APPLICATION OF THE CONICAL APPROXIMATION OF NAVIER-STOKES EQUATIONS TO COMPUTER MODELLING OF THE STRUCTURE OF SUPERSONIC SHEAR FLOWS

Abstract

The study of supersonic turbulent separation flows is one of the main problems of modern aerodynamics, which has both fundamental and practical significance. From a practical point of view, the spatial distributions of gas-dynamic parameters affect the aerodynamic characteristics of supersonic aircraft, compressors, and turbines. The theoretical interest in this class of flows is due to the fact that all the main phenomena characteristic of viscous-inviscid interactions occur here: significant parameter gradients, flow separation, turbulence, intensive heat exchange with the flowing surface. Investigation of the physical features of the shock waves/turbulent boundary layers interactions (SWBLI) acquires special importance.Known results of studies of the interaction of shock waves with boundary layers were obtained mainly by experi- mental methods. However, the conducting of the blowing in wind tunnels or full-scale flight tests is associated with both large financial costs and a limited amount of measured data.The Navier – Stokes equations, Reynolds or Favre averages (RANS), are currently the basis of computational aero- dynamics. Complete information about the flow provides the researcher with more opportunities to identify the character- istic physical features of the interacting flows. The use of modern numerical methods, differential turbulence models, and detailed computational grids allows the flow under study to be reproduced with a high degree of reliability.The conical approximation of the compressible gas Navier – Stokes equations makes it possible to use a more detailed calculation grid for modeling supersonic flows with the appropriate symmetry of the flow separation, which in turn leads to the possibility of computer reconstruction of small details of the interactions. The implicit finite-volume technique in present paper is based on the second order Roe scheme. The implementation of the Spalart – Allmaras differential turbulence model adapted to supersonic flows is considered. Verification of the developed algorithms and the program complex was carried out on the problem of supersonic turbulent flow around a sharp cone at a supercritical angle of attack.