The description of combustion in high-speed turbulent flows, where turbulent mixing, compressibility effects, and chemical kinetics processes are competing, still remains a challenging issue for numerical simulations. The key features of such turbulent supersonic reactive flows are integrated into a turbulence-chemistry interaction closure, which relies on the partially stirred reactor framework. The corresponding closure, hereafter denoted as the unsteady partially stirred reactor model, is incorporated into the ONERA computational fluid dynamics code CEDRE. The computational model is used to investigate a Mach 12 rectangular-to-elliptical-shape-transition scramjet engine developed and operated at the University of Queensland. Results of Reynolds-averaged Navier-Stokes numerical simulations based on either the unsteady partially stirred reactor concept or the classical quasi-laminar closure are presented and compared. Similar results in terms of pressure distributions are obtained, thus confirming that the essential point to cope with such scramjet engine conditions is to represent satisfactorily the compressible flowfield. The Reynolds-averaged Navier-Stokes numerical simulations are subsequently used to investigate the engine performance, through the calculation of energetic efficiencies. The obtained results bring useful insights into the classical quasi-one-dimensional performance analyses. In particular, the inlet injection scheme is found to display the best performance with a combustion efficiency of 78%.