Numerical simulation of Görtler vortices in hypersonic compression ramps

A numerical study of the formation and evolution of Görtler type vortices over a compression ramp under an hypersonic flow is presented. Numerical predictions in laminar compression ramps (body/body-flaps configurations) usually require the inclusion of three-dimensional effects to correlate separation lengths with experimental measurements. Moreover, in the presence of large recirculation regions, the heat transfer calculated over the compression ramp severely underestimate experimental values. This discrepancy could be explained at least in part by the presence and effects of centrifugal disturbances. Indeed the regular striation patterns in heat transfer rates seen in experiments suggest this. In the present work numerical simulations were carried out over three-dimensional 15° compression ramps in a laminar hypersonic flow at Mach 6.85 and a Reynolds number per unit length of 2.45 × 106 m−1. The relatively high Görtler numbers obtained suggested that Görtler vortices might be important. In most cases, a spanwise periodic velocity perturbation is imposed on the flat plate ahead of separation. However for one case, which had a grid with a higher spanwise resolution, a regular striation pattern emerged without forcing. In this case, the pattern had a wavelength comparable to that found in experiments and as predicted from linear theory. A spanwise variation of 5-15% in the heat transfer close to the centreline was obtained in this case.