Explicit Algebraic Stress Model of Turbulence with Anisotropic Dissipation

摘要

Turbulent flows near solid boundaries-or at low turbulence Reynolds numbers-can exhibit significant anisotropies in the turbulent dissipation rate.1 Nevertheless, Reynolds stress turbulence closures are routinely formulated that neglect such effects by invoking the Kolmogorov assumption of local isotropy.2 Recently, however, attempts have been made to extend full Reynolds stress turbulence closures to incorporate the effects of anisotropic dissipation.3"6 These more sophisticated Reynolds stress turbulence closures can involve the solution of up to 12 additional transport equations. As such, most of these models are not currently feasible for the solution of complex turbulent Hows in an engineering setting. During the past few years, explicit algebraic stress models have been developed that are formally consistent with full second-order closures in the limit of homogeneous turbulence in equilibrium.7 These models allow for the solution of complex turbulent flows with a substantially reduced level of computation compared with full second-order closures, since they constitute two-equation models.7-* The purpose of the present Note is to show how the effects of anisotropic dissipation can be systematically incorporated into these explicit algebraic stress models by a simple readjustment of the coefficients. For homogeneous turbulent (lows that are close to equilibrium, it will be shown that the results obtained with such models are virtually indistinguishable from those obtained using a full second-order closure model with the anisotropic dissipation rate model of Speziale and Gatski.4 All of this extra turbulence physics is incorporated within the framework of a two-equation model that is not much more computationally expensive to implement than the standard K-B model.