Exact compressible transport equation for the unresolved stresses and PANS-RSM simulation of transonic buffet

The exact compressible-flow tensorial transport-equations for the unresolved stresses of the density-weighted filtered (Favre) velocity field are reformulated without using mixed Favre-Reynolds central moments. The exact equation for the dissipation-rate of the unresolved turbulent-kinetic-energy is derived for constant density-flow and extended to compressible flows invoking Morkovin's hypothesis. The term-by-term correspondence of the transport equations for the unresolved stresses and dissipation-rate with the corresponding exact transport equations for the Reynolds stresses and turbulence-kinetic-energy dissipation-rate is exploited to derive the closure for the subgrid-scales (SGS) equations by applying the partially averaged Navier-Stokes (PANS) framework to an underlying Reynolds-stress model (RSM). The paper assesses the prediction of transonic buffet on the OAT15A supercritical airfoil using a PANS–RSM approach. Experimental data for transonic buffet flow around the supercritical OAT15A airfoil are compared with computations, using both PANS-RSM and Reynolds averaged Navier-Stokes (RANS-RSM), demonstrating the potential of PANS–RSM to predict the low-frequency self-sustained shock-wave oscillations. •Exact compressible-flow equations for the unresolved stresses.•Symbolism for Reynolds- and Favre-filtered resolved/unresolved variables.•Partially-averaged Navier-Stokes differential Reynolds-stress model.•Transonic buffet prediction using 3-D PANS-RSM.