Development of models for compressible flow over rough surfaces using Direct Numerical Simulations: report on Work Package 2

In this report, Direct Numerical Simulation (DNS) of compressible flow over a set of smooth and rough surfaces is carried out in a turbulent channel flow configuration. The aim is to quantify the Hama roughness function for different rough wall geometries under the effects of compressibility as well as to obtain an estimate for the overall surface heat flux. Four different rough surfaces are considered. They are a grit-blasted, a graphite and two manufactured sawtooth surfaces with different mean roughness height. The manufactured sawtooth surface is provided by Oxford University as part of an ongoing experimental campaign. The peak to trough height of the first sawtooth surface is scaled based on the mean roughness height of the grit-blasted surface. The peak to trough height of the second sawtooth surface is scaled based on the maximum peak to trough height of the grit-blasted surface. A level set ghost-fluid method is used to represent the rough wall geometry. In particular, adaptive mesh refinement is used for the first time in such a flow configuration. It is found that permanently flagging a fixed region near the wall with a finer mesh, while providing an adaptive mesh at the region closer to the outer layer of the boundary, is the most optimal meshing approach. Furthermore, the selection of an appropriate parameter value, that governs the switch from a central to a weighted-essentially non-oscillatory scheme, is necessary to minimize numerical dissipation and allow the flow to quickly transition into a turbulent state while ensuring numerical stability. Planar double-averaged statistical flow and surface quantities as well as instantaneous flow fields are reported for different bulk Mach and Reynolds numbers. While the expected behaviour in the Hama roughness function could be reproduced also in the supersonic flow regime, this investigation reveals that a direct comparison of surface heat fluxes for compressible channel flows replicating hypersonic boundary layers will likely require a more active control of the bulk temperature flow field in future work.