Large eddy simulation of transonic flow with shock wave/turbulent boundary layer interaction

Licentiatavhandling, 2004

Large eddy simulations (LES) of shock wave/turbulent boundary layer interaction (SWTBLI) have been carried out. The flow configuration was that of transonic flow over a bump with inlet Mach number 0.75 and maximum Mach number 1.27. The Reynolds number based on the free stream velocity and inlet momentum loss thickness was 2400. The Favre filtered Navier-Stokes equations were solved using a finite volume solver. The convective fluxes were discretized with a low dissipative third order upwind scheme and the viscous fluxes were discretized using a second-order central scheme. The subgrid stresses were modeled using a compressible version of Smagorinsky's model. Time marching was performed using a low-storage three-stage Runge-Kutta scheme. In each stage of the Runge-Kutta scheme, cells close to a solid wall were pre-conditioned using a newly developed pre-conditioning \newline method saving up to 60 % of the computational time. The computational domain was discretized using block structured grids, the largest one with approximately 6.7⋅106 nodes. Time dependent inlet data constructed from measurements and DNS computations were used and the computations were performed on parallel computers using message-passing interface MPI. Computations from three different grids were compared to ensure good enough resolution and wide enough domain to contain all structures of the flow. PDF of the skin friction coefficient and large amplification of the Reynolds stresses suggest strong separation at the SWTBLI. Still, no shock movement could be detected, which is in contradiction with measurements made at KTH. The form factor of the incoming boundary layer never exceeds 2 which is much lower than the conventional condition for separation. By fast Fourier transforms of autocorrelations, characteristic frequencies could be found in the separated region. These frequencies could all be found also in the autocorrelations of the incoming boundary layer. The bursting frequency of the incoming boundary layer was found to be in agreement with the outer scaling 0.14U∞/δ99, but it could not be detected anywhere in the separated region.