetic models are compared with the predictions of molecular dynamics simulations of a nearly equivalent system.   

Experimental measurement of the stress tensor in a granular gas

We study a quasi-2D granular gas that is vertically vibrated. Precision particle tracking from video at 60 kHz allows us to accurately measure the momentum transfer from individual collisions as well as from particle motion. This allows experimental measurement of the stress tensor. The time averaged stress shows good agreement with the requirement of hydrostatic balance, indicating that we are adequately resolving the stress. Time resolved measurements of the collisional stress show the serrated structure that appears in the shock waves in this system. These measurements allow direct evaluation of the constitutive equation for stress used in hydrodynamic models.   

A quadrature-based kinetic model for a dilute non-isothermal granular gas

A dilute non-isothermal inelastic granular gas between two stationary Maxwellian walls is studied by means of numerical simulations of the Boltzmann kinetic equation with hard-sphere collisions. The behavior of a granular gas in these conditions is influenced by the thickness of the wall Knudsen layer: if its thickness is not negligible, the traditional description based on the Navier-Stokes-Fourier equations is invalid, and it is necessary to account for the presence of rarefaction effects using high-order solutions of the Boltzmann equation. The system is described by solving the full Boltzmann equation using a quadrature-based moment method (QMOM), with different orders of accuracy in terms of the moments of the distribution function, considering moments up to the seventh order. Four different inelastic collision models (BGK, ES-BGK, Maxwell hard-sphere, Boltzmann hard-sphere) are employed. QMOM results are compared with the predictions of molecular dynamics (MD) simulations of a nearly equivalent system with finite-size particles, showing the agreement of constitutive quantities such as heat flux and stress tensor.   

The effect of finite container size on granular jet formation

When an object is dropped into a bed of fine, loosely packed sand, a surprisingly energetic jet shoots out of the bed. In this work we study the effect that boundaries have on the granular jet formation. We did this by (i) decreasing the depth of the sand bed and (ii) reducing the container diameter to only a few ball diameters. These confinements change the behavior of the ball inside the bed, the void collapse, and the resulting jet height and shape. From these results we propose a new explanation for the thick-thin structure observed experimentally and reported previously.   

Session GV: Swimming II

Repeatability of arm pull patterns in front crawl swimming

The arm pull in human swimming has seen extensive study, particularly involving the front crawl stroke. This work has primarily been aimed either at clarifying the mechanisms of thrust generation by the arm and hand, or at comparing the relative performance of different canonical pulling patterns. In this work we investigate the degree to which swimmers adjust their arm and hand trajectories in response to instantaneous ambient conditions. Video imaging data from competitive swimmers indicates that there may be wide stroke-to-stroke variations in pull trajectories. This suggests that optimal stroking form may be less about a swimmer's ability to repeat idealized pull patterns, than about the swimmer's ability to respond to local flow conditions, or what is referred to in the swimming vernacular as the ``feel'' for the water.   

Dynamics of wake structure in clapping propulsion

Some animals such as insects and frogs use a pair of symmetric flaps for locomotion. In some cases, these flappers operate in close proximity or even touch each other. In order to understand the underlying physics of these kinds of motion, we have studied the wake structures induced by clapping and their associated thrust performance. A simple mechanical model with two acrylic plates was used to simulate the power stroke of the clapping motion and three-dimensional flow fields were obtained using defocusing digital particle image velocimetry. Our studies show that the process of vortex connection plays a critical role in forming a downstream closed vortex loop. Under some kinematic conditions, this vortex loop changes its shape dynamically, which is analogous to the process of an elliptical vortex ring switching its minor and major axis. As the length of the plate along the rotating shaft decreases to change an aspect ratio, the downstream motion of the vortex is retarded due to the outward motion of side edge vortices and less propulsive force is generated per the surface area of the plate. The impact of compliance and stroke angle of the plate on wake structures and thrust magnitudes are also presented.   

Can drag and thrust be separated in undulatory swimming?

Aquatic organisms are motivating new biomimetic underwater vehicles. To that end it is essential to obtain the swimming velocity and efficiency of organisms using reduced order models. The swimming velocity is often determined by equating the drag and thrust on swimming bodies. This has led to many conflicting results in the past. It has been proposed that one of the root causes of the disagreements is that, in general, drag and thrust on swimming bodies can not be separated from each other. This is considered to be true when movement is generated by undulations as in anguilliform, gymnotiform, and balistiform modes of swimming, among others. We did high-resolution numerical simulations to study the forces acting on the undulatory ribbon fin of a gymnotiform swimmer -- the black ghost knifefish. In spite of the above expectations, we have surprisingly found a new way to approximately decompose the net force into drag and thrust producing mechanisms in undulatory swimming modes. Such decomposition is unexpected for non-linear finite Reynolds number problems. This result appears conceptually analogous to how a linearization of the Navier--Stokes equations, or Carrier's equation, captures the drag-determining features of the flow around objects.   

The effects of fluid viscosity on undulating swimmers

The swimming behavior of the nematode \emph{C. elegans} ($L\approx$~1 mm) as a function of the surrounding fluid viscosity $\mu$ is investigated using both particle- and nematode-tracking methods. Nematode tracking data show that \emph{C. elegans} move in a highly periodic fashion characterized by traveling waves. The nematode swimming speed $U$ decays nonlinearly with increasing fluid viscosity such that $U\sim \mu^{-0.2}$. Velocimetry data shows flow re- circulation regions along the nematode's body. The velocity profiles measured in the direction normal to the swimming nematode show a decay that is similar for fluid viscosities ranging from from 1 cP to 20 cP. The normalized velocity decays follow a single mater curve with $d/L$ as the independent variable, where $d$ is the normal distance from the swimming nematode. This result suggests that \emph{C. elegans} may be a good canditate to investigate low Re locomotion.   

High speed x-ray observation of a sand swimming lizard

We use high-speed x-ray imaging to reveal how a small (10~cm) desert dwelling lizard, the sandfish ({\em Scincus scincus}), swims within a granular medium, and how its locomotion is affected by the volume fraction $\phi$ of the media~\footnote{Maladen et. al, Science, {\bf 325}, 314, 2009}. We use an air fluidized bed to prepare 0.3~mm glass beads (similar in size to desert sand) into naturally occurring loose ($\phi=0.58$) and close ($\phi=0.62$) packed states. On the surface, the lizard uses a standard diagonal gait, but once below the surface, the organism no longer uses limbs for propulsion. Instead it propagates a large amplitude single period sinusoidal traveling wave down its body and tail to propel itself at speeds up to $\approx 1$ body-length/sec. For fixed $\phi$ the animal increases forward swimming speed $v_f$ by increasing temporal frequency $f$. For fixed $f$, $v_f$ is independent of $\phi$, despite resistance forces that nearly double from loose to close packed states. Surprisingly, the greatest sandfish velocity (and $f$) occur in the close packed state.   

Resistive force theory for sand swimming

We discuss a resistive force theory~\footnote{Maladen et. al, Science, \textbf{325}, 314, 2009} that predicts the ratio of forward speed to wave speed (wave efficiency, $\eta$) of the sandfish lizard as it swims in granular media of varying volume fraction $\phi$ using a sinusoidal traveling wave body motion. In experiment $\eta\approx0.5$ independent of $\phi$ and is intermediate between $\eta \approx 0.2$ for low $Re$ Newtonian fluid undulatory swimmers like nematodes and $\eta \approx 0.9$ for undulatory locomotion on a deformable surface. To predict $\eta$ in granular media, we developed a resistive force model which balances thrust and drag force over the animal profile. We approximate the drag forces by measuring the force on a cylinder (a ``segment'' of the sandfish) oriented at different angles relative to the displacement direction. The model correctly predicts that $\eta$ is independent of $\phi$ because the ratio of thrust to drag is independent of $\phi$. The thrust component of the drag force is relatively larger in granular media than in low $Re$ fluids, which explains why $\eta$ in frictional granular media is greater than in viscous fluids.   

Sandfish numerical model reveals optimal swimming in sand

Motivated by experiment and theory examining the undulatory swimming of the sandfish lizard within granular media~\footnote{Maladen et. al, Science, \textbf{325}, 314, 2009}, we study a numerical model of the sandfish as it swims within a validated soft sphere Molecular Dynamics granular media simulation. We hypothesize that features of its morphology and undulatory kinematics, and the granular media contribute to effective sand swimming. Our results agree with a resistive force model of the sandfish and show that speed and transport cost are optimized at a ratio of wave amplitude to wavelength of $\approx0.2$, irrespective of media properties and preparation. At this ratio, the entry of the animal into the media is fastest at an angle of $\approx20^{\circ}$, close to the angle of repose. We also find that the sandfish cross-sectional body shape reduces motion induced buoyancy within the granular media and that wave efficiency is sensitive to body-particle friction but independent of particle-particle friction.   

No slip locomotion of hatchling sea turtles on granular media

Sea turtle locomotion occurs predominantly in aquatic environments. However after hatching from a nest on a beach, the juvenile turtles (hatchlings), must run across several hundred meters of granular media to reach the water. To discover how these organisms use aquatically adapted limbs for effective locomotion on sand, we use high speed infrared video to record hatchling Loggerhead sea turtles (\textit{Caretta caretta}) kinematics in a field site on Jekyll Island, GA, USA. A portable fluidized bed trackway allows variation of the properties of the granular bed including volume fraction and angle up to the angle of repose. Despite being adapted for life in water, on all treatments the turtles use strategies similar to terrestrial organisms when moving on sand. Speeds up to 3 BL/sec are generated not by paddling in sand, but by limb movement that minimizes slip of the flippers, thus maintaining force below the yield stress of the medium. We predict turtle speed using a model which incorporates the yield stress of the granular medium as a function of surface angle.   

Tree-inspired Piezoelectric Energy Harvesting

We design and build a tabletop wind energy harvester inspired by the swaying of trees. The device consists of cantilevered cylinders (``tree trunks'') arranged linearly downwind. The bases of the cylinders contain piezoelectric transducers that capture energy from vibration of the cylinder transverse to the flow. For a particular Reynolds number, and ratio of vortex shedding frequency to cylinder natural frequency, we experimentally measure the power generated ($\sim $ 1 micro-watt) as a function of cylinder arrangement. We report optimal spacings for generating peak power. We also report the distribution of power down the array. We qualitatively account for these trends using flow visualizations of vortex shedding using a flowing soap film dynamically matched with our piezoelectric system.   

Flow energy harvesting -- another application of the biomimetic flapping foils

Imitating fish fins and insect wings, flapping foils are usually used for biomimetic propulsion. Theoretical studies and experiments have demonstrated that through specific combinations of heaving and pitching motions, these foils can also extract energy from incoming wind or current. Compared with conventional flow energy harvesting devices based upon rotating turbines, this novel design promises mitigated impact upon the environment. To achieve the required motions, existing studies focus on hydrodynamic mode coupling, in which a periodic pitching motion is activated and a heaving motion is then generated by the oscillating lifting force. Energy extraction is achieved through a damper in the heaving direction (representing the generator). This design involves a complicated control and activation system. In addition, there is always the possibility that the energy required to activate the system exceeds the energy recovered by the generator. We have discovered that a much simpler device without activation, a 2DOF foil mounted on a rotational spring and a damper undergoing flow-induced motions can achieve stable flow energy harvesting. Using Navier-Stokes simulations we predicted different behaviors of the system during flow-induced vibrations and identified the specific requirements to achieve controllable periodic motions essential for stable energy harvesting. The energy harvesting capacity and efficiency were also determined.   

Session GW: Mini-Symposium on Fluid Dynamics at Super-repellent Surfaces

Unusual dynamical properties of water repellent materials

The reason why water repellent materials have been attracting such an attention for about ten years is mainly related to the remarkable dynamical properties they generate. Paradoxically, apart from the question of slip on such surfaces, only a few quantitative studies were devoted to these properties. In our talk, we plan to describe different ways of reaching superhydrophobicity, by texturing the underlying solid or the deposited liquid, or by heating the substrate. Then we list and describe the different specific dynamical behaviours which are observed, such as ultra-low hysteresis, (fast) running, bouncing or self-motion   

Drag reduction in laminar and turbulent flows past superhydrophobic surfaces

A series of experiments and direct numerical simulations (DNS) will be presented which demonstrate significant drag reduction for both laminar and turbulent flows of water through channels using superhydrophobic surfaces with well-defined micron-sized surface roughness. The surfaces are fabricated from PDMS to incorporate precise patterns of ridges or posts that can support a shear-free air-water interface. A flow cell is used to measure the pressure drop and velocity profile as a function of the flow rate for a series of channel geometries and superhydrophobic surface designs. DNS are performed for flow past superhydrophobic surfaces which both complement and extend the range of geometries and Reynolds number obtained in the experiments. We will show that drag reductions up to 75\% and slip lengths up to 150$\mu$m can be obtained in turbulent flows past superhydrophobic surfaces. Additionally, we will show that slip along the air water interface forestalls the transition from laminar to turbulent flow. The drag reduction is found to increases with increasing post/ridge spacing and the fraction of air-water interface. In turbulent flows, the drag reduction increases with Reynolds number before eventually reaching a plateau. These results suggest that in turbulent flows, the drag reduction scales with the thickness of the viscous sublayer and not the overall channel height as in laminar flows.   

Controlling inertia dominated flows with super-repellent surfaces

The possibility to affect liquid flows through surface properties was naturally put forward by the recent emergence of small-scales fluidic devices, as downsizing invariably emphasizes the role of surfaces, with respect to bulk properties. Such strategy of flow modification by surface effects is \textit{a priori} restricted to the natural scales setting the interactions between the surface and the nearby liquid that is, essentially to nanometric scales. In this context, super-repellent surfaces have emerged as possessing not only remarkable (non-)wetting properties but also unique dynamical properties. The latter manifest on their ability to promote large boundary slippage, characterized by slip lengths from 1 to hundreds of microns, that make them capable of modifying flows up such micro-scales. More fundamentally, this raises the question of how far this strategy of flow control through surfaces can be pushed, and of how deep the modification of liquid flows close to super-repellent surface is: can it persist at large scales or large velocities? After briefly going through the properties of super-repellent surfaces in laminar viscous flows, I will discuss their impact on different macro-scale experimental configurations involving inertia-dominated flows. Focusing on splashing and dripping phenomena - the latter being associated to the well-known teapot effect- I will show that although surface effects are usually ignored in such situations, in view of the large values of the Weber number, it is still possible to shape the liquid flows by tailoring surface properties, with optimized effects obtained for super-repellent surfaces.   

Promoting Giant Liquid Slip on Omniphobic Surfaces with Re-entrant Textures

It is now well-known that by controlling the surface chemistry and topographic details of a textured surface one can generate composite air-liquid-solid interfaces or ``Cassie-Baxter states.'' If the surface topography becomes \textit{re-entrant} (i.e. multi-valued) and very low surface energy coatings are employed, then it becomes possible to create superoleophobic surfaces that are not wetted even by low-tension liquids such as oils and alcohols. Such robustly liquid-repellent (or \textit{omniphobic}) surfaces lead to very high apparent contact angles, low contact angle hysteresis and the possibility of ``giant liquid slip'' over the microscopic air pockets or ``plastron film'' trapped in the re-entrant textured surface. Lithographic fabrication approaches have been proposed for developing such re-entrant textured surfaces - a major challenge with such approaches is to develop viable manufacturing protocols that can be readily extended to larger areas. In the present work we use periodic woven fiber meshes of controlled feature size and weave, coupled with a simple elastomeric fluoropolymer dipcoating protocol, to prepare a series of model re-entrant and friction-reducing surfaces. We use parallel-plate rheometry to explore the degree of friction reduction that can be achieved as the geometric details of the meshes are varied and compare the experimental results with recent scaling theories. Apparent slip lengths of greater than 500$\mu$m are observed for optimal textures and coatings. By varying the thickness and viscosity of the sheared fluid layer, the robustness of the plastron air film to increasing pressure differentials can also be explored in parallel.   

Development of Surface Structures for Large Effective Slip: How Much Slip Is Possible in Ideal, Lab and Real Conditions?

An ideal condition to reduce the drag of a liquid flowing on a solid surface is maintaining a lubricating gas layer between the solid and the liquid. For water flowing on a 1 or 10 $\mu$m-thick air layer, for example, the slip length is calculated to be roughly 50 or 500 $\mu$m, respectively - large enough to benefit a wide range of engineering applications. Unfortunately, however, the above ideal water-levitating condition is only imaginary, because such a liquid-gas meniscus cannot be sustained in nature. Instead, water-repelling structured surfaces bring us closer to the imaginary condition by minimizing the liquid-solid interface and keeping the water mostly on a layer of air. The underlying goal in developing a large-slip surface is, therefore, to create a condition as close as possible to the uniform air lubrication, which is often overlooked. For example, while a large contact angle on a superhydrophobic surface helps keep the liquid fakir, note that once levitated, the contact angle has little effect on increasing the slip length. Instead, the geometrical parameters of the surface structures, e.g., air fraction, pitch and depth of the structures, are the determining factors. A series of development efforts to create surfaces that bring us closer to the ideal air-lubricating condition will be presented, with the slip length currently measured as large as 400 $\mu$m. However, it will be also noted that they are valid only in laboratory conditions, where the sample is fabricated to near perfection and the pressure in the flowing liquid is under strict control. In real-life engineering conditions, which include high and fluctuating pressure, defective surfaces, and liquids full of impurities and particles, it remains to be seen if we will ever be able to create a slip surface that can be field-deployed - a millennium-old dream.