基于非线性耦合本构关系的改进边界条件

doi:10.7527/S1000-6893.2018.22057

流体力学与飞行力学

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基于非线性耦合本构关系的改进边界条件

江中正, 赵文文, 袁震宇, 陈伟芳

浙江大学航空航天学院, 杭州 310027

收稿日期:2018-01-29 修回日期:2018-05-15 出版日期:2018-10-15 发布日期:2018-05-28
通讯作者: 赵文文 E-mail:wwzhao@zju.edu.cn
基金资助:
国家自然科学基金（11502232，11572284，51575487，61627901）；国家重点基础研究发展计划（2014CB340201）；国家建设高水平大学公派研究生项目（留金发[2017]3109号，学号201706320214）

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

JIANG Zhongzheng, ZHAO Wenwen, YUAN Zhenyu, CHEN Weifang

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

Received:2018-01-29 Revised:2018-05-15 Online:2018-10-15 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)

摘要/Abstract

摘要： 非线性耦合本构关系（NCCR）模型是在Eu的广义流体动力学方程（GHE）基础上，通过绝热假设、Eu封闭和Myong简化推导出的关于非守恒量（黏性应力与热流）的非线性代数方程，有效拓展了线性的纳维-斯托克斯-傅里叶（NSF）本构模型在非平衡流动中的模拟能力，为快速准确模拟连续与稀薄耦合流动问题提供了强有力的理论工具。针对该模型开展滑移边界条件研究，结合努森层内物理量非线性分布的特点，提出一套在物面处与模型精度相一致的非线性修正滑移边界条件。在有限体积框架下，采用AUSMPW⁺格式和LU-SGS方法以及NCCR的完整耦合求解算法，对不同稀薄程度的高超声速单原子氩气圆柱绕流和平板绕流问题进行数值模拟。研究结果表明，基于NCCR模型的修正边界条件准确刻画出物面努森层内流动的非线性特点，有效提高了固壁滑移边界的精度。采用非线性修正边界的NCCR模型准确预测了连续流、滑移流和过渡流域的物面压力、摩阻与热流系数。

关键词: 稀薄气体流动, 滑移边界条件, 广义流体动力学方程, 本构关系, 有限体积法, 最速下降法, 圆柱和平板绕流

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

中图分类号:

V411.3
O356

江中正, 赵文文, 袁震宇, 陈伟芳. 基于非线性耦合本构关系的改进边界条件[J]. 航空学报, 2018, 39(10): 122057-122057.

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.

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基于非线性耦合本构关系的改进边界条件

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

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