Turbulence Model Behavior in Low Reynolds Number Regions of Aerodynamic Flowfields

Abstract

The behaviors of the widely used Spalart-Allmaras and Menter shear-stress transport turbulence models at low Reynolds numbers and under conditions conducive to relaminarization are documented. The flows used in the investigation include 2-D zero-pressure-gradient flow over a flat plate from subsonic to hypersonic Mach numbers, 2-D airfoil flow from subsonic to supersonic Mach numbers, 2-D subsonic sink flow, and 3-D subsonic flow over an infinite swept wing (particularly its leading-edge region). Both models exhibit a range over which they behave transitionally even with inflow values set to cause immediate growth of the turbulence quantities, in the sense that the flow is neither laminar nor fully turbulent, but these behaviors are different: the shear-stress transport model typically has a well-defined transition location, whereas the Spalart-Allmaras model does not. Both models are predisposed to delayed activation of turbulence with increasing freestream Mach number. Also, both models can be made to achieve earlier activation of turbulence by increasing their freestream levels, but too high a level can disturb the turbulent solution behavior. The technique of maintaining freestream levels of turbulence without decay in the shear-stress transport model, introduced elsewhere, is shown here to be useful in reducing grid dependence of the model's transitional behavior. Both models are demonstrated to be incapable of predicting relaminarization; eddy viscosities remain weakly turbulent in accelerating or laterally strained boundary layers for which experiment and direct simulations indicate turbulence suppression. The main conclusion is that these models are intended for fully turbulent high Reynolds number computations, and using them for transitional (e.g., low Reynolds number) or relaminarizing flows is not appropriate. Competing models which fare better in these areas have not been identified.