Turbulence models are developed by supplementing the renormalization group (RNG) approach of Yakhot and Orszag [J. Sci. Comput. 1, 3 (1986)] with scale expansions for the Reynolds stress and production of dissipation terms. The additional expansion parameter (η≡SK̄/■̄) is the ratio of the turbulent to mean strain time scale. While low-order expansions appear to provide an adequate description for the Reynolds stress, no finite truncation of the expansion for the production of dissipation term in powers of η suffices−terms of all orders must be retained. Based on these ideas, a new two-equation model and Reynolds stress transport model are developed for turbulent shear flows. The models are tested for homogeneous shear flow and flow over a backward facing step. Comparisons between the model predictions and experimental data are excellent.

The modelling of the pressure-strain correlation of turbulence is examined from a basic theoretical standpoint with a view toward developing improved second-order closure models. Invariance considerations along with elementary dynamical systems theory are used in the analysis of the standard hierarchy of closure models. In these commonly used models, the pressure-strain correlation is assumed to be a linear function of the mean velocity gradients with coefficients that depend algebraically on the anisotropy tensor. It is proven that for plane homogeneous turbulent flows the equilibrium structure of this hierarchy of models is encapsulated by a relatively simple model which is only quadratically nonlinear in the anisotropy tensor. This new quadratic model - the SSG model - appears to yield improved results over the Launder, Reece & Rodi model (as well as more recent models that have a considerably more complex nonlinear structure) in five independent homogeneous turbulent flows. However, some deficiencies still remain for the description of rotating turbulent shear flows that are intrinsic to this general hierarchy of models and, hence, cannot be overcome by the mere introduction of more complex nonlinearities. It is thus argued that the recent trend of adding substantially more complex nonlinear terms containing the anisotropy tensor may be of questionable value in the modelling of the pressure–strain correlation. Possible alternative approaches are discussed briefly.

Explicit algebraic stress models that are valid for three-dimensional turbulent flows in non-inertial frames are systematically derived from a hierarchy of second-order closure models. This represents a generalization of the model derived by Pope [J. Fluid Mech. 72, 331 (1975)] who based his analysis on the Launder, Reece and Rodi model restricted to twodimensional turbulent flows in an inertial frame. The relationship between the new models and traditional algebraic stress models -as well as anistropic eddy viscosity models -is theoretically established. The need for regularization is demonstrated in an effort to explain why traditional algebraic stress models have failed in complex flows. It is also shown that these explicit algebraic stress models can shed new light on what second-order closure models predict for the equilibrium states of homogeneous turbulent flows and can serve as a useful alternative in practical computations.

A spatially developing supersonic adiabatic flat plate boundary layer flow (at M-infinity=2.25 and Re(theta)approximate to4000) is analyzed by means of direct numerical simulation. The numerical algorithm is based on a mixed weighted essentially nonoscillatory compact-difference method for the three-dimensional Navier-Stokes equations. The main objectives are to assess the validity of Morkovin's hypothesis and Reynolds analogies, and to analyze the controlling mechanisms for turbulence production, dissipation, and transport. The results show that the essential dynamics of the investigated turbulent supersonic boundary layer flow closely resembles the incompressible pattern. The Van Driest transformed mean velocity obeys the incompressible law-of-the-wall, and the mean static temperature field exhibits a quadratic dependency upon the mean velocity, as predicted by the Crocco-Busemann relation. The total temperature has been found not to be precisely uniform, and total temperature fluctuations are found to be non-negligible. Consistently, the turbulent Prandtl number is not unity, and it varies between 0.7 and 0.8 in the outer part of the boundary layer. Nonetheless, a modified strong Reynolds analogy is still verified. In agreement with the low Mach number results, the streamwise velocity component and the temperature are only weakly anti-correlated. The turbulent kinetic energy budget also shows similarities with the incompressible case provided all terms of the equation are properly scaled; indeed, the leading compressibility contributions are negligible throughout the boundary layer. (C) 2004 American Institute of Physics

A CFD validation workshop for synthetic jets and turbulent separation control (CFD-VAL2004) was held in Williamsburg, Virginia in March 2004. Three cases were investigated: synthetic jet into quiescent air, synthetic jet into a turbulent boundary layer cross ow, and ow o ver a hump model with no-ow-control, steady suction, and oscillatory control. This paper is a summary of the CFD results from the workshop. Although some detailed results are shown, mostly a broad viewpoint i s t a k en, and the CFD stateof-the-art for predicting these types of ows is evaluated from a general point of view. Overall, for synthetic jets, CFD can only qualitatively predict the ow p h ysics, but there is some uncertainty regarding how to best model the unsteady boundary conditions from the experiment consistently. As a result, there is wide variation among CFD results. For the hump ow, CFD as a whole is capable of predicting many of the particulars of this ow provided that tunnel blockage is accounted for, but the length of the separated region compared to experimental results is consistently overpredicted.