Session EA: Turbulent Boundary Layers: Theory

Near-wall behavior of turbulent wall-bounded flows

A data base compiling a large number of results from direct numerical simulations and physical experiments is used to explore the properties of shear and normal Reynolds stresses very close to the wall of turbulent channel/pipe flows and boundary layers. Three types of scaling are mainly investigated:\ classical inner, standard mixed, and pure outer scaling. The study focuses on the near-wall behavior, the location and the value of the peak Reynolds shear stress and the three normal stresses. A primary observation is that all of these parameters show a significant K\'{a}rm\'{a}n number dependence. None of the scalings investigated works in an equal manner for all parameters. It is found that the respective first-order Taylor series expansion satisfactorily represents each stress only in a surprisingly thin layer very close to the wall. In some cases, a newly introduced scaling based on $u_{\tau}^{3/2}u_{e}^{1/2}$ offers a remedy.   

Recent developments in scaling of wall-bounded flows

Proper scaling of a fluid flow permits convenient, dimensionless representation of experimental data, prediction of one flow based on a similar one, and extrapolation of low-Reynolds-number, laboratory-scale experiments to field conditions. This is a particularly powerful technique for turbulent flows where analytical solutions derived from first principles are not possible. We extend in this presentation our recent work on scaling of turbulent wall-bounded flows ({\it Prog.\ Aerospace Sciences} {\bf 42}, p.\ 419--467, 2007) with respect to the most topical developments. The actual research tendencies in scaling go more and more toward investigating boundary layers under the influence of pressure gradient and/or of wall-roughness. Additionally, some new ideas employing local Kolmogorov scales arose. All together four main groups of questions are formulated that hopefully will be answered by future research.   

$2D/3C$ Model of Turbulence in Plane Couette Flow

Given the consensus that turbulent flow is characterized by coherent structures and observations of streamwise-elongated structures in numerical simulations and experiments (in the near wall region), we model the mean behavior of fully developed turbulent plane Couette flow using a streamwise constant projection of the Navier Stokes (NS) equations, (the so-called $2D/3C$ model). The unforced $2D/3C$ model has been analytically shown to have a single globally stable solution. This property lends to analysis of the system using tools from robust control theory where one can represent model uncertainties or experimental errors through the addition of noise forcing. In the present work this nonlinear $2D/3C$ model is driven with small amplitude stochastic noise to produce fully developed turbulent plane Couette flow with low order statistics that are qualitatively consistent with experiments. The large scale features of the resulting flow are compared to both experiments (Kitoh and Umeki 2008) and DNS data (Tsukahara, Kawamura and Shingai 2006).   

Correlation of Fluctuating Vorticity in Turbulent Wall Layers

It is commonly known that Reynolds shear stress $$ scales with the friction velocity $u_{\ast }^{2}$. On the other hand, Degraaff and Eaton ( JFM, \textbf{422, }p 319 ) and Metzger and Klewicki ( P of F, \textbf{13}, p 6 92 ) have shown that the streamwise Reynolds stress \textit{$<$uu$>$} scales more nearly as $U u_{\ast }$. Townsend proposed that motions were ``active'' if they contributed to the Reynolds shear stress and ``inactive'' otherwise. Here, Townsend's definition is modified to say that motions are ``active'' if they scale with $u_{\ast }$; the same scaling as the Reynolds stress. A fluctuation that does not scale with $u_{\ast }$ is ``inactive.'' Vorticity profiles from the DNS (described in the various papers of Del Alamo, Jimenez, Zandonade, Moser, and Hoyas (P of F \textbf{15}, L-41; JFM, \textbf{500},p135, P of F, \textbf{18}, 011702) ) are reviewed. It is found that, in the limit of high Reynolds number, the outer region is free of vorticity. In the inner region the vortcity $<${\_}$_{y}${\_}$_{y}>$ is active with no inactive component. The other components, $<${\_}$_{x}${\_}$_{x}>$ and$<${\_}$_{z}${\_}$_{z}>$, have active components that scale as $<${\_}{\_}{\_}${\rm g}{\rm v}{\rm g}{\rm o} u_{\ast }^{4}$\textit{/{\_}}$^{{\rm y}}) $and inactive components that scale as $<${\_}{\_}{\_}${\rm g}{\rm v}{\rm g}{\rm o}{\rm o} u_{\ast }$\textit{/{\_}${\rm p}$}$^{{\rm y}} u_{\ast }U. $Since at the wall the vorticity and shear stress are proportional, the wall stress fluctuations are found to be: $<${\_}$_{x{\rm w}}{\rm g}${\_}$_{x{\rm w}}>$ / ${\rm o}$\textit{{\_}}$^{{\rm y}} u_{\ast }^{3}U)=0.007$and $<${\_}$_{z{\rm w}}{\rm g}${\_}$_{z{\rm w}}>$ / ${\rm o}$\textit{{\_}}$^{{\rm y}} u_{\ast }^{3}U)=$ 0.0038.   

The Reynolds shear stress in zero pressure gradient turbulent boundary layers derived from log-law asymptotics

The Reynolds shear stress (RS) in zero pressure gradient turbulent boundary layers is established using recently developed composite mean velocity profiles based on the ``log-law'' in the overlap region between inner and outer profiles. The contribution of the normal stress difference is discussed and considered to be of secondary importance. From this analysis, an asymptotic expansion for the maximum RS and its location is developed. The hypotheses underlying this analysis are discussed and the results are compared with experiments and DNS. Using the friction velocity as scale, the analytic approximation of the RS agrees reasonably well with low-Re experimental results. However, when comparing with high-Re experiments, the agreement is generally limited as the experimental accuracy and resolution becomes problematic near the wall. Comparison with DNS, on the other hand, is shown to be affected by the delicate numerical treatment of the free stream boundary condition. Finally, the present asymptotics will be compared to the results of Sreenivasan, Panton and others for channels and pipes.   

Optimal transient growth and very large scale structures in turbulent boundary layers

We compute the optimal energy growth sustained by a turbulent boundary using the mean flow proposed by Monkewitz et al. (Phys. Fluids 2007) and the associated eddy viscosity as recently done for channel flows (del \'Alamo \& Jim\'enez, J. Fluid Mech. 2006). Large transient energy growths are obtained for streamwise vortices evolving into streamwise streaks. For sufficiently large Reynolds numbers two distinct optimal spanwise walengths exist. The first, $\lambda^+ \sim 80 $, scales in inner units and is associated with most probable buffer layer streaks. The second, $\lambda \sim 8\,\delta$ scales in outer units and corresponds to optimal vortices centred near the boundary layer edge and to optimal streaks spreading in the whole boundary layer. These streaks scale in outer variables in the outer region and in wall units in the inner region of the boundary layer.   

Modified law of the wall leading to turbulent channel flow universal velocity profiles valid down to $Re_{\tau}=395$

Velocity profile modeling is revisited using the results from databases of turbulent channel flow DNS at $Re_{\tau}=u_{\tau}\,h/ \nu= 2000$, $950$, $550$, and $395$. We consider the turbulent region: $y^+ = Re_{\tau}\,\eta$ (with $\eta=y/h$) larger than $70$). A new model for the effective turbulent viscosity, $\nu_t=-\overline{u'v'}/\frac{d\overline{u}}{dy}$, is proposed, that fits well the DNS results all the way to the channel center. The velocity profile is then obtained by integration: it corresponds to a ``modified law of the wall,'' $\frac{1} {\kappa}\left(\log(y^+ + y_0^+) -\eta\right) + C$, with the added classical ``law of the wake,'' $D\,g(\eta)$. The new $- \eta$ term in the modified law of the wall is really required in such still limited Reynolds number channel flows, as an important correction to the usual log term: both terms ``work together,'' as both are multiplied by the same $\frac{1}{\kappa} $ value (recall that $D$ is not related to $\kappa$). Only at the highest Reynolds numbers does this correction become negligible. As to the $y_0^+$ shift in the log term itself (value around 6), something also recently proposed by Spalart et al (Phys. Fluids in press), it too is required as a consequence of the $\nu_t$ near wall behavior. The present velocity profile is quite universal: it fits very well, with the same value of all constants, all $Re_{\tau}$ cases. In particular, the von K\`arm\`an constant is obtained as $\kappa=0.37$: same as Zanoun et al (Phys. Fluids 15 (10):3079, 2003), and close to $0.38$ as Spalart et al.   

Further insight into physics of rough-wall turbulent boundary layer

To get a good understanding of the effect of surface-roughness in altering the flow in a turbulent boundary layer it is important to understand the alterations in the dynamical activity of the flow. For this purpose direct proper orthogonal decomposition (POD) has been used as a tool. The data used for the POD has been obtained from direct numerical simulation of flow in a channel with egg-carton roughness elements. In this talk the effects of surface-roughness on the temporal flow dynamics such as bursting frequency of the energetic structures in the flow will be discussed. VITA detection technique has been used to obtain the bursting frequency. It has confirmed that rough-wall has a shorter bursting period and a higher turbulence activity compared to the smooth-wall. The results have confirmed the existence of roll and propagating modes for flow over rough-wall. In addition to the turbulent kinetic energy, the concept of entropy that has been introduced in this study within the context of degree of distribution of energy over range of scales, is a useful metric to categorize the rough-wall flow dynamics.   

Advection, diffusion \& dispersion: effective diffusion for transient mixing vs. stirring with steady sources \& sinks

The effective diffusion coefficient $\kappa_{eff}$ of a flow is often defined in terms of passive tracer particle dispersion. For some high P\'eclet number flows $\kappa_{eff}$ may be as large as $\kappa_{molec} \times Pe^{2}$ where $\kappa_{molec}$ is the molecular diffusion coefficient and the P\'eclet number $Pe = U\ell/\kappa_{molec}$ is defined in terms of characteristic velocity ($U$) and length ($\ell$) scales in the flow. On the other hand for stirring in the presence of steady sources and sinks an equivalent diffusion coefficient $\kappa_{eq}$ may be defined in terms of (statistical steady state) passive scalar concentration variance suppression. A theorem states that $\kappa_{eq} \le \kappa_{molec} \times Pe \times (L/\ell)$ as $Pe \rightarrow \infty$ where $L$ is a characteristic length scale of the sources-sink distribution. We discuss the origin and resolution of this discrepancy: effective diffusion coefficients proportional to $Pe^{2}$ arise in the large time asymptotic limit of particle dispersion while equivalent diffusion coefficients defined by concentration variance suppression for scalars sustained by steady sources are dominated by short-time transport characteristics of the flow. The theories may be reconciled by considering a time dependent effective diffusion coefficient that includes the transient---and not just time asymptotic---tracer particle dispersion.   

Session EB: Turbulence Simulations III

A narrow-stencil formulation of subgrid-scale models in large-eddy simulation: application to the stretched vortex model for compressible flows

Finite-difference approximations of second-order derivatives involving variable coefficients, as those discretizing subgrid-scale models of large-eddy simulation, are investigated. It is observed that use of the first-order derivative operators successively result in poor resolution and negligible contribution of the subgrid-scale models at the highest wavenumber supported by the mesh. This affects the stability of these simulations negatively. Low and high-order, narrow stencil, numerical discretizations are developed and applied to large-eddy simulation of compressible turbulent flows using the stretched-vortex subgrid scale model. These discretizations are based on a narrow-stencil formulation, which is constructed by requiring that the ellipticity property of the operators, when the variable coefficients are positive, is preserved. Such an approach is found to be discretely conservative, stable, resolves the subgrid model contribution at the smallest wavenumber supported by the mesh better and enables energy transfer from the resolved to the subgrid scales at all discrete modes of the mesh. We investigate the new discretizations in homogeneous decaying turbulence and temporally evolving shear layers.   

Hybrid RANS/LES simulation of a flow with mild separation

The flow past a ramp with mild separation zone has been computed using LES and hybrid approaches. In the hybrid calculations, the RANS equations are solved throughout the boundary layer in the equilibrium region of the flow, while a wall-resolved LES is used to compute the separation and recovery regions. The LES results are used to assess the accuracy of hybrid RANS/LES approach. The accuracy of the hybrid approach depends on the generation of resolved fluctuations at the RANS/LES interface and often needs a long transition region before realistic turbulent fluctuations are generated. When the RANS/LES interface is near the separation point, forcing provided by the addition of synthetic turbulence at the interface results in faster generation of turbulent fluctuations, which is aided by the inflectional instability of the mean velocity profile. When the RANS/LES interface is in the equilibrium boundary layer region, on the other hand, even the addition of synthetic turbulence does not cause fast generation of turbulence fluctuations, resulting in reduction of skin-friction and early separation of the flow. Strategies that promote the fast generation of realistic eddies in the equilibrium region, resulting in a short transition zone, will be discussed.   

Large Eddy Simulation of Ducted Propulsors in Crashbac

Flow around a ducted marine propulsor is computed using the large eddy simulation methodology under crashback conditions. Crashback is an operating condition where a propulsor rotates in the reverse direction while the vessel moves in the forward direction. It is characterized by massive flow separation and highly unsteady propeller loads, which affect both blade life and maneuverability. The simulations are performed on unstructured grids using the algorithm developed by Mahesh at al. (2004, J. Comput. Phys 197). The flow is computed at the advance ratio J=-0.7 and Reynolds number Re=480,000 based on the propeller diameter. Average and RMS values of the unsteady loads such as thrust, torque, and side force on the blades and duct are compared to experiment. It is seen that even though effects of the duct on thrust and torque are not large enough, those on the side force are significant. The rms of side forces is much higher in the presence of the duct. Pressure distributions on blade surfaces and duct surface are examined and used to explain this effect. This work was supported by the United States Office of Naval Research under ONR Grant N00014-05-1-0003.   

Visualization of Vortex Shedding in the Turbulent Flow Over A Surface Mounted Obstacle

The three dimensional turbulent flow over a surface mounted obstacle is studied as a numerical experiment that takes place in a wind tunnel. The transient Navier Stokes equations are solved directly with Galerkin finite elements. The Reynolds number defined with respect to the height of the wind tunnel is 12518. Instantaneous streamline patterns are shown, that give a complete picture of the flow phenomena which include the vortex shedding phenomenon and the flapping of the recirculation bubble downstream the obstacle. Both phenomena are considered as inherent unsteady features of separated flows and have not been visualized before apart from one attempt in a two-dimensional simulation of the same flow by the same author. A movie is going to be shown where the motion of the vortical structures is demonstrated. The energy spectrum yields the -5/3 law dependence with respect to the frequency. Mean values of velocities and root mean square fluctuations are compared with available experimental results. Other statistical characteristics of turbulence such as Eulerian autocorrelation coefficients, longitudinal and lateral coefficients are also computed. Finally, oscillation diagrams of computed velocity fluctuations yield the chaotic behavior of turbulence. The computer code developed for this work is a parallel program written in Fortran 90 that uses the MPI-paradigm and runs in distributed memory systems.   

A dynamic multi-scale approach for turbulent inflow generation in spatially-developing boundary layers with streamwise pressure gradients

A novel method for generating realistic turbulent velocity and thermal inlet boundary conditions is presented for simulations of evolving turbulent boundary layers. The approach is based on the rescaling-recycling method proposed by Lund et al. (1998). The standard rescaling process requires prior knowledge about how the appropriate velocity and length scales are related between the inlet and recycle stations (e.g. classic scaling laws). Here a dynamic approach is proposed in which such information is deduced dynamically by involving an additional plane, the ``test plane'', which is located between the inlet and recycle stations. This improvement, as well as the use of multiple velocity scales, permits the simulations of turbulent boundary layers subjected to arbitrary pressure gradients. DNS for zero (ZPG), adverse (APG) and favorable (FPG) pressure gradient flows are discussed. The agreement obtained by comparing present results with experimental and numerical data demonstrates the suitability of the present method as a turbulent inflow generator.   

Turbulence production and shear stress partitioning in rough-walled channel flow DNS

The effects of roughness in an incompressible turbulent boundary layer include the increased production of turbulence kinetic energy (TKE) and altered the nature of the skin drag. By formulating the exact Reynolds-averaged Navier-Stokes turbulence kinetic energy equations in a manner that includes an arbitrary roughness, the averaged terms representing the roughness production of TKE and the roughness drag can be written explicitly. Similar transport equations for TKE can be formulated wherein the roughness geometry is represented using the immersed boundary methodology. These terms are calculated from a collection of direct numerical simulations (DNS). The roughness geometry is limited to a simple array of vertically oriented cylinders with roughness heights range from $2 l^+$ to $50 l^+$. The primary results include an examination of the partitioning of the production of TKE into canonical shear production and into production by roughness, and the partitioning of drag into form drag and viscous shear drag. The relevance of the partitioning will be discussed in the context of turbulence modeling.   

A dynamic surface rougness model for large-eddy simulation of atmospheric boundary layer flow over fractal-like evolved fluvial landscapes

Evolved fluvial landscapes are characterized by a multi-scale composition of channels which display scale-invariance properties. A high-resolution evolved landscape is obtained through solution of a modified version of the Kardar-Parisi-Zhang equation. This landscape is spatially filtered to various resolutions for large-eddy simulations (LES) of the atmospheric boundary layer flowing over such surfaces. In the LES the subgrid-scale motions are parameterized using the Lagrangian scale-dependent dynamic model (Bou-Zeid et al. 2005). The boundary condition at the lower boundary is prescribed using a roughness length that is modeled as the product of local standard deviation of the unresolved height field and an unknown dimensionless coefficient. This coefficient is evaluated dynamically by comparing the plane-average force due to wall-stress at two resolutions. The results illustrate that the challenges posed by the multi-scale interactions of fluvial fractal-like lower surface boundary condition with the atmospheric turbulence may be addressed using a dynamic model for unresolved surface roughness.   

On the modification of particle dispersion in isotropic turbulence by free rotation of particle

Effect of a particle's spin is investigated numerically by considering the effect of lift occurring due to difference of rotations of a particle and of fluid such as the Saffman lift and Magnus force. These lift forces have been neglected in many previous works on particle-laden turbulence. The trajectory of particles can be changed by the lift forces, resulting in significant modification of the stochastic characteristics of heavy particles. Probability density functions and autocorrelations are examined of velocity, acceleration of solid particle and acceleration of fluid at the position of solid particle. Changes in velocity statistics are negligible but statistics related with acceleration are a little bit changed by particle's rotation. When a laden particle encounters with coherent structures during the motion, the particle's rotation might significantly affects the motion due to intermittently large fluid acceleration near coherent structures. The result can be used for development of stochastic model for particle dispersion. Detailed physical interpretation will be presented in the meeting.   

Behavior of small particles in isotropic turbulence in the presence of gravity

The motion of small heavy particles in homogeneous isotropic turbulence in the presence of gravity is investigated using Direct Numerical Simulations (DNS) at moderate Reynolds number. The Lagrangian velocity and acceleration statistics of particles and of flow for a wide range of Stokes number, defined as the ratio of the particle response time to the Kolmogorov time scale of turbulence, were obtained for the direction of the gravity and normal direction, respectively. It is found that particles lose their correlation faster than the case without gravity. Then, a significant increase in the average settling velocity was observed for a certain range of Stokes number. Our focus is placed on gravitational effect on very small particles. Our simulations show that as the Stokes number reduces to zero, their mean settling velocity approaches the terminal velocity in still fluid, which is rather odd considering that the trajectory of a small particle approaches the trajectory of a fluid particle which does not settle. Detailed physical mechanism will be presented in the meeting.   

Comparing experimental and Direct Numerical Simulation results from a turbulent channel flow

Remarkable progress has been made in the direct numerical simulation (DNS) of wall-bounded turbulence; particularly of turbulent channel flow, with numerical data now available above $Re_{\tau} \approx 2000$. Yet there are only very limited comparisons with experimental data in the literature. As such, this investigation compares a well-documented, high Reynolds number ($Re_{\tau} = 934$), large box size DNS from Del Alamo, Jimenez, Zandonade \& Moser (JFM, 2004) and laboratory channel flow data measured by the authors. Results show excellent agreement of streamwise velocity statistics. The spectra are also very similar, however, throughout the logarithmic region the secondary peak in energy is significantly reduced in the DNS results. Since the wavelengths associated with the energy difference are close to the DNS box length, it is recommended that longer box lengths should be investigated. Another spectral discrepancy results from an incorrect convection velocity when using Taylor's hypothesis for the temporal laboratory data. A convection velocity modification function is tentatively proposed giving good agreement between the data sets.   

Session EC: Turbulence Modeling II

Improving the near-wall behavior of multiscale models for LES

The multiscale models (in fact the ``multiscale approaches'' applied to the Smagorinsky model) have gained a growing interest in the LES community because of the appealing properties resulting from the involved high-pass filtering (HPF). One could hope that this filtering is sufficient for wall-resolved LES; hence no need for further near-wall damping (explicit or using a dynamic procedure). Unfortunately, the dissipation profile of such models does not tend to zero at the wall, even though the dissipation is indeed reduced compared to the corresponding unfiltered model. This leads to relatively poor results and, quite importantly, to severe and unpractical time-step restrictions because of stability issues. This unsatisfactory behavior is basically due to the fact the HPF velocity field has the same near-wall scaling as the unfiltered field. Hence, the SGS viscosity scalings previously developed to provide the proper $y^3$ near-wall dissipation behavior when computed using the unfiltered field, also provide the proper behavior when computed using the HPF field. In this study, several new and classical scalings, used in the multiscale approach, are investigated in turbulent channel flow LES at $Re_\tau = 395$ using a fourth order finite difference solver.   

A mixed LES model based on the residual-based variational multiscale formulation

In the residual-based variational multiscale (VMS) formulation of large eddy simulation (LES) a projection operator is used to separate the solution of the Navier-Stokes equations into coarse and fine scales. The coarse scale equations are solved numerically while the fine scale equations are solved analytically. In particular, an algebraic approximation for the fine scale velocities is derived wherein they are expressed in terms of the residual of the Navier Stokes operator applied to the coarse scale solution. In this talk we analyze the residual-based VMS model in wavenumber space and conclude that while it accurately models the cross-stress term, it under-estimates the contribution from the Reynolds-stress term. To remedy this we add to it a Smagorinsky eddy viscosity which provides a good approximation to the Reynolds-stress term. This leads us to a mixed model capable of accurately modeling all components of the subgrid stress. We implement the mixed model in a Fourier-spectral method and use it to predict the decay of homogeneous isotropic turbulence. We determine the two unknown parameters in this model dynamically using the variational counterpart of the Germano identity. We note that the mixed model yields better agreement with direct numerical simulation than either of its components: the dynamic Smagorinsky model and the dynamic version of the residual-based VMS model.   

Sequential approximation of velocity fields using episodic POD

The problem of approximating velocity fields at future and past times based on information available at the current time is addressed. A novel method called ``episodic POD'' is described that enables us to achieve our objective. Application of episodic POD to an ensemble of flow data results in a set of spatio-temporal eigenfunctions and a set of coefficients associated with the eigenfunctions. From these eigenfunctions, we develop two models called the ``forward model'' and ``inverse model'' that enable us to approximate the velocity fields at future and past times based on information provided at the current time. A second set of models, the forward and inverse sequential models are also developed that enable the dynamic update of approximated velocity fields when new information is made available, making these models more adept at on-line estimation. Different examples are used to validate and highlight the proposed method. It is also shown that episodic POD outperforms the linear Kalman filters in the presence of noise.   

Radial basis function approach to modeling dynamical systems.

We are interested in developing dynamical systems models that are based on discrete multivariate time series information only, with application to fluid flow phenomena. A method that uses radial basis functions and linear multi-step methods is developed to construct continuous nonlinear models that approximate the original dynamical system. Information, such as the structure of the original system, is incorporated into the models through weak constraints. The formulation of the model and its advantages associated with modeling are described. Different examples are presented that highlight the various characteristics of the model and its effectiveness in dealing with various problems encountered in fluid flow.   

A generalized Landau model for oscillatory to complex shear flows --- enablers for reduced, low and least-order Galerkin models

Landau's (1944) celebrated amplitude equation $dA/dt = \sigma A - \beta A^3$ for a supercritical Hopf bifurcation connects linear instability with a nonlinear amplitude saturation mechanism, thereby describing the transient and post-transient phase of oscillations. This model is significantly generalized for a much larger class of laminar to turbulent shear flows within the finite-time thermodynamics (FTT) formalism (Noack et al.\ 2008 JNET). In this talk, we highlight the critical role of FTT in deriving reduced to least-order Galerkin models for oscillatory to complex shear flows. This includes shift modes as well as a novel nonlinear subgrid turbulence representation. Intriguingly, both can lead to a similar, nonlinear damping term for fluctuation energy as described by Landau's model.   

A study of the sensitivity of the POD eigenvalues to the density of the resolved measurement grid.

A study of the sensitivity of the convergence of the POD eigenvalues to the discretization of the measurement / computational grid is presented using a number of different experimental data sets. The purpose is to determine the necessary conditions, base on an a prior understanding of the statistical properties of the turbulence field, for sufficiently obtaining a reduced order representation of the system. The analysis is important for two reasons. The first is that when the grid resolution is too coarse, the first few POD eigenvalues are overestimated followed by underestimates in the higher POD eigenvalues. Conversely, for grid resolutions that are too dense, superfluous information is carried. Where the latter is concerned, the performance of physics based control architectures that are designed around low-dimensional analysis tools can be seriously hindered.   

A priori study of SGS flux of a passive scalar in LES

The DNS data is used to explore the properties of subgrid-scale flux $\tau_\phi$ of a passive scalar $\phi$ in the framework of Large Eddy Simulation. Geometrical characteristics such as alignment trends between the flux and resolved and SGS structures are studied. It is shown that the direction of the flux is strongly coupled with the SGS stress axes rather than the resolved flow quantities such as strain $\bar{S}_{ij}$, vorticity $\bar{\omega}$ or scalar gradient $\nabla \bar{\phi}$. We derive an approximate transport equation for the subgrid-scale flux of a scalar and look at the relative importance of the terms in the transport equation. A particular form of LES tensor-viscosity model for the scalar flux is investigated, which includes the subgrid-scale stress: $\tau_{i\phi}=1/|\bar{S}| \tau_{ij} \bar{\phi}_{,j}$. Effect of different models for the subgrid-scale stress $\tau_{ij}$ on the model for the subgrid-scale flux $\tau_{\phi}$ is studied.   

Computational and Experimental Investigations of Turbulent Flow Past Projectiles

Experimental and computational investigations of turbulent flow past projectiles is modeled as axial flow past a cylinder with a free-spinning base. A subsonic wind tunnel with a forward-sting mounted spinning cylinder is used for experiments. In addition, a free-jet facility is used for benchmarking the experimental set up. Experiments are performed for a range of spin rates and free stream flow conditions. An anisotropic two-equation Reynolds-stress model that incorporates the effect of rotation-modified energy spectrum and swirl is used to perform computations for the flow past axially rotating cylinders. Both rigid cylinders as well as that of cylinders with free-spinning base are considered from a computational point of view. Applications involving the design of projectiles are discussed.   

Mixing in turbulent clouds

Turbulent clouds in the earth's atmosphere constantly entrain dry air from the surrounding environment, and this entrainment process influences the cloud microphysical properties, and therefore cloud optical properties relevant to climate. How cloud droplet size distributions respond to turbulent mixing is analogous to the problem of turbulent reactive flows, and therefore depends on relative time scales for mixing and for water phase changes (Damkoehler number). We have studied turbulent mixing in small cumulus clouds using a helicopter-borne instrument payload with high resolution measurements of the three-dimensional wind, temperature and humidity fields, and the droplet size distribution. Small Damkoehler numbers correlate uniform evaporation of droplets, while large Damkoehler numbers correlate with constant mean droplet size and a reduction in droplet number density due to complete evaporation of a subset of droplets. In some cases the latter, inhomogeneous mixing led to the formation of drops that are larger than in the unmixed adiabatic cloud core, which is of potential importance for precipitation formation in warm cumulus clouds.   

Session ED: Instabilities in Jets

The twisted global instability of lifted flames on round variable-density jets

The theory of resonant modes is revisited and extended to finite length systems containing pinch points $(k_0, \omega_0)$ with arbitrary $\omega^0_{kk} = \partial^2 \omega / \partial k^2$. When ${\mathrm{Im}\left(\omega^0_{kk}\right)} > 0$, the pinch point is twisted, and the system may be destabilized by resonant modes with growth rates greater than that of the unbounded absolute mode, \emph{i.e.} the system may be globally unstable while locally only convectively unstable. Lifted flames on round variable-density jets serve as motivation for this theory since the premixing zone between the nozzle and flame is an example of a streamwise-confined system containing a twisted pinch point. This flow is studied by means of direct numerical simulation (DNS) and linear stability analysis, the latter of which is used to calculate the locus of resonant modes in the complex $k$- and $\omega$-planes. In agreement with DNS observations, inspection of the solution curve in the $\omega$-plane suggests both a mechanism for stabilization with decreasing system length $l$ and a mechanism for low-frequency fluctuations owing to beating between modes of closely-spaced frequencies.   

The Forced Motion of a Flag

The prevailing view of the dynamics of flapping flags is that the onset of motion is caused by linear instability of the initial planar state. This view is reexamined by considering the forced motion of a flag immersed in a high-Reynolds number flow and subject to vortex shedding from its cylindrical pole. Vortex shedding is represented by a ``street'' of discrete line vortices released periodically from the pole and convected in the mean wind over the surfaces of the flag. It is found that forced motion is possible when the flag is still temporally stable, which suggests that the present mechanism should be taken into account in future high-Reynolds experimental investigations.   

Static shapes and instability of hanging flags conveying fluid

We investigate the interaction between a fluid jet and a long, thin sheet, \emph{i.e.} ``flag'', clamped to the jet-nozzle. The jet wets and flows along one side of the flag from base (clamped end) to tip, which hangs freely. Experiments reveal a lateral force at the ``free'' end of the hanging flag; this force arises from the minimization of surface-energy as the jet detaches from the flag surface. At low Weber numbers (\emph{i.e.} low flow rates), the tip force produces stable, static flag shapes with wavelengths inversely proportional to the flow rate. The static shapes are well described by a simple model coupling linear beam bending and inviscid flow. At higher Weber numbers, static shapes become unstable, leading to periodic oscillations analogous to previous work on hanging cantilever tubes conveying fluid (Paidoussis, 1970; Doar\'e and Langre, 2002). The observed critical flow rates for instability agree well with those predicted by linear stability analysis.   

Global linear stability analysis of the jet in crossflow

The global linear stability analysis of the jet in crossflow to three-dimensional perturbations is numerically investigated. At velocity ratio $R=3$, defined as the ratio of jet velocity to free-stream velocity, the flow is globally linearly unstable. The baseflow for the stability analysis is a steady solution of Navier-Stokes, obtained by damping the unstable temporal frequencies using the selective frequency damping method (SFD). The steady state consists of a dominant counter-rotating vortex pair in the far field emerging from the near field vorticity of the shear layer. The eigenvalue problem is solved using the ARPACK library and the linearized DNS as a time stepper. The most unstable mode takes the shape of a localized wavepacket, wrapped around the counter-rotating vortex pair. Further, higher velocity ratios are considered in order the examine the transition from convective to absolute stability of the studied flow case.   

Open Loop Control of Self-Excited Transverse Jets

Recent experiments have explored the response of a gaseous, isodensity jet in crossflow to controlled acoustic forcing. Focusing on jet-to-crossflow velocity ratios R below 3.5, for which prior experiments \footnote{Megerian, et al., {\bf JFM}, 593, pp. 93-129, 2007} suggest that the upstream shear layer is globally unstable, alternative jet forcing amplitudes and temporal waveforms are explored. Very strong sinusoidal jet forcing at a frequency different from that of the global instability is observed to replace the self-excited mode, consistent with similar open loop forcing results for the globally unstable, low density jet in quiescent surroundings \footnote{Hallberg \& Strykowski, {\bf Phys. Fluids}, 20, 041703, 2008}. Yet in many cases for the forced, globally unstable transverse jet, sinusoidal excitation is not observed to have as great an effect on jet penetration and spread as does square wave forcing with the same $\rm U'_{j,rms}$; such forcing can introduce a characteristic time scale associated with optimal vorticity generation. When the upstream jet shear layer is convectively unstable, on the other hand, for values of R above 3.5, strong and moderate sinusoidal excitation can produce the same level of jet spread and penetration as does square wave forcing.   

Measurements of instability waves in a high speed liquid jet

Measurements of instability surface waves present in the near exit region of a high-speed liquid jet are presented. The backlit images, exposed at 1 $\mu $-sec, provide a statistically significant number of measurements so that wavelength and wave velocity can be determined. It is found that the waves stretch as they travel in the downstream direction and that the axial wavelength changes significantly depending on its streamwise location. These results emphasize the importance of stating the axial position of any analytical wavelength resulting from spatial stability analyses. Images also show a strong three dimensional flow, in the form of wave packets, in regions closest to the jet's exit. It is observed that these wave packets merge downstream. Stability analyses suggest the waves are generated by a pocket of absolute instability located at the exit of the jet, and the most dominant mode is determined by the location where the flow transitions to a region of convective instability.   

Numerical simulation of Kelvin-Helmholtz instability and liquid breakup

A diffuse interface model is used to model a two-phase flow. It is incorporated into an incompressible Navier-Stokes solver based on a multi-directional finite difference method with third-order upwinding. In order to test the reliability of the code, 2D simulations are performed of a jet into a still fluid. The evolution of the jet is captured with the instability manifesting itself as waves along the surface of the fluids. A simple comparison between the wavelength obtained here and that given by the Kelvin-Helmholtz instability theory shows excellent agreement with the discrepancy been less than 5{\%}. These instabilities grow, and finally break-up into separate chunks, filaments and droplets. This behavior is in qualitative agreement with those reported in the literature. The present results show the accuracy of the present method with consideration of compressibility effects left for future investigation.   

Session EE: Free-Surface Flows: Computational Studies

Precursors to Droplet Splashing on a Solid Surface

We consider a liquid droplet moving towards a solid surface with sufficiently high velocity. We demonstrate that in the absence of intermolecular attraction between the liquid and the solid, the liquid does not contact the solid, and instead spreads on a very thin air film. The junction between the air film and the spherical droplet develops a high curvature and emits capillary waves. We hypothesize that the amplification of these capillary waves is the primary cause of splashing.   

Numerical simulation of a liquid-metal circular hydraulic jump using a level-set method

New reactor concepts (e.g., Accelerator-Driven Systems) that utilize the impact of a high-energy particle beam onto a liquid-metal surface have driven the need for improved predictive techniques for high-speed flows of high-surface-tension liquid metals. We study here the flow in a liquid-metal circular hydraulic jump (CHJ), to compare the predicted results with those from a companion experimental investigation. The flow differs from the traditional CHJ in that outflow over the weir is confined to a few discrete locations in the experimental protocol. The level-set method was employed for numerical simulations. Theoretically, the height of the CHJ and a height correction at the weir were obtained through balancing surface-tension and gravitational forces using the Young-Laplace equation for a static situation. Results are in good agreement with experiment, including the numerical prediction of ``fingering'' in the flow upstream of the jump under certain wettability and flow conditions.   

Shapes of Floating Liquid Sheets Spreading Against an Imposed Bath Flow

We have investigated the spreading from a central static source of a viscous floating liquid sheet, above a more heavy bath, the bath itself drifting at a constant imposed velocity. This kind of situation is of great interest for environment problems and for industrial processes. The sheet exhibits surprising change of shape depending on its own flow rate and on the velocity of the bath. Circular for a static bath, it becomes oval at low velocity and exhibits a ribbon like shape at high velocity. In this high velocity limit, the sheet shape is initially oval and exhibits a transition to the ``ribbon'' shape, across a transient pear like shape. At low flow rate and high velocity, the ribbon becomes unstable and pinch off occurs. We have also investigated theoretically the evolution of the thickness distribution of the sheet. Because of complicated competitions between the sheet and bath viscosities, surprising behaviors can take place. For instance, in the case of a static bath and depending on the sheet flow rate, the final thickness can be larger than the static equilibrium height predicted by Langmuir.   

Computation of Viscous Free-Surface Hydrodynamics for Ships during Free-Roll, Wave-Excited Roll and Prescribed Motions

Prediction of ship motions in waves and the role of viscous effects remains an important problem in naval hydrodynamics. A computational fluid dynamics (CFD) solver has been developed which can simulate the unsteady turbulent boundary layer, wave field, and 6DOF dynamics of a floating body in waves. The solver is based upon the Reynolds-averaged Navier-Stokes equations, and volume-of-fluid (VOF) and dynamic-meshing algorithms. It is used to study free-roll, wave-excited roll, and forced heave and sway motions. Solution validation is achieved by comparing roll-amplitude decay, natural frequency, and response amplitude operator (RAO) for a 2D box barge in regular waves to experimental data. As a practical example, a ship hullform, with and without bilge keels, is studied when undergoing prescribed roll, sway, and heave motions. Details of the fluid dynamics and forces and moments will be correlated to motion amplitudes and frequencies.   

Swirling flow in presence of a moving free surface

The incompressible swirling flow of a viscous fluid enclosed in a cylindrical container with a freely-moving top surface and driven by the steady rotation of the bottom wall is studied both experimentally and numerically. This work is aimed at increasing our understanding of the influence of the presence of a moving free surface on this swirling flow dynamics. New flow states corresponding to a Reynolds number of $6'000$ are investigated based on the fully three-dimensional solution of the Navier--Stokes equations for this free-surface cylindrical swirling flow, without resorting to any symmetry properties unlike all other results available in the literature. The numerical results are thoroughly compared to PIV measurements for the exact same configuration. To our knowledge, this study delivers the most general available results for this moving free-surface problem due to its original treatment.   

A Numerical Study of Interfacial Turbulent Transport of Passive Scalars

We perform direct numerical simulation (DNS) to study interfacial transport of passive scalars in free-surface turbulence. Based on DNS data, we obtain correlation between surface flux and surface age, which is defined based on the intervals of replacements of fluid elements close to the surface with fluid elements from the bulk of the flow. Contribution of different turbulence structures to interfacial transport has been quantified. It is found that surface age distribution can be used to quantify interfacial scalar transport accurately. The random surface renewal theory of Danckwerts (1951) has been modified to obtain an appropriate distribution of surface age. This modified distribution agrees well with the numerical result obtained with a highly accurate Lagrangian-Eulerian method that we develop for surface element residence time quantification. The new distribution with its clear physical explanation can be used to model interfacial transport of passive scalars including gas and heat.   

The unsteady dynamics of the interface separating two fluids under the influence of electric fields

Direct Numerical Simulations (DNS) are carried out to study the dynamics of a horizontal interface separating two fluids, having different electrical properties, under the influence of AC and uniform DC electric fields. A front tracking/finite difference scheme is used, in conjunction with Taylor's leaky dielectric model, to solve the governing electrohydrodynamics equations in both fluids at finite Reynolds numbers. The methodology and the code are validated by comparing the results with those of the analytical studies developed at the linear stability limit and it is shown that a very good agreement exists between the two. The results of this study show interesting interface behavior depending on the parameters of the problem. In all the cases considered, the interface becomes unstable beyond a critical voltage and starts to oscillate as it moves toward its (quasi) steady-state shape which is a vertical column pointing from the liquid of higher electric conductivity to the one with a lower conductivity. The shape of the column, however, will vary depending on the individual governing parameters.   

Flow Visualization and Pattern Formation in Vertically Falling Liquid Films

Analytical results of a low-dimensional two equation h-q model and results of a direct numerical simulation of the transient two-dimensional Navier Stokes equations are presented for vertically falling liquid films along a solid wall. The numerical study aims at the elucidation of the hydrodynamics of the falling film. The analytical study aims at the calculation of the parameter space where pattern formation occurs for this flow. It has been found that when the wave amplitude exceeds a certain magnitude, flow reversal occurs in the film underneath the minimum of the waves [1]. The instantaneous vortical structures possess two hyperbolic points on the vertical wall and an elliptic point in the film. As the wave amplitude increases further, the elliptic point reaches the free surface of the film and two more hyperbolic points are formed in the free surface that replace the elliptic point. Between the two hyperbolic points on the free surface, the streamwise component of velocity is negative and the film is divided into asymmetric patterns of up and down flows. Depending on the value of the Kapitza number, these patterns are either stationary or oscillatory. Physical reasons for the influence of the Kapitza number on pattern formation are given. Movies are shown where the pattern formation is demonstrated. [1] N.A.Malamataris and V.Balakotaiah (2008), AIChE J., 54(7), p. 1725-1740   

Session EF: Film Instabilities

Nonlinear stability analysis of a thin-melt film on its crystalline phase

The instability of an ultra-thin, metallic melt film, situated between its non-premelting crystalline phase and a gas phase, is studied using bifurcation analysis near the instability threshold. The threshold is finite wave number due to competition between a stabilizing thermal gradient and gas-melt capillary forces and the destabilizing attractive van der Waals forces. At fixed mode-number the amplitudes of the two interfaces obey coupled nonlinear evolution equations that admit standing and traveling waves all of which bifurcate subcritically. The additional effects of repulsive intermolecular interactions and crystal-melt surface tension on the nature of the bifurcation are presented.   

Mechanism Leading to Formation of Periodic Nanopillar Arrays in Confined Ultrathin Polymer Films

Previous groups have reported the spontaneous formation of periodic nanopillar arrays in ultrathin polymer films (order 100 nm in thickness) confined inbetween two flat smooth substrates and subject to an ultrahigh transverse thermal gradient (order $10^6-10^7$ $^{\circ}$K/cm). Crucial to these experiments is the presence of an overlying nanofilm of a second fluid to preserve a deformable interface at the polymer-fluid boundary. The formation of structures resembling stripes, columns or spirals has been attributed to a normal interfacial radiation pressure arising from phonon-like reflections at the interface separating media with different acoustic impedance. A linear stability analysis of a thin bilayer film within the lubrication approximation shows that tangential thermocapillary stresses at the free interface can well explain the phenomena observed. Predictions of the most unstable wavelength as a function of the plate spacing, thermal gradient, and material parameters provide a good fit to the experimental data. This instability can be classified as a long wavelength B\'{e}nard instability studied a decade ago by VanHook \textit{et al}. The parameter range in current experiments, however, as characterized by the ratio of thermocapillary to capillary to gravitational forces, falls beyond the range studied previously.   

AC electrohydrodynamic instabilities in thin liquid films

When DC electric fields are applied to a thin liquid film, the interface may become unstable and form a series of pillars. We examine the possibility of using AC electric fields to exert further control over the size and shape of the pillars. For perfect dielectric films, linear stability analysis shows that the influence of an AC field can be understood by considering an effective DC field. For leaky dielectric films, Floquet theory is applied to carry out the linear stability analysis, and it reveals that high frequencies may be used to inhibit the accumulation of interfacial free charge, leading to a lowering of growth rates and wavenumbers. Nonlinear simulations confirm the results of the linear stability analysis while also uncovering additional mechanisms for tuning overall pillar height and width through adjustment of the magnitude and frequency of the AC field. The results presented here may of interest for the controlled creation of surface topographical features in applications such as patterned coatings and microelectronics.   

Instability of Free Films with Plateau Borders

A surfactant-free foam of low liquid fraction coarsens by the rupture of the free films separating adjacent gas bubbles. One can find asymptotic solutions for the film and Plateau borders (Brush, L.~N.~\& Davis, S.~H., \emph{J.~Fluid Mech.}, \textbf{534}, 2005, 227-236). Using this time-dependent, flowing, non-planar solution as a basic state, we examine the linearized instability numerically. The numerical method utilizes grid generation to facilitate a finite difference calculation of the linear stability problem.   

Dynamics and line tension in thin nematic films

Line tension is important in phase transitions for monolayer systems and in biophysics. Nevertheless, experimental studies about hydrodynamics with line tension are still lacking compared to surface tension ones. We consider here a thin nematic film deposited at the air/water interface with hybrid anchoring conditions. This situation is very special because instability patterns exist and the nematic film coexists with a trilayer structure which leads to a line tension between the nematic and the trilayer. We made some dynamic measurements of line tension by analyzing the relaxation of two domains after coalescence. We propose here a comparison between dynamic and static measurements. We then study the early stage of coalescence between two nematic domains with high speed camera. We will explain why this ``true'' 2D case of coalescence is different from the usual 2D case with surface tension.   

Impact of a vibration on the behavior of a dewetting thin film

It is well known that volatile van der Waals thin films often dewet from a substrate and rupture. Thus is it important to identify and study physical mechanisms that can suppress dewetting instability. We have found that vibration of the substrate, which has been studied previously in the context of thick films, can provide desired stabilization. The large differences in characteristic length and time scales make possible the application of the time-averaging methods from the dynamical systems theory for the analysis of film dynamics. Using these methods, we obtained the nonlinear amplitude equation for the film thickness. We show that horizontal vibration produces a finite impact on the dynamics of the film when the amplitude the vibration is of the order of the film thickness. When vibration is vertical, its amplitude must be larger than the film thickness. Stabilization of the film is possible only in the latter case.   

Regular non-coarsening surface patterns on evaporating heated films

We study a thin liquid film with a free surface on a uniformly heated substrate. The film is heated from the gas side. We show that if the fluid is initially in equilibrium with its own vapor in the gas phase, regular long-scale surface patterns in the form of long-wave hexagons or stripes having a well defined lateral length scale can be observed [1]. This is in sharp contrast to the case without evaporation where coarsening or rupture to larger and larger patterns is seen in the long time limit. In this way, evaporation could be used for regular structuring of the film surface. Finally we show how other stability mechanisms can be included, e.g. the Marangoni effect or Van der Waals forces in ultra thin films. In this way, a much richer pattern dynamics is expected, showing also squares, stripes and hexagons. and transitions among them. \\[3ex] [1] M. Bestehorn, D. Merkt, Phys. Rev. Lett. {\bf 97}, 127802 (2006)   

Distinguishing viscosity and surface friction in quasi-2D flows

In many experimental and natural quasi-two-dimensional (Q-2D) flows the effects of internal viscosity and surface friction are significant but difficult to distinguish. We demonstrate precise, independent measurements of both kinematic viscosity and coefficient of external drag in a Q-2D experiment using soap films in a circular Couette cell configuration, using a combination of vortex decay rates and steady-state shear lengths. Dynamics at scales shorter (longer) than the shear length are dominated by internal viscosity (surface friction). The technique can be generalized to other flow configurations and promises to aid in the quantitative analysis of many Q-2D experiments. Currently the measurements are being used to make quantitative tests of the theoretical stability threshold in 2D vortex arrays.   

Planar extensional motion of an inertially-driven liquid sheet

We examine the planar extensional motion of a liquid sheet driven by inertia and derive a time-dependent exact solution of the free surface problem for the Navier-Stokes equations. The linear stability of the exact solution to 1- and 2-D symmetric perturbations is examined in the inviscid and viscous limits within the framework of the slender body equations. Both transient growth and long-time asymptotic stability are considered. For 1-D perturbations in the axial direction, viscous and inviscid sheets are asymptotically marginally stable, though depending on the Reynolds and Weber numbers transient growth can have an important effect. For 1-D perturbations in the transverse direction, inviscid sheets are asymptotically unstable to perturbations of all wavelengths. For 2-D perturbations, inviscid sheets are unstable to perturbations of all wavelengths with the transient dynamics controlled by axial perturbations and the long-time dynamics controlled by transverse perturbations. The asymptotic stability of viscous sheets to 1-D transverse perturbations and to 2-D perturbations depends on the capillary number Ca; in both cases, the sheet is unstable to longwave transverse perturbations for any finite Ca.   

Lateral shaping and stability of a stretching viscous sheet

We investigate the changes of shape of a stretching viscous sheet by controlling the forcing at the lateral edges, which we refer to as lateral shaping. We propose a one-dimensional model to study the dynamics of the viscous sheet and systematically address stability with respect to draw resonance. Two class of lateral forcing are considered: (i) For the case that the tension at the edges is specified, we show that a pure outward normal tension $S_{\rm n}$ is usually unfavorable to the draw resonance instability as compared to the case of stress-free lateral boundaries. Alternatively, a pure streamwise tangential tension $S_{\rm t}$ is stabilizing. (ii) For the case that the lateral velocity at the edges is specified, we show that the stability properties are problem specific but can be rationalized based on the induced tension components ($S_{\rm n}$, $S_{\rm t}$).   

Session EG: Drops III

Model-dependence of Marangoni forces for volatile sessile drops

The problem of volatile sessile drops, although apparently simple, involves a complex interplay of several physical mechanisms -- the conduction of heat through the solid and the liquid, the phase transition with associated cooling of the evaporating interface, and the diffusion of the vapor through the surrounding gas phase. In this work we discuss the predictions of two commonly used evaporation models regarding Marangoni forces along the interface of evaporating drops. The material parameters required for careful modeling are extracted from our own experimental data. We find striking differences between the two models -- in particular, the qualitatively different temperature profiles at the evaporating interface. These predicted temperature profiles remain to be measured experimentally.   

Evaporation of femtoliter sessile droplets

The evaporation of sessile microdroplets with diameter in the millimeter range has been studied for a long time both theoretically and experimentally. However, experimental data are lacking on evaporation in the micron range despite its importance in the development of micro and nanofluidics. We show here that this problem can be addressed by a combination of two newly developed techniques. We recently demonstrated that droplets in the femto to attoliter range can be deposited in a surface using an atomic force microscope-based method so-called NADIS[1]. Using nanopositioning technique such ``femtodroplets'' could be deposited on a quad-beam resonator (QBR), ultrasensitive mass sensor with a mass resolution more that 1000 times better than quartz microbalance. During evaporation, we monitored temporal evolution of the droplets mass down to 10 fg (10 attoliters volume) resolution. The results obtained on glycerol droplets with initial volumes ranging from 0.2 fL to 20 fL are interpreted in the framework of existing models [2]. \\[0pt] [1] A.Fang, E. Dujardin, T.Ondarcuhu, NanoLett. 6 (2006) 2368. \\[0pt] [2] J. Arcamone et al, J.Phys.Chem.B 111 (2007) 13020.   

Leidenfrost Drop on a Step

When deposited on a hot plate, a water droplet evaporates quickly. However, a vapor film appears under the drop above a critical temperature, called Leidenfrost temperature, which insulates the drop from its substrate. Linke \& al (2006) reported a spontaneous movement of such a drop, when deposited on a ratchet. We study here the case of a flat substrate decorated with a single micrometric step. The drop is deposited on the lower part of the plate and pushed towards the step at small constant velocity. If the kinetic energy of the drop is sufficient, it can climb up the step. In that case, depending on the substrate temperature, the drop can either be decelerated or accelerated by the step. We try to understand the dynamics of these drops, especially the regime where they accelerate. Taking advantage of this phenomenon, we could then build a multiple-step setup, making it possible for a Leidenfrost drop to climb stairs.   

Vibration-induced Wenzel to Cassie Transition on a Superhydrophobic Surface

A drop on a roughened superhydrophobic surface will exhibit either the Cassie state, where the drop sits on the air-filled textures, or the Wenzel state, where the drop wets the cavities of the textures. The superhydrophobic Cassie state is the preferred state with a small contact angle hysteresis and high drop mobility. Although superhydrophobic surfaces can be designed to make the Cassie state energetically more favorable, drops often end up trapped in a metastable Wenzel state and an energy barrier has to be crossed for reversal to the desired Cassie state. We show that mechanical vibration can be used to cross this energy barrier without resorting to liquid-vapor phase change. A complete Wenzel to Cassie dewetting transition is accomplished by vibrating a metastable Wenzel drop on a superhydrophobic lotus leaf. A water drop in a metastable Wenzel state is obtained by exploiting the differential evaporation rate of water and ethanol. The dewetting transition requires minimum external forcing when the vibration is in resonance with the drop. The vibration-induced Wenzel to Cassie transition is a plausible mechanism used by water-repellant plants to maintain superhydrophobicity, and is applicable to a variety of engineering systems requiring sustained superhydrophobicity.   

Rapid Drop Dynamics During Superhydrophobic Condensation

Rapid drop motion is observed on superhydrophobic surfaces during condensation; condensate drops with diameter of order 10~$\mu $m can move at above 100G and 0.1 m/s. When water vapor condenses on a horizontal superhydrophobic surface, condensate drops move in a seemingly random direction. The observed motion is attributed to the energy released through coalescence of neighboring condensate drops. A scaling analysis captured the initial acceleration and terminal velocity. Our work is a step forward in understanding the dynamics of superhydrophobic condensation occurring in both natural water-repellant plants and engineered dropwise condensers.   

The Vibration of an Inviscid Incompressible Sessile Drop

The fundamental frequencies and modes of vibration of a free spherical drop of inviscid incompressible fluid were computed 129 years ago by Lord Rayleigh. The analysis was possible because of simplifications resulting from the use of spherical coordinates. These same simplifications don't occur for a sessile drop, i.e., when the drop is supported on a horizontal planar surface, except for the case of a hemispherical drop. The present work describes an integrated analytical and numerical technique for the computation of the fundamental frequencies and modes of vibration of a supported sessile drop. Spherical coordinates are used to describe the interface shape, but the flow field inside the drop is computed numerically using the finite element method. Combining these techniques produces a linear eigenvalue problem that is solved numerically. Results will be presented for sessile drops with different contact angles without gravity and compared to experimental data. This technique can also be extended to sessile drops with gravity, in which the drop shape is flattened, and to substrate geometries that are not planar, such as a drop in a shallow cavity or hole.   

Flow in an evaporating sessile drop

Exact analytical solutions are derived for the Stokes flows within evaporating sessile drops of cylindrical and spherical cap shapes. The results are valid for arbitrary contact angle. The field equations, $E^4\psi =0$ and $\nabla ^4\psi =0$, are solved for the spherical and cylindrical cases, respectively. For the spherical cap, when the contact angle lies in the range $0\le \theta _c <\pi /2$, the boundary condition defined by the solution to the vapor phase transport must be modified since it becomes non-physical (singular) at the contact line. Solutions are obtained for any physically meaningful distribution of mass flux along the free surface as long the flux approaches a constant value at the contact line. The vapor phase transport has been written to include the mean flow velocity induced by the mass transfer. This leads to advective transport in the vapor phase in contrast to the simple diffusive transport which has been previously treated. The computed solutions demonstrate that the streamlines for viscous flow lie farther from the substrate than the corresponding streamlines for inviscid flow.   

Stability of toroidal drops

Using co-flowing liquids we are able to generate drops with the shape of a torus. We will present experimental results on the stability of these unusual drops and on how they evolve into spheres. We find two distinct scenarios depending on the torus aspect ratio, which we quantify using optical imaging.   

Stability of the Taylor--Culick receding rim: surprising observations

When punctured, a uniform liquid sheet is known, since Taylor and Culick, to recess at a constant speed balancing surface tension and inertia. For planar soap films, this steady solution holds until the initially smooth receding rim is violently destabilized, exhibiting deep indentations from which droplets are ejected. A surprising new three dimensional mechanism explaining this destabilization and resulting wavelength has been evidenced~: because of the shear between the still outer medium and the receding liquid, the film flaps through a Kelvin--Helmholtz instability, itself inducing an acceleration perpendicular to the film, which intensifies with the flapping amplitude. To this acceleration is associated a classical Rayleigh--Taylor mechanism, promoting the rim indentations. The same mechanism holds for a punctured round bubble, for which the relevant acceleration is the Culick velocity squared divided by the bubble radius. The bearing of this phenomenon on aerosols formation in Nature will be underlined.   

Stability of a stationary moving droplet in porous medium

We consider sedimentation of a drop in a porous medium saturated by another fluid. Brinkman model is applied, whereas the interface of drop is assumed sharp and the capillary forces are neglected. The velocity of stationary sedimentation for the spherical drop is obtained. The resulting expression matches both the Hadamard-Rybczynski formula and the result for the conventional Darcy model in corresponding asymptotic limits. Stability of the stationary motion is studied. It is shown, that the drop is always unstable to perturbations that lead to formation of a cusp in the vicinity of the rear stagnation point. This behavior is similar to that for a drop in the absence of the porous matrix. Thus, the Brinkman model eliminates the unphysical features inherent to the Darcy model.   

Session EH: Bubbles III

Numerical study on the drag coefficient for an ellipsoidal bubble with fore-aft asymmetry

We evaluate the drag coefficient for ellipsoidal clean bubbles rising steadily at high \textit{Re}. Flow fields and bubble shapes are obtained using a numerical simulation. The method is based on a finite-difference solution of the equation s of motion on an orthogonal curvilinear coordinate system [Takagi et al., \textit{Phys. Fluids} (1994), Ryskin {\&} Leal, \textit{J. Fluid Mech.} (1984)]. The degree of fore-aft asymmetric bubble shape is quantitatively evaluated using Legendre polynomials. The numerically obtained drag coefficients are compared with those of experimental results. In addition, by comparing the drag coefficients with those for symmetric ellipsoidal bubble obtained analytically by Moore [\textit{J. Fluid Mech.} (1965)], and via numerical simulation by Blanco {\&} Magnaudet [\textit{Phys. Fluids} (1995)], the effect of fore-aft asymmetry on a drag coefficient is evaluated. Furthermore the formation of the standing eddy at the rear of deformable bubbles is discussed.   

Turbulence characteristics of liquid motion induced by single rising bubble

Characteristics of the surrounding liquid motion of a single rising bubble were experimentally investigated. A single bubble with three kinds of diameters was released under complete control of initial diameter, orientation and launch timing using a bubble generator. Especially, we focused on the bubbles with zigzagging motion. Both the surrounding liquid motion and bubble motion were simultaneously visualized via PIV measuremen. Vorticity distribution and standard deviation of liquid-phase velocity were calculated. Moreover, we analyzed the turbulence intensity of liquid-phase motion induced by the bubble within measurement time. We clarify both the distribution of disturbance and the intensity of disturbance. As a result,each bubble formed various vorticity distributions in its vicinity during the bubble rising. On the other hand, the turbulence intensity of the liquid-phase velocity was obviously different. Associated with increase in the bubble radius, the area of disturbance region induced by bubble was spread. The horizontal component of the turbulence intensity was increased by the bubble with significant interface motion.   

Evolution and axial symmetry breaking of the toroidal vortex behind a clean bubble

We experimentally observed the wake structure behind a rising clean bubble by using silicon oil solution of photochromic dye. Clean bubble condition was realized since both the dye and the silicon oil are non-polar. A single bubble was generated just below a colored region where the dye was activated by UV sheet light illumination. Once the bubble passed the colored part of the liquid, the bubble was accompanied by some portion of activated dye. Hence the flow structure in the rear of the single rising bubble was visualized. In this visualization method, we are able to distinguish the liquid portion trapped behind the bubble from the non-colored surrounding liquid that flows in the colored trapped portion. We precisely controlled the size of the bubble in order to observe how the size of the toroidal vortex behind a bubble evolves and the axial symmetry breaks. The relation between the in-flow of the surrounding liquid into the toroidal vortex and the bubble motion was studied in detail.   

Magnetic Bubbles

Bubbles in liquids driven by a sound field are used in many disciplines: for example bubbles clean surfaces in ultrasonic water bathes, they catalyze unique chemical reactions in sonochemistry, and under special conditions even create light. However, conventional bubbles have a major limitation when placed in an acoustic field: it is extremely hard to control their position. Here we present a new type of bubble that has permanent magnetization originating from a shell of self-assembled nanoparticles, so that magnetic fields can be used to control the bubble's position independently. We will report on the recipe and the experiment to study bubble oscillations in weak magnetic fields. The magnetic susceptibility of the bubbles is proportional to their surface area,$\chi =(9\pm 3\times 10^{-6}m)r^2$, where $r$ is the radius. Also they are compressible in moderate acoustic fields and induce a microstreaming flow with a toroidal vortex at the upper pole of the bubble. Similar microstreaming flows have been used to transport and rupture cells at small scales. Thus we envision applications in manipulation of biological materials and in microfluidic devices using acoustic and magnetic forces.   

Interaction of gas bubbles with a shock wave near a solid boundary

The interaction of both single and multiple gas bubbles in water with an initially planar shock in the neighbourhood of a solid boundary is considered. The compressible Euler equations in each phase are solved in axisymmetric and 3-D Cartesian geometry using up to a third-order accurate ENO-Roe scheme for the spatial fluxes in characteristics space; the solutions are evolved temporally using a third-order accurate TVD RK method. The interface between the water and gas phases is tracked with a level set function and interfacial boundary conditions are imposed using the Ghost Fluid method. The solid boundary is captured by employing reflection computational boundary conditions. In the case of a single bubble, the effect of the shock strength and of the initial location of the bubble relative to the boundary on the resultant bubble shapes, liquid jet shapes and velocities is assessed. The importance of the shock wave reflection from the boundary on the resultant dynamics is studied, together with incurred modifications due to bubble multiplicity. This work has applications in shock wave lithotripsy, cavitation-induced damage and surface cleaning.   

On the stabilization of surface nanobubbles

Recent experiments have convincingly demonstrated the existence of surface nanobubbles on submerged hydrophobic surfaces. However, classical theory dictates that small gaseous bubbles quickly dissolve because their large Laplace pressure causes a diffusive outflux of gas. Here we first present atomic force microscopy (AFM) data on the geometric shape of these surface nanobubbles over more than one decade in magnitude, revealing that the contact angle $\theta$ (defined on the gas side) goes to zero for small surface nanobubbles, which leads to a reduction of the Laplace pressure. Based on these data, we then suggest that the surface bubbles are further stabilized by a continuous influx of gas near the contact line, due to the gas attraction towards hydrophobic walls. This influx balances the outflux and allows for a meta-stable equilibrium, which however vanishes in thermodynamic equilibrium.   

Bubble pinch-off in a stagnant liquid pool at high Reynolds numbers

We present a theoretical, numerical and experimental study of the \emph{symmetric} pinch-off which takes place when a bubble is grown from a nozzle placed at the bottom of a stagnant pool of liquid. Our experiments show that the initial stages of bubble pinch-off are driven not only by surface tension, but also the by the liquid hydrostatic pressure. Moreover, we obtain a simple scaling law for the global collapse time which is shown to be consistent with the experimental results. Boundary integral numerical simulations are also shown to be in excellent agreement with the experiments. In addition, we discuss the dynamics of the final stages previous to pinch-off, providing with a simple model, based on the \emph{local slenderness} around the neck, which is shown to closely reproduce the time evolution of both the minimum radius and the local axial curvature once surface tension and viscous effects are self-consistently incorporated. This is confirmed by experiments performed with water as well as with different silicone oils. Finally, the dynamics of azimuthal perturbations around the zeroth-order collapse solution is addressed.   

Evolution of Bubbles through Gas Injection from a Micro-Tube into Liquid Cross-Flow

Generation of small-size bubbles is of importance in many processes such as chemical, medical and food industries. The most common method of bubble generation is injection of gas from an orifice into the liquid phase. In spite of simplicity of this method, appropriate conditions should exist to avoid bubble growth and obtain required small-size bubbles. Thorough understanding of the bubble formation and growth can reveal the required conditions and ensure detachment of the bubbles from the orifice with desired timing to control their size. In this work, evolution of bubbles from a micro-size gas injection tube into liquid cross-flow is investigated. Special attention has been devoted to optimize the conditions to generate micro-size bubbles. Specifically, the influence of gas injection tube size and location, gas and liquid Reynolds numbers and the geometry of the mixing chamber on the bubbles evolution is studied. High-speed shadowgraphy technique is applied to investigate bubbles size and shape. A Particle Tracking Velocimetry algorithm is also applied to calculate bubbles velocity. The velocity field of the liquid flow surrounding the bubbles is also characterized using a Mirco-Stereo-Particle Image Velocimetry technique.   

The effect of bubbles on flow structure and heat transfer in laminar boundary layers

We develop a mathematical model of the effect of a vapor or gas bubble trapped between liquid and a flat plate on the laminar boundary-layer-type flow in the liquid. For very thin bubbles the effect amounts to simple modification of the no-slip condition, but as the bubble height increases, there are significant changes in the structure of the boundary layer formed behind the bubble. We investigate how these changes affect the heat transfer in the boundary layer. The model is used to explain some recent surprising experimental findings showing an increase of the wall heat transfer coefficient during boiling under the microgravity conditions compared to its value under normal gravity.   

Direct numerical simulation of single gas bubbles in pure and contaminated liquids

Disperse gas bubbles play an important role in many industrial applications. Knowing the rising velocity, the interfacial area, or the critical size for break-up or coalescence in different systems can be crucial for the process design. Hence, knowing the fundamental behaviour of a single bubble appears mandatory for the examination of bubble swarms and for the Euler-Lagrange or Euler--Euler modelling of disperse systems. In the present work a level--set--based volume--tracking method is implemented into the CFD--code OpenFOAM to follow the free interface of a single bubble. The volume-tracking method is coupled with a transport model for surfactants on the interface, including adsorption and desorption processes. The dependency of surface tension on the local surfactant concentration on the interface is modelled by a non-linear (Langmuir) equation of state. Marangoni forces, resulting from surface tension gradients, are included. The rise of a single air bubble (i) in pure water and (ii) in the presence of surfactants of different strengths is simulated. The results show good agreement with available (experimental and theoretical) correlations from literature.   

Session EJ: Bio-Fluids: General I

Microfluidic Separation of Chiral Particles

We present a combined theoretical and experimental investigation of the fluid mechanics of a helix exposed to a shear flow. In addition to classic Jeffery orbits, Resistive Force Theory predicts a drift of the helix across streamlines, perpendicular to the shear plane. The direction of the drift is determined by the direction of the shear and the chirality of the helix. We verify this prediction experimentally using microfluidics, by exposing Leptospira biflexa, a non-motile strain of helical-shaped bacteria, to a plane parabolic flow. As the shear in the top and bottom halves of the microchannel has opposite sign, we predict and observe the bacteria in these two regions to drift in opposite directions. The magnitude of the separation is in good quantitative agreement with theory. This setup can be used to separate microscale chiral objects.   

Gyrotactic trapping: a bifurcation in vertical motility triggers formation of thin phytoplankton layers

Characterized by spikes in cell concentration orders of magnitude above ambient, thin layers of phytoplankton are recurrent features of the coastal ocean, yet the mechanism of their formation remains unclear. We propose that cell motility in combination with depth-variable fluid shear can form thin layers via a mechanism we call ``gyrotactic trapping.'' The swimming direction of many motile phytoplankton is set by a balance between a gravitational torque (caused by cell asymmetry) and a viscous torque (caused by shear). Local peaks in shear disrupt this torque balance, producing a gradient in vertical cell flux and leading to intense cell accumulation. We tested gyrotactic trapping using two species of phytoplankton exposed to a lid-driven cavity flow, observing strong thin layers for both. The experimental layers closely matched results from individual-based simulations. Furthermore, an advection-diffusion model reveals that gyrotactic trapping can generate thin phytoplankton layers under realistic conditions in the ocean, where vertical distances are on the order of meters and layers are subject to dissipation by turbulence.   

Predation by the Dwarf Seahorse on Copepods: Quantifying Motion and Flows Using 3D High Speed Digital Holographic Cinematography - When Seahorses Attack!

Copepods are an important planktonic food source for most of the world's fish species. This high predation pressure has led copepods to evolve an extremely effective escape response, with reaction times to hydrodynamic disturbances of less than 4 ms and escape speeds of over 500 body lengths per second. Using 3D high speed digital holographic cinematography (up to 2000 frames per second) we elucidate the role of entrainment flow fields generated by a natural visual predator, the dwarf seahorse (\textit{Hippocampus zosterae}) during attacks on its prey, \textit{Acartia tonsa}. Using phytoplankton as a tracer, we recorded and reconstructed 3D flow fields around the head of the seahorse and its prey during both successful and unsuccessful attacks to better understand how some attacks lead to capture with little or no detection from the copepod while others result in failed attacks. Attacks start with a slow approach to minimize the hydro-mechanical disturbance which is used by copepods to detect the approach of a potential predator. Successful attacks result in the seahorse using its pipette-like mouth to create suction faster than the copepod's response latency. As these characteristic scales of entrainment increase, a successful escape becomes more likely.   

Control volume based hydrocephalus research

Hydrocephalus is a disease involving excess amounts of cerebral spinal fluid (CSF) in the brain. Recent research has shown correlations to pulsatility of blood flow through the brain. However, the problem to date has presented as too complex for much more than statistical analysis and understanding. This talk will highlight progress on developing a fundamental control volume approach to studying hydrocephalus. The specific goals are to select physiologically control volume(s), develop conservation equations along with the experimental capabilities to accurately quantify terms in those equations. To this end, an \textit{in vitro} phantom is used as a simplified model of the human brain. The phantom's design consists of a rigid container filled with a compressible gel. The gel has a hollow spherical cavity representing a ventricle and a cylindrical passage representing the aquaducts. A computer controlled piston pump supplies pulsatile volume fluctuations into and out of the flow phantom. MRI is used to measure fluid velocity, and volume change as functions of time. Independent pressure measurements and flow rate measurements are used to calibrate the MRI data. These data are used as a framework for future work with live patients.   

Transition to organized behavior on suspensions of concentrated bacteria

Concentrated populations of the swimming bacterium Bacillus subtilis develop a collective phase, the Zooming BioNematic, that exhibits large-scale coherence analogous to the molecular alignment of nematic liquid crystals. Bacterial suspensions were prepared in order to experimentally measure the transition to organized behavior as a function of the cell number concentration. PIV analysis was used to obtain cell velocities and define an order parameter in order to characterize the dynamics of the system.   

The low Reynolds hydrodynamics of bent rods precessing above flat planes

We examine the role of bend in rods precessing upright cones above flat planes in Newtonian fluids at low Reynolds. We experimentally document that the effect of bend in the rod is the creation of a novel set of nested tori on which fluid particles live: for straight rods, the tori degenerate into points in a Poincare section, while any amount of bend breaks symmetry and creates these tori. We present slender body asymptotic models which predict quantitatively and qualitatively similar behavior.   

Effects of bulk and free surface shear flows on amyloid fibril formation

Amyloid diseases such as Alzheimer's and Huntington's, among others, are characterized by the conversion of monomers to oligomers (precursors) and then to amyloid fibrils. Besides factors such as concentration, pH, and ionic strength, evidence exists that shearing flow strongly influences amyloid formation in vitro. Also, during fibrillation in the presence of either gas or solid surfaces, both the polarity and roughness of the surfaces play a significant role in the kinetics of the fibrillation process. By studying the nucleation and growth of a model system (insulin fibrils) in a well-defined flow field, we can identify the flow and interfacial conditions that impact protein aggregation kinetics. The present flow system consists of an annular region, bounded by stationary inner and outer cylinders and driven by rotation of the floor, with either a hydrophobic (air) or hydrophilic (solid) interface. We show both the combined and separated effects of shear and interfacial hydrophobicity on the fibrillation process, and the use of interfacial shear viscosity as a parameter for quantifying the oligomerization process.   

A quantitative study of the adhesive locomotion of terrestrial gastropods

The locomotion of terrestrial gastropods exhibits unique characteristics which allow these soft-body animals to crawl while adhering to steep surfaces. Gastropods move by gliding over a ventral foot lubricated by a thin layer of mucus. They generate trains of pedal waves through periodic muscle contractions in the central portion of the ventral foot, producing a forward traction, while the rim of the foot glides over the substrate. We analyzed the kinematics and dynamics of locomotion by conducting two sets of experiments. In the first set, we used digital image processing techniques to correlate the frequency and wavelength of the pedal waves to the migration velocity. In the second set, we computed the spatial and temporal evolution of the traction forces transmitted across the thin lubricating layer from measurements of the deformation of an elastic substrate of known properties and calculate the mechanical work used for crawling. We found that the pedal waves accelerate as they move forward along the ventral foot producing a breaking in symmetry which could contribute to the generation of a net traction force.   

The locomotion of marine and terrestrial gastropods: can the acceleration of the ventral pedal waves contribute to the generation of net propulsive forces?

Marine and terrestrial gastropods move by gliding over a ventral foot that is lubricated by secreted mucus (terrestrial) or simply by water (marine). The rim of the ventral foot generates suction forces that keep the animal adhered to the substrate. The central part of the foot produces a net propulsive force by generating trains of pedal waves through periodic muscle contractions. Recent experiments show that, in some gastropods, these pedal waves become faster and longer as they move forward, suggesting a mechanism for the generation of net propulsive forces by building a pressure difference across consecutive waves. We have investigated the efficiency of this mechanism through a theoretical analysis of a two-dimensional lubrication layer between a train of waves of slowly varying length and speed, and a flat, rigid, impermeable surface. The inhomogeneity of the speed and length of the pedal waves has been modeled through multiple-scale asymptotics. We have considered a Newtonian fluid to separate the effect of this inhomogeneity from the viscoelastic propulsion reported in previous works.   

Session EK: Free Surface Flows III

How do hydraulic jumps form?

We present an experimental and theoretical study of the formation of stationary hydraulic jumps in a narrow channel. We start each measurement with an empty channel and change the flow-rate abruptly from zero to a constant positive value. This leads to the formation of a stationary hydraulic jump in a two stage process: first the channel fills by the advancing fluid front, which undergoes a transition from supercritical to subcritical at some position in the channel, and later the influence of the downstream boundary conditions makes the jump move upstream to its final position with exponentially decreasing speed. We compare our experimental findings with theoretical predictions based on Rayleigh type shock theory.   

Substrate hydrophobicity and meandering

We present a study of the effect of surface properties on the meandering of a rivulet flowing down a non-eroding inclined plane. In this plane, we consider the behavior of meandering amplitude of the rivulet $h(x,t)$ for a variety of substrates, from partially wetting to hydrophobic, and present our results in terms of Fourier spectra of $h$ and in terms of the dimensionless growth rate of averaged absolute values of $h$ vs. downstream distance $x$. While the spectra have certain similarities in their scaling behavior for all the surfaces we studied, the dimensionless amplitude growth rate appears to depend rather strongly on the static contact angle characterizing the substrate.   

Scaling laws for meandering streams

We report on the scaling laws associated with meandering of a rivulet flowing down a non-erodible, partially wetting incline. The meandering streams in this experiment are triggered by flow rate fluctuations and sustained by external noise forcing. In our experiments, the former is provided by an electronically controlled valve, and the latter is due to fluid droplets left on the surface by previous meanderings. Over the entire range of scales we observe, the averaged spectrum of the deviations of the stream from its centerline demonstrates a power-law scaling, thus precluding the possibility of a preferred wavelength in ongoing meandering. We derive a simple theoretical model of rivulet meandering from first principles, incorporating stream dynamics and external noise forcing. The model provides an accurate statistical description of the stream deviation from a non-meandering path.   

The effect of surface conditions on the statistics of the surface temperature field during mixed convection

The statistics of the surface temperature field of an air/water interface are presented for the case of a clean water surface and a water surface covered with the surfactant monolayer oleyl alcohol. Experiments were conducted in a wind/water tunnel where the wind speed ranged from 1 - 4 m/s and the water was warmer than the air. The surface temperature field was acquired using an infrared camera. The root-mean-square and the skewness of the surface temperature field were computed and related to the heat flux and the wind speed for both the clean and surfactant-covered cases. Probability density functions of surface temperature were also computed and are presented to further reveal the effect of surfactant on the relationship between heat flux and wind speed and the surface temperature field. Some discussion of the mean temperature field is also presented.   

Meandering instability of a rivulet confined between two plates

We have investigated experimentally and theoretically the meandering instability of a rivulet flowing vertically between two plates. In contrast with previous works, we considered pure fluids with no surfactant effects. Experiments on silicon oils of low viscosities, reveal that there is a spontaneous instability leading to traveling meandering patterns, often disordered, but with a well defined wavelength. Strongly ordered patterns can be selected by forcing the entry with a well defined frequency. In both cases, the obtained wavelength is centimetrical and with a week dependence upon flow rate. Theoretically, this instability can be interpreted in terms of centrifugal effects competing with the friction of contact lines on the two plates. Starting from hydrodynamic equations, we have obtained a reasonably simple dispersion relationship that allows us to recover the selected wavelength and the pattern phase velocity. We suggest that this theory should also hold for rivulet on inclined plates, provided that the hysteresis and the noise introduced by the substrate are not too high.   

Detection of a liquid-metal surface using the DLP technique

Numerous new reactor concepts (e.g., Accelerator-Driven Systems) utilize the impact of a high-energy particle beam onto a liquid-metal surface as a vital part of the reactor design. Consequently, there is a need to detect the liquid-metal surface with high spatial and temporal resolution. The detection of liquid-metal surfaces has inherent difficulties that limit the use of common measurement techniques, e.g., high reflectivity in vacuum coupled with high flow velocity and rapid surface motion. In order to develop a method capable of meeting the needs of such systems, a projection method has been modified by adding a second (transparent) screen. The resulting Double-Layer-Projection (DLP) technique was applied to obtain spatially and temporally resolved measurements of a circular hydraulic jump using the eutectic liquid GaInSn as the test fluid. The jump position and height were measured with the required accuracy of $\pm $0.3mm. The velocity of the dominant waves and the superimposed high-frequency disturbances of the liquid metal surface were also detected.   

Law of spreading of the crest of a breaking wave

In a wide range of conditions ocean waves break. This can be seen as the manifestation of a singularity in the dynamics of the fluid surface, moving under the effect of the fluid motion of the underlying fluid. We show that, for shallow water waves at the onset of breaking, the wave crest expands in the span-wise direction as the square root of time. This is first derived from a theoretical analysis and then compared with experimental findings. The agreement is excellent. We then explore another configuration where the waves are generated by a parabolic wave maker. The focusing of the initially parabolic fronts induces interferences and also breaking of the waves if their amplitude is large enough. In this case a widening of the breaking proportional to the power $3/2$ of time is expected as it follows the Huygens cusp shape.   

Stagnation, folding, coiling, and breakup of viscous jets: a synthesis

Using laboratory experiments and theoretical modeling, we have studied the dynamics of a thin jet of viscous fluid falling from a substantial height (tens of cm) onto a solid surface. Our experiments reveal surprisingly complex behavior as the viscosity decreases for a fixed flow rate. For the highest viscosities used, the jet coils at all heights for which it remains intact. As the viscosity decreases, one observes (1) chaotic alternation between coiling and planar folding; (2) alternation between coiling, folding, and axisymmetric stagnation-point flow; and (3) stagnation-point flow alone. In all cases, the jet breaks up via the Rayleigh instability if the fall height becomes sufficiently large. To understand these results theoretically, we have developed a mathematical model of a thin viscous jet that includes an exact representation of surface tension forces. The linearized forms of these equations that describe the stability of stagnation-point flow comprise three uncoupled subsets, corresponding respectively to planar folding, helical coiling, and the Rayleigh instability. We solve these equations numerically to determine phase diagrams for the different types of instability, and compare the results with our experimental observations.   

Apex Jets from Impacting Drops

A new jetting phenomenon has been observed experimentally when a viscous drop, such as glycerin, impacts onto a low-viscosity, low-surface tension liquid pool, such as methanol. This jet is produced by the ejecta sheet which emerges from the free surface of the pool, moves up along and wraps around the surface of the drop. The convergence and closure of this sheet at the top apex of the drop produces a thin vertical jet along the axis of symmetry at velocities of more than 10 times that of the drop. These jets are only observed for a narrow range of impact conditions. The drop impact velocity must be high enough that the ejecta sheet has sufficient inertia to reach the apex, but not so high that it detaches. Thus we identify critical Reynolds and Weber numbers. Jetting has been observed both for drops which are miscible and immiscible with the pool liquid, under a different range of impact conditions but never for pools of water, as the surface tension is then significantly larger than that of the drop. Marangoni stresses may act in this case to promote separation and prevent the jetting.   

Thin-films flows over microtextured surfaces: Polygonal water sheets

We study water sheets and bells resulting from the impact of a water jet onto circular targets of comparable diameter. Depending on the physical properties of the target surface, which may or may not be covered with a roughness at the micron-scale, i.e. arrays of cylindrical micron-size posts arranged on regular lattices, we obtain a variety of stable shapes including circles and polygons such as hexagons, eight corner stars. We vary the topographic features (height of the posts, lattice distance and geometry) and the jet properties (size of the nozzle, flow rate) and we measure the size and shape of the liquid sheet. We rationalize our results by taking into account the additional friction induced by the lattice providing a fluid velocity that depends on the orientation of the lattice.   

Session EL: Bio-Fluids: Lungs

Clearance of a Mucus Plug

Mucus plugging may occur in pulmonary airways in asthma, chronic obstructive pulmonary disease (COPD) and cystic fibrosis. How to clear the mucus plug is essential and of fundamental importance. Mucus is known to have a yield stress and a mucus plug behaves like a solid plug when the applied stresses are below its yield stress $\tau _{y}$. When the local stresses reaches $\tau _{y}$, the plug starts to move and can be cleared out of the lung. It is then of great importance to examine how the mucus plug deforms and what is the minimum pressure required to initiate its movement. The present study used the finite element method (FEM) to study the stress distribution and deformation of a solid mucus plug under different pressure loads using ANSYS software. The maximum shear stress is found to occur near the rear transition region of the plug, which can lead to local yielding and flow. The critical pressure increases linearly with the plug length and asymptotes when the plug length is larger than the half channel width. Experimentally a mucus simulant is used to study the process of plug deformation and critical pressure difference required for the plug to propagate. Consistently, the fracture is observed to start at the rear transition region where the plug core connects the films. However, the critical pressure is observed to be dependent on not only the plug length but also the interfacial shape.   

The effect of viscoelasticity on the stability of the lung's liquid layer

The lungs consist of a network of bifurcating airways that are lined with a thin liquid film. This film is a bilayer consisting of a mucus layer on top of a periciliary fluid layer. Mucus is a non-Newtonian fluid possessing viscoelastic characteristics. Surface tension induces flows within the layer which may cause the lung's airways to close due to liquid plug formation if the liquid film is sufficiently thick. The stability of the liquid layer is also influenced by the viscoelastic nature of the liquid which is modeled here as a Jeffreys fluid. To examine the role of mucus alone, we model a single layer of a visco-elastic fluid. Nonlinear evolution equations are derived using lubrication theory for the film thickness and the film flow rate. A uniform film is initially perturbed and a normal mode analysis is carried out that shows that the growth rate for a viscoelastic layer is larger than for a Newtonian fluid with the same viscosity. Solutions of the nonlinear evolution equations reveal that the closure time, defined to be the time required for a plug to form, decreases with increasing film thickness and viscoelasticity. Some results obtained from direct numerical simulations are also presented and compared with the lubrication theory model.   

Liquid Plug Propagation in a Flexible Microchannel: Experimental and Numerical Studies

The lung's small airways can close due to the formation of a liquid plug bridge, or airway wall collapse or a combination of both in diseases such as chronic obstructive pulmonary disease (COPD) and respiratory distress syndrome (RDS), and in the external instillation of therapeutical drugs or surfactants.~ The propagation of a formed plug can produce high pressure, high shear stress, and large gradients of each, which may damage the cells lining the airway walls. This study is motivated by an interest in the effect of wall flexibility on the plug propagation and its resulting wall stresses in small airways. We fabricated a flexible microchannel to mimic the flexible small airways using soft lithography. As the plug propagates along the flexible microchannels, the local wall deformation is observed in the plug core region, which increases with plug speed but slightly increases with plug length. The pressure drop across the plug is measured and observed to increase with plug speed and is slightly smaller in a flexible channel compared to that in a rigid channel. A computational model is then presented to model the steady plug propagation through a flexible channel corresponding to the middle plane in the experimental device. The results show qualitative agreements with the experimental measurement.   

Motion of a semi-infinite bubble in a liquid filled channel using the level set method

The study of plug propagation in lung airways is of interest in the treatment of medical conditions such as asthma and in drug delivery. The problem of a semi-infinite bubble steadily displacing a liquid in a 2D channel (planar Bretherton problem) is computed using a fractional-step method on a Cartesian grid to solve the Navier-Stokes equations and a level-set formulation for resolving the air-liquid interface. We matched with available literature the geometry of the front and rear menisci of this semi-infinite bubble, stresses on the channel walls, and the maximum pressure drop as a function of the Capillary number -- the ratio of viscous to surface tension effects. Furthermore, we present preliminary results for flows within tapered walls to address area expansion near airway bifurcations.   

Particle Deposition for Flow over a Wedge

Particle transport and deposition associated with flow over a wedge is investigated as a model for particle transport and flow at an airway bifurcation. Using matched asymptotics, a uniformly valid solution is obtained to represent the high Reynolds number flow over a wedge which considers both the viscous boundary layer near the wedge and the outer inviscid region, and is then used to solve the particle transport equations. The phenomenon of boundary layer shielding is investigated and is characterized by a positive normal velocity component near the wall that pushes particles in the boundary layer away from the wall and prevents particle impaction. Additionally, deposition efficiency and relative distribution of impacted particles are presented. The present model compares well to more complex ones that consider the three dimensional structure of an airway, but is advantageous in that the boundary layer phenomena can be closely investigated.   

Anomalous bubble propagation in elastic tubes

Airway reopening is an important physiological event, as exemplified by the first breath of an infant that inflates highly collapsed airways by driving a finger of air through its fluid-filled lungs. Whereas fundamental models of airway reopening predict the steady propagation of only one type of bubble with a characteristic rounded tip, our experiments reveal a surprising selection of novel bubbles with counter-intuitive shapes that reopen strongly collapsed, liquid-filled elastic tubes. We characterize these bubbles in terms of their dimensionless speed and the initial level of tube collapse, and find sub-critical exchanges of stability between them. Moreover, our multiple bubbles are associated with a discontinuous relationship between bubble pressure and speed that sets exciting challenges for modellers.   

Reopening of a microfluidic airway tree in the presence of liquid plugs

Many respiratory diseases are associated with the occlusion of pulmonary airways with liquid plugs, which are generally assumed to cause the collapse of the airways. Previous work has shown that the reopening of the airways proceeds through avalanches occurring over several generations, although measurements on real lungs are limited to single point measurements at the trachea. Here, we present a microfluidic model airway tree which consists of five generations of bifurcations that are partially occluded with liquid plugs. The initial distribution of the plugs in the tree displays high sensitivity to initial conditions with evidence of chaotic distribution. The reopening is achieved by applying a constant pressure or constant flow rate at the root of the tree and cascades of different types are observed in the two cases: While the constant pressure forcing is found to open the whole tree, a constant flow rate forcing opens only a single path. Finally we observe that the elasticity of the airways is not a necessary ingredient for the cascades to occur.   

Numerical analysis of the formation process of aerosols in the alveoli

For a successful diagnosis of lung diseases through an analysis of non-volatile molecules in the exhaled breath, an exact understanding of the aerosol formation process is required. This process is modeled using Computational Fluid Dynamics (CFD). The model shows the interaction of the boundary surface between the streamed airway and the local epithelial liquid layer. A 2-D volume mesh of an alveolus is generated by taking into account the connection of the alveoli with the sacculi alveolares (SA). The Volume of Fluid (VOF) Method is used to model the interface between the gas and the liquid film. The non-Newtonian flow is modeled by the implementation of the Ostwald de Waele model. Surface tension is a function of the surfactant concentration. The VOF-Method allows the distribution of the concentration of the epithelial liquid layer at the surface to be traced in a transient manner. The simulations show the rupturing of the liquid film through the drop formation. Aerosol particles are ejected into the SA and do not collide with the walls. The quantity, the geometrical size as well as the velocity distributions of the generated aerosols are determined. The data presented in the paper provide the boundary conditions for future CFD analysis of the aerosol transport through the airways up to exhalation.   

Session EM: Bio-Fluids: Flight III

Interactions between butterfly scales and unsteady flows during flapping flight

Recent research has shown that the highly flexible wings of butterflies in flapping flight develop vortices along their leading and trailing edges. Butterfly scales (approximately 100 microns) have a shingled pattern and extend into the boundary layer. These scales could play a part in controlling separation in this 3-dimensional complex flow field. Biomimetic applications of butterfly scales may aid in the development of flapping wing micro air vehicles. In this study, we observed that the orientation of the scales may relate to the local flow field, and might move or shift during flight. Monarch butterflies were trained to fly in a low speed smoke tunnel for visualization. Scales were removed from the leading and trailing edges and specimens were photographed at 500 frames per second. Variation in flapping pattern and flight fitness are discussed.   

A Study of the Aerodynamics of Small Insect Flight

The lift production in the flapping flight of fruit flies at Reynolds numbers of approximately 120 has been attributed to the generation of a stable leading edge vortex that remains attached during the entire stroke of its motion cycle (see Birch et al., J. Exp. Biol., 2004). Little is known, however, about the aerodynamics of flight in the smallest flying insects such as haplothrips (Re = 5). In this presentation, we consider Reynolds numbers from 1 to 80. We used quantitative experimental flow field and force measurements on a dynamically scaled model with angles of attack varying from 0 to 90 degrees. The three-dimensional kinematics of the actual insect flight is simplified herein, and the motion of the wing in pure translation and rotation are considered. In the context of vortex dynamics, two interesting regimes are observed in the flow field: a stable leading edge vortex and a detached trailing edge vortex at the higher end of Re, and attached leading and trailing edge vortices in the lower end of Re. The implications of these flow field regimes in relation to the lift production and the biological limit of flying insects will be presented.   

Wake structure and wing motion in bat flight

We report on experiments concerning the wake structure and kinematics of bat flight, conducted in a low-speed wind tunnel using time-resolved PIV (200Hz) and 4 high-speed cameras to capture wake and wing motion simultaneously. 16 Lesser dog-faced fruit bats (\textit{C. brachyotis}) were trained to fly in the wind tunnel at 3-6.5m/s. The PIV recordings perpendicular to the flow stream allowed observing the development of the tip vortex and circulation over the wing beat cycle. Each PIV acquisition sequence is correlated with the respective kinematic history. Circulation within wing beat cycles were often quite repeatable, however variations due to maneuvering of the bat are clearly visible. While no distinct vortex structure was observed at the upper reversal point (defined according the vertical motion of the wrist) a tip vortex was observed to develop in the first third of the downstroke, growing in strength, and persisting during much of the upstroke. Correlated to the presence of a strong tip vortex the circulation has almost constant strength over the middle half of the wing beat. At relatively low flight speeds (3.4 m/s), a closed vortex structure behind the bat is postulated.   

A new fluid dynamics model to evaluate the contractile force of a biological spring, \textit{Vorticella convallaria}

\textit{Vorticella convallaria}, a sessile peritrich having a body and spring-like stalk, is a model for a bioinspired actuator because of its remarkably fast (msec) and powerful contractions (nN). An example of a biological spring, the stalk converts biochemical energy to physical motion, but the mechanics of contraction are poorly understood. To evaluate contraction force, past models have assumed the body to be a sphere moving in quiescent water and have equated contraction force to drag force on the body described by Stokes' law. However, flow induced by contracting \textit{Vorticella} does not satisfy conditions of Stokes' law because the flow is unsteady (Womersley number $>$ 1) and bound with a solid substrate to which the cell is tethered. We develop a more rigorous model for contraction force evaluation by assuming the body to be a sphere unsteadily moving perpendicularly toward a solid surface. The model comprises quasi-steady drag force, added mass force and history force with wall effect correction terms for each force. \textit{Vorticella} not only generates a maximum contraction force greater than Stokes' drag, but it also experiences drag force in the direction of contraction in the later stage of contraction due to the memory effect of water.   

Particle image velocimetry and thrust of flagellar micro propulsion systems

Miniature smart devices and micro-swimming robots that can perform in vivo interventions and diagnostic procedures inside the human body require efficient low Re number propulsions systems. A static test-bench to acquire simultaneous thrust and 3D velocity measurements of flagellar micro-propulsion systems is developed. Validation experiments of this set-up involving full computational fluid dynamics (CFD) solutions and approximate Resistive Force Theory (RFT) comparisons at variable rotational speeds (5-13 Hz) and for two different parametric thruster configurations are performed up to Re=0.1. 3D velocity fields are obtained with both side view and bottom view PIV configurations are evaluated for the single helix flagellar thruster configuration. To calculate the control volume thrust 20 PIV slices (acquired by 18 degrees shift of the encoder trigger signal) are interpolated on a cylindrical volumetric grid. CFD studies are in progress. A comparison between PIV results, thrust-cell measurements and RFT theory indicated high sensitivity on RFT drag coefficients. In future studies this measurement protocol will be applied to alternative and non-conventional bio-inspired thruster-configurations.   

Observation of Flow-Induced Synchronization of Eukaryotic Flagella

Colonial algae serve as model organisms for the study of evolutionary transitions to multicellularity, with species ranging from unicellular {\it Chlamydomonas} to {\it Volvox}, with thousands of biflagellated somatic cells. Locomotion and phototaxis of the multicellular species depends on the degree of coordination among those flagella, but little quantitative information has been available on the nature and degree of their spatio- temporal organization. Taking advantage of the spherical organism geometry, novel micromanipulation techniques, and high-speed imaging, we quantify in {\it V. carteri} the complex temporal dynamics of the flagella of individual somatic cells and the correlations of beat plane and beat phase between nearby cells. These flagella display the phenomenon of rhythm-splitting, well-known in the dynamics of coupled oscillators, and external flow is shown to strongly modify the degree of synchronization of flagella pairs.   

Experimental and Numerical Study of the Role of Elytra on Beetles Flapping Flight

The effect of flapping elytra of a beetle on aerodynamic force is investigated by particle image velocimetry (PIV) experiment and a two-dimensional numerical analysis. During the transition period from the up-stroke to the down-stroke, the positions of the hind and elytrum wings become close to each other and then the elytrum strongly affects on the aerodynamic forces. Through experimentally method, the quantitative velocity, vorticity, and pressure fields around the both wings are measured. A big leading edge vortex (LEV) is observed on the upper surfaces of the elytrum and the hind wings from the measured quantities at the initial instance of the down-stroke. Numerical result shows that the at first, elytrum hinders vortex generation on the hind wing due to its position is ahead along the streamline direction, then it contributes for vortex generation as the hind wing goes down. The elytrum itself generates big vertical force and small horizontal force during flapping due to that its curved geometry interacts with flow around. Conclusively, the total aerodynamic force by the both wings is lager than that by the hind wing without the elytrum considered.   

A novel automated method for studying free-flight insect maneuvers

Insects in flight often accomplish startling maneuvers via remarkably small adjustments in wing kinematics. For example, angle of attack modulations and asymmetries of less than 10 degrees can be the difference between an individual continuing forward, or entering a sharp turn. Hence, in order to study maneuvering flight in insects, a reliable, low-error method of determining body and wing kinematics is necessary. In this talk, we will describe a novel automated algorithm which extracts full, three-dimensional kinematics from high-speed video images of freely flying insects. This method is shown to be robust, fast, and versatile, with only small, well-characterized errors.   

Wing Deformation and Control in Insect Flight

By computing the aerodynamic forces on the wings of flying insects, we have previously shown evidence that the wing pitching associated with flapping flight can be passive. Presently, we extend this work to show that it is possible to extract information about muscle control directly from experimental observations. Using a combination of numerical simulations and novel visualization of experimental data we analyze the torsional waves present during wing pitching and infer about the presence of muscle control during various flight sequences.   

Session EN: Applied Fluid Dynamics

Lagrangian Particle Hydrodynamics for Fluid Structure Collision Analysis in Advanced Aerostructures

One of the key aerostructure certification criteria pertaining to the design phase, particularly in advanced structural concepts, addresses fluid-structure crash scenarios such as aircraft ditching on the water surface and bird-strike. Destructive trials on full-scale aerospace prototypes to evaluate damage sustained during fluid-structure collisions are extremely costly. Therefore, efforts have been made to numerically model such events with sufficient accuracy to significantly reduce the minimum number of tests required for design approval procedures. This presentation identifies the simulation strategies adopted using the Lagrangian particle hydrodynamics methodology in pursuit of such an investigation.   

Comparison of PIV and CFD for a Formula 1 Racing Car Front Tire

A 60 percent scale model of a complete Formula One wheel assembly including a deformable tire and brake components is being used to validate the accuracy of CFD results using a variety of simulation techniques and turbulence models. The tire is loaded to match real word deformation and contact patch conditions and is tested at a Reynolds number based on tire diameter of approximately 500,000. PIV measurements are taken around both a simplified model geometry with flat wheel covers and a complex case with full brake cooling ducts and passages. Measurements are compared to RANS, URANS, and LES calculations using parameters identical to those of the experiment. The ability of each these techniques to capture the vortex structures and separation regions of the wake is determined by the similarity of their velocity fields and turbulence values to the experimental results.   

Aero-Thermal Prediction in High Pressure Turbine Cascade using Large Eddy Simulation

The aero-thermal performance of an uncooled, smooth high pressure (HP) turbine cascade in the presence of free-stream turbulence is studied using a high-order overset mesh Large Eddy Simulation (LES) procedure. A HP vane cascade designed at the von Karman Institute (VKI) for fluid dynamics, Belgium, is used as the model geometry. Simulations matching experimental conditions, except for the Reynolds number which is about half of the experimental value, have been carried out. Significant enhancement in the blade heat-transfer is seen in the presence of inflow turbulence. Eddies from the free-stream turbulence get stretched around the blade, creating long streaky structures in the blade boundary layer. These structures quickly break down on the suction side, while they persist on the pressure side. The blade heat transfer signature from the simulations does not show transition of the boundary layer at the Reynolds number of the simulation. This is consistent with the trend seen in the experiments where transition is delayed by lowering the Reynolds number. New simulations matching the experimental Reynolds number are currently under way.   

Direct Numerical Simulations of the Flow around a Golf Ball: Effect of Rotation

Golf ball flight is affected by rotation of the ball (lift generation) and dimpling on the surface (drag reduction). Direct Numerical Simulation (DNS) is being developed for the flow around a rotating golf ball using an immersed boundary method. Adding to the computational cost is that the moving body must be re-located as the ball rotates. In the present effort, interface-tracking of the moving body is optimized using the Approximate Nearest Neighbor (ANN) approach. The code is parallelized using domain decomposition and message passing interface (MPI), and parallel performance results are presented for a range of grid sizes. Results are presented from a series of validation cases for flow over a smooth sphere and a golf ball.   

Stator-Induced Circumferentially-Varying Preswirl Propulsor

A propuslor capable of producing maneuvering forces in all directions effectively eliminates the need for additional control surfaces. Side forces can be generated by the propeller through the variation of the inflow swirl velocity to a conventional propeller. These control forces are generated based on the same geometric principles as a helicopter swash-plate. Instead of cyclically adjusting the propeller blade pitch angle, the relative pitch angle of a fixed pitch propeller is cyclically altered through a preswirled inflow generated by an upstream stator row. Experiments were conducted in a wind tunnel to quantify the effectiveness of an upstream stator row to generate a circumferentially varying swirled flow. Global flow measurements were acquired through static pressure and PIV measurements on a simplified propulsor model. From these and future measurements a full understanding of the fluidic interactions associated with the non-uniform upstream stator row and the propeller can be made.   

Flow Structure along a Delta Wing with Straight and Sinusoidally-Shaped Leading-Edges

The time evolution of the three-dimensional flow patterns along a delta wing of moderate sweep angle is characterized using a technique of stereoscopic particle image velocimetry. The relationship between the three-dimensional flow structure above the surface of the wing and the near-surface topology has been established, at successive instants following termination of a pitch-up maneuver. In addition, the near-surface flow patterns are characterized for sinusoidally-shaped leading-edges having various values of amplitude and wavelength. Topological features of streamline patterns, in conjunction with patterns of surface-normal vorticity and velocity, are used to evaluate the effectiveness of this type of passive control. The dimensionless ratio of wavelength to amplitude \textit{$\lambda $}/\textit{$\phi $} of the sinusoidally-shaped edge was found to be a predominant parameter. In essence, the near-surface flow structure is substantially altered for relatively small values of \textit{$\lambda $}/\textit{$\phi $}, and the largest changes were obtained by keeping the wavelength \textit{$\lambda $}/C small and the amplitude \textit{$\phi $}/C sufficiently large. These alterations involve either a decrease in the extent of three-dimensional separation or its elimination altogether.   

Drag reduction of a heavy vehicle by means of a trailer underbody fairing

On a modern heavy vehicle, one of the sources of aerodynamic drag is trailer underbody drag, which arises due to flow impingement upon the trailer wheels and flow separation downstream of the pseudo-backward facing step formed by the tractor drive wheels, chassis, and trailer underbody. In an effort to mitigate this source of drag, trailer side skirts, which are flat panels suspended on either side of the trailer underbody, have been previously evaluated in a number of wind tunnel, track, and on-the-road studies. Although the skirts have been shown to reduce the vehicle drag coefficient by as much as 0.04, they have not been widely accepted by the heavy vehicle industry due to a number of operational deficiencies in the skirt design. To overcome these deficiencies, we are investigating the performance characteristics of an alternate drag reduction device, which is comprised of a tapered fairing located on the trailer underside. RANS simulations have demonstrated that the fairing surface promotes re-attachment of the separated flow downstream of the tractor drive wheels and chassis, thereby reducing the drag coefficient by an amount as much as that of side skirts. These computational results will be validated by conducting a wind tunnel study of a full-scale heavy vehicle that employs fairings of varying length and design. This work performed under the auspices of the US DOE by LLNL under contract DE-AC52-07NA27344.   

Numerical modelling of a minimal transport model in tokamak edge plasma

Plasma flows at the transition between the core and the scrape off layer (SOL) of tokamaks play a crucial role in determining the confinement properties of the plasma. The spreading of SOL flow patterns into the edge plasma is investigated numerically in geometry relevant to limiter plasma, using a model in which the coupling between parallel momentum and plasma density is considered. The flow pattern is mainly governed by the density diffusion. It can either exhibit sharp radial gradients at the interface, or spread from the SOL into the edge plasma, depending on the effective diffusion coefficient. Parallel flows with non-zero velocity, resulting from spreading of parallel momentum into the core, are also readily observed in the edge around the limiter. Such features are important to understand the edge/SOL interplay, and model 3D effects including Kelvin Helmholtz instabilities that may be triggered by the strong radial shear on parallel velocity in the transition region. 3D computations taking into account the dynamics in the poloidal direction are already in progress.   

Experiments and simulations of flow noise inside a cylinder aligned with the flow

This work uses Lighthill's acoustic analogy to investigate noise generated by a turbulent boundary layer surrounding a cylinder aligned with the flow direction. Based on a DNS of channel flow with a Reynolds number $Re_\tau=180$, both the direct and the acoustic pressure fluctuations (self-noise) from the turbulent boundary layer surrounding the cylinder are computed. The computational domain is surrounded by a Perfectly Matched Layer (PML) absorbing boundary conditions. The result from the simulation is compared with noise data recorded on a purpose built experimental seismic streamer towed in the ocean. We do this to gain knowledge about how turbulent flow noise in a ``towed'' cylinder behaves and to compare the turbulent flow noise with other sources of noise found in towed sonar arrays, commonly used for maritime surveillance and geophysical exploration. Based on both simulations and measurements we present spectral estimates of the acoustic field and estimates of the spatial coherence ``distance'' of the noise.   

Flow measurements in indoor office environment

Experiments are being conducted to study the nature of flow near the human breathing zones. PIV measurements are being made around two thermal manikins and a table placed in an office space provided with displacement ventilation. The velocity profiles at various positions near the breathing zone and at various instants of the breathing cycle are being studied to understand how the breathing influences the air flow and mixing near the breathing zone, in a flow that is primarily driven by natural convection. These results can help us understand the transport of freely suspended particulate matter in indoor environments into the breathing zone and be used for validating computer models for indoor environments.   

Session EP: Basic Separated Flows

Unsteady Aspects of Turbulent Boundary Layer Separation

This experimental study is focused on the physics of unsteady turbulent boundary layer separation under conditions relevant to the dynamic stall process that occurs in helicopter rotors. A flat boundary layer development plate allows for the growth of a nominally zero pressure gradient turbulent boundary layer of thickness sufficient for high spatial resolution measurements. Downstream of the flat plate, a convex ramp section imposes a streamwise adverse pressure gradient that gives rise to boundary layer separation. In order to impose an unsteady pressure gradient, an airfoil equipped with leading edge plasma flow control is located above the ramp section. With the airfoil placed at a post-stall angle of attack, the boundary layer on the ramp remains attached but near a state of incipient separation. Plasma flow control is used to alternately attach and separate the airfoil flow which gives rise to unsteady turbulent boundary layer separation on the convex ramp. The resulting unsteady turbulent boundary layer separation is investigated via phase-locked two-component PIV, unsteady surface pressure measurements and high speed digital imaging.   

An Experimental Study of Near Wake Structure Behind Two Circular Cylinders with Heat Addition

In this study, we present flow visualization data on the effect of heat addition on the near wake structure behind two identical circular cylinders separated in the span-wise direction perpendicular to the flow at Re = 350. Flow visualization is done using the hydrogen bubble technique. The spacing between the two cylinders is T/D = 1.7, where T = center-to-center spacing and D = cylinder diameter. The gap flow is known to be intermittently bi-stable at this spacing, which is clearly demonstrated in the study. The present study focuses on the response of the gap flow to the heat release in one cylinder. The study shows clearly that the gap flow deflects towards the heated cylinder resulting in a narrower wake behind the heated cylinder as compared to the wake behind the unheated cylinder. The response of the gap-flow is further demonstrated by turning the heat off on one cylinder and switching the heat on the other cylinder resulting in the gap flow deflection as well. The cylinders in the present experiments are heated by joule heating with an estimated wall temperature difference of 30$^{\circ}$C in water at the given Reynolds number resulting in Richardson number of about 0.2 in the present experiments.   

Three-dimensional Dynamics of the Gravity Current Flow past a Submerged Cylinder

The three-dimensional dynamics of the gravity current flow past a submerged cylinder are investigated by means of large eddy simulations. The geometries considered are a bottom-mounted rectangular cylinder and a circular cylinder mounted above a bottom wall. The Reynolds number is of O(100). The agreement with previous experimental measurements of the drag and lift coefficients is excellent. The simulation for the rectangular cylinder case shows that the gravity current front's lobe-and cleft structure sets the characteristic length of the spanwise variation of the drag during impact, while an unsteady cellular flow structure upstream of the cylinder sets this characteristic length during the later quasi-steady stage. The simulation for the circular cylinder case shows during the quasi-steady stage the shedding of primary Karman vortices, the presence in the near wake of, apparently, secondary mode-B streamwise vortices, and an interaction further downstream between the Karman vortices and the boundary layer at the bottom wall and the shear layer between the two fluids.   

Nonlinear spacing and frequency effects of an oscillating cylinder in the wake of a stationary cylinder

Nonlinear responses to a transversely oscillating cylinder in the wake of a stationary upstream cylinder are studied theoretically by using an immersed-boundary method. It is found that flow around the two cylinders varies with different spacing between the two cylinders and the oscillation frequency of the downstream cylinder. As known in a stationary tandem-cylinder system, there exist the ``vortex suppression regime'' (VS) and the ``vortex formation regime'' (VF). These two regimes are divided by a critical spacing. When the downstream cylinder is forced to oscillate at a fixed amplitude but different frequency, different flow patterns appear in each of the regime. On the other hand, at the same oscillating frequency but different spacing, the response state (lock-in, transient or non-lock-in) changes. While each state has periodic or quasi-periodic behaviors, nonlinear responses appear. All of the analyses are based on vorticity contours, time histories of the velocities in the near wake regions, spectral analyses, and related phase portraits.   

The effect of Reynolds number on the dynamics of freely rising and falling spheres

In this study, we investigate the effect of Reynolds number on the dynamics and vorticity patterns of spheres rising or falling freely through a fluid. Initially, our experiments focused on two Reynolds numbers, \textit{Re} = 450 and 10,000. At both \textit{Re}, all falling spheres, with a mass ratio (or density relative to the fluid), $m* >$ 1, are found to descend rectilinearly. For rising spheres, we observe that contrary to previous studies, rectilinear trajectories persist until some critical mass ratio, $m*_{crit}$, below which the spheres suddenly begin to vibrate vigorously in a vertical plane. At \textit{Re} $\approx $ 10,000, we find $m*_{crit}$ = 0.61, while at \textit{Re} = 450, the critical mass is distinctly lower, $m*_{crit}$ = 0.36. To explore the dynamics of spheres over a wide range of \textit{Re}, we controlled the fluid viscosity using glycerin-water mixtures, and considered over 130 cases of $m*$ = 0.08-1.5 and \textit{Re} = 100-15,000. For all \textit{Re} studied, we find a wide range of spheres that rise rectilinearly, yielding $m*_{crit}$ significantly below 1. The only regimes observed in our study are rectilinear motion and periodic zigzag vibration. The vortex wakes for the rectilinear regime resemble those of a fixed sphere at similar \textit{Re}, either a single-sided chain (\textit{Re} = 450), or a double-sided chain (\textit{Re} $\approx $ 10,000) of vortex rings. However, for the whole range of \textit{Re} studied, we discover that the periodic zigzag regime is associated with a new vortex formation mode comprising \textit{four vortex rings} per cycle of oscillation.   

Hydrodynamic Forces On A Cylinder Vibrating Transversely And In-Line To A Steady Stream

We present computational results on the flow structure and forces in flow past a circular cylinder oscillating transversely and in-line to a uniform stream at Reynolds number 400. Three values of the transverse vibration frequency are implemented, corresponding to 1.0, 0.9 and 1.1 times the natural frequency of the Karman vortex street. The in-line vibration occurs at twice the frequency of the transverse oscillation. The cylinder thus follows an ``eight''-like trajectory, emulating the trajectory of a free vortex-induced vibration. We find that the results of the simulation are greatly influenced by the direction in which the ``eight'' figure is traversed. We distinguish between a ``counterclockwise'' mode (if the upper part of the trajectory is traversed counterclockwise), and a ``clockwise'' mode (if the upper part of the trajectory is traversed clockwise). We find that the counterclockwise mode results in larger fluid forces than the clockwise mode for the same amplitude of oscillation. The power transfer from the fluid to the cylinder remains positive for the counterclockwise mode at higher values of the amplitude-over-diameter-ratio than it does either for the clockwise mode or for a transversely only vibrating cylinder.   

LES of flows around a circular cylinder at critical and supercritical Reynolds numbers

It is well known that the flow around a circular cylinder in the critical Reynolds number region represents an intricate combination of laminar separation, turbulence transition, reattachment and turbulent separation of a boundary layer on the cylinder. According to previous experimental studies, separation bubbles are formed in association with the process of a separation-to-reattachment flow on the cylinder. Also, the structure of a separation bubble and its behavior is sensitively changed, dependent on the Reynolds number from the critical to the supercritical region. In this research, LES method is applied to the flow around a circular cylinder in the supercritical as well as the critical Reynolds number region. Detailed structures of the separation bubble are investigated by using time-sequential computed results as the Reynolds number changes. We have found a divergent type of flow with 3D structures near the reattachment area and its physical meaning is discussed.   

Flow Pattern past Two Spheres in Proximity

As a follow-up study of flow-induced forces on two nearby spheres [Phys. Fluids 19, 098103 (2007)], this paper establishes a systematic characterization of flow patterns past two identical spheres in proximity at Re=300. We consider all possible arrangements of two spheres in terms of the distance between the spheres and the angle inclined with respect to the main flow direction. It turns out that significant changes in shedding characteristics are noticed depending on how the two spheres are positioned. Ten distinct flow patterns are identified in total, and a detailed description is given to each pattern. Collecting all the numerical results obtained, we propose two comprehensive tables; one for flow pattern for each arrangement of the spheres and the other for Strouhal number of the corresponding vortex shedding. The perfect geometrical symmetry implied in the flow configuration allows one to use those tables for any two identical spheres arbitrarily positioned in physical space with respect to the main flow direction.   

Flow past an Inclined Square Cylinder

Numerical investigation has been carried out for laminar flow (\textit{Re}$\le $150) past an inclined square cylinder in cross freestream. The motivation stems from characterization of flow-induced forces on a sharp-edged cylindrical object immersed in cross flow with an angle of attack. From the viewpoint of wind hazards, this study would be the first step towards understanding flow-induced forces on cylindrical structures under a strong gust of wind. In this flow configuration, there exist two kinds of critical Reynolds numbers in laminar regime; flow separation occurs at a lower critical Reynolds number (\textit{Re}$_{c1})$ and flow becomes unsteady at an upper critical Reynolds number (\textit{Re}$_{c2})$. It is seen that the values of \textit{Re}$_{c1}$ and \textit{Re}$_{c2}$ change depending on the inclination angle (\textit{$\theta $}) of the cylinder. In particular, \textit{Re}$_{c2}$ decreases as \textit{$\theta $} increases, being consistent with the instability theory based on Stuart-Landau equation in literature. Furthermore, the cylinder vertices at which flow separation takes place are determined by \textit{$\theta $}. Consequently, key flow characteristics such as drag/lift forces on the cylinder and vortex-shedding frequency could drastically alter depending on \textit{$\theta $}. We propose contour diagrams of mean drag/lift coefficients, Strouhal number (\textit{St}) of vortex shedding, and rms of lift coefficient fluctuation$_{ }$on \textit{Re}--\textit{$\theta $} plane.   

Session EQ: Reacting Flows II: Detonations & Modeling

Effects of Stochasticity on Deflagration-to-Detonation Transition in Obstructed Channels

Deflagration-to-Detonation Transition (DDT) in obstructed channels involves multiple stochastic phenomena, including flow instabilities, turbulence, many interactions between shocks, flames, and vortices, and the resulting hot-spot formation. Since the detonation usually arises from one of many hot spots that stochastically appear in the system, there is some uncertainty in time and location for the detonation initiation. Small fluctuations of density, temperature, and composition play an important role in the development of stochasticity in experimental systems, which are also affected by uncertainties in initial conditions. The real cause of stochasticity, however, is embedded in the complexity of underlying physical phenomena, and can cause a stochastic behavior of numerical solutions that model these phenomena. Here we use a deterministic numerical model based on reactive Navier-Stokes equations that are solved using a deterministic method. Stochastic properties of the model system are evaluated using multiple numerical experiments for the same configuration. To trigger the stochastic response, we vary the initial background temperature within an interval of 0.01~K, which is too small to have systematic effects on the solution. Resulting run-up distances to DDT show a stochastic dispersion similar to that observed in physical experiments.   

Initial-value problem for small perturbations in an idealized CJ detonation

The initial-value problem for perturbations in idealized overdriven detonations was considered by Erpenbeck (Phys. Fluids, Vol. 5, No. 1962, pp. 604-614) and Tumin (Phys. Fluids, Vol. 19, No. 10, 2007). The solution requires an analysis of fundamental solutions for homogeneous systems of ODEs of the direct and adjoint problems. Because the fundamental solutions can be singular at the end of the reaction zone, the initial-value problem requires a more detailed asymptotic analysis in the vicinity of the sonic point. Sharpe (PRSL A, Vol. 453, 1997, pp. 2603-2625) and Short et al. (JFM, Vol. 595, 2008, pp. 45-82) provided a rigorous asymptotic analysis of the direct problem in the case of idealized gaseous and condensed-phase models of detonations. In the present work, the asymptotic analysis of the adjoint problem in the vicinity of the sonic point is completed. Analysis of the fundamental solutions leads to a conclusion that the structure of the initial-value problem remains the same as for the overdriven detonation.   

Detonation attenuation by a porous medium and its subsequent re-initiation

The detonation attenuation by a series of cross-flow cylinders, and its subsequent re-initiation mechanisms are studied experimentally and numerically, for a one-step chemically reacting fluid. A decrease in the scale of the blocking cylinders, or an increase in the number of the cylinders, is seen to delay the re-establishment of a self-sustained detonation. A detailed reconstruction of the detonation reflection and diffraction around the obstacles will be given, along with the complex flow fields involving wave reflections at the exit of the porous medium. The re-initiation mechanism is observed to be a function of not only the strength of wave reflections, but also the strength of the expansion wave following the reactive front, which affects the chemical kinetic rates behind the shock. A global model is proposed, which takes into account the momentum losses in terms of the flow blockage by the porous medium.   

Simulations of Pulse Detonation Engines with MHD Thrust Augmentation

Pulse detonation rocket engines (PDREs) have received significant attention in recent years due to their potentially superior performance over constant-pressure engines. Yet unsteady chamber pressures cause the PDRE flow to be either over-expanded or under-expanded for the majority of the cycle, with substantial performance loss in atmospheric flight applications. The present computational studies examine the potential benefits of using magneto-hydrodynamic (MHD) thrust augmentation by extracting energy via a generator in the PDRE nozzle and applying it to a separate, secondary stream. In the present studies, which involve both transient quasi-1D and 2D numerical simulations, the energy extracted from the nozzle flow is directly applied to a by-pass air stream through an MHD accelerator. The air stream is first shocked by the under-expanded nozzle flow and raised to high temperature, allowing thermal ionization. The specific conditions for thrust augmentation are examined. Alternative configurations utilizing a magnetic piston in the PDRE chamber are also explored. Results show potential performance gains but with significant challenges, depending on the operating and flight conditions.   

Solution of Reactive Compressible Flows Using an Adaptive Wavelet Method

This work presents numerical simulations of reactive compressible flow, including detailed multicomponent transport, using an adaptive wavelet algorithm. The algorithm allows for dynamic grid adaptation which enhances our ability to fully resolve all physically relevant scales. The thermodynamic properties, equation of state, and multicomponent transport properties are provided by CHEMKIN and TRANSPORT libraries. Results for viscous detonation in a H$_2$:O$_2$:Ar mixture, and other problems in multiple dimensions, are included.   

Multidomain spectral collocation method for three-dimensional perturbations in idealized CJ detonations

The spectral collocation method for stability analysis of detonations allows computing the eigenvalue map for unstable modes. A multidomain version of the method provides more control over the distribution of the collocation points throughout the reaction zone. In the case of three-dimensional perturbations, the radiation condition that is usually used in the stability analysis is a nonlinear function of the eigenvalue, and it could not be incorporated explicitly into the spectral method. Recent rigorous asymptotic analysis of stability of detonations for an idealized condensed-phase model by M. Short et al. (JFM, 2008, Vol. 595, pp. 45-82) provides the radiation condition for three-dimensional perturbations that is a linear function of the eigenvalue for CJ detonations. The latter allows a direct inclusion of the radiation condition into the spectral method. In the present work, details of the multidomain spectral collocation method for CJ detonations are discussed. The results are illustrated by computations of eigenvalue maps for three-dimensional perturbations in gaseous and condensed-phase idealized one-dimensional detonations.   

Multiscale Adaptive Model Reduction in Reactive Flows

The numerical solution of mathematical models for reacting flows is a challenging task because of the simultaneous contribution of a wide range of time scales present in the system. However, the dynamics can develop very-slow and very-fast time scales separated by a range of active scales. The complexity of the problem can be reduced when fast/active and slow/active time scales gaps becomes large. We propose a numerical technique named the \textsl{G-Scheme}, to achieve multiscale adaptive model reduction. We assume that the dynamics is decomposed into active, slow, fast, and when applicable, invariant subspaces. We introduce a locally curvilinear frame of reference, defined by a set of orthonormal basis vectors, with corresponding coordinates, attached to this decomposition. The evolution of the coordinates associated with the active subspace is described by non-stiff DEs, whereas that associated with the slow and fast subspaces is accounted for by applying algebraic corrections derived from asymptotics of the original problem. Adjusting the active DEs dynamically during the time integration is the most significant feature of the \textsl{G-Scheme}, since the numerical integration is accomplished by solving a number of DEs typically much smaller than the dimension of the original problem. The effectiveness of the \textsl{G-Scheme}, is demonstrate by solving a number of relevant problems.   

Effect of Initial Disturbance on The Detonation Front Structure

Effect of initial disturbance on the detonation front structure is studied by 3D numerical simulation. The numerical method used is the high resolution computations using a fifth-order weighted essentially non-oscillatory (WENO) scheme with a third order TVD Runge-Kutta time stepping method. Two types of disturbances are used to give perturbation for the detonation development in a narrow duct. One is the random disturbance which is imposed on the whole front, and another is the symmetrical disturbance, which is inputted within a band along the diagonal direction on the front. The results show that the developing processes of two kinds of disturbances in the detonation are different. For the random disturbance, the detonation front displays a stable spinning detonation. For the symmetrical diagonal disturbance, the detonation front displays a diagonal pattern at the earlier stage, but this pattern is unstable. Shortly, it breaks down and finally it evolves into a spinning detonation. The spinning detonations formed with the two types of disturbances are the same. This means that spinning detonation is the most stable mode for the simulated narrow duct. Therefore, for narrow ducts, implementing spinning detonation is the effect way to realize stable detonation as well as to speed the DDT (deflagration to detonation transition) process.   

Session ER: CFD: Discrete Methods

Simulation Approach for Microscale Noncontinuum Gas-Phase Heat Transfer

In microscale thermal actuators, gas-phase heat transfer from the heated beams to the adjacent unheated substrate is often the main energy-loss mechanism. Since the beam-substrate gap is comparable to the molecular mean free path, noncontinuum gas effects are important. A simulation approach is presented in which gas-phase heat transfer is described by Fourier's law in the bulk gas and by a wall boundary condition that equates the normal heat flux to the product of the gas-solid temperature difference and a heat transfer coefficient. The dimensionless parameters in this heat transfer coefficient are determined by comparison to Direct Simulation Monte Carlo (DSMC) results for heat transfer from beams of rectangular cross section to the substrate at free-molecular to near-continuum gas pressures. This simulation approach produces reasonably accurate gas-phase heat-transfer results for wide ranges of beam geometries and gas pressures. Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.   

Stochastic Particle Advection in Hybrid Large Eddy Simulation/Filtered Density Function Methods

We describe an efficient combination of interpolation and stochastic time integration schemes for the advection of computational particles in Large Eddy Simulation/Filtered Density Function (LES/FDF) methods. In this setting, particle positions evolve by a standard diffusion process whose drift and diffusion coefficients are determined from flow properties which are known in the form of face- and cell-average values. We demonstrate that a stochastic time integration scheme, developed by Cao and Pope in 2003, yields second-order accurate values of the particle position density function, provided that the interpolation schemes used reconstruct the diffusion and drift terms with second-order accuracy, and their first derivatives with first-order accuracy. Here, we present a velocity interpolation scheme, called the Polar Parabolic Edge Reconstruction Method (PPERM), and a scalar interpolation scheme, called the Multilinear Gradients Method (MLG), which satisfy these requirements, and we compare the performance of the Cao {\&} Pope SDE integration scheme with that of a weak second-order accurate derivative-free scheme proposed by Tocino and Vigo-Aguiar in 2002.   

Simulation of the Dynamics of Bubble Rising in viscous fluid using Lattice Boltzmann Equation Method

A stable Lattice Boltzmann Equation (LBE) Model based on the Cahn-Hilliard diffuse interface approach is presented for simulation of incompressible two-phase flows having large density and viscosity ratios. This model utilizes two particle distribution functions which recover the evolution of composition, pressure and momentum. This model is validated by analyzing the dynamics of a single rising gas bubble in viscous fluid. Terminal shape and Reynolds number (Re) are interactive quantities that depend on size of bubble, surface tension, viscosity and density of surrounding fluid. Accurate simulation of terminal shape and Re are obtained for different regimes. The regimes achieved were spherical, ellipsoidal, skirted and spherical cap. These were successfully achieved by systematically changing the values of Morton number (Mo) and Bond number (Bo) within the following ranges (10$^{-12} \quad <$ Mo $<$ 10$^{6})$ and (1 $<$ Bo $<$ 10$^{3})$. Re and final bubble shape for each regime could be satisfactorily predicted and simulated since they are also function of Morton and Bond number. Re results are compared with previous simulation and experimental results.   

3D Phase-Field Simulations of Interfacial Dynamics in Viscoelastic Fluids with Adaptive Meshing

We have developed a diffuse-interface algorithm for computing two-component interfacial flows of Newtonian and non-Newtonian fluids in 3D. An adaptive meshing scheme produces fine grid near the interface and coarse mesh in the bulk, and leads to accurate resolution of the interface at moderate computational cost. Another advantage of the method is that there is no need for manual intervention during topological changes of the interface such as rupture and coalescence. However, the fully implicit time-stepping results in a large matrix system for complex 3D flows, with high demands for memory and CPU speed. As validating examples, we discuss a drop spreading on a partially wetting substrate and drop deformation in Newtonian and viscoelastic fluids. The results show very good agreement with those from the literature and our own 2D axisymmetric simulations.   

Lattice Boltzmann simulation of dynamics of plunge and pitch of 3D flexible wing

The method of lattice Boltzmann (LB) simulation has been used to simulate fluid structures and motion of a flexible insect wing in a 3D space. In the method, a beam has been discretized into a chain of rigid segments. Each segment is connected through ball and socket joints at its ends. One segment may be bent and twisted with its neighboring segment. A constraint force is applied to each joint to ensure the solid structure moving as a whole flexible elastic body.We have demonstrated that the LB method is suitable for modeling of aerodynamics of insects flight at low Reynolds numbers. First, a simulation of plunging and pitching of a rigid wing is performed at $Re=75$ in a 2D space and the results of lift forces and flow structures are in excellent agreement with the previous results. Second, plunging and pitching of a flexible wing in span-wise direction is simulated at $Re=136$ in a 3D space. We found that when twisting elasticity is large enough the twisting angle could be controlled at a level of smaller than 0.2 degree. It is shown that as bending and twisting elasticity is large enough, the motion of flexible wing approaches that of a rigid membrane wing. The simulation results show that the optimization of flexibility in span-wise direction will benefit thrust and an intermediate level is favorable. The results are consistent with experimental finding.   

Numerical Simulation of a Droplet Bouncing on a Soap Film

We present a numerical method to simulate the interaction of a droplet with a soap film. Our numerical method uses two level set functions to track respectively the droplet and the soap film. The Navier-Stokes equations are solved in 3D using finite differences and a projection method. The proper jump and boundary conditions are enforced in a sharp (sub-grid) manner to maintain accuracy in the zone where both interfaces are close. We validated our approach by reproducing experiments performed by Gilet and Bush at MIT. We will show the ability of the method to reproduce bouncing, break-through, and partial break-through and conclude with some future applications.   

Direct Numerical Simulations of Turbulent Flows over Superhydrophobic Surfaces

Direct numerical simulations are used to investigate the drag reducing performance of superhydrophobic surfaces in turbulent channel flow. Slip velocities, wall shear stresses, and Reynolds stresses are considered for a variety of superhydrophobic surface micro-feature geometry configurations at a friction Reynolds number of Re$_{\tau }$ = 180. For the largest micro-feature spacing of 90$\mu $m an average slip velocity over 75{\%} of the bulk velocity is obtained, and the wall shear stress reduction is nearly found to be nearly 40{\%}. The simulation results suggest that the mean velocity profile near the superhydrophobic wall continues to scale with the wall shear stress, but is offset by a slip velocity that increases with increasing micro-feature spacing.   

Eigenvalue Analysis for Error Dynamics of Measurement Integrated Simulation to Reproduce Real Flows

A measurement-integrated simulation (MI simulation) is a numerical simulation with a feedback loop to compensate the difference between the simulation and real phenomena in a condition of different boundary/initial condition. The origin of this methodology is the observer in the control theory. Although the validity of MI simulation has been proved in several applications, such as an ultrasonic measurement integrated simulation of blood flow or hybrid wind tunnel to reproduce Karman vortex street, a theory of MI simulation has not been established yet. As a fundamental consideration to construct a general theory of MI simulation, we formulated the linearized error dynamics equation to express time development of the error between the simulation and the real flow, and its eigenvalue analysis. The validity of the method was investigated for the problem of the low-order model problem of the turbulent flow in a square duct. The result of numerical experiment of MI simulation was well predicted by a result of eigenvalue analysis proving the validity of the eigenvalue analysis of liearaized error dynamics in evaluating the effectiveness of MI simulation.   

Adaptive Moment-of-Fluid Method for Multi-Material Flow

A novel adaptive mesh refinement (AMR) strategy based on Moment-of-fluid (MOF) method for volume-tracking evolving interface computation is presented. Moment-of-fluid method is a new interface reconstruction and volume advection method using volume fraction as well as material centroid. Using the AMR-MOF method, the accuracy of volume-tracking computation with evolving interfaces is improved significantly compared to other published results. The effectiveness and efficiency of AMR-MOF method is demonstrated with classical test problems, such as Zalesak's disk and reversible vortex problem. The comparison with previously published results for these problems shows the superior accuracy of the AMR-MOF method over other methods. In addition, two new test cases with severe deformation rates are introduced, namely droplet deformation and $\mathcal{S}$-shape deformation problems, for further demonstrating the capabilities of the AMR-MOF method. Extensions to multi-material ($n_{mat}>2$) and compressible flow cases will also be addressed.   

Session ES: Rotating Flows

Lagrangian statistics in rotating turbulence

Background rotation becomes important when the ratio of the nonlinear acceleration over the Coriolis force becomes small enough. The Coriolis force has an anisotropic effect on the flow, and leads to the formation of columnar vortex structures and Ekman boundary layers close to the horizontal no-slip boundaries. The first aim of this work is to feed the fundamental investigation of turbulence with experimental data, giving further insight into the anisotropic effects of rotation on turbulent particle-pair dispersion and quantifying this anisotropy through the comparison of the horizontal (normal to the rotation axis) dispersion and the reduced vertical one, together with some other relevant manifestations of anisotropy. A series of experiments of electromagnetically forced turbulence ($Re_{\lambda}\sim 150$) is performed in a confined tank put on a rotating table and the Rossby number is varied between 1 and 0.08. A 3D-PTV technique is used to extract trajectories in a volume comparable with the integral scale of the flow and with space- and time-resolutions adequate to resolve the Kolmogorov scales.   

Twisted wake of a sphere in rotating fluid

The Taylor-Proudman theorem has simple and interesting consequences, illustrating the fact that rotating fluids exhibit a range of phenomena not found in non-rotating fluids. The principal phenomenon of these is the formation of Taylor Columns. The phenomena occur if there are relative motions between a flow in a strongly rotating system and an obstacle in the flow. In our research, effect of the background rotation on the wake of flow past a solid sphere has been studied experimentally. The sphere is hung in a rotating tank filled with water. While the sphere is towed along the centre line of the rotation, the wake region was chased with a digital video camera and a light sheet that illuminates the area. The experiments were performed in various range of the Rossby number. The visualization from the same inertia frame yields striking results. Twisting columnar flow, which looks quite similar to Taylor Column, visualized in the wake of a sphere in rotating fluid. Taking PTV (Particle Tracking Velocimetry) analysis, velocity fields of the flow were obtained. With the help of the results, discussions about the development of the twisted columnar flow and its structure will have been taken place in the conference.   

Gravitationally forced surface waves in a rotating cylinder

A thin layer of fluid, flowing axially along the inner surface of a horizontal rotating cylinder is subjected to a periodic forcing due to the gravitational acceleration. Since the frequency of the forcing lies within the critical range ($[0,\,2 \Omega]$) for which the inviscid problem is of a hyperbolic nature, the solution which in this case may be obtained on closed form displays a characteristic ``Mach wave''-like behavior.   

Experimental Study of Energy Transfer by Inertial Waves During the Build up of Turbulence in a Rotating System

We study the transition from fluid at rest to turbulence in a rotating water cylinder. We show that the energy, injected at a given height, is carried by inertial wave packets through the volume. These waves serve as the main energy transport mechanism and even when they are of large amplitude, they propagate in velocities consistent with those calculated form linearized theory. Nonlinear energy transport is governed by a second time scale, which depends on the velocity of the flow. It, thus, takes place only at long times and allows for the observed extended linear behavior. The observed linear effects that are unique to rotating flows can, therefore, highly impact energy transfer, distribution and statistics, even at high Reynolds numbers. Such effects are of special importance when considering rotating turbulent fields that are driven by intermittent energy sources.   

Direct Numerical Simulation and Coherent Vortex Extraction of sheared and rotating turbulent flow

The effect of rotation on the structure and dynamics of homogeneous sheared turbulence is investigated using direct numerical simulation (PoF, 20, 045103 (2008)). We consider shear flow without rotation, with moderate and with strong rotation, where the rotation axis is either parallel or anti-parallel to the mean flow vorticity. For moderate rotation an anti-parallel configuration increases the growth of the turbulent kinetic energy for a limited range of rotation ratios, while the parallel case reduces the growth as compared to the non-rotating case. For strong rotation energy decay is observed and linear effects dominate. Flow visualizations show that the inclination angle of vortical structures depends on the rotation rate and orientation and that the inclination angle is related to the growth of the turbulent kinetic energy. Coherent vortex extraction, based on the orthogonal wavelet decomposition of vorticity, is applied to split the flow into coherent and incoherent parts. The coherent part preserves the vortical structures using only a few percent of the degrees of freedom, while the incoherent part was found to be structureless and of dissipative nature. With increasing rotation rates, the number of wavelet modes representing the coherent vortices decreases, indicating an increased coherency of the flow. Restarting the DNS with the filtered fields confirms that the coherent component preserves the temporal dynamics of the total flow.   

Modeling the effects of system rotation on the turbulent heat fluxes

A new model is proposed for accounting for the effects of system rotation on the turbulent scalar fluxes. The model is based on extension to rotating frames of an explicit, algebraic model derived using tensor representation theory. The outcome is a rational model which allows for the turbulent scalar fluxes to depend on the details of the turbulence field and on the gradients of both the mean velocity and temperature. Such dependence, which is absent from conventional gradient-transport models, is required by the exact equations governing the transport of the heat fluxes. An a priori assessment of the model is performed using results from Direct Numerical Simulations of heated flows in channels rotated about their streamwise, spanwise and wall-normal axes. The results are generally in close agreement with the DNS but some important differences remain. The reasons for these are discussed. Further assessment is carried out by actual computations of heated flow in a channel rotated about a spanwise axis with suction through one wall and blowing through the opposite wall. Comparisons are made with experimental data and with results from a complete scalar-flux transport model. Conclusions are drawn from these results, and from a variety of other flows with system rotation, streamline curvature and swirl.   

Laminarization mechanisms in rotating channel flow

The influence of moderate rotation rate on turbulent channel flow is that the turbulence is suppressed on the stable side and augmented on the unstable side because of the Coriolis force. When the rotation increases the turbulent region becomes restricted to an increasingly thin zone near the unstable wall. For a rotation rate, $Ro>3$ (normalized by bulk velocity and channel height) inviscid linear theory yields a stable laminar flow (Bradshaw JFM 1969) and a recent DNS study (Grundestam et al., JFM 2008) indicates that the turbulent flow laminarizes for $Ro$ slightly below 3. By including viscous effects in a novel linear stability analysis the critical $Ro$ has been identified for different $Re$ and has been verified by DNS. The most unstable modes are tilted slightly oblique streamwise vortices clearly visible in the DNS. TS waves are unaffected by rotation and are always unstable for supercritical $Re$ but with a different length scale and an interesting interaction with the other modes.   

Numerical and mathematical approaches to analyses of water-circulator-induced flow in ponds

Pollution and muddiness of natural and artificial reservoirs that are used to supply water irrigation have become important problems in recent years. A rotating propeller operating at low speed set on a lake surface is proposed because it is expected that the device can induce vertical circulating flow by the centrifugal force. Although various experiments have shown clearly that the water quality in a lake is improved by operation of such equipment, the flow mechanism is not fully understood. This study is intended to characterize vertical circulating flow resulting from the propeller's action. To survey such a fluid motion numerically and mathematically in simple systems, the flow induced by the top boundary condition which forces a horizontal rotating flow is investigated here. Simulations of flows created by the top boundary condition are carried out to obtain steady-state solutions with various Reynolds numbers and aspect ratios.   

Rayleigh-Taylor instability in rotating volcanic umbrellas

We study the shape of an expanding volcanic umbrella that is turbulent and is rotating about a vertical axis though the center of the umbrella. We argue that the centrifugal forces associated with the rotation of the umbrella trigger a turbulent variant of the Rayleigh--Taylor instability. As a manifestation of this instability, the edge of the umbrella becomes wavy. As a test case, we consider the wavy umbrella from the climactic eruption of Mount Pinatubo on June 15, 1991.   

Premixed laminar flame propagation in a rotating vessel

Combustion in a swirling flow is devoted to burn lean mixture in spark ignition engines since it provides fuel economy and exhaust emission reduction. Therefore it is important to know the flame behavior under centrifugal forces. The flame in a rotating gas is modified by an aerodynamic mechanism due to action of centrifugal forces instead the laminar burning velocity due to chemical kinetics. The paper deals with important characteristics of eddy combustion mechanism such as: flame shape and propagation as a function of the rotation rate. Therefore pictures captured by a video camera are treated with the image processing toolbox from Matlab in order to establish the main characteristics of the flame kernel of a mixture propane -- air at different rotation rates ranging from 500 to 4000 rpm. It is observed that the flame propagates along the rotation axis and that the extinguishing of the flame is involved with the heat losses as soon the flame reaches the wall of the chamber. In addition, the flame shape is quite similar to the intrusion head of a light fluid penetrating into a stagnated heavy fluid.   

Session ET: Experimental Techniques III

Plasma Sensor Suite

Progress has been made towards the development of a new class of sensors which have the potential to overcome the temperature limitations found in conventional sensors, thus addressing an important measurement challenge faced in the measurement of high speed flows. The new approach is based on the a.c.-driven mass-flow laboratory plasma anemometer developed by Matlis et al. and uses a weakly ionized glow discharge encapsulated between two electrodes as the sensing element. These sensors will feature proven elements of the technology used in the plasma anemometer, but will be extended for high-temperature, multiparameter operation. The sensitivity to different parameters can be provided by the design and orientation of the electrodes. The objective is to replace conventional sensors which provide diagnostics in the laboratory but are known to fail in real-world applications with a suite of rugged sensors optimized to measure wall shear-stress, pressure, temperature, heat flux, mass-flow, strain, and gas species. The advantages of the plasma sensor are that it has no mechanical parts (like a pressure transducer diaphragm) to fatigue or break, its operation is insensitive to temperature, it has a very high frequency response (2MHz +), and its output can be received wirelessly. These advantages over other sensors makes it ideal for use in high speed flows.   

Falling Spheres in Sharply Stratified Fluids

We explore the motion of heavy spheres falling through a sharp salt stratified fluid layer in which an intriguing levitation phenomena is observed: the heavy sphere experiences a transient levitation in which the sphere descends through the sharp transition, stops, and rises back into the layer before ultimately returning to descent. Careful new measurements will be presented showing how the bounce amplitude depends upon layer thickness. The hydrodynamics, which involves a strong coupling between variable density fluid, and moving solid boundary, entrained, turbulently mixed fluid, and strong internal waves will be discussed. We will discuss exact and asymptotic calculations in potential flows yielding the potential energy associated with the sharp interface which may provide an arrestment criteria for the falling sphere.   

Rotational-Vibrational Raman Spectroscopy for the Measurement of Thermochemistry in Nonisobaric Flames

The present work examines the feasibility of Raman line imaging spectroscopy for multiscalar measurements of thermochemistry in reacting flows under varying pressure. Line imaging of the rotational and vibrational Raman scattering was combined onto a single detector, thus allowing for a single-shot measurement of major species, pressure, and temperature in turbulent nonisobaric conditions. The diagnostic technique also allows for the calculation of two important derived quantities of interest, namely a conserved scalar and its dissipation rate. Additionally the present work introduces ``canonical'' flows that are optically accessible and involve high-speed, supersonic combustion with pressure variation. Small-scale, nonreacting supersonic underexpanded jets have been studied experimentally, using both a Schlieren system and the Raman line imaging technique, and computationally, using a method of characteristics approach.   

A Two-Color Fluorescent Thermometry Technique for Microfluidic Systems

The feasibility of implementing a two-color laser-induced fluorescence (LIF) technique to study thermal transport at the microscale is investigated. A temperature-sensitive fluorescent dye (Rhodamine B) and a temperature-insensitive fluorescent dye (Sulforhodamine-101) are used in tandem to determine fluid temperature with high accuracy and low noise using a pulsed Nd:YAG laser as an illumination source. While the fluorescence intensity of the temperature-sensitive dye is proportional to temperature, it is also biased by variations in the illuminating intensity. Therefore, a second temperature-insensitive dye is utilized in order to compensate for such biases. Calibration of the two-color LIF system reveals that the two-dye mixture in water yields a temperature sensitivity of 2.7\%/K with volumetric illumination from the pulsed Nd:YAG laser. Additionally, the feasibility of this methodology for conducting temperature measurements is explored by measuring a steady-state temperature gradient generated across a microfluidic channel array by two large hot and cold reservoirs. These measurements yielded mean steady-state temperatures in the microchannels within $\pm0.3\,^{\circ}$C of the predicted temperatures, with experimental uncertainties in the range $\pm0.48\,^{\circ}$C to $\pm0.56\,^{\circ}$C. Finally, this technique is applied to study the thermal transport characteristics of laminar and transitional flow within a heated rectangular copper microchannel.   

Orthogonal Double View Digital Holographic Diagnostics for Random Motion of Micro Polymer Jet by Electrospinning

An experimental investigation of three-dimensional random behavior of polymer micro jet generated by electrospinning is described. Two frequency doubled Nd:YAG lasers were used as the light source and a commercial grade CCD sensor (Nikon D-70) was used for holograms recording. The two lasers could be fired with a pulse separation as small as 100 ns, and the two laser beams were aligned with three polarized beam splitter cubes. Orthogonal double-view and double-pulses were recorded on the same camera frame. The camera frame was split into two, and both of the halves of the frame were used for each view. Two objective lenses (M 5x) and two spatial filters (Pinhole $\sim $ 5$\mu $m) were used to generate expanding laser beams in the digital microscopic holography (DMH) optical setup. As the electric field ($\sim $20 kV) was intensified, the polymer solution formed a charged filament (or multiple filaments) from the tip of the Taylor cone. As the filament was accelerated toward the collector, its diameter was shrunk and axisymmetric disturbances grew further away from the exit. The polymer was randomly deposited on the collector as non woven microfiber.   

An Experimental Study of Turbulent Vortex Rings

Vortex rings in this laboratorial study is generated by pushing a piston through a tube with an orifice opening in water environment. In this paper, turbulent vortex rings upon formation was studied. Turbulence is produced by increasing the Reynolds number (based on slug model) and the piston stroke length over critical values, the vortex ring is then highly excited. Up to date, the only systematic study of turbulent vortex rings is by means of Laser Doppler Velocimeter (LDV), which can only give velocities at one point. The entire ring structure has to be visualized by some statistical treatments which maybe smear out some important physics inside a single turbulent vortex ring and can include errors because of dispersion. In this paper, turbulent vortex rings are studied by means of Stereoscopic Particle Image Velocimetry (PIV), which is able to give three-dimensional velocity field on the entire plan of interest and to overcome the disadvantages of LDV mentioned above.   

Facility documentation measurements in ``new'' 7-inch high-speed water tunnel

A small high-speed, variable-pressure water tunnel was relocated from St.\ Anthony Falls Laboratory (SAFL), U.\ of MN, to the University of New Hampshire (UNH). The water tunnel was originally designed and constructed at SAFL in the late 1940s for a series of physical model studies for the design of a 60-inch high-speed water tunnel at the Navy's David Taylor Model Basin (now Carderock Division, NSWC). The 1:10 scale model water tunnel initially had a circular cross section with 6 inch I.D. It was tested in many configurations through the 1950s, with different test sections (incl.\ a free jet) and features such as a gas absorption dome and a two-story tall resorber in the return leg. In the 1980s it was retrofitted with a new test section of 7 inch width/height with fillets, for an octagonal cross section of 47 sq.in. The water tunnel is fitted with an axial flow propeller pump, which at 1500 rpm is capable of producing flow rates of 280 l/s. Based on the original model study data (15 m/s in 6 inch TS), a maximum velocity greater than 9 m/s will be achievable in the current square/octagonal 7-inch test section. The water tunnel has been restored and connected to a compressor and vacuum pump. Preliminary velocity distribution and pressure measurements are presented and compared to the original model study results. Head losses are measured for the various tunnel parts and compared to the original configuration.   

Characteristics of Single Dielectric Barrier Discharge Plasma Actuators at Sub-atmospheric Pressures

Experiments were performed to determine the effect of static air pressure on the performance of single dielectric barrier discharge (SDBD) plasma actuators. This was motivated by the need for expanding the validity of numerical models for plasma actuators to include changes in air properties. The performance metric chosen for the actuator was the amount of the thrust force generated by the actuator. The experimental setup consisted of a plasma actuator mounted on a flat surface that was standing vertically on a digital scale placed in a vacuum vessel. The dependence of the generated thrust on the air pressure was then documented, for a range of input ac voltages and frequencies, the area of the covered electrode, and the dielectric characteristics. The pressures ranged from atmospheric to 10in-Hg absolute. As the pressure was lowered, the threshold voltage to ionize the air decreased, thereby generating thrust at lower voltages. Up to the maximum thrust limit, the thrust was proportional to the applied voltage to the 7/2 power previously observed at atmospheric pressure. The maximum thrust could be limited by having too small of a covered electrode area, or by a transition from a diffuse plasma to concentrated filaments. As the pressure was lowered, filaments occur at lower input voltages. A summary map of operation is presented.   

A newly developed optical fiber probe processed by femtosecond pulses for a measurement of micro bubbles and droplets

Optical fiber probes can be applied to an efficient and reliable measurement for gas-liquid two-phase flows. This measurement technique enables a real-time and high-accuracy measurement of characterization of bubbles/droplets. In this study, we newly developed an optical fiber probe processed by femtosecond pulses (fs-Probe) in order to measure tens-of-micrometers bubbles/droplets. The new fs-Probe whose detecting point is formed at tens micrometer from its tip using fs pulses can detect gas-liquid interface velocity. We demonstrated a measurement of millimeters size bubbles/droplets and discussed its capability for measurement of velocities and diameters of them using fs-Probe. Furthermore, we visualized contact processes between fs-Probe and bubbles/droplets on the measurement. We discussed the relation between output signal characteristics and contact processes depending on a geometry of fs-Probe, wettability, and so on.   

Session EU: Vortex Flows III

Linear stability of relative equilibria of identical point vortices

The linear stability analysis of relative equilibria of $N$ identical point vortices is reconsidered. First, we show that the problem can be reduced to evaluating the eigenvalues and eigenvectors of a certain Hermitean matrix. Then, the exact solution of the linear stability problem for the collinear relative equilibria is given following work by Calogero and Bruschi from the late 1970's. We consider the possibility of extending these largely algebraic results to general configurations, and we explore the class of relative equilibria for which such calculations may be carried through. The regular polygons certainly fall in this class, but the known families of nested, regular polygons may also allow at least a partial analytical stability analysis. The role of the generating polynomial in stability calculations is explored, and also the link between stability of a relative equilibrium and the existence of an axis of symmetry of the configuration. Such a link was suggested to the author by D. L. Vainchtein several years ago.   

Structures in the wake of a long flexible cylinder undergoing vortex-induced vibrations

An investigation of the vortex structures in the wake of a long flexible cylinder responding at low mode numbers is presented. The experiments consisted of a cylinder model instrumented with strain gauges, with an external diameter of 16 mm and a total length of 1.5 m giving an aspect ratio of about 94. Reduced velocities based on the fundamental natural frequency up to 16 were reached, with Reynolds numbers up to 12000. The mass ratio was 1.8 (mass divided by mass of displaced fluid) and the combined mass-damping parameter was about 0.05. A detailed investigation of the strain signals, focused on cross-flow and in-line amplitudes, x-y trajectories and phase synchronisation, dominant frequencies, modal amplitudes and drag coefficients, has already shown the dynamic response of the model. Particle Image Velocimetry interrogations were done at two different positions along the length of the model, in order to observe the spanwise variation of the vortex structures and here, a fuzzy clustering technique has been used to identify them.   

Velocity statistics distinguish quantum from classical turbulence

We present experimental studies of the velocity statistics of decaying quantum turbulence in superfluid $^{4}$He. By analyzing the trajectories of solid hydrogen tracers, we observe velocity distributions with strongly non-Gaussian 1/$v^{3}$ power-law tails. These statistics differ from the near-Gaussian distributions observed in homogenous and isotropic classical turbulence. We attribute the distinction with classical turbulence to quantized vortex dynamics and reconnection, which produces high, atypical velocities. We identify and analyze the dynamics of approximately 40,000 individual reconnection events and show by simple scaling arguments that they produce the observed power-law velocity tails. The potential implications for multifractal models of classical turbulence are discussed.   

Azimuthal Instability of a Vortex Ring Computed by a Vortex Sheet Panel Method

A Lagrangian panel method is presented for vortex sheet motion in 3D flow. The sheet is represented by a set of quadrilateral panels with a quadtree structure. The panels have active particles carrying circulation and passive particles used for adaptive panel subdivision. The Biot-Savart kernel is regularized and the particle velocity is computed using a treecode. The method is applied to study the azimuthal instability of a vortex ring. Results are presented showing the following sequence of events: wavy deformation of the ring axis, first collapse of the core, appearance of secondary structures wrapped around the core, second collapse of the core out of phase with first collapse, and radial ejection of ringlets. These events are accompanied by local axial flow in the core.   

Mixing in Oscillatory Flows Generated by Electromagnetic Forcing

The continuously driven laminar flow produced by an oscillating electromagnetic force in a thin electrolytic fluid layer is studied experimentally and numerically. The flow is generated by the interaction of an injected alternate electric current and a steady magnetic dipole field normal to the layer. Alternate currents with frequencies and amplitudes in the range of 10-50 mHz and 1-5 mA, respectively, are explored. The electromagnetic force stirs the fluid and produces an oscillating dipole vortex that enhances the fluid mixing. A numerical 2D solution of the full MHD equations that considers an analytical expression to model the non-uniform magnetic field is obtained. The mixing efficiency is measured by the use of a new semi-Lagrangian numerical scheme which allows to solve the diffusion of a scalar at very high Peclet numbers (up to infinite). This method gives the scalar field as a function of time and also allows to reconstruct the PDF of the scalar analytically as a measure of the degree of mixing. Numerical results show a good qualitative agreement with the experiments. The mixing can be enhanced even more when an array of magnetic dipole fields is considered.   

Three-dimensional vortex dynamics in oscillatory flow separation

The three-dimensional (3D) dynamics of coherent vortices and their interactions in an oscillatory flow past an obstacle are examined experimentally. The main focus is in the low Keulegan-Carpenter number range (KC $<$ 5), and for moderate Reynolds numbers (2000 $<$ Re $<$ 10000). This parameter space corresponds to the vortex pairing regime, in which vortex dipoles can propagate away from the boundary and provide a direct mechanism for the transfer of momentum and enstrophy to the outer region. The vortex breakdown mechanisms are elucidated via flow visualizations and digital particle image velocimetry (DPIV). Volumetric dye visualizations reveal complex 3D vortex interactions and explosive vortex breakdown. These visualizations suggest that the initial instability of the spanwise vortices is an elliptical instability of the strained vortex cores. This is confirmed by detailed DPIV measurements which have identified the elliptical instability eigenmode. The periodic features of the flow, including the energetics and enstrophy dynamics, are examined using phase-averaging. The phase-averaged dynamics are then interpreted in light of the results obtained from the time domain observations of the vortex instabilities.   

Unstable vortical flow produced by an oscillatory non-uniform magnetic field

We report two-dimensional numerical simulations of an electromagnetically forced flow, produced by the interaction of an imposed direct electrical current and a localized time-dependent magnetic field. The field is produced by a permanent dipolar magnet that oscillates harmonically along a direction parallel to the injected current with fixed frequency and amplitude. When the magnet remains steady, the localized Lorentz force produces a vortex dipole with a jet-like flow along the symmetry line in the direction of the force, perpendicular to both the injected current and the normal magnetic field. For certain oscillation frequencies of the magnet, the jet-like flow is destabilized and local vortical structures, formed in the neighborhood of the magnet, are swept away periodically by the base flow. Numerical results show a qualitative agreement with preliminary experiments performed in a shallow electrolitic fluid layer.   

The Breakdown of Compressible Vortex Flows

The theoretical foundation for the global analysis of the dynamics of vortex flows is extended to the case of subsonic compressible swirling flows in a finite-length, straight, circular pipe. A novel nonlinear partial differential equation for the solution of the flow stream function is developed in terms of the incoming specific total enthalpy, specific entropy, and circulation functions. Solutions of the resulting nonlinear ordinary differential equation for the columnar case together with a newly derived flow-force condition describe the flow outlet state. These solutions are used to form the bifurcation diagrams of steady, compressible flows with swirl as the swirl level is increased. These provide theoretical predictions of the critical swirl ratio for the first appearance of vortex breakdown as function of Mach number.   

Radiative instability of a stratified Lamb-Oseen vortex

Le Diz\`{e}s and Billant have shown that a Lamb-Oseen vortex with a strong stratification along the vortex axis is inviscidly unstable. The unstable modes are radiative and extend far from the vortex core. In this work, our objective is to analyse the effects of viscosity and stratification on these unstable modes. A linear temporal stability analysis is performed using a Chebychev collocation spectral code. The equations are the linearized Navier-Stokes equations with Boussinesq approximation. We show that the instability is the strongest for a Froude number around one and that the vortex remains unstable for all Reynolds numbers. We shall explain that the stabilization for small Froude number is due to the scaling in $\frac{1}{F}$ of the most unstable wavenumber and that the stabilization for large Froude number is linked to the appearance of a critical layer. For intermediate Froude numbers, another instability mechanism due to resonances between radiative modes and Kelvin modes has been discovered .   

Searching for Euler Singularities Through Vortex Filaments

Numerical simulations over the past decade have suggested that if a singularity of the Euler equation exists, it is likely to be unstable. The question therefore becomes how to devise schemes for searching for unstable singular solutions of the initial value problem. I will summarize our recent efforts to carry out such searches using interacting vortex filaments.   

Session EV: Geophysical Flows: Mixing

Transient growth of perturbations on stratified mixing layers

We perform a study on the optimal perturbations developing on mixing layers. The basicly 2-dimensional Kelvin-Helmoltz instability that develops in this type of flow is known to become unstable leading to the development of streamwise vortices and eventually turbulence. This process is essential in many geophysical and industrial flows, where it greatly influences mixing and dissipation. We explore different types of 3-D optimal perturbations by means of numerical integration of the direct and adjoint Navier-Stokes equations in the Boussinesq approximation. Knowledge of these optimal perturbations reveals characteristics of the flow receptivity and helps to understand the different physical mechanisms present in its dynamics. These are key aspects in order to predict and control the flow evolution.   

LES of mixing in coastal areas

Large eddy simulations of near shore mixing are carried out using a new large-scale model, LES-COAST. The model integrates the Boussinesq form of the NS equations using a curvilinear formulation of the fractional step method. Complex geometry is reproduced with a combination of curvilinear mesh and immersed boundaries. Anisotropy of the problem ($\Delta x_{vert}/\Delta x_{hor} \sim 10^{-2}$) has required a two eddy-viscosities model. Specifically we use a mixed model, composed of an anisotropic scale-similar part and an eddy viscosity, Smagorinsky part. Two eddy-viscosities are used, $\nu_{T,v/h}=(C_{v/h} \Delta_{v/h})^2 |\overline{S}_ {v/h}|$ respectively in the two directions. The quantities $\Delta_{v/h}$ are chosen proportional to the local grid spacings in the two directions. Density stratification is also considered using a very simple SGS model, based on the assumption that $Pr_T = Sc_T =1$. The algorithm is being used for real applications. The following studies will be discussed: the intrusion of fresh water of the Tevere river in the Tirreno sea; mixing in the Muggia Bay (Region of Trieste) under the action of the breeze forcing. Results have clearly shown the reliability of new- generation LES large-scale models for applications in problems with horizontal and vertical scales respectively of the order of $10 km$ and $50 m$.   

Mixed surface layer deepening by Langmuir circulation and shear turbulence

We consider upper layer mixing by mixing processes such as by shear generated turbulence and by Langmuir circulation that are relevant to the surface mixed layer deepening in oceans and large lakes. In order to gain insight into the mixing process by continuously driven horizontal vortices, such as Langmuir circulation, with respect to mixing by shear generated turbulence, we consider recent experimental results on the mixing at a two-layer fluid interface by Taylor vortices. Relating the vortex induced mixing and the shear induced mixing to a surface friction-velocity $u^*$, we show that up to a Richardson number of $Ri_*= \frac{\Delta b h}{u_*^2} \leq 80$ layer deepening is dominated by shear turbulence, whereas it is taken over by Langmuir circulation for $Ri_* > 80$. The mixing efficiency of Langmuir circulation decreases gradually with increasing Richardson number, implying significant mixing also for higher Richardson numbers. As a consequence, there is no critical Froude-number criterion for the arrest of mixing by Langmuir cells as has been suggested previously. In agreement with in situ observations, the initial upper layer deepening is dominated by shear turbulence, and the subsequent principal layer deepening is due to Langmuir circulation.   

Large-eddy simulation of tidally driven mixing in estuaries

The estuarine boundary layer is affected by the horizontal density gradient and exhibit mixing and restratification over a tidal cycle. Large Eddy Simulation(LES) is used to investigate the physics controlling the entrainment and growth of the boundary layer during the flood tide and the restratification during the ebb tide. While small-scale turbulent eddies generated by the bottom stress are the major flux-carriers in the well-mixed bottom boundary layer, relatively large spanwise vortices, dominate salt and momentum fluxes in the outer part of the bottom boundary layer between mid-flood and mid-ebb. Turbulent kinetic energy, momentum flux and bottom stress show a strong flood-ebb asymmetry. Strong bed stress during the flood tide causes the entrainment and growth of the bottom boundary layer whereas tidal straining during the ebb tide causes restratification in the water column. Additional LES runs conducted by switching off the baroclinic pressure gradient term in the momentum equation and the tidal straining term in the salinity equation show that the baroclinic pressure gradient is the main mechanism responsible for generating the flood-ebb asymmetry in turbulent mixing.   

Gas transfer through the air-water interface in LES of Langmuir circulation in shallow water

Over the past century the study of gas exchange rates between the atmosphere and the ocean has received increased attention because of concern about the fate of slightly soluble, greenhouse gases such as CO$_{2}$ released into the atmosphere. Of recent interest is the oceanic uptake of CO$_{2}$ along US shallow water coastal regions (e.g. see http://www.nacarbon.org). We present surface gas transfer results from large-eddy simulation (LES) of wind-driven shallow water flow with and without wave effects. Wave effects, parameterized by the well-known Craik-Leibovich vortex force, lead to the generation of Langmuir circulation (LC), serving as a mechanism for surface renewal of low concentration fluid. Our computations are motivated by the infrared imagery of Marmorino et al. (2004) suggesting that LC can affect gas transfer across the surface through straining and stretching of the gas concentration boundary layer. Preliminary LES shows that shallow water LC can increase the surface gas transfer rate by about 30 percent. Here we will focus on the accuracy of surface renewal models in predicting gas transfer velocity, a measure of gas transfer efficiency, in the presence of LC. Gas transfer velocity predicted by the surface renewal models will be compared to the prediction obtained directly from the LES.   

Transition in energy spectrum of stably stratified turbulence

Energy spectra for forced stably stratified turbulence are investigated numerically using the Direct Numerical Simulations (DNS) with $1024^3$ grid points. The calculation is done by solving the 3D Navier-Stokes equations under the Boussinesq approximation pseudo-spectrally. Using toroidal-poloidal decomposition (Craya-Herring decomposition), the velocity field is divided into the vortex mode ($\phi_1$) and the wave mode ($\phi_2$). With the initial kinetic energy being zero, the $\phi_1$ spectra as a function of horizontal wave numbers, $k_{\perp}$, first develops a $k_{\perp}^{- 3}$ spectrum for the whole $k_{\perp}$ range, and then $k_{\perp}^{-5/3}$ part appears with rather a sharp transition wave number. Meanwhile the $\phi_2$ spectra shows $k_{\perp}^{-2}$ first, and then $k_{\perp}^{-5/3}$ part appears with the same transition wave number. Spectra for different values of the Brunt-- V\"ais\"al\"a frequency $N^2=1, 10, 50 {\rm and} 100$ are investigated, and we found that the $k_{\perp}^{-3}$ part at the large scale in the $phi_1$ spectra is characterized as 2d turbulence, and that the whole spectrum has the form of $E(k_{\perp})=a\eta_{\perp\phi_1}^{2/3}k_{\perp}^{-3}+C_K \varepsilon_{\perp\phi_1}^{2/3}k_{\perp}^{- 5/3}$ where $\eta_{\perp\phi_1}$ is the horizontal enstrophy dissipation based on the $\phi_1$ energy, and $\varepsilon_{\perp\phi_1}$ is the horizontal $\phi_1$ energy dissipation. Meanwhile we obtain $E(k_{\perp})=b\sqrt{N\varepsilon_{\perp\phi_2}} k_{\perp}^{-2} +C_K\varepsilon_{\perp\phi_2}^{2/3}k_{\perp}^{-5/3}$ for $\phi_2$ where $\varepsilon_{\perp\phi_2}$ is the horizontal $\phi_2$ energy dissipation. For both cases, $C_K\approx 1.2\sim2.0$ is obtained being close to the Kolmogorov constant.   

Turbulence Identification in Stably Stratified Flows

Flows subject to stable density stratification often occur in natural settings such as the ocean and atmosphere. Unlike turbulence in homogeneous flows, when turbulence occurs in density stratified flows it does so in localized, intermittent patches. It is in these turbulent patches that important features of the flow occur, e.g., mixing of species, dissipation of energy. As such, it would be beneficial to be able to identify where turbulent patches occur. Turbulence is a three dimensional phenomena associated with flow vorticity. In this talk, several published vortex identification methods are employed to identify turbulent patches from three dimensional high resolution direct numerical simulations (DNS) of density stratified flows. Vortex identification methods include those based on the second invariant as well as the eigenvalues of the velocity gradient tensor $\nabla v$. The use of DNS allows the results of the identification methods to be compared with actual flow dynamics, such as areas of high energy dissipation rate and enstrophy. Results suggest that while each vortex identification method is able to efficiently extract areas of turbulent activity, they depend on a subjective threshold criterion for meaningful results.   

Direct numerical simulations of stratified turbulence at higher Reynolds numbers

Stratified turbulence\footnote{D.K.\ Lilly, 1983, {\em J.Atmos.\ Sci.}, {\bf 40}, 749.} is a flow dominated by stable density stratification, and is characterized by low internal Froude numbers and high Reynolds numbers; such parameter regimes occur often in the atmosphere and oceans. We report on direct numerical simulations of stratified turbulence at very high resolution (up to 2048$^3$ grid points) enabling, in particular, fairly high Reynolds numbers to be achieved, well above the critical value at which instabilities and smaller-scale turbulence are expected to occur. A highly parallelized 3D Fourier pseudo-spectral code based on a ``pencils'' domain decomposition is used to solve the Navier-Stokes equations, and the Boussinesq approximation is made in accounting for stable density stratification. Both decaying and statistically stationary, forced flows are simulated. We examine various features of the flows, including the spectral energy transfer, horizontal fluid particle dispersion, mechanisms leading to instabilities and smaller-scale turbulence, and the parameterization of these flows for larger-scale models.   

Wind-driven turbulent oscillating channel flow under a stable stratification

An LES investigation of the oscillating channel flow subjected to a constant wind stress revealed strong shear production of the turbulence in the wall and free-surface layers. The flow during most of the phases is well described by a combination of two log-law boundary layers. If the driving oscillating pressure gradient and wind stress are aligned turbulent streaks are observed in the entire domain. For a wind stress at a $45^{\circ}$ angle, the streaks in the free-surface and wall layer are not aligned. This results to more isotropic turbulence in the interior. We aim to investigate the effects if a stable stratification is added to this model problem for estuarine flows. The stratification is caused by a constant heat flux at the free-surface. Previous studies observed a strong stratification in the free-surface layer, which suppresses turbulent fluctuations. This might lead to a partially decoupling of the top and bottom layers. Moreover, internal waves could stir up the dynamics of the flow.   

Two-layer continuously stratified flow

Continuously stratified flow in two layers is considered. The interface between layers is defined by a jump in the Brunt-Vaisala frequency, N, and a sudden shift in the direction of the mean horizontal wind. This configuration is suggested by recent observations over isolated mountains showing the presence of very large amplitude internal waves. A coordinate system is chosen that makes this background state equivelent to the two-dimensional Kelvin-Helmholtz problem, now with the jump in N. Previous work has shown that resonant over-reflection, where the mean flow creates waves without any incident wave, may occur even with constant N throughout. Linear theory shows that the addition of the jump in N results in a larger interval of wavenumbers for resonant over-reflection. Linear and weakly nonlinear theory do not show any evidence of larger amplitude motion near the interface, and this feature of the experiments may be a strongly nonlinear phenomena. Numerical simulation with this background state shows that waves are not spontaneously created in the parameter region where resonant over-reflection should occur, but must be initiated with some type of disturbance. The results depend strongly on the form and strength of this disturbance. Internal waves and incoherent noise have been separately treated as disturbances. The results indicate that resonant over-reflection is one plausible explanation for the large amplitude waves that were found in the measurements.   

Session EW: Mini-Symposium: Lagrangian Coherent Structures in Fluid Flows

Lagrangian Coherent Structures: Introduction and Applications

Lagrangian Coherent Structures (LCS) are distinguished material surfaces that organize the global mixing and transport of fluid particles. While these surfaces define a skeleton that governs all mixing events even in turbulent flows, LCS remain hidden to traditional coherent structure detecting methods based on vorticity, pressure, streamlines, or other frame-dependent quantities. Here we review the mathematical foundations of LCS and discuss how they can be located in an objective (frame-independent) way in complex flows. We also highlight applications to experimental and numerical flow data analysis. Examples include two-dimensional rotating turbulence, hairpin vortices in three-dimensional numerical simulations, passive ocean pollution control and atmospheric clear-air turbulence detection. Some of these examples will be discussed in more detail in later talks within this minisymposium.   

Lagrangian Coherent Structures in Blood Flow

Knowledge of fluid transport is particularly compelling in understanding the function of cardiovascular processes. Transport of chemicals, cells, and compounds in the vascular system is influenced by local flow structures in large vessels. Local flow features can also induce cell-signaling pathways and biologic response critical to maintaining health or disease progression. Complex vessel geometry, the pulsatile pumping of blood, and low Reynolds number turbulence leads to complex flow features in large vessels. However, we are gaining the ability to study transport in large vessels with unprecedented detail, which is in part allowing us to broaden the ``shear-centric'' view of hemodynamics. In this talk we will describe the application of computational fluid mechanics and the computation of Lagrangian coherent structures (LCS) to study transport in various cardiovascular applications. We will discuss some of the challenges of this work and some results of computing LCS in several regions of the vascular system. In collaboration with Charles Taylor, Stanford University.   

Lagrangian Coherent Structures in Three-Dimensional Fluid Flows

We use Finite-Time Lyapunov Exponents (FTLE) to identify Lagrangian Coherent Structures in several three-dimensional flows, including a single isolated hairpin vortex, and a fully developed turbulent flow. These results are compared with commonly used Eulerian criteria for coherent vortices. Despite additional computational cost, the FTLE method has several advantages over Eulerian methods, including greater detail and the ability to define structure boundaries without relying on a preselected threshold. We also describe an application involving transport of charged particles in a toroidal magnetic field, which illustrates some limitations of the standard FTLE method when applied to a compressible medium. In collaboration with Melissa Green and Peter Norgaard, Princeton University.   

Lobe Dynamics in Hurricanes

The classical theory of \textit{lobe dynamics} describes transport across a homoclinic trajectory in the flow of a periodically perturbed dynamical system. The flow during a single period of the perturbation defines a discrete flow map called the Poincar\'e map. Hyperbolic fixed points of the Poincar\'e map exhibit stable and unstable manifolds whose intersections define lobes and the \textit{homoclinic tangle} of chaotic dynamics. This elegant theory exists only for two-dimensional flows with periodic or quasi-periodic time-dependence. We demonstrate that Lagrangian Coherent Structures (LCS) provide an effective method for visualizing lobe dynamics in continuous flows with arbitrary time-dependence in both two and three dimensions. This method applied to reanalysis flow data for hurricanes indicates that transport in the synoptic scale flow is dominated by lobe dynamics. Furthermore, visualization of the LCS near the eyewall reveals the Lagrangian transport structures responsible for the process of eyewall replacement, a process that has been widely identified in the hurricane forecasting community as the principal mechanism for fluctuations in hurricane intensity. In collaboration with Jerrold Marsden, Caltech.   

Lagrangian Coherent Structures and the Kinematic Theory of Unsteady Separation

The problem of determining where unsteady fluid flow separates from a no-slip boundary is long-standing and challenging. Despite some landmark advances, a practical criterion remains elusive. Recent theoretical developments in Lagrangian Coherent Structures, however, have a suggested a new approach to the problem. We review these ideas, and present the results of a combined experimental and numerical study of unsteady flow separation for a canonical flow geometry. Experimentally-detected material spikes are directly compared to separation profiles predicted from numerical shear-stress and pressure data. For steady, periodic, quasi-periodic and random forcing, fixed separation is observed, and experimental observations and theoretical predictions are in close agreement. The transition from fixed to moving separation is also reported, and methods for dealing with this scenario are discussed. In collaboration with Matthew Weldon, Gustaff Jacobs, San Diego State University; and George Haller, Morgan Stanley.   

The ``upstream wake'' of swimming and flying animals revealed by Lagrangian coherent structures

The interaction between swimming and flying animals and their fluid environments generates downstream wake structures such as vortices. In most studies, the upstream flow in front of the animal is neglected. In this study, we use Lagrangian coherent structures (LCS) to demonstrate the existence of upstream fluid structures even though the upstream flow is quiescent or possesses a uniform incoming velocity. Using a computational model, the flow generated by a swimmer (an oscillating flexible plate) is simulated and an LCS analysis is applied to the flow to identify the upstream fluid structures from the forward finite-time Lyapunov exponent (FTLE) field. These upstream structures show the exact portion of fluid that is going to interact with the swimmer. A mass flow rate is then defined based on the upstream structures and a metric for propulsive efficiency is established using the mass flow rate and the kinematics of the swimmer. We propose that the unsteady mass flow rate defined by the `upstream wake' can be used as a metric to measure and objectively compare the efficiency of locomotion in water and air. In collaboration with Jifeng Peng, Graduate Aeronautics Laboratories and Bioengineering.