Near Wall Resolution Requirements for High-Order FR/CPR Method for Wall-Resolved Large Eddy Simulations

This study aims to establish near wall numerical resolution requirements for wall resolving Large Eddy Simulations (LES) using the Flux Reconstruction / Correction Procedure via Reconstruction (FR/CPR) method. FR/CPR method is relatively new and its numerical capabilities for LES are not well established. A high-order unstructured Large Eddy Simulation (LES) solver GENESIS (based on hpMusic) based on the FR/CPR approach was used to study two canonical flow problems of interest for turbo-machinery. The first problem concerns wall resolved LES simulations of spatial development of a turbulent flat plate boundary layer. The grid resolution requirements for various polynomial orders is established and the skin-friction and near wall turbulence is compared to past DNS results. The second problem studied is the two-dimensional wall film first published by Kacker and Whitelaw [1-3]. The fundamental temperature mixing problem consists of a two-dimensional jet for different mass flow ratios and different plate thicknesses. This study focuses on thin plate for two different mass flow ratios. It is shown that the standard eddy diffusivity model with a constant turbulent Prandtl number fails to predict the mixing between the coolant and main gas. The LES simulations, however, show an excellent predictive capability for this fundamental problem. The impact of polynomial order (p-convergence) and grid resolution (h-convergence) is shown. Finally, the impact of inlet turbulence on the mixing shear layer and heat transfer results are studied.

References

[1] S. C. Kacker and J. H. Whitelaw, "An experimental investigation of the influence of the slot lip-thickness on the impervious-wall effectiveness of the uniform-density, two-dimensional wall jet," Int. J. Heat Mass Transfer, vol. 12, pp. 1196-1201, 1969.

[2] S. C. Kacker and J. H. Whitelaw, "The effect of slot height and slot-turbulence intensity on the effectiveness of the uniform density, two-dimensional wall jet," Journal of Heat Transfer, no. 11, pp. 469-475, 1968.

[3] S. C. Kacker and J. H. Whitelaw, "Some properties of the two-dimensional, turbulent wall jet in a moving stream," Journal of Applied Mechanics, no. 12, pp. 641-651, 1968