Improvements to a One-Dimensional Stagnation Line Model of Bow Shock Freestream Disturbance Interactions

The behaviour, shape, and strength of bow shocks have crucial aerothermodynamic impacts on a wide array of aerospace engineering problems. The interaction of these shock waves with freestream disturbances has important implications for turbulence and transition, heat transfer prediction, and aerodynamics. Furthermore, these interactions have recently been shown to impact widely used intrusive diagnostics such as pitot tubes and hot wires. Focusing on the latter application, this paper summarizes recent advances made in efforts to develop a fast and accurate one-dimensional framework for the modelling of bow shock behaviour when subjected to various freestream disturbances. The present approach simplifies the governing Euler equations along the stagnation line and solves them using a shock-fitted finite difference approach. The model requires minimal input from a precursor steady state CFD simulation (in this case performed in OpenFOAM), then dynamically calculates the standoff distance of the shock and simulates the behaviour of fluctuations within the shock layer. The present work presents advancements in the modelling of the shock motion and incorporates thermally perfect gas properties and angled freestream disturbances. These new approaches are applied to the problem of measured spectra of pitot tubes in hypersonic flow with freestream disturbances. Calculations are performed for a variety of freestream disturbances and compared to DNS data published in the literature. The results show significant improvement in agreement between the present work and DNS simulation results, both qualitatively and quantitatively.