Apparent transition behavior of widely-used turbulence models

The Spalart–Allmaras and the Menter k–ω SST turbulence models are shown to have the undesirable characteristic that, for fully turbulent external flow computations, a transition region can occur whose extent varies with grid density. Extremely fine two-dimensional grids over the front portion of an airfoil are used to demonstrate the effect. As the grid density is increased, the laminar region near the nose becomes larger. In the Spalart–Allmaras model this behavior is due to convergence to a laminar-behavior fixed point that occurs in practice when freestream turbulence is below some threshold. It is the result of a feature purposefully added to the original model in conjunction with a special trip function. This degenerate fixed point can also cause non-uniqueness regarding where transition initiates on a given grid. Consistent fully turbulent results can easily be achieved by either using a freestream turbulence level higher than the threshold or by making a simple change to one of the model constants. Near the area where turbulence initiates, the SST model exhibits sensitivity to numerical resolution, but its solutions are unique on a given grid. Inconsistent apparent transition behavior with grid refinement in this case does not stem from the presence of a degenerate fixed point. A nullcline analysis is used to visualize the local behavior of the model.