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Numerical Simulation of One-Dimensional Compressible Flow with Real Gas Effects by Solving Boltzmann Equation Using High-Order Accurate Finitedifference Method

Heydarzadeh, Amir Hossein | 2022

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 55813 (45)
  4. University: Sharif University of Technology
  5. Department: Aerospace Engineering
  6. Advisor(s): Hejranfar, Kazem
  7. Abstract:
  8. In this study, the Shokov-BGK model of the Boltzmann equation is reformulated and generalized to consider the real gas effects. At first, the formulation is performed to consider an arbitrary specific heats ratio and the correct Prandtl number for polyatomic gases. Here, the resulting equations of the present formulation are numerically solved by applying the high-order finite-difference weighted essentially non-oscillatory (WENO) scheme. The present solution method is tested by computing the one-dimension Reiman problem with different specific heats ratios for a wide range of the Knudsen numbers. The results are compared with the available gas-kinetic results which show good agreement. It is indicated that the generalized formulation of the Boltzmann equation with the Shokov-BGK model can correctly simulate the rarefied gas flows with different specific heats ratios. Then, the Shokov-BGK model of the Boltzmann equation is generalized to consider the real gas effects by incorporating the relations of the equilibrium air model in the formulation. To validate the present formulation, the one-dimensional Reiman problem is simulated with the real gas effects and the corresponding results are compared to the available results and good agreement is observed. It is shown that the generalized formulation of the Boltzmann equation can be used to effectively compute the rarefied gas flows in a wide range of Knudsen numbers considering the real gas effects
  9. Keywords:
  10. Compressible Rarfied Gas Flow ; Boltzman Equation ; Shakhov Model ; Real Gas Effects ; High-Order Accurate Finite-Difference Method ; Arbitrary Specific Heats Ratio

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