Effects of Chemistry Modeling on Hypersonic Boundary Layer Linear Stability Prediction

The prediction of transition to turbulence in boundary layers on hypersonic vehicles is important to accurately predict the skin friction and heating. Linear stability calculations including transient growth depend on the models and assumptions used to obtain the mean flow and the stability equations. The current work considers the effects of different chemistry models for thermodynamic, transport, and chemical reactions and different wall boundary conditions. Using different chemistry models in predicting 2nd mode growth rates in a Mach 10 flat plate boundary layer leads to differences greater than the differences observed for different chemical conditions (frozen, equilibrium, chemical non-equilibrium and thermo-chemical non-equilibrium). For transient growth different chemistry models leads to differences in optimal transient growth but different chemical conditions and wall cooling lead to much larger differences. Wall cooling leads to the destabilization of 2nd mode instabilities and decreased optimal transient growth. The aerodynamics of entry/reentry vehicles involve complex thermo-chemical processes. These processes greatly affect the heat flux to the surface of the vehicle . For convective heating, a turbulent boundary layer leads to larger heat fluxes than a laminar boundary layer due to the increased convective transport associated with turbulence. Fully turbulent flow is typically assumed in predicting convective heating on blunt bodies in order to conservatively design spacecraft. This could lead to excessive TPS (Thermal Protection System) weight or require the selection of a different TPS material. This uncertainty in heating prediction could be reduced if accurate prediction of boundary layer transition could be obtained. Transition from laminar to turbulent flow over a hypersonic vehicle is complex and may take one of many distinct paths depending on the flow conditions and disturbance environment. Two important processes associated with linear transition are modal instabilities (classically called linear stability theory) and transient growth. Modal instabilities begin with the receptivity of small disturbances into the boundary layer. Individually disturbance modes either grow or decay exponentially. Growing waves may become large enough to modify the boundary layer base flow. This potentially leads to secondary instabilities and the breakdown to transition. For modal transition, linear stability equation and the parabolized stability equations can be used to analyze the development of unstable disturbances in the boundary layer. The parabolized stability equations (PSE) are more detailed and consider the effect of non-parallel flow and can be used for weakly non-linear problems. Johnson and Candler have developed a PSE code which has been used for many different cases including blunt reentry vehicles and blunt and sharp cones. 1, 2 Transient growth is the algebraic growth of disturbances. Since the Orr-Sommerfeld and the equivalent operator for compressible flow are not self-adjoint, the resulting eigenmodes are non-orthogonal. As different individual disturbance modes decay, their superposition can lead to a growth in energy. If this growth is large enough, secondary instabilities can develop and lead to the breakdown to turbulence.