This paper presents numerical results comparing the performance of the 2008 Wilcox $mathcal{k}-{omega}$ turbulence model to the one of the 1988 Wilcox $mathcal{k}-{omega}$ model for supersonic flows. A comparison with experimental data is offered for a shock wave/turbulent boundary layer interaction case and two ramp injector mixing cases. Furthermore, 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. It is found that the maximum injectant mass fraction of some ramp injector cases is better predicted using the 1988 Wilcox model. On the other hand, the 2008 model performs better in simulating shock-boundary layer cases.