Session AA: Turbulent Boundary Layers: DNS & LES

Chasing eddies and their wall signature in turbulent boundary layers at Mach 3 through 10

We use a direct numerical simulation database of turbulent boundary layers,\footnote{Martin, M.P., JFM, vol. 570, pp. 347- 364, 2006}$^,$\footnote{Martin, M.P., AIAA Paper 2004-2337}$^,$\footnote{Beekman \& Martin, APS DFD08} statistical tools,\footnote{Brown \& Thomas, Phys. Fluids, vol. 20, pp243-251, 1977} scientifically-rooted packet-pattern recognition,\footnote {Ringuette, Wu \& Martin, JFM, vol. 594, pp. 59-69, 2008} and validated visualization algorithms\footnote{O'Farrell, C. Senior Thesis, Princeton University 2008} to identify hairpin packets and their wall signature. We investigate the variation of time scales and length scales associated with coherent structures and the role of hairpin packets on the generation of skin friction, wall-pressure loading and heat transfer.   

Wall turbulence without walls

Direct numerical simulations are presented of isolated logarithmic layers without an underlying buffer zone. They are implemented by enforcing artificial boundary conditions within the logarithmic layer which are synthesized from values from the interior of the flow. As an example, simulations of a half-channel employing this technique are discussed. The results exhibit logarithmic mean velocity profiles, and velocity fluctuation intensities that are similar to those obtained by the full DNS of half or full channels. Those results strongly suggest that the formation of a logarithmic layer is not overly dependent on the presence of a near-wall region, and that such a flow can exist by itself. The technique enables us to perform conceptual experiments to clarify what is essential to the logarithmic layer. For example, preliminary results show that the logarithmic layer cannot be created only by a non-uniform shear, and requires a spatial gradient of the scales of the fluctuations. Somewhat surprisingly, some simulations result in K\'arm\'an constants fairly different from $\kappa=0.4$, providing clues to what determines $\kappa$ in real wall turbulence.   

Direct numerical simulations of reacting boundary layers

Direct numerical simulations (DNS) of turbulent boundary layers\footnote{Mart\'in \& Candler, Phys. Fluids, vol. 10, pp. 11715-1724, 1998}\footnote{Mart\'in \& Candler, AIAA Paper 2001- 2717} show that there is a strong coupling between temperature fluctuation and chemical composition. Small temperature fluctuations result in large fluctuations in the chemical composition of the gas. The maximum fluctuation levels occur when the reactions are exothermic, right at the surface, where the coupling with the surface chemistry is important. In this work, we conduct DNS of reacting turbulent boundary layers, including non-catalytic, partially catalytic and fully catalytic wall conditions, and we explore the feedback mechanisms between the surface reactions at the wall, near-wall gas phase chemistry, and turbulent boundary layer.   

Effect of heat transfer on turbulent boundary layers

We use direct numerical simulation to gather a database of hypersonic turbulent boundary layers at different flow conditions varying heat transfer. A statistical description of the data is given, including the effect of wall-temperature condition on fluctuation levels, Reynolds stresses, energy and vorticity budgets, Reynolds analogies, skin friction, wall- pressure loading, and entrainment. Additionally, the turbulence structure is visualized and characterized.   

LES of Turbulent Channel Flow at Large $Re_{\tau}$

Large-eddy simulation (LES) of turbulent channel flow will be discussed. A special near-wall, subgrid-scale (SGS) model is developed based on wall-normal averaging of the streamwise momentum equation and local inner scaling combined with an extended form of the stretched-vortex, subgrid-scale (SGS) model. The latter incorporates production of Reynolds shear stress produced by the winding of streamwise momentum by near-wall, attached, SGS vortices. This then allows calculation of an instantaneous slip velocity that is then used as a ``virtual-wall'' boundary condition for the LES within the log region. A K\'arm\'an-like constant is calculated dynamically as part of the LES. With this closure, LES of turbulent channel flow will be presented for $Re_{\tau}$ in the range $2\,\times 10^3$ -- $2\,\times 10^7$.   

Comparison between turbulent boundary layers and channels from direct simulation

Results are presented from a new simulation of the ZPG turbulent boundary layer at $Re_{\theta}=1000-2100$, and compared to turbulent channels at similar Reynolds numbers. Even the low order statistics differ between the two flows, including within the buffer layer. The pressure and the transverse velocity fluctuations are stronger in boundary layers, even if the wall-parallel scales derived from the spectra and the two-point correlations are similar in both cases. On the other hand, the streamwise fluctuation intensities are roughly similar in both flows, but their scales are shorter and narrower in boundary layers. The differences are traced to an excess of turbulent energy production in the outer part of the boundary layer, compared to channels, associated with the stronger wake component of the mean velocity profile. Most of this excess is compensated by stronger pressure fluctuations and by the pressure-strain term, which redistribute the energy to the transverse components. The differences persist in higher Reynolds numbers experiments, suggesting caution in mixing results from different flows when documenting,for example, Reynolds number effects.   

Simulations of High-Reynolds Number Turbulent Boundary Layers

Direct and large-eddy simulations (DNS and LES) of spatially developing turbulent boundary layers under zero pressure gradient up to relatively high Reynolds numbers ($Re_{\theta}$ = 3000 and above) are performed. The computational quantities include the velocity plus passive scalar fields at Prandtl numbers between 0.2 and 2. The inflow is located at $Re_{\delta^*}$ = 450, a position where natural transition to turbulence can be expected. In addition to fully-resolved DNS, several carefully validated and promising subgrid-scale closures shall be applied together with a well-resolved, spectral numerical method. The results are extensively compared to available measurements, e.g. the ones obtained by \"Osterlund et al. (1999). Additionally, quantities difficult or impossible to measure, e.g. pressure fluctuations and complete Reynolds stress budgets, shall be presented. The goal of the project is to provide the research community with reliable numerical data for high- Reynolds number, spatially evolving wall-bounded turbulence. In addition, it shall be shown that with today's computer power Reynolds numbers relevant for industrial application can be within reach for DNS/LES.   

Analysis of vortical structures in highly compressible turbulent boundary layers

The coherent vortical structures in spatially developing supersonic turbulent boundary layers are analyzed by means of direct numerical simulation of the compressible Navier-Stokes equations. Three Mach numbers, M=2,4,6 are investigated to get some insight into the effect of flow compressibility on the size, orientation, and strength of the structures. To capture even the finest scale structures a very small grid spacing is used, corresponding to 4.5 wall units both in the streamwise and the spanwise directions. For all test conditions the same qualitative behavior is observed: consistent with incompressible dynamics, the near-wall layer is found to consist of quasi-streamise vortices strongly associated with meandering, low-speed streaks. In the outer layer, the vortex orientation statistics are consistent with the occurrence (at least in statistical sense) of ring-like vortices oriented at a shallow angle with respect to the wall plane. Good scaling of the vortex with wall properties is observed, even for the stronger Mach numbers. The analysis of the dilatation field show the onset of turbulence shocklets starting at M=4. Shocklets are found to be more intense in the very-near wall region, and to be statistically associated with sweeps of high-momentum fluid towards the wall.   

Statistical properties for homogeneous isotropic turbulence and turbulent channel flows using a coherent structure function

Coherent structures in turbulence are usually extracted by the second invariant of a velocity gradient tensor. Coherent fine scale eddies can be scaled by the Kolmogorov microscale and the rms of the velocity fluctuation, and the scaling is universal in homogeneous isotropic turbulence, turbulent channel flows and turbulent mixing layers. On the other hand, a coherent structure function is defined as the second invariant normalized by the magnitude of the velocity gradient tensor. The coherent structure function $F_{CS}$ extracts the statistical properties of turbulent flow fields, and has been successfully used to a local subgrid-scale model for complex geometries. Since the $F_{CS}$ has distinct upper and lower limits, it may be convenient to use $F_{CS}$ rather than the second invariant whose magnitude depends on Reynolds number. The statistical properties of $F_{CS}$ are shown with outstanding DNS databases for homogeneous isotropic turbulence and turbulent channel flows.   

Session AB: Turbulence Simulations I

Enhancement of artificial bulk viscosity method for predicting sound and aero-optics in transonic regimes

Alternative formulations of Cook and Cabot shock capturing model (Journal of Computational Physics, 2005) is investigated using large-eddy simulation (LES) of transonic flow over a cylinder at Re=10,000 and M=0.85. The original model uses an artificial bulk viscosity to adaptively thicken shocks over a few grid cells, and uses high order Laplacian of strain rate tensor magnitude to trigger the bulk viscosity coefficient. This model is employed in a 6th order staggered LES code on a structured mesh and found to cause unnecessary dissipation of dilatation in flow regimes other than shock regions. In particular, artificial viscosity magnitude was found to be an order of magnitude higher than physical viscosity in sound propagating regimes. Using derivatives of dilatation field as model's coefficient, instead of strain rate magnitude, is shown to significantly remove the unnecessary dissipation from the leading portion of the cylinder. Furthermore, employing a shock sensor switch to turn-off the model in the far-field is found to enhance prediction of flow generated noise. The impact of artificial dissipation on aero-optics will also be discussed.   

Grid Independent Large-Eddy Simulation using Explicit Filtering

The governing equations for large-eddy simulation are derived from the application of a low-pass filter to the Navier-Stokes equations. It is often assumed that discrete operations performed on a particular grid act as an implicit filter causing results to be sensitive to the mesh resolution. Alternatively, explicit filtering separates the filtering operation from the underlying mesh distribution, thereby eliminating grid sensitivities. We investigate the use of explicit filtering in large-eddy simulation in order to obtain numerical solutions that are grid independent and are not influenced by numerical errors. The extension and implementation of high-order, commuting filters (Vasilyev \emph{et. al}, \emph{J. Comp. Phys.}, 1998) in the context of wall-bounded flows will be discussed. The convergence of simulations using a fixed filter width with varying mesh resolutions to a \emph{true} LES solution will be analyzed, with particular attention to the performance of the chosen subgrid scale model. Results from planar channel flow simulations using LES with explicit filtering at $Re_{\tau} = 180$ and $395$ will be presented.   

Minimization of the Germano--identity error in the dynamic Smagorinsky model

We revisit the Germano--identity error in the dynamic modeling procedure in the sense that the current modeling procedure to obtain the dynamic coefficient may not truly minimize the error in the mean and global sense. A ``corrector step'' to the conventional dynamic Smagorinsky model is proposed to obtain a corrected eddy viscosity which further reduces the error. The change in resolved velocity due to the coefficient variation as well as nonlocal nature of the filter and flow unsteadiness is accounted for by a simplified suboptimal control formalism without resorting to the adjoint equations. The cost function chosen is the Germano--identity error integrated over the entire computational volume and pathline. In order to determine corrected eddy viscosity, the Fr\'echet derivative of the cost function is directly evaluated by a finite--differencing formula in an efficient manner. The proposed model is applied to isotropic turbulence and turbulent channel flow at various Reynolds numbers and resolutions to obtain noticeable reduction in the Germano--identity error and significantly improved flow statistics.   

Large eddy simulation of an urban-type boundary layer

Large eddy simulations based on the scale-dependent Lagrangian dynamic model (Meneveau, Phys. Fluids (17), 2005) allow for scale dependence. This is particularly relevant when the filter scale approaches the upper limits of the inertial range, which is typically the case when modeling urban boundary layers. Scale-dependent Lagrangian dynamic models are also known to exhibit favorable dissipation characteristics. In this talk we present the results of a numerical simulation of an urban-type boundary layer described in the talk by Monnier, Neiswander, Wark {\&} Rempfer at the 2007 APS/DFD meeting. The domain consists of 4 rows of 3 cuboids placed in a wind tunnel. The inlet velocity conditions are obtained from hot-wire measurements upstream of the blocks. The flow is simulated using the dynamic Smagorinsky model available with the commercial software FLUENT and the scale-dependent Lagrangian dynamic model available with spectral element code nek5000. These results are compared with the PIV data obtained from the experiments.   

A dynamic wall model constrained by external Reynolds stress

We propose a new approach of incorporating RANS constraints into SGS models, and discuss the corresponding dynamic wall model. Unlike conventional approaches, given Reynolds stresses are not imposed as the solution, but are used as constraints on the mean SGS stress so that the given Reynolds stress closely matches the computed stress only in the mean sense. Also, since LES in general outperforms RANS even at coarse resolution except very near the wall, RANS constraints are limited to the points where the LES solution is expected to be erroneous. We use the Germano--identity error as an indicator of LES quality so that the RANS constraints are activated only where the Germano--identity error exceeds a certain bound. The proposed model is applied to LES of turbulent channel flow at various Reynolds numbers and grid resolutions to obtain significant improvement over the dynamic Smagorinsky model, especially at coarse resolutions.   

Theoretically Based Optimal LES

A major obstacle to the practical application of optimal LES modeling has been the use of DNS statistical data for the multi-point velocity correlations that are needed in the formulation. Here we show that for high Reynolds number turbulence for which small-scale isotropy is valid, the Kolmogorov inertial range theory, the quasi-normal approximation and a model form for the three-point third-order velocity correlation are sufficient to define the optimal LES model. Only two flow-dependent constants remain, the velocity variance $u^2$ and the dissipation $\epsilon$. These constants are determined via a dynamic procedure in which the statistics of the unfiltered turbulence are reconstructed from the LES statistics. These theoretical optimal models are applied to a finite-volume LES formulation of isotropic turbulence, and the resulting LES perform very well. In these finite-volume LES, an optimal model for the convective momentum flux through finite volume cell boundaries replaces the normal finite volume schemes. The model can thus be considered to be a finite volume LES operator. The spectral properties of the LES operators have been compared to those of standard finite volume schemes, and there are several surprising differences, which have important implications for the formulation of LES models.   

Large-Eddy Simulations of turbulent hydrodynamic and magnetohydrodynamic channel flows

We perform Large-Eddy Simulations of incompressible hydrodynamic and magnetohydrodynamic channel flows at low magnetic Reynolds numbers (i.e. in the framework of the quasi-static approximation where the Lorentz force is treated as an explicit contribution to the momentum balance). The computations are performed using a pseudospectral and a second-order collocated finite volume method. Two eddy-viscosity type models are compared for different mesh resolutions: the dynamic Smagorinsky (DSM) and the Wall-Adapting Local Eddy-viscosity (WALE) model. We examine in detail the contributions to the kinetic energy budget of each term appearing in the Navier-Stokes equations. In particular, the results show that the subgrid-scale dissipation measured in the finite volume simulations is systematically much lower than in the spectral ones.   

On discretization errors and subgrid scale model implementations in Large Eddy Simulations

We analyze the impact of discretization errors on the performance of the Smagorinsky model in Large Eddy Simulations (LES). To avoid difficulties related to solid boundaries, we focus on decaying homogeneous turbulence. It is shown that two numerical implementations of the model in the same finite volume code lead to significantly different results in terms of kinetic energy decay, time evolutions of the viscous dissipation and kinetic energy spectra. In comparison with spectral LES results, excellent predictions are however obtained with a novel formulation of the model derived from the discrete Navier-Stokes equations. We also highlight the effect of discretization errors on the measurement of physical quantities that involve scales close to the grid resolution.   

Rapid Spin-Up of MHD Turbulence

Direct numerical simulations of two-dimensional decaying MHD turbulence in bounded domains show the rapid generation of angular momentum in non-axisymmetric geometries. It is found that magnetic fluctuations enhance this mechanism. The subsequent generation of a magnetic angular momentum or angular field is due to the relaxation of the flow towards an aligned state. For axi-symmetric geometries the generation of angular momentum is absent, nevertheless a weak angular field can be observed. The derived evolution equations for both angular momentum and angular field yield possible explanations for the observed behaviour.   

Magnetic Structures Produced by the Small-Scale Dynamo

Small-scale dynamo action has been obtained for a flow previously used to model fluid turbulence, where the sensitivity of the magnetic field parameters to the kinetic energy spectrum can be explored. We apply quantitative morphology diagnostics, based on the Minkowski functionals, to magnetic fields produced by the kinematic small-scale dynamo to show that magnetic structures are predominantly filamentary rather than sheetlike. Our results suggest that the thickness, width, and length of the structures scale differently with magnetic Reynolds number as $R_m^{-2/(1-s)}$ and $R_m^{-0.55}$ for the former two, whereas the latter is independent of $R_m$, with $s$ the slope of the energy spectrum.   

Session AC: Turbulence Modeling I

A modified artificial viscosity approach for compressible turbulence simulations

Standard high-order methods give rise to spurious oscillations near shocks which can be controlled by using localized artificial viscosity (AV). Schemes which give a high wavenumber bias to the numerical dissipation around shocks are gaining popularity. Using simulations of compressible isotropic turbulence with optimized high-order schemes at different resolutions we investigated the range of scales where artificial dissipation is active. We observed that the impact of AV was not limited to high wavenumbers. This is especially true for moderately high Mach number isotropic turbulence which spontaneously forms shocklets, for which the AV method is found to excessively damp the dilatational motions. We propose a modified form using a dynamic coefficient which activates AV only in the regions of strong compression, such as shocks, turning it completely off for turbulence and expansion waves. This is found to give improved statistics for all quantities, not just dilatation. This formulation reverts back to the traditional one for strong shocks, so that its shock capturing capability is not compromised.   

Finite-Volume Optimal LES Formulations for Coarsely Resolved Channel Flows

In finite-volume formulations of optimal LES (OLES), the effects of unresolved turbulence are represented in terms of models for the momentum fluxes through the finite-volume cell boundaries. The models are quadratic in the velocities of the cell volumes, and given the finite-volume stencil to be used are optimized using stochastic estimation. The resulting model is effectively a finite-volume scheme that has been designed to represent the effects of subgrid turbulence. This approach has been found to be highly effective in isotropic turbulence, but in a wall-bounded flow, new complications arise. These include the treatment of the mean velocity, subgrid anisotropy and the momentum flux to the wall. In this study, correlations derived from DNS of turbulent channel flow are used to perform the stochastic estimation for a number of model dependencies (stencils), and the properties of the resulting OLES models are evaluated. Of particular interest are stability of the schemes, energy transfer to the small scales, and the {\it a posteriori} accuracy of the resulting LES. Schemes that correctly represent energy transfer can easily be constructed, but stable and accurate LES results are more sensitively dependent on the formulation of the schemes and their interaction with models for the wall shear stress. The properties of models that perform well {\it a posteriori} will be discussed.   

Large-eddy simulations based on the subgrid-scale kinetic energy transport equation

This presentation focusses on the development of SGS models based on transport equations for the SGS kinetic energy and SGS scalar variance. These models do not suffer from the limitations of the local equilibrium assumption that is used by the great majority of existing SGS models. In virtually all SGS models using transport equations, the diffusion terms are lumped together, and their joint effect is modeled using a ``gradient-diffusion'' model. It is shown that this is a poor approximation for inertial range filter sizes and high Reynolds numbers. The reason for this lies in a loss of local balance between the SGS turbulent diffusion and diffusion caused by GS/SGS interactions, and in the deficient modeling of the diffusion by SGS pressure-velocity interactions. In order to improve this situation, a new model, inspired by Clark's SGS model, is developed for this term. The new model shows very good agreement with the exact SGS pressure-velocity term in a priori tests and better results than the classical model in a posteriori LES tests. We assess several models currently used for the molecular/viscous SGS dissipation terms. The model used in hybrid RANS/LES tested here gives very poor results. The reason behind this is connected with the deficient spectral representation of the exact molecular SGS dissipation term.   

Energy transfers in shell models for MHD turbulence

A systematic procedure to derive shell models for MHD turbulence is proposed. It takes into account the conservation of ideal quadratic invariants such as the total energy, the cross-helicity and the magnetic helicity as well as the conservation of the magnetic energy by the advection term in the induction equation. This approach also leads to simple expressions for the energy exchanges as well as to unambiguous definitions for the energy fluxes. When applied to the existing shell models with nonlinear interactions limited to the nearest neighbour shells, this procedure reproduces well known models but suggests a reinterpretation of the energy fluxes. This formalism also yields general constraints on the shell models that are independent of the shell model expressions for the helicities. The final structure of the shell model requires however explicit definitions for both the vorticity and the magnetic potential vector in terms of the shell variables.   

Stochastic Coherent Adaptive Large Eddy Simulation of forced isotropic turbulence with variable thresholding

In this talk we discuss the progress in the development of the novel methodology for the numerical simulation of turbulent flows, called Stochastic Coherent Adaptive Large Eddy Simulation (SCALES). SCALES is an extension of the Large Eddy Simulation approach that uses a wavelet filter-based dynamic grid adaptation strategy to solve for the most energetic coherent structures in a turbulent flow field, while modelling the effect of the less energetic background flow with a local dynamic subgrid-scale (SGS) model. In contrast to previous formulations that used a global relative wavelet threshold, in this study we explore the {\em spatially variable} wavelet thresholding strategy to ensure the adequate resolution of local flow characteristics. For example, the local wavelet thresholding level can be adjusted by ensuring a prescribed level of SGS dissipation with respect to the resolved viscous dissipation. A number of numerical experiments for linearly forced homogeneous turbulence are presented and the results are compared with pseudo-spectral reference solutions. The agreement holds not only in terms of global statistical quantities but also in terms of spectral distribution of energy and, more importantly, enstrophy all the way down to the dissipative scales.   

Helical vortex-based model of deterministic stresses for Large-Eddy-Simulation of a wind turbine wake

When representing a wind turbine in LES using a drag disk (e.g. A. Jimenez et al. 2007), the periodic effects due to the turbine's rotating elements remain unresolved. The periodic effects on the mean flow can be represented in a simulation using deterministic stresses in the wake. In this work, based on the Biot-Savart law with a helical vortex street and various simplifications, we develop an analytical expression for the deterministic, periodic velocity fluctuations in the wake. Then, the deterministic stress tensor is obtained by the product of the approximated fluctuating components of velocity, and integration over a helical period. The resulting model is implemented within a Large Eddy Simulation of an array of wind turbines, using the scale-dependent Lagrangian dynamic model (Bou-Zeid et al. 2005). The importance of the deterministic stresses on the computed wake structure is examined by varying the strength of the helical vortices.   

A dynamical systems approach to modeling the rapid pressure strain correlation

Models for the rapid pressure strain correlation, under the auspices of the classical Reynolds stress closure schemes, represent dynamical systems in the state space composed of the Reynolds stress tensor components. For 2 dimensional mean flows, these are single parameter systems, dependent on the mean flow gradient. A classification of the topology and behavior of the same would provide invaluable guidelines for developing improved models. In line with the maxim of understanding before prediction, the authors aim to classify the dynamical behavior of this hypothetical system. With the objective of isolating the effects of pressure strain correlation, the behavior of the Navier Stokes equations is contrasted against its pressure released analogue, the Burgers equations, in the rapid distortion limit. The authors carry out numerical simulations, in addition to the analytical modeling, for both the systems. The corresponding invariant set topologies are classified and a concomitant bifurcation analysis is conducted. Some salient issues addressed in this study include the requisite nature of the model, viz. a linear or nonlinear structure; and the inability of models to capture elliptic flows.   

Truncated Navier-Stokes Equations with the Automatic Filtering Criterion

Truncated Navier-Stokes (TNS) methodology is a LES technique in which Navier Stokes equations are solved in the DNS mode on a coarse LES mesh. Because no explicit SGS model is used, such simulations would quickly depart from DNS results obtained on a full DNS mesh, with departures observed first in the small scales. In TNS this process is controlled by periodically filtering out the small scales of the numerical solution and replacing them by new, estimated scales. In previous work the filtering time interval was normally fixed through trial and error. We report details of a modified TNS procedure where the filtering interval is determined automatically during the course of the simulations. The procedure employs the criterion that prevents the energy buildup in the small scales beyond limits allowed by the inertial and dissipation range dynamics. The procedure is tested in a sequence of TNS simulations for turbulent channel flow and several Reynolds numbers for which detailed DNS data are available for comparison, up to $Re_{\tau}=2000$.   

A kinematic sub-grid scale model for large-eddy simulation of turbulence-generated sound

In the hybrid simulation of large-eddy simulation (LES) and Lighthill's acoustic analogy for turbulence-generated sound, an LES is used to solve the Navier-Stokes equations and the turbulence-generated sound at far fields is calculated from Lighthill's acoustic analogy. As only the filtered velocity fields are available from the LES, the Lighthill stress tensor, serving as a source term in Lighthill's acoustic equation, has to be evaluated from the resolved velocity fields and thus, the unresolved velocity fields are missing in the conventional LES. The sound of missing scales has been shown to be important and hence need to be modeled. The present study proposes a kinematic sub-grid model which recasts the unresolved velocity fields into Lighthill's stress tensors. A kinematic simulation is used to construct the unresolved velocity fields with an imposed temporal statistics, which is consistent with the random sweeping hypothesis. The model is used to calculate sound power spectra from isotropic turbulence with an improved result: the missing portion of the sound power spectra is approximately recovered in this calculation.   

Session AD: Stability and Transition

Effect of Wall-Temperature Variation in Laminar Boundary Layer Stability

A high-fidelity three-dimensional numerical study is performed to explore the effect of thermal perturbation in a Mach 1.5 flat plate laminar boundary layer. The thermal bump is pulsed at a frequency determined from the linear stability theory. A high-speed and low-speed streaky region is formed downstream in response to the pulsing. The flow stability characteristics are assessed by varying the initial disturbance amplitude, pulsing frequency and the shape of the thermal bump. The rectangular and circular shape are considered. The former one generates two pairs of counter-rotating streamwise vortices at the four edges, while the latter one generates only one pair. The mean flow is greatly distorted, which makes it susceptible to secondary instabilities. The transition mechanism is evaluated using the transient growth and the traditional linear stability theory.   

Experimental investigation of boundary layer transition in the presence of a step

A fundamental experimental study of the influence of a sharp-edged step on the stability of a laminar boundary layer over a range of step sizes, Reynolds numbers and pressure gradients was performed. The unique test facility, the Towing Wind Tunnel at Tohoku University in Japan, allowed measurements of disturbance growth and transition to be made in a minimal disturbance environment at unit Reynolds numbers of order 10$^{6}$/m. Velocity fluctuations were recorded with an array of hot-wire sensors in the boundary layer downstream of the step, alongside complementary Pitot tube measurements of the mean velocity of the flow. Disturbance spectra, critical transition Reynolds numbers and ``N-factors'' at different flow conditions and step sizes will be discussed.   

Boundary Layer Driven Cavity Flow: Effect of Aspect Ratio

A 2-D, square, transverse cavity model with variable aspect ratio, embedded below a laminar boundary layer, was used to study the formation of Taylor-Gortler like (TGL) vortices through fluorescent dye flow visualization and Digital Particle Image Velocimetry (DPIV). The length to width aspect ratio was varied from 22:1 to 1:1 to evaluate how this affected the formation of secondary TGL vortices within the primary cavity vortex flow field. The results show that for the same freestream velocity, weaker TGL vortices were observed for the lower aspect ratios. In the 1:1 aspect ratio case, no TGL vortices were observed even at the highest freestream velocity. Using the aspect ratio of 22:1, dye visualization was used to study the flow within several adjacent cavities. TGL vortices were not evident in the first two cavities while the third cavity showed definite signs of the beginning stages of TGL vortex formation. Further downstream boundary layer transition was observed, which induced larger velocities inside the cavities and stronger TGL vortices.   

Amplitude Equation for Instabilities Driven at Deformable Surfaces - Rosensweig Instability

The derivation of amplitude equations from basic hydro-, magneto-, or electrodynamic equations requires the knowledge of the set of adjoint linear eigenvectors. This poses a particular problem for the case of a free and deformable surface, where the adjoint boundary conditions are generally non-trivial. In addition, when the driving force acts on the system via the deformable surface, not only Fredholm's alternative in the bulk, but also the proper boundary conditions are required to get amplitude equations. This is explained and demonstrated for the normal field (or Rosensweig) instability in ferrofluids as well as in ferrogels. An important aspect of the problem is its intrinsic dynamic nature, although at the end the instability is stationary. The resulting amplitude equation contains cubic and quadratic nonlinearities as well as first and (in the gel case) second order time derivatives. Spatial variations of the amplitudes cannot be obtained by using simply Newell's method in the bulk.   

Effect of parameter modulation on the dynamo effect in a rapidly rotating spherical shell

The dynamo effect is the process by which the magnetic field of the Earth is generated. In the presence of a small initial magnetic field, convective motions in the fluid outer core produce currents and thus a magnetic field which can reinforce the initial field and sustain it against ohmic diffusion. There is also a feedback of the magnetic field on the flow which limits its growth. Our direct numerical approach consists in solving the equations for the velocity field, the magnetic field and the temperature in a rapidly rotating spherical shell. Convective motions in our system originate from a thermal forcing. The effect on the flow of this forcing can be modulated in time through a modulation of the control parameter. We first focus our study on the impact of this modulation on convection without magnetic field. Depending on parameters and characteristics of the modulation, many interesting features such as shifts of the convective threshold and resonances are found. The magnetohydrodynamic case is then considered. The impact of the parameter modulation on the dynamic of the magnetic field and on the dynamic of reversals of its polarity is studied.   

The Bullard Von K\'arm\'an experiment

Since Larmor at the beginning of the XX$^{\circ}$ century, the magnetic field of the earth is thought to be produced from motions of the liquid iron core. Part of the kinetic energy of the flow is converted into magnetic energy. A generic model of the dynamo instability is based on two induction processes, namely $\alpha$ and $\omega$. The $\alpha$- effect is the production of a current density $\vec{j}$ parallel to the initial magnetic field $\vec{b}$, and the $\omega$-effect is linked to the velocity $\vec{v}$ gradients via the term $\vec{b}\cdot\vec\nabla\vec{v}$ in the induction equation. We developed an experimental semi homogeneous $\alpha-\omega$ dynamo (a model commonly used in astrophysics) in a Von K\'arm\'an flow : motion is imparted to liquid Gallium by the counter-rotation of two coaxial impellers with blades. The $\omega$ effect is due to the shear in the mid plane of a Von K\'arm\'an flow and fully includes turbulence. The $\alpha$- effect is simulated by current flow in two coils. Complex dynamics of the dynamo (On-Off intermittency, chaotic reversals, excursions) are observed to be linked with the statistics of the turbulent $\omega$ induction process.   

Stability characteristics of a rotating Poiseuille flow about the streamwise axis

A more complete understanding of transition to turbulence in a Poiseuille flow rotating about the streamwise axis is sought by studying the stability of the flow. Using the classical theory of modal analysis, the stability characteristics of this flow setup are investigated. We find that the addition of the Coriolis force significantly increases the growth rates achieved compared to the non-rotating channel flow until a certain point, after which the high Rossby numbers stabilize the flow. Given the non-normality of the equations governing the flow, we investigate the transient energy growth. We show that the energetic growth can be, as in the non-rotating case, of the order of $O\left(10^3\right)$ and that the maximal growth is caused by disturbances nearly perpendicular to the main flow. The maximal growth is achieved by crosswise perturbations until the point of alpha transition, after which the maximal growth is created by an oblique disturbance. The induced crosswise double-S velocity profile found in previous investigations is explained by the optimal initial disturbances leading to this maximal growth.   

A scenario for transition to turbulence in a rotating boundary layer

The transition process in a rotating boundary layer is numerically investigated through spectral DNS. The configuration consists of an annular cavity made of two parallel co-rotating disks of finite radial extent, with a forced inflow at the hub and free outflow at the rim. Impulsively disturbed the flow supports a self-sustained saturated wave, matching the description of a nonlinear global `elephant' mode as described by Pier [J.FLUID MECH. 435 135 2001]. This saturated wave is shown to be itself absolutely unstable with respect to secondary perturbations of zero Floquet number, giving birth to a very unorganized state, which can be labeled as turbulent. This scenario relies on a sufficiently strong impulsive perturbation as the first global bifurcation is known to be subcritical (see Viaud, Serre {\&} Chomaz [J.FLUID MECH. 598 451 2008]). On the other hand, strong convective instabilities, in the form of traveling wave packets coming from upstream, are shown to be able to inhibit the formation of the primary front, thus impairing this scenario.   

Stability of the flow past a magnetic obstacle

The concept of a magnetic obstacle in an electrically conducting fluid flow refers to the opposing Lorentz force induced by a localized magnetic field that is in relative motion with the surrounding fluid. The name stems from some similarities that occur between the flow past a rigid obstacle and that generated by a localized magnetic field. In this work, the stability of a flow past a magnetic obstacle is described in terms of the Hartmann and Reynolds numbers of the imposed flow (the Hartmann number squared estimates the ratio of magnetic to viscous forces). We find that for a given Hartmann number the flow is steady for small Reynolds numbers and becomes time-dependent, shedding vortices periodically as the Reynolds number grows. But in sharp contrast to the case of a rigid obstacle, for even larger Reynolds numbers, the flow may become steady again. The dependence of the Strouhal number on the governing parameters is also explored.   

Sensitivity Analysis for the Stability and Control of Spiral Vortex Breakdown

The physical origin of spiral vortex breakdown is investigated using the direct and adjoint Navier-Stokes equations linearized around axisymmetric vortex breakdown. The axisymmetric solution is computed using a Newton solver for the steady nonlinear Navier-Stokes equations. As a result of the so-called convective non-normality the direct and adjoint global modes for helical perturbations are located downstream and upstream, respectively. In particular, the adjoint mode is dominant in the recirculation bubble where the flow is thus most sensitive to periodic forcing. The wave modes region, defined as the overlap region between the adjoint and direct global modes, allows us to determine whether the wake of the recirculation region or the recirculation region itself causes the spiral vortex breakdown.   

Session AE: Flow Control I

Unsteady Aerodynamics Effected by Controlled Trapped Vorticity Concentrations

The transitory response of the flow-about a free-moving airfoil to time-dependent fluidic actuation that yields aerodynamic forces and moments in the absence of conventional control surfaces is investigated in wind tunnel experiments. Desired maneuvers are achieved using a 2-DOF feedback-controlled traverse that is programmed for trim and dynamic characteristics. Bi-directional changes in the pitching moment are effected by controllable, nominally-symmetric trapped vorticity concentrations on both the suction and pressure surfaces near the trailing edge. Actuation is independently applied on each surface by hybrid actuators that are each comprised of a miniature [O(0.01c)] obstruction integrated with synthetic jets which manipulate and regulate vorticity flux near the surface. Simultaneous measurements of the unsteady forces and moments and of the associated velocity field above and in the near wake of the airfoil are used to asses the coupling between the flow and vehicle dynamics with emphasis on control authority and optimal actuator placement and operating parameters. Flow control effectiveness is demonstrated by closed-loop response to a momentary force disturbance analogous to the response to a sudden gust in free flight.   

Low-Order Modeling of Airfoil Pitch Control Effected by Trapped Vorticity Concentrations

We describe construction of spanwise vorticity modes by proper orthogonal decomposition (POD) using data obtained by two- component PIV measurements in turbulent flow past a NACA 4415 airfoil undergoing time-periodic pitching motion due to synthetic-jet actuation near the trailing edge. Three- dimensional effects are characterized in terms of a ``mass deficit'' in the phase-averaged continuity equation. Such effects, in the actuated or unactuated flow, are significant in the near wake, are thought to arise from the three- dimensionality of the geometry of the actuators, and are accounted for in the model. The incorporation of forcing by the jets into two- and three-dimensional models, and the use of vorticity POD modes, are discussed in the context of low-order modeling for feedback control. The vorticity transport equation is used to obtain an ordinary differential equation (ODE) system by Galerkin projection, whose solution behavior is discussed.   

Unsteady Flow Simulation of a Controlled Airfoil

An airfoil moving with two degrees of freedom (pitching and plunging) is simulated with a closed-loop flow control system. The simulation of the unsteady airfoil is computed using a Delayed Detached Eddy Simulation (DDES), a hybrid non-zonal RANS-LES turbulence model based on DES. The control system controls the airfoil in two modes, first through direct application of forces and torques, and second, through the use of tangential synthetic jet actuators. The approach was designed for an investigation of flow control via synthetic jet actuators on a pitching and plunging airfoil in A. Glezer's wind tunnel at Georgia Tech. The software definition of the controller used for the wind tunnel facility, which includes a robust servomechanism Linear Quadratic Regulator (LQR) and a neural network based adaptive controller, is coupled to a CFD model, which includes a model for the synthetic jet actuators. The coupled CFD/controller model is used to simulate maneuvers of the airfoil as performed in the wind tunnel, and the coupled model is validated against experiment results. Both the results of the validation, and the characteristics of the controlled flows will be discussed.   

Aerodynamic Control of a Wing at Low Angles of Attack using Synthetic Jets and a Gurney Flap

Experimental tests were performed on a symmetric wing at low angles of attack to determine the effectiveness of pairing an array of synthetic jet actuators with a Gurney flap for active, aerodynamic flow control of the wing. Sectional lift and quarter-chord pitching moment data were acquired at $Re_c = 1.45 \times 10^{5}$ for different configurations of the Gurney flap and synthetic jet array. For configurations where significant aerodynamic control was observed, the flow physics in the vicinity of the flap and actuators were investigated with PIV. The net effect of the Gurney flap and synthetic jet actuator control scheme was an increase in the wing section lift and a corresponding decrease in the pitching moment. These effects were the result of an increase in the circulation of the wing section by a modification of the trailing edge flow with the synthetic jet control.   

Trailing Edge Flow Modification on a Wing by a Near-Trailing-Edge Gurney Flap

A Gurney flap is a small, perpendicular tab placed at or near the trailing edge of an airfoil. The effect of the tab is to augment the lift of the airfoil with no attendant increase in drag. A set of experiments were performed on a wing section at low-to- moderate angles of attack with a 2\% x/C Gurney flap located at x/C~=~0.95 on the lower surface of the airfoil. The configuration was tested at $Re_c = 1.45 \times 10^{5}$ to determine the sectional lift and quarter-chord pitching moment characteristics for the Gurney flap when not located exactly at the trailing edge. For this flap position, an increment in lift was still observed and was accompanied by an associated decrease in the pitching moment. Two-component velocity measurements were taken with PIV in the near wake region of the model to develop of an understanding of the flow physics in the wake of the Gurney flap. These measurements revealed that the closed recirculation region present in the lee of the flap at low angles of attack decreased in size as the angle of attack increased and eventually was eliminated completely when the angle of attack reached 12$^{\circ}$.   

Active Flow Control on Low-Aspect Ratio, Low-Reynolds Number Airfoils

Insect flight observations show high-lift mechanisms that rely on leading-edge vortex stabilization. These processes are intimately coupled to the flapping motion of the insect wing. In fixed wing applications, suitable for micro-air vehicles, active flow control may be capable of providing similar influence over vortex formation and stabilization. Steady and pulsed mass injection strategies are used to explore the open-loop response of both the evolution of the flow structures and the forces experienced by the wing. Flow structures will be quantitatively visualized using Defocused Digital Particle Image Velocimetry (DDPIV) and forces measured via a six-axis balance. Insect flight typically occurs at Reynolds numbers of 10$^{2}$ to 10$^{4}$, and aspect ratios near three. For this investigation, Reynolds numbers are approximately 10$^{3}$. The airfoil models are NACA 0012 profiles with aspect ratio two.   

Lift force time delays on 2D and 3D wings in unsteady flows

Active flow control (AFC) used for enhancing the maneuverability of wings is usually applied during conditions of steady external flow. However, when the external flow is unsteady or the wing is maneuvering, then at least two time delays become important; namely, the time delay of the lift to changes in external flow, $\tau _{f}$, and the time delay to changes in AFC actuation, $\tau _{a}$. These time delays were measured in wind tunnel experiments using two- and three-dimensional wings in an oscillating freestream and with variable duty cycle actuation. Dimensionless freestream oscillation frequencies from k = 0.01 to k = 0.2 with amplitudes of 5 percent of the mean speed were used to characterize the system. As a demonstration of the important role of the two time constants, AFC is used to damp lift force oscillations occurring in an unsteady freestream using a feed forward control system. The instantaneous velocity provides input to a control algorithm which adjusts the duty cycle of the AFC actuator to suppress lift fluctuations.   

Lift Enhancement through the Modification of the Three-Dimensional Wake Vortex Dynamics

Three-dimensional flow simulations are performed to understand the flow physics around low-aspect-ratio wings at low Reynolds numbers of 300 and 500. The aerodynamic characteristics of such wings and the dynamics and stability of the wake vortices are investigated. Of particular interest in the current research is the application of flow control to alter the vortex formation and evolution for lift enhancement at high angles of attack. Unlike separation control or circulation control, we modify the dynamics of the wake vortices to achieve lift increase. Steady downstream blowing at the trailing edge is found to be particularly effective. Such forcing allows for the tip vortices to be strengthened and generate stronger downward induced velocity upon the leading-edge vortices. Close roll-up of the leading-edge vortices results in the placement of the low-pressure core directly above the wing for lift enhancement, in some cases by double.   

Active flow control over a finite wing. Part 1: Experimental investigation

The effect of active flow control, via arrays of synthetic jet actuators, on the flow field around a finite wing was investigated experimentally and numerically. In the present abstract, the experimental component is discussed. To fully and properly implement flow control, a fundamental understanding of the interaction of the synthetic jets with the three-dimensional cross flow must be possessed. The experiments were conducted in a wind tunnel on a finite wing having a cross-sectional profile of NACA 4421at a wide range of angles of attack, Reynolds numbers, and several arrangements of synthetic jets. Stereoscopic PIV data were collected in conjunction with dynamic surface pressure. Using these data, the complex 3-D interactions were analyzed to form a cohesive understanding of the parameters that may impact the effectiveness of flow control on 3-D configurations.   

Active flow control over a finite wing. Part 2: Numerical investigation

In complement to the experimental investigations, numerical simulations are performed to study the effects of active flow control via arrays of synthetic jet actuators. The complexity of flow structures due to 3D interactions over varied range of angles of attack, sweep, Reynolds numbers, and arrangements of synthetic jets, create a need for adaptive flow simulations. In this work, solution-based mesh adaptivity is applied in order to effectively capture the flow features and relevant quantities by attaining local mesh resolution that matches the physical length scales of the flow structures in a non-uniform fashion. Furthermore, anisotropy in the flow field is also taken into account by adaptively constructing anisotropic elements, especially layered and graded elements in the boundary layers to resolve near-wall flow structures. Using these techniques the 3D interactions in the flow field are studied and compared with the experimental data to analyze the effectiveness of flow controls on 3D configurations.   

Session AF: Interfacial Instabilities

Convective and absolute instabilities in stratified flow of Newtonian and Bingham-like layers.

The stability of an interface separating either two Newtonian fluids or a Newtonian and a Bingham-like fluid in pressure-driven channel flow at moderate Reynolds numbers is analysed both theoretically and numerically. Inertia, interfacial tension and gravity are also accounted for in the study. In the linear regime, our theoretical analysis reveals that the interface is absolutely unstable over an intermediate range of Reynolds numbers and interfacial depths; convectively unstable regimes are present in the complimentary ranges of these parameters. Increasing the viscosity ratio and/or the yield stress of the Bingham layer promotes the absolute nature of the interfacial instability. Results obtained from numerical simulations elucidate~the nonlinear evolution of the interface which is accompanied by ligament formation leading to pinchoff. The transition point from a convective to an absolute regime predicted by simulations also agrees well with the theoretical analysis. Simulations with Bingham layers (although initiated from a fully-yielded base state) show that~unyielded regions~appear in the wave troughs during late stages of wave evolution.   

Instability in turbulent stratified channel flow

We determine the stability properties of a deformable interface separating a fully-developed turbulent gas flow in a channel from a thin laminar liquid layer. To do this, we derive a linear model to describe the interactions between the turbulent gas flow and the interfacial waves. This model involves two steps. First, we derive a flat-interface base-state velocity. This takes account of the laminar sublayer present in the near-interfacial region of the gas, and provides a way of determining the wall and interfacial shear stresses as a function of the applied pressure gradient. Next, we perform an Orr-Sommerfeld analysis on the Reynolds-averaged Navier-Stokes equations. This necessitates the selection of a turbulent-stress closure scheme. This approach gives the growth rate of the wave amplitude, as a function of the relevant dimensionless system parameters and turbulence closure relations. It also extends previous work by accounting for the effects of the thin liquid layer on the dynamics.   

Viscosity stratification in miscible channel flow

The stability of two-layer miscible flows in planar channels, focusing on the neutrally-buoyant displacement of a highly viscous fluid by a less viscous one, is studied. The flow dynamics are governed by the continuity and Navier-Stokes equations coupled to a convective-diffusion equation for the concentration of the more viscous fluid through a concentration-dependent viscosity. A generalized linear stability analysis (in which both the spatial wavenumber and temporal frequency are complex) is carried out, which allows the demarcation of the boundaries between convectively and absolutely unstable flows in the space of relevant parameters: the Reynolds and Schmidt numbers, and a viscosity ratio. The flow in the linear regime delineates the presence of convective and absolute instabilities and identifies the vertical gradients of viscosity perturbations as the main destabilizing influence. Our transient numerical simulations demonstrate the development of complex dynamics in the nonlinear regime, characterized by roll-up phenomena and intense convective mixing; these become pronounced with increasing flow rate and viscosity ratio, as well as weak diffusion.   

Numerical simulations of immiscible two-fluid channel flow in the presence of phase changes

We study the interaction between a fast-flowing fluid over a highly viscous layer in a two-dimensional channel using direct numerical simulations; the two fluids are immiscible. The flow regime varies from stratified-wavy to dispersed for moderate to high Reynolds numbers, respectively. The equations of mass, momentum and energy conservation in both fluids are solved using a procedure based on the diffuse interface method. This equation set is complemented by the Cahn-Hilliard equation for the volume fraction. No-slip and no-penetration conditions are imposed at the walls, and constant flow rate and outflow conditions are prescribed at the inlet and outlet, respectively. Our model accounts for the formation of the highly viscous fluid due to phase change in the bulk fluid, which is ultimately deposited at the wall. This is driven by thermal instability, which is taken into account using a chemical equilibrium model based on the Gibbs free energy. We present results showing typical flow dynamics and the effect of system parameters on the average deposit thickness. This work is of direct relevance to `fouling' in oil-and-gas refineries.   

Pressure-driven miscible two-fluid channel flow with density gradients

We study the effect of buoyancy on pressure-driven flow of two miscible fluids in inclined channels via direct numerical simulations. The flow dynamics are governed by the continuity and Navier-Stokes equations, without the Boussinesq approximation, coupled to a convective-diffusion equation for the concentration of the more viscous fluid through a concentration-dependent viscosity and density. The effect of density ratio, Richardson number, and channel inclination on the flow dynamics is examined, for moderate Reynolds numbers and viscosity ratios. We present results showing the spatio-temporal evolution of the flow together with an integral measure of mixing.   

Effect of solubility on the interfacial-surfactant instability of shear flows

A slow flow of a two-layer system with a soluble surfactant in the film and on the interface is considered. The linear stability theory of the plane Couette flow is developed for the liquid film adjoining a thicker layer of fluid. For the (Frenkel and Halpern 2002) non-inertial longwave instability which results from an interplay between the interfacial surfactant and flow shear, the effect of the surfactant solubility is studied, assuming a Langmuir-type adsorption-desorption kinetics at the interface and the advection-diffusion dynamics of the bulk surfactant. It is not a priori clear that the instability persists for the non-zero values of the surfactant solubility: The limit of vanishing solubility might be different from the case of zero solubility (= an insoluble surfactant case). For certain parametric regimes, this work analytically demonstrates that the instability does persist for non-zero surfactant solubilities; however, no matter how weak the surfactant solubility, its mitigating effect on the instability is found to be arbitrarily large for sufficiently long waves. Thus, the insoluble surfactant approximation fails for such waves.   

Wetting failure and contact line dynamics in a Couette flow

Liquid-liquid wetting failure is investigated in a two-dimensional Couette system with two immiscible fluids of arbitrary viscosity. The problem is solved exactly using a sharp interface treatment of hydrodynamics (lubrication theory) as a function of the control parameters: capillary number, viscous ratio and separation of scale. The transition at a critical Capillary number, from a stationary to a non-stationary interface, is studied at changing the control parameters. Comparisons with similar existing analysis for other geometries, as for the Landau-Levich problem, are also carried out. A numerical method of analysis is also presented, based on diffuse interface models obtained from multiphase extensions of the lattice Boltzmann equation (LBE). Sharp interface and diffuse interface models are quantitatively compared, face to face, indicating the correct limit of applicability of the diffuse interface models.   

Linear and nonlinear stability of a two-fluid interface in channel flow under the influence of parallel and normal electric fields

The use of an electric field on a two-fluid interface has been shown to be an efficient way to trigger an interfacial instability which, in turn, can enhance mixing or lead to droplet formation in a microfluidic channel. Keeping the latter applications in mind, the instability of a flat interface between two liquids confined in a channel and subjected to Poiseuille flow is studied in the presence of an electric field either parallel or normal to the flat interface. The liquids are considered to be viscous, incompressible and leaky dielectric. We have analyzed the effect of various parameters, as well as compared the role played by a parallel versus normal electric field on the dispersion curve, i.e., the growth rate as a function of wavenumber. While the flow is found to have no direct effect on the linear stability of the interface, its effect can be clearly observed in the nonlinear regime.   

Dynamics of a two-fluid interface in a channel in the presence of electric fields

We study the stability of the interface between two superposed fluids in a channel in the presence of a uniform electric field acting horizontally with respect to the undisturbed configuration. The two fluids are taken to be inviscid, incompressible and nonconducting, but can have different densities and permittivities. We consider the physical effects of surface tension, gravity and electrically induced forces. The approach involves the derivation of a set of nonlinear evolution equations for the interfacial shape, horizontal velocity and electric potential of the upper layer. The electric field effects enter nonlocally. Linear stability analysis reveals that the presence of the electric field causes a stabilization of the flow in the sense that it can compete with the unstable density stratification. In particular, it is shown that for given physical parameters, there exists a critical value of the voltage potential difference between electrodes, above which the electric field suppresses the Rayleigh-Taylor instability. Traveling waves are calculated and their behavior studied as the electric field increases.   

Interfacial Instabilites in Two-Layer Flows of Viscoelastic Fluids

We consider interfacial instability of pressure-driven, two-layer flows with one of the fluids being viscoelastic (like a polymeric solution or a polymer melt). We build on the work of Ganpule and Khomami (JNNFM, v.81, pp.27-69, 1999) by including finite extensibility in a complete way (as appropriate for the strong elongational flows that drive our present interest), and by extending the parameter space considered by them. While from the complete model they find only a Yih mode, and while by matching viscosities they find an elastic mode, we find the simultaneous existence of both modes. The parameter space for this occurrence is a subset of conditions from 1$<$De$<$5, 5$<$n$<$30, k$>$4.5, and viscoelastic layer thicknesses less than the Newtonian one (less viscous). In the above, n is the viscosity ratio (solution divided by the solvent) and k is the wave number. For Re$>$40, the elastic mode disappears, and the shear (T-S) becomes dominant mode.   

Session AG: Drops I

A Mesh-Dependent Model For Applying Dynamic Contact Angles To VOF Simulations

Typical VOF algorithms rely on an implicit slip that scales with mesh refinement, to allow contact lines to move along no-slip boundaries. As a result, solutions of contact line phenomena vary continuously with mesh spacing; this study presents examples of that variation, when applying both no-slip and Navier-slip boundary conditions. A mesh-dependent dynamic contact angle model is then presented, that is based on fundamental hydrodynamics and serves as a more appropriate boundary condition at a moving contact line. This new boundary condition eliminates the stress singularity at the contact line; the resulting problem is thus well-posed and yields solutions that converge with mesh refinement. This scaling relationship is then used as a means to evaluate the contact angle boundary condition as a function of the apparent contact angle, $\theta_{app}$, the capillary number, $\mathbf{Ca}$, and the mesh size, that yields mesh-independent solutions of dynamic contact line phenomena. Numerical results are presented of a solid plate withdrawing from a fluid pool, and of spontaneous droplet spread at small capillary and Reynolds numbers.   

VOF-Based Height Function Method for 3D Calculation of Contact Line Phenomena

A rigorous methodology is presented for applying a contact angle as a contact line boundary condition within a 3D VOF-based flow algorithm. Based on the recently-developed height function methodology, an approach for modeling contact lines is presented that yields accurate interface normals and curvatures from volume fractions and allows the rigorous representation of surface tension forces at contact lines, values that converge with spatial refinement. Although VOF methods have been used before to model phenomena that includes contact lines, the implementation details have rarely been presented. Here a detailed implementation is presented, that includes algorithms for identifying so-called ``contact line'' and ``adjacent'' cells, as well as for calculating normals and curvatures in these cells. The efficacy of this approach is demonstrated via examples of both static and dynamic contact line phenomena. The model is shown to accurately predict steady state configurations defined by the imposed contact angles, from initial conditions far from equilibrium.   

The crown splash

The impact of a drop onto a liquid layer and the subsequent splash has important implications for diverse physical processes such as air-sea gas transfer, cooling, and combustion. In the {\it crown splash} parameter regime, the splash pattern is highly regular. We focus on this case as a model for the mechanism that leads to secondary droplets, and thus explain the drop size distribution resulting from the splash. We show that the mean number of secondary droplets is determined by the most unstable wavelength of the Rayleigh-Plateau instability. Variations from this mean are governed by the width of the spectrum. Our results for the crown splash will provide the basis for understanding more complicated splashes.   

A droplet of spectroscopy

Droplet coalescence in a liquid bath can be delayed by oscillating the surface of the bath vertically (frequency from 20 Hz to 400 Hz), the droplet bounces on the interface [1,2]. A low viscous oil droplet is dropped on a high viscous oil bath. We observe that the conditions for bouncing depends on the frequency, more precisely we observe resonance when the eigenfrequency of the droplet is excited. In some conditions, droplet presents a non axi-symmetric mode of deformation. That leads to a rotation of the drop and to a horizontal displacement. \newline [1] Y. Couder, E. Fort, C. H. Cautier and A. Boudaoud, Phys. Rev. Lett. \textbf{94}, 177801 (2005) \newline [2] N. Vandewalle, D. Terwagne, K. Mulleners, T. Gilet and S. Dorbolo, Phys. Fluids \textbf{18}, 091106 (2006)   

Viscous Impact

The splashing of both inviscid and viscous drops on smooth, dry surfaces can be completely suppressed by decreasing the pressure of the surrounding gas [1,2,3]. However, at sufficiently high pressure when splashing does occur, the shape and dynamics of the ejected liquid sheets depends strongly on the liquid viscosity. This, as well as the dependence of the threshold pressure on viscosity [2], suggests that the splashing of viscous and inviscid liquids is caused by different mechanisms. When a low-viscosity ($\sim 1$ cst) liquid splashes, a corona is ejected immediately upon impact. In more viscous fluids (10 cst silicone oil), our experiments show that a thin sheet, resembling a flattened version of the corona seen in the inviscid case, emerges out of a much thicker spreading film. However, for these viscous fluids, the ejection of the thin sheet does not occur immediately. As the ambient pressure is lowered, the sheet ejection time is delayed longer and longer after impact until no sheet is ejected at all. [1] L. Xu, W.W. Zhang, S.R. Nagel, Phys. Rev. Lett. 94, 184505 (2005). [2] L. Xu, Phys. Rev. E 75, 056316 (2007). [3] C. Stevens et al., FC.00003 DFD 2007   

Impulsive water bells

The impact of a liquid half-sphere located on a falling rigid rod is considered. Following the impact, the drop is strongly deformed into a liquid sheet evolving into the impulsive analogue of Savart's waterbell. We investigate the dynamics of this drop impact model by deriving the initial velocity field within the drop. Interestingly enough, it appears that viscosity plays a major role in the initial development of the liquid film. This behaviour is confirmed by detailed experiments conducted with high-speed video recording and numerical simulations. The subsequent development of the liquid layer, its ejection angle and ultimate formation of the waterbell is considered as well.   

Computational Analysis of Inkjet Drop Impact on Dry Surfaces with Different Wetting Characteristics

Numerical simulations of micron-scale water drop impact on dry surfaces are carried out over a wide range of impact velocities ($1\leq We\leq 100$, $100\leq Re\leq 1,000$, and $Oh\sim 0.015$) and equilibrium contact angles ($6^{\circ}-107^{\circ}$). A two-distribution function lattice Boltzmann equation (LBE) method is employed, which recovers the advective Cahn-Hilliard and the incompressible Navier-Stokes equations for binary fluids. Minimization of the total free energy subject to the polynomial wall free energy implicitly predicts the contact angle and the density profile at solid surfaces. The evolution of the drop on substrate after initial spreading is most sensitive to the wall free energy. Dimensionless diameter and height of the drop obtained from the simulations are compared with experimental results with reasonable accuracy. In inkjet printing, the maximum spreading ratio is an important parameter for its significant effect on the dot size. For higher contact angle surfaces, the maximum spreading ratio based on the wetted surface area is noticeably smaller than the maximum dimensionless diameter that is experimentally measured.   

The fluid trampoline: droplets bouncing on a soap film

We present the results of a combined experimental and theoretical investigation of droplets falling onto a horizontal soap film. Both static and vertically vibrated soap films are considered. A quasi-static description of the soap film shape yields a force-displacement relation that provides excellent agreement with experiment, and allows us to model the film as a nonlinear spring. This approach yields an accurate criterion for the transition between droplet bouncing and crossing on the static film; moreover, it allows us to rationalize the observed constancy of the contact time and scaling for the coefficient of restitution in the bouncing states. On the vibrating film, a variety of bouncing behaviours were observed, including simple and complex periodic states, multiperiodicity and chaos. A simple theoretical model is developed that captures the essential physics of the bouncing process, reproducing all observed bouncing states. Quantitative agreement between model and experiment is deduced for simple periodic modes, and qualitative agreement for more complex periodic and chaotic bouncing states.   

Impact of a complex fluid droplet on wettable and non wettable surfaces

The impact of liquid droplets is a phenomenon prevalent in many natural and industrial processes. Such events include rain drops, fuel injection, and ink-jet printing. To date, research in atomization and droplet impact has been focused on Newtonian fluids. In the coating of pharmaceutical tablets, the coating solutions contain polymers, surfactants, and large concentrations of insoluble solids in suspension which inherently exhibit non-Newtonian behavior. In this work, we will present ongoing droplet impact experiments using complex rheology fluids under a wide range of Weber and Ohnesorge numbers. Both hydrophilic and hydrophobic surfaces are been studied, and the effect of surface roughness has also been considered. We will describe the limits of bouncing, spreading, and splashing for these complex fluids. We will also discuss quantitative information such as spreading rates and contact angle measurements on wettable and non-wettable surfaces obtained from high speed images.   

Session AH: Bubbles I

Role of Gas Pressure and Molecular Weight in Bubble Pinch-Off from an Underwater Nozzle

We report on experiments that explore the role of gas pressure and molecular weight near the pinch-off of an air bubble from an nozzle submerged in water. We use high-speed video to image the dynamics close to the singularity occurring at pinch-off.\footnote{N.~C.\ Keim et al., \emph{PRL} 97, 144503 (2006).} As the neck collapses to a radius of several microns, the effects of the Bernoulli pressure associated with gas flow inside the neck begin to alter the bubble's shape and evolution, as was recently proposed.\footnote{J.~M.\ Gordillo, M.~A.Fontelos, \emph{PRL} 98, 144503 (2007).} We address the role that the gas plays in creating satellite bubbles during the pinch-off process, and its influence on the evolution of perturbations to axisymmetric collapse.\footnote{L.~E.\ Schmidt et al., in preparation.}   

Hourglass Bubble Plumes

We present an experiment in which millimetric bubbles are injected into water from a small number of closely-spaced pipettes. These bubbles form a dilute plume with a repeated hourglass pattern of widening and narrowing diameter. We detail parameters affecting the formation and characteristics of this pattern. Two factors are shown to be particularly important: the initial radial spread of the bubbles from their sources, and their subsequent helical trajectories. A simple model which treats the bubbles as independent reproduces the hourglass pattern.   

Bubble chains in magnetic fluids

Interactions between small numbers of bubbles of non-magnetic fluid immersed in a magnetic fluid (ferrofluid) are examined by direct numerical simulation using a volume of fluid (VOF) interface capturing method coupled to a magneto-quasistatic Maxwell solution. Constant magnetic susceptibility (linear magnetic material) is assumed and the Reynolds number is small, but does not vanish. For small gravitational and magnetic Bond numbers, the dynamics of multiple bubbles is controlled by the dipole fields induced by the bubbles, which for certain initial configurations leads naturally to the formation of linear chains of nearly spherical bubbles. The study of bubble chains using a VOF approach is facilitated by introducing multiple VOF phase functions, surpressing merger of bubbles. At larger Magnetic Bond numbers, the bubbles also elongate in the direction of the magnetic field, altering the coalescence process. Model results are shown to be in agreement with experiments performed using high resolution X-ray images of air bubbles in ferrofluid. The complementary problem of magnetic fluid droplets is also examined for its utility as a possible model for the microstructure of ferrofluids that can be used to predict their rheological properties, in particular the competition between shear and chain structures.   

Asymmetric bubble collapse

Recent studies reveal that an inertial implosion, analogous to the collapse of a large cavity in water, governs how a submerged air bubble disconnects from a nozzle. For the bubble, slight asymmetries in the initial neck shape give rise to vibrations that grow pronounced over time. These results motivate our study of the final stage of asymmetric cavity collapse. We are particularly interested in the generic situation where the initial condition is sufficiently well-focused that a cavity can implode inwards energetically. Yet, because the initial condition is not perfectly symmetric, the implosion fails to condense all the energy. We consider cavity shapes in the slender-body limit, for which the collapse dynamics is quasi two-dimensional. In this limit, each cross-section of the cavity evolves as if it were a distorted void immersed in an inviscid and irrotational fluid. Simulations of a circular void distorted by an elongation-compression vibrational mode reveal that a variety of outcomes are possible in the 2D problem. Opposing sides of the void surface can curve inwards and contact smoothly in a finite amount of time. Depending on the phase of the vibration excited, the contact can be either north-south or east-west. Phase values that lie in the transition zone from one orientation to the other give rise to final shapes with large lengthscale separation. We show also that the final outcome varies non-monotonically with the initial amplitude of the vibrational mode.   

Acoustic measurement of bubble size and position in a piezo driven inkjet printhead

A bubble can be entrained in the ink channel of a piezo-driven inkjet printhead, where it grows by rectified diffusion. If large enough, the bubble counteracts the pressure buildup at the nozzle, resulting in nozzle failure. Here an acoustic sizing method for the volume and position of the bubble is presented. The bubble response is detected by the piezo actuator itself, operating in a sensor mode. The method used to determine the volume and position of the bubble is based on a linear model in which the interaction between the bubble and the channel are included. This model predicts the acoustic signal for a given position and volume of the bubble. The inverse problem is to infer the position and volume of the bubble from the measured acoustic signal. By solving it, we can thus acoustically measure size and position of the bubble. The validity of the presented method is supported by time-resolved optical observations of the dynamics of the bubble within an optically accessible ink-jet channel.   

Airflow driven bubble pinch-off

We create air bubbles at the tip of a ``bathtub vortex'' which reaches to a finite depth. The bathtub vortex is created by letting water drain through a small hole at the bottom of a rotating cylindrical container. For sufficiently large rotation rates the tip of this needle-like surface depression becomes unstable and emits bubbles. The collapse follows a $R(t)\propto \tau^{1/3}$ power law for the minimal neck radius which is indicative of the balance between liquid inertia and the under pressure due to the airflow in the neck. In a variety of systems it is the under pressure created by airflow that induces and/or propagates the pinch-off of a bubble. In a co-focused jet, and the equivalent flow-focusing devices, it is the externally induced airflow that breaks up the bubbles. In other systems the collapse itself induces an airflow which becomes dominant in the final stages of bubble pinch-off (Phys. Rev. Lett. \textbf{98}, 144503 (2007)). Our system illustrates the importance of both contributions to the airflow, i.e., the external airflow induced by surface oscillations of the tip and the airflow induced in the neck by the collapse itself. Both of these contributions are of the same order and in Bernoulli's law the unsteadiness gives rise to terms of similar order. Surprisingly enough, all of these terms contribute with the same scaling exponent to the under pressure.   

Spherical cap bubbles with a bubbly crown

Single large bubbles typically have a spherical cap shape with bubbles of larger volume rising faster than ones of smaller volume. However, except in well-controlled experiments, the released gas splits into a leading cap bubble followed by a crown of satellite bubbles that can contain up to 50\% of the total volume of gas. We find that in this case the satellite bubbles rearrange in a characteristic toroidal crown and the leading bubble takes a lenticular shape. The ratio of the torus radii to the leading cap curvature radius and the rise speed of these multipart bubbles are quite constant and predictable in the mean and are furthermore independent of the gas partitioning between the leading and the crown of satellite bubbles. We also show that this multi-part bubble rises slightly faster than a single cap bubble with the same total injected volume of gas.   

Bubble interactions with a traveling vortex tube

We simulate the interaction of large bubbles with a traveling vortex tube using an Eulerian-Lagrangian discrete bubble model. The cases presented are 2D simplifications of a vortex ring studied experimentally by Sridhar \& Katz [JFM vol 397, 1999]. A plane jet is pulsed into a rectangular domain. After roll up into a vortex tube, eight bubbles are injected into its path to study the subsequent entrainment and vortex distortion. Three modeling approaches are considered: (a) one-way coupling; where the bubbles travel passively in the fluid, (b) two-way coupling; where the momentum exchange between the fluid and the bubbles is modeled, and (c) volumetric coupling; where the volume displacement of the fluid by the bubble motion and the momentum-exchange are modeled. It is found that a volumetric coupling model is critical to obtain any vortex distortion due to entrained bubbles. Parametric studies varying buoyancy effects relative to the vortex strength indicate that the greatest distortion of the vortex results from bubbles which continue to circle the vortex core after entrainment. Despite the two-dimensional approximation, bubble settling locations agree well with the experimental data.   

History force effects on contrast agent microbubbles in an ultrasound field

We study experimentally the radial and translational dynamics of an ultrasound contrast agent microbubble pair pulsating in an ultrasound field. The two bubbles attract each other through the so-called secondary Bjerknes force; quantifying these bubble-bubble interactions is therefore crucial for optimized medical imaging protocols. Using optical tweezers, we trap and control the distance between two microbubbles (BR-14, Bracco Research S.A., Geneva). We position the bubble pair away from the sample chamber wall, to prevent wall effects and quantify purely the acoustic bubble-bubble interaction and the dissipation due to viscosity in the fluid. The ultra-high speed Brandaris camera recorded the bubble dynamics at 15 million frames per second; from the optical measurements we track the instantaneous bubble radii and positions. We write a force balance for each bubble, assuming a no-slip boundary condition since the bubble interface is coated with a lipid monolayer to prevent dissolution. By comparison with the experimental results, we find that history effects are crucial to correctly account for the viscous forces.   

Session AJ: Bio-Fluids: Cell/Vesicle Dynamics I

Red Blood Cell Deformation Under Shear Flow: The Effect of Changing Cell Properties

The deformability of red blood cells plays a major role in the pathology of several diseases, including malaria, sickle cell anemia and spherocytosis. Moreover, deformations are believed to trigger the release of adenosine triphosphate, which helps regulate vascular tone and is consequently an important factor in various vascular diseases. Here we investigate single-cell viscoelastic responses to increased shear stress in poly(dimethylsiloxane) channels with a single constriction 2-4 times larger than a typical erythrocyte. These channels mimic arteriole-sized vessels, and have the advantage that the cell membrane is not in contact with the channel walls which have vastly different mechanical and material properties than living tissue. High-speed video and image analysis were used to quantify the trajectories and deformations of cells exposed to varied doses of diamide, a chemical known to ``rigidify'' erythrocytes. Our results show that (i) deformation is proportional to shear rate and (ii) the deformability of diamide-treated cells is greater than that of untreated cells. The latter is an unforeseen result because micropipette aspiration experiments have shown the opposite. We expect that the experimental procedure described here will be useful for characterizing the effect of different therapeutic agents on cellular deformability.   

Measuring morphological response of endothelial cells in shear flow

The normal physiological endothelial cell response to hemodynamic loadings can be categorized into morphological and biological responses. Cell morphological response includes changes in shape, size, height, and orientation. Cells sense mechanical stimuli and transduce them into chemical signals involving gene and protein expression, mechanotransduction. Abnormal endothelial response has been implicated in the localization of arterial disease like atherosclerosis. Though mechanotransduction involves a coupled ($i.e.$ morphological and biological) process, to date many investigations into endothelial cells are still done in the decoupled way. The ultimate goal of our study is simultaneous flow and biological measurements to better understand arterial disease at the cellular and sub-cellular level. \textit{In vitro} $\mu$ PIV measurements have been made in steady flow over live human aortic endothelial cells flush-mounted in a small rectangular channel. Cells are subjected to a step change in shear stress from zero to 15 dynes/cm$^{2}$. Cell surface maps, surface pressure, and wall shear stress are extracted from measurements taken 0, 3, 6, 12, 18, and 24 hours after applying shear. This work has laid a framework for future simultaneous measurements.   

Deformation of Elastic Particles in Viscous Shear Flow

The dynamics of two dimensional elastic particles in a Newtonian viscous shear flow is studied numerically. A constitutive equation is constructed for an incompressible ``Neo-Hookean'' elastic solid where the extra stress tensor is assumed to be linearly proportional to the Almansi strain tensor. A monolithic finite element solver which uses Arbitrary Lagrangian-Eulerian moving mesh technique is then implemented to solve the velocity, pressure and stress in both fluid and solid phase simultaneously. It is found that the deformation of the particle in the shear flow is governed the Reynolds number (Re) and the Capillary number (Ca). In the Stokes flow regime, the particle deforms into an ellipse while the material points inside experience a tank- treading like motion, and the deformation of the elastic particle is observed to vary linearly with Ca. Interactions between two particles in a viscous shear flow show that after the initial complicated interactions, both particles reach an equilibrium elliptic shape which is consistent with that of a single particle. Both rigid body rotation and buckling motion are observed when an elastic long particle is suspended in a shear flow.   

Simulating Cell Deformation with Optical Forces using the Immersed Boundary Method

The mechanical deformation of biological cells is an efficient experimental method to study the cellular properties and identify diseased cells. Optical forces have been successfully used to induce small and even large scale deformations that do not alter the cellular properties, mainly due to minimal direct contact, compared to other experimental techniques (micro-pipette aspiration, atomic force microscopy). A review on the recent advances in the area of optical cell deformation shows that a variety of deforming conditions can be imposed using different methods (optical tweezers and optical stretcher) to simulate the different biological conditions. Computational simulations, on the other hand, can be used to guide and explain the experimental observations. In this work, we will present a new numerical simulation of cell optical deformability using the immersed boundary method. Cells are considered as 3D elastic capsules immersed in a fluid. Optical forces are calculated using the ray optics technique and applied on the capsule membrane that inducing transient Stokes flow. The current study is primarily focused on the deformation of spherical cells as well as biconcave discoid representing red blood cells. The deformation pattern and relaxation time will be reported over a range of forces.   

Extreme deformation of vesicle membrane under DC electric fields

Electrodeformation refers to the deformation of cell or vesicle lipid membranes under the application of an electric field. This phenomenon often accompanies electroporation, an important technique to introduce molecules into the cells \textit{via} electric-field-induced membrane permeabilization. On the other hand, it can be also harnessed to probe the mechanical and dynamic properties of the lipid membranes. Recent studies suggest that the electrical conductivity difference across the membrane is a dominant factor in determining the regimes of deformation. In this work, the deformation of vesicular cellular mimics is systematically investigated, in particular with respect to varying electric field strengths, and a wide range of conductivity ratios. The results reveal that, under moderate values of the conductivity ratio, the membranes exhibited moderate deformations, in agreement with previous reports in the literature. Furthermore, under high conductivity ratios ($\sim $100), the vesicle membranes exhibited atypical, extreme elongations previous not reported. This phenomenon suggests a new regime of membrane electrodeformation which awaits further study. The current work also attempts to establish the correlation between the extreme deformation and membrane permeabilization (electroporation).   

The deformed behavior of multiple red blood cells in a capillary flow

The detailed deformation of multiple red blood cells in capillary flows is investigated computationally and hydrodynamics in the capillary flow accompanied with the deformation of red blood cells are analyzed. The membrane of red blood cell is modeled as a hyperelastic thin-shell and the immersed boundary method is used for the fluid-structure coupling in the present simulations. Numerical results show that the apparent viscosity in the capillary flow increases with the increase of the shear coefficient in the membrane of red blood cell, while this change for the viscosity is not obvious when the stiffness of the membrane changes. The distribution of multiple red blood cells in a capillary with branches is also simulated which shows that the apparent viscosity in the flow and the distribution of the cells affect each other interactively.   

Lateral migration and deformation of a vesicle in Poiseuille flow

The lateral migration and deformation of a suspended vesicle in Poiseuille flow is investigated numerically in the low Reynolds number limit. We consider two cases, the external suspended fluid is unbounded or bounded by a steady infinite solid wall. Using the boundary integral method we solve the corresponding hydrodynamic flow equations and we track explicitly the vesicle dynamics in 2D. Here we limited our study to vesicles without viscosity contrast between their internal and external fluids. In the unbounded geometry case, we find that the nonlinear character of the Poiseuille flow causes the lateral migration of the vesicles towards the flow centerline, this is in a marked contrast to the migration of droplets, which are known to migrate outward the centerline in the absence of a viscosity contrast. Once the vesicles reach the centerline they keep moving just parallel to the flow direction with a steady parachute-like shape. We find that the lateral migration velocity normalized by the curvature of the Poiseuille flow velocity profile is a universal function of the local capillary number. In the wall-bounded geometry, an additional lift force caused by the presence of the wall appears. Here we considered one wall in order to be able to investigate the interplay between the wall- and the Poiseuille flow curvature- induced lift forces. We find that the closer the vesicle is to the centerline, the more the curvature induced lift force is dominant.   

Motion and deformation of a vesicle in a Wall-Bounded Shear Flow

The motion of a lipid vesicle near a plane wall is studied using a 3-d boundary integral method. Initially the vesicle is considered to be immersed in a quiescent semi infinite fluid and its motion is driven by the buoyant force due to which the vesicle moves downwards towards the wall. A contact area is formed between the vesicle and wall which will depend on the magnitude of the buoyant force and the elastic properties of the membrane (relationship characterized by the Bond number). Results are compared to experimental data obtained using giant lipid vesicles. When the external fluid is set to a shear flow, the motion of the vesicle is driven by the hydrodynamic forces acting on it. These forces deform the vesicle and sets it in motion. The shape and velocity of the vesicle depend on the intensity of the flow and the vesicle's membrane elastic properties (relationship characterized by the dimensionless capillary number). The velocity of motion of the particle is reported as function of both the Bond and the capillary numbers and different flow regimes are identified.   

The effect of electrical conductivity on pore resistance and electroporation

Electroporation is an elegant means to gain access to the cytoplasm, and to deliver molecules into the cell while simultaneously maintaining viability and functionality. In this technique, an applied electric pulse transiently permeabilizes the cell membrane, through which biologically active agents such as DNA, RNA, and amino acids can enter the cell, and perform tasks such as gene and cancer therapy. Despite wide applications, current electroporation technologies fall short of desired efficiency and reliability, in part due to the lack of fundamental understanding and quantitative modeling tools. This work focuses on the modeling of cell membrane conductance due to the formation of aqueous conducting pores. An analytical expression is developed to determine effective pore resistance as a function of the membrane thickness, pore size, and intracellular and extracellular conductivities. The availability of this expression avoids empirical or \textit{ad hoc} specification of the conductivity of the pore-filling solution which was adopted in previous works. Such pore resistance model is then incorporated into a whole-cell electroporation simulation to investigate the effect of conductivity ratio on membrane permeabilization. The results reveal that the degree of permeabilization strongly depends on the specific values of the extracellular and intracellular conductivities.   

Session AK: Free Surface Flows I

Droplet Impact Onto A Flat Plate: Inclined Verses Moving Surfaces

Much research has been conducted on the impact of droplets normal to flat surfaces. However, very little research has been carried out on oblique impacts, even though they occur frequently in nature and industry. We experiment with the effects of tangential and normal impact velocities on the behavior of a droplet as it impacts a flat plate. The plate is inclined in the first case, and in the second case the plate is rotated via an electric motor. The asymmetric nature of the impact causes asymmetric splashing, such that under certain conditions only part of the rim splashes. Using a high-speed camera, we demonstrate that the splash threshold of inclined and moving surfaces are quantitatively similar, with only small differences. We also develop a phase diagram of splashing showing which phase occurs given a tangential and normal impact velocity. Such a phase diagram is useful for both engineering design and for the evaluation of splash-prediction models.   

Shallow-angle water entry of ballistic projectiles

The water-entry of ballistic projectiles is investigated using high-speed digital imaging. Projectiles enter the water at shallow angles to the free surface, $5^{\circ}-15^{\circ}$, without ricochet at Mach numbers between 0.3 and 2.0. Projectile dynamics, critical entry angle, and cavity growth are discussed. Geometric modifications to a projectile allow it to travel large distances underwater assuming a sufficiently large air-cavity is formed after impact, which dramatically decreases drag on the projectile. Results show that successful water-entry occurs for projectiles with modified tip geometries at Mach numbers ranging from 0.3 to 2; these projectile modifications include tip geometry and material properties. A theoretical cavity model compares well with the experimental data and will be discussed for a range of experimental conditions.   

Open-Channel Capillary Flow in Helical Support Structures

When gravitational effects are negligible compared to capillary effects, it is possible to achieve capillary flow in a helical wire support. The global dynamics of open-channel capillary flow in helical support structures are modeled by one-dimensional continuity and momentum equations where the pressure is related to the local curvature of the free surface. Equal volumetric flow rates at entrance and exit are prescribed. The pressure difference across the interface, or Laplace pressure, is predicted as a function of the helix geometry and contact angle. Local flow analysis (FEM) has been performed to determine viscous losses as a function of the dimensions of the support and the configuration of the free surface, where the free surface shapes are taken to be the equilibrium shapes computed for static conditions. The global model predicts that for a given helix geometry and contact angle and for a given flow rate below a critical value, there exists a range of channel volumes that give a stable flow. Preliminary experimental evidence suggests that a channel with an imposed flow rate can adjust its volume to achieve stable flow.   

Experimental measurement of vorticity flux across the interface of an unsteady breaking wave

The nature of the vorticity and vorticity flux on the air and water side of an unsteady breaking wave is examined using fully time-resolved Particle Image Velocimetry (PIV), with the aim of better understanding the physics of air-sea interaction. Results reveal regions of strong vorticity in the air, in the absence of wind, as well as distinct vortical regions in the water beneath the crest region, which persist through the breaking process; these regions of vorticity are mechanisms for mixing and transport. The near-surface vorticity is correlated with the viscous flux of vorticity at the surface on both sides of the air-water interface to gain further insight into the physical processes during breaking. The method used to calculate vorticity flux follows the methods presented in previous work [1,2]. Using this analysis, the physical flow characteristics associated with the vorticity flux can also be examined. [1] Gharib, M. and A. Weigand, \textit{J. Fluid Mech}. 321:59--86 (1996). [2] Dabiri, D. and M. Gharib, \textit{J. Fluid Mech}. 330:113-139 (1997).   

Playing with inclined circular hydraulic jumps

We have investigated the structure of the circular hydraulic jump, when the jet impacts an inclined plate. At low plate slope, quasi-circular shapes, evolving towards elliptic shapes are observed. At moderate inclinations, the upper and lower jumps become markedly different, and the lower jump is even rejected to infinity when a critical inclination is reached. Above this critical inclination, the jump is coupled to an outer dewetting contact line to give a specific object (expanding impact sheet feeding a curved rim in which the liquid is flowing tangentially). In this regime, both the position and curvature of the upper jump follows unusual scalings with the flow rate that completely differ from those observed on horizontal plates. Finally we have looked to metastable drops trapped in the circular jump at very small inclinations. As reported in a previous APS, the lowest position in the jump can become unstable and the drops oscillate around the jump perimeter. We show that this behavior requires very specific conditions of surface tension and viscosity and propose simple interpretations for the instability mechanism.   

Deformation of a liquid surface induced by an air jet

An experimental and theoretical study is performed to characterize the depression of a liquid surface due to an air jet exiting a nozzle from above. The Reynolds number of the jet is confined to a moderate range($\sim $100). In order to obtain more stable surface profiles, we use a viscous fluid (silicone oil) instead of water. Based on the data acquired from experiments, we find how the depth and diameter of the cavity are dependent on the radius and height of the nozzle, and the exit velocity of the jet. Theoretical explanations are provided both in the two dimensional (2-D) and three dimensional (3-D) cases. In the 2-D case, a free surface equation and the asymptotic expansion of its solution are obtained by employing a conformal mapping method. In the 3-D case where this technique fails, we propose a different model using an exact axisymmetric solution to Euler's equation.   

Flow patterns in free liquid film exposed to temperature gradient

Thermocapillary-driven flow induced in a free thin liquid film under a temperature gradient parallel to the free surfaces is examined with experimental and numerical approaches. Under a small temperature gradient, a two-dimensional flow inside the film is realized in which the fluid returns in the middle region of the film. By increasing the temperature gradient, instability takes place to realize a three-dimensional flow. The authors will introduce a unique flow pattern in the presentation.   

The impact of surface conditions on gas exchange across an air/water interface during mixed convection

The effect of surface conditions on the transport of oxygen across an air/water interface was investigated experimentally for mixed convection conditions. A wind/water tunnel was used to gather the requisite data and the resulting Sherwood numbers are presented as a function of the Rayleigh and Reynolds numbers. Wind speeds for both clean and surfactant covered surfaces were varied from 1 to 4 m/s in increments of 1 m/s. Water surfaces devoid of surfactant monolayers were studied, along with oleyl alcohol covered water surfaces. The surfactant monolayer existing on a tap water surface was also studied. The results show the effect of surface conditions, as well as the relative importance of free and forced convection on gas exchange.   

Surface flow, shapes and stability of rotating triangles on a water surface

We present an experimental study of polygons forming at the free surface of a water flow driven by a rotating bottom and confined to a stationary cylinder, as described in Jansson et al., Phys. Rev. Lett. {\bf 96}, 174502 (2006). In particular, we study the case of a triangular structure, either completely floating or with a dry center. For these structures, we present measurements of the surface flows, the surface shapes and the process of structure formation, and we analyze our results in terms of a collection of discrete vortices. We show that partial blocking of the surface flow destroys the triangular structure and reestablishes the circular symmetry.   

Session AL: Bio-Fluids: Phonation/Glottal Flows

Towards Computational Modeling of Phonation Using CT--Based Laryngeal Models

The oscillatory flow generated in human larynx plays a key role in the process of phonation. While much has been done to understand the main features of such flow by using idealized geometry models and simplified flow conditions, there is still little known about the 3D features of laryngeal flow. In this work, anatomically realistic models of the human larynx are used to analyze the fluid dynamics of 3D laryngeal flow using high--fidelity numerical simulations. A Cartesian--grid--based, finite--difference Navier--Stokes solver is used to carry out these simulations. Three--dimensional models of human larynx are extracted from CT images and unstructured surface grids are generated for the model geometries. The pressure driven flow is simulated for a range of Reynolds numbers. The main objective in this work is to understand more in--depth the effect of 3D geometric features of glottal airway on the laryngeal flow structure.   

Aeroacoustic source spectrum for fricative consonant speech sounds

The aeroacoustic source spectrum is experimentally determined for flow within an open-ended duct. The source region comprises a jet, formed at a constriction within the duct, which then interacts with an obstacle placed further downstream. The physical model dimensions are commensurate with a life-size vocal tract to enable study of the physics of human speech sound production. Two methods are used to estimate the aeroacoustic source spectrum. The first estimate results from inverse-filtering radiated sound measured outside the duct. The transfer function between the source and microphone locations is constructed from two-microphone-method measurements of the acoustic field inside the duct. The second estimate uses measurements of the jet flow near the obstacle as input to aeroacoustic theory. Comparison of the two estimates is presented.   

Role of jet asymmetry in glottal flow aerodynamics

Finite element computations of flow through a constriction are used to illuminate the role of the Coanda effect in glottal flow and voice production. Steady-state computations were performed for a series of constriction openings. One set of simulations enforced transverse flow symmetry, while the other allowed the flow to develop naturally. Comparisons of measures relevant to vocal fold vibration and sound production are presented. These comparisons show that the Coanda effect primarily affects the differential transverse force on the vocal fold walls, while the axial force differs little from the symmetric case. These results suggest strongly that the primary role of the Coanda effect in speech is to drive asymmetric vocal fold vibration patterns, and that glottal jet instability contributes to voice perturbations and fluctuations.   

Dynamic importance of unsteady effects in glottal flow aerodynamics

Finite element computations of flow through a constriction are used to illuminate the role of unsteady flow dynamics in glottal flow and voice production. Unsteady computations were performed for a series of prescribed idealized vocal fold wall motions over reduced frequencies f*=0, 0.04 and 0.08, which correspond to quasi-steady, adult male and adult female speaking voices, respectively. Glottal resistance and estimates of the relative magnitudes of the various terms of the integral momentum equation are presented. Results suggest that glottal flow is inherently unsteady.   

Measurement of glottal flow across scaled up dynamic vocal fold motion

Preliminary measurements of flow of water through a scaled-up model of the human vocal folds will be presented. The vocal fold model is a new design, improving upon that of previous work (Krane, Barry, and Wei, \textit{JASA} 2007). The new model preserves the advantages of the previous experimental rig, enabling time-resolved velocity measurements, but is more physiologically accurate in terms of shape and motion. In particular, both the rocking as well as the oscillatory open/close motions are incorporated into the model. In addition, the vocal fold walls are made of flexible PVC, allowing simulation of fluid-structure interactions along the walls. The details of the new design will be presented, as well as preliminary DPIV measurements of the flow.   

Computational Investigation of Dynamic Glottal Aperture Effects on Respiratory Airflow

The periodic movement of the glottal aperture (vocal folds) during tidal breathing has been long recognized as a factor in altering the airflow dynamics in the tracheobrnchial region. The potential influence from these altered flow structures on the transport and deposition of inhaled particles is not known. However, studies devoted to this dynamic physiological feature are scarce due to the complex anatomy in of the larynx and numerical challenges in simulating dynamic geometries. In this study, a high-fidelity immersed boundary solver is used to investigate this problem. A 3D human oral-larynx-lung model is firstly reconstructed from MRI data. The role of the vocal fold movement and associated airflow characteristics such as vortex shedding, Coanda effect etc. during inhalation and exhalation are then numerically studied.   

Quantifying the influence of flow asymmetries on glottal sound sources in speech

Human speech is made possible by the air flow interaction with the vocal folds. During phonation, asymmetries in the glottal flow field may arise from flow phenomena (e.g. the Coanda effect) as well as from pathological vocal fold motion (e.g. unilateral paralysis). In this study, the effects of flow asymmetries on glottal sound sources were investigated. Dynamically-programmable 7.5 times life-size vocal fold models with 2 degrees-of-freedom (linear and rotational) were constructed to provide a first-order approximation of vocal fold motion. Important parameters (Reynolds, Strouhal, and Euler numbers) were scaled to physiological values. Normal and abnormal vocal fold motions were synthesized, and the velocity field and instantaneous transglottal pressure drop were measured. Variability in the glottal jet trajectory necessitated sorting of the data according to the resulting flow configuration. The dipole sound source is related to the transglottal pressure drop via acoustic analogies. Variations in the transglottal pressure drop (and subsequently the dipole sound source) arising from flow asymmetries are discussed.   

Unsteady flow motions in the supraglottal region during phonation

The highly unsteady flow motions in the larynx are not only responsible for producing the fundamental frequency tone in phonation, but also have a significant contribution to the broadband noise in the human voice. In this work, the laryngeal flow is modeled either as an incompressible pulsatile jet confined in a two-dimensional channel, or a pressure-driven flow modulated by a pair of viscoelastic vocal folds through the flow--structure interaction. The flow in the supraglottal region is found to be dominated by large-scale vortices whose unsteady motions significantly deflect the glottal jet. In the flow--structure interaction, a hybrid model based on the immersed-boundary method is developed to simulate the flow-induced vocal fold vibration, which involves a three-dimensional vocal fold prototype and a two-dimensional viscous flow. Both the flow behavior and the vibratory characteristics of the vocal folds will be presented.   

Dynamics of Voluntary Cough Maneuvers

Voluntary cough maneuvers are characterized by transient peak expiratory flows (PEF) exceeding the maximum expiratory flow-volume (MEFV) curve. In some cases, these flows can be well in excess of the MEFV, generally referred to as supramaximal flows. Understanding the flow-structure interaction involved in these maneuvers is the main goal of this work. We present a simple theoretical model for investigating the dynamics of voluntary cough and forced expiratory maneuvers. The core modeling idea is based on a 1-D model of high Reynolds number flow through flexible-walled tubes. The model incorporates key ingredients involved in these maneuvers: the expiratory effort generated by the abdominal and expiratory muscles, the glottis and the flexibility and compliance of the lung airways. Variations in these allow investigation of the expiratory flows generated by a variety of single cough maneuvers. The model successfully reproduces PEF which is shown to depend on the cough generation protocol, the glottis reopening time and the compliance of the airways. The particular highlight is in simulating supramaximal PEF for very compliant tubes. The flow-structure interaction mechanisms behind these are discussed. The wave speed theory of flow limitation is used to characterize the PEF. Existing hypotheses of the origin of PEF, from cough and forced expiration experiments, are also tested using this model.   

Session AM: Bio-Fluids: Flight I

Why Twist?

Free swimming and flying animals twist their wings. But why? We have carried out force and efficiency measurements with twistable finite fins in water. Twist increases the hydrodynamic efficiency of a rolling and pitching fin, but only up to 5{\%}. Animals tend to operate in narrow frequency ranges of flapping oscillation and amplitude. In such kinematic constraint, twist can increase thrust forces by 20{\%}--a large range, while Strouhal number is held constant (frequency, tow speed and roll angle are held constant) and maximum efficiency is retained. Less than 5{\%} of the roll power is spent in twist to produce this variation in thrust force. Therefore, while our biorobotic underwater vehicles have so far used the square of frequency for thrust control, animals that have resonant design could use twist for control of both cruise and maneuvering. The angle of attack along the span becomes more uniform with twist, becoming the most uniform at 20 degrees. We propose that twist is a method for controlling the direction of the induced flow jetting out of the closed stall vortex that is shed from the fin.   

Spider capture thread: form and function

We present the results of a combined theoretical and experimental investigation of spider capture thread. While the radial threads in a spider web are simply cylindrical, the circumferential threads are pre-wound helices immersed in a viscous fluid. These so-called capture threads are subject to an instability reminiscent of Rayleigh-Plateau that results in the formation of a series of droplets along the thread, each filled with a series of coils. We demonstrate that this instability is a natural example of capillary origami that will arise when the surface tension exceeds the tension of the spring. Moreover, we demonstrate its efficacy in prey capture through augmenting damping during prey impact.   

Sideways flight of insects by phased wing flips

Insects are enviable flyers and are capable of unusual maneuvers, such as sideways flight. We show that fruit flies generate sideways forces in flight, and we propose an aerodynamic mechanism that takes advantage of the unique features of flapping flight. Specifically, flies induce asymmetries between the right and left wing angles of attack just as the wings rapidly flip over, and this leads to unbalanced drag forces that contribute to the lateral force. Remarkably, these delicate asymmetries can be simply induced by flipping each wing at slightly different times. We measure that fruit flies use wing rotation timing differences of around 1 millisecond while undergoing a half $g$ lateral acceleration.   

Rotational timing and the alteration of aerodynamic forces in insect flight

Delayed pronation and advanced supination enable the insects using inclined stroke plane motion to generate forces substantially higher than those predicted using quasi-steady aerodynamic principles. Insects, by controlling the timing of wing rotation, subtly modulate the magnitude and direction of aerodynamics forces generated by them, and can perform complex aerial maneuvers by adjusting the timing of rotation in each wing independently. The goal of the present study is to investigate the fluid dynamic changes and the corresponding alterations in forces generated by their flapping wings. The Immersed Boundary Method is used to simulate the flow field over a 2D flat plate of thickness ratio 0.02 undergoing prescribed wing kinematics along the 45$^{0}$ inclined stroke plane at Re=100. The pronation and supination timings are varied independently and the influence of these changes on the force production is investigated. In all the simulations, the downstroke and upstroke angle of attack are held constant.   

Leaping of a flexible loop on water

Small aquatic arthropods, such as water striders and fishing spiders, are able to leap on water to a height several times their body length. We study a simple model using a floating flexible loop to provide fundamental understanding and mimicking principle of the leaping on water. Motion of a loop, initially bent into an ellipse from equilibrium circular shape using a thin thread, is visualized with a high speed camera upon cutting the thread with a laser. We find that the loop may merely oscillate while afloat, penetrate into the water, or soar into air depending on the hydrophobicity, the bending stiffness, the weight and the degree of initial deflection of the loop. We also construct a scaling law for the leaping height by balancing the initial elastic bending energy with the loop's translational and vibrational energy and a loss imparted to the water in the forms of interfacial, kinetic and viscous energy.   

Three-dimensional vortical structures around the fore- and hind-wings of dragonfly in hovering motion

In the present study, we investigate three-dimensional vortical structures around the fore- and hind-wings of dragonfly in hovering motion. The three-dimensional wing shape is based on that of {\it Aeschna juncea} (Noberg, JCP 1972) and numerically realized using an immersed boundary method (Kim et al., JCP 2001). The wing motion is modelled using sinusoidal functions and the mid-stroke angles of attack are 60$^\circ$, 20$^\circ$ with the stroke plane angle 60$^\circ$. The Reynolds numbers considered are 150 and 1000 based on the maximum translational velocity and mean chord length. During the downstroke, the strong wing- tip vortex produces the vortex ring and the downwash, and at the supination this vortex influences the force generation in a similar way to the normal hovering of {\it Drosophila}. During the stroke reversal, dipole vortices are observed all over the spanwise direction, but the time sequence of their development is different at different spanwise location. Near the wing tip, two vortex pairs are generated at the leading and trailing edges, respectively. To further understand the interaction between the wing and vortices, the wing-sectional force and torque are examined. The results will be discussed in the presentation.   

High-Fidelity Computational Models of Insects in Flight: Wing Deformation and Flight Maneuvers

Highly accurate kinematical and geometrical models are used to examine the aerodynamics of insect flight. The simulations employ a sharp-interface immersed boundary method for the flow simulations, and the non-dissipative numerical method used, allows us to capture the vortex dynamics of the wake. One focus of the current study is on understanding the role of wing deformation in insect flight and for this, we examine the flight of a moth in hover with deformable and rigid wings. The second focus of the current work in on flight maneuvers in insects and the presentation will also show preliminary results from simulations of flight maneuvers in butterflies.   

Session AN: Micro Fluids I

Particle ordering in inertially focused microfluidic flows

We study inertially driven focusing of particles [1], which has recently been exploited in a controlled fashion in microfluidic devices [2]. In particular, we characterize the focusing as a function of particle and channel Reynolds number by reporting particle position in directions perpendicular to the flow, and a large distance from the fluid inlet. Focusing of dilute suspensions leads to a linear arrangement of particles whose spacing is primarily a function of concentration and channel aspect ratio. All results are compared with simulations, which provide mechanistic insights into particle behavior.\\ \\ $[1]$ G. Segr\'{e} and A. Silberberg, Nature \textbf{189}, 209 (1961). \\ $[2]$ D. Di Carlo, D. Irimia, R. G. Tompkins, and M. Toner, Proc. Nat. Acad. Sci. U.S.A. \textbf{104}, 18892 (2007).   

The effective slip length and vortex formation in laminar flow over a rough surface

The flow of viscous incompressible fluid over a periodically corrugated surface is considered by the numerical solution of the Navier-Stokes equation. We define the effective slip length with respect to the level of the mean height of the surface roughness. With increasing corrugation amplitude the effective no-slip boundary plane is shifted towards the bulk of the fluid what implies a negative effective slip length. Analysis of the flow streamlines shows that a flow circulation is developed in the grooves of the rough surface provided that the local boundary condition is no-slip. By applying a local slip boundary condition, the location of vortex is displaced towards the bottom the grooves and the effective slip length increases. For values of the local slip length larger than the period of the surface corrugation, the vortical structure disappears, the flow streamlines are deformed to follow the surface curvature, and the effective slip length saturates to a constant value. Inertial effects promote vortex flow formation in the grooves and reduce the effective slip length.   

Dual-tracer laser-induced fluorescence thermometry in microchannels

Laser-induced fluorescence (LIF) thermometry measures liquid temperatures based on changes in fluorescence intensity. In dual-tracer or ratiometric LIF thermometry, liquid temperatures are based on the ratio of the fluorescent signals from two different fluorophores, since this ratio is independent of changes in fluorescence intensity due to variations in the excitation. Recently, a dual-tracer LIF technique using two species with opposite temperature sensitivities, fluorescein 27 and Kiton Red (sulforhodamine B), excited at 532~nm has been reported with temperature sensitivities as great as 7\% per $^\circ$C [Sutton {\it et al.} (2008) {\it Exp. Fluids} DOI 10.1007/s00348-008-0506-4]. We describe here a similar technique using fluorescein and sulforhodamine B, which have intensities that increase by 2.2\% and decrease by 1.3\%, respectively, per $^\circ$C when volumetrically illuminated at 514 nm. The ratio of these two signals gives temperature sensitivities as great as 9\% per $^\circ$C. This LIF technique is used to measure temperature distributions in water flowing through a 500 $\mu$m $\times$ 1000 $\mu$m polydimethylsiloxane (PDMS) microchannel covered with a glass lid with localized heating to create temperature gradients up to about 15 $^\circ$C /mm. The results are compared with FLUENT predictions.   

Nonuniform particle distributions in near-wall particle-image velocimetry

Multilayer nano-particle image velocimetry ({\mbox MnPIV}) uses fluorescent colloidal tracers illuminated by evanescent waves to visualize the flow within the first 500~nm next to the wall. Because the evanescent-wave intensity decays exponentially with wall-normal distance {\it z}, the {\it z-} position of each tracer particle can be correlated to the intensity of its image, assuming that the particle image and illumination intensities behave in a similar fashion. Recent experimental calibrations suggests that the z-position of 100~nm fluorescent polystyrene spheres can be determined with an accuracy of about 20~nm [Li \& Yoda (2008) {\it Meas. Sci. Technol.} {\bf 19}, 075402]. Near-wall particle distributions were obtained as a function of {\it z} for the Poiseuille flow of monovalent electrolyte solutions at various pH and ionic strengths through bare hydrophilic and coated hydrophobic fused- quartz microchannels with similar nominally rectangular cross- sections. The tracers were then divided into three sub-layers, each containing about $1/3$ of the particles, based on the measured particle distribution, and the average velocities in each layer were placed at the average {\it z-}position sampled by the particles in that layer. The effect of pH and wall properties on the near-wall particle distributions and the resultant {\mbox MnPIV} data is discussed.   

Drop break-up and pressure measurements in a microfluidic device

We study experimentally the flow of an emulsion passing through one or a few constrictions placed in a microfluidic channel. Using a high-speed differential manometer placed in the same device (M. Abkarian et al. PNAS 200:16407104 (2006)) we have measured the dynamic pressure as a drop breaks up when it meets one or several constrictions. We can then study how a global measurement of the pressure drop indicates the sequence of phenomena occurring in the channel (breakup, trapped and squeezed drops etc.). In a separate set of experiments with a microfluidic model of a two-dimensional porous medium through which drops flow we can observe the various phenomena and thus correlate the pressure fluctuations to single events at the pore scale.   

Effect of divalent ions on electroosmotic flow

The electroosmotic flow (EOF) rate in fused silica microchannels is found to decrease when trace quantities of salts containing the divalent cations $\rm {Ca}^{2+}$ and $\rm {Mg}^{2+}$ are added to a background electrolytic solution (BGE) containing a salt of monovalent ions. Moreover, the observed effect is quantitatively different for the two ions $\rm {Ca}^{2+}$ and $\rm{Mg}^{2+}$. Since electrostatic interactions should be identical for ions of the same valence modeled as point charges, a description of the electric double layer (EDL) based on the Poisson-Boltzmann equation alone cannot account for these experimental observations. Experiments to measure EOF in the presence of $\rm {Ca}^{2+}$ and $\rm{Mg}^{2+}$ in the BGE were carried out using nano-particle image velocimetry (nPIV). A model for the charge development at the silica-BGE interface (site binding model) that accounts for the chemical interactions of the BGE ions with the silica surface is developed. The model predictions are in good agreement with the experimental observations on the effect of divalent cations as well as data from the literature on how properties such as pH and ionic strength affect electroosmotic flow rates in a BGE containing only monovalent ions.   

Dynamics of polymer solutions and polymer/vesicle mixtures during microchannel flow

Addition of small amounts of long-chain polymers to blood has been found to have dramatic effects on its flow in the microcirculation. To address the mechanisms underlying these phenomena, we use a real-space P$^3$M method for Stokes flow including Brownian fluctuations to study the dynamics of polymer solutions and polymer/vesicle mixtures in microscale flows. Both a simple slit geometry and a grooved cavity flow are studied and polymer concentrations from ultradilute up to near the overlap concentration are considered. As concentration increases, the hydrodynamic migration effects observed in dilute solution unidirectional flows become less prominent, virtually vanishing as the overlap concentration is approached. In a grooved channel geometry, the groove is almost completely depleted of polymer chains at high Weissenberg number in the dilute limit, but at finite concentration this depletion effect is dramatically reduced. In suspensions of vesicles, the presence of polymer molecules has a substantial effect on the dynamics of pair collisions and on migration of the vesicles from microchannel walls.   

Nanoscale Wicking Structures

Heat pipes have been used extensively as heat transfer systems due to their low maintenance and lack of moving parts. These characteristics allow the heat transfer system to be compact for increasingly miniature electronic devices. The fluid flow is possible through the pressure gradient induced by the capillary force and is unaided by external power sources. However, since there is no external force driving the flow, the fluid is entirely dependent on the dimensions and capillary characteristics of the wicking structure. Since the convective and latent heat transfer is strongly dictated by mass flow of the fluid, the wicking structure dimensions should be optimized in order to achieve a maximum flow rate. In order to optimize the dimensions of the wicking structure, a fluidic model was developed to simulate fluid flow based on existing capillarity, Bernoulli and Stokes flow equations for a nanoscale posts array. This fluidic analysis was the initial platform on which thermal performance was based. These results were then compared with experimental data to validate and further examine the effects of wicking structure geometry and wetting characteristics.   

Flow of a rarefied gas in a micro channel caused by oscillatory heating of a wall

A rarefied gas in a micro channel where one of the channel wall is heated periodically in time is studied numerically on the basis of the linearized Boltzmann equation for a hard sphere molecular gas. The time-dependent motion of the gas caused by the heating is investigated with the aid of a deterministic numerical method for a wide range of the Knudsen number (=mean free path/channel with $D$) and the Strouhal number (=frequency $\times D$ /sound speed). The gas motion is highly induced by the heating when Sh $=3\sim 4$, for $0.1\le \textrm{Kn} \le 10$, so the normal stresses of the gas acting on the walls are. At about Sh$=1.5\sim 2$, the normal stress acting on the heated wall exhibits a rather sharp minimum with respect to Sh, while no such sharp minimum is found in that on the other wall.   

A new electrohydrodynamic flows due to field-induced conductivity gradient in dielectric liquids

A dielectric liquid is often preferred as a host fluid of a colloidal system under an electric field, because one can utilize the full benefits of a strong electric field with little concern for occurrence of electrolysis. Hence, dielectric liquids have been employed in many practical applications such as electrorheological fluids, electrophoretic deposition, and electrophoretic display. Nonetheless, the dynamics of colloidal particles in dielectric liquids is poorly understood compared to that in aqueous solutions. In the present paper, we report a novel electrohydrodynamic (EHD) flow which occurs near the objects immersed in dielectric liquids containing small amounts of polar additives. We suggested that the EHD flow is generated due to a electrical conductivity gradient induced by a non-uniform electric-field. Analytical and numerical solutions are obtained and verified by comparision with experimental results. We discuss the effect of electric-field strength, particle size, and ac frequency on velocity and pattern of the EHD flow.   

Session AP: Multiphase Flows I

Role of slip between a probe particle and a gel in microrheology

In the technique of microrheology, rheological information is deduced from the behavior of microscopic probe particles under thermal or active forcing. Microrheology requires knowledge of the force felt by a probe particle in response to displacements, which we investigate for a spherical particle using the two-fluid model. The gel is represented by a polymer network coupled to a surrounding solvent via a drag force. We obtain an analytic solution for the response function in the limit of small volume fraction of the polymer network, and neglecting inertial effects. We use no-slip boundary conditions for the solvent at the surface of the sphere. The boundary condition for the network at the surface of the sphere is a kinetic friction law specifying the tangential stress. We show that the far field motion and the force on the sphere are controlled by the solvent boundary conditions at high frequency and by the network boundary conditions at low frequency. At low frequencies compression of the network can also affect the force on the sphere. We find the crossover frequencies at which the effects of sliding of the sphere past the polymer network and compression of the gel become important.   

Quasi-2D foam: Rheology and fracture

A single layer of acqueous foam bubbles captured between parallel plates in a Hele-Shaw rectangular-channel geometry is a system with many desirable qualities: the foam can be observed over the entire width and length of the channel and interpreted as effective medium, but at the same time all information about every single bubble (size, shape, deformation) is readily available. We show that a proper modification of Bretherton's single-bubble theory allows for a quantitative description of foam rheology in this quasi-2D set-up, both for the general flow resistance of the foam and for the motion of individual bubbles. For the latter, the viscous flow resistance can be related to pressure and stress distributions in the foam when it is driven by imposed external pressure. Such a foam ultimately undergoes fracture in two modes aptly described as ``brittle'' and ``ductile,'' and the rheology measurements yield a criterion for the transition point between these two behaviors.   

Numerical Simulations of a Biomass Fluidizing Bed with Side Port Air Injection

Fluidized beds can be used to gasify biomass in the production of producer gas, a flammable gas that can replace natural gas in process heating. As part of the reactor design, side air ports strategically placed along the reactor column can help promote and improve mixing. Modeling these reactors using computational fluid dynamics is advantageous when performing parametric studies for design and scale-up. From a computational point of view, two-dimensional simulations are easier to perform than three-dimensional simulations, but they may not capture the proper physics. Comparisons of two- and three-dimensional simulations in a 10.2 cm diameter cold-flow fluidized bed with side air injection are used to determine when two-dimensional simulations are adequate to capture the bed hydrodynamics. The medium used to represent biomass is ground walnut shell, which has been shown to have desirable fluidization characteristics. The simulations will be quantitatively compared with X-ray computed tomography experiments for pressure drop through the bed, particle distribution and bed expansion height.   

Measurement and Modeling of Channel Wall Vibration Subjected to Internal Bubbly Flow

The effect of a bubbly flow, injected into both a square and rectangle channels, on channel wall vibrations is studied experimentally and theoretically. The vibrations are measured under various gas void fractions, bubble diameters and channel dimensions. A theoretical model, based on a waveguide theory and bubble dynamics, is developed to predict the dominant frequencies in vibration spectra, the corresponding decay rates and propagation phase speeds. Results show that, compared with no bubble case, the presence of bubbles substantially enhances the power spectral density of vibrations, by up to 27 dB in a square channel and 37 dB in a rectangular channel. The origin of enhanced vibrations is attributed to the excitation of the streamwise propagating pressure waves, created by an initial acoustic energy generated during bubble formation. The model predicts very well the magnitudes and trends of the dominant spectral frequencies, the corresponding decay rates and phase speeds. The frequency, attenuation and phase speed decrease substantially with increasing void fraction but slightly with increasing diameter.   

Optical measurements of phase concentration and velocity distributions of a horizontal gas jet in a 2D bubbling fluidized bed

Optical measurement techniques are used for spatially and temporally resolved measurements of phase concentrations and velocities in a horizontal gas jet injected in a 2D bubbling fluidized bed. A fiber optic probe has been developed to measure Laser Induced Fluorescence (LIF) signals from an acetone tracer to quantify jet gas concentration and elastic Mie scatter from the bed particles to determine the solids fraction in a localized region. These two optical signals are spectrally separated and therefore enable simultaneous measurements of the two phases. In addition, jet gas and particles velocities are obtained with a Laser Doppler Velocimetry (LDV) system. These measurements yield phase concentration and velocity profiles necessary to characterize the dynamic behavior of gas jets in fluidized beds.   

Assembly of particles at fluid-fluid interfaces using electric fields

In this talk, we present a new technique to assemble micro- and nano-sized particles into monolayers (two-dimensional arrays). For this, we sprinkle particles at a fluid-fluid interface (or at the free surface of a liquid) and apply a uniform electric field normal to the interface. The electric field generates horizontal electrostatic forces on the particles due to dipole-dipole forces which, together with the capillary forces, put the particles into motion until their reach an equilibrium position where the two forces balance each other. In the final arrangement, particles are placed at a certain distance of one another, a distance which can be controlled by varying the electric field strength. The technique, which works on a variety of particles, including micro/nano-sized and neutral particles, is investigated both experimentally and theoretically. A good quantitative agreement between the two approaches is found.   

Redistribution and removal of particles from drops surfaces

It was recently shown by us that particles distributed on the surface of a drop can be concentrated at its poles or the equator by subjecting it to a uniform electric field. In this talk we show that the method can be used to separate particles experiencing positive dielectrophoresis on the surface a drop from those experiencing negative dielectrophoresis. This, in fact, can be used to form a composite (Janus) drop by aggregating particles of one type near the poles and of the second type near the equator. We also show that when the ratio of the distance between the electrodes to the drop diameter is smaller than a critical value the drop bridges the gap between the electrodes and then breaks into two or more major droplets. For the larger values of this ratio the drop undergoes tip-streaming. The former case is used to remove particles concentrated near the drop's equator and the latter for removing particles at the poles.   

Unsteady Forces on Particles in Viscous Compressible Flow

The primary objective of our work is the study of unsteady forces on particles in compressible flow. In incompressible flow, unsteady inviscid and viscous forces arise from the no-penetration and no-slip conditions on the surface of a particle. In prior work, building on results by Miles and Longhorn, we have investigated the unsteady force on particles in inviscid compressible flow at finite Mach numbers. The results indicate that the unsteady force can become about twice as large as the incompressible value even for subcritical Mach numbers. The contributions of this work are twofold. First, based on the kernel for the unsteady inviscid force in compressible flow, we present a simple model for the unsteady force on particles arising from shock-wave impact, and assess it by comparison with experimental and computational results. Second, we construct a unified model based on an unified kernel for the unsteady inviscid and viscous forces in compressible flow.   

Blocking effects of a sphere or spheroid immersed in linear shear flows in the Stoke's regime

Building on work by Wu and Chwang who developed closed form exact solutions of the Stokes for the case of a sphere or spheroid embedded in a linear shear layer, we study the behavior of fluid particles in such flows and document rigorously that the blocking behavior which was observed by Wu and Chwang for the two dimensional case occurs in the fully 3D case well. We compute explicitly the volume of the blocking region, which is seen to be infinite, and present the explicit and analytic solution for the particle trajectories for this fully 3D flow. Time permitting, we explore cases when the sphere or spheroid have centers displaced from the background shear symmetry line. We document an interesting bifurcation in the particle trajectories using numerical techniques.   

Session AQ: Reacting Flows I: Turbulent Flames

Large-Eddy Simulations of Reacting Liquid Spray

Numerical simulation, which is commonly used in many stages of aero-engine design, still has to demonstrate its predictive capability for two-phase reacting flows. This study is a collaboration between Stanford University and CERFACS to perform LES of a realistic spray combustor installed at ONERA, Toulouse. The experimental configuration is computed on the same unstructured mesh with two different solvers: Stanford's CDP code and CERFACS's AVBP code. CDP uses a low-Mach, variable-density solver with implicit time advancement. Droplets are tracked in a Lagrangian point-particle framework. The combustion model uses a flamelet approach, based on two transported scalars, mixture fraction and reaction progress variable. AVBP is a fully compressible solver with explicit time advancement. The liquid phase is described with an Eulerian method. The flame-turbulence interaction is modeled using a dynamically-thickened flame. Results are compared with experimental data for three regimes: purely gaseous non-reacting flow, non-reacting flow with evaporating droplets, reacting flow with droplets. Both simulations show a good agreement with experimental data and also stress the difference and relative advantages of the numerical methods.   

Numerical Simulation of Highly Turbulent Hydrogen Combustion

The behaviour of hydrogen combustion under highly turbulent conditions is investigated. Simulations are performed using a parallel low Mach number adpative mesh computational method. The study was designed such that the chemical kinetics are well-resolved while relying on an implicit LES approach to capture the turbulence. We present numerical results to validate the approach and discuss the implications for hydrogen combustion in this regime.   

Simultaneous 3D Volumetric PIV and 2D OH PLIF in the Far-Field of a Nonpremixed Turbulent Jet Flame

Cinematographic stereoscopic PIV, combined with Taylor's hypothesis, is used to generate quasi-instantaneous volumes of the 3D velocity field in the far field of a turbulent nonpremixed jet flame at a jet exit Reynolds number of 8,000. The 3D data enable computation of the nine components of the velocity gradient tensor and its derived kinematic quantities. The volumetric PIV is combined with simultaneously acquired OH PLIF to mark the instantaneous reaction zone. The combined data sets enable investigation of the relationship between the jet kinematics and the reaction zone. Three-dimensional rendering of regions of intense vorticity and dissipation reveals that sheet-like layers of vorticity and dissipation tend to coincide and are aligned with the OH layers. Due to the stabilizing effect of heat release on this relatively low Reynolds number jet flame, intense dissipation is mostly due to the laminar shear caused by the presence of the flame rather than the strain generated by vortical structures as typically observed in non-reacting jets. It is further observed that both positive and negative dilatation is present and is believed to be mainly due to convection of regions of varying density rather than to instantaneous heat release rate.   

Statistics and Modeling of the Scalar Dissipation and its Relation to the Filtered Mixture Fraction

Scalar dissipation is an important quantity for characterizing turbulent mixing and chemical reactions in combustion. It exhibits highly intermittent statistical properties, which have been shown to produce one-point probability density functions that agree well with a log-normal distribution. In large eddy simulation, only the filtered mixture fraction is available to calculate the scalar dissipation. The filtered scalar dissipation, however, is not of primary relevance when modeling phenomena that is sensitive to the smallest scale of the turbulence. Ideally, a statistical approximation of the true scalar dissipation is required. This study examines how filtering mixture fraction affects estimates of the scalar dissipation. Statistics are investigated using DNS databases of turbulent shear layers with different levels of heat release. Using these databases, the effects of filter size to Kolmogorov scale and heat release are determined. A stochastic model of the filtered scalar dissipation that mimics the effects of filtering mixture fraction is then proposed and used as an inverse model to estimate the statistics of the true scalar dissipation.   

Large Eddy Simulations of Two-phase Turbulent Reactive Flows in IC Engines

The two-phase filtered mass density function (FMDF) subgrid-scale (SGS) model is used for large-eddy simulation (LES) of turbulent spray combustion in internal combustion (IC) engines. The LES/FMDF is implemented via an efficient, hybrid numerical method. In this method, the filtered compressible Navier-Stokes equations in curvilinear coordinate systems are solved with a generalized, high-order, multi-block, compact differencing scheme. The spray and the FMDF are implemented with Lagrangian methods. The reliability and the consistency of the numerical methods are established for different IC engines and the complex interactions among mean and turbulent velocity fields, fuel droplets and combustion are shown to be well captured with the LES/FMDF. In both spark-ignition/direct-injection and diesel engines, the droplet size and velocity distributions are found to be modified by the unsteady, vortical motions generated by the incoming air during the intake stroke. In turn, the droplets are found to change the in-cylinder flow structure. In the spark-ignition engine, flame propagation is similar to the experiment. In the diesel engine, the maximum evaporated fuel concentration is near the cylinder wall where the flame starts, which is again consistent with the experiment.   

A flamelet-based approach for combustion systems with convective heat-losses

A new flamelet method is proposed for modeling turbulence/chemistry interactions in large-eddy simulations (LES) of non-premixed combustion with convective heat-losses. The new method is based on the flamelet/progress-variable approach of Pierce \& Moin (2004) and extends that work to include the effects of thermal-losses on the combustion chemistry. In the new model, chemistry databases are constructed by solving 1D diffusion/reaction equations which have been constrained by scaling the enthalpy of the system between the adiabatic state and a thermally-quenched reference state. The solutions are parameterized and tabulated as a function of the mapping variables: mixture fraction, progress-variable, and normalized enthalpy. The model is implemented in a LES solver which computes the filtered values of the mapping variables, and interpolates other pertinent quantities (such as density and reaction rates) from the chemistry database. The new model is applied to LES of non-premixed methane-air combustion in a coaxial-jet geometry with isothermal wall-conditions to describe heat transfer to the confinement. The resulting velocity, species concentration, and temperature fields are compared to the experiment of Spadaccini, \emph{et al.} (1976) and numerical results from the adiabatic model.   

Large Eddy Simulation of a Sooting Jet Diffusion Flame

The understanding of soot particle dynamics in combustion systems is a key issue in the development of low emission engines.~ Key mean quantities of the population such as total volume fraction and number density can be predicted without solving for the entire distribution, by just solving for a few moments of the distribution.~ The newly developed Hybrid Method of Moments (HMOM) allows for an efficient and accurate prediction of moments of the soot Number Density Function (NDF).~ This method has been validated for laminar premixed and diffusion flames with detailed chemistry and is now implemented in a semi-implicit low Mach number Navier-Stokes solver.~ A Large Eddy Simulation (LES) of a piloted sooting jet diffusion flame (Delft flame) is performed to study the dynamics of soot particles in a turbulent environment.~ Combustion in the LES is modeled with the Flamelet/Progress Variable Approach (FPVA) to properly account for the effects of temperature on soot formation and growth.~ Profiles of temperature and major species as well as soot volume fraction are compared with experimental measurements.~ In addition, the influence of the turbulent environment on particle shape and size is investigated.   

Scalar Filtered Density Function for Large Eddy Simulation of a Bunsen Burner

The scalar filtered density function (SFDF) methodology is extended for large eddy simulation (LES) of a turbulent, stoichiometric premixed methane/air flame. The SFDF takes account of subgrid scales (SGS) by considering the mass weighted probability density function (PDF) of the SGS scalar quantities. A transport equation is derived for the SFDF in which the effects of chemical reactions appear in closed form. The SGS mixing is modeled via the linear mean square estimation (LMSE) model, and the convective fluxes are modeled via a SGS viscosity. The modeled SFDF transport equation is solved by a hybrid finite-difference/Monte Carlo scheme. A novel irregular domain decomposition procedure is employed for scalable parallelization which facilitates affordable simulations with realistic chemical reactions and flow parameters. Oxidation chemistry is modeled via a 5-step reduced, and a 15-step augmented reduced mechanism. Results are presented of the mean and rms values of the velocity, the temperature, and mass fractions of the major and the minor species. These results are assessed by comparison against laboratory data.   

Formation and properties of distributed flames

Interaction of flames with turbulence is a ubiquitous process encountered in a wide variety of systems, ranging from terrestrial flames to thermonuclear burning fronts in supernovae. Burning can alter the turbulent field by injecting additional energy on multiple scales thereby modifying its spectral energy distribution. On the other hand, turbulence itself can have pronounced effect on the flame changing its morphology, properties, etc. In this work we present results of detailed numerical and theoretical modeling of the interaction of flames in stoichiometric methane-air and hydrogen-air mixtures with turbulence of varying intensity and spectrum. We demonstrate the transition with increasing turbulent intensity from the laminar flame to the corrugated flamelet and finally to the distributed reaction zone. The latter represents a quasi-steady-state propagating burning front in which thermal conduction and species diffusion are mediated by turbulent transport. We discuss properties of such flames and their potential implications for deflagration-to-detonation transition both in confined and unconfined systems.   

Measurement of Three-Dimensional Flame Structure by Simultaneous Dual-plane CH PLIF, Single-plane OH PLIF and Stereoscopic PIV

To investigate three-dimensional flame structures of turbulent premixed flame, dual-plane planar laser induced fluorescence (PLIF) of CH radical has been developed. The newly-developed dual-plane CH PLIF is combined with single-plane OH PLIF and stereoscopic particle image velocimetry (SPIV) to clarify the relation between flame geometry and turbulence characteristics. The laser sheets for OH PLIF and SPIV measurement are located at the center of two planes for CH PLIF. The separation between these two CH PLIF planes is selected to $500\mu$m. The measurement was conducted in relatively high Reynolds number methane-air turbulent jet premixed flame. The experimental results show that various three-dimensional flame structures such as the handgrip structure, which has been shown by DNS, are included in high Reynolds number turbulent premixed flame. It was shown that the simultaneous measurement containing newly-developed dual- plane CH PLIF is useful for investigating the three-dimensional flame structure.   

Session AR: CFD: Immersed Boundary and Computational Methods

An Incremental Improvement to the Feedback-Forcing Immersed Boundary Method

The immersed boundary method (IBM) has been applied in a variety of forms, but all of them represent a boundary implicitly on a grid that need not conform to the boundary contour. We confine our interest to one of the simpler forms of IBM, the feedback-forcing approach, and apply it via user-defined functions in the commercial cell-centered finite-volume CFD code, FLUENT. The only modification that we make is the addition of a forcing term $\vec{f}= C_{\rm IBM}\left(\vec{v}-\vec{u}\right)$, where $C_{\rm IBM}$ is a problem-dependent penalty parameter, $\vec{v}$ is the velocity of the immersed boundary, and $\vec{u}$ is the fluid velocity. For cells completely contained inside the boundary, we use the forcing term as-is. Cells that are only partially contained inside the boundary are more difficult to treat. In this situation, one approach that has been successfully applied in the literature is to scale the forcing by the fraction of cell volume contained within the boundary. We investigate a modification that scales the forcing in the coordinate directions separately. To test the concept, we applied this modification to two-dimensional flow over a circular cylinder. We found that this approach allows access to higher values of penalty parameter, which typically improves the solution. Tests with other flows are underway at the time of this writing.   

A low-numerical dissipation immersed interface method for the compressible Navier-Stokes equations

Immersed interface methods are an alternative methodology to unstructured methods for solving fluid dynamical problems around complex geometries. In this approach, a Cartesian mesh is used to discretize the governing equations and a regular numerical method is used everywhere in the domain, except around the complex boundaries, where special stencils are used. We present and discuss results using a stable numerical methodology for the compressible Navier-Stokes equations that uses centered stencils. Specially designed stencils are constructed around the complex objects to ensure stability. These non-dissipative methods are beneficial in the study of noise and turbulence where numerical dissipation tends to attenuate the relevant flow physics. Furthermore, it is shown that the stiffness introduced by the high-order derivatives of the viscous and heat conduction terms in the discretized equations due to non-deforming boundaries can be resolved into an explicit method. Examples of compressible flows with multiple complex objects at different Mach numbers and Reynolds numbers are presented and convergence of the solutions is investigated as a function of resolution and relative position of the objects with respect to the Cartesian mesh.   

Curvilinear immersed-boundary method for simulating unsteady flows in shallow natural streams with arbitrarily complex obstacles

Unsteady 3D simulations of flows in natural streams is a challenging task due to the complexity of the bathymetry, the shallowness of the flow, and the presence of multiple nature- and man-made obstacles. This work is motivated by the need to develop a powerful numerical method for simulating such flows using coherent-structure-resolving turbulence models. We employ the curvilinear immersed boundary method of Ge and Sotiropoulos (Journal of Computational Physics, 2007) and address the critical issue of numerical efficiency in large aspect ratio computational domains and grids such as those encountered in long and shallow open channels. We show that the matrix-free Newton-Krylov method for solving the momentum equations coupled with an algebraic multigrid method with incomplete LU preconditioner for solving the Poisson equation yield a robust and efficient procedure for obtaining time-accurate solutions in such problems. We demonstrate the potential of the numerical approach by carrying out a direct numerical simulation of flow in a long and shallow meandering stream with multiple hydraulic structures.   

The Immersed Interface Method for Insect Flight Simulation

The effect of a fluid-solid interface can be represented as a singular force in the Navier-Stokes equations. Two problems arise from this representation. One is how to calculate the force density, and the other is how to treat the force singularity. In the immersed interface method, the latter is solved with second-order accuracy and the sharp fluid-solid interface by incorporating singularity-induced flow jump conditions into discretization schemes. This talk focues on the former problem. In particular, I will present approaches to calculating the force density for both flexible and rigid solids. Results from insect flight simulation will be shown to demonstrate the approaches.   

Efficient Unstructured Cartesian/Immersed-Boundary Method with Local Mesh Refinement to Simulate Flows in Complex 3D Geometries

Image-guided computational fluid dynamics has recently gained attention as a tool for predicting the outcome of different surgical scenarios. Cartesian Immersed-Boundary methods constitute an attractive option to tackle the complexity of real-life anatomies. However, when such methods are applied to the branching, multi-vessel configurations typically encountered in cardiovascular anatomies the majority of the grid nodes of the background Cartesian mesh end up lying outside the computational domain, increasing the memory and computational overhead without enhancing the numerical resolution in the region of interest. To remedy this situation, the method presented here superimposes local mesh refinement onto an unstructured Cartesian grid formulation. A baseline unstructured Cartesian mesh is generated by eliminating all nodes that reside in the exterior of the flow domain from the grid structure, and is locally refined in the vicinity of the immersed-boundary. The potential of the method is demonstrated by carrying out systematic mesh refinement studies for internal flow problems ranging in complexity from a 90 deg pipe bend to an actual, patient-specific anatomy reconstructed from magnetic resonance.   

Domain Decomposition Methods for Solving Stokes-Darcy Systems Based on Boundary Integrals

We consider a coupled problem of Stokes and Darcy equations. This involves solving PDEs of different orders simultaneously. To overcome this difficulty, we apply a non-overlapping domain decomposition method based on a Robin boundary condition obtained by combining the velocity and pressure interface conditions. The coupled system is then reduced to solving each problem separately by an iterative procedure using a Krylov subspace method. The numerical solution in each subdomain is based on the boundary integral formulation, where the kernels are regularized and the leading term in the regularization error is eliminated for higher order accuracy.   

Unstructured Grid Generation via Bubble Packing Method

Unstructured grid is necessary to numerically simulate the fluid flow in complicated domain. In order to improve the accuracy and efficiency of numerical simulation, a modified physically-based Bubble Packing Method to generate unstructured grid is proposed. In this method the local grid refinement is achieved by adding arbitrary size Bubbles to the real vertices and artificial vertices of the domain. And Shepard interpolation method is used to transfer information from vortices to the inner nodes of the domain, so the mesh density of region can be simply controlled, through which the quality of grid can be improved greatly. At the same time, for the case of curve boundary, the process of initial Bubble and dynamic relaxation is realized by mapping the curve to a straight line and the parameterization of arc-length, which ensures that all edge Bubbles move only on their associated curve. Moreover, the improved BPM is applied to generate unstructured grid with local refinement near the boundary of square domain to simulate the lid-driven flow in a square cavity with Re=1000. The good agreement between numerical result and the benchmark verifies the grid quality and the validation of numerical algorithm on the unstructured grid.   

Fluid Velocity Superposition method for fluid-structure interaction in viscous flows using the Immersed Boundary Method

The Immersed Boundary Method conventionally uses Chorin's spectral projection method as a viscous flow solver due to its computational speed and high degree of convergence. These advantages hold most fully for Fourier basis functions (which suppose periodic boundary conditions). It is advantageous to extend the capabilities of the spectral projection method to viscous flow with non-periodic boundary conditions. Here, a technique is proposed in which fluid velocity is represented as the superposition of a non-periodic mean velocity profile and a periodic disturbance due to the presence of an immersed body. The spectral projection method is then applied only to the disturbance velocity. The proposed method is tested by simulating the deformation of a capsule in unbounded linear flow fields with both extensional and shear components, as well as in shear flows near a wall. Accuracy of these results is confirmed by comparison with theory in the limit of small deformations and numerical results for finite deformation from the literature.   

Session AS: Buoyancy-Driven Flows I

Rotating turbulent Rayleigh-B\'enard convection: Effect of weak rotation on boundary layers and heat transfer

The Grossmann-Lohse (GL) theory\footnote{Grossmann and Lohse, J. Fluid Mech. 407, 27 (2000)} for the heat transfer in turbulent Rayleigh-B\'enard (RB) convection heavily builds on the Prandtl-Blasius laminar boundary layer (BL) theory, according to which the thermal BL thickness $\lambda_\theta$ scales as $L Pr^{-1/2}$ in the low $Pr$ regime and with $L Pr^{- 1/3}$ in the high $Pr$ regime. In an attempt to extend the GL theory to the rotating RB case, we study the influence of rotation on the thermal BL thickness in flow above an infinite rotating disk. We show that with rotation $\lambda_\theta \propto Pr^{-1}$ in the low $Pr$ regime, whereas in the high $Pr$ regime the scaling remains unchanged. Furthermore, we obtain an analytic expression for the Nusselt number in the Ekman case (fluid at infinity rotates at almost the same speed as the disk). We moreover introduce a model to explain the experimentally\footnote{Rossby, {\emph{J. Fluid Mech.}} {\bf {36}}, 309 (1969)} and numerically\footnote{Oresta et al {\emph {Eur. J. Mech.}} {\bf{26}}, 1 (2007); Kunnen et al {\emph{Phys. Rev. E}} {\bf{74}}, 056306 (2006).} observed increased heat transfer (as compared to RB without rotation) at weak rotation.   

Interacting Stokes layers and wall modes in modulated rotating convection

Thermal convection in a rotating cylinder near onset is investigated using direct numerical simulations of the Navier--Stokes equations with the Boussinesq approximation in a regime dominated by the Coriolis force. For thermal driving too small to support convection throughout the entire cell, convection sets in as alternating pairs of hot and cold plumes in the sidewall boundary layer, the so-called wall modes of rotating convection. We subject the wall modes to small amplitude harmonic modulations of the rotation rate over a wide range of frequencies. The modulations produce Stokes boundary layers which drive a time-periodic large-scale circulation that interacts with the wall-localized thermal plumes in a non-trivial manner. The resultant phenomena include a substantial shift in the onset of wall mode convection to higher temperature differences for a broad band of frequencies, as well as a significant alteration of the precession rate of the wall mode at very high modulation frequencies due to the mean azimuthal streaming flow resulting from the modulations.   

Rotating High Rayleigh Number Convection

Very high Rayleigh number convection with rotation is studied using cryogenic helium gas as the working fluid. Rayleigh and Taylor numbers were obtained up to maximum values of $Ra=4 \times 10^{15}$ and $Ta = 3 \times 10^{15}$ under Boussinesq conditions. For these experiments the Rossby number was in the range 0.4 $<$ Ro $<$ 1.6 and Prandtl number varied as 0.7 $<$ Pr $<$ 6. Under all conditions, the effect of added steady rotation was to diminish the heat transfer. However, a sinusoidal time- variation of the rotation rate provided periodic spin-up which led to significant enhancement of the Nusselt number, presumably due to Ekman pumping, in the case when the Taylor number based on the modulation amplitude surpassed a critical value, roughly $10^{14}$. Otherwise the periodic spin-up caused a reduction in the heat transfer as in the case when the rotation rate was held constant. The effect on heat transfer did not appear to be sensitive to the period of the modulation, which was nominally set to be comparable to the turn-over time of the large-scale mean wind.   

Double Diffusive Plumes

Sour gas flares attempt to dispose of deadly $H_2S$ gas through combustion. What does not burn rises as a buoyant plume. But the gas is heavier than air at room temperature, so as the rising gas cools eventually it becomes negatively buoyant and descends back to the ground. Ultimately, our intent is to predict the concentrations of the gas at ground level in realistic atmospheric conditions. As a first step towards this goal we have performed laboratory experiments examining the structure of a steady state plume of hot and salty water that rises buoyantly near the source and descends as a fountain after it has cooled sufficiently. We call this a double-diffusive plume because its evolution is dictated by the different (turbulent) diffusivities of heat and salt. A temperature and conductivity probe measures both the salinity and temperature along the centreline of the plume. The supposed axisymmetric structure of the salinity concentration as it changes with height is determined by light-attenuation methods. To help interpret the results, a theory has been successfully adapted from the work of Bloomfield and Kerr (2000), who developed coupled equations describing the structure of fountains. Introducing a new empirical parameter for the relative rates of turbulent heat and salt diffusion, the predictions are found to agree favourably with experimental results.   

Numerical experiments on salt finger type convection

Salt finger type convection is formed where hot, salty water overlying colder, less salty water. In the ocean, solar radiation may warm the surface layer of the sea but this may also give a high evaporation rate increasing the salt concentration. Therefore, salt fingers are often observed undersea. Double diffusive convection of salt finger type has been studied experimentally and numerically very much. However, some interesting problems remain. In the last our numerical study of salt finger type convection, it was simulated two dimensionally that under a condition, a large convective flow occurs which mixes fluid, and forms an uniform layer. In this study, we try to simulate this phenomenon three dimensionally, and carry out salt finger type convection under other conditions. In the computation, the governing incompressible Navier-Stokes equations are solved by the multidirectional finite-difference method. For high-Reynolds-number flows, the third-order upwind scheme is utilized for the convective terms to stabilize the computation. Results of the computation are visualized extensively.   

Thermal-hydraulic characterization of the natural circulation of air between two vertical cylinders enclosed in a rectangular cavity

This work presents the results of an experimental analysis focused on the characterization of the natural circulation of air in the vicinity of two vertical cylinders. A three dimensional cavity encloses each cylinder, where one of them is a heat source and the other is a heat sink. A wall with two holes of variable diameter delimits and connects the two enclosures in order to restrict the air flow exchanged between them. The distance between the center lines of the cylinders was varied with the purpose of measuring the effect of the surrounding walls on the natural circulation. All configurations were tested for different heat generation rates. A Particle Image Velocimeter was used to obtain the flow patterns and a set of thermocouples was installed to measure the temperature field. The experimental results are analyzed and discussed.   

Three-dimensional measurement of temperature and velocity field in buoyancy driven flows

Three-dimensional measurements of temperature and velocity field in buoyancy driven flows are carried out using a background oriented Schlieren combined with tomographic reconstruction technique. This method is based on the refractive index measurement in the three-dimensional flow field, and the corresponding velocity field is evaluated from the displacement of the measured temperature field. The accuracy of this measurement is examined using the artificial images derived from the numerical simulation.   

Time dependent ventilation flows driven by opposing wind and buoyancy

We consider flow in an enclosure containing an isolated heat source, ventilated by a windward high level opening and a leeward low level opening, so that prevailing wind acts to oppose buoyancy driven flow. Following the ``emptying filling box'' approach of Linden {\it et al.}\footnote{Linden, Lane-Serff \& Smeed, {\emph{J. Fluid Mech.}} {\bf{212}}, 309 (1990).}, Hunt \& Linden\footnote{Hunt \& Linden, {\emph{J. Fluid Mech.}} {\bf{527}}, 27 (2005).} demonstrate that multiple steady states can exist above a critical wind strength. We develop time dependent models for this system and apply them to an initial value problem - box filling with constant opposing wind. We identify the final state attained for any given heat load, wind strength and vent size. We note that the interface between the upper region of hot plume fluid and the lower region of cool ambient air can dramatically overshoot its final level before relaxing to equilibrium; in some cases, a fully mixed transient can occur before the stratified steady state is reached. Analogue laboratory experiments confirm the existence of these transient phenomena and elucidate the range of validity of our predictions.   

Buoyancy effects on added mass in density-stratified fluids

In the presence of stable density stratification, owing to buoyancy, fluid motion gives rise to internal gravity waves which redistribute momentum and energy through the fluid. As a result, the added mass of moving bodies is modified and becomes anisotropic and frequency-dependent. The influence of these modifications on the definition itself of added mass and on its relation to hydrodynamic pressure, impulse, energy and to the dipole strength of the bodies is discussed. Coefficients of added mass are calculated explicitly for the small oscillations of spheres and circular cylinders. Implications for energy radiation and for the motion of floats are considered. In the first case the existence of a maximum at a frequency of oscillation equal to a fixed fraction 0.8 of the buoyancy frequency, practically independent of the direction of oscillation, is pointed out together with possible inferences for turbulent motion. In the second case classical results by Larsen on neutrally buoyant spheres and cylinders are recovered.   

Session AT: Experimental Techniques I

Nano-PIV for flows near nano-structured surfaces

Previous studies have shown that nano-structured surfaces can exhibit different wetting characteristics and higher slip-length values compared to smooth (i.e. non-structured) surfaces. In order to quantitatively measure the flows near such nano-structured surfaces, a Nano-PIV method with high spatial and temporal resolution is required. The TIRF-based PIV is a good candidate because it has been successfully applied for 3D nano-velocimetry near smooth surfaces, but it cannot be applied in a simple and direct manner since the nano-structures optically complicates the measurements: (i) they spatially influence and modulate the TIRF illumination, and (ii) they increase the probability of obtaining errors caused by the tracers' own emitted evanescent-waves. For fabricated periodic nano-structures with known dimensions and geometry, however, the spatially modulated TIRF illumination can be very useful for (i) a simple estimation of the illumination depth directly inside the microfluidic channels, and (ii) detection and measurement of the thin layer of air bubbles trapped at the nano-structures in the `Cassie-Baxter' wetting mode.   

Improving the Accuracy of the Laser Doppler Accelerometer Technique

The measurement of particle accelerations gives insights into the fundamental properties of fluid flows. The basic principles of the Laser Doppler Accelerometer (LDA) technique follows closely those introduced in Lehmann et al. (2002). Recently it was successfully applied to a commercial of-the-shelf laser Doppler system by Kinzel et al. (2006). Since then we implemented numerous improvements in the signal processing and increased the reliability. In order to reach acceptable resolution of the measurement system, both, the optical setup and the signal processing system must realize the highest possible accuracies. The main contribution of this study is the assessment of the accuracy of the method, and the quantification of the errors due to optical fringe divergence in the detection volume and due to signal processing using a falling wire as a reference. --- Lehmann B, Nobach H, Tropea C (2002): Measurement of acceleration using the laser Doppler technique. Meas. Sci. Technol. 13(9):1367-1381 --- Kinzel M, Nobach H, Tropea C., Bodenschatz E (2006): Measurement of Lagrangian acceleration using the laser Doppler technique. Proc. 13th Int. Symp. on Appl. of Laser Techn. to Fluid Mech., Lisbon, Portugal   

Accuracy of Velocity Estimation Using Global Variational Methods

In this work a method of processing digital images, such as those from PIV, MTV, or LIF, for flow velocities using Global Variational Method (GVM) is investigated. This technique is based on principles of Frobenius-Perron (FP) operator theory in which image sequences can be related to the infinitesimal generator of the FP operator to motivate a flow-recovery constraint. A regularization method is then used to minimize this constraint along with an additional constraint required to stabilize a solution. Synthetic images, with typical MTV tagging patterns, and variable noise levels were first created and then displaced using analytically derived flow fields. Displacements were calculated from pairs of images and the error was determined by comparing the measured displacements to those of the analytical flow field. A direct correlation technique (DCT) was also used to process the synthetically derived images for comparison. Results show that the GVM error levels are nominally 5-10 times higher than for the DCT. While the error is higher for GVM compared to DCT the results show potential for using this technique to provide quantitative flow measurements in cases where DCT cannot be applied.   

The Development of a Feature Comparison Based Technique to Analyze PTV Results

A new post processing technique based on feature comparison is developed for analysis of Particle Tracking Velocimetry (PTV) results. Similar to methods employed in Finite Element Modeling, fluid properties such as shear strain rate and rotation are calculated for the centers of triangular features whose vertices are particle locations. These features are created using Delaunay Tessellation. In addition, no interpolation step is required, meaning that derivative data can be obtained directly from nonuniform velocity data, increasing computational efficiency. Analysis of the validity of this novel technique is given, showing that a least squares fit is required to find two directional derivatives from three data points (vertices) in each feature. Comparisons to traditional differentiation methods for various examples of fluid flow are given.   

Nano-scale thermal anemometry probe

A nano-scale thermal anemometry probe is being developed with high spatial and temporal resolution to measure small-scale turbulence in high Reynolds number flows. Manufactured using a combination of semiconductor and micro-electromechanical manufacturing processes, two sizes of probe have been manufactured. Each probe consists of a platinum sensing wire of length 60$\times $1$\times $0.1 $\mu $m or 20$\times $0.1$\times $0.1 $\mu $m suspended between two contact pads. Preliminary measurements have been made comparing the nano-scale probe to a conventional hot-wire probe in both a zero pressure gradient turbulent boundary layer and in turbulent pipe flow using constant current anemometry and constant temperature anemometry. Results indicated that the nano-scale probe exhibits typical hot-wire behavior, but with a frequency response of at least three-times that of a conventional probe.   

A Comparison of Condensation Fog and Wide-Field PIV Measurements in a Mach 5 Turbulent Boundary Layer

Condensation fog planar laser scattering has been used to visualize the structure of supersonic turbulent shear flows. Some previous work at Princeton in a supersonic boundary layer has suggested that the scattering from CO$_{2}$ clusters closely reflects the fluctuating density field. However, the relationship between the fog scattering and the velocity field has not been established. In the current study wide-field, side-view PIV measurements of a turbulent boundary layer that develops naturally on the floor of a Mach 5 wind tunnel is performed using three 1k$\times $1k resolution cameras. For the PIV, TiO$_{2}$ particles are seeded into the flow, but the particle images also reveal a fog of ice crystals that is formed due to isentropic cooling in the nozzle from the water vapor already present in the flow. This natural fog in the freestream evaporates and disappears in the boundary layer forming a clear demarcation of the boundary layer edge. The interface between the fog and the boundary layer seems to correlate with the instantaneous velocity contours. The measurements suggest that the structures observed with the fog technique are dynamically significant and not just artifacts of an advecting passive scalar. A similar comparison is made in the plan view to visualize the very large-scale coherent structures that have been observed in previous studies at lower Mach number.   

The microPIVOT: An Integrated Micron Resolution Particle Image Velocimeter and Optical Tweezers Instrument for Microscale Studies

An instrument to manipulate and characterize the mechanical environment around microscale objects has been developed by integrating two laser-based techniques: micron-resolution particle image velocimetry (microPIV) and optical tweezers (OT) [Meas. Sci. Technol. 19 (2008) 095403]. The integrated device, the microPIVOT, was validated by comparing computational flow predictions to the measured velocity profile around a trapped particle in either a uniform flow or an imposed, gravity driven microchannel flow. Interaction between both techniques is shown to be negligible for 15 to 35 micron diameter trapped particles subjected to fluid velocities from 50 to 500 microns/s even at the highest laser power. The integrated techniques will provide insight into microscale phenomena including single-cell biomechanics, non-Newtonian fluid mechanics, and single particle or particle-particle hydrodynamics.   

Micro-PIT/V --- Simultaneous temperature and velocity fields in microfluidic devices

The use of encapsulated thermochromic liquid crystals (TLC) for the simultaneous measurement of temperature and velocity fields in microfluidic devices has been demonstrated. Implementation of TLC thermometry at the micro-scale is significantly different than at the macro-scale due to the constraints on imaging and illumination configurations and the proximity of the measurements to interfaces and surfaces from which light will scatter. Unlike in micro-PIV, wavelength filtering (such as with fluorescent particles) cannot be used to remove undesired reflections, because the temperature information is carried by the particle color. Therefore, circular polarization filtering is used, exploiting the circular dichroism of TLC. Micro-PIT/V will enable new investigations into the physics of microfluidic devices involving temperature gradients, such as thermocapillary actuated devices and many ``lab-on-a-chip'' applications involving temperature sensitive chemical and biological processes. In addition, the design of operational devices can be improved by applying micro-PIT/V to the characterization of prototypes.   

Influence of the accuracy in index of refraction matching on fluid flow measurements

Fluid flow imaging through curved surfaces suffers from optical distortion caused by the mismatch in the refractive indices of the fluid and the solid surface, leading to errors in velocity measurements and the resulting estimates of wall shear stress. Examples include imaging of flow through porous media and in-vitro studies of biological flow problems. A common approach for minimizing optical distortions is to adjust the refractive index of the fluid to closely match that of the solid. In this study we investigate how the accuracy in the index of refractive matching influences the image distortion and, in particular, the measurement accuracy of wall shear stress, a critical property in biofluid dynamics. A ray-tracing approach is used to simulate the optical distortion and is validated against experiments in a simple geometry, i.e. imaging of a liquid flow inside a cylindrical tube. Ray-tracing is implemented through an in-house code for simple geometries and the results are compared with simulations using a more complete (free) software that is already available online and can deal with complex geometries. Results show that a slight mismatch in the indices of refraction, as small as one part in a thousand, can lead to a significant error in the estimate of wall shear stress.   

Session AU: Vortex Flows I

Experimental characterization of thermally driven superfluid flow

We characterize the flow of superfluid $^{4}$He by analyzing trajectories of solid hydrogen seed particles.~ A thermal counterflow is driven by heating the bottom of a cylindrical channel filled with superfluid $^{4}$He while also cooling the free surface. While all particles feel Stokes drag with the normal fluid, some subset are scattered or trapped by quantized vortices of the superfluid. Particle tracking is used, instead of particle image velocimetry cross-correlations, due to this lack of a single underlying velocity field. We find that upward moving particles show the expected normal fluid velocity for all measured temperatures and heat fluxes. Tracers affected by the quantized vortices move downward, opposing the motions driven by Stokes drag, and exhibit erratic trajectories.   

Bifurcation analysis of an infinite array of von Karman Streets

This research investigates the behavior of an infinite array of (inverse) von Karman streets.~Primary motivation is to model the wake dynamics in large fish schools. Ignoring the fish we focus on the dynamic interaction of multiple wakes.~In particular, we investigate~the problem of fluid transport between adjacent vortex streets for its relevance to understanding the transport of oxygen and nutrients to inner fish in large schools as well as understanding flow barriers to passive locomotion. We prove that the configuration of vortices is in relative equilibrium, meaning that the streamline pattern remains steady in the frame moving with vortices.~We~look at the topology of these streamline patterns plotted in the moving frame which lends insight to fluid transport through the mid-wake region.~ Fluid is advected along different paths depending on the distance separating two adjacent streets. When the streets are far apart, the dynamics is decoupled and fluid is transported globally between two adjacent streets. When the streets get closer to each other, the number of streets that enter into partnership in transporting fluid among themselves increases. This observation motivates a bifurcation analysis which links the distance between streets to the maximum number of streets transporting fluid among themselves.   

Characterization of the interaction of two unequal co-rotating vortices

The interaction of two co-rotating vortices in a viscous fluid is investigated. Two-dimensional simulations of initially equal sized vortices with varying relative strengths are performed. In the case of equal strength vortices (Brandt and Nomura, J. Fluid Mech., 2007), the mutually induced strain deforms and tilts the vortices which leads to a core erosion process. As the vortices are jointly entrained, they rapidly move towards each other and the flow eventually transforms into a single vortex. With unequal strengths, the disparity of the vortices alters the interaction and merger may not occur. The flow behavior is distinguished based on the relative onset of the core erosion process. Through scaling analysis and simulation results, a critical nondimensional strain rate characterizing the onset of erosion is determined. If the disparity of strengths is sufficiently large, the critical strain rate is not attained by the stronger vortex and the vortices do not merge.   

Wavelet analysis of vortex bursting

We study the quasi-periodic bursting of a three-dimensional vortex immersed in a laminar channel flow. We measure the velocity field by PIV and analyze the time evolution of the bursting process. We use the orthogonal wavelet transform to separate the flow into coherent and incoherent components and then the continuous wavelet transform to analyze the evolution of each component separately. We found that the coherent flow is intermittent, long-range correlated and sustain the turbulent cascade, while the incoherent flow is non intermittent, exhibits an enstrophy equipartition spectrum and leads to turbulent dissipation. In order to better understand the buildup of the turbulent cascade and to quantify the flow intermittency, we have designed new wavelet-based diagnostics which find out, when in time, where in space, and at which scale, the activity is dominant . We observe that the bursting process starts as an excitation of the small scales inside the vortex core, and then spreads in space and all over the inertial scales. We recover the Kolmogorov k$^{-5/3}$ scaling only for time averages, since the spectral slope of energy varies in time, between k$^{-1}$ during bursting, and k$^{-2}$ after vortex bursting.   

Determining the stability of steady inviscid flows through ``Imperfect Velocity-Impulse'' diagrams

More than a century ago, Lord Kelvin proposed a variational argument for determining the stability of steady inviscid flows; while the underpinnings of the method are well established, its application has been the subject of extensive debate. Considering, for example, a vortex configuration rotating at a rate $\Omega$ with impulse $J$ and energy $E$, Kelvin argued that an equilibrium corresponds to a stationary point of $H = E -\Omega J$. Since $H$ is conserved, the second variation $\delta^2 H$ constrains the dynamics and can be used to assess stability. Unfortunately, computation of $\delta^2 H$ is often impossible or impractical. Saffman \& Szeto (1980) suggested that extrema in a plot of $E$ vs $J$ could be used to identify changes in $\delta^2 H$. However, Dritschel (1985) later pointed out the lack of a firm link between $\delta^2 H$ and a plot of $E$ vs $J$. Furthermore, he stated that even if such link could be proven, changes of stability could also occur, at bifurcations, away from extrema in $E$ and $J$. We address both issues by proposing a new approach. We introduce a theorem from dynamical systems theory to prove that extrema in a plot of $J$ vs $\Omega$ (instead of $E$ vs $J$) are indeed related to the properties of $\delta^2 H$, while we use ideas from imperfection theory to ensure that bifurcations are detected by means of an ``imperfect velocity-impulse'' (IVI) diagram. By applying our approach to several classical flows, we obtain stability results in agreement with linear analysis, while additionally discovering new steady solutions.   

Elementary vortex systems and the generation of internal waves

As a first step toward improving our understanding of the behavior of a turbulent patch in a stratified fluid, we investigate the effects of stable stratification on different configurations of two-dimensional horizontally oriented vortices. The vortex systems considered, which consist of initially Lamb-Oseen vortices, include a single vortex, co-rotating vortex pair, counter-rotating vortex pair, two sets of co-rotating vortex pairs in a quadrapole configuration, and two sets of counter-rotating vortex pairs in a quadrapole configuration. Analytical and numerical methods are used to compute the linear and nonlinear interactions of the vortices and the generated internal waves, as well as the transport of vorticity and energy associated with each vortex configuration. These fundamental findings provide further insight on wave-vortex interactions and vortex structure decay.   

Chaotic scattering of two vortex pairs

Chaotic scattering of two vortex pairs with slightly different circulations was considered by Eckhardt \& Aref in 1988. A new numerical exploration suggests that the motion of two vortex pairs, with constituent vortices all of the same absolute circulation, also displays chaotic scattering regimes. The mechanisms leading to chaotic scattering are different from the ``slingshot effect'' identified by Price [{\it Phys. Fluids} A, {\bf 5}, 2479 (1993)] and occur in a different region of the four-vortex phase space. They may in many cases be understood by appealing to the solutions of the three-vortex problem obtained by merging two like-signed vortices into one of twice the strength, and by assuming that the four-vortex problem has unstable, periodic solutions similar to those seen in the thereby associated three-vortex problems. The integrals of motion, linear impulse and Hamiltonian, are recast in a form appropriate for vortex pair scattering interactions that provides constraints on the parameters characterizing the outgoing vortex pairs in terms of the initial conditions.   

Statistics of vortex tube properties in isotropic turbulence

The vortex tubes of isotropic turbulence are statistically analyzed by means of a feature-extraction algorithm applied to DNS data at several value of the Taylor Reynolds number. It is found that the main geometric parameters of the vortices (radius, induced velocity, core vorticity) exhibit log-normal distributions, and very nearly collapse in terms of Kolmogorov units. Consistent with pevious studies, we have found that vortex tubes are special instances of the vorticity field associated with intensity stronger than the mean and local alignment of the vorticity vector, which subjected to the r.m.s background strain. Contrary to previous findings, however, we find that the vortex core radius and the local strain are nearly statistically independent, thus raising doubts on the relevance of vortex models based on stretched axi-symmetric vortices. The analysis of the azimuthal velocity profiles indicate scaling of the induced velocity similar to recent experimental findings, but very different from Burgers vortex model.   

Session AV: Geophysical Flows I

Hurricane Formation in Diabatic Ekman Turbulence

This study numerically examines the evolution of Diabatic Ekman Turbulence (DET) under various conditions. DET is quasi 2D turbulence that is modified by surface friction and parameterized cumulus convection. The self-organization of DET is here simulated in a 3-layer troposphere. In our primary model, winds over the ocean elevate the moist entropy of boundary layer air, whose convergence may then generate deep convection. After an incubation period, the influence of deep convection can supercede ideal 2D processes such as vortex merger. A strong cyclone-anticyclone asymmetry can develop, with relatively intense cyclones dominating the system. ``Hurricanes'' form at sufficiently high values of the sea-surface temperature (SST), the Coriolis parameter, and the surface-exchange coefficient for moist entropy~$C_E$. Increasing the momentum exchange coefficient $C_D$ shortens the incubation period, but decelerates the subsequent intensification of an emerging hurricane. Increasing $C_E$ or the SST accelerates all stages of hurricane genesis. As in more complex models, DET hurricanes can exhibit mesovortices and eyewall cycles. Moreover, their intensities increase with the SST and the ratio~$C_E/C_D$. In some regions of parameter space, low-level noise can evolve into a hurricane {\it or} a synoptic scale circulation. The effects of using different representations of cumulus convection or surface friction will be discussed. Supported by NSF-ATM-0750660.   

Velocity Fields of Jovian Dynamical Features using the Advection Corrected Correlation Image Velocimetry Method

We present the Advection Corrected Correlation Image Velocimetry (ACCIV) automated method for producing velocity fields from satellite and spacecraft image pairs of planetary atmospheres. The method combines a laboratory technique for tracking fluid motion, Correlation Image Velocimetry (CIV), with simulations of cloud advection to produce velocity fields with uncertainties as small as 3 ms$^{-1}$. On Jupiter, ACCIV has been most successful when applied to sets of images in which some image pairs are separated by short periods of time ($\sim $1 hour) and some image pairs are separated by longer periods ($\sim $10 hours). Given appropriate sets of images, ACCIV achieves unprecedented accuracy by combining the very large numbers of data points that automated techniques provide with the ability to track cloud features over long periods of time ($\sim $10-12 hours), previously only attainable by manual tracking methods. We present the application of ACCIV to the Great Red Spot, the Red Oval BA and several other dynamical features on Jupiter. We also present a velocity map of the entire Jovian cloud deck between 60\r{ } N and 60\r{ } S latitude produced from Cassini approach images from December 2000.   

Dynamics and Interactions of Jovian Vortices During the Last Year

Jupiter's atmosphere has been active during the last year with the Great, Little, and Oval Red Spots merging, almost merging, or repelling each other. These jovian storms are all anticyclonic vortices, with small Rossby numbers, embedded in an atmosphere with strong vertical stratification and horizontal shear. We use numerical and analytic models to compute and explain these vortex interactions. Many of the interactions are sensitive to equilibrium values of the ambient jovian atmosphere that are difficult to measure directly, such as the vertical shear and the vertical stratification. We show that the errors in the velocity measurements of the jovian vortices are sufficiently small, the equations are sufficiently well-conditioned, and the 3D models of the vortices sufficiently complex that the ``inverse problem'' can be solved and that we can determine many of the equilibrium values of the ambient jovian atmosphere.   

Zonal winds generated by tides

The fundamental role of tides in geo and astrophysics has been the subject of multiple studies for several centuries. Beyond the well known quasi periodic flows of ocean water on our shores, tides are also responsible for phenomena as varied as the intense volcanism on the Jovian satellite Io, or the synchronization of the Moon spin on its rotation around the Earth. We describe here a new phenomenon of zonal wind generation by tidal forcing. Following a recent theoretical and numerical analysis of Tilgner [1], we present the first experimental evidence that the nonlinear self-interaction of a tidally forced inertial mode can drive an intense axisymmetric flow in a rotating sphere. These results are relevant for zonal wind generation in planets and stars. [1] A. Tilgner, Zonal wind driven by inertial modes, {\it Phys. Rev. Lett.} {\bf 99}, 194501 (2007).   

Interaction of alternating oceanic zonal jets and wind-driven gyres

Recent evidence has unmasked the presence of alternating zonal jets superimposed on the larger scale midlatitude ocean circulation. Analogous jets are well-known from $\beta$-plane turbulence and are associated w ith a halting of the 2d inverse energy cascade by Rossby wave dispersion. Both the $\beta$-plane turbulence and the gyre scale dynamics are nonlinear and it seems reasonable to anticipate that the two will inter act. Some evidence for these interactions comes from observations: e.g., jets in the N. Atlantic are aligned at an angle to latitude circles, following a direction nearly parallel to the seaward extension of the Gulf Stream. In the North Pacific, both the jets and the Kuroshio extension are more nearly zonal. How jets interact with the wind-driven cirulation is considered in the quasi-geostrophic equations in a box ge ometry forced by i) a large scale wind, ii) a small scale stochastic forcing and iii) both. The first cas e is the classic midlatitude double gyre problem, the second has previously been used to model the jets an d the third allows us to consider interactions between the two. We focus primarily on the energetics.   

Kinematic dynamo of inertial waves

Inertial waves are natural oscillatory tridimensional perturbations in rapidly rotating flows. They can be driven to high amplitudes by an external oscillatory forcing such as precession, or by a parametric instability such as in the elliptical instability. Inertial waves were observed in a MHD-flow (Gans, 1971, JFM ; Kelley et al., 2008, GAFD) and could be responsable of dynamo action. For travelling waves, a constructive alpha-effect was identified (Moffatt, 1970, JFM), but it does not apply to confined inertial wave flows. Yet, recent numerical work demonstrated that precession driven MHD flows can sustain magnetic fields (Tilgner, 2005, POF; Wu \& Roberts, 2008, GAFD). This motivates us to study more precisely how inertial waves can exhibit dynamo action. Using a numerical code in cylindrical geometry, we find that standing inertial waves can generate a kinematic dynamo. We show that the dynamo-action results from a second order interaction of the diffusive eigenmodes of the magnetic field with the inertial wave. Scaling laws are obtained, which allows us to to apply the results to flows of geophysical interest.   

Spherical Couette flow in a three meter diameter system

Construction of the three-meter diameter spherical Couette experiment at the University of Maryland is complete. Prior to sodium experiments measurements have been performed using water as a test fluid. Pressure measurements are provided by three piezo-electric transducers mounted on the outer sphere inner surface at a colatitude of 23.6$^{\circ}$ and separated 90$^{\circ}$ azimuthally. In addition, a hot-film wall shear stress probe located near one of the pressure probes complements the measurements. Direct optical imaging of tracer particles in the fluid is also implemented. Preliminary analysis show evidence of inertial modes and non-linear interactions among them.   

A hydromagnetic spherical Couette experiment with a soft iron core

Understanding the geodynamo remains a central pursuit of Earth science. Increasingly powerful numerical simulations and the experimental generation of a magnetic field by a Von K\'{a}rm\'{a}n flow raise questions about the roles of turbulence and ferromagnetic materials. We present experimental studies of 110~L of conductive fluid (sodium) in a differentially rotating spherical Couette cell with Earth-like geometry. The inner boundary is ferromagnetic soft iron, which has large permittivity but small remembrance, and which was chosen in an attempt to better understand the results of Monchaux \textit{et.\ al} (2007). We measure magnetic induction via an array of Hall probes and project the data onto the vector spherical harmonics up to degree four, producing time series of Gauss coefficients. Varying the Ekman number, rotation rate ratio, and magnetic Reynolds number, we observe a variety of behaviors, including large induced fields, large resulting torques, intermittent broadband induction, Earth-like dipolar fields, and bistability.   

Dynamics of Pure Ice Streams and Surges

We examine a bottom sliding law that is capable of explaining pure ice streams and glacier surges within a simple model of ice flow over a homogeneous bed. The model resolves longitudinal stresses, and assumes a plug flow as supported by ice stream observations. The flow law is Newtonian and hence we neglect thermo-viscous and shear-thinning effects. The bottom sliding law is a multivalued relation between the bottom stress and the ice velocity, similar to that suggested by previous work (e.g. Fowler \& Johnson, 1996). The multivaluedness can be heuristically justified by variations in bed lubrication caused by changes in water formation rate and rearrangement of the drainage system. This sliding law accounts for two fundamental modes of flow, depending on the magnitude of the mass accumulation forcing: (i) a steady stream pattern, due to the coexistence of two stable velocities for a given bottom stress, the faster corresponds to an ice stream region and the slower to an inter-stream region. (ii) a relaxation oscillation mode (a surge).   

Wind-transport of barchan dunes in modulated gravity

Barchan dunes can be found in sand barren regions under steady wind conditions. They translate in the direction of the wind while their shape remains unchanged. They have a minimal length in the order of ten meters, which renders laboratory experiments almost impossible. The length scale is set by the details of the sand-wind interaction. Smaller dunes do not evolve into the typical barchan dune shape. Our experimental approach produces dramatically scaled down barchan dunes. The idea is to modulate gravity by vertical oscillation of the sand bed. We produce small dunes that travel in the turbulent boundary layer of an open windtunnel. Particle image velocimetry on the surface of moving dunes reveals the flux of creeping sand, while measurement of sand grains flying through the air quantifies the key mechanism that moves sand by wind: saltation. While the amount of sand flying with the flow does not vary strongly in an oscillation cycle, the sand creeping over the dune surface is only in motion when the effective gravity is smaller than g. Thus, modulation of gravity provides a unique view on sand transport in wind. Saltation is an activation process, and we demonstrate the importance of turbulence.   

Session AW: Mini-Symposium: Videos and Multimedias for Fluids Instruction

Videos and images from 25 years of teaching compressible flow

Compressible flow is a very visual topic due to refractive optical flow visualization and the public fascination with high-speed flight. Films, video clips, and many images are available to convey this in the classroom. An overview of this material is given and selected examples are shown, drawn from educational films, the movies, television, etc., and accumulated over 25 years of teaching basic and advanced compressible-flow courses. The impact of copyright protection and the doctrine of fair use is also discussed.   

eFluids Video Gallery: a ``YouTube'' for Fluid Mechanics

The research and educational value of videos of fluid mechanical phenomena cannot be overstated, yet there are literally hundreds of videos that, while posted on various websites, can be difficult to find. eFluids.com has launched a new video gallery website highlighting all aspects of fluid mechanics that will hopefully serve as a repository for this material. The gallery receives submissions using a user-friendly interface modeled on the popular YouTube site. Submissions can be in any format and any size up 50MB and up to 5 minutes long. The galleries are searchable and are classified in 23 categories, including subject-specific categories such as ``Laminar Flow,'' ``Turbulence,'' ``Vortices,'' ``Biological Flows,'' etc., as well as ``Recent Postings'' and links to fluids videos on other sites such as YouTube. The Video Gallery is integrated with the other Galleries on eFluids, including the long-established Gallery of Images, Gallery of Experiments, and Gallery of Problems. The presentation will show examples, demonstrate the submission interface, and the integration with the other galleries. In collaboration with George Homsy and Gordon McCreigh, www.eFluids.com.   

Interactive multimedia demonstrations for teaching fluid dynamics

We present a number of multimedia tools, developed by undergraduates, for teaching concepts from introductory fluid mechanics. Short movies are presented, illustrating concepts such as hydrostatic pressure, the no-slip condition, boundary layers, and surface tension. In addition, we present a number of interactive demonstrations, which allow the user to interact with a simple model of a given concept via a web browser, and compare with experimental data. In collaboration with Mack Pasqual and Lindsey Brown, Princeton University.   

Fluidica CFD software for fluids instruction

{\it Fluidica} is an open-source freely available {\it Matlab} graphical user interface (GUI) to to an immersed-boundary Navier- Stokes solver. The algorithm is programmed in Fortran and compiled into Matlab as mex-function. The user can create external flows about arbitrarily complex bodies and collections of free vortices. The code runs fast enough for complex 2D flows to be computed and visualized in real-time on the screen. This facilitates its use in homework and in the classroom for demonstrations of various potential-flow and viscous flow phenomena. The GUI has been written with the goal of allowing the student to learn how to use the software as she goes along. The user can select which quantities are viewed on the screen, including contours of various scalars, velocity vectors, streamlines, particle trajectories, streaklines, and finite-time Lyapunov exponents. In this talk, we demonstrate the software in the context of worked classroom examples demonstrating lift and drag, starting vortices, separation, and vortex dynamics.   

Teaching through Simple Experiments

Our main goal in this proposed talk is to start a discussion among faculty around the power of simple in-class experiments to teach fundamental fluid mechanics. Many introductory fluid mechanics classes are highly theoretical and mathematical, with students becoming experts in applying mathematical recipes without truly understanding the underlying concepts and assumptions. Often, these fundamental concepts can be taught through asking the students to design and execute experiments, but this can take substantial class time. Our long term goal is to develop a library of short and cheap (2-5 min and under {\$}1) experiments that all students can execute in class. These experiments promote discussion between the students and through that, a better fundamental grasp of the material. In this talk, we will show a number of experimental videos that we are developing for the Gallery of Experiments at eFluids.com. We will present both common experiments and those in areas students usually do not experience in an introductory course: low Reynolds number and non-Newtonian fluids. We will end with a discussion with the audience to look for new ideas and potential experiments. In collaboration with Gareth McKinley, Massachusetts Institute of Technology.