Turbulence modeling: Present and future Comment 2

Abstract

The thrust of the position paper by Launder is that second-order closure models represent the best hope for the reliable prediction of the complex turbulent flows of technological interest both now and in the foreseeable future. By building on the pioneering research of Rotta [1] and by introducing some fundamental new ideas, the work of Launder, Lumley, and others has without doubt made significant contributions to the advancement of second-order closures. In the position paper by Launder, a strong case is made for the superior predictive capabilities of second-order closures in comparison to two-equation models or eddy viscosity models. Most notably, turbulent flows involving rotations and streamline curvature have been shown by Launder and others [2,3] to be better described by second-order closure models. The same is true for turbulent flows with stratification and relaxation effects. Launder very aptly cites four active areas of research for the improvement of second-order closures: (i) models for the rapid pressure strain correlation, (ii) models for the turbulent diffusion terms, (iii) adjustments for near wall turbulence effects, and (iv) modeled transport equations ~or the turbulent dissipation rate or length scale. In the sections to follow, by making use of some simple examples from homogeneous turbulence, the primary point made by Launder concerning the superior predictive capabilities of second-order closures will be amplified. Most notably, it will be shown that second-order closures are capable of describing the stabilizing or destabihzing effect of rotations on shear flow-a problem which cannot be even remotely analyzed by the simpler models. However, some lingering problems concerning the development ~ of adequate models for the rapid pressure-strain correlation and the turbulent length scale will be emphasized (see Speziale [4]). In regard to the latter issue, the strengths and weaknesses of the commonly used modeled dissipation rate transport equation will be discussed and a definitive argument will be put forth as to why previous attempts at the development of an improved dissipation rate transport equation have failed. Alternative 490