Volume 12, Issue 7, July 2000
 LETTERS


An approach to wall modeling in largeeddy simulations
View Description Hide DescriptionChannel flow with frictionReynolds number as high as 80 000 is treated by largeeddy simulation at a moderate cost, using the subgridscale model designed for detachededdy simulations. It includes wall modeling, and was not adjusted for this flow. The grid count scales with the logarithm of the Reynolds number. Three independent codes are in fair agreement with each other. Reynoldsnumber variations and grid refinement cause trades between viscous, modeled, and resolved shear stresses. The skinfriction coefficient is too low, on the order of 15%. The velocity profiles contain a “modeled” logarithmic layer near the wall and some suggest a “resolved” logarithmic layer farther up, but the two layers have a mismatch of several units in
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 ARTICLES


Nonlinear dynamics of threedimensional longwave Marangoni instability in thin liquid films
View Description Hide DescriptionThe threedimensional evolution of the longwave Marangoni instability of thin liquid films is studied. According to earlier theoretical predictions no continuous steady states exist and the film ruptures. As in two dimensions, the mechanism of fingering is found to be a main route to rupture. A fourfold rotational symmetry of the film interface is retained, when a square periodic domain and the harmonic initial disturbance are used. A use of initial random disturbances in general eliminates the square symmetry of the solution. An increase of the domain size results in a growing complexity of the emerging patterns. In contrast with the dynamics in two dimensions the evolution of the interface in three dimensions and in particular the pattern emerging at rupture may strongly depend on the choice of the initial condition. The twodimensional evolution of the film is found to be unstable to small threedimensional random disturbances.

Spreading and imbibition of viscous liquid on a porous base. II
View Description Hide DescriptionThe competition between viscous spreading of a liquid on a substrate and its absorption by a dry porous substrate is studied in two dimensions. The effect of capillary suction into the pores vies with contactline slip on the substrate to determine the lifetime of the drop.

Optimization of fluid front dynamics in porous media using rate control. I. Equal mobility fluids
View Description Hide DescriptionIn applications involving the injection of a fluid in a porous medium to displace another fluid, a main objective is the maximization of the displacement efficiency. For a fixed arrangement of injection and production points (sources and sinks), such optimization is possible by controling the injection rate policy. Despite its practical relevance, however, this aspect has received scant attention in the literature. In this paper, we provide a fundamental approach based on optimal control theory, for the simplified case when the fluids are miscible, of equal viscosity, and in the absence of dispersion and gravity effects. Both homogeneous and heterogeneous porous media are considered. From a fluid dynamics viewpoint, this is a problem in the deformation of material lines in porous media, as a function of timevarying injection rates. It is shown that the optimal injection policy that maximizes the displacement efficiency, at the time of arrival of the injected fluid, is of the “bang–bang” type, in which the rates take their extreme values in the range allowed. This result applies to both homogeneous and heterogeneous media. Examples in simple geometries and for various constraints are shown, illustrating the efficiency improvement over the conventional approach of constant rate injection. In the heterogeneous case, the effect of the permeability heterogeneity, particularly its spatial correlation structure, on diverting the flow paths, is analyzed. It is shown that bang–bang injection remains the optimal approach, compared to constant rate, particularly if they were both designed under the assumption that the medium was homogeneous. Experiments in a homogeneous HeleShaw cell are found to be in good agreement with the theory.

Electrohydrodynamic effects on the deformation and orientation of a liquid capsule in a linear flow
View Description Hide DescriptionThe role of a uniform electric field on the deformation and orientation of a liquid capsule with a viscoelasticmembrane is considered analytically in the small deformation limit. The capsule is freely suspended either in a quiescent fluid or in a shear flow. The viscoelasticity of the membrane is taken into account by the Kelvin–Voigt model and the electrohydrodynamicflow is analyzed on the basis of the leaky dielectric model. In this article, we consider three different prototype models of capsules; viz., a neoHookean (incompressible isotropic) membrane, a red blood celltype (areapreserving) membrane, and an interfacialtension droplet. The deformed capsule shape from its initial sphericity and its orientaion are determined from the linearized governing equations and boundary conditions in the limit of small deformations. The asymptotic theory shows that the degree of capsule deformation induced by a uniform electric field alone is independent of the surface viscosity of the capsule as well as the viscosity ratio between the two fluids inside and outside the capsule. Meanwhile, in the presence of an imposed shear flow, the degree of deformation depends on the surface viscosity with preserving still the independence of the viscosity ratio. For an illustrative purpose, experimental results for the role of a uniform electric field on the orientation of an interfacialtension droplet in a shear flow are discussed briefly.

Interfacial instabilities of a fluid annulus in a rotating Hele–Shaw cell
View Description Hide DescriptionWe have studied the interfacial instabilities experienced by a liquid annulus as it moves radially in a circular Hele–Shaw cell rotating with angular velocity Ω. The instability of the leading interface (oil displacing air) is driven by the density difference in the presence of centrifugal forcing, while the instability of the trailing interface (air displacing oil) is driven by the large viscosity contrast. A linear stability analysis shows that the stability of the two interfaces is coupled through the pressure field already at a linear level. We have performed experiments in a dry cell and in a cell coated with a thin fluid layer on each plate, and found that the stability depends substantially on the wetting conditions at the leading interface. Our experimental results of the number of fingers resulting from the instability compare well with the predictions obtained through a numerical integration of the coupled equations derived from a linear stability analysis. Deep in the nonlinear regime we observe the emission of liquid droplets through the formation of thin filaments at the tip of outgrowing fingers.

On the rapid estimation of permeability for porous media using Brownian motion paths
View Description Hide DescriptionWe describe two efficient methods of estimating the fluid permeability of standard models of porous media by using the statistics of continuous Brownian motion paths that initiate outside a sample and terminate on contacting the porous sample. The first method associates the “penetration depth” with a specific property of the Brownian paths, then uses the standard relation between penetration depth and permeability to calculate the latter. The second method uses Brownian paths to calculate an effective capacitance for the sample, then relates the capacitance, via angleaveraging theorems, to the translational hydrodynamicfriction of the sample. Finally, a result of Felderhof is used to relate the latter quantity to the permeability of the sample. We find that the penetration depth method is highly accurate in predicting permeability of porous material.

Mechanism of air entrainment by a disturbed liquid jet
View Description Hide DescriptionIt was shown in recent work that the crests of surface disturbances on a falling jet are a powerful agent for air entrainment at the free surface of a liquid pool. The paper explores the opposite case in which the jet is disturbed so as to form an axisymmetric trough, rather than a crest. It is found that no air is entrained in this case. The paper concludes with some considerations on the validity of a recently proposed model for air entrainment.

Weakly nonlinear saturation of shortwave instabilities in a strained Lamb–Oseen vortex
View Description Hide DescriptionA Lamb–Oseen vortex in a planar straining field is known to be subject to 3D (threedimensional) shortwave instabilities which are due to the resonance of the straining field and two stationary Kelvin waves characterized by the same axial wave number and by azimuthal wave numbers equal to −1 and +1. The linear regime has been described by Moore and Saffman (1975). In this article, we extend this analysis to the weakly nonlinear regime. The emerging eigenmode is characterized by a complex amplitude whose behavior is governed by an amplitude equation. It is shown that the unstable perturbation corresponds to an oscillation of the vortex in a plane inclined at an angle while the amplitude of these oscillations is proportional to The vortex centers are defined as the points where the velocity of the vortex is zero, which also corresponds to the points where the pressure is minimum. We show that these instabilities saturate. The saturation amplitudes are evaluated numerically and expressed in terms of oscillation amplitudes of the vortex centers. If denotes the internal radius of the vortex and if the straining field is due to a counterrotating vortex of same strength, located at a distance then the maximum amplitude Δ of the vortex oscillations is This result is in agreement with those of the experiments of Leweke and Williamson (1998) for which It also shows that in aeronautical situations, for which is smaller, i.e., the considered shortwave instability will saturate at very low amplitude.

Axisymmetric instabilities of Bödewadt flow
View Description Hide DescriptionA spatial linear stability analysis of Bödewadt’s selfsimilar solution for the rotating flow over a flat plate is performed. In particular, considered is the stability of axisymmetric perturbations propagating towards the axis of rotation, which are the most important ones observed experimentally. Viscous and nonparallel effects on the stability of the perturbations are retained up to the order of the inverse of the local Reynolds numberR. The resulting parabolic stability equations are solved numerically using a spectral collocation method varying the nondimensional frequency q and R. The instability region on the plane is discussed and compared with existing experimental data and direct numerical simulation results. The circular waves observed experimentally and in numerical simulations are shown to correspond to an inertial instability mode which becomes stabilized as R decreases below a critical value.

Threedimensional centrifugaltype instabilities of twodimensional flows in rotating systems
View Description Hide DescriptionThis paper deals with the stability of incompressible inviscid planar basic flows in a rotating frame. We give a sufficient condition for such flows to undergo threedimensional shortwave centrifugaltype instabilities. This criterion reduces to the Bradshaw–Richardson (1969) or Pedley (1969) criterion in the specific case of parallel shear flows subject to rotation, to Rayleigh’s centrifugal criterion (1916) in the case of axisymmetric vortices in inertial frames, to the Kloosterziel and van Heijst (1991) criterion in the case of axisymmetric vortices subject to rotation and to Bayly’s criterion (1988) in the case of general twodimensional flows in inertial frames. The criterion states that a steady 2D basic flow subject to rotation Ω is unstable if there exists a streamline for which at each point where W is the vorticity of the streamline, R is the local algebraic radius of curvature of the streamline and V is the local norm of the velocity. If this condition is satisfied then the flow is unstable according to the geometrical optics method introduced by Lifschitz and Hameiri (1991), which consists in following wave packets along the flow trajectories using a Wentzel–Kramers–Brillouin formalism. When the streamlines are closed, it is further shown that a localized unstable normal mode can be constructed in the vicinity of a streamline. As an application, this new criterion is used to study the centrifugaltype instabilities in the Stuart vortices, which is a family of exact solutions describing a row of periodic corotating eddies. For each solution of that family and for each rotation parameter we give the unstable streamline interval, according to the criterion of instability. This criterion gives only a sufficient condition of centrifugal instability. The equations of the geometrical optics method are therefore numerically solved to obtain the true centrifugally unstable streamline intervals. It turns out that our criterion gives excellent results for highly concentrated vortices, i.e., the two approaches yield the same unstable streamline intervals. In less concentrated vortices, some streamlines undergo centrifugal instability although our criterion is not fulfilled. From these numerical results, another criterion of centrifugal instability for a flow with closed streamlines is conjectured which reduces to the change of sign of the absolute vorticity somewhere in the flow.

Receptivity to harmonic forcing of a finitewidth mixing layer just downstream of the trailing edge of a flat plate
View Description Hide DescriptionAnalytical solutions for the receptivity of a piecewise linear mixing layer to harmonic disturbances at the trailing edge of a flat plate are presented. The solution is for an ideal fluid, with viscous effects at the trailing edge being accounted for by imposing an unsteady Kutta condition. The wake from the flat plate is included in the model. Initial mixing layer response for the discrete and continuous modes of instability is determined as a function of forcing strength, Strouhal number, and cross stream location. Forcing frequencies throughout the unstable regime are considered. The various components of the perturbation field and their contributions to the perturbation velocity and vorticity are investigated in the near field of the trailing edge. In the limit that the forcing frequency approaches zero, the amplification of the streamwise velocity and vorticity associated with the growing instability mode is shown to be inversely proportional to the forcing frequency, in agreement with previous results obtained using the vortex sheet approximation. In contrast, the initial cross stream velocity of the disturbance is quite small for low frequencies, and reaches a peak at the most amplified frequency of the mixing layer profile. The analysis also shows that at higher frequencies the continuous modes of instability become increasingly important channels whereby vorticity is carried away from the trailing edge. The differences in wave number between the various competing components at these higher frequencies leads to the appearance of nodes in the timeaveraged perturbation quantities downstream. The entire perturbation is examined at the most amplified frequency.

Firespread through fuel beds: Modeling of windaided fires and induced hydrodynamics
View Description Hide DescriptionThe propagation of windaided line fires through fuel beds is simulated by using a multiphase approach. In this approach, a gas phase flows through Nsolid phases which constitute an idealized reproduction of the heterogeneous combustible medium. A set of timedependent equations is obtained for each phase and the coupling between the gas phase and the solid phases is rendered through exchange terms of mass, momentum, and energy. Turbulence is approached by using a RNG statistical model constructed from the Favre averaging method. The radiative transfer equation extended to multiphase media is solved using the discrete ordinates method (DOM). Soot formation is taken into account for the evaluation of the absorption coefficient of the soot/fuel particles/combustion products mixture using the gray gas assumption. Firstorder kinetics is incorporated to describe water vaporization, pyrolysis, and char combustion processes. The solution is performed numerically by a finitevolume method including a highorder upwind convective scheme and a flux limiter strategy along with a projection method for the pressure–velocity coupling. This model has been applied to describe the unsteady behavior of windaided fires spreading through a litter of dead pine needles and the induced hydrodynamics. The numerical results obtained from our model are presented and compared to measurements and predictions from other laboratorybased models.

Twodimensional Navier–Stokes simulations of gaseous mixtures induced by Richtmyer–Meshkov instability
View Description Hide DescriptionTwodimensional numerical calculations of the fluid instability of shockaccelerated interfaces between a heavy fluid and a light one are carried out in order to simulate experiments performed by Poggi et al. [Phys. Fluids10, 2698 (1998)]. In these experiments, the laser Doppler anemometry technique gives measurements of the fluctuating velocity. Experimental data show that a turbulent mixing zone is generated by the incident shock wave. This turbulent regime is reproduced by twodimensional calculations. Before the first reshock, several quantities in the mixing zone, such as bubble and spike fronts, turbulent kinetic energy, enstrophy, adopt a quasi selfsimilar behavior versus time. In particular, we can see in numerical simulations the decay of the turbulent kinetic energy before the first reflected shock wave–mixingzone interaction and its strong enhancement by reshocks. Furthermore, spectral analysis of the numerical results exhibit a energy spectrum. Experimental measurements also show that the turbulent boundary layers which develop on the shocktube walls accelerate the fluid flow in the middle of the tube. Numerical simulations clearly reproduce both this acceleration and the lambdashock structure observed in experiments.

Receptivity of threedimensional boundarylayers to localized wall roughness and suction
View Description Hide DescriptionThe receptivity of threedimensional, incompressible, boundarylayer flows to localized roughness or suction is studied theoretically and numerically. Threedimensional boundarylayer flows have a strong “nonparallel” component due to the curvature of the potentialflow streamlines. Our theoretical model extends the Fouriertransform methodology to nonparallel flows using a Taylor expansion of the laminar meanflow at the location of the roughness. Both the nearfield and the farfield solutions are contained in the model. Additionally, the use of MacLaurin expansions in the complex plane leads quickly to the receptivity factors of eigenmodes. The theoretical results are validated with solutions to the linearized Navier–Stokes equations efficiently obtained by replacing the actual wall forcing with a smoother, but equivalent, forcing. We find that the farfield response is proportional to both and where is the Fourier transform of the forcing distribution, and is the eigenmode’s wave number. The receptivity coefficient for decreases when nonparallelism is included in our models, while that for increases.

A physicalspace version of the stretchedvortex subgridstress model for largeeddy simulation
View Description Hide DescriptionA physicalspace version of the stretchedvortex subgridstress model is presented and applied to largeeddy simulations of incompressible flows. This version estimates the subgridkinetic energy required for evaluation of the subgridstress tensor using local secondorder structurefunction information of the resolved velocity field at separations of order the local cell size. A relation between the structure function and the energy spectrum is derived using the kinematic assumptions of the stretchedvortex model for locally homogeneous anisotropicturbulence. Results of largeeddy simulations using this model are compared to experimental and direct numerical simulation data. Comparisons are shown for the decay of kinetic energy and energy spectra of decaying isotropic turbulence and for mean velocities, rootmeansquare velocity fluctuations and turbulencekinetic energy balances of channel flow at three different Reynolds numbers.

The simulation and interpretation of free turbulence with a cognitive neural system
View Description Hide DescriptionAn artificial neural network, based on fuzzy ARTMAP, that is capable of learning the basic nonlinear dynamics of a turbulent velocity field is presented. The neural system is capable of generating a detailed multipoint time record with the same structural characteristics and basic statistics as those of the original instantaneous velocity field used for training. The good performance of the proposed architecture is demonstrated by the generation of synthetic twodimensional velocity data at eight different positions along the homogeneous (spanwise) direction in the far region of a turbulent wakeflow generated behind a cylinder at The analysis of the synthetic velocity field, carried out with spectral techniques, POD and pattern recognition, reveals that the proposed neural system is capable of capturing the highly nonlinear dynamics of free turbulence and of reproducing the sequence of individual classes of relevant events present in turbulent wakeflows. The trained neural system also yields patterns of the coherent structures embedded in the flow when presented with input data containing partial information of the instantaneous velocity maps of these events. In this way, the neural network is used as an expert system that helps in the structural interpretation of turbulence in a wake flow.

Statistics of pressure and of pressurevelocity correlations in isotropic turbulence
View Description Hide DescriptionSome pressure and pressurevelocity correlations in a direct numerical simulations of a threedimensional turbulent flow at moderate Reynolds numbers have been analyzed. We have identified a set of pressurevelocity correlations which possess a good scaling behavior. Such a class of pressurevelocity correlations is determined by looking at the energybalance across any subvolume of the flow. According to our analysis, pressure scaling is determined by the dimensional assumption that pressure behaves as a “velocity squared,” unless finiteReynolds effects are overwhelming. The SO(3) decompositions of pressure structure functions has also been applied in order to investigate anisotropic effects on the pressure scaling.

A thickened flame model for large eddy simulations of turbulent premixed combustion
View Description Hide DescriptionA subgrid scale model for large eddy simulations of turbulent premixed combustion is developed and validated. The approach is based on the concept of artificially thickened flames, keeping constant the laminar flame speed This thickening is simply achieved by decreasing the preexponential factor of the chemical Arrhenius law whereas the molecular diffusion is enhanced. When the flame is thickened, the combustion–turbulence interaction is affected and must be modeled. This point is investigated here using direct numerical simulations of flame–vortex interactions and an efficiency function E is introduced to incorporate thickening effects in the subgrid scale model. The input parameters in E are related to the subgrid scale turbulence (velocity and length scales). An efficient approach, based on similarity assumptions, is developed to extract these quantities from the resolved velocity field. A specific operator is developed to exclude the dilatational part of the velocity field from the estimation of turbulent fluctuations. The combustionmodel is then implemented in a compressible parallel finite volume–element solver able to handle hybrid grids to simulate a lateral injections combustor (LIC). Results are in agreement with the available experimental data.

Demonstration of a oneway flow of a rarefied gas induced through a pipe without average pressure and temperature gradients
View Description Hide DescriptionA simple experiment is performed to demonstrate that a oneway flow of a rarefied gas can be induced through a pipe without average pressure and temperature gradients by devising the shape of the pipe. A oneway flow is found to be induced through a pipe consisting of two circular pipes of different diameters connected and heated at their joint in the middle part of the pipe. The flow is from the thinner pipe to the thicker. In a pipe of a uniform diameter, no oneway flow is induced even when it is heated at a position away from the middle of the pipe.
