Chapter 15: Modeling of Turbulent Compressible Near-Wall Flows

Abstract

Semiempirical turbulence models for numerical calculation of near-wall flows of a compressible gas are presented. Various issues of modification of both algebraic and differential models, which were originally developed for low-velocity flows, to studying supersonic and hypersonic near-wall flows with intense heat exchange with the surface and the applicability limits of these models determined by the free-stream parameters and the temperature factor of the surface are considered.Semiempirical turbulence models are introduced in numerical investigations of external high-velocity flows of a compressible gas with turbulent regimes to close systems of Reynolds-averaged or boundary layer equations. The models are classified in accordance with known criteria. Two major classes (algebraic and differential models) are usually distinguished. These classes, in turn, are divided on the basis of accepted hypotheses; in addition, the second class is divided in terms of the number of differential equations.Differential models can be conventionally divided into one-equation, two-equation, and multiequation models. Two simple subclasses consist of one-equation and two-equation models based on equations derived by Kolmogorov [1] and Prandtl [2], which were further developed, for instance, in Refs. 3-5. These models are widely used not only for solving boundary layer problems, but also for analyzing more general formulations of fluid flows with allowance for viscosity.The most effective models of these classes discussed in this chapter were developed for calculating low-velocity flows with allowance for the properties of the near-wall region of the boundary layer. Later on, the range of problems solved with the use of these models was extended to regions with low Reynolds numbers, laminar-turbulent transition, and separation. It is also possible to take into account the three-dimensional character of the flow with anisotropic properties. The range of these problems also includes the calculation of high-velocity flows with heat transfer and with gas/surface interaction. For near-wall supersonic flows, the use of these model is justified by Morkovin's hypothesis with allowance for variability of the mean density of the flow only. Extension of the area of applicability of semiempirical models to hypersonic nonequilibrium flows with shock