Development of efficient hypersonic air-breathing propulsion system requires under-standing the mixing of fuel in a supersonic flow. Experiments1-3 at the S3L facility in Caltech investigate fundamental mixing of fuel with supersonic gas stream in an expansion-ramp configuration. The flow is turbulent and exhibits spatio-temporal pressure and density variations due to compressibility and heat release. The present work aims to develop and study subgrid-scale models for simulating the flow in the experiment. In particular, we focus on incorporating the baroclinic (pertaining to pressure-gradient and density) and dilatational effects at subgrid-scales. These subgrid-scale effects cannot be directly represented in conventional density-filtered LES formulation using algebraic models available in the literature. We develop and a new concise filtered-velocity based LES formulation and simulate a specific flow-case studied in the experiments. A posteriori observations of the proposed formulation are reported on two-dimensional and three-dimensional simulations. The effect on key flow statistics is discussed.