Laminar and turbulent convective heat transfer over bodies at an angle of attack

The axisymmetric analogue (small cross flow approximation) is employed to develop methods for calculating laminar and turbulent heat transfer over bodies of revolution at angles of attack. These methods are restricted to hypersonic flows over bodies with highly cooled walls.

A method is presented for determining the surface inviscid streamline geometry and coordinate scale factors, which are required in the axisymmetric analogue. This method requires the surface pressure distribution to be known, whether theoretical or experimental. A theoretical pressure distribution is developed using combinations of Modified Newtonian pressures, Prandtl-Heyer relations, and the second-order shock expansion method.

Results are presented for spheres, paraboloids, and spherically blunted cones at angles of attack. Surface pressures and streamline geometries were found to compare favorably with experimental data and the three-dimensional method of characteristics. Laminar heat transfer results were also found to compare favorably with experimental data. The turbulent heating rates yielded results close to those of Vaglio-Laurin's method.

It was found that the surface pressure distribution affected laminar heating rates more than the inviscid streamline geometry. The choice of reference conditions and the exponent in the viscosity-temperature relationship highly affected the turbulent heating rates.