Simulation of supersonic axisymmetric base flow with a data-driven turbulence model

Abstract

Axisymmetric base flow involves massive flow separation which is challenging for a typical Reynolds-averaged Navier-Stokes (RANS) turbulence model. Furthermore, a supersonic condition imposes additional difficulties to a turbulence model in predicting strong compressibility effects associated with the flow separation phenomena. A data-driven approach is pursued here to improve a turbulence model. The Spalart-Allmaras model is corrected from an optimization process, and then the model correction is mapped to local flow features through a machine learning process. For the optimization-combined machine learning method, the field inversion and machine learning framework is adapted here with three major modifications. First, a zonal-field inversion method is suggested to avoid the undesired modification of attached flow in the optimization process for the model correction. Second, the RANS model is modified by adjusting a net balance between the production and destruction terms in the RANS equation. Third, the local Mach number is included in the machine learning process to incorporate compressibility effects of the supersonic flow. The current study indicates that the improved RANS model reduces the eddy viscosity in the separated region, compared to the baseline RANS model. The reduction of the eddy viscosity helps to predict the base expansion of the supersonic flow and the size of the recirculation region. Current computations are compared with relevant literature data including wake velocity profiles and the base pressure in the wide range of the supersonic Mach number.