Transonic flow: large eddy simulation, numerical methods and subgrid modeling

Doctoral thesis, 2006

Shock wave turbulent boundary layer interactions (SWTBLI) commonly arise in turbomachinery and aerospace applications and on the exterior of high speed aircrafts. In all these cases, SWTBLI can significantly change the flow and hence the physical load imposed by it. Despite numerous experimental investigations, only a basic understanding of SWTBLI has been achieved. The bulk of the existing calculations are from Reynolds averaged Navier-Stokes computations since the high computational cost has long hindered more advanced and accurate calculations. This thesis deals with large eddy simulations of SWTBLI to develop numerical methods and subgrid models and to gain a deeper understanding of the phenomenon. A semi-implicit preconditioning scheme has been developed. It utilizes the high aspect ratio of the cells close to the walls to decouple the implicit time stepping formulation in all but the wall-normal direction. The scheme allows the otherwise explicit Runge-Kutta scheme to take five times larger time steps than is possible with a pure explicit scheme. The scheme reduces the computational time by 60 % without any reduction in the accuracy of the calculations. It is shown that large scale movement of the whole shock is not a local phenomenon. For strong enough shocks, elliptic leakage can trigger movement of the part of the shock closest to the wall. This movement has however no direct relation to the bursting events of the boundary layer approaching the shock. It is also shown that strong separation can occur without triggering any shock motion at all. A zonal hybrid method for computation of wall-bounded flows was developed. Data from a direct numerical simulation of channel flow at Reynolds number 500 were filtered and the subgrid stresses expanded in a series using proper orthogonal decomposition. The series was truncated. A feed forward neural network was trained to estimate the coefficient of the series. The neural network and the orthonormal base from the expansion were applied together with a Smagorinsky subgrid model to channel flow at Reynolds number 500 with good results. Generalization to higher Reynolds numbers is briefly discussed.