Modelling flow transition in a hypersonic boundary layer with Reynolds-averaged Navier-Stokes approach

Abstract

Based on Reynolds-averaged Navier-Stokes approach, a laminar-turbulence transition model is proposed in this study that takes into account the effects of different instability modes associated with the variations in Mach numbers of compressible boundary layer flows. The model is based on k-ω-γ three-equation eddy-viscosity concept with k representing the fluctuating kinetic energy, ω the specific dissipation rate and the intermittency factor γ. The particular features of the model are that: 1) k includes the non-turbulent, as well as turbulent fluctuations; 2) a transport equation for the intermittency factor γ is proposed here with a source term set to trigger the transition onset; 3) through the introduction of a new length scale normal to wall, the present model employs the local variables only avoiding the use of the integral parameters, like the boundary layer thickness δ, which are often cost-ineffective with the modern CFD (Computational Fluid Dynamics) methods; 4) in the fully turbulent region, the model retreats to the well-known k-ω SST (Shear Stress Transport) model. This model is validated with a number of available experiments on boundary layer transitions including the incompressible, supersonic and hypersonic flows past flat plates, straight/flared cones at zero incidences, etc. It is demonstrated that the present model can be successfully applied to the engineering calculations of a variety of aerodynamic flow transition.