Homogeneous Shear Flow Research Articles

Drop shape dynamics of a Newtonian drop in a non-Newtonian matrix during transient and steady shear flow

Transient and steady deformation of a single Newtonian drop immersed in a non-Newtonian matrix subjected to a homogeneous shear flow is investigated microscopically. Two model Boger fluids have been used as non-Newtonian matrices. The three-dimensional drop shape is completely determined as observations from both the velocity-vorticity and velocity-velocity gradient plane are available. Start-up and relaxation are investigated varying both the capillary number and the elasticity of the matrix fluid, while the viscosity ratio is kept constant. The extensive data set demonstrates that matrix elasticity reduces the steady drop deformation and promotes droplet orientation, can induce a drop deformation overshoot in the start-up experiments and slows down the relaxation phenomena. The experimental results have been compared with predictions of a phenomenological model [M. Minale, J. Non-Newtonian Fluid Mech. 123, 151–160 (2004)], that is slightly modified in the present work. It shows good agreement with the e...

A stochastic subgrid model with application to turbulent flow and scalar mixing

A new computationally cheap stochastic Smagorinsky model which allows for backscatter of subgrid scale energy is proposed. The new model is applied in the large eddy simulation of decaying isotropic turbulence, rotating homogeneous shear flow and turbulent channel flow at Reτ=360. The results of the simulations are compared to direct numerical simulation data. The inclusion of stochastic backscatter has no significant influence on the development of the kinetic energy in homogeneous flows, but it improves the prediction of the fluctuation magnitudes as well as the anisotropy of the fluctuations in turbulent channel flow compared to the standard Smagorinsky model with wall damping of CS. Moreover, the stochastic model improves the description of the energy transfer by reducing its length scale and increasing its variance. Some improvements were also found in isotropic turbulence where the stochastic contribution improved the shape of the enstrophy spectrum at the smallest resolved scales and reduced the time scale of the smallest resolved scales in better agreement with earlier observations.

Inertial range scaling of scalar flux spectra in uniformly sheared turbulence

A model based on two-point closure theory of turbulence is proposed and applied to study the Reynolds number dependency of the scalar flux spectra in homogeneous shear flow with a cross-stream uniform scalar gradient. For the cross-stream scalar flux, in the inertial range the spectral behavior agrees with classical predictions and measurements. The streamwise scalar flux is found to be in good agreement with the results of atmospheric measurements. However, both the model results and the atmospheric measurements disagree with classical predictions. A detailed analysis of the different terms in the evolution equation for the streamwise scalar flux spectrum shows that nonlinear contributions are governing the inertial subrange of this spectrum and that these contributions are relatively more important than for the cross-stream flux. A new expression for the scalar flux spectra is proposed. It allows us to unify the description of the components in one single expression, leading to a classical K−7∕3 inertial range for the cross-stream component and to a new K−23∕9 scaling for the streamwise component that agrees better with atmospheric measurements than the K−3 prediction of J. C. Wyngaard and O. R. Coté [Quart. J. R. Met. Soc. 98, 590 (1972)].

On fully self-preserving solutions in homogeneous turbulence

Mathematical attributes of full self-preserving solutions (‘full’ meaning self-similar at all scales with non-zero viscosity) for isotropic decay as well as for homogeneous shear flow turbulence are examined from a fundamental theoretical standpoint. Fully self-preserving solutions are those wherein the two-point double and triple velocity correlations are self-similar at all scales. It is shown that the full self-preserving solutions for isotropic decay corresponds to a t −1 asymptotic power law decay, consistent with earlier studies. Fully self-preserving solutions for homogeneous shear flow correspond to a production-equals-dissipation equilibrium, with bounded turbulent kinetic energy and dissipation. It is then shown that the fully self-preserving solutions of isotropic decay and of homogeneous shear flow both require severe constraints on the behavior of the low-wavenumber energy spectra. These constraints render the full self-preserving solutions as mathematical consistent but having no physical relevance. The implications of the dependence of the full self-preserving solutions on the low-wavenumber spectra for one-point (engineering) turbulence models is discussed. Invited speaker, Santa Fe CNLS-LANL Workshop on Turbulence and Cascade.

G1302 主流方向系回転一様剪断乱流の数値解析的研究(2)(GS13 数値シミュレーション,一般セッション)

Direct numerical simulation (DNS) for homogeneous turbulent shear flows in the streamwise system rotating is performed. In the turbulence energy, the streamwise rotation effect is smaller than the shear-direction and spanwise ones. In the budget of the Reynolds stress, the rotation term balances with the pressure strain one at the strong rotation case. The streamwise rotation effect has influence on the small-scale motion.

고체입자가 부상된 균질 난류 전단유동의 2차-모멘트 모형화

A second-moment closure is applied to the prediction of a homogeneous turbulent shear flow laden with mono-size particles. The closure is carried out based on a 'two-fluid' methodology in which both carrier and dispersed phases are considered in the Eulerian frame. To reduce the number of coupled differential equations to be solved, Reynolds stress transport equations and algebraic stress models are judiciously combined to obtain the Reynolds stress of carrier and dispersed phases in the mean momentum equation. That is, the Reynolds stress components for carrier and dispersed phases are solved by modelled transport equations, but the fluid-particle velocity covariance tensors are treated by the algebraic models. The present predictions for all the components of Reynolds stresses are compared to the DNS data. Reasonable agreements are observed in all the components, and the effects of the coupling of carrier and dispersed phases are properly captured in every aspects.

G1302 主流方向系回転一様剪断乱流の数値解析的研究(1)(GS13 数値シミュレーション,一般セッション)

G1302 主流方向系回転一様剪断乱流の数値解析的研究(1)(GS13 数値シミュレーション,一般セッション)

An improved algorithm for simulating three-dimensional, viscoelastic turbulence

We present a new finite-difference formulation to update the conformation tensor in dumbbell models (e.g., Oldroyd-B, FENE-P, Giesekus) that guarantees positive eigenvalues of the tensor (i.e., the tensor remains positive definite) and prevents over-extension for finite-extensible models. The formulation is a generalization of the second-order, central difference scheme developed by Kurganov and Tadmor [A. Kurganov, E. Tadmor, New high-resolution central schemes for nonlinear conservation laws and convection–diffusion equations, J. Comput. Phys. 160 (2000) 241–282] that guarantees a scalar field remains everywhere positive. We have extended the algorithm to guarantee a tensor field remains everywhere positive definite following an update. Extensive testing of the algorithm shows that the volume average of the conformation tensor is conserved. Furthermore, volume averages of the conformation tensor in homogeneous turbulent shear flow made over the Eulerian grid are in quantitative agreement with Lagrangian averages made over fluid particles moving throughout the domain, highlighting the accuracy of the treatment of the convective terms.

Objective tensorial representation of the pressure–strain correlations of turbulence

An explicit algebraic model for the fluctuating pressure–strain rate correlations of turbulence is developed by the use of representation theorems for tensor-valued isotropic tensors, and by invoking the principle of objectivity. The resulting model differs from others by the absence of the vorticity tensor from its formulation. The new model is calibrated by reference to data from homogeneous shear flows, and its potential as a practical tool for the analysis of turbulent flows is demonstrated by numerical simulations of a benchmark two-dimensional shear layer.

Test of large-eddy simulation models for homogeneous-shear turbulence in stratification

Numerical tests of various subgrid-scale (SGS) models were conducted for turbulence in thermally stratified homogeneous-shear flow at a relatively low Reynolds number. Compared with a direct numerical simulation (DNS), we found that nondynamic isotropic SGS models are not able to represent the energy spectrum very well because the energy decays considerably during the transition between an initial random stage and a stage of coherent turbulent structures. Dynamic models performed well for simulating the energy spectrum and the change of GS properties with time; anisotropy is not a necessary feature under the present simulation conditions, although one of the special features of stratified turbulence is anisotropy. This may be because the present grids for large-eddy simulation were fine enough to resolve the patches of counter-gradient heat fluxes, which play an important role in the evolution of turbulent energy in stratified turbulence. With respect to the domain-averaged values of SGS stresses, only the dynamic two-parameter mixed (DTM) model produced results of the same order of magnitude as those of filtered DNS. This is because of the terms arising from re-decomposing of the SGS stresses in the DTM model. It was also found that this incompetence in simulating the SGS stress is not necessary to simulate GS energy evolution, as is known for wall turbulence.

Effect of stable-density stratification on counter gradient flux of a homogeneous shear flow

We performed direct numerical simulations of homogeneous shear flow under stable-density stratification to study the buoyancy effects on the heat and momentum transfer. These numerical data were compared with those of a turbulent channel flow to investigate the similarity between the near-wall turbulence and the homogeneous shear flow. We also investigated the generation mechanism of the persistent CGFs (counter gradient fluxes) appearing at the higher wavenumbers of the cospectrum, and lasting over a long time without oscillation. Spatially, the persistent CGFs are associated with the longitudinal vortical structure, which is elongated in the streamwise direction and typically observed in both homogeneous shear flow and near-wall turbulence. The CGFs appear at both the top and bottom of this longitudinal vortical structure, and expand horizontally with an increase in the Richardson number. It was found that the production and turbulent-diffusion terms are responsible for the distribution of the Reynolds shear stress including the persistent CGFs. The buoyancy term, combined with the swirling motion of the vortex, contributes to expand the persistent CGF regions and decrease the down gradient fluxes.

Dissipation element analysis of scalar fields in turbulence

The field of the fluctuating scalar obtained from Direct Numerical Simulation (DNS) in homogeneous shear flow is subdivided into finite size regions within which it varies monotonously. These regions are called dissipation elements and are identified by calculating trajectories normal to isoscalar surfaces starting from every grid point until a minimum and a maximum point is reached. Two parameters describe the statistical properties of dissipation elements sufficiently well: the linear distance between the minimum and maximum points and the absolute value of the scalar difference at these points. The joint probability density function of these parameters decomposes into a conditional pdf of the scalar difference and the marginal pdf of the distance between the minimum and maximum points, the latter being the object of this study. For the length scale distribution function a stochastic evolution equation was derived in a companion paper. It implies the cutting and reconnection of linear elements and the effect of molecular diffusion. The equation is an integral equation and must be solved numerically. In this paper we show how one-dimensional simulations of randomly generated scalar profiles would illustrate the cutting and reconnection processes as well as the drift and disappearance of small elements by molecular diffusion. The resulting distribution function from the simulation shows good agreement with the predicted distribution function. It is concluded that the mean distance between extremal points is of the order of the scalar Taylor length. To cite this article: N. Peters, L. Wang, C. R. Mecanique 334 (2006).

Anisotropic developments for homogeneous shear flows

The general decomposition of the spectral correlation tensor Rij(k) by Cambon et al. [J. Fluid Mech. 202, 295 (1989); 337, 303 (1997)] into directional and polarization components is applied to the representation of Rij(k) by spherically averaged quantities. The decomposition splits the deviatoric part Hij(k) of the spherical average of Rij(k) into directional and polarization components Hij(e)(k) and Hij(z)(k). A self-consistent representation of the spectral tensor is constructed in terms of these spherically averaged quantities. The directional and polarization components must be treated independently: representation of the spectral tensor using the spherical average Hij(k) alone proves to be inconsistent with Navier-Stokes dynamics. In particular, a spectral tensor consistent with a prescribed Reynolds stress is not unique. Since spherical averaging entails a loss of information, the description of an anisotropic correlation tensor by spherical averages is limited to weak departures from isotropy. The degree of anisotropy permitted is restricted by realizability requirements. More general descriptions can be given using a higher-order expansion of the spectral tensor. Directionality is described by a conventional expansion in spherical harmonics, but polarization requires an expansion in special tensorial quantities generated by irreducible representations of the rotation group SO3. These expansions are considered in more detail in the special case of axial symmetry.

Numerical simulation of compressible turbulent flow using algebraic Reynolds stress model

The explicit incompressible algebraic Reynolds stress model proposed by Gatski and Speziale [J. Fluid Mech. 254, 59 (1993)] has been extended to be applied to compressible turbulent flows. This extension is based on the modeled compressible transport equations for the Favre-averaged Reynolds stress tensor. The resulting model is tested in a variety of compressible turbulent flows which include the homogeneous shear flow and the compressible mixing layer. Comparisons between the present model predictions and the results of direct numerical simulations and experiments are quite encouraging.

On the behavior of two-equation models in nonequilibrium homogeneous turbulence

The class of turbulence models that utilize two-equation differential transport equations is investigated. A dynamical systems analysis is performed on these transport equations to identify the various critical points and associated stability characteristics. The goal is to understand the transient solution behavior and to identify the possible solution fixed points. The analysis is restricted to homogeneous flows with constant and time-dependent mean shear. The transient behavior of the turbulence variables identifies possible pseudolaminar solutions that can be generated. These solutions are unphysical and need to be avoided. The present study provides the necessary framework for analyzing such two-equation turbulence models. Finally it is shown that models rigorously derived from Reynolds-stress transport models by utilizing the algebraic stress approximation, e.g., explicit algebraic stress models, still constitute a justifiable method also when the mean shear varies in time, provided that the time variation is sufficiently slow. Closed form algebraic time dependent solutions are derived for some commonly used models in homogeneous shear flows.

A Low-Reynolds Number Explicit Algebraic Stress Model

A low-Reynolds number extension of the explicit algebraic stress model, developed by Gatski and Speziale (GS) is proposed. The turbulence anisotropy Πb and production to dissipation ratio P∕ϵ are modeled that recover the established equilibrium values for the homogeneous shear flows. The devised (Πb, P∕ϵ) combined with the model coefficients prevent the occurrence of nonphysical turbulence intensities in the context of a mild departure from equilibrium, and facilitate an avoidance of numerical instabilities, involved in the original GS model. A new near-wall damping function fμ in the eddy viscosity relation is introduced. To enhance dissipation in near-wall regions, the model constants Cϵ(1,2) are modified and an extra positive source term is included in the dissipation equation. A realizable time scale is incorporated to remove the wall singularity. The turbulent Prandtl numbers σ(k,ϵ) are modeled to provide substantial turbulent diffusion in near-wall regions. The model is validated against a few flow cases, yielding predictions in good agreement with the direct numerical simulation and experimental data.

A new methodology for Reynolds-averaged modeling based on the amalgamation of heuristic-modeling and turbulence-theory methods

A new methodology for the Reynolds-averaged Navier-Stokes modeling is presented on the basis of the amalgamation of heuristic-modeling and turbulence-theory methods. A characteristic turbulence time scale is synthesized in a heuristic manner through the combination of several characteristic time scales. An algebraic model of turbulent-viscosity type for the Reynolds stress is derived from the Reynolds-stress transport equation with the time scale embedded. It is applied to the state of weak spatial and temporal nonequilibrium, and is compared with its theoretical counterpart derived by the two-scale direct-interaction approximation. The synthesized time scale is justified through the agreement of the two expressions derived by these entirely different methods. The derived model is tested in rotating isotropic, channel, and homogeneous-shear flows. It is extended to a nonlinear algebraic model and a supersonic model. The latter is shown to succeed in reproducing the reduction in the growth rate of a free-shear layer flow, without causing wrong effects on wall-bounded flows such as channel and boundary-layer flows.

A multiscale model for dilute turbulent gas-particle flows based on the equilibration of energy concept

The objective of this study is to improve Eulerian-Eulerian models of particle-laden turbulent flow. We begin by understanding the behavior of two existing models—one proposed by Simonin [von Kármán Institute of Fluid Dynamics Lecture Series, 1996], and the other by Ahmadi [Int. J. Multiphase Flow 16, 323 (1990)]—in the limiting case of statistically homogeneous particle-laden turbulent flow. The decay of particle-phase and fluid-phase turbulent kinetic energy (TKE) is compared with direct numerical simulation results. Even this simple flow poses a significant challenge to current models, which have difficulty reproducing important physical phenomena such as the variation of turbulent kinetic energy decay with increasing particle Stokes number. The model for the interphase TKE transfer time scale is identified as one source of this difficulty. A new model for the interphase transfer time scale is proposed that accounts for the interaction of particles with a range of fluid turbulence scales. A new multiphase turbulence model—the equilibration of energy model (EEM)—is proposed, which incorporates this multiscale interphase transfer time scale. The model for Reynolds stress in both fluid and particle phases is derived in this work. The new EEM model is validated in decaying homogeneous particle-laden turbulence, and in particle-laden homogeneous shear flow. The particle and fluid TKE evolution predicted by the EEM model correctly reproduce the trends with important nondimensional parameters, such as particle Stokes number.

Asymmetry of temporal cross-correlations in turbulent shear flows

We investigate spatial and temporal cross-correlations between streamwise and normal velocity components in three shear flows: a low-dimensional model for vortex-streak interactions, direct numerical simulations for a nearly homogeneous shear flow and experimental data for a turbulent boundary layer. A driving of streamwise streaks by streamwise vortices gives rise to a temporal asymmetry in the short time correlation. Close to the wall or the bounding surface in the free-slip situations, this asymmetry is identified. Further away from the boundaries the asymmetry becomes weaker and changes character, indicating the prevalence of other processes. The systematic variation of the asymmetry measure may be used as a complementary indicator to separate different layers in turbulent shear flows. The location of the extrema at different streamwise displacements can be used to read off the mean advection speed; it differs from the mean streamwise velocity because of asymmetries in the normal extension of the structures.

Large eddy simulation of homogeneous shear flows with several subgrid-scale models

In this article, large eddy simulation is used to simulate homogeneous shear flows. The spatial discretization is accomplished by the spectral collocation method and a third-order Runge–Kutta method is used to integrate the time-dependent terms. For the estimation of the subgrid-scale stress tensor, the Smagorinsky model, the dynamic model, the scale-similarity model and the mixed model are used. Their predicting performance for homogeneous shear flow is compared accordingly. The initial Reynolds number varies from 33 to 99 and the initial shear number is 2. Evolution of the turbulent kinetic energy, the growth rate, the anisotropy component and the subgrid-scale dissipation rate is presented. In addition, the performance of several filters is examined. Copyright © 2005 John Wiley & Sons, Ltd.