Predicting equilibrium states with Reynolds stress closures in channel flow and homogeneous shear flow

Abstract

DnyC QUALM'XfflpErD a Turbulent channel flow and homogeneous shear flow have served as basic building block flows for the testing and calibration of Reynolds stress models. In this paper, a direct theoretical connection is made between homogeneous shear flow in equilibrium and the loglayer of fully-developed turbulent channel flow. It is shown that if a second-order closure model is calibrated to yield good equilibrium values for homogeneous shear flow it will also yield good results for the log-layer of channel flow provided that the Rotta coefficient is not too far removed from one. Most of the commonly used second-order closure models introduce an ad hoc wall reflection term in order to mask deficient predictions for the loglayer of channel flow that arise either from an inaccurate calibration of homogeneous shear flow or from the use of a Rotta coefficient that is too large. Illustrative model calculations are presented to demonstrate this point which has important implications for turbulence modeling.

Some dynamical features of the turbulent flow of a viscoelastic fluid for reduced drag

“…This value is somewhat below the accepted value of 0.56 (see [39] and the references therein), indicating that the Newtonian flow is still Reynolds number dependent at Re τ 0 = 1000. For FENE-P [ Figure 17(b)], we do not observe any sign of an emerging constant value over a significant y-range.…”

Evaluation of Reynolds stress turbulence closures in compressible homogeneous shear flow

“…Homogeneous shear flow is an important building-block flow since it encapsulates some of the important features of an equilibrium turbulent boundary layer in a simplified setting that is unencumbered by the effects of turbulent diffusion or wall blocking. It has been an extremely useful test case for the calibration and screening of turbulence models for incompressible flows [6][7][8]. However, no comprehensive test of compressible Reynolds stress models has been made using these new DNS data bases for compressible homogeneous shear flow.…”

The Explicit Algebraic Reynolds Stress Models for Turbulent Flows

“…In the 1970s, the applications of turbulence modeling became very popular; however, most of the applications and calculations were two dimensional (Abid & Speziale, 1992). In the 1980s, the computations and applications have been extended to three dimensional problems and the use of more turbulence models, many of them were based on the Reynolds stress models (Ching-Jen & Shenq-yuh, 1997).…”