Showing papers on "Shear flow published in 1991"

Near-wall turbulence closure modeling without ``damping functions''

Abstract: An elliptic relaxation model is proposed for the strongly inhomogeneous region near the wall in wall-bounded turbulent shear flow. This model enables the correct kinematic boundary condition to be imposed on the normal component of turbulent intensity. Hence, wall blocking is represented. Means for enforcing the correct boundary conditions on the other components of intensity and on the k — ɛ equations are discussed. The present model agrees quite well with direct numerical simulation (DNS) data. The virtue of the present approach is that arbitrary “damping functions” are not required.

A Powerful Local Shear Instability in Weakly Magnetized Disks. II. Nonlinear Evolution

Abstract: We consider the dynamical evolution of an accretion disk undergoing Keplerian shear flow in the presence of a weak magnetic field. A linear perturbation analysis presented in a companion paper shows that such a flow is dynamically unstable; here we consider some nonlinear consequences of this instability. We solve the equations of compressible magnetohydrodynamics using a two-dimensional finite-difference code. The Keplerian disk is threaded with a weak magnetic field that has a magnetic energy density much less than the thermal pressure

Flow and Reactions in Permeable Rocks

Abstract: Preface 1. Introduction 2. The governing principles 3. General flow characteristics: patterns of flow 4. General flow characteristics: patterns of reactions 5. Instabilities 6. Pressure-driven flows 7. Thermal convection References Index.

Motion of particles with inertia in a compressible free shear layer

Abstract: The effects of the inertia of a particle on its flow-tracking accuracy and particle dispersion are studied using direct numerical simulations of 2D compressible free shear layers in convective Mach number (Mc) range of 0.2 to 0.6. The results show that particle response is well characterized by tau, the ratio of particle response time to the flow time scales (Stokes' number). The slip between particle and fluid imposes a fundamental limit on the accuracy of optical measurements such as LDV and PIV. The error is found to grow like tau up to tau = 1 and taper off at higher tau. For tau = 0.2 the error is about 2 percent. In the flow visualizations based on Mie scattering, particles with tau more than 0.05 are found to grossly misrepresent the flow features. These errors are quantified by calculating the dispersion of particles relative to the fluid. Overall, the effect of compressibility does not seem to be significant on the motion of particles in the range of Mc considered here.

Analysis of turbulence in the orthonormal wavelet representation

Abstract: The usefulness of the wavelet transform for the analysis of turbulent flow fields is explored by examining the wavelet transform properties of a decomposition of turbulent velocity fields into modes that exhibit the localization in a wavenumber and physical space. The calculations are performed on 3D fields from direct numerical simulations of isotropic flow and homogeneous shear flow, and from measurements in two laboratory wind-tunnel experimental velocity signals (boundary layer and wake behind a circular cylinder). The analysis confirmed that there is strong spatial intermittency in nonlinear quantities; their mean spectral behavior results from a delicate balance between large positive and negative excursions. The wavelet analysis is a way to quantify these observations in a standardized fashion by using 'flow-independent eddies' to decompose the velocity field.

Inertial migration of a small sphere in linear shear flows

Abstract: The motion of a small, rigid sphere in a linear shear flow is considered. Saffman's analysis is extended to other asymptotic cases in which the particle Reynolds number based on its slip velocity is comparable with or larger than the square root of the particle Reynolds number based on the velocity gradient. In all cases, both particle Reynolds numbers are assumed to be small compared to unity. It is shown that, as the Reynolds number based on particle slip velocity becomes larger than the square root of the Reynolds number based on particle shear rate, the magnitude of the inertial migration velocity rapidly decreases to very small values. The latter behaviour suggests that contributions that are higher order in the particle radius may become important in some situations of interest.

On Local Isotropy of Passive Scalars in Turbulent Shear Flows

Abstract: An assessment of local isotropy and universality in high-Reynolds-number turbulent flows is presented. The emphasis is on the behaviour of passive scalar fields advected by turbulence, but a brief review of the relevant facts is given for the turbulent motion itself. Experiments suggest that local isotropy is not a natural concept for scalars in shear flows, except, perhaps, at such extreme Reynolds numbers that are of no practical relevance on Earth. Yet some type of scaling exists even at moderate Reynolds numbers. The relation between these two observations is a theme of this paper.

Brownian diffusion of submicrometer particles in the viscous sublayer

Abstract: Diffusion of Brownian submicrometer particles from a point source in the vicous sublayer of a turbulent shear flow near a solid smooth wall is considered in this paper. The equation of motion of particles including the Brownian effect is considered. Ensembles of 500 particle trajectories are evaluated, compiled, and statistically analyzed. Effects of particle size, density ratio, and source distance from the wall on particle concentration profile and wall deposition rate are studied. The results are compared with those obtained from the exact solution to the corresponding convective diffusion equation in the absence of turbulent fluctuations. The effect of turbulence near a wall is also considered. The results show that the Brownian effects play a significant role in the diffusion of submicrometer particles at distances less than 2 wall units from the solid surface. The effect of turbulence, however, could become significant during the ejection/inrush process.

On the dynamics of near-wall turbulence

Abstract: A model of the dynamic physical processes that occur in the near-wall region of a turbulent flow at high Reynolds numbers is described The hairpin vortex is postulated to be the basic flow structure of the turbulent boundary layer It is argued that the central features of the near-wall flow can be explained in terms of how asymmetric hairpin vortices interact with the background shear flow, with each other, and with the surface layer near the wall The physical process that leads to the regeneration of new hairpin vortices near the surface is described, as well as the processes of evolution of such vortices to larger-scale motions farther from the surface The model is supported by recent important developments in the theory of unsteady surface-layer separation and a number of `kernel' experiments which serve to elucidate the basic fluid mechanics phenomena believed to be relevant to the turbulent boundary layer Explanations for the kinematical behaviour observed in direct numerical simulations of low Reynolds number boundary-layer and channel flows are given An important aspect of the model is that it has been formulated to be consistent with accepted rational mechanics concepts that are known to provide a proper mathematical description of high Reynolds number flow

Experimental observations of particle migration in concentrated suspensions: Couette flow

Abstract: Nuclear magnetic resonance (NMR) imaging was used to observe the evolution of radial concentration and velocity profiles of initially well‐mixed concentrated suspensions of spheres in viscous Newtonian liquids undergoing flow between rotating concentric cylinders (wide‐gap, annular Couette flow). In Couette flow, particles migrate from the high shear‐rate region near the inner rotating cylinder to the low shear‐rate region at the outer wall. The particle concentration near the outer wall approaches maximum packing for randomly distributed spheres at steady state, and velocity profiles reveal that the suspension is almost stagnant in these regions. For unimodal suspensions of spheres, the shear‐induced migration of large particles results in concentric two‐dimensional, circular sheets of particles arranged in hexagonal close‐packed arrangements extending inward from the outer wall. This paper examines the functional dependence of particle migration in concentrated suspensions undergoing shear flow in a wid...

Kinetic theory for granular flow of dense, slightly inelastic, slightly rough spheres

Abstract: A general set of conservation equations and constitutive integrals for the dynamic properties of the rapid flow of a granular material consisting of slightly inelastic and slightly rough spherical particles is derived by following an approach used in the kinetic theory of dense gases. By taking moments of the translational and rotational particle velocities in the general transport moment equation and making the Enskog approximation, the singlet velocity distribution function is determined. As a result, the constitutive relations and coefficients such as stresses, energy fluxes, rates of translational and rotational energy interchanges, shear viscosity, spin viscosity, bulk viscosity and ‘thermal’ conductivities are obtained. The present theory incorporates the kinetic as well as the collisional contributions for stresses and energy fluxes. Thus, it is appropriate for dilute as well as dense concentrations of solids. For the case of simple shear flow, there is favourable agreement between the theoretical predictions of stresses and both the experimental measurements and the results from computer simulations.

Application of a Reynolds stress turbulence model to the compressible shear layer

Abstract: Theoretically based turbulence models have had success in predicting many features of incompressible, free shear layers However, attempts to extend these models to the high-speed, compressible shear layer have been less effective In the present work, the compressible shear layer was studied with a second-order turbulence closure, which initially used only variable density extensions of incompressible models for the Reynolds stress transport equation and the dissipation rate transport equation The quasi-incompressible closure was unsuccessful; the predicted effect of the convective Mach number on the shear layer growth rate was significantly smaller than that observed in experiments Having thus confirmed that compressibility effects have to be explicitly considered, a new model for the compressible dissipation was introduced into the closure This model is based on a low Mach number, asymptotic analysis of the Navier-Stokes equations, and on direct numerical simulation of compressible, isotropic turbulence The use of the new model for the compressible dissipation led to good agreement of the computed growth rates with the experimental data Both the computations and the experiments indicate a dramatic reduction in the growth rate when the convective Mach number is increased Experimental data on the normalized maximum turbulence intensities and shear stress also show a reduction with increasing Mach number

The stability of a sheared density interface

Abstract: This study investigates the stability of stratified shear flows when the density interface is much thinner than, and displaced with respect to, the velocity interface. Theoretical results obtained from the Taylor–Goldstein equation are compared with experiments performed in mixing layer channels. In these experiments a row of spanwise vortex tubes forms at the level of maximum velocity gradient which, because of the profile asymmetry, is displaced from the mean interface level. As the bulk Richardson number is lowered from a high positive value the effects of these vortex tubes become more pronounced. Initially the interface cusps under their influence, then thin wisps of fluid are drawn from the cusps into asymmetric Kelvin–Helmholtz billows. At lower Richardson numbers increasingly more fluid is drawn into these billows. The inherent asymmetry of flows generated in mixing layer channels is shown to preclude an effective study of the Holmboe instability. Statically unstable flows (negative Richardson numbers) are subject to the Rayleigh–Taylor instability. However, if the absolute value of the Richardson number is sufficiently small the Kelvin–Helmholtz instability dominates initially.

Effect of molecular elasticity on out-of-plane orientations in shearing flows of liquid-crystalline polymers

Abstract: The Doi equation for the time-dependent orientational Distribution function of rodlike molecules in a nematic monodomain is solved for Startup of a simple shearing flow with director orientation initially oriented at various angles with respect to the shearing plane, where the shearing plane is defined to be parallel to both the velocity and its gradient. Two numerical solution techniques are used; one is an expansion in spherical harmonic functions, which is a generalization of a technique derived earlier for a director confined to the shearing plane, and the second is a stochastic method that integrates the equations of motion for a large ensemble of molecules. We find that at low and modest shear rates, the director can be attracted either to a time-periodic tumbling orbit that lies in the shearing plane or to an orbit that lies out of the shearing plane. This latter orbit is either a steady "log-rolling" state with average orientation perpendicular to the shearing plane or a time-periodic "kayaking" state with an orbit oblique to the shearing plane. The final state of the system depends on the shear rate and the strength of the nematic potential. In some cases both the in-plane tumbling and log-rolling (or kayaking) states are attractors; the final state then depends on the initial director.

Mesoscopic domain theory for textured liquid crystalline polymers

Abstract: Here we present a mesoscopic theory of the low‐flow‐rate rheological properties of textured or polydomain samples of liquid crystalline polymers. In this theory, the Leslie–Ericksen equations are assumed to apply to each domain; these equations are averaged over a spatial region, large compared to a single domain, yet small compared to bulk dimensions. Along with these averaged equations, phenomenological expressions are postulated that allow us to obtain a relatively simple set of coupled equations for the domain size and the mesoscopic orientation and stress tensors. The values of the Leslie–Ericksen viscosities that appear in the equations are obtained from the Doi theory for nematic polymers. We apply the theory to several shear flows, namely recoverable shear after cessation of steady shearing, and step reversal and step increase of shear rate. In each case promising agreement is found between the predictions of the mesoscopic theory and measurements on lyotropic liquid crystalline polymers.

Evolution and dynamics of shear-layer structures in near-wall turbulence

Abstract: Near-wall flow structures in turbulent shear flows are analyzed, with particular emphasis on the study of their space-time evolution and connection to turbulence production. The results are obtained from investigation of a database generated from direct numerical simulation of turbulent channel flow at a Reynolds number of 180 based on half-channel width and friction velocity. New light is shed on problems associated with conditional sampling techniques, together with methods to improve these techniques, for use both in physical and numerical experiments. The results clearly indicate that earlier conceptual models of the processes associated with near-wall turbulence production, based on flow visualization and probe measurements need to be modified. For instance, the development of asymmetry in the spanwise direction seems to be an important element in the evolution of near-wall structures in general, and for shear layers in particular. The inhibition of spanwise motion of the near-wall streaky pattern may be the primary reason for the ability of small longitudinal riblets to reduce turbulent skin friction below the value for a flat surface.

Compressibility effects on the growth and structure of homogeneous turbulent shear flow

Abstract: Compressibility effects within decaying isotropic turbulence and homogeneous turbulent shear flow have been studied using direct numerical simulation. The objective of this work is to increase our understanding of compressible turbulence and to aid the development of turbulence models for compressible flows. The numerical simulations of compressible isotropic turbulence show that compressibility effects are highly dependent on the initial conditions. The shear flow simulations, on the other hand, show that measures of compressibility evolve to become independent of their initial values and are parameterized by the root mean square Mach number. The growth rate of the turbulence in compressible homogeneous shear flow is reduced compared to that in the incompressible case. The reduced growth rate is the result of an increase in the dissipation rate and energy transfer to internal energy by the pressure-dilatation correlation. Examination of the structure of compressible homogeneous shear flow reveals the presence of eddy shocklets, which are important for the increased dissipation rate of compressible turbulence.

Stability of Transverse Shear Flows in Shallow Open Channels

Abstract: The bed-friction effect on the stability of transverse shear flows in shallow open channels is examined using a linear and “inviscid” theory. Numerical calculations are conducted for four groups of parallel flows with inflection-point velocity profiles. The necessary conditions for the transverse shear flows to become unstable, so that the large-scale transverse motion may coexist with the small-scale bed-generated turbulence, are determined from the calculations. The results are correlated with two dimensionless parameters: a bed-friction number and an ambient-velocity parameter. The bed-friction number quantifies the stabilizing effect of the bed-friction. The ambient-velocity parameter characterizes the changes in depth and roughness across the open-channel flows. In the limiting case of a weak transverse shear flow, when the change in velocity across the flow is small, the bed-friction number becomes the only dimensionless parameter governing the stability of the transverse shear flows. The critical values of this bed-friction number for the weak transverse shear flows with hyperbolic-tangent and hyperbolic-secant velocity profiles, are 0.120 and 0.145, respectively.

The linear and nonlinear shear instability of a fluid sheet

Abstract: A theoretical and computational investigation of the inviscid Kelvin–Helmholtz instability of a two‐dimensional fluid sheet is presented. Both linear and nonlinear analyses are performed. The study considers the temporal dilational (symmetric) and sinuous (antisymmetric) instability of a sheet of finite thickness, including the effect of surface tension and the density difference between the fluid in the sheet and the surrounding fluid. Previous linear‐theory results are extended to include the complete range of density ratios and thickness‐to‐wavelength ratios. It is shown that all sinuous waves are stable when the dimensionless sheet thickness is less than a critical value that depends on the density ratio. At low density ratios, the growth rate of the sinuous waves is larger than that of the dilational waves, in agreement with previous results. At higher density ratios, it is shown that the dilational waves have a higher growth rate. The nonlinear calculations indicate the existence of sinuous oscillating modes when the density ratio is of the order of 1. Sinuous modes may result in ligaments interspaced by half of a wavelength. Dilational modes grow monotonically and may result in ligaments interspaced by one wavelength.

Nematic to smectic-A phase transition under shear flow: A nonequilibrium synchrotron x-ray study.

Abstract: We report on x-ray scattering studies of the nematic to smectic-A transition in 4-cyano-4'-octylbiphenyl under nonequilibrium shear-flow conditions. As the transition is approached, the interplay between the viscous frictional and the flow-induced-fluctuation forces on the nematic director leads to a series of regimes whose occurrence results from the divergence in one of the viscosities due to the critical slowing down of the smectic-A order-parameter fluctuations. The experiments demonstrate that, under flow, synchrotron x-ray-diffraction techniques provide a powerful structural probe of steady-state dynamical behavior.

Kinetic theory and rheology of dilute, nonhomogeneous polymer solutions

Abstract: A phase‐space kinetic theory of dilute polymer solutions is developed to account for the effects of nonhomogeneous velocity and stress fields. The theory allows the configuration distribution function to depend on spatial location and explicitly treats the polymer molecule as an extended object in space. Constitutive equations for the mass flux vector and stress tensor are derived that predict polymer migration induced by stress gradients and nonuniform velocity gradients. In addition, the constitutive equation for stress contains a diffusive term in stress, and hence the model does not fall within the class of simple fluids. Simple shear flow between parallel plates is solved to illustrate the features of the constitutive equations. Asymptotic analysis and numerical calculations show the formation of boundary layers in stress, velocity gradient, and polymer concentration that arise near solid walls as a result of preferential orientation of the polymer molecules there. The thickness of these layers scale...

Local Anisotropy in Strained Turbulence at High Reynolds Numbers

Abstract: It is shown that the hypothesis of local isotropy is implausible in the presence of significant mean rates of strain. In fact, it appears that in uniform shear flow near equilibrium, local isotropy can never constitute a systematic approximation, even in the limit of infinite Reynolds number. An estimate of the level of mean strain rate for which local isotropy is formally a good approximation is provided.

Measurement of the drift of a droplet due to the presence of a plane

Abstract: The drift of a deformable droplet of low viscosity (viscosity ratio λ=0.08) in a Couette device is examined. The drift is measured both in the plane of shear (due to the rigid outer bounding walls of the Couette device) and also normal to the plane of shear (due to the upper bounding stress‐free surface). A general relationship between normal stresses induced by the deformation of a droplet in an arbitrary shear flow and the leading‐order drift normal to rigid and stress‐free plane surfaces is described theoretically. This relationship is consistent with previous theoretical predictions for droplet migration in shear flows, and is used to compare results from the drift measurement experiments with first‐order deformation theories. The measured drift velocities are in reasonable agreement with the theory of Schowalter et al. [J. Colloid Interface Sci. 26, 152 (1968)].

Ballooning instabilities in tokamaks with sheared toroidal flows

Abstract: The stability of ballooning modes in the presence of sheared toroidal flows is investigated. The eigenmodes are shown to be related by a Fourier transformation to the nonexponentially growing Floquet solutions found by Cooper [Plasma Phys. Controlled Fusion 30, 1805 (1988)]. It is further shown that the problem cannot be reduced further than to a two‐dimensional partial differential equation. Next, the generalized ballooning equation is solved analytically for a circular tokamak equilibrium with sonic flows, but with a small rotation shear compared to the sound speed. With this ordering, the centrifugal forces are comparable to the pressure gradient forces driving the instability, but coupling of the mode with the sound wave is avoided. A new stability criterion is derived that explicitly demonstrates that flow shear is stabilizing at constant centrifugal force gradient.

On the mechanism of aggregation in the shear flow of suspensions

Abstract: A theoretical analysis of aggregation and disaggregation processes in the laminar shear flow of a suspension is presented. Aggregate formation is attributed to orthokinetic coagulation, which is considered in terms of the hierarchical model (i.e., only the collisions of equal-sized aggregates are taken into account, whereas all other types of collisions are shown to be ineffective). Different limiting mechanisms of aggregate growth are considered. They include breakup of an aggregate due to the Brownian motion of particles or due to viscous stresses and its contraction, i.e., the increase in its fractal dimension. Three types of experiments are quantitatively interpreted in terms of the considered model of aggregation: the reduction of aggregate number concentration in flow due to orthokinetic coagulation, the measurement of the maximum aggregate size vs shear rate, and rheological tests.

Edge turbulence scaling with shear flow

Abstract: A formula relating turbulence levels with arbitrary shear flow is derived. When the diffusion coefficient is made a functional of the corresponding turbulence level, it is found that the scaling laws governing turbulence suppression are considerably modified. The results are compared with known formulas in various limiting cases, indicating that turbulence suppression mainly pertains in the moderate shear flow regime. The results also show that a flattened (steep) radial equilibrium gradient tends to enhance (eliminate) turbulence suppression due to the shear flow.

Theory of shear suppression of edge turbulence by externally driven radio-frequency waves

Abstract: Here, we propose and analyze a technique for active suppression of tokamak edge turbulence. Suppression occurs due to the effects of a sheared radial electric field generated by externally driven radio-frequency waves. Plasma flow is induced by radially varying wave-driven Reynolds and magnetic stresses, and opposed by neoclassical damping. For Alfv\'enic flow drive, the predicted shear flow profile is determined by ion inertia and electron dissipation effects. Results indicate that a modest amount of absorbed power is required for edge-turbulence suppression. More generally, several novel results in the theory of momentum transport by electromagnetic fluctuations are presented.

Experimental investigation of coherent structures in turbulent boundary layers

Abstract: The events which are responsible for strong Reynolds-stress production in the near-wall region of a bounded turbulent shear flow have been investigated in a turbulent boundary layer at a Reynolds number based on momentum thickness of Reθ = 4650. The coherent structures associated with the production process have been studied using the quadrant detection technique. All three velocity components were measured in a three-dimensional sampling volume about the point of detection. The conditional ensemble-averaged velocity field associated with the detection of a sweep or an ejection is presented and compared with non-conditioned space–time correlations. Conditional space–time probability density distributions were calculated at all measurement locations based on the occurrence of a Reynolds-stress-producing event at the detection point. The resulting three-dimensional representation of the conditional probability demonstrates that a significant fraction of the events are relatively large in scale, that a hierarchy of sizes exists and that there is a link between the outer flow and the ’bursting’ process. However, many investigators have shown that the ’bursting’ frequency scales with wall variables. Therefore all indications suggest that the scales are generated by a wall-layer mechanism but grow to sizes and convect with velocities scaling with the outer layer.