Turbulent flows. Models and numerical investigations. A review

Abstract

Russian papers on differential models of turbulence and numerical simulation of nonequilibrium turbulent flows of liquids, gases, and conducting media, published for the most part in this journal over the last 10–15 years, are reviewed. The turbulence models considered in this review are based on Kolmogorov's ideas, which generated a new approach to the mathematical modeling of turbulent flows consisting in the use of transport equations for the turbulence properties. The subsequent development of these models was due to the emergence of computers which made it possible to change over from a qualitative analysis in particular regions to obtaining quantitative results with the influence of viscosity, and also such effects as diffusion and convection, taken directly into account in the mathematical simulation of turbulent flows. In this review the models are selected in accordance with the following criteria. 1. Only differential models are considered, that is models in which transport equations are used for the main turbulence properties: the turbulence energy, shear stress or the turbulent viscosity and a parameter involving the integral turbulence scale. According to the number of the transport equations the models are classified as one-, two-, or three-parameter. The application of the models is restricted to flows for which the boundary layer approximation holds true. 2. The models must have been put to practical use in the analysis of particular flows, and their most efficient areas of application specified. The models must have been tested by comparison with the most reliable experimental data. The models must be highly universal, thus making it possible, without adjusting the constants entering into the model, to take into account the inlet and boundary conditions, the variations of the physical properties of the medium, and external influences. The review aims to demonstrate the potential of the turbulence models considered in relation to a wide variety of flows in boundary layers and channels, and also to draw them to the attention of users and researchers developing scientific and applied computational programs for the description and control of devices with complicated working processes in aviation and space technology, and other areas.