Tsan-Hsing Shih

KOLMOGOROV BEHAVIOR OF NEAR-WALL TURBULENCE AND ITS APPLICATION IN TURBULENCE MODELING

SUMMARY The near-wall behavior of turbulence is re-examined in a way different from that proposed by Hanjalic and Launder1 and followers2,3,4,5. It is shown that at a certain distance from the wall, all energetic large eddies will reduce to Kolmogorov eddies (the smallest eddies in turbulence). All the important wall parameters, such as friction velocity, viscous length scale, and mean strain rate at the wall, are characterised by Kolmogorov microscales. According t o this Kolmogorov behavior of near-wall turbulence, the turbulence quantities, such as turbulent kinetic energy, dissipation rate, etc. at the location where the large eddies become “Kolmogorov” eddies, can be estimated by using both direct numerical simulation (DNS) data and asymptotic analysis of near-wall turbulence. This information will provide useful boundary conditions for the turbulent transport equations. As a n example, the concept is incorporated in the standard κ - emodel which is then applied t o channel and boundary layer flows. ...

CALCULATION OF WALL-BOUNDED COMPLEX FLOWS AND FREE SHEAR FLOWS

Various wall-bounded flows with complex geometries and free shear flows have been studied with a newly developed realizable Reynolds stress algebraic equation model. The model development is based on the invariant theory in continuum mechanics. This theory enables us to formulate a general constitutive relation for the Reynolds stresses. Pope (J. Fluid Mech., 72, 331–340 (1975)) was the first to introduce this kind of constitutive relation to turbulence modelling. In our study, realizability is imposed on the truncated constitutive relation to determine the coefficients so that, unlike the standard k–ϵ eddy viscosity model, the present model will not produce negative normal stresses in any situations of rapid distortion. The calculations based on the present model have shown encouraging success in modelling complex turbulent flows.

Remarks on turbulent constitutive relations

Abstract The paper demonstrates that the concept of turbulent constitutive relations introduced by Lumley [1] can be used to construct general models for various turbulent correlations. Some of Generalized Cayley–Hamilton formulas for relating tensor products of higher Extension to tensor products of lower Extension are introduced. The combination of dimensional analysis and invariant theory can lead to “turbulent constitutive relations” (or general turbulence models) for, in principle, any turbulent correlations. As examples, the constitutive relations for Reynolds stresses and scalar fluxes are derived. The results are consistent with ones from RNG theory and two-scale DIA method, but with a more general form.

Critical comparison of second-order closures with direct numerical simulations of homogeneous turbulence

Recently, several second order closure models have been proposed for closing the second moment equations, in which the velocity-pressure gradient (and scalar-pressure gradient) tensor and the dissipation rate tensor are two of the most important terms. In the literature, these correlation tensors are usually decomposed into a so called rapid term and a return-to-isotropy term. Models of these terms have been used in global flow calculations together with other modeled terms. However, their individual behavior in different flows have not been fully examined because they are un-measurable in the laboratory. Recently, the development of direct numerical simulation (DNS) of turbulence has given us the opportunity to do this kind of study. With the direct numerical simulation, we may use the solution to exactly calculate the values of these correlation terms and then directly compare them with the values from their modeled formulations (models). Here, we make direct comparisons of five representative rapid models and eight return-to-isotropy models using the DNS data of forty five homogeneous flows which were done by Rogers et al. (1986) and Lee et al. (1985). The purpose of these direct comparisons is to explore the performance of these models in different flows and identify the ones which give the best performance. The modeling procedure, model constraints, and the various evaluated models are described. The detailed results of the direct comparisons are discussed, and a few concluding remarks on turbulence models are given.

Second-order modelling of a variable-density mixing layer

On utilise une methode de moyenne conventionnelle pour etudier les ecoulements turbulents a densite variable en particulier une couche de melange helium-azote

Second-order modelling of particle dispersion in a turbulent flow

A set of second-order modelled equations for the motion of particles are presented. We consider the effects of the particle inertia and the crossing-trajectories effect on the particle dispersion. A simple case of a particle mixing layer in a decaying homogeneous turbulence for light and heavy particles is calculated. The results show that the crossing-trajectories effect on particle dispersion is very significant, while inertia only has a slight effect. This behaviour has been observed in experiments (Wells & Stock 1983) and is well predicted by an asymptotic analysis (Csanady, 1963). The calculation also shows that there is a significant difference between Favre-averaged particle velocity and conventional-averaged particle velocity in the low-particle-concentration region. All calculations are in good agreement with Wells & Stocks experimental data.

Influence of timescale ratio on scalar flux relaxation: modelling Sirivat & Warhaft's homogeneous passive scalar fluctuations

A second-order modelling technique is used to investigate the behaviour of homogeneous scalar turbulence. Special attention is paid to the influence of timescale ratio on scalar flux relaxation. We develop a model for the scalar flux equation in a homogeneous turbulence and consider both a scalar field without mean-scalar gradients and one with constant mean-scalar gradients based on Sirivat & Warhaft (1981) experiments. Good agreement with experiment in all the cases is obtained.

A Length-Scale Equation

We derive an equation for the average length-scale in a turbulent flow from a simple physical model. This is a tensorial length-scale. We use as a model the evolution of a blob of turbulent kinetic energy under the influence of production, dissipation, and transport, as well as distortion by the mean motion. A single length-scale is defined which is biased toward the smallest of the scales in the various directions. Constants are estimated by consideration of homogeneous decay. Preliminary computations are carried out in a mixing layer and a two-dimensional jet, using the new length-scale equation and the equation for the turbulent kinetic energy. The results are compared with data and with the predictions of the classical k-epsilon equations; the new results are quite satisfactory. In particular, the plane jet/round jet anomaly is approximately resolved.

Bypass transitional flow calculations using a Navier-Stokes solver and two-equation models

Bypass transitional flows over a flat plate were simulated using a Navier-Stokes solver and two equation models. A new model for the bypass transition, which occurs in cases with high free stream turbulence intensity (TI), is described. The new transition model is developed by including an intermittency correction function to an existing two-equation turbulence model. The advantages of using Navier-Stokes equations, as opposed to boundary-layer equations, in bypass transition simulations are also illustrated. The results for two test flows over a flat plate with different levels of free stream turbulence intensity are reported. Comparisons with the experimental measurements show that the new model can capture very well both the onset and the length of bypass transition.