Approximate Method for Computing Laminar and Turbulent Convective Heating on Hypersonic Vehicles Using Unstructured Grids

Abstract

*† ‡ 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. One code, called LATCH, has been used successfully in conjunction with inviscid flowfield codes computed on single block structured grids. More recent inviscid codes have been developed that use unstructured grids, which greatly reduce grid generation time for complex configurations. A heating code, called UNLATCH2, had been used successfully with unstructured inviscid flowfield codes to compute laminar 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 boundarylayer and Navier-Stokes calculations. However, some anomalies were encountered in the stagnation region. This paper describes an improved version of the approximate heating code, UNLATCH3, which provides much better heating results in the stagnation region. In addition the new 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 laminar heating. A new improved axisymmetric analog method is developed to calculate inviscid surface streamlines and metric coefficients based on unstructured grids. Results are calculated and compared with both boundary-layer and Navier-Stokes solutions for a range of typical hypersonic vehicles. The new code is directed toward the development of more efficient and accurate approximate engineering methods for predicting heating on hypersonic vehicles and to better understand how these methods can be integrated with more detailed Navier-Stokes results to improve the overall vehicle/TPS design process.