Calculations of Shock-Boundary Layer Interaction for a Supersonic Ramp Flow by DNS, Using a Fourth order Finite Difference Method

Abstract

Despite intensive theoretical and experimental research, transition to turbulence in separated hypersonic ramp flows is still a challenge to predict. One of the most successful approaches to model the dominant mechanisms is the direct numerical simulation approach, which has demonstrated, despite the well known drawback of computationally costly simulations, the capability to generate reliable datasets. To allow calculations of the transition process on ramp configurations a validated DNS code with high resolution of the turbulent structures in the hypersonic flow regime is a necessity. The abilities of the 4th-order finite-difference version of the DLR FLOWer code, derived originally for Large Eddy Simulations (LES) over recent years is a promising choice for the requested properties. In fact, it was shown in former studies that the resolution of transitional instabilities in supersonic boundary layers is very well within the range of this code. In the present study, different supersonic test cases are chosen from literature and compared with the actual simulations using this high-order version of the DLR FLOWer code. The results using higher-order Pade-filter approaches are encouraging. With this validation as a background, a supersonic ramp-test case was chosen for study. To resolve the transition process, different ramp-angles and Reynolds numbers were investigated to determine a transitional test case, for which turbulence can be resolved behind re-attachment. A hypersonic ramp with 12 degree angle of attack at a moderate Reynolds number was then chosen for three-dimensional DNS calculations of the transition process. These DNS were carried out with various grid densities and grid extents in the wall-normal and spanwise direction with good success. The investigation of different spanwise extents of the simulation region has demonstrated the capabilities of the code to predict the supersonic transition process.