Abstract
The hypersonic leading edge problem is studied within the framework of the kinetic theory of gases. The Boltzmann equation with the Bhatnagar–Gross–Krook model is used as the governing equation. The method of discrete ordinates developed by Huang and previously applied to the supersonic flow case is extended and applied to the present problem. The local molecular distribution functions for the entire flow field have been calculated for M∞ = 5, 10, and 20, and thus the complete flow field has been generated for Tw = T∞, 0.1 T0, and 0.15 T0. The calculated results clearly define the structure of shock waves and 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. Results for shock position, surface pressure, and the slip velocity at plate are found to be in reasonably good agreement with the experimental data of Becker and Boylan, Harbour and Lewis, McCrosky, Bogdonoff, and McDougall, and Becker. The calculated local molecular velocity distribution functions which are useful in the direct comparison with the molecular beam experimental results are also presented.
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