A Transport Intermittency Model for Supersonic/Hypersonic Boundary Layer Transition

Modelling of flow transition has always been a research focal point in turbulence study. Currently, the RANS approach is still the main tool in the transition/turbulence modelling in engineering application. Since it is proved that turbulence model without making use of the intermittency are often extremely unreliable in the prediction of transition [1], there appear many correlation-based transition models involving the intermittency factor. However, these models include non-local formulations which are not easily compatible with modern CFD methods. The models based on local variables are thus much preferred for the application purpose. A successful example is the work of Menter et al. [2], which is now implemented in a commercial software package. However, the existing local-variable-based models are not validated for the transition in supersonic flows or for the cross-flow transition. One reason is that these models rely on heavy load of numerical validation rather than the fundamental physical phenomena responsible for actual transition process, e.g. the flow instability mode can be rather different in supersonic boundary layers than that in incompressible or subsonic flows. The purpose of this investigation is to develop an improved flow transition model applicable to supersonic as well as three-dimensional flows. Thus, a transition model based on k-ω-γ transport equations is proposed here. The model converts to the standard SST model [3] in the fully turbulent region. The fluctuating kinetic energy k includes the non-turbulent, as well as turbulent parts. The intermittency factor, γ, is set to play as a weight number between the non-turbulent and the turbulent components of stress in Pk and Pω, i.e. the production terms of equations for k and ω. This approach focuses on the determination of effective viscosity of nonturbulent fluctuations, µnt, as derived from the linear stability theory (LST). Both the LST and experimental observations give that at low Mach number the socalled ‘first-mode’ disturbance is the primary cause of instability while the effect of ‘second-mode’ disturbances becomes prominent at high Mach number flows. This mode variation, related to the effect of compressibility, is accommodated inherently in the present model through the local relative Mach number, i.e. Mrel = (U - cr) / a, where U stands for the local mean velocity related to wall, a is the local sound speed, and cr represents the phase velocity, as the same value, of all Mack-mode disturbances. µnt is