Supersonic Leading Edge Problem according to the Ellipsoidal Model

The supersonic leading edge problem is solved by the molecular approach of kinetic theory using the nonlinear Boltzmann equation with the ellipsoidal model as the governing relation and using the discrete ordinate method as a tool. The local molecular distribution functions for the entire flow field have been calculated, and thus the complete flow field including properties on the plate surface has been generated for the case of M ∞ = 1.5 and for various plate temperatures. The calculated results offer considerable insight into the behavior of a rarefied gas flow as it traverses the complete spectrum of flow regimes from near free molecular to continuum. Since the present solutions are based on the ellipsoidal model which yields the correct Prandtl number for a monatomic gas (Pr = 2 3 ) and is more realistic than the Bhatnagar‐Gross‐Krook model (Pr = 1) , the calculated results can be used for direct comparison with the existing experimental data. Comparisons between these results and those of the BGK model indicate that the ellipsoidal model gives a thicker boundary layer and slightly stronger shock profiles than the BGK model does.