Validation of the Wilcox k-omega Model for Flows Characteristic to Hypersonic Airbreathing Propulsion

Abstract

Numerical results obtained with the WARP code solving the 1988 Wilcox k‐ω two-equation model are compared with experimental data of flowfields characteristic of hypersonic airbreathing propulsion. The problems chosen for the comparison include a shock/boundary-layer interaction case, a reacting and inert planar mixing case, and two ramp injector mixing cases. In addition, a comparison is performed with empirical correlations on the basis of skin friction for flow over a flat plate and shear layer growth for a free shear layer. The agreement between the numerical and experimental results varies between being reasonable and excellent, with a discrepancy generally not exceeding 20%. It is found that the grid-induced error can be reduced to an acceptable level for most problems with a reasonable mesh size. However, the free shear layer and the shock/boundary-layer interaction cases require a considerably finer mesh. The Wilcox dilatational dissipation correction is seen to be beneficial in predicting the growth of a free shear layer at a high convective Mach number, but its use is considered either questionable or detrimental for the other cases. A proper choice of the turbulent Schmidt number is observed to be crucial in predicting the injectant mole fraction contours for one of the ramp injector cases, with the best agreement obtained with Schmidt number Sct fixed to 0.25. For the inert planar mixing case, overall better agreement is obtained when setting both the turbulent Prandtl and Schmidt number to 0.5.