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Grid criteria for numerical simulation of hypersonic aerothermodynamics in transition regime

Published online by Cambridge University Press:  24 October 2019

Xiang Ren Open the ORCID record for Xiang Ren [Opens in a new window] ,
Junya Yuan ,
Bijiao He ,
Mingxing Zhang  and
Guobiao Cai
Xiang Ren
Affiliation:
School of Astronautics, Beihang University, Beijing 100191, China
Junya Yuan
Affiliation:
School of Astronautics, Beihang University, Beijing 100191, China
Bijiao He
Affiliation:
School of Astronautics, Beihang University, Beijing 100191, China
Mingxing Zhang
Affiliation:
Beijing Institute of Space Long March Vehicle, Beijing 100076, China
Guobiao Cai*
Affiliation:
School of Astronautics, Beihang University, Beijing 100191, China
*
†Email address for correspondence: cgb@buaa.edu.cn
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Abstract

Grid is an important factor in numerical simulation of hypersonic aerothermodynamics. This paper introduces three criteria for determining grid size in the transition flow regime when using the computational fluid dynamics (CFD) method or the direct simulation Monte Carlo (DSMC) method. The numerical relationship between these three criteria sizes is deduced according to the one-dimensional fluid theory. Then, the relationship is verified using the CFD method to simulate the flow around a two-dimensional cylinder. At the same time, the dependence of simulation accuracy on grid size in the CFD and DSMC methods is studied and the mechanism is given. The result shows that the simulation accuracy of heat flux especially depends on the normal grid size next to surfaces, where the $Re_{\mathit{cell},w}$ criterion and the $\unicode[STIX]{x1D706}_{w}$ criterion based on local parameters are applicable and equivalent, while the $Re_{\mathit{cell},\infty }$ criterion based on the free-stream parameter is only applicable under the assumption of constant viscosity coefficient and constant temperature wall conditions. On the other hand, the trend of the heat flux changing with grid size obtained by CFD and DSMC is exactly the opposite. Therefore, the grid size must be strictly satisfied with the grid criteria when comparing CFD with DSMC and even the hybrid DSMC with Navier–Stokes method.

JFM classification

Aerodynamics: High-speed flow Convection: Plumes/thermals

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Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 881 , 25 December 2019 , pp. 585 - 601
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© 2019 Cambridge University Press 

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