Discernment of Wall Functions and Turbulence Statistics for Common Supersonic Retropropulsion Configurations

Turbulence is generated during supersonic retropropulsion (SRP), wherein a spacecraft descends towards a celestial body’s surface and utilizes retro-firing nozzles to decelerate. This motivates using large-eddy simulation (LES) to achieve full resolution of turbulence up to the subgrid-scale, as opposed to Reynolds-averaged Navier-Stokes or detached eddy simulation (DES) which employ temporal averaging in all or some of the computational domain and thus miss velocity fluctuations and the turbulent behavior of the flow. To make LES tractable in the descent environment, wall-modeled LES must be used wherein flow at the wall is modeled rather than resolved. This work therefore presents an investigation into four different wall functions that can be used for simulating SRP. Three of the examined wall functions were developed in the literature, and one is presented for the first time here. The four functions are compared in two test case simulations: a subsonic NACA airfoil and a shock impinging upon a flat plate. From the results of the two test case simulations, ideal wall functions for simulating powered descent are selected and applied to a 2010 SRP wind tunnel test problem. These wall-modeled LES results are ultimately presented and compared with both experiment and literature results, including an examination of force and surface pressure coefficients, as well as qualitative comparisons with test video. Lastly, to firmly understand the flow physics generated during SRP, a detailed description of turbulence statistics for the wall-modeled LES simulations is presented.