A computation of turbulent supersonic flows

Аuthors

Kryukov I. A.

Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences, 101-1, prospekt Vernadskogo, Moscow, 119526, Russia

e-mail: kryukov@ipmnet.ru

Abstract

Some modifications of the k-ε turbulence model are considered as applies to numerical simulation of supersonic turbulent flows. Strong compressibility and occurrence of regions with large parameter gradients (i.e. with dynamical gas medium discontinuities) are typical for these flows. An equation for turbulent kinetic energy in compressible case contains normally three new terms. These terms discussed briefly in the paper are compressible dissipation, pressure-dilatation and turbulent mass flow. Existence of discontinuities leads to considerable increasing of turbulent kinetic energy production due to gradients of mean velocity. It results in significant deviation from equilibrium state near discontinuities. It is for this reason that some non-equilibrium modifications of the k-ε turbulence model are suggested in the article. All considered modifications are analyzed basing onflow calculation results in regard to a supersonic under-expanded jet with complex shock wave structure and flow as well as in regard to a supersonic nozzle with separation. A new version of the k-ε turbulent model is suggested to contain considered modifications. This version is able to calculate both flow classes with a good accuracy.

Keywords:

turbulent flows; k-ε turbulence model; numerical Godunov scheme; dilatation dissipation; non-equilibrium turbulence; nozzle; boundary-layer separation