On the use of Boussinesq approximation in turbulent supersonic jet modeling

The problem of turbulent supersonic jet modeling within the limits of Reynolds-averaged Navier-Stokes equations and Boussinesq approximation was considered. The time-asymptotic technique for full Navier-Stokes equations and the space-marching technique for parabolized Navier-Stokes equations were used to solve this problem. A variety of turbulence models was applied in an effort to obtain a good consistency with the experimental data on two distinct features of non-isobaric jets, namely, the mean flow decay and the shock wave attenuation. It was revealed that the Boussinesq approximation in its general form used in the full Navier-Stokes equations fails to reproduce these two features together. As regards the parabolized Navier-Stokes equations, such an abbreviated form gets practically rid of this failure. A solid theoretical interpretation of this effect was found, whereupon new forms of the turbulent viscosity terms were proposed and analyzed. It was ascertained that they offer considerable advantages over the Boussinesq approximation in some CFD applications.