Large-Eddy and Direct Numerical Simulations of the Bachalo-Johnson Flow with Shock-Induced Separation

Abstract

The Bachalo-Johnson experiment on an axisymmetric bump has been a primary validation case for turbulence models in shock-boundary-layer interactions since the 1980’s. In the present work, Wall-Modelled Large-Eddy Simulations (WMLES) of this flow were conducted using Improved Delayed Detached-Eddy Simulation (IDDES) as the sub-grid-scale (SGS) and wall model, with a synthetic turbulence generator, expecting close enough agreement with experiment. However, the WMLES results are disappointing, even in terms of the shock position, even though the results from two grids with 4.7 × 108 and 1.6 × 109 cells respectively agree well with each other. This failure of grid refinement to warn of an inaccurate simulation is of great concern, and the reasons for it are explored. We then conducted a Direct Numerical Simulation (DNS) embedded in the LES over a reduced domain, with 8 × 109 grid cells. The DNS has a far more accurate shock position and overall pressure distribution. The skin friction in the favourable pressure gradient is also much higher than in the LES; thus, wide differences appear upstream of the shock wave, most probably caused by the rapid acceleration which leads to atypical shear-stress profiles. Other SGS models were tried, and performed worse than IDDES. The DNS essentially fulfils the initial expectations although in a reduced domain and provides data for turbulence-modelling studies, for instance by extracting an effective eddy viscosity from it. The most noticeable remaining disagreement with experiment is over the Reynolds shear stress.