SUPERSONIC FLUX-SPLIT PROCEDURE FOR 2ND MOMENTS OF TURBULENCE

A finite volume procedure which combines flux-difference splitting and flux-vector splitting is presented in this paper. The diffusive fluxe s are treated explicitly to preserve the upwinding structure of the sp lit Euler fluxes. This procedure is extended in this paper from its es sentially laminar or eddy viscosity form to include the equations for the six components of the Reynolds stress tenser and an additional equ ation for the solenoidal dissipation. The models used for the unclosed terms are presented as are the extensions of the numerical procedures to cover the turbulence equations. To validate the proposed procedure s, a compressible turbulent flow over a flat plate at Mach number M(in finity) = 2.87 and Reynolds number per unit length Re/m of 6.5 X 10(7) was calculated and compared with experimental measurements. Also simu lated was the case when the foregoing boundary-layer flow was made to pass over a ramp. A strong adverse pressure gradient case in which bou ndary-layer thickness-to-curvature ratio (delta/R(c)) is 0.1 was consi dered. In this case, the supersonic turbulent boundary layer experienc es the combined effects of an adverse pressure gradient, bulk compress ion, and concave streamline curvature. For the various tests, the resu lts obtained from our calculations are in agreement with the experimen tal measurements.