A Pseudo-3D Extension to the Johnson King Model and Its Application to the EuroExpt S-Duct Geometry

摘要

This paper presents a submission to the T1 Test Case problem of the LausanneERCOFTAC Workshop on Numerical Simulation of Unsteady Flows, Transition to Turbulence and Combustion. The model adopted for these calculations is a new 3-D version of that originally proposed, by Johnson & King [1], for non-equilibrium 2-D flows approaching separation, referred to hereafter as the J&K model. Being, in the taxonomy of the 1980-81 Stanford Conference, only a 'half-equation' model (because it employs just an ordinary differential equation (ODE) for the maximum shear stress, (tau)_(m) and a prescribed mixing length, 1) this closure scheme is of considerable interest to those attempting to improve current Navier-Stokes solutions for compressible flow, both through and around complex geometries, which employ the simpler well-known Baldwin-Lomax or Cebici-Smith prescriptions for 1 alone. In fact a number of attempts have already been made to extend the original 2-D J&K model to handle 3-D flows. In particular Abid [2] has described a scheme in which the principal shear stress uv, mean strain, and mean velocity were replaced by the corresponding resultant quantities for 3-D flow.