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Volume 11, Issue 2, February 1999
 LETTERS


Dynamic testing of subgrid models in large eddy simulation based on the Germano identity
View Description Hide DescriptionNormally the Germano identity is used in large eddy simulation(LES) of turbulent flows to evaluate model coefficients so as to minimize the square error associated with replacing a particular model in the identity. However, one can also explicitly evaluate this error and thus establish the accuracy with which a particular model is capable of reproducing the flow features at scales between the grid and test filters. This idea is tested a priori based on tophat filtered experimental data in the far field of a round jet [Liu et al., J. Fluid Mech. 275, 83 (1994)]. Of the models considered, the mixed nonlinear model yields the smallest error. This approach offers the capability to dynamically choose among available parametrizations, based only on the resolved fields during LES.

Vorticity flux control for a turbulent channel flow
View Description Hide DescriptionA feedback control algorithm using wall only information has been applied in simulations of low Reynolds numberturbulent channel flow. The present control scheme is based on the manipulation of the vorticity flux components, which can be obtained as a function of time by measuring the instantaneous pressure at the wall and calculating its gradient. The strength of the unsteady mass transpiration actuators can be derived explicitly by inverting a system of equations whose terms depend on the relative locations of the sensors and actuators. The results of the simulations indicate a large (up to 40%) drag reduction. Moreover it appears that using the present methodology openloop control laws can be devised.

 ARTICLES


Stokes flow in the presence of a planar interface covered with incompressible surfactant
View Description Hide DescriptionThe Lorentz solution for Stokes flow in the presence of a plane wall is generalized to a surfactantcovered interface, and the Stokeslet solution is derived. The result is used to describe the motion of a small particle in the presence of the interface. The surfactant is insoluble and nondiffusing. The effects of surface viscosity are included. Small variations in surfactant concentration are assumed; this assumption usually holds under small capillary number conditions.

Correlations between dispersion and structure in porous media probed by nuclear magnetic resonance
View Description Hide DescriptionMagnetic Resonance Imaging(MRI) and Pulsed Gradient Stimulated Echo (PGSTE) Nuclear Magnetic Resonance(NMR)experiments have been used to probe structure and dispersion in a model porous system formed from a packed bed of spherical particles. The structure of the pore space is characterized from the MRIimages by determining radial distribution functions for the pore space. The PGSTE experiments yield an average displacement propagator from which the variance of the average molecular displacement and dispersion coefficient are determined at a range of times over which the flow develops. Experiments have been performed over a wide range of Péclet number and flow velocity. The behavior of the dispersion is shown to be closely related to the structure of the pore space. Dispersion transverse to the direction of superficial flow is dominated by Taylor dispersion. In the axial direction, nonFickian effects become important, even for flow within a single pore. The axial dispersion coefficient approaches an asymptotic limit characterized by a scale length that corresponds to the poretopacking correlation length in the direction of flow, suggesting that the nonFickian dispersion reaches a limiting behavior after just one mixing between streams merging from two interconnected pores.

Ensembleaverage versus suspensionscale Cauchy continuummechanical definitions of stress in polarized suspensions: Global homogenization of a dilute suspension of dipolar spherical particles
View Description Hide DescriptionThe macroscale rheological properties of a dilute suspension exposed to a uniform external field and composed of identical, rigid, inhomogeneous, dipolar, spherical particles dispersed in an incompressible Newtonian fluid and possessing the same mean density as the latter fluid are derived from knowledge of its microscale properties by applying a global ensembleaveraging technique. Each dipole, which is permanently embedded in the particle, is assumed to be generated by the presence of an inhomogeneous external bodyforce field in the particle interior resulting from the action of the uniform external field on an inhomogeneous distribution of interior matter. It is shown that although the ensembleaverage stress tensor is symmetric, the suspension nevertheless behaves macroscopically as if it possessed an asymmetric stress tensor. This seeming contradiction can be traced to the fact that the average body force acting on the contents of any arbitrarily drawn volume lying in the interior of the suspension does not vanish despite the fact that each particle is “neutrally buoyant.” That this force is not zero stems from the fact that some particles necessarily straddle the closed surface bounding that volume, and that the distribution of external body forces over the interiors of these particles is nonuniform. As such, that portion of the spherical particle lying outside of the surface enclosing the domain exerts a force on the remaining portion of the sphere lying within that domain. We then demonstrate that the natural macroscopic model, which is derived by equating the divergence of the suspensionscale stress appearing in that model to the ensembleaverage external bodyforce field, and which predicts a symmetric stress tensor, is macroscopically deficient with respect to the more intuitive asymmetric stress model usually proposed by continuum mechanicians for such a suspension. It is shown that the latter, continuummechanical model recovers all the physically interesting properties of the suspension.

On acoustic cavitation of slightly subcritical bubbles
View Description Hide DescriptionThe classical Blake threshold indicates the onset of quasistatic evolution leading to cavitation for gas bubbles in liquids. When the mean pressure in the liquid is reduced to a value below the vapor pressure, the Blake analysis identifies a critical radius which separates quasistatically stable bubbles from those which would cavitate. In this work, we analyze the cavitation threshold for radially symmetric bubbles whose radii are slightly less than the Blake critical radius, in the presence of timeperiodic acoustic pressure fields. A distinguished limit equation is derived that predicts the threshold for cavitation for a wide range of liquid viscosities and forcing frequencies. This equation also yields frequencyamplitude response curves. Moreover, for fixed liquid viscosity, our study identifies the frequency that yields the minimal forcing amplitude sufficient to initiate cavitation. Numerical simulations of the full Rayleigh–Plesset equation confirm the accuracy of these predictions. Finally, the implications of these findings for acoustic pressure fields that consist of two frequencies will be discussed.

Simulation of threedimensional flow around a square cylinder at moderate Reynolds numbers
View Description Hide DescriptionDirect numerical simulations of twodimensional (2D) and 3D unsteady flow around a square cylinder for moderate Reynolds numbers (Re=150–500) are performed, employing an implicit fractional step method finitevolume code with secondorder accuracy in space and time. The simulations, which are carried out with a blockage ratio of 5.6%, indicate a transition from 2D to 3D shedding flow between Re=150 and Re=200. Both spanwise instability modes, A and B, are present in the wake transitional process, similar to the flow around a circular cylinder. However, seemingly in contrast to a circular cylinder, the transitional flow around a square cylinder exhibits a phenomenon of distinct lowfrequency force pulsations (Re=200–300). For 3D simulations, the Strouhal number and the mean drag coefficient are in general agreement with existing experiments. Between Re=300 and 500, an increase in the spanwise coupling of fluctuating forces is indicated. The influence of the spanwise aspect ratio using periodic boundary conditions, a finer grid, and a finer time step is also investigated.

The growth of leadingedge distortions on a viscous sheet
View Description Hide DescriptionThe results of a set of experiments to determine some features of the undulations that develop on the leading edge of a sheet of fluid on an inclined plane are presented. A range of fluid viscosities, fluid volumes, and plate angles was used. In nearly all the cases, the observed disturbances had a triangular or sawtooth shape, with only a single example of a finger or parallelsided shape appearing. The powerlaw exponents for the position down the plate of both the tips of the disturbances and their roots, that is, the points where they join the uniform sheet above them, were calculated from a series of photographs, and the corresponding wavelengths measured. The exponents are broadly in line with those that can be deduced from a simple model including viscosity, gravity, and volume flux, and ignoring all capillary effects. This conclusion suggests that the criterion for distinguishing the two types of disturbance does not depend on the global dynamics of the developing structures, and that a detailed analysis of the tip and root regions, where capillarity will be significant, is needed for further progress to be made.

Streamline topologies near simple degenerate critical points in twodimensional flow away from boundaries
View Description Hide DescriptionStreamline patterns and their bifurcations in twodimensional incompressible flow are investigated from a topological point of view. The velocity field is expanded at a point in the fluid, and the expansion coefficients are considered as bifurcation parameters. A series of nonlinear coordinate changes results in a much simplified system of differential equations for the streamlines (a normal form) encapsulating all the features of the original system. From this, we obtain a complete description of bifurcations up to codimension three close to a simple linear degeneracy. As a special case we develop the theory for flows with reflectional symmetry. We show that all the patterns obtained can be realized in steady Navier–Stokes or Stokes flow, but an unresolved difficulty arises in the symmetric case for Navier–Stokes flow. The theory is applied to the patterns and bifurcations found numerically in two recent studies of Stokes flow in confined domains.

Inertial particle motion in a Taylor Couette rotating filter
View Description Hide DescriptionIn rotating filtration, which is based on supercritical cylindrical Couette flow with a rotating porous inner cylinder, the motion of particles in the suspension depends on both centrifugal sedimentation and transport due to the vortical motion of Taylor vortices. We have simulated the motion of dilute, rigid, spherical particles in Taylor Couette flow using computational particle tracking in an analytic velocity field for flow just above the transition to supercritical Taylor vortexflow. Neutrally buoyant particles follow fluid streamlines closely, but not exactly due to the curvature of the velocity field very near the particle. The motion of particles with a density greater than the fluid is primarily determined by the competition between the centrifugal sedimentation related to the primary cylindrical Couette flow and the secondary radial and axial transport of the Taylor vortexflow. As a result, particles that start near the outer edge of a vortex spiral inward toward a limit cycle orbit. Likewise, particles initially near the center of a vortex spiral outward toward the same limit cycle orbit. Even when a small radially inward throughflow is imposed, particles can remain trapped in retention zones that are away from the wall of the annulus. Consequently, the dynamics of the flow field result in particles tending to be transported away from the porous inner cylinder, thus contributing to the antiplugging character of rotating filter devices.

The structure of energy conserving loworder models
View Description Hide DescriptionGeneral principles for developing physically sound loworder models in fluid dynamics are discussed. It is shown that loworder models with energy conserving properties of the original equations that arise in various important problems (Rayleigh–Bénard convection,rotating fluid,magnetohydrodynamicconvection) may be presented in the form of coupled threemode systems known in mechanics as Volterra gyrostats (plus terms describing forcing and friction). When these models are expanded by increasing the order of approximation or by adding new physical mechanisms, they still have the structure of coupled gyrostats. Conversely, when a loworder model cannot be transformed into coupled gyrostats, this may indicate that its conservation properties should be questioned. For instance, while the widely used (in convection studies) Howard–Krishnamurti model [J. Fluid Mech. 170, 385 (1986)] is not energy conserving and does not have a gyrostatic form, its simple extension to a system of coupled gyrostats possesses inviscid energy invariants. Integrals of motion in the fluid are shown to have their analogs in systems of coupled gyrostats. Thus, giving loworder models a gyrostatic structure ensures that certain important physics from the original fluid dynamicalequations is retained. Finally, this approach is used to develop a coupled gyrostat model of turbulence that exhibits Kolmogorov spectral behavior.

Stability of a stratified viscous shear flow in a tilted tube
View Description Hide DescriptionThe present investigation is concerned with the effects of viscosity on the stability of a bounded stratified shear flow with Prandtl number Theoretical results obtained from the solution of the Orr–Sommerfeld equation extended to stratified fluids are compared with experiments performed in a tilting tube filled with water and brine.Theoretical analysis shows that a complete stabilization of the flow field with respect to infinitesimal disturbances is attained, irrespective of the Richardson number J, as the Reynolds number Re decreases below 75. This damping action of viscosity is shown to appreciably reduce the critical Richardson number with respect to the inviscid limit even at moderately high Re. On the other hand, the destabilizing action enhanced by viscosity through the diffusion of momentum leads to a viscous mode of instability that may develop if J decreases below a threshold value. An extensive series of experiments has been carried out in a long tilting tube in order to verify theoretical results. The agreement between observations and theory is quite satisfactory. Kelvin–Helmholtz waves grow whenever theoretical unstable conditions are attained. The values of measured wavelengths well correspond to maximum growth rate wave numbers. The comparison between theoretical and experimental results also shows that acceleration plays a stabilizing action.

Analysis and simulation of a turbulent, compressible starting vortex
View Description Hide DescriptionThe numerical simulation of a shock induced, turbulent compressible vortex is analyzed. The vortex is generated by the movement of an (unsteady) shock over the trailingedge of a twodimensional airfoil at different incidence angle. A theoreticalanalysis is performed for the case of a turbulent line vortex, at a low (vortex)Mach number and high Reynolds number, as a basis of comparison for the dynamic structure of the starting vortex. This theoreticalanalysis confirms the existence of an equilibrium structure of the isolated vortex similar to the laminar case. In the numerical computations, both an isotropic eddy viscosity twoequation turbulencemodel and an algebraic stress model are employed to assess the influence of turbulencemodel on the predictive capabilities of such a flow including the realization of the selfsimilar behavior found in the isolated vortex case. The results are also compared to theoretical estimates of the productiontodissipation rate ratio for both types of turbulencemodels, and to recent experiments on such flows.

Coherent structure and heat transfer in geostrophic flow under density stratification
View Description Hide DescriptionThe mechanism of heat transport in geostrophic flows under various density stratifications has been studied by using both direct numerical simulation and rapid distortion theory. It is found that in cases with rotation, the isosurfaces of the temperature fluctuations are aligned in the direction of the rotational axis, and they become very close to twodimensional. Under stable stratification with rotation, the velocity and temperature fluctuations tend to oscillate with the Brunt–Väisälä frequency, while they tend to oscillate with a longer period in cases without rotation. Under unstable stratification with rotation, on the other hand, vortex columns are formed in the direction parallel to the axis of rotation owing to the effects of nonlinear interactions.

Twophase modeling of deflagrationtodetonation transition in granular materials: A critical examination of modeling issues
View Description Hide DescriptionThe twophase mixture model developed by Baer and Nunziato (BN) to study the deflagrationtodetonation transition (DDT) in granular explosives is critically reviewed. The continuummixture theory foundation of the model is examined, with particular attention paid to the manner in which its constitutive functions are formulated. Connections between the mechanical and energetic phenomena occurring at the scales of the grains, and their manifestations on the continuum averaged scale, are explored. The nature and extent of approximations inherent in formulating the constitutive terms, and their domain of applicability, are clarified. Deficiencies and inconsistencies in the derivation are cited, and improvements suggested. It is emphasized that the entropyinequality constrains but does not uniquely determine the phase interaction terms. The resulting flexibility is exploited to suggest improved forms for the phase interactions. These improved forms better treat the energy associated with the dynamic compaction of the bed and the singlephase limits of the model. Companion papers of this study [Kapila et al., Phys. Fluids 9, 3885 (1997); Kapila et al., in preparation; Son et al., in preparation] examine simpler, reduced models, in which the fine scales of velocity and pressure disequilibrium between the phases allow the corresponding relaxation zones to be treated as discontinuities that need not be resolved in a numerical computation.

Instantaneous, quantitative measurements of molecular mixing in the axisymmetric jet near field
View Description Hide DescriptionResults from a dualtracer planar laserinduced fluorescence (PLIF) technique for making instantaneous, quantitative measurements of molecularly mixed fluid fraction are presented for an axisymmetric jet in a slow coflow. The twocamera, twolaser technique uses PLIF of nitric oxide seeded in a nitrogen jet to mark the unmixed jet fluid fraction, while PLIF of acetone seeded into the low velocity air coflow marks the total coflow fluid fraction. By combining data from these two simultaneous images, quantitative measurements of molecularly mixed jet fluid fraction can be made on a pixelbypixel basis, while simultaneously allowing visualizations of largestructure behavior and regions of subresolution stirring. Instantaneous images of molecularly mixed jet fluid fraction and jet fluid mixing efficiency, probability density functions(PDFs) of mixed jet fluid fraction, and associated statistics are presented for 5000, 10,000, 50,000, and 100,000. For fully turbulent conditions stirring at subresolution scales is detected primarily on the jet side of the mixing layer. This creates a hybrid PDF behavior (stationary on the jet side of the mixing layer, marching on the coflow side) that is not shown by passive scalar methods at equivalent image resolution.

Very largescale motion in the outer layer
View Description Hide DescriptionVery largescale motions in the form of long regions of streamwise velocityfluctuation are observed in the outer layer of fully developed turbulent pipe flow over a range of Reynolds numbers. The premultiplied, onedimensional spectrum of the streamwise velocitymeasured by hotfilm anemometry has a bimodal distribution whose components are associated with largescale motion and a range of smaller scales corresponding to the main turbulent motion. The characteristic wavelength of the largescale mode increases through the logarithmic layer, and reaches a maximum value that is approximately 12–14 times the pipe radius, one order of magnitude longer than the largest reported integral length scale, and more than four to five times longer than the length of a turbulent bulge. The wavelength decreases to approximately two pipe radii at the pipe centerline. It is conjectured that the very largescale motions result from the coherent alignment of largescale motions in the form of turbulent bulges or packets of hairpin vortices.

Experimental analysis of intermittent coherent structures in the near field of a high Re turbulent jet flow
View Description Hide DescriptionExperimental data obtained in the near region of a turbulent jet flow (from up to where D is the jet diameter and x is the axial coordinate) are processed through wavelet decomposition. A wavelet based technique for coherent structures identification is applied to the longitudinal and transverse velocity data series obtained by X probe hot wire anemometry measurements. This methodology permits the evolution with x of the time signature of coherent structures to be analyzed. The statistics of the local turbulent energy magnitude is also discussed and the temporal dynamics is studied by the analysis of the time of appearance of the most energetic structures evolving with

Roughnessinduced receptivity to crossflow vortices on a swept wing
View Description Hide DescriptionThe generation of stationary crossflow vortices on the 45 degree swept NLF (2)0415 airfoil at the Arizona State University Unsteady Wind Tunnel (AIAA Paper No. 960184, 1996; Ph.D. thesis, Arizona State University, 1996) is analyzed using a finite Reynoldsnumber linear receptivity theory. The receptivity theory is based on the locallyparallel flow approximation and also neglects surface curvature. The vortices are excited by a spanwise periodic array of circular roughness elements located near the attachment line. The amplitudes of the crossflow vortices at the source location are computed and compared with the experimental results. In general, the agreement is remarkably good. This suggests that the combined effect of nonparallel flow and surface curvature on the receptivity is not significant for the range of conditions considered. The linear analysis captures the receptivity variations with Reynolds number, roughness geometry, and roughness location. When the roughness height is small, the initial amplitudes of the roughnessgenerated crossflow vortices are well predicted using the finite Reynoldsnumber receptivity theory. Nonlinear effects appeared to become significant only when the roughness height exceeds about 10% of the local boundary layer displacement thickness.

The linear stability of thermally stratified rotating channel flow
View Description Hide DescriptionA linear stabilityanalysis has been made of the hydrodynamicstability of viscousflow in a thermally stratified rotating channel. To understand the competition mechanism of the flow stabilization and destabilization, an inviscid stability criterion including effects of the rotation and stratification was first formulated for indicating the stable and unstable regimes of the flow. Then, an eigenvalue problem was derived for the viscousflow and solved using a shooting method. The combined effect of the Coriolis force and centrifugaltype buoyancy force on the longitudinal rollcell instability was examined. For Prandtl number 7.11, the critical Reynolds number, corresponding critical wave number, and induced cell pattern of the longitudinal vortices are shown for various values of the rotation number and rotational Rayleigh number. Based on the analytical results, we predict the onset of the longitudinal rollcell instability in this nonisothermal rotating channel flow. As compared to the isothermal rotating channel flow case, not only the critical Reynolds number but also the onset mode of the roll cell are altered significantly by the centrifugaltype buoyancy force. It is found that the flow may be stabilized or destabilized depending on the rotation and stratification of the channel. In the presence of a positive rotational Rayleigh number, the flow becomes more stable as compared with the isothermal rotating channel flow, otherwise, the flow becomes more unstable.
