On The Implicit Large Eddy Simulation of Turbomachinery Flows Using The Flux Reconstruction Method

Abstract: A high-order flux reconstruction solver has been developed and validated to perform implicit large-eddy simulations of industrially representative turbomachinery flows. The T106c low-pressure turbine and VKI LS89 high-pressure turbine cases are studied. The solver uses the Rusanov Riemann solver to compute the inviscid fluxes on the wall boundaries, and HLLC or Roe to evaluate inviscid fluxes for internal faces. The impact of Riemann solvers is demonstrated in terms of accuracy and non-linear stability for turbomachinery flows. It is found that HLLC is more robust than Roe, but both Riemann solvers produce very similar results if stable solutions can be obtained. For non-linear stabilization, a local modal filter, which combines a smooth indicator and a modal filter, is used to stabilize the solution. This approach requires a tuning parameter for the smoothness criterion. Detailed analysis has been provided to guide the selection of a suitable value for different spatial orders of accuracy. This local-modal filter is also compared with the recent positivity-preserving entropy filter in terms of accuracy and stability for the LS89 turbine case. The entropy filter could stabilize the computation but is more dissipative than the local modal filter. Regarding the spanwise spacing of the grid, the case of the LS89 turbine shows that a $z^+$ of approximately $45 - 60$ is suitable for obtaining a satisfactory prediction of the heat transfer coefficient of the mean flow. This would allow for a coarse grid spacing in the spanwise direction and a cost-effective ILES aerothermal simulation for turbomachinery flows.