The Freestream Matching Condition for Stagnation Point Turbulent Flows: An Alternative Formulation

The problem of plane stagnation point flow with freestream turbulence is examined from a basic theoretical standpoint. It is argued that the singularity which arises in the standard K–ε model results from the use of an inconsistent freestream boundary condition. The inconsistency lies in the implementation of a production-equals-dissipation equilibrium hypothesis in conjunction with a freestream mean velocity field that corresponds to homogeneous plane strain—a turbulent flow for which the standard K–ε model does not predict such a simple equilibrium. The ad hoc adjustment that has been made in the constants of the ε-transport equation to eliminate this singularity is shown to be inconsistent for homogeneous plane-strain turbulence as well as other benchmark turbulent flows. An alternative means to eliminate this singularity—without compromising model predictions in more basic turbulent flows—is proposed based on the incorporation of nonequilibrium vortex stretching effects in the turbulent dissipation rate equation.