Wall-Modeled LES of supersonic turbulent boundary layers over a compression ramp

The necessity of predicting the physics behind shock turbulent boundary layer inter- actions is one of the crucial subjects for aerospace engineering applications, ranging from atmospheric reentry, efficient propulsion system design to fluid-structure in- teraction and noise reduction in high-speed aircraft. The prohibitive computational cost required to resolve all the scales present in a flow is a significant challenge in numerical simulations. Direct numerical simulations (DNS) are limited to relatively low Reynolds numbers due to their high computational cost, while large-eddy simu- lations (LES) use subgrid-scale models to represent the unresolved small-scale turbu- lent motions, thereby enabling simulations at higher Reynolds numbers. Reynolds- averaged Navier-Stokes (RANS) simulations, because of their low computational cost can be used over a wide range of Reynolds numbers, as they provide access to the mean flow field at the expense of time-resolved representation of local flow features. However, capturing the boundary-layer structures generated by solid walls is still computationally prohibitive for most practically relevant flow conditions. The purpose of this work is to implement a wall-model technique for large-eddy sim- ulation for the first time using an Immersed Boundary Method (IBM) in the open source numerical solver STREAmS, reducing the computational cost of describing the interaction between a supersonic flow over a compression ramp, given the value of a certain distance from the wall, called the matching location. The main focus is the implementation of the same setup and validation against a recent work presented by Dawson et al., (2013), where the free-stream Mach number is M∞ = 2.9 and the ramp angle θ = 24°. The results obtained using grid configurations ranging from coarse to fine and different matching locations are consistent with theoretical predictions. The choice of matching location has an higher impact than the specific mesh configuration over the predicted friction co- efficient and mean pressure distribution across the domain, highlighting that, for a fixed matching location but different grid configurations, the finer grid captures the influence of the adverse pressure gradient more effectively. They emphasizes the limitations of the equilibrium wall model in faithfully representing the physics when flow separation occurs, especially when compared to a DNS and experimental analysis, Wu & Martin (2008) and Riguette et al., (2009). Concerning the oblique shock wave, the model predicts accurately the fluid properties jump over the shock wave itself and the oblique angle with a deviation error lower than ϵprop = 4% and ϵβ = 2% respectively. In the future, it may be useful to investigate implementing a wall model that can represent strongly non-equilibrium flow features and rough surfaces, in order to ob- tain a more complete understanding of the supersonic case.