High-altitude hypersonic aerodynamics of blunt bodies

A computational fluids dynamics scheme is presented to solve the unsteady Thin-Layer Navier-Stokes (TLNS) equations over a blunt body at high altitude, high Mach number atmospheric reentry flow conditions. This continuum approach is directed to low density hypersonic flows by accounting for non-zero bulk viscosity effects in near frozen flow conditions. The TLNS equations are solved over an axisymmetric body at zero incidence relative to the free stream. The time dependent axisymmetric governing equations are transformed into a computational plane, then cast into weak conservative form and solved using a first-order fully implicit scheme in time with second-order flux vector splitting for spatial derivatives. The resulting implicit matrix from this finite-difference scheme is inverted using a line successive-over-relaxation (SOR) method. The numerical procedure also utilizes an increasing Courant-Friedrichs-Lewy (CFL) number with time resulting in a non-time accurate scheme which provides accelerated convergence to the desired steady-state solution. The computational space is defined over representative sphere and sphere/cone geometries using a body-fitted clustered algebraic grid within a fixed domain (i.e., shock capturing).; The thermo-chemical effects at high altitudes are modeled using a frozen flow assumption. At lower altitudes, an equilibrium chemistry package is used to model real gas effects. The effects of high temperature transport properties are included (i.e., viscosity, thermal conductivity, diffusion). At the present time, nonequilibrium thermo-chemistry effects are not modeled. Catalytic wall, ionization and radiation effects are also excluded from the current analysis. However, the significant difference from previous studies is the inclusion of the capability to model non-zero bulk viscosity effects. The importance of bulk viscosity is reviewed and several blunt body flow field solutions are presented to illustrate the potential contribution of this phenomena at high altitude hypersonic conditions. The current technique is compared with experimental data and other approximate continuum solutions. A variety of test cases are also presented for a wide range of free stream Mach conditions. Discussion of the results includes representative trends at chemical equilibrium as well as at frozen flow conditions.