Experimental Validation of the Quadratic Constitutive Relation in Supersonic Streamwise Corner Flows

Abstract

The quadratic constitutive relation is a simple extension to the linear eddy-viscosity hypothesis and has shown some promise in improving the computation of flow along streamwise corner geometries. In order to further investigate these improvements, the quadratic model is validated by comparing RANS simulations of a Mach 2.5 wind tunnel flow with high-quality experimental velocity data. Careful set up and assessment of computations using detailed characterisation data of the overall flow field suggests a minimum expected discrepancy of approximately 3% for any experimental–computational velocity comparisons. The corner regions of the rectangular cross-section wind tunnel exhibit velocity differences of 7% between experimental data and computations with linear eddy-viscosity models, but these discrepancies are reduced to 4–5% when the quadratic constitutive relation is used. This improvement can be attributed to a better prediction of the corner boundary-layer structure, due to computations reproducing the stress-induced streamwise vortices which are known to exist in this flow field. However, the strength and position of these vortices do not correspond exactly with those in the measured flow. A further observation from this study is the appearance of additional, non-physical vortices when the value of the quadratic coefficient in the relation exceeds the recommended value of 0.3.