In the present study, an aerothermodynamic analysis of high-speed flow fields through a divergent duct (similar to a supersonic combustor: hereafter referred to as supersonic combustor in the paper), without injection and with high enthalpy cross injection, has been performed. Initially, the thermal and flow analyses of the combustor are carried out by passing vitiated air at a temperature of 607.5 K, and this is followed by a computational analysis of the interaction of the flow field with the structure, when high enthalpy air is injected. The flow is turbulent in the combustor and the k-ω model has been considered to be appropriate for such cases, as it can resolve vorticity and highly strained flows. The study also emphasizes on the advantages of two-dimensional modelling over three dimensional modelling for cold flow cases in supersonic combustors, which could serve as an alternative, for wind tunnel tests as well as computationally expensive three dimensional numerical analysis. A comparison of various turbulence models for supersonic flows without cross injection has been carried out to arrive at the suitable model. For the cases of cross/transverse injection, the Mach numbers considered for investigation are 2, 2.5 and 3. The pressure, temperature and heat flux predictions for the cases with and without injection compare well with the experimental results.