Session PA: Turbulent Boundary Layers: Computational Studies

Application of the Sensitivity Equation Method to Examine Low-Reynolds Number Effects in Turbulent Channel Flow

The sensitivity equation method (SEM) has been implemented in the context of direct numerical simulations of fully-developed turbulent channel flow to explore low Reynolds number effects on the profiles of the mean velocity and Reynolds stresses. Simulations were performed at Reynolds numbers of 100, 150, and 180, based on the friction velocity and channel half-width. In SEM, the governing equations are differentiated with respect to the parameter of interest, in this case the Reynolds number, yielding a set of sensitivity equations, which are subsequently discretized and numerically solved concurrently with the discretized equations for the primitive variables (i.e., velocity and pressure). The present study utilizes a finite-volume, fractional step computational scheme to solve both the governing equations and the sensitivity equations. Turbulent velocity statistics compare very well to others in the literature (Kim et al., 1987; Kuroda et al., 1989). The results from SEM correctly predict the Reynolds number trend in the wall shear stress. The SEM method also provides quantitative information about the rate of change of the mean streamwise velocity profile with respect to Reynolds number. Finally, wall-normal profiles of the higher order moments of the sensitivity of all velocity components were calculated, along with the sensitivity profiles of the Reynolds stresses.   

Theory and numerical computation of the von Karman constant in two-dimensional turbulent flows

We present a calculation of the velocity profile in two-dimensional (2D) turbulent flows. The method is based upon the momentum-transfer theory for the friction factor, proposed by Gioia and Chakraborty, and when fitted to a putative law of the wall profile yields a value for the von K\'{a}rm\'{a}n constant which is in satisfactory agreement with direct numerical simulations at width Reynolds numbers between 20,000 and 80,000. We compare the theoretical results with experimental results on turbulent 2D soap films, taking into account the effects of air resistance. Our findings indicate that the von K\'{a}rm\'{a}n constant in 2D is significantly less than the accepted value in 3D.   

Turbulent pipe flow drag reduction by discrete counter-rotating strips.

Spanwise wall oscillations have been shown to result in as much as 45{\%} drag reduction in turbulent channel flows, as widely reported in the literature. A recent study [Duggleby et al., Phys. Fluids \textbf{19}, 125107 (2007)] has shown that in turbulent pipe flow with $Re_\tau =150$, a 27{\%} increase in mean velocity, corresponding to reduced drag, results when the entire pipe wall is oscillated about the axis of the pipe. In the current study, we show that significant drag reduction still occurs when a series of discrete circumferential strips, placed at finite intervals along the axis of the pipe, are rotating in alternating directions. Results for this new method of drag reduction are presented for a turbulent pipe flow with $Re_\tau =150$. Computations were performed with two separate codes: a finite volume Large Eddy Simulation (LES) code and a spectral element Direct Numerical Solution (DNS) code. Both methods show a flow rate increase of about 10{\%} when the flow is driven by a constant pressure gradient. The effect of strip width and spacing between strips is examined.   

Composite Expansions for Active and Inactive Motions in the Streamwise Reynolds Stress of Turbulent Boundary Layers

Proper scaling of streamwise Reynolds stress in turbulent boundary layers has been controversial for more than a decade as its Reynolds Number dependence can not be removed by normal scaling. One issue that explains the behavior of the streamwise Reynolds stress is that it is affected by both active and inactive motions per Townsend's hypothesis. The goal of this research is to develop a composite expansion for the streamwise Reynolds stress that considers active and inactive motions, explains various Reynolds Number dependencies, and agrees with available data. Data from four sources are evaluated. A new asymptotic representation for the Reynolds shear stress, $<$uv$>$+, that meets the requirements for a proper composite expansion is developed. The streamwise Reynolds stress, $<$uu$>$+, can be separated into active and inactive parts with Reynolds shear stress as the active part. An outer correlation equation with the correct asymptotic limits for the inactive streamwise Reynolds stress is developed and shown to fit the outer $<$uIuI$>$\# data. A separate correlation equation for $<$uIuI$>$\# is developed and fit to data. These two equations form a composite expansion for the inactive streamwise Reynolds stress. This composite expansion can be combined with the + expansion to produce predictions for $<$uu$>$+. Thus a composite expansion for predicting streamwise Reynolds stress in turbulent boundary layers is developed and shown to agree with available data and to explain the Reynolds Number dependence streamwise Reynolds stress.   

DNS of turbulent channel flow subject to a model dynamically rough wall

While there is an extensive literature on the influence of surface roughness on wall turbulence, the influence of a spatially-distributed roughness with a time-varying amplitude, a ``dynamically rough'' wall, has not been so extensively explored. There are fundamentally interesting questions about the influence of a roughness timescale and structured energy addition on the development of the near-wall flow as well as potential applications in flow control for this kind of wall actuation. Results from a Direct Numerical Simulation of a linearized model of dynamic wall roughness in a turbulent channel flow with $Re_{\tau} \sim 500$ are presented. The channel flow DNS of Flores \& Jimenez (2006) was modified to incorporate a time-dependent boundary condition in which the no-slip and impermeability constraints are replaced with a specific temporally-harmonic distribution of streamwise and wall-normal velocities at the wall, which can be considered as a crude linearized approximation to boundary conditions corresponding to dynamic roughness linearized about the turbulent mean velocity profile. It is shown that a global response to this forcing occurs when the first harmonic of the forcing frequency is excited. This work was performed as part of the CTR Summer program 2008. The generosity of Javier Jimenez in allowing the use of the DNS code is gratefully acknowledged.   

A formula for the von K\'arm\'an constant in terms of the flow structure of wall bounded turbulence

We perform Direct Numerical Simulations (DNS) of turbulent channel flows with and without several types of simulated wall activation. These DNS support our theoretical prediction that the von K\'arm\'an constant can be calculated from the formula $1/\kappa = C_s (B_2/B_1^2) \mathcal{D}$ where $B_1$ is the constant of proportionality between the Taylor microscale and the average distance between stagnation points (both of which depend on height from the wall without $B_1$ depending on it in the log-layer), $C_s$ is a number of stagnation points of the fluctuating velocity field at the upper edge of the buffer layer, $B_2$ tends to 1 as $Re_\tau >> 1$ and $ \mathcal{D}$ characterises the anisotropy of the fluctuating velocity field in the log-layer. This formula accounts for the possibility of non-universality of $1/\kappa$ in the sense of Reynolds number and wall-flow type dependencies.   

Entropy generation in a transitioning boundary layer

Insight into entropy generation is a key to increasing efficiency. For viscous wall layers, it is reasonably understood and predictable for laminar and developed turbulent flows. However, results apparently are not yet available for the pointwise entropy generation rate for transitional boundary layers, even for zero pressure gradients, except with an approximate treatment. The present study applies the numerical simulations of Brandt et al. [JFM 2004] to address this deficiency. Predicted spatial distributions are presented for an initial Reynolds number (Uinf,in x delta,star,in/nu) of 300, a length scale (L/delta,star,in) of five and a moderate turbulence level of 4.7 per cent; they are compared to approximate predictions/measurements.   

The structures of the momentum transfer in turbulent channels

We analyze the geometry and the spatial distribution of structures with $-uv > 1.75 u'v'$, in a turbulent channel with $Re_{\tau}=10^3$. Even if they cover less than 10\% of the wall-parallel area, they contribute up to 60\% of the mean Reynolds stresses. Most of them are wall-attached, forming a self-similar family in which the objects lengths and widths are proportional to their heights. They are classified into Q2 ejections ($v>0, u<0$) and Q4 sweeps ($v<0, u>0$), usually forming side by side pairs, several (3--4) of which tend to be aligned in the streamwise direction, with a weak tendency for larger objects to be downstream of smaller ones. While the geometric and spatial characteristics of Q2s and Q4s are very similar, the velocity fields conditioned to them show higher log-layer streaks associated with the Q4s. The streak length decreases when conditioned only to isolated objects, suggesting that the observed very long streaks are due to the streamwise grouping of the pairs. A special class is formed by events with heights of the order of the channel half-width, with ``packets lengths'' of the order of the full simulation domain $(25 h)$. Funded by CICYT.   

Session PB: Turbulence Simulations IV

A robust non-dissipative all-mach number scheme for unstructured grids

We are interested in simulations of high speed external flows, and those in scramjet like geometries (of which supersonic jets in crossflow are an example). We are therefore developing an algorithm that solves the compressible equations on unstructured grids using a predictor-corrector approach, a novel scaling for pressure, and a characteristic filter based shock-capturing. Hou and Mahesh (J. Comp. Phys., vol 205) formulated an all-Mach number approach to solve compressible flows on structured grids, that this work has extended to unstructured grids. The attraction of this method is that the compressible Navier Stokes equations naturally revert to Zero-Mach number equations in the incompressible limit (the discrete energy equation results in the divergence-free condition at zero Mach number), avoiding the stiffness in the equations without preconditioning or artificial compressibility. The shock capturing scheme employed in the present algorithm was developed by Park and Mahesh (AIAA paper, 2007-722) for unstructured grids, and is implemented as a predictor-corrector approach. This ensures that shock-capturing is active only in regions of discontinuity, avoiding any dissipation in regions away from shocks. This feature improves the overall accuracy of the simulations. We will present issues regarding the algorithm, its implementation, and some example results/simulations.   

Numerical simulation of the thermal effect of a laser--induced plasma on isotropic turbulence

The interaction of a laser--induced plasma with isotropic turbulence is studied using numerical simulations. The simulations use air as the working fluid and assume local thermodynamic equilibrium. The numerical method is fully spectral and uses a shock capturing scheme in a corrector step. Turbulent Reynolds number $ Re_\lambda = 30 $ and fluctuation Mach numbers $M_t = 0.001$ and $0.3$ are considered. $M_t$ of $0.001$ is chosen to correspond to low speed experiments (e.g. Comte--Bellot and Corrsin 1971). Here, the shock wave propagates on a much faster time--scale compared to the turbulence evolution. The turbulence ahead of the shock is therefore almost frozen. At $M_t$ of $0.3$ the time--scales of the shock wave are comparable to that of the background. In both cases, the mean flow has a significant effect on the turbulence. The effect of the turbulence on the time scale of shock formation and the shock velocity and distortion is studied. The turbulence experiences strong compression due to the shock wave and strong expansion in the core. Turbulence intensities are enhanced and suppressed due to the effects of compression and expansion respectively. This behavior is spatially inhomogeneous and non--stationary in time. Spatial and one--point temporal statistics are discussed. Also kinetic energy budgets are computed and will be discussed.   

DNS of Decaying Compressible Turbulence Using Gas Kinetic Scheme

We apply the gas-kinetic scheme to direct numerical simulation of decaying compressible turbulence. We compute the kinetic energy $K(t)$, dissipation rate $\varepsilon(t)$, probability density functions (PDFs) of the two-point longitudinal velocity difference, shocklet strength, and local Mach number. Our results reveal the following features of decaying compressible turbulence: (1) With the initial Taylor microscale Reynolds number $\mbox{Re}_\lambda$ fixed, increase of initial turbulent Mach number $\mbox{Ma}_{\rm t}$ leads to an increase of the dissipation rate $\varepsilon$ at the initial stage; (2) Change of $\mbox{Ma}_{\rm t}$ has little effect on $K(t)$ and the long-time asymptotics of $\varepsilon(t)$; (3) At the lower $\mbox{Ma}_{\rm t}$ ($\approx 0.1$), intermittency persists, while at the higher $\mbox{Ma}_{\rm t}$ ($\approx 0.5$), intermittency quickly dissipates, \emph{i.e.}, the PDF of the two-point longitudinal velocity difference becomes Gaussian independent of the separation distance $\delta r$; and (4) the PDF's of both shock strength and the local Mach number all appear to follow scaling laws.   

Direct simulation of a turbulent channel with wire in cross flow

We present results from a direct numerical simulation study of turbulent channel flow across a thin, cylindrical wire. This model mimics flow through the wire-wrapped fuel pins typical of most fast neutron reactor designs. Mean fow develops both along the wire and across the wire, leading to the formation of a turbulent cross-flow regime in the channel. The friction Reynolds number in the axial direction is approximately 303. Cross-flow friction Reynolds numbers ranging from 0 to 115 are examined for several wire-diameter to channel height ratios. The numerical method uses spectral elements in the plane perpendicular to the wire axis and a Fourier decomposition in the direction of the axis of the wire. The simulations use up to 78 million collocation points and were performed at the Argonne Leadership BG/P supercomputer. The flow field statistics are investigated, including mean flow, turbulence statistics and instantaneous flow structures. Shear stress distributions on the walls, and in particular along the recirculation zones behind the wire, are also investigated. Implications of these results for large-eddy simulation of turbulent flows with recirculation will be discussed.   

Lattice Boltzmann and Pseudo-Spectral Methods for Decaying Turbulence

We conduct a comparison of the lattice Boltzmann and the pseudo-spectral methods for DNS of decaying turbulence in a 3D periodic cube. We use a mesh size of $128^3$ and the Taylor micro-scale Reynolds number $24.35 \leq \mbox{Re}_\lambda \leq 72.37$. All simulations are carried out to $t \approx 30 \tau_0$, where $\tau_0$ is the turbulence turnover time. We compare instantaneous velocity $\mathbf{u}$ and vorticity $\mathbf{\omega}$ fields, the energy $K(t)$, the energy spectrum $E(k,\, t)$, the dissipation rate $\varepsilon(t)$, the rms pressure fluctuation $\delta p(t)$, the pressure spectrum $P(k,\, t)$, the skewness, and flatness. Our results show that the LB method compares well with the PS method in terms of accuracy and efficiency: the flow fields and all the statistical quantities, except $\delta p(t)$ and $P(k,\, t)$, obtained from the two methods agree well with each other when the initial flow field is adequately resolved by both methods. Our results indicate that the LB method resolution requirement is $\eta_0 / \delta x \geq 1.0$, where $\eta_0$ and $\delta x$ are the initial Kolmogorov length and the grid spacing, respectively.   

Lagrangian triangle and tetrad statistics in isotropic turbulence

We study the displacement statistics of three- and four-particle clusters extracted from direct numerical simulations of three-dimensional isotropic turbulence at Reynolds numbers ranging from \(R_{\lambda} \approx 240\) to 650. These statistics determine the third and fourth moments, respectively, of scalar concentration fields. Our focus is on the nature of non-Gaussian dynamics expressed via the shape factors \(I_i=g_i/R^2,(i=1,2,3)\) which are defined in terms of the eigenvalues \(g_i\) of the moment-of-inertia tensor and the radius of gyration \(R\), which represents the linear size of the cluster. Shape factors computed from clusters with initial sizes in the inertial sub-range approach constant values at intermediate times. The average values obtained, \(\langle I_1 \rangle \approx 0.83\), \(\langle I_2 \rangle \approx 0.16\) and \(\langle I_3 \rangle \approx 0.015\) for four-particle clusters, are insensitive to Reynolds number in the present data range, possibly indicating an approach to self-similar inertial sub-range behavior. These results differ from their respective Gaussian values of 0.75, 0.22 and 0.03. High-order statistics conditioned on cluster size are used to explore the nature and origins of these departures from Gaussian behavior and guide development of maximum-entropy theories of cluster shape.   

Direct Numerical Simulation of Instabilities in MHD Duct Flows

Magnetohydrodynamics (MHD) --- which governs the flow of an electrically conducting fluid in presence of a magnetic field --- has applications in the steel industry (where magnetic fields are used to damp or to stir the turbulent motions) and in nuclear fusion devices (i.e. tokamaks). There, the liquid lithium, used as coolant, undergoes the effect of the plasma-confining magnetic field. When a magnetic field is applied perpendicularly to a rectangular duct whose walls are electrically conducting, the Lorentz force strongly modifies the the flow and gives rise to an M shaped velocity profile with two strong jets in the vicinity of the walls parallel to the magnetic field. Because of the important shear they generate, those jets are unstable at sufficiently high Reynolds number. Using Direct Numerical Simulations, we compute the critical Reynolds number as a function of the wall conductivity and the strength of the magnetic field. The frequency and form of the corresponding instabilities are also studied. Finally, turbulence statistics and mean velocity profiles in the fully developed regime are discussed.   

Direct and Large-Eddy Simulation of Turbulent Flow in a Plane Asymmetric Diffuser by the Spectral Element Method

Turbulent flow in a plane asymmetric diffuser is simulated by the spectral element method (SEM) as a direct numerical simulation (DNS) and with large-eddy simulation (LES) using an adapted version of the dynamic Smagorinsky model. The SEM, which is a high-order numerical method, has opened the possibility to accurately simulate fluid phenomena known to be very sensitive to numerical discretization errors, e.g. flows exhibiting separation. In addition, SEM exhibits favorable parallelization properties. Due to the development of tools for numerical stabilization specific for SEM, SEM is now suitable for turbulence simulations at moderate to high Reynolds numbers. Results from investigations on the influence of such stabilization tools are presented. For the turbulent diffuser flow case, results are presented for Re=4,500 and Re=9,000 (based on bulk velocity and channel half-height) and compared to results by Herbst et al. (2007). Quantities of interest include e.g. the size of the separation bubble and turbulent stresses.   

Large-eddy simulations of flow around a circulation control airfoil

Circulation control, proposed in NASA's Cruise Efficient Short Take-off and Landing (CESTOL) concept, has the potential to increase air-traffic throughput and reduce the noise footprint. Circulation control obtains a substantial increase in lift coefficient by using a wall-jet that blows tangentially on a rounded (Coanda) surface deflected at the trailing edge. The flow has proven to be difficult to reliably predict using Reynolds-averaged models. We undertake large-eddy simulations to better understand underlying mechanisms and create a database for modelers. Simulations are patterned after Novak et al.'s (1987) experiment, which, despite its faults, is the best documented to date. A Reynolds number of 10\^{}6 and two cases with low and high blowing are considered using Stanford's unstructured solver CDP. The upper surface begins with laminar to turbulent transition following a region of weak shear stress. Then strong favorable pressure gradient as the jet slot is approached leads to a raised log-law. There exists a region over the Coanda surface where the mean flow development collapses very well in wall-jet similarity coordinates, indicating that a portion of the near-wall region maintains classical wall-jet characteristics. At the present time, the lower surface has delayed transition due to lack of tripping in the simulations and considerable discrepancies with the experiments for second-order statistics.   

Session PC: Turbulence Modeling III

Further Analysis of Hybrid-Filtered Navier-Stokes Equations

We have shown that Germano's hybrid-filter approach is both a physically and mathematically correct method of blending the Reynolds-Averaged Navier-Stokes (RANS) and large-eddy simulation (LES). The hybrid-filtered Navier-Stokes (HFNS) equations provides correct behavior in the crossover region via three means: (1) presence of extra terms in the governing equations, (2) presence of a fluctuation-like term in the modeled part of the Reynolds shear stress, and (3) presence of a smooth blending function. In many existing hybrid methods, the governing equations were modified in an {\it ad hoc} manner in order to achieve improved behavior at the RANS-LES crossover. We have shown that such a fix is not necessary in the current approach. For example, our full simulation of HFNS equations showed that the extra terms enhanced the wall-normal transport of resolved turbulence fluctuations, thus alleviating the need for an artificial backscatter-like term. Further investigations of the effects of grid and blending function revealed no evidence of deterioration of the solution upon progressive refinement of the grid, contrary to many conventional hybrid methods. We also found that the blending function -- its magnitude near the wall and its shape in the crossover region -- must be chosen to be consistent with the grid used in these regions. Otherwise, the solution deteriorates, primarily due to its inability to resolve the LES part.   

A poor man's compressible Navier--Stokes equation

We outline derivation of a ``poor man's compressible Navier--Stokes'' (PMCNS) equation, a discrete dynamical system (DDS) extending analyses of McDonough and Huang (Int.\ J.\ Numer. Meth.\ Fluids 44, 545, 2004) for the 2-D incompressible Navier--Stokes (N.--S.) equation to the 3-D compressible counterpart, and we indicate a method for computing bifurcation parameters of the DDS directly from those of the original differential equations, along with known physical parameters such as transport properties. We briefly provide a mathematical characterization of the PMCNS equation, in particular noting an approximate relationship to micro-local analysis of a pseudo-differential operator of the compressible N.--S. equation. We then investigate time series, power spectra and bifurcation diagrams of this DDS for various combinations of bifurcation parameters, including those most closely corresponding to homogeneous, isotropic turbulence; and we present comparisons of PMCNS calculations with extant experimental and DNS compressible flow data. We conclude by discussing application of this discrete dynamical system to construction of subgrid-scale models for LES of compressible flows within a synthetic-velocity/multi-scale framework.   

Assessment of regularization models for LES of high-$Re$ turbulent flows

Regularization-based SGS turbulence models for LES are quantitatively assessed for decaying homogeneous turbulence (DHT) and transition to turbulence for the Taylor-Green vortex (TGV) through comparisons to laboratory measurements and DNS respectively. LES predictions using the Leray-$\alpha$, LANS-$\alpha$, and Clark-$\alpha$ regularization-based SGS models are compared to the classic non-dynamic Smagorinsky model. Regarding the regularization models, this work represents their first application to relatively high $Re$ decaying turbulence with comparison to the active-grid-generated decaying turbulence measurements of Kang {\sl et al.} (JFM, 2003) at $Re_\lambda \approx 720$ and the $Re=3000$ DNS of transition to turbulence in the TGV of Drikakis {\sl et al.} (J. Turb., 2007). For DHT the non-dynamic Smagorinsky model is in excellent agreement with measurements for t.k.e., but higher-order moments show slight discrepancies and for TGV, the energy decay rates agree reasonably well with DNS. Regarding the regularization models stable results are not obtained as compared to Smagorinsky at the same grid resolution for various values of $\alpha$, and at higher resolutions, they are in worse agreement. However, with additional dissipation such as in mixed $\alpha$-Smagorinsky models, results are acceptable, but show slight deviations from Smagorinsky.   

Comparative study of SGS scalar models for LES of turbulent mixing

For LES of applications involving scalar transport and mixing, the smallest scales of the molecular mixing process are unresolved, so understanding the effects of SGS modeling on the resulting concentration fields is particularly important. Comprehensive analyses of the range of modeling approaches for scalar transport and mixing have yet to be conducted. The present objective is to analyze the impact of different modeling approaches on the statistics of the resolved-scale scalar concentration. We perform LES of passive scalar mixing in a turbulent, round jet. The SGS scalar flux term in the scalar transport equation is closed using four different models, including: the dynamic eddy diffusivity and mixed models, the dynamic structure model (Chumakov, 2004) and the multi-fractal model (Burton, 2008). Results are analyzed by comparing mean concentration profiles and scaling, fluctuating quantities at the grid scale, scalar PDFs and spectra, and individual terms in the resolved-scale scalar transport equations. Particular attention is paid to the performance and behavior of SGS scalar models through analyses of model parameters, energy transfer, and structural fidelity.   

Investigation of turbulent transport in hybrid PANS model

Partially Averaged Navier-Stokes (PANS) turbulence method provides a closure model for any degree of velocity field filtering - ranging from completely resolved Direct Numerical Simulation (DNS) to completely averaged Reynolds Averaged Navier-Stokes (RANS) method. The physical closure investigation of PANS presented here is the validation of closure model chosen to describe the transport of the unresolved kinetic energy, k$_{u}$, and unresolved dissipation, $\varepsilon _{u}$, due to the resolved velocity fluctuations. The three models presented are the Zero Transport Model (ZTM), the Maximum Transport Model (MTM) and the Boundary Layer Transport Model (BLTM). In the ZTM it is assumed that the resolved velocity fluctuations do not contribute to the transport of the turbulent quantities. The MTM suggests that the transport of the unresolved scales of the turbulent quantities is proportional to the ratio of the unresolved to total viscosity. The BLTM is developed from the physics of the boundary layer. These models are tested against experimental results for flow past a circular cylinder.   

Assessment of the {\it t}-model as a SGS model for LES of high-$Re$ turbulent flows

The recently developed optimal prediction-based {\it t}-model (PNAS, 2007) is quantitatively assessed as a SGS turbulence model for LES of decaying homogeneous turbulence (DHT) and transition to turbulence for the Taylor-Green vortex (TGV) through comparisons to laboratory measurements and DNS. The {\it t}-model is based on the idea the motion of a vortex at one scale is influenced by the past history of motion of vortices in other scales (``long memory'' effects). {\it t}-model predictions are compared to the classic non-dynamic Smagorinsky model. Regarding the {\it t}-model, this work represents its first application to decaying turbulence with comparison to active-grid-generated decaying turbulence measurements of Kang {\sl et al.} (J. Fluid Mech., 2003) at $Re_\lambda \approx 720$ and $Re=3000$ DNS of transition to turbulence in the TGV of Drikakis {\sl et al.} (J. Turb., 2007). For DHT non-dynamic Smagorinsky is in excellent agreement with measurements for t.k.e. but higher-order moments show slight discrepancies and for TGV, energy decay rates agree reasonably well with DNS. Regarding the {\it t}-model, predictions are worse than Smagorinsky at the same grid resolution due to the insufficient resolution of small scales. Improved results are obtained at higher resolutions, but are still not as good as Smagorinsky.   

Implementation of a Spectral Decomposition of the Boltzmann Equation with the Streaming in the Lattice-Boltzmann Method

Recent developments in mathematics have allowed for the collision process of the Boltzmann equation to be discretized using spectral methods. This new method has the potential for replacing the Bhatnagar-Gross-Krook (BGK) approximation used in approaches such as the lattice-Boltzmann method (LBM). This would end the need for a low Mach approximation to the linearized Boltzmann equation in LBM. This allows solving the full Boltzmann equation and should therefore avoid many of the limitations of current approxima- tions. This paper shows a derivation for the spectral method as well as an implementation for a 2-D and 3-D test cases with results. A simulation of decaying isotropic turbulence is also presented.   

Towards understanding of near wall behavior in two-equation models for supersonic flows

The standard two-equation models over-predict the turbulent viscosity and turbulent kinetic energy in the near wall region for supersonic flows. There are several approaches to tune the model behavior to agree with experimental values. In the present approach we modify C$_{\mu}$ along the lines of Durbin stagnation point correction. The influence of the turbulent Prandtl numbers - $\sigma _{k}$, $\sigma _{\varepsilon}$, $\sigma _{\omega}$-- are also examined.   

Modeling Low Reynolds Number Homogeneous Decaying Turbulence

Very low Reynolds number nearly homogeneous turbulence can occur in the free-stream outside of a turbulent boundary layer. It is also found in nocturnal atmospheric and oceanic boundary layers. Low Reynolds number turbulence represent the interesting situation where the nonlinear terms in the Navier-Stokes equations are weak, and therefore negligible or linearizable, and yet a turbulence model is still required because the initial conditions are unknown and a variety of length scales are still present. This work considers the behavior of two-equation turbulence models in the low Reynolds number limit. It is shown that some models are unstable in this limit and others result in inconsistent or incorrect decay rates. Perhaps most importantly, all current models involve an ad hoc blending function to include the low Re limit. In this work a low Reynolds number correction to classic two-equation models is proposed which requires no blending functions, which obtains the correct decay limits (for any low wavenumber spectra), and which is simple. The performance of the model is compared with a variety of experiments and simulations over a range of Reynolds numbers.   

Session PD: Instabilities in Wakes

Wakes of Self-propelled Bodies in Stratified Fluids

Using high Reynolds number (Re=10$^{4}$-10$^{5})$ experiments, the dynamics of stratified momentum wakes of self-propelled underwater and surface bodies were studied in (i) deep linearly stratified (deep ocean pycnocline), (ii) two layer (shallow pycnocline), and (iii) surface stratified (turbocline) fluids, and theoretical models wee advanced to explain the flow behavior. These models: (i) predict conditions under which submerged wakes signatures penetrate to the water surface, as expressed by the Confinement and Contrast numbers, and (ii) describe IR (infra-red) surface wakes signatures, as expressed by the Contrast and modified Froude numbers. If decaying turbulence is present surrounding the wake, the penetration of wake signature to the surface is still possible. Estimates for typical oceanic cases are given. PIV, LIF and high sensitivity Infrared Imaging cameras were employed for flow diagnostics.   

Dynamic 3-D vortex structure of the laminar separation bubble on SD7003 airfoil

Recent increasing interest in laminar separation bubble (LSB) is aroused by the development of the micro air vehicles (MAVs), which normally cruise in the Reynolds number range of 50,000-200,000. This paper studies the LSB over the SD 7003 airfoil at the angle of attack $\alpha $=4$^{\circ}$ and at \textit{Re}=60,000 using the time-resolved PIV technique. A Nd:Yag laser operated at 1000 Hz and a high speed CMOS camera was synchronized to capture the particle images with the full resolution of 1504 x 1128 pixels at 1000 fps. Measurements were carried out from two orthogonal views: in the stream-wise wall-normal plane and the quasi-surface-parallel plane. 3-D disturbance was observed to start even prior to the point of transition. Vortex shedding in transition near the reattachment region of the LSB was clearly identified in the span-wise wall-normal plane, with the dominant K-H frequency of around 10.7 Hz. And subsequent vortex evolution in the reattached turbulent boundary layer was found to be characterized by paired positive and negative vorticity packets transported downstream.   

Experiments and nonlinear evolution of instabilities in the sphere wake

We performed precise and systematic experiments with PIV in order to measure the velocity field in the wake of a solid sphere in a water channel, in the range of Reynolds number between 200 and 400, where stationary and oscillatory instabilities appear, including hairpin shedding regime. From these experimental data, we are studying the modal decomposition of the streamwise vorticity in an instationnary case with standing waves and we describe the full nonlinear evolution of the bifurcation branches. We are comparing these results with recent theoretical and numerical studies on instability in the spherical wake at these intermediate Reynolds numbers.   

Hydrodynamics of an oscillating sphere in water

We have studied the flow patterns and damping of a one inch steel ball oscillating in water. The suspension was a 120 cm copper wire which allowed electrical connection to the water bath providing visualization by means of the Baker technique. The ball could be set into motion by means of a linear motor arranged to oscillate in the horizontal direction at the top of the suspension. Alternatively the bob could be set in motion and allowed to decay freely. The range of Reynolds numbers based on the maximum velocity ranged from $<$100 to over 2500 and the Carpenter-Keulegan numbers from 0.3 to 10. The period of oscillation was 2.5 sec. For Reynolds numbers up to about 400 we observed a boundary layer on the ball with a suggestion of a laminar wake spreading from the equator in the direction of oscillation. At higher Reynolds numbers around 550 we began to see periodic structure developing on the wake. By Re$\sim $700 it is clear the disturbances are a series of vortex rings which form on the rear of the sphere during an oscillation, and leapfrog over the sphere and propagate away when the direction of oscillation is reversed.   

Slowing of Vortex Rings

We have investigated the slowing of vortex rings in water which are created with very thin cores. We find that these rings propagate with no measurable change in diameter or core size. The drag appears to be the result of viscous forces on the core. A simple model for this drag describes experimental data in terms of a drag coefficient, which depends only on Reynolds number. Barenghi's group at Newcastle found that the translational velocity of a ring in an \textit{inviscid} fluid perturbed by Kelvin waves decreases with increasing amplitude of Kelvin waves. This suggests that the velocity of vortex rings in a viscous fluid may well depend on the amplitude of Kelvin waves at the time of formation. Rings with substantial amplitude of Kelvin waves will be expected to move more slowly than rings with little or no Kelvin wave amplitude. We present experimental data confirming this suggestion.   

Convective instability in inhomogeneous media: the impulse response in a subcritical cylinder wake

We study experimentally the impulse response of a cylinder wake below the critical Reynolds number of the B\'enard-von K\'arman instability. In this subcritical regime, a localized region of convective instability exists which determines an initial perturbation to be transiently amplified. Previous experimental works [Le Gal and Croquette, Phys. Rev. E 62, 4424 (2000)] have used the spatiotemporal evolution of streaklines from dye visualizations to analyze the evolution of a wave packet, but this has not permitted to give a correct picture of the transient energy growth. The aim of this work is to quantify the evolution of this convective instability using 2D particle image velocimetry in a hydrodynamic tunnel experiment. The velocity fields allow us to describe the evolution of the wave packet in terms of two control parameters: the Reynolds number and the strength of the imposed perturbation. The energy exhibits a transient algebraic growth followed by an exponential decay. A scaling law with respect to the Reynolds number was evidenced for the later decay, but not for the initial growth, which is consistent with the picture of transient growth in inhomogeneous media governed by the interaction of non-normal modes.   

Secondary instability in the wake of the flow around two circular cylinders in tandem arrangements

The stability of three-dimensional perturbations about two-dimensional time-periodic vortex wakes of the flow around two identical circular cylinders in tandem arrangements is investigated. The centre-to-centre separation is varied from 1.5 to 5 cylinder diameters. Direct linear stability analysis is employed to determine the shape, wavelength and onset of unstable three-dimensional perturbations. In addition the non-linear character of the bifurcations is identified through three-dimensional direct numerical simulations performed in the vicinity of the critical points. It is found that, for configurations with large cylinder separations, the first stages of the wake transition are similar to those observed in the flow around an isolated cylinder, although the onset of the secondary instability occurs at a lower Reynolds number. In contrast, for small separations the transition route is significantly different, resembling that of the flow in a periodically driven cavity. For these configurations the onset of the first instability arises at a higher Reynolds number than in the case of an isolated cylinder.   

Session PE: Porous Media II

Numerical Analysis of Turbulent Flow in Porous Media

Modeling techniques and simulation of laminar flow through porous media have been applied for a number of years for designing particulate filters, catalytic reactors, thermal and sound insulators, combustors, and more recently fuel cells. Essential for further analysis, and in support of new synthesis, is the modeling necessary for simulating turbulent flows in porous media. This has been studied in the present work, in principle, through modeling that is an alternative to Direct Numerical Simulation. A natural approach to build a turbulence model for flow in porous media is to simply apply the time averaging (for handling turbulence) and the space averaging (for handling the morphology) to the microscopic equations valid at the pore level. When pursuing a combined time and space averaging approach, the averaging order (i.e. space-time or time-space) matters. The difference in pursuing a time-space or a space-time averaging order is now known to essentially impact the way in which the resulting model treats the interaction of a large flow structure. In the current study, these two different approaches have been investigated in parallel to the experiments for their validity range. The comparisons are based on flow structure visualization and on values of turbulence characteristics obtained from direct measurements of fluid velocity via digital particle image velocimetry.   

Plume dynamics in heterogeneous porous media

Buoyancy driven flows in layered porous media are present in many geological settings and play an important role in the mixing of fluids, from the dispersal of pollutants in underground aquifers to enhanced oil recovery techniques and, of more recent importance, the sequestration of carbon dioxide (CO$_2$). Seismic images of the rise of a buoyant CO$_2$ plume at Sleipner in the North Sea indicate that these plumes are greatly influenced by a vertical array of thin lenses of relatively low permeability material. We model propagation of CO$_2$ at each layer as a gravity current in a porous medium which propagates along, and drains through, a thin, low permeability seal. Drainage, driven both by hydrostatic pressure and the body force on the draining fluid, leads to an initial rapid advance followed by a gradual retreat of the current to a steady-state. By incorporating a vertical array of these single layer models we are able to capture the rise of the buoyant plume in layered reservoirs. We find that the plume is characterized by a broad head with a tail given by the steady state extent.   

The competition between buoyancy and flow focussing in a two layer porous media flow

Flow of relatively dense gravity currents in saturated porous media with two distinct layers has been pursued theoretically and experimentally and will be demonstrated by a table-top experiment. In such systems, where fluid flow is driven by buoyancy, there exists a competition between gravity acting on the heavy fluid and flow focusing driven by ease of flow within the high permeability layer. When these two effects act together -- the lower layer is more permeable -- the current extends more rapidly than in a uniform medium of equivalent permeability. When gravity and the permeability structure act in opposition there is a critical flux $Q_C=(g'k_LH/\nu)f(k_U/k_L)$, where $f(x)=0.9(x-1)^{-1/3}$, beyond which the upper layer attracts the current sufficiently to overrun the lighter interstitial fluid in the lower layer ($k_U$ and $k_L$ are the permeabilities of the upper and lower layers and $H$ is the lower layer depth). When the system is at an angle to the horizontal, flow is driven by the component of gravity down the incline, rather than by the slope of the upper surface of the current, with the critical flux dependent on the angle. The studies have applications to sequestering supercritical carbon dioxide in saline aquifers 1 to 2 km beneath the surface of the Earth.   

Ensemble Phase Averaged Equations for Multiphase Flows in Porous Media

Many multiphase flows in porous media are modeled by application of Darcy's law to each phase separately. Sometimes, often in a fluid imbibition process, the flow is modeled as a diffusion process. Both models have been found applicable in some cases, but insufficient for others. In the present work, using the ensemble phase averaging technique for continuous multiphase flows, averaged momentum equations for multiphase flows in porous solids are studied. Under the assumption that the typical dimension of fluid interfaces is small compared to the macroscopic length scale, the averaged momentum equations for fluids are found to be in a form similar to Darcy's law, but with additional terms representing the effect of phase interactions on fluid interfaces. In a simple example of two fluids in a porous solid, we find that the difference in the average pressures of the two fluids is not necessary related to the surface tension effect. If the pressure difference, or the capillary pressure, is decomposed into a static part, representing the surface tension effect, and a dynamic part, then the dynamic part of the capillary pressure appears as terms in the averaged momentum equations. We also study conditions under which a fluid imbibition process can be modeled as a diffusion process.   

On electronkinetically driven flows in swelling clays

Clays are formed in parallel layers of minerals, called lamellae, which have negative surface charge due to imperfections in the crystal lattice. The space between the lamellae, the galley, is filled with a liquid in which cations are drawn to the charged platelet surfaces, resulting in a double-layer. The aspect ratio of the galley thickness to its length is small. Spatial variations on the lamella shape depend on the mechanical stresses being applied to the clay, the local flow rate, and the local cation and anion concentrations. We have developed a model in the small tortuosity limit for the bulk flow in the clays which takes into account local charge distributions, local displacements, and applied electric fields. Lubrication theory is applied to an individual galley/lamella system to describe the charge concentration and flow and electric fields and local displacements in the lamella. These fields then provide jumps in shear and tangential stresses within the lamellae, whose net force balance is found through homogenization over the size of the sample. Numerical simulations of the model are presented and are compared to experiments.   

Onset of density-driven convection in heterogeneous porous media: Non-modal stability analysis

When carbon dioxide (CO$_{2})$ is injected into saline aquifers, it slowly dissolves into the brine resulting in a gravitationally unstable state. Under suitable conditions, this instability manifests itself in the form of ``fingers'' of CO$_{2}$-rich brine penetrating into the system resulting in a significant enhancement of the rate of dissolution of CO$_{2}$ into the system. Recently, we applied the idea of non-modal growth of perturbations to compute the length and time scales characteristic of the onset of convection in a homogeneous porous medium. Non-modal stability theory is a theoretically rigorous extension of the traditional eigenvalue approach to non-normal and non-autonomous operators. In this work, we extend this approach to horizontally layered porous media generated with a Gaussian covariance model. We use a Monte-Carlo approach to analyze the effects of correlation length and the variance of the log-permeability field on the critical time for the onset of convection. We present the probability density function for the critical time and show that its variance increases with both the variance of the permeability field and its correlation length.   

Analytical Model for Post-Injection Spreading and Migration of CO$_2$ in Saline Aquifers, including Capillary Trapping, Solubility, and Leakage

In geological CO$_2$ storage, careful site selection and effective injection methods are the two primary means of maximizing reservoir ``fill'' and assessing and avoiding potential leakage paths. An accurate understanding of the subsurface spreading and migration of mobile CO$_2$ during and after injection is essential for these purposes. We present an analytical model for the post-injection spreading and migration of a plume of CO$_2$ in a saline aquifer, including the effects of gravity segregation, capillary trapping, natural groundwater flow, dissolution of CO$_2$ into groundwater, and leakage through the caprock. We account rigorously for the injection period, using the true end-of-injection plume shape as an initial condition. This comprehensive model allows us to estimate reservoir capacity for CO$_2$ storage at the basin scale, and to assess dynamically the relative importance of structural, capillary, and solution trapping mechanisms.   

An airborne jet train that flies on a soft porous track

This paper explores the quantitative feasibility of developing an airborne jet train that flies on a soft porous track within centimeters of the earth's surface at speeds approaching current commercial jet aircraft. The jet train employs a lift mechanism first proposed in Feng {\&} Weinbaum (2000) J. Fluid Mech. 422:282 and a nearly frictionless track suggested in Wu et al. (2004) Phys. Rev. Lett. 93(19):194501. Using an asymptotic analysis for large values of the permeability parameter H/$\surd K_{p}$, where H is the porous layer thickness and $K_{p}$ the Darcy permeability, we first show that it is possible to support a 70 metric ton jet train carrying 200 passengers on a confined porous material if its $K_{p}$ is approximately 5 x 10$^{-9}$ m$^{2}$. For this $K_{p }$one finds that the tilt of the planform is $<$ 0.1 degrees and the lift-off velocity is $<$ 5 m/s. Compression tests on a fiber-fill material with these properties show that the fibers contribute $<$ 0.2 percent of the total lift and hence the friction force of the fiber phase is negligible. Using jet engines of 10,000 lbf thrust, about 1/5 that of a 200 passenger jet aircraft, one is able to obtain a cruising velocity approaching 700 km/hr. This would allow for huge fuel savings, especially on short flights where much of the energy is used to climb to altitude and overcoming lift induced drag.   

Session PG: Drops VIII

Absolute-convective instability of coaxial jets

A well established route for the massive microencapsulation of labile materials, microorganisms, pharmaceutical principles, flavors, or any active ingredients of any kind involves the generation and breakup of coaxial capillary jets. Here, surface tension is the ultimate molding mechanism, and therefore experience teaches that the product quality is optimized within operating condition ranges where Weber and Capillary numbers attain limited values. These ranges allow for a precise control of the product structure. However, surface tension also mandates whether compound capillary jets may form or not: Weber and Capillary numbers maps exhibit ``hard'' boundaries where jets become locally unstable (absolutely unstable) as opposed to convectively unstable, and the product shows dramatic changes in structure (generally a degradation) across these boundaries. In this work we perform a linear spatiotemporal analysis of coaxial capillary jets to provide cartographic maps of viable regions in the Weber and Capillary numbers space. A discussion on the connection of these maps with the morphology of the resulting products is also given, together with comparisons with published experimental literature.   

Swirl Flow-Focusing: a new way for the generation of Microbubbles

A volume of fluid (VOF) numerical method is used to predict the dynamics of bubble formation in an axisymmetric flow-focusing microfluidic device. Our numerical results for several gas- liquid configurations show that in all cases analyzed, the introduction of co-axial swirl in the focusing liquid fosters the stabilization of the gas-liquid meniscus promoting tapered geometries. Consequently, the use of swirl leads to a dramatic reduction of the size of the bubbles generated by the flow focusing device. Preliminary experiments support our numerical findings.   

Viscoelastic effects on the jetting-dripping transition in co-flowing capillary jets

Linear hydrodynamics stability analysis is used to determine the influence of elasticity on the jetting-dripping transition and on the temporal stability of non-axisymmetric modes in co-flowing capillary jets. The critical Weber number for which axisymmetric perturbations undergo a transition from convective to absolute instability is calculated from the spatio-temporal analysis of the dispersion relation for Oldroyd-B liquids, as a function of the density and viscosity ratios, and the Reynolds and corresponding Deborah numbers. Here we show that elasticity increases the critical Weber number for all cases analyzed and, consequently, fosters the transition from jetting to dripping. The temporal analysis of the dispersion relation for the $m=1$ non-axisymmetric mode shows that elasticity does not affect its stability.   

Vortex Dynamics from 2D PIV Data in a Bubble Plume

Bubble plumes are commonly used for aeration and destratification in lakes and show potential as a delivery method for carbon sequestration. The need to design bubble plumes for these uses has led to an increase in research and development of models. However, the dynamics of turbulence in bubble plumes has yet to be quantified. Physical experiments were conducted to quantify turbulence in bubble plumes with air flow rates of 0.5, 1.0, and 1.5L/min. A camera imaged the bubble plume illuminated along a plane with an Argon-Ion laser at 250Hz. The images were processed to remove all bubbles resulting in a new image with only seeding particles. These images were processed using Particle Image Velocimetry giving 2D vector fields for the fluid phase. These vector fields were spatially analyzed to identify vortices and their properties in the field of view. The results show that the expected non-dimensional vortex size is the same for all three flow rates. The results also show that when properly non-dimensionalized the time-average vortex properties such as size and circulation across the width of the bubble plume are similar for all three air flow rates. Finally, the data is used to find the turbulent energy spectrum and the characteristic length scale within the plume. These results agree with the identified vortex results and show the modulation of the turbulence due to the presence of bubbles.   

Session PH: Surface Tension Effects II

Stretching and Slipping Liquid Bridges near Cavities

The dynamics of liquid bridges are relevant to a wide variety of applications including high-speed printing, extensional rheometry, and floating-zone crystallization. Although many studies assume that the contact lines of a bridge are pinned, this is not the case for printing processes such as gravure, lithography, and microcontacting. To address this issue, we use the Galerkin/Finite-Element method to study the stretching of a finite volume of Newtonian liquid confined between two flat plates, one of which is stationary and the other moving. The contact lines are allowed to slip, and we evaluate the effect of the capillary number and contact angle on the amount of liquid transferred to the moving plate. Liquid transfer to the moving plate is found to increase as the contact angle of the stationary plate increases relative to that of the moving plate. When the contact angle is fixed and the capillary number is increased, the liquid transfer improves if the stationary plate is wetting, but worsens if it is non-wetting. The presence of a cavity on the stationary plate significantly affects the contact line motion, often causing pinning at the cavity corner. In these cases, liquid transfer is controlled primarily by the cavity shape, suggesting that the effects of surface topography dominate over those of surface wettability.   

Imbibition in geometries with axial variations

When surface wetting drives liquids to invade porous media or microstructured materials with uniform channels, the penetration distance is known to increase as the square root of time. We demonstrate, experimentally and theoretically, that shape variations of the channel, in the flow direction, modify this ``diffusive'' response. At short times, the shape variations are not significant and the imbibition is still diffusive. However, at long times, different power law responses occur, and their exponents are uniquely connected to the details of the geometry. Experiments performed with conical tubes clearly show the two theoretical limits.   

Interconnectivity in Surface Wicking Structures

Surface wicking structures possessing strong interconnectivity are designed and examined. The designs aim to optimize the structure's ability to transport fluids by exploiting capillary driven flow in interior corners combined with interconnectivity and alignment. `Waffle-like' structures consisting of vertical rectangular vanes at a variety of orientations are employed as the basic repeat unit. Due to this arrangement, such surfaces possess interconnectivity that is stronger than that of other existing designs such as those composed of micro posts. This strong interconnectivity provides several advantages. For example, it is found that the transport of fluid by wicking can be controlled by a clever choice of the interconnectivity and vane alignment. As a result, the shape of the moving front during wicking can be circular, elliptical, or rectangular. The observations as well as a study of the dynamics of the wicking flow will be presented.   

Influence of surfactant solubility on the deformation and breakup of a bubble or thread in a viscous fluid

In a previous paper (JFM 594, 307-340, 2008) we studied effects of insoluble surfactant on the pinch-off of an inviscid bubble surrounded by a viscous fluid theoretically and numerically. In the present study the surfactant solubility is included. The adsorption-desorption kinetics of surfactants is assumed to be in the diffusion-dominated regime, and equations governing the evolution of the interface and surfactant concentration in zero-Reynolds-number flow are derived using a long wavelength approximation. Results of the long wavelength model are compared against numerical simulations of the full Navier-Stokes equations, performed using an accurate arbitrary Lagrangian-Eulerian method. The presence of insoluble surfactant significantly retards pinch-off (JFM 594, 307-340, 2008): This is due to the development of a long, slender, quasi-stable cylindrical thread at the location of minimum radius, where the destabilizing influence of capillary pressure is balanced by the internal pressure. For soluble surfactant, depending on parameter values, a thin thread forms first but pinches off later due to the exchange between bulk and surface surfactants. In some cases the collapsing of bubble is completely inhibited by the soluble surfactant.   

Liquid flow over a substrate structured by seeded nanoparticles and slip boundary condition

Recent experiments have demonstrated that already sparsely distributed, over a solid substrate, nanoparticles can change substantially the amount of liquid slip at the surface. Inspired by the observations, the flow past small particles seeded on a solid substrate is investigated theoretically on the basis of an interface formation model. It has been demonstrated, for the first time, that even a single seeded particle can create sufficient surface tension gradient, with the characteristic length scale independent of the particle size, to reduce significantly the (measurable) tangential component of hydrodynamic velocity at the substrate and thus to adjust the slip boundary condition. But, it has been established, that the effect from the particle is essential for the actual slippage, while the apparent slip would be only partially disturbed. This outcome of the analysis is crucial for future experiments and can be potentially used to identify exactly the mechanism of slip in particular situations. A comparison with the experiments has shown that the results of the theoretical analysis are quantitatively consistent with the experimental measurements, in particularly the maximal separation distance between the particles to observe the deterioration of slip.   

Spreading of a Fluorescent Surfactant on a Glycerine Layer

We study the spreading of a fluorescent surfactant on a thin layer of glycerine. Measurements of the height profile of the capillary ridge are conducted as the surfactant travels outward from the point of deposition. We examine the dynamics of the ridge as a function of the volume of surfactant released, and find that for the largest volumes the shape and speed of the spreading ridge are influenced by the outer edge of the underlying glycerine layer. The intensity of the fluorescence is also used to visualize the position and the concentration of surfactant as it spreads. The location of the surfactant is compared to the location of the capillary ridge.   

Session PJ: Bio-Fluids: Undulatory Flapping III

Parameters Governing the Wake Structure of a Low-Aspect-Ratio Pitching Panel at $Re_C=640$

Measurements of the wake structure and thrust performance of a rigid rectangular low-aspect-ratio panel pitching about its leading edge have been previously reported (Buchholz, J.H.J and Smits, A.J, {\em J. Fluid Mech}, 603, pp. 331--365). Such a simplified propulsor has proven to be a useful platform for the investigation of the physics of aquatic animal swimming. Wake visualizations at $Re_C = 640$ yielded vortex skeleton models that were used to understand the structure of the wake at $Re_C = O(10^4)$; however, at this low Reynolds number, only a single value of panel aspect ratio and pitching amplitude were investigated, for three representative Strouhal numbers. In the present work, we investigate variations in aspect ratio and pitching amplitude, and consider additional pitching frequencies in order to further elucidate parameters governing the structure of the wake at $Re_C = 640$.   

Effect of aspect ratio on the hydrodynamics of a self-propelled elliptic foil

Flapping wings or fins are commonly used by birds, insects, fishes and some Micro Air Vehicles to generate propulsive force. In most of the studies on flapping wings, the foil is placed in a steady stream and the motion in the horizontal direction is constrained. However, the condition in these studies is completely different from that in real self-propelled locomotion. Alben and Shelly (PNAS, 102, 11163-11166 (2005)) have performed a pioneering study on fundamental hydrodynamics of a self-propelled flapping foil. In this study, we investigate the effect of geometrical shape on the hydrodynamics by varying the aspect ratio of the elliptical foil. Three different dynamic modes of the foil have been identified with the increase of aspect ratio, i.e. fore-aft symmetry, non-periodic motion and unidirectional motion with periodic velocity oscillation. It is observed that the dynamics of the body are closely related to various vortical patterns around the foil. The formation of the vortices during the starting procedure and their subsequent disposition in the wake will be described. The implication of the current study on the optimization of the foil shape in obtaining locomotion is given.   

3D vortex formation of drag-based propulsors

Three dimensional vortex formation mechanism of impulsively rotating plates is studied experimentally using defocusing digital particle image velocimetry. The plate face is normal to the moving direction to simulate drag-based propulsion and only one power stroke is considered. In order to compare the effect of shape on vortex generation, three different shapes of plate (rectangular, triangular and duck's webbed-foot shapes) are used. These three cases show striking differences in vortex formation process during power stroke. Axial flow is shown to play an important role in the tip vortex formation. Correlation between hydrodynamic forces acting on the plate and vortex formation processes is described.   

Propulsion of a flexible foil in a fluid

The dynamic properties such as time dependent pressure loading, free stream velocity, and local acceleration of the hydrofoil determine the instantaneous deformation of a flexible foil. The present work is concerned with the effect of structural dynamic terms and inertia loads on a flexible foil undergoing large amplitude rigid body harmonic wave-like motion in an unsteady potential flow. The hydrofoil structural dynamics is modeled as an Euler-Bernoulli beam finite element. The unsteady fluid dynamic force is evaluated using a numerical discrete vortex implementation of an unsteady incompressible potential flow model. The hydrofoil is fixed at its leading edge and it moves with velocity parallel to its length in the undeformed state. The propulsion of the hydro-elastic system is studied in terms of the mass ratio of the foil and the fluid, as well as its structural flexibility. It is shown that the thrust coefficient and propulsive efficiency of the flexible foil decreases with increase in structural flexibility. We made a comparison of the effect of structural flexibility on the thrust coefficient and propulsive efficiency considering models of the oscillating foil with inertia and without inertia effects present. Detailed parametric studies of the effect of different parameters on propulsion of the foil were made. Including inertia loads and structural dynamic terms significantly affect the propulsive efficiency and thrust coefficient.   

Effect of Pitching and Heaving Motions of SD8020 Hydrofoil on Thrust and Efficiency for Swimming Propulsion

The thrust producing performance and efficiency of an SD8020 foil hydrofoil that undergoes rotational and translational oscillating motions was studied and optimized through force and torque measurement and dye flow visualization, in the water tunnel at low Reynolds number of 13,000-16,000. The foil was set into pitching and heaving motion under different oscillation patterns to mimick the flapping and swimming motion of the marine creatures. The force and moment data were collected and used as optimization basis for best flapping motion combination. The propulsive efficiency and thrust coefficient of the pitching foil were determined as a function of the Strouhal number, pitch amplitude and angular frequency. Based on the force and efficiency data collected for the pure pitching motion, increasing pitch amplitude and angular frequency was associated with a decrease in propulsive efficiency and an increase in thrust forces produced. A high propulsive efficiency of 70{\%}, accompanied by a thrust coefficient of order one was found at a pitch amplitude of 30\r{ } and angular frequency of 0.873 rad/s, Strouhal number of 0.24, and freestream of 0.1368 m/s (Reynolds number of 16416). This presented the best conditions for thrust production observed at low Strouhal and Reynolds numbers.   

Passive mechanics in jellyfish-like locomotion

The aim of this work is to identify possible benefits of passive flexibility in biologically-inspired locomotion. Substantial energy savings are likely achieved in natural locomotion by allowing a mix of actively controlled and passively responsive deformation. The jellyfish is a useful target of study, due to its relatively simple structure and the availability of recent kinematics and flow-field measurements. In this investigation, the jellyfish consists of a two-dimensional articulated system of rigid bodies linked by hinges. The kinematics -- expressed via the hinge angles -- are adapted from experimentally measured motion. The free swimming system is explored via high-fidelity numerical simulation with a viscous vortex particle method with coupled body dynamics. The computational tool allows the arbitrary designation of individual hinges as ``active'' or ``passive,'' to introduce a mix of flexibility into the system. In some cases, replacing an active hinge with a passive spring can enhance the mean swimming speed, thus reducing the power requirements of the system. Varying the stiffness and damping coefficients of the spring yield different locomotive results. The numerical solution is used to compute the finite-time Lyapunov exponents (FTLE) throughout the field. The FTLE fields reveal manifolds in the flow that act as transport barriers, uncovering otherwise unseen geometric characteristics of the flow field that add new insight into the locomotion mechanics.   

A Propulsive Efficiency Model for Pulsed-Jet Propulsion

Mechanical pulsed jets functionally similar to those utilized by biological jetters such as squid are known to yield elevated thrust in comparison to equivalent steady jets due to the formation of vortex rings with each jet pulse and the concomitant over-pressure at the nozzle exit plane. Although speculated to have advantages for propulsive efficiency as well, the influence of vortex ring formation and over-pressure on propulsive efficiency has not been quantified. The present work proposes a simple model of pulsed jet propulsion where the effect of vortex ring formation on thrust and kinetic energy are accounted for through lumped over-pressure terms in the momentum and energy equations. Time-averaged propulsive efficiency is then formulated from the resulting expressions for thrust and excess kinetic energy. For comparison with steady jet propulsion, it assumed that the vehicle drag is the same for pulsed and steady propulsion at the same vehicle speed. Using measurements of the over-pressure terms from static pulsed jets, the results suggest that the propulsive efficiency of pulsed jets can exceed that for steady jets for short pulses and low vehicle Reynolds number.   

Propulsive efficiency of a self-propelled pulsed jet vehicle at low Re

Steady jet propulsion systems like propellers and jets predominate for large scale systems. The propulsive efficiency of these systems decreases as the Reynolds number (Re) decreases; however, making pulsed jet propulsion appealing at low Re due to its higher thrust compared to an equivalent steady jet. In order to compare the propulsive efficiency of steady and pulsed jets at low Re, a mechanical pulsed-jet underwater vehicle (dubbed ``Robosquid'' after its biological counterpart) was built and tested. The system allows control of piston velocity program, pulsing frequency, and piston stroke-to-nozzle diameter ratio (L/D).The propulsive efficiency of this system was measured using digital particle image velocimetry (DPIV) for L/D = 2 -11 and vehicle Re between 1000 and 2500. The results show that propulsive efficiency increases as L/D decreases, suggesting vortex ring formation plays a key role in increasing propulsive efficiency. Propulsive efficiencies comparable to and above those for steady jet propulsion were obtained for L/D $<$ 3. Results for Robosquid in a more viscous liquid to achieve Re $<$ 1000 will be presented.   

Session PK: Nano-fluids III

The decay of thermal capillary waves on thin liquid films

Thermal fluctuations are expected to excite capillary waves on free surfaces of liquids. For a liquid film on a solid wall, continuum models predict that waves of wavesnumber $q$ will decorrelate at rate $\omega$ that scales as $\omega \sim q^4$ for thin films (the lubrication limit with a no-slip boundary condition) and as $\omega \sim q$ for thick films (flow in a viscous half-space). Atomistic simulations of model polymeric fluids are employed to confirm these expected scalings and probe how this behavior fails as the atomic granularity of the fluid becomes important. These expected scalings are indeed found, but an unexpected $\omega \sim q^2$ powerlaw is also evident at shorter wavelengths than the $\omega \sim q$ region. For these same $q$ values, the capillary waves still seem to obey equipartition with energies defined simply by surface curvature, suggesting that there is not a complete failure of a continuum description of the fluid for these $q$. A $\omega \sim q^2$ would be expected for a slip boundary condition at the wall boundary, but no such slip is observed. Results for different polymer lengths collapse in this $q^2$ region when scaled with the radius of gyration of the polymer, suggesting that the anomaly is the result of a breakdown of the constitutive model.   

Ionic separation in nanofluidic channels

Ionic species of equal electrophoretic mobility (or charge-to-size ratio) may not be separated in electroosmotic or pressure-driven flow along microfluidic channels. In nanofluidic channels, however, the enormous electric fields inside electrical double layers cause transverse species distributions yielding charge-dependent species speeds in the flow. Those species of equal mobility can thus be separated solely by charge (or equivalently, size). Here we develop an analytical model to optimize and compare the separation of such ionic species in electroosmotic (termed nanochannel electrophoresis) and pressure-driven (termed nanochannel chromatography) flows along nanochannels in terms of selectivity, plate height and resolution. Both planar and cylindrical geometries are considered. It is found that nanochannel chromatography offers a larger selectivity (good) while a larger plate height (bad) than nanochannel electrophoresis does. The maximum resolution of ionic separation is therefore comparable between the two nanofluidic approaches. The optimal channel half-height or tube radius is found within the range of 1 to 10 times the Debye length.   

The Study of Solvation Effects on Thermodynamic Properties of Nanofluids Using Molecular Dynamics

Liquid layering around nano-particles is proposed to be a major contributor in the surprisingly unpredictable properties of nanofluids. Equilibrium molecular dynamic simulations are presented for a water-based nanofluid with gold nano-particles. It makes use of state-of-the-art force fields to capture a broad spectrum of realistic physical phenomena. Thermodynamic properties, such as internal energy, heat capacity, enthalpy and entropy of the nanofluid are analyzed for different particle configurations. The understanding of basic thermodynamic effects in nanofluids is a stepping stone for further studies.   

Equilibrium statistical mechanics of films on a substrate

We investigate the small-scale behavior of a fluid (liquid or gas) film in contact with a substrate by using a density-functional-theory approach in the context of the description of the statics and dynamics of interphase boundaries. The fluid-fluid interaction potential is divided into a short-range repulsive component and a long-range attractive one. Different types of interaction potentials are considered as well as the influence of the wall potential onto the fluid density profile and a comparison with a gradient theory obtained from the density-functional approach is also made. Emphasis is then put on examining the case of a three-phase conjunction and the connection between the micro- and the meso-scale.   

Biomolecular transport through hemofiltration Membranes

A theoretical model for filtration of large solutes through a nanopore in the presence of transmembrane pressures, applied/induced electric fields, and dissimilar interactions at the entrance and exit to the nanopore is developed to characterize the experimental performance of a hemofiltration membrane designed for a proposed implantable Renal Assist Device (RAD). The model reveals that the sieving characteristics of the nanopore membrane can be improved by applying an external electric field, and ensuring a smaller ratio of the pore-feed and pore-permeate equilibrium partitioning coefficients when diffusion is present. The model is then customized to study filtration of both charged and uncharged solutes in the slit-shaped nanopores of the hemofilter for the RAD. Experimental data on the sieving coefficient of serum proteins are reported and compared with the theoretical predictions. Both steric and electrostatic partitioning are considered and the comparison suggests that in general electrostatic effects are present in the filtration of proteins though some data, particularly those recorded in a strongly hypertonic solution (10$\times$PBS), show better agreement with the steric partitioning theory.   

Selection of Non-Equilibrium Over-Limiting Currents: Universal Depletion Layer Formation Dynamics and Vortex Instability

We report the first direct experimental proof for Rubinstein's instability [1] by using an applied AC electric field across a straight nano-slot, whose transverse dimension is at least 10 times larger than the depletion layer, EO convective flow is completely arrested and ion transport is dominated by diffusion and electro-migration. The ion flux dynamics is imaged using fluorescent dye molecules in combination with confocal microscopy, to understand the non-equilibrium phenomenon of over-limiting current density across a nanoporous membrane. With a slow AC field, an ion depletion front is generated intermittently from one end of the nano-slot and a vortex instability is found to arrest the self-similar diffusive front growth. This electrokinetic instability evolves into a stationary interfacial vortex array that specifies the over-limiting current, independent of external stirring or convective flow. [1] I. Rubinstein, E. Staude and O. Kedem, Desalination 69, 101 (1988).   

Rotational-Translational Coupling in Nanopores

A rare combination of molecularly smooth walls and hydrophobicity of the surface make carbon nanotube (CNT) membranes fast transporters of water. Though bi-directional single file water transport in ``bursts'' through a (6,6) CNT and collective intermittent reversing of water dipolar orientations has been observed in molecular dynamics simulation for short tubes, the molecular mechanism governing the relation between the dipole orientation and the flow direction has not been elucidated. Here we show that when the orientation of the water molecules is maintained along one direction in longer tubes, a net water transport along that direction can be attained due to coupling between rotational and translational motions. The rotations of the water molecules are correlated more with the translation of the neighboring water molecule with the acceptor oxygen than the neighbor with the donor hydrogen. By applying an electric field or by attaching chemical functional groups at the tube ends, the orientations can be maintained and this mechanism of rotational-translational coupling can be used to pump confined water through nanotubes.   

Session PL: Bio-Fluids: Flight IV

Modeling flexible wing flapping at low Reynolds number

Using computational modeling, we study the aerodynamics of flapping wings in hovering flight. The wings are thin, flexible structures and can extensively bend due to hydrodynamic forces and wing inertia. To capture the dynamics of oscillating flexible wings at low Reynolds number, we develop a three-dimensional computational model for fluid structure interaction that combines the lattice Boltzmann model for fluid dynamics and the lattice spring model for the micromechanics of elastic solids. We examine the unsteady forces and flows during the wing beat cycle and probe how wing bending affects the flight performance and flow structures around the flexible wings. The results could prove useful in designing micro air vehicles that employ elastic flapping wings for propulsion and flight control and in understanding the mechanics of flapping flight of small insects.   

Optimal wing flapping via elastic coupling

We consider a prototypical experimental setup, comprising a pitching and heaving rectangular plate. The plate is heaving sinusoidally at constant frequency and variable amplitudes, and a rotational spring generates the pitching motion passively. The rotational spring is simulated by a servo motor driven by a model following controller, and a genetic algorithm optimizes the spring parameters so as to maximize the average lift produced. We present results showing the relationship between optimal parameters for linear and nonlinear springs, and we also investigate the effect of the tip region flow on optimality.   

High Speed Videogrammetry Study of Flexible Wings in Flapping Flight

Recent interest in the area of micro and nano air vehicle (MAV and NAV) development has called for a better understanding of the mechanics of natural flight at very low $Re$. Of particular interest is the area of mammalian flight, which has adapted a highly flexible membrane for creating lift. A high-speed videogrammetry system along with a two-axis lift balance was developed in order to better understand how flexible membrane wing systems work. Two MotionPro X high-speed cameras recorded the motions of the wings. These videos were then analyzed using the Photomodeler software package, which built a 3D model of the wing motion. Using this system, wings of several varying geometries and flexibilities were tested and compared with each other. Flapping frequencies from 1 Hz up to 30 Hz have been examined. The effect of chord-wise wing-stiffeners on wing deformation and lift generation has also been examined. The wing system was placed in a gust/shear tunnel to examine the effect of varying free-stream velocities on the wing deformations during steady and unsteady flight and its gust alleviation behavior.   

The influence of low-order chord-wise flexibility on the performance of a flapping wing

The aerodynamic role of flexible fight structures in airborne creatures is still poorly understood. The objective of this study is to distill the basic phenomena of flapping with deformable wings for their use in the efficient design of bio-inspired flight vehicles. The target of the study is a two-dimensional wing with rigid components connected by damped torsion springs. This simplified structure reduces the complexity of the problem, while retaining the leading-order influence of wing flexion. The motion of the leading portion of the wing is prescribed with hovering-type kinematics, while the trailing portions respond passively. Numerical simulations are performed with a viscous vortex particle method with strongly-coupled structural dynamics. The investigation focuses on the influences of several key parameters: spring stiffness (from rigid to very flexible), the location of axis of rotation, and the timing between the rotational and translational components of the kinematics. The effects are quantified via several performance measures, including production of mean and rms lift, the mean consumption of power, and the lift per unit power. Some important correlations are identified between the input parameters and the performance metrics, the passive wing deflection and the wake structure. It is shown that variation in the rotation phase lead are accompanied by topological changes in the wake vortex dynamics.   

Characterization of fluid transport due to multiciliary beating

Understanding fluid transport caused by beating cilia can give insight on biological systems such as transport of respiratory mucus, ovum transport in the oviduct, and feeding currents around unicellular organisms. Here we investigate fluid transport due to coordinated beating of motile cilia based upon a computational model that couples their internal force generating mechanisms with external fluid dynamics. Velocity field data is used to identify Lagrangian Coherent Structures (LCS) within the domain. These coherent structures give spatial information on fluid mixing and nutrient transport within this dynamic environment.   

Flapping wings: viscous effects in Lighthill--Weis-Fogh mechanism

The Lighthill--Weis-Fogh ``clap-fling-sweep'' description of insect flight involves a novel mechanism, which can apparently operate in a strictly inviscid fluid, of generation of circulation and lift through instantaneous change of topology. However, viscous effects substantially influence this mechanism, both near the sharp edges of the wings by the well-known vortex-shedding process, and in the neighbourhood of the ``hinge,'' where the local Reynolds number is necessarily low. In this investigation, we focus on viscous effects at and around the instant of separation of the wings. The local flow near the hinge is described by similarity solutions of the Stokes (biharmonic) equation, and a logarithmic singularity of the pressure is identified. Numerical simulation of the process provides support for the analytical description.   

Session PP: Multiphase Flows VII

Multi-Discipline Collaboration for Sustainability in Heating Buildings

It was a dark and stormy night. The storyteller said, ``Let us each tell a story.'' The physicist expounded, ``Capture heat from rain on roofs to melt stored ice. Re-freeze melted ice with heat pumps. My new through-wall, multi-phase, mass-flow meter controls collecting, storing, transferring and pumping heat.'' At dawn, the engineer explained, ``Design a system to collect roof-heat from rain, solar and wind inputs. Heat is stored in freeze-thaw tanks and in soil under buildings and driveways.'' The architect adapted the new designs to beguile builders with plans for zonal heating that offers rapid zonal recovery, on demand. The businessman spun a tale of a new industry to mass produce affordable systems. The storyteller next instructed the team, ``Make it so.'' It was a dark and snowy night five years later. The homeowner said, ``My heat pump uses electricity from wind power to pump two thirds of my heat using stored energy from rain, sun, wind and soil.'' Sustainable heating of buildings will not be mythical if physicists develop new models for fluid motion and collaborate on educating other team members.   

Particle Velocity Fluctuations in a Liquid Fluidized Bed

The random motion of solid particles in a liquid fluidized bed has been investigated using high speed video, in the range of high particle Reynolds and moderate Stokes number. Matching the refractive index of both phases allows the recording of a single colored particle 3-D trajectory within the bed. The particle velocity \textit{pdf} and variance following the particle motion have been derived for each velocity component, in a wide range of solid fraction. Instantaneous velocity signal is composed of large amplitude low frequency fluctuations and small amplitude fluctuations at higher frequency. The large scale motion is much more pronounced in the longitudinal direction than in the transverse one, resulting in a significant anisotropy of the fluctuating motion. For each component, the velocity \textit{pdf} is centered on zero and can be well fitted by a Gaussian distribution at low to moderate solid fraction. The velocity variance of each component is found to be a decreasing function of the sold fraction. These results have been interpreted in the frame of an averaged statistical model derived from kinetic theory of granular media.   

Effect of Ambient Turbulence on the Drag Force of Particle at High Stokes Number

Velocity of solid particle (diameter is 2 mm) free-falling in a nearly isotropic turbulent airflow has been investigated using an ingenious experimental setup to achieve high Stokes number. Turbulent intensity around the particle is large enough to have eddies of comparable size to the thickness of boundary layer (approximately 0.2 mm) that is estimated in a laminar flow. As a result of measurement, an ensemble averaged particle velocity is larger than the velocity predicted with Schiller and Naumann's drag coefficient (Muto \textit{et al}., 2007). To investigate this reduction of drag force, flow aspects near the particle are observed using a numerical simulation of rotating spherical particle (periodically rotates in opposite direction) in a uniform flow. As a result, a modulation of drag force is found and it depends on period and amplitude of the rotation. A reason of the change of drag force in both experiment and numerical simulation is deduced that eddies included in an approach flow to particle, or periodic rotation of particle affect its boundary layer, and the wake of particle is suppressed.   

A study on the interactions between femtosecond-pulse laser and water from a viewpoint of multiphase flows

Femtosecond-pulse lasers (fs pulses) cause very interesting phenomena due to their extremely high energy density. The effects on substances are not thermal, but multi-photon absorption. When this multi-photon absorption of fs pulses operates on water, extraordinary phenomena different from laser-induced cavitation by usual laser such as nano- or pico-pulse laser are induced. Fs pulses of 60 femtoseconds in duration, 1kHz in repetition rate and 0.2--0.9$\mu $J in pulse energy are focused at pure water in a glass cell through several types of lens. The fs pulses split from original beams through a beam splitter are used as probe light. The Femtosecond-order Time-resolved Optical Measurement is realized by adjusting a light path length of the probe light (fs pulses). We elucidate the changes of refraction index of the water, the bubble generation process and the bubble properties. On the basis of these results, we discuss a relationship between the bubble motion and the field irradiated by fs pulses.   

Experimental Research on Turbulent Mixing Layer Flow with Polymer Additives

We present the results of an experimental study of fluids with polymer additives mixed by a specially designed splitter plate in a vertical rectangular channel. This arrangement is perhaps the simplest in which mixing effects can drive instability in the fluid. The velocity ratio between high and low speed is 4:1 and the Reynolds number based on the velocity difference of two steams and hydraulic diameter of the channel ranges are from 22800 to 87120. The flow field and turbulent parameters of different concentration polymer additives are measured and compared with water flow, which shows that the dynamic development of mixing layer is great influenced by polymer addictives. Our investigations reveal that similar with pure water case, the Reynolds stress and voticity still concentrate in a coniform area of central mixing flow field part. But compared with pure water case, the coniform width of polymer additives case is larger which means the polymer additives will lead to the diffusion of coherent structure. The peak value of vorticity in different cross section will decrease with the development of mixing layer. Compared with pure water case, the vorticity is larger at the beginning of the mixing layer but decreases faster.   

Measurements of the average properties of a bidisperse suspension of bubbles rising in a vertical channel

This investigation presents an experimental study of a system for which the bubble size is not monodisperse. In this work an experimental equipment was designed to study the behaviour of a bidisperse suspension of bubbles rising in a vertical channel, in which the dual limit of small Weber and large Reynolds number is satisfied. Bubbles were produced using capillaries of two distinct inner diameters. Using water and water-glycerin mixtures, the range of Reynolds numbers was extended from 50 to 500, approximately. To avoid coalescence, a small amount of salt was added to the interstitial fluid, which did not affect the fluid properties significantly. Measurements of the size, bubble velocity, aspect ratio as well the equivalent diameter of the bubbles were obtained as a function of gas volume fraction. We found that the bidisperse nature of the flow changes the dynamics in a significant manner. We observed a modification of the flow agitation, characterized by the liquid velocity variance. Although the decrease of the mean velocity with gas volume fraction is similar to that observed for monodisperse flows (Mart\'inez et. al. 2007), a general increase of the magnitude of fluctuations is observed for certain combinations of bubble size and gas fraction ratios.   

Image Treatment of Hybrid Drops in Low Reynolds Number Flow

Hybrid drops, also known as compound drops, consisting of two dissimilar configurations are encountered in processes such as melting of ice particles in the atmosphere, liquid membrane technology, evaporation of drops in a superheated liquid and in other various industrial operations. The flow fields around such hybrid drops form a basis for a better understanding of these industrial applications. Here we provide exact analytic solutions for a class of $3D$/$2D$ hybrid drops immersed in an infinite viscous domain in the limit of low Reynolds number. For mathematical convenience, the geometry of the multiphase droplet is composed of two overlapping spheres (infinitely long cylinders for $2D$ case) $S_a$ and $S_b$ of radii $a$ and $b$, respectively, intersecting at a vertex angle $\frac{\pi}{2}$. The composite inclusion has the shape resembling a {\it figure-eight lens} type of object with a vapor $S_a$ partly protruded into a fluid sphere $S_b$ with a viscosity different from that of the host fluid. The mathematical problem with this twin-sphere assembly in the Stokes flow environment is formulated in terms of Stokes stream function with mixed boundary conditions and solved using the classical method of images. Singularity solutions are obtained for the hybrid droplet embedded in several unbounded flow fields and the force acting on the drop is computed in each case. Streamline topologies show interesting flow patterns and surprising, but interesting flow features are noticed in the case of two-dimensional flows.   

Heat transfer in ordered and random arrays of spheres at low Reynolds number

Direct simulation of passive scalar transport in steady flow past arrays of spheres is performed using the immersed boundary method. We investigate the dependence of the Nusselt number on different sphere arrangements (simple cubic, face--centered cubic and random) as a function of solid volume fraction and Reynolds number ($0.01 < Re < 20$) for Prandtl number $\mbox{Pr} =0.7$. Our results compare well with the established correlations for low solid volume fractions ($<0.1$). At higher solid volume fractions, existing correlations are found to underpredict the heat transfer with significant departures in the Nusselt number at the highest volume fraction of $0.4$. The simulations motivate an improved heat transfer correlation for gas-solids flow at low Reynolds numbers.   

Session PQ: Particle Laden Flows IV

Direct Visualization of Rapid Convective Deposition of Microsphere Monolayers

Micron-sized microspheres were deposited into thin films via rapid convective deposition using a similar method to that studied by Prevo and Velev, Langmuir, 2003. By varying deposition rate and blade angle, the optimal operating ranges in which 2D close-packed arrays of microspheres existed were obtained. Previous models do not consider the effect of blade angle and blade surface energy on the deposition rate. Using a confocal laser scanning microscope, dynamic self-assembly of colloidal particles under capillary force during solvent evaporation was revealed. The resulting microstructure controlled by varying the macroscale parameters and interaction between substrate and colloidal particles played an important role in formation of ordered crystalline arrays. These interactions were explored through a model comparing the residence time of a particle in the thin film and the characteristic time of capillary-driven crystallization to describe the morphology and microstructure of deposited particles.   

Lagrangian statistics of inertial particles in turbulent flow

Being able to accurately model and predict the dynamics of dispersed inclusions transported by a turbulent flow, remains a challenge with important scientific, environmental and economical stakes. One critical and difficult point is to correctly describe the turbulent dynamics of particles over a wide range of sizes and densities. We present high resolution acoustical Lagrangian measurements of inertial particles transported in a grid generated turbulent flow. The size of the particles and their density have been systematically varied. Our measurements show that Lagrangian statistics of the dispersed particles do exhibit non tirvial, and so far unpredicted, size and density effects. This has important consequences in terms of modelling of the turbulent transport of dispersed inclusions.   

Transport of Finite-Sized Particles in Chaotic Flow

By extending traditional particle tracking techniques, we study the dynamics of neutrally buoyant finite-sized particles in a quasi-2D spatiotemporally chaotic flow. We simultaneously measure the flow field and the trajectories of millimeter-scale particles so that the two can be directly compared. While the single-point statistics of the particles are indistinguishable from the flow statistics, the particles often move in directions that are systematically different from the underlying flow. These differences are especially evident when Lagrangian statistics are considered.   

Towards quantifying the collision kernel of inertial particles in homogeneous isotropic turbulence

We present digital holographic particle image velocimetry (DHPIV) measurements of the radial distribution function (RDF) and the relative velocity probability density function (PDF) of inertial particle pairs in homogeneous isotropic turbulence generated by fans in an enclosed box. The RDF and relative velocity PDF are the essential statistical inputs to the particle-pair collision kernel (Sundaram \& Collins 1997). The measurements are compared to direct numerical simulations (DNS) at a similar Reynolds number. Results show qualitative agreement of the relative velocity PDF from experiments and DNS. Measurements of the temporal development of the RDF demonstrate the existence of an extended quasi-steady-state regime, over which comparisons of the measured two-particle statistics to DNS can be made, justifying a previous RDF comparison by Salazar et al (2008). Further considerations of finite-volume effects on the RDF are considered.   

Particle suspension by a vortex ring convecting parallel to a planar surface

Experiments to qualitatively characterize the flow disturbance due to a vortex ring at the surface of a plane horizontal solid wall are described. The ultimate goal of this study is to characterize the role of turbulent boundary layer coherent structures in suspending particles into the flow. Experiments were performed by introducing vortex rings into a stationary fluid. The motion of the rings, tagged with dye, was recorded with digital video. The current study focuses on the effect of the planar wall on the vortex ring trajectory and topology, as well as the velocity and pressure disturbances induced at the wall by the ring. These observations are reported for a range of vortex ring strengths and distances between the vortex ring and the wall.   

Influence of gravity on inertial particle clustering in turbulence

We report results from experiments aimed at studying inertial particles in homogeneous, isotropic turbulence, under the influence of gravitational settling. Conditions are selected to investigate the transition from negligible role of gravity to gravitationally dominated, as is expected to occur in atmospheric clouds. We measure droplet clustering, relative velocities, and the distribution of collision angles in this range. 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 particles of various Stokes and Froude numbers and use digital holography to obtain 3D particle positions and velocities. From particle positions, we investigate the impact of gravity on inertial clustering through the calculation of the radial distribution function and we compare to computational results and other recent experiments.   

Session PR: General Fluid Mechanics: Numerical Simulations

Chaotic Advection with Inertia in a 2D Cavity Flow

The mechanisms underlying chaotic advection and mixing in inertial flow above the Stokes flow regime are incompletely understood. We performed numerical simulations of chaotic advection and mixing for time-periodic inertial flow in a two-dimensional rectangular cavity driven by alternating motion of the upper and lower walls. The effects of inertia were analyzed in terms of the flow topology and tracer dynamics. The Poincar\'{e} map evolves as the Reynolds number increases. Periodic points shift in position from their original locations in Stokes flow, and the Poincar\'{e} sections transition from those characteristic of Stokes flow to a different characteristic pattern at higher Reynolds numbers. Tracer motion exhibits increasing degrees of disorder with increasing Reynolds number and decreasing forcing frequency resulting in increased chaotic mixing. The forcing frequency has a much greater impact on chaotic advection and mixing than inertial effects.   

Realistic Simulations of the Turbulent Plasma Dynamics on the Sun

The objective of this research is to model the turbulent dynamics of the upper convective boundary layer of the Sun and investigate how magnetic field affects the structure and dynamics of solar convection and the sources that drive the waves in the Sun. We use a 3D, compressible, non-linear radiative magnetohydrodynamics code developed by Alan Wray for simulating the upper solar convection zone and the lower atmosphere. We have carried out the numerical simulations using a hyperviscosity approach and various physical Large-Eddy Simulation (LES) models (Smagorinsky and dynamic models) to investigate how the differences in turbulence modeling affect the damping and excitation of the oscillations and their spectral properties and to compare with observations from the SOHO and Hinode space missions. We find that the dynamic turbulence model provides the best agreement with the observations. We have studied the effects of magnetic field on the spatial-temporal spectrum of the turbulent convection, and found that these simulations can explain the observed changes of the granular dynamics and the enhanced emission of high-frequency waves in magnetic regions (effect of ``acoustic halo'').   

Direct Numerical Simulation of the turbulent flow over an urban canopy made of cubical obstacles

Computations of flow over staggered arrays of cubes with various plan area density are presented and discussed. A DNS technique, using an immersed boundary method for the obstacles, was employed. It is shown that the surface drag is predominantly form drag, which has a maximum for an area coverage around 15{\%}. As the effective roughness of the surface increases, so does the ratio of the spatially averaged vertical and axial normal turbulence stresses at the obstacle height, so a major effect of roughness is to change the structure of the turbulence field, thus altering the way that pollutants emitted within the canopy are transported. Time history of the total drag shows large scale oscillations. This should be related to large-scale pair of axially-orientated vortex rolls which are not stable, but ``come and go'' roughly periodically in time. These vortex structures appear to be much weaker when the total drag has its lowest magnitude. Such rolls are perhaps not unexpected. They have been found in boundary layers developing over similar surfaces but in that case appear to be essentially steady.   

A front tracking technique for direct numerical simulations of multiphase flows in complex geometries

Experimental studies have been the main thrust of microfluidic research so far; however, numerical simulations are gradually gaining acceptance as their importance is being more and more recognized by researchers in the field. Accurately capturing the liquid/liquid or liquid/gas interface is only part of the challenge in simulating fluid flow in lab-on-a-chip; the complex solid boundaries must also be accurately represented. Handling complex boundaries has been one of the challenges of CFD from the very beginning and one can identify roughly three stages. Crude representation of curved boundaries on a fixed grid by stair-stepping, body-fitted structured grids, and body-fitted unstructured grids. Current commercial codes almost exclusively use some variants of the last approach. However, while very common, unstructured grids generally lead to inefficient and inaccurate codes. Here, we present a front tracking technique to simulate the motion of drops and bubbles through complex geometries using regular structured meshes, where solid boundaries are represented as immersed boundaries and fluid boundaries are explicitly tracked. The methodology is validated and the code is used to study the dynamics of pressure-driven bubbles in a complex network of channels.   

Study on the preconditioning method of a finite element combined formulation for fluid-structure interaction

Preconditioners for a two-dimensional combined finite element formulation were devised and tested for fluid-structure interaction (FSI) problems. A fluid-structure interaction code simulating the interaction of circular bodies with an unsteady flow is based on a P2P1 finite element method using combined formulation. Extending the AILU preconditioners proposed by Nam et al.[2002] for P2P1 finite element formulation, four preconditioners were proposed for combined finite element formulation. Numerical simulations were performed for some two-dimensional FSI problems. It has been shown that two preconditioners among them perform well with respect to computational memory and convergence for a bench-mark problem.   

Vorticity dynamics in turbulence growth

The statistical and structural properties of fully developed isotropic turbulence can be reproduced at high $R_\lambda$ by numerical simulation with random forcing at large scales. A $k^{-5/3}$ energy spectrum range is observed. To understand why this range is formed inviscid and viscous time developing numerical simulations are performed starting with a certain number of Lamb dipoles. Inviscid simulations lead to a very strong vorticity amplification, which close to the eventual finite time singularity produces a $k^{-3}$ range. The viscous simulations, depending on the viscosity, show an enstrophy production differing from the inviscid simulations. the enstrophy dissipation becomes of the same order of the enstrophy production, which does not blows-up and reaches a maximum. At this point the $k^{-5/3}$ range forms. The analysis in the strain-rate tensor principal axes shows that the enstrophy production is correlated with the intermediate $\widetilde{S}_2$ accounting for sheet-like structures.   

Session PS: Convection III

Aspect ratio dependence of heat transport in Rayleigh-B\'{e}nard convection

The variation of heat transfer with respect to two of the three dimensionless control parameters in confined convection, namely the Rayleigh number and Prandtl number, has been the focus of most experiments and simulations. The dependence of the third parameter- the aspect ratio $\Gamma=D/H$, with $D$ is the diameter and $H$ is the height of the cell- has, however, been studied little. We, therefore, want to investigate the aspect ratio dependence of convective turbulence in a cylindrical cell by three-dimensional direct numerical simulations. The study emphasizes on two questions: Does the turbulent heat transport at a fixed Rayleigh number $Ra$ depend on the aspect ratio variation? Which changes in the global flow structures are associated with the aspect ratio variation? The analysis is conducted at several $Ra$ with a fixed Prandtl number of $0.7$. In addition, we quantify the fraction of the total kinetic energy that is contained in large-scale flow patterns by the so-called snapshot analysis.   

Proper orthogonal decomposition of turbulent thermal convection

The determination of the empirical eigenfunctions, which result from the Proper Orthogonal Decomposition (POD) procedure, is considered for Rayleigh-B\'enard convection in rectangular boxes. Periodic boundary conditions correspond to continuous symmetries and eigenmodes in the lateral translation-invariant directions, which are Fourier modes. These symmetries reduce the dimensionality of the eigenvalue problem. Free-slip boundary conditions in the vertical direction $y$, correspond to so-called discrete symmetries which can be handled by group theoretical considerations, with a significant increase in the available database. Several data sets at different Rayleigh number, are analyzed. We study how much kinetic energy is contained in the first POD modes, and how it changes with Rayleigh number. The most energetic POD modes give us also a hint on the dynamic dominance of coherent flow patterns, and how well the original inhomogeneous flow can be modeled with a reduced number of modes.   

Thermal convection at high Rayleigh and Prandtl numbers

We conducted laboratory experiments to study the convective patterns developping in a fluid with strongly temperature-dependent viscosity. As the viscosity ratio $\gamma$ increases, the thermal structure of the tank becomes asymmetric, the more viscous cold thermal boundary layer (TBL) at the top becoming thicker than the bottom hot TBL, and moving much more slowly (``sluggish lid regim''). For high Rayleigh numbers($> 10^{6}$) and intermediate viscosity ratios ($\gamma < 4000$), the temperature and velocity fields show that three different scales of convection develop: the largest convective scale is cellular, with cold downwelling sheets of viscous fluid encasing hotter, less viscous, parts of the tank. Within each of those cells develop several (typically $3$ to $7$) hot $3D$ upwelling plumes. Upon impinging under the cold TBL, each plume in turn generates locally a small ring of cold material which does not reach the bottom of the tank. A regim diagram of the multiscales convection existence and scaling laws describing the characteristics of the instabilities have been obtained.   

Time-dependent plume dynamics

We generalize the classical turbulent plume model of Morton, Taylor \& Turner (1956) to consider time-varying isolated sources of buoyancy in both unstratified and stratified environments. When the source buoyancy flux is reduced rapidly, we find that the plume narrows transiently from the classical straight-sided similarity solution towards another straight-sided similarity solution originally considered in the context of statically unstable ambient density distributions by Batchelor (1954). We verify this behaviour quantitatively by considering a large ensemble of laboratory experiments. Our results suggest that plume pinch-off is typically quite difficult to achieve. Conversely, when the source buoyancy flux increases rapidly, we find that a transient ``bulge'' propagates up the plume, separating regions of the plume associated with the original and final plume source conditions. We identify scaling laws for the various properties of this bulge, which are verified numerically by an ensemble of large eddy simulations. We show that our model equations can also be applied directly to the starting plume model of Turner (1962) if the increased entrainment through the top of the starting plume is accounted for appropriately.   

Probing modal dynamics of Rayleigh-B\'{e}nard convection using optical actuation

We report on a new experimental approach to investigate the dominant modes governing instability in Rayleigh-B\'{e}nard convection. ~The convective fluid is a gas that strongly absorbs incident infrared laser light. Laser light absorption results in localized heating, thereby altering the fluid flow. Rapid scanning of the light by servo mirrors allows actuation at multiple spatial points nearly simultaneously. This approach provides a tool for repeatedly imposing a given convection pattern, e.g., straight rolls. Selected perturbations are applied to this initial pattern, thus providing an ensemble of systems with nearby initial conditions. Modal dynamics are extracted from the subsequent pattern evolutions, monitored via time series of shadowgraph images.   

Reducing the Dimensionality of Spatio-Temporal Data in Rayleigh- B\'{e}nard Convection using Homology {\&} Karhunen- Lo\`{e}ve Decomposition

We present two different approaches to obtain a reduced dynamical description of spatio-temporal chaos in Rayleigh B\'{e}nard convection experiments. Computational Homology, a topological characterization technique, and Karhunen- Lo\`{e}ve (KL) decomposition are applied to time series of shadowgraph images. Homology computations for each image produce a set of non-negative integers called Betti numbers defining different characteristic topological properties of convective flows. Quantitative information is obtained from the probability distributions constructed from a time series of Betti numbers to identify different spatio-temporal states at different control parameters in experiments. For comparison, analogous information content at the same parameter values is captured by normalized eigenvalue spectra obtained by KL decomposition of shadowgraph images. We discuss strengths and weaknesses of these methods for characterizing spatio-temporal dynamics.   

Centrifugal effects in rotating convection: nonlinear dynamics

Rotating convection in cylindrical containers is a canonical problem in fluid dynamics, in which a variety of simplifying assumptions have been used in order to allow for low-dimensional models or linear stability analysis from trivial basic states. An aspect of the problem that has received limited attention is the influence of the centrifugal force, because it makes it difficult or even impossible to implement the aforementioned approaches. In this study, the mutual interplay between the three forces of the problem, Coriolis, gravitational and centrifugal buoyancy, is examined via direct numerical simulation of the Navier--Stokes equations in a parameter regime where the three forces are of comparable strengths in a cylindrical container with the radius equal to the depth so that wall effects are also of order one. A variety of bifurcated solutions and several codimension-two bifurcation points acting as organizing centers for the dynamics have been found. A main result is that the flow has simple dynamics for either weak heating or large centrifugal buoyancy. The limit of zero centrifugal buoyancy is singular, and the bifurcations found by decreasing it are subcritical. Centrifugal effects primarily lead to the axisymmetrization of the flow and a reduction in the heat flux.   

Session PV: Suspensions II

Force induced microdiffusivity of colloidal particles

\newcommand{\te}[1]{\mbox{\boldmath$ #1 $}} In constant force microrheology the velocity of the probe particle fluctuates owing to interactions with the surrounding medium. On long time scales, this fluctuating velocity gives rise to a diffusive motion of the probe particle. We study this diffusive motion as the Peclet number, $Pe$ -- the ratio of the strength of the external driving force, $\te{F}^{ext}$, compared to thermal forces, $kT/a$ -- is varied. Here, $kT$ is the thermal energy and $a$ the probe size. At small $Pe$, Brownian motion dominates and the diffusive behavior characteristic of passive microrheology is recovered. At the other extreme of high Peclet numbers the motion is still diffusive, and the diffusivity becomes ``force-induced'' scaling as $\te{F}^{ext}/\eta$, where $\eta$ is the viscosity of the solvent. Specific calculations are performed for a probe particle of size $a$ immersed in a background of colloidal bath particles of size $b$. The diffusive motion becomes increasingly anisotropic as the Peclet number is increased -- motion parallel to the direction of forcing exceeding that transverse. The ``force-induced'' microdiffusivity is compared with the analogous ``shear-induced'' diffusivity found in macrorheological measurements.   

Self-organization of fibers in a flow between two counter-rotating discs

The behavior of fibers suspended in a flow between two flat counter-rotating discs has been studied experimentally. A CCD-camera was used to capture images of the fibers in the flow. Image analysis based on the concept of steerable filters extracted the position and orientation of the fibers in the plane of the discs. Experiments were performed for gaps between the discs of 0.2 to 0.9 fiber lengths, and for equal absolute values of the velocities for the upper and lower disc. The length-to-diameter ratio of the fibers was 23. Depending on the angular velocities of the discs and the gap between them, the fibers were found to organize themselves in fiber trains. A fiber train is a set of fibers positioned one after another in the tangential direction with a close to constant fiber-to-fiber distance. Each individual fiber is aligned in the radial direction (i.e. normal to the main direction of the train). The experiments show that the number of fibers in a train increases when the gap between the discs decreases. Furthermore, the number of fibers in a train decreases at both high and low angular velocities with an optimum in between.   

High Gradient AC Dielectrophoretic Filtration

Dielectrophoresis is the motion of an object under forces resulting from electric field gradients. Unlike a mechanical filter, particles flowing through a dielectrophoretic filter are attracted towards the electrodes and captured in the filter by the dielectrophoretic force, even though their average size can be substantially smaller than the filter pore size. We report a new, economic, easily scaled up method for the fabrication of dielectrophoretic filters. The concept utilizes winding of metal and plastic meshes. In this design, two metal meshes serving as energized and grounded electrodes are mechanically and electrically separated with a plastic mesh. The proposed technology d allows for a reduction in the applied AC voltage and electric power by employing fine mesh materials. The particle captivity of an AC dielectrophoretic filter is governed by the mesh size, the particle size and polarizability, the flow rate, the field frequency, and the peak-to-peak voltage.   

Effect of hydrodynamic forces on particle velocity fluctuations in suspensions at moderate Reynolds number

Direct numerical simulations (DNS) of monodisperse suspensions with high particle inertia and moderate fluid inertia are performed using an immersed boundary method (IBM) to quantify the effect of hydrodynamic forces on particle velocity fluctuations. The evolution of the second moment of particle velocity fluctuations is driven by the correlation between fluctuating particle acceleration and fluctuating particle velocity. This correlation arises in part due to hydrodynamic interactions with neighboring particles, and it is not satisfactorily predicted by existing drag laws for the particle acceleration used in conjunction with the particle velocity distribution. A new Langevin model for the fluctuating particle acceleration is proposed, which yields promising results when compared with the DNS data. The source and sink terms in the particle velocity second moment equation that arise due to hydrodynamic interactions are quantified using the DNS data.   

Filtration of a fiber suspension: velocity measurements and Fokker-Planck orientatation simulations

We present an experimental and numerical study on the filtration of a dilute suspension of flexible fibers. The experiments were performed in a vertical channel, and sedimentation occurred in the direction of the filtration flow. The channel had a square cross section. The suspension was made optically transparent by matching the index of refraction of fluid (mixture of glycerine) and fibers (fluorocarbon, d=260 $\mu$m, l=9.8, 18.6 mm), and Particle Image Velocimetry was used to measure the time-resolved velocity field of the fluid phase in the proximity of a permeable screen, where the fibers were retained. The velocity was measured in a vertical plane located in a region where wall-effects are negligible. The evolution of the orientation distribution of the fibers in this plane was calculated with the Fokker-Planck equation, based on the measured flow fields. This was done under the assumption of creeping flow. Both filtration velocity and fiber aspect ratio have a considerable effect on the final orientation distribution of the network formed on the wire. Our methodology allows us to distinguish between these two factors.   

Hydrodynamic Interactions Mediated by Polymer Depletion Effect

Polymer depletion has significant impact on the transport and binding of proteins as well as the aggregation of macromolecules in a molecularly crowded environment. In many synthetic colloid-polymer mixtures, polymer depletion can be used to control the stability and dynamics of colloidal dispersions. For nonadsorbing polymer solutions in which depletion phenomenon occurs, polymer chains tend to move away from the region surrounding the suspended particles to avoid the loss of configuration entropy. This depletion zone complicates particle's diffusion behavior and may cause depletion-induced flocculation due to the unbalanced osmotic force. The thermodynamic origin of the depletion-induced entropy force is well understood, but the hydrodynamics involved in particle-particle interactions taking into account the depletion effect has not been previously studied. We analyze the hydrodynamic mobility of a pair of interacting Brownian particles mediated by the polymer depletion effect. Analysis will be presented specially for limiting cases when depletion zones of uncharged particles overlap. The proposed theoretical model is important for predicting the aggregation kinetics of nucleation- and diffusion-limited flocculation processes.   

Coating with colloids by receding contact line

Many coating processes use evaporation. But such coatings are usually inhomogeneous because of the evaporation singularity at the contact line. We are thus investigating the effect of this singularity on dip-coating. In dip-coating, two flows are in competition: one inwards due to the receding contact line, the other outwards due to evaporation, and the equiibrium of thes flows predicts the thicknes of the deposit. There are two dip-coating regimes: one controlled by evaporation, and the known Landau-Levich regime. A minimum deposit thickness is expected between these two regimes. Using different microscopy techniques, we found out that there was a minimum in the deposit thickness, but that the actual mesoscopic order strongly varies depending on the contact line velocity. In the stick-slip regime, we can also link the spatial frequency of the stick-slip motion with the contact line velocity. Eventually, the thinnest deposits exhibits iridescence, which means that we are close to a photonic cristal structure.   

Expansion flows in suspensions

Suspension flows can lead to variations in particle volume fraction, thus making the particle phase compressible on a macroscopic scale. The stress in such a flow is characterized by an effective bulk viscosity ($\kappa_{eff}$) in addition to the effective shear viscosity of the suspension. The bulk viscosity of a suspension of particles relates the deviation of the trace of the macroscopic or averaged stress from its equilibrium value to the average rate of expansion. The equilibrium stress is the sum of the fluid pressure and the osmotic pressure of the suspended particles. Variations in particle volume fraction are modeled by having a compressible fluid expand uniformly at a constant rate, causing the particles suspended in it to move apart. The rigid particles cannot expand, and create a disturbance flow that contributes to the total mechanical pressure in the system, thereby changing the effective bulk viscosity. Explicit formulae have been derived to compute the bulk viscosity for all volume fractions of suspended rigid particles and for all expansion rates. The hydrodynamic forces between particles including the strong lubrication interactions near contact play an important role at high concentrations. The bulk viscosity of concentrated suspensions with full hydrodynamic interactions is determined via direct simulation by adapting the Stokesian Dynamics paradigm to allow for a uniform rate of expansion.