An enhanced wall-boundary condition based on nonlinear coupled constitutive relations

JIANG Zhongzheng; ZHAO Wenwen; YUAN Zhenyu; CHEN Weifang

doi:10.7527/S1000-6893.2018.22057

ACTA AERONAUTICAET ASTRONAUTICA SINICA >

2018 , Vol. 39 >Issue 10: 122057 - 122057

DOI: https://doi.org/10.7527/S1000-6893.2018.22057

Fluid Mechanics and Flight Mechanics

An enhanced wall-boundary condition based on nonlinear coupled constitutive relations

JIANG Zhongzheng ,
ZHAO Wenwen ,
YUAN Zhenyu ,
CHEN Weifang

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School of Aeronautics and Astronautics, Zhejiang University, Hangzhou 310027, China

Received date: 2018-01-29

Revised date: 2018-05-15

Online published: 2018-05-28

Supported by

National Natural Science Foundation of China (11502232, 11572284, 51575487, 61627901); National Basic Research Program of China (2014CB340201); National High-level University Government-sponsored Postgraduate Program (China Scholarship Council [2017]No. 3109, Student number 201706320214)

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Abstract

On the basis of Eu's Generalized Hydrodynamic Equations(GHE), a set of nonlinear algebraic equations for non-conserved variables (shear stress and heat flux), namely Nonlinear Coupled Constitutive Relations (NCCR), is derived to extend linear Navier-Stokes-Fourier (NSF) constitutive models' capability for simulating non-equilibrium flows under adiabatic assumption through Eu's closure and Myong's simplification, providing a strong theoretical tool for predicting continuum-rarefied flows accurately and quickly. Based on this set of nonlinear algebraic equations, this paper proposes a set of nonlinear modified boundary conditions to ensure prediction with the same accuracy at the wall, considering the characteristics of nonlinear distribution in Knudsen layer. Within the finite volume framework, the AUSMPW⁺ scheme, the LU-SGS implicit method and the coupled algorithm are utilized to solve the NCCR equations completely. The hyperbolic flows of a monatomic argon gas around a cylinder and a flat plate for several different flow regimes from continuum to rarefied gas are numerically simulated. The simulation results show that our NCCR-based enhanced boundary conditions can reflect the nonlinearity of the Knudsen layer the at wall, and can improve the accuracy with slip boundary conditions. It is also demonstrated that the NCCR model in conjunction with the enhanced boundary conditions are capable of accurately predicting the surface aerothermodynamic properties of continuum, slip and transitional flow regimes.

Key words： rarefied gas flow; slip boundary condition; generalized hydrodynamic equations; constitutive relations; finite volume method; steepest descent method; flows around a cylinder and a flat plate

Cite this article

JIANG Zhongzheng , ZHAO Wenwen , YUAN Zhenyu , CHEN Weifang . An enhanced wall-boundary condition based on nonlinear coupled constitutive relations[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2018 , 39(10) : 122057 -122057 . DOI: 10.7527/S1000-6893.2018.22057

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