Study of the Issues of Computational Aerothermodynamics Using a Riemann Solver

by Henderson, Sean James

This work is part of a project to more accurately model hypersonic flow. A number of issues in hypersonic flow are addressed. The first issue addressed is that of air properties at increased temperatures. In particular the thermodynamic and transport properties of chemical equilibrium air are found for temperatures up to 30,000 K for a pressure range from 1x10-4 to 100 atm. This work provides properties at slightly higher temperatures for the lower pressure region than can be found in the literature. This work also covers adding equilibrium air chemistry to the computational fluid dynamics computer code known as AVUS. The second issue addressed is commonly referred to as the carbuncle phenomenon. The carbuncle phenomenon is a numerical instability that affects the capturing of strong shocks when using a Riemann solver with low numerical dissipation. The carbuncle phenomenon manifests itself in the inability to compute uniform flow conditions downstream of a normal or nearly normal shock. Prior work has been done in this area to accurately capture strong shocks; and great progress has been made in reducing the effects of the carbuncle phenomenon. Even with these improvements the heat transfer profiles in the stagnation region still show some distortion from small upstream perturbations convected downstream to the wall. It has been determined that the grid quality in the region of the shock is a major factor in the inability of Riemann solvers to accurately capture the flow in the stagnation region. For this reason this work performs a grid study and makes recommendations as to what types of structured grids should be used to accurately capture strong shocks and predict heat transfer profiles at the body surface. This grid study shows that some types of grids suffer more than others from the carbuncle problem. The reason for this is the numerical dissipation that is introduced from the numerical routine. This work shows that grid aspect ratio and the alignment of the grid to the flow can be used to reduce the effects of the carbuncle phenomenon. This work also shows that another mechanism for the carbuncle phenomenon is the alignment of the grids with the shock. The heat transfer profile cannot be properly captured if the grid is not aligned well with the shock. The third issue addressed in this work is the domain of applicability of the perfect gas model, the equilibrium air model, the nonequilibrium air model, and the thermo-chemical nonequilibrium air model. A computational study is carried out using AVUS to determine the regions of applicability of these air models for a blunt body at various velocities and altitudes. This type of altitude-velocity plot has already been produced by previous researchers, but the dividing lines between the different gas models were found using residence times. This work looks at temperature and heat transfer profiles for a blunt body in a high speed air flow to determine the dividing lines between the regions of applicability of the different air models. Unlike the previous work, this work provides specific error values for using a given model in a certain flight regime. It is found that the dividing lines between chemical equilibrium and chemical nonequilibrium have two dips in the curve that were not shown by previous researchers. These dips correspond to regions where O2 and N2 strongly dissociate.