Approximate Method for Computing the Effect of a Finite Catalytic Wall on Laminar Heating Rates in an Equilibrium-Air Flowfield

The ability to predict surface heating rates as well as shear and pressure forces is fundamental to the analysis and design of the thermal protection system (TPS) of hypersonic vehicles. Approximate engineering codes that can be used to rapidly predict heating rates are extremely useful in the preliminary or conceptual design phase, while more detailed and expensive Navier-Stokes codes are generally used to provide more accurate heating rate predictions for final design. A heating code, called UNLATCH3, had been used successfully with unstructured inviscid flowfield codes to compute laminar and turbulent heating on general three-dimensional vehicles using unstructured grids and the heating rates over most of the vehicle have been shown to compare favorably with results from both boundary-layer and Navier-Stokes calculations. This code includes the capability to calculate both laminar and turbulent heating rates for either perfect gas or equilibrium air chemistry with radiation equilibrium wall boundary conditions and an approximate expression has been added to account for the effect of velocity gradient on heating. In the flight environment it has been assumed the flow both in the inviscid flowfield and in the boundary layer are in local chemical equilibrium. This is equivalent to assuming that the local chemical reaction rates are infinite so that the chemical constituents at each point within the flowfield are always at their local equilibrium value. However, in reality the chemical reaction rates are finite and in many cases the fluid, particularly in the boundary layer near the surface, remains in a state of chemical nonequilibrium. For moderate flight velocities associated with return from earth orbit some of the energy in the fluid near the surface remains bound up in the dissociation of the oxygen and nitrogen molecules. In these cases the heat transfer to the surface is reduced below the level associated with equilibrium flow. Dr. George Inger has developed an approximate boundary layer analysis for recombination dominated flows which can be used with equilibrium air chemistry heating calculations such as those obtained with the UNLATCH3 code to approximate the effect of finite surface catalysis on heating. In this paper the procedure developed by Dr. Inger will be presented and used within the UNLATCH3 code to calculate the heating on the Shuttle orbiter returning from earth orbit for a finite catalytic wall. The results will be compared with both Navier-Stokes calculations and with flight data.