Volume 13, Issue 2, February 2001
 ARTICLES


Influence of inertia, gravity, and substrate topography on the twodimensional transient coating flow of a thin Newtonian fluid film
View Description Hide DescriptionThe interplay between inertia, gravity, and substrate topography is examined in this study for the transient twodimensional flow of a thin Newtonian film. Surface tension effect is assumed to be negligible. The fluid emerges from a channel and is driven by a pressure gradient maintained inside the channel. The substrate is assumed to be stationary and of arbitrary shape. The lubricationequations are solved by expanding the flow field in terms of orthonormal modes in the vertical direction and using the Galerkin projection, combined with a timestepping implicit scheme, and integration along the flow direction. The leadingorder mode is found to be clearly dominant. Gravity and substrate topography can have a significant effect on transient behavior, but this effect varies significantly, depending on the level of fluid inertia. The wave and flow structures are examined for high and lowinertia fluids. It is found that lowinertia fluids tend to accumulate near the channel exit, exhibiting a standing wave that grows with time. This behavior clearly illustrates the difficulty faced with coating highviscosity fluids. The topography of the substrate has a drastic effect on the flow. A secondary wave emerges in the presence of a bump or a depression in the substrate. The wave structure is again highly dependent on the level of inertia.

Spontaneous thermocapillary interaction of drops: Unsteady convective effects at high Peclet numbers
View Description Hide DescriptionInitial nonequilibrium distribution of temperature or surfactant concentration between suspended drops and the continuous fluid in a suspension results in an unsteadystate heat/mass transfer between the phases. Nonuniformities of temperature or solute concentration, which arise as a natural result of local geometrical inhomogeneities in the suspension, produce temperature/concentration gradients along the interfaces that, in turn, generate thermocapillary fluid motion along the interfaces and migration of drops toward or apart from each other. Asymptotic analysis of the process is carried out for large Peclet numbers of the dispersed phase. The dynamics of drops is studied and the approach time is estimated for the limiting cases of small and large Peclet numbers of the continuous phase.

Nonisothermal modification of purely elastic flow instabilities in torsional flows of polymeric fluids
View Description Hide DescriptionPrevious experimental measurements and linear stability analyses of curvilinear shearing flows of viscoelastic fluids have shown that the combination of streamwise curvature and elastic normal stresses can lead to flow destabilization. Torsional shear flows of highly elastic fluids with closed streamlines can also accumulate heat from viscous dissipation resulting in nonuniformity in the temperature profile within the flow and nonlinearity in the viscometric properties of the fluid. Recently, it has been shown by AlMubaiyedh et al. [Phys. Fluids 11, 3217 (1999)] that the inclusion of energetics in the linear stability analysis of viscoelastic Taylor–Couette flow can change the dominant mode of the purely elasticinstability from a nonaxisymmetric and timedependent secondary flow to an axisymmetric stationary Taylortype toroidal vortex that more closely agrees with the stability characteristics observed experimentally. In this work, we present a detailed experimental study of the effect of viscous heating on the torsional steady shearing of elastic fluids between a rotating cone and plate and between two rotating coaxial parallel plates. Elastic effects in the flow are characterized by the Deborah number, De, while the magnitude of the viscous heating is characterized by the Nahme–Griffith number, Na. We show that the relative importance of these two competing effects can be quantified by a new dimensionless thermoelastic parameter, which is a material property of a given viscoelastic fluid independent of the rate of deformation. By utilizing this thermoelastic number, experimental observations of viscoelasticflow stability in three different fluids and two different geometries over a range of temperatures can be rationalized and the critical conditions unified into a single flow stability diagram. The thermoelastic number is a function of the molecular weight of the polymer, the flow geometry, and the temperature of the test fluid. The experiments presented here were performed using test fluids consisting of three different high molecular weight monodisperse polystyrene solutions in various flow geometries and over a large range of temperatures. By systematically varying the temperature of the test fluid or the configuration of the test geometry, the thermoelastic number can be adjusted appreciably. When the characteristic time scale for viscous heating is much longer than the relaxation time of the test fluid (Θ≪1) the critical conditions for the onset of the elasticinstability are in good agreement with the predictions of isothermal linear stability analyses. As the thermoelastic number approaches a critical value, the strong temperature gradients induced by viscous heating reduce the elasticity of the test fluid and delay the onset of the instability. At even larger values of the thermoelastic parameter, viscous heating stabilizes the flow completely.

Measurement of shearinduced dispersion in a dilute emulsion
View Description Hide DescriptionThe timedependent drop distribution of a dilute, polydisperse emulsion is measured in a simple shear flow. The suspending fluid is much more viscous than the dispersed phase (1:1000). Drops are found to drift away from either bounding wall and accumulate near the center of the gap, due to the anisotropy of droplet–plane interactions. An expression for this drift velocity has been derived for single drops by Chan and Leal [J. Fluid Mech. 92, 131 (1979)] and was in agreement with isolated drop migration observed in our work. Eventually the inward drift is balanced by a shearinduced gradient diffusivity, and a steadystate concentration distribution is reached. When the drops are sufficiently far from either wall a selfsimilar, parabolic concentration profile is predicted at all times. Droplet diffusivities were determined for capillary numbers between 0.17 and 0.92, where is the shear rate, is the mean drop radius, μ is the viscosity of the suspending fluid, and σ the interfacial tension. The values obtained are an order of magnitude lower than theoretical predictions of Loewenberg made in the limit of small deformation.

Scale dependence, correlations, and fluctuations of stresses in rapid granular flows
View Description Hide DescriptionIt is shown that, unlike in simple molecular fluids, the stress field in granular fluids may be strongly scale, or resolution, dependent. This is a result of the intrinsic lack of scale separation in these fluids. Another consequence of the lack of scale separation in granular fluids is that microscopic stress fluctuations, whose origin (like in molecular fluids) is the underlying discreteness of the system, may appear as observables in macroscopic measurements; the correlation (or decay) time of the stress fluctuations is of the order of the meanfree time, which is also a macroscopic time. All of these properties are intrinsic to granular fluids and not (for example) results of the practical lack of scale separation that is dictated by the fact that grains are of macroscopic dimensions or the limited statistics in simulations. Numerical evidence, based on moleculardynamic simulations of shear flows of smooth disks in a twodimensional enclosure, serves to demonstrate the above phenomena.

Flow coherence in a bead pack observed using frequency domain modulated gradient nuclear magnetic resonance
View Description Hide DescriptionWe have used a new nuclear magnetic resonance(NMR) method based on periodic wave form magnetic field gradients to investigate temporal correlations for flow in porous media. The frequency domain modulated field gradient NMR technique directly yields the frequencydependentdispersion coefficient, i.e., the spectral density of the velocity autocorrelation function. Our measurements of dispersion spectra have been carried out, in the direction transverse to the mean flow, for water flowing in a monodisperse latex bead pack (diameters 50–136 μm) and at Péclet numbers ranging from 10 to 5000. We observe spectral peaks at a frequency corresponding to the inverse time for flow around a bead, an effect we attribute to coherent meandering flow around the bead. This observation is in close agreement with the recent computer simulations of Maier et al., in which negative velocity autocorrelation function transients are seen.

An experimental investigation of the surface temperature field during evaporative convection
View Description Hide DescriptionMeasurements of the surfacetemperature field are presented for a water surface undergoing evaporation. These temperature fields were measured using an infrared camera for a range of heat fluxes Experiments were conducted for water surfaces with and without a surfactantmonolayer. A statistical analysis of the data is presented which shows the effect of heat flux and surfactants on the root mean square and skewness of the field. The data reveals a linear increase in the rms with increasing heat flux, which is similar for clean and surfactant conditions. In contrast, the skewness is markedly different for the clean and surfactantcovered cases. For clean surface conditions, the skewness attains large, negative values, becoming increasingly negative as increases. When the surface is covered with a surfactantmonolayer, however, the skewness exhibits small, negative values which approach zero as the heat flux increases. This behavior is reflected in the pdf which is clearly asymmetric in the clean case and virtually symmetric in the surfactant case. A physical mechanism is presented to explain these results. Temporal power spectra are presented which reveal the role of heat flux and surfactants on the temporal evolution of the surfacetemperature field.

Ekman decay of a dipolar vortex in a rotating fluid
View Description Hide DescriptionThe evolution of quasitwodimensional (2D) dipolar vortices over a flat bottom in a rotating fluid system is studied numerically, and the main results are experimentally verified. Our aim is to examine the dipole decay due to bottom friction effects. The numerical simulations are based on the 2D physical model derived by Zavala Sansón and van Heijst [J. Fluid Mech. 412, 75 (2000)], which contains nonlinear Ekman terms, associated with bottom friction, in the vorticityequation. In contrast, the conventional 2D model with bottom friction only retains a linear stretching term in the same equation. It is shown that the dipole trajectory is deflected towards the right (i.e., in the anticyclonic direction) when nonlinear Ekman terms are included. This effect is not observed in simulations based on the conventional model, where the dipole trajectory is a straight line. The basic reason for this behavior is the slower decay of the anticyclonic part of the dipole, with respect to the cyclonic one, due to nonlinear Ekman effects. Another important result is the exchange of fluid between the cyclonic part and the ambient, leaving a tail behind the dipole. By means of laboratory experiments in a rotating tank, these results are qualitatively verified.

Control of vortex breakdown by a transversely oriented wire
View Description Hide DescriptionA small wire oriented orthogonally to the axis of the leadingedge vortex on a delta wing at high angle of attack generates substantial changes in the vortex structure, which is characterized using a technique of highimagedensity particle image velocimetry. A wire having a diameter two orders of magnitude smaller than the diameter of the leadingedge vortex prior to the onset of vortex breakdown can substantially advance the onset of breakdown by as much as 15 vortex diameters. Depending upon the dimensionless diameter of the wire and wire location along the axis of the vortex, the onset of vortex breakdown can occur either upstream or downstream of the wire. Contours of constant velocity indicate that the rate of decrease of streamwise velocity along the centerline of the vortex is substantially enhanced, even for locations well upstream of the wire, relative to the case of vortex breakdown in the absence of a wire. Patterns of instantaneous vorticity in the presence of the wire typically exhibit a form characteristic of either a spiral or bubblelike mode of breakdown that occurs in the absence of the wire.

New results on the model problem of the diffusion of turbulence from a plane source
View Description Hide DescriptionThe problem of the diffusion of turbulence from a plane source is addressed in the context of twoequation eddyviscosity models and Reynoldsstresstransport models. In the steady state, full analytic solutions are given. At second order, they provide the equilibrium value of the anisotropy level obtained with different combinations of returntoisotropy and turbulentdiffusion schemes and confirm the results obtained by Straatman et al. [AIAA J. 36, 929 (1998)] in an approximate analysis. In addition, all the characteristics of the turbulence decrease can be determined and it is shown that a special constraint on the value of the modeling constants should hold if turbulence fills the whole surrounding space. In a second step, precise results can be given for the unsteady model problem at the firstorderclosure level. The evolution cannot be described with a single set of characteristic scales and one has to distinguish the cases of short and large times. In the shorttime regime, the flow is governed by the characteristic scales of turbulence at the source and contamination of the flow proceeds as At large times, the flow is governed by timedependent characteristic scales that correspond to the solution of the steady problem at the instantaneous location of the front. Contamination of the flow proceeds as a power of time that can be related to the value of the modeling constants. The role of a combination of these constants is emphasized whose value can be specified to produce a solution that matches simultaneously the experimental data for the decrease of turbulent kinetic energy in the steady state and the exponent of the propagation velocity in the transient regime.

On the radiated noise computed by largeeddy simulation
View Description Hide DescriptionThis paper addresses the problem of the estimation of the noise radiated by forced isotropic turbulence using an hybrid largeeddy simulation/Lighthill analogy approach. The scale separation associated with the LES approach leads to splitting the acoustic source term as the sum of several contributions. The subgrid scale and high frequency contributions to radiated acoustic spectrum are first evaluated on the ground of filtered direct numerical simulations. The parametrization of subgrid scale effects based on a scale similarity model is addressed. Both a priori and a posteriori tests demonstrate the efficiency of the proposed model.

Linear eddy simulations of Reynolds number and Schmidt number effects on turbulent scalar mixing
View Description Hide DescriptionEffects of molecular diffusion on turbulent scalar mixing are studied using the linear eddymodel. Unlike the energy spectrum which is determined only by the viscous and eddy time scales, the scalar spectra also depend on the diffusion time scales. The linear eddymodel, being onedimensional, offers an inexpensive way of capturing these time scale dependencies. Some of the observations made using experiments and direct simulations are verified using the model. Simulations reported here indicate that certain features of scalar mixing continue to depend on the Reynolds number and the Schmidt number (Sc) in the range of parameter space and that is unattainable using the current direct simulation capabilities. However, some of the models developed for differential diffusion using direct simulations are shown to be accurate even when the difference in the Schmidt numbers of the scalars and (or) the Reynolds numbers are very high.

Proper representation of the subgridscale eddy viscosity for the dynamic procedure in large eddy simulation using finite difference method
View Description Hide DescriptionAlternative representation of the dynamic eddyviscosity coefficient to the traditional Smagorinsky model is investigated for the application of the model to the finite difference method. The model is derived by considering the consistency of the numerical error between and in the dynamic procedure. The proposed model is validated in the plane channel flow at the of up to 590 and is found to be less sensitive to the discretized test filtering operation.

The multiscale formulation of large eddy simulation: Decay of homogeneous isotropic turbulence
View Description Hide DescriptionThe variational multiscale method is applied to the large eddy simulation(LES) of homogeneous, isotropic flows and compared with the classical Smagorinsky model, the dynamic Smagorinsky model, and direct numerical simulation (DNS) data. Overall, the multiscale method is in better agreement with the DNS data than both the Smagorinsky model and the dynamic Smagorinsky model. The results are somewhat remarkable when one realizes that the multiscale method is almost identical to the Smagorinsky model (the least accurate model!) except for removal of the eddyviscosity from a very small percentage of the lowest modes.

Active control of laminarturbulent transition using instantaneous vorticity signals at the wall
View Description Hide DescriptionMany approaches with the objective to actively delay the laminarturbulent transition in boundary layers are currently under investigation. These approaches, which are mostly based on the superposition of antiphase disturbances, fail in cases where high (nonlinear) disturbance amplitudes occur. One possible solution to overcome this problem is the direct feedback of instantaneous flow signals from the wall. In our case the spanwise vorticity on the wall is sensed, multiplied by a certain factor A and prescribed as a new boundary condition at the wall with some time delay This procedure (called control ) yields a robust algorithm which is less influenced by nonlinearities than other processes based on the linear superposition of disturbances (waves). The method was developed and evaluated using both linear stability theory and a threedimensional spatial DNS code solving the complete Navier–Stokes equations.

The influence of control on proper orthogonal decomposition of wallbounded turbulent flows
View Description Hide DescriptionThis paper explores the effects of several wallbased, turbulence control strategies on the structure of the basis functions determined using the proper orthogonal decomposition (POD). This research is motivated by the observation that the POD basis functions are only optimal for the flow for which they were created. Under the action of control, the POD basis may be significantly altered so that the common assumption that effective reducedorder models for predictive control can be constructed from the POD basis of an uncontrolled flow may be suspect. This issue is explored for plane, incompressible, turbulent channel flow at Reynolds number, Based on well resolved large eddy simulations, POD bases are constructed for three flows: no control; opposition control, which achieves a 25% drag reduction; and optimal control, which gives a 40% drag reduction. Both controlledflows use wall transpiration as the control mechanism and only differ in the technique used to predict the control. For both controlledflows, the POD basis is altered from that of the nocontrol flow by the introduction of a localized shear layer near the walls and a nearly impenetrable virtual wall that hinders momentum transfer in the wallnormal direction thereby leading to drag reduction. A major difference between the two controlledflows is that the shear layer and associated virtual wall are located farther away from the physical wall when using optimal compared to opposition control. From this investigation, it is concluded that a nocontrol POD basis used as a lowdimensional model will not capture the key features of these controlledflows. In particular, it is shown that such an approximation leads to grossly underpredicted Reynolds stresses. These results indicate that a nocontrol POD basis should be supplemented with features of a controlledflow before using it as a lowdimensional approximation for predictive control.

A scaling analysis of turbulent flows driven by Rayleigh–Taylor and Richtmyer–Meshkov instabilities
View Description Hide DescriptionWe investigate inertial subrange energy spectra associated with turbulent flows developed by the Rayleigh–Taylor instability and Richtmyer–Meshkov instability(RMI). We argue that the extended Kolmogorov–Kraichnan phenomenology originally developed for turbulent flows with an external agent should also be applicable to these instability driven turbulent flows. A prediction of the mixing zone width for the RMI induced turbulent flow is presented using the RMI modified energy spectrum and a twoequation turbulencemodel. A possible application to subgrid modeling for largeeddy simulation is discussed briefly.
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 BRIEF COMMUNICATIONS


Energy spectrum in the enstrophy transfer range of twodimensional forced turbulence
View Description Hide DescriptionNumerical simulations of twodimensional forced turbulence suggest that the enstrophy transfer range energy spectrum a little steeper than is robust in the sense that it may be realized in a wave number range under different run conditions. It is shown that such energyspectra fit well where is a dimensionless constant, the enstrophy transfer rate per unit mass and a wave number at the bottom of the range. The simulations give in fairly good agreement with the existing theoretical estimates.
