Diffusion in Hypersonic Flows

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Gür H. B. , Eyi S.

in: A Closer Look at the Diffusion Equation , Hristov,Jordan, Editor, NOVA Science Publishers Inc. , New York, pp.27-54, 2020

  • Publication Type: Book Chapter / Chapter Research Book
  • Publication Date: 2020
  • Publisher: NOVA Science Publishers Inc.
  • City: New York
  • Page Numbers: pp.27-54
  • Editors: Hristov,Jordan, Editor


In hypersonic flows, air goes into chemical reaction due to high temperature. Therefore, in addition to the Navier-Stokes Equations, chemical reaction equations need to be solved to analyze hypersonic flows. A model may be need to simulate the diffusion phenomena among chemical species. It is possible to implement Fick's Law of Diffusion as well as Stefan-Maxwell Diffusion Equation. Basically, in Fick's Law of Diffusion, the driving force is the species concentration differences. This method is similar to the Fourier Law of Conduction and defines a diffusion coefficient called Diffusivity. The value of this coefficient is constant for all species in this method. In order to improve the accuracy, more complex models, such as Stefan Maxwell Diffusion Equation, may be used. The driving forces, in this method, are not only the concentration differences but also the interactions of species with each other. Results are evaluated by solving the Navier Stokes and finite-rate chemical reaction equations around the Apollo AS-202 Command module. Eleven species are utilized. As diffusion models, Fick's Law of Diffusion, the Diffusivity calculation with binary collision theory and the Stefan-Maxwell Equation are implemented.  Result show that more realistic models may be needed for diffusion flux calculations. Due to its elementary formulation, a rough estimation is possible using the Fick's Law. However, it is possible to improve this elementary formulation using the Binary Diffusion Model. On the other hand, Stefan-Maxwell Equation gives more detailed results since it uses more accurate formulation. In this study, the performances of these models are analyzed in hypersonic flow conditions.