无网格法耦合RNGk-ε湍流模型在亚、跨声速翼型黏性绕流中的数值模拟

doi:10.7527/S1000-6893.2014.0120

流体力学与飞行力学

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无网格法耦合RNGk-ε湍流模型在亚、跨声速翼型黏性绕流中的数值模拟

王园丁¹, 谭俊杰¹, 蔡晓伟¹, 任登凤¹, 马新建²

1. 南京理工大学能源与动力工程学院, 南京 210094;
2. 上海新力动力设备研究所, 上海 201109

收稿日期:2014-04-18 修回日期:2014-06-13 出版日期:2015-05-15 发布日期:2014-06-16
通讯作者: 谭俊杰Tel.: 025-84315508 E-mail: dlxyjx@mail.njust.edu.cn E-mail:dlxyjx@mail.njust.edu.cn
作者简介:王园丁男, 博士研究生。主要研究方向:计算流体力学,飞行器气动分析。 E-mail: wyd19870328@163.com;谭俊杰男, 硕士, 教授, 博士生导师。主要研究方向:计算流体力学。 Tel: 025-84315508 E-mail: dlxyjx@mail.njust.edu.cn
基金资助:
国家自然科学基金 (11072114);上海航天科技创新基金(SAST201365)

Numerical simulation of subsonic and transonic viscous flow around airfoil using meshless method coupled with RNG k-ε turbulent model

WANG Yuanding¹, TAN Junjie¹, CAI Xiaowei¹, REN Dengfeng¹, MA Xinjian²

1. School of Energy and Power Engineering, Nanjing University of Science and Technology, Nanjing 210094, China;
2. Shanghai Xinli Power Equipment Research Institute, Shanghai 201109, China

Received:2014-04-18 Revised:2014-06-13 Online:2015-05-15 Published:2014-06-16
Supported by:
National Natural Science Foundation of China (11072114); Science and Technology Innovation Foundation of Shanghai Aerospace (SAST201365)

摘要/Abstract

摘要：

基于移动最小二乘无网格方法,耦合RNG (Re-Normalisation Group) k-ε湍流模型求解雷诺平均Navier-Stokes方程。采用AUSM (Advection Upstream Splitting Method)⁺-up迎风格式求解数值通量,应用在高度各向异性点云结构中取得良好结果的点云重构技术结合移动最小二乘法拟合空间导数,并用三阶SSP (Strong Stability Preserving)型Runge-Kutta显式时间推进格式求解离散后的控制方程。在此基础之上,实现了对NACA0012、RAE2822翼型亚、跨声速黏性绕流的数值模拟,给出了翼型表面压力系数分布曲线、不同位置处的平均速度剖面、马赫数等值线等计算结果,并与实验值及相关文献数值模拟结果进行比较,结果吻合较好。表明所发展的结合点云重构技术的无网格方法耦合RNG k-ε湍流模型能够成功模拟翼型亚、跨声速黏性绕流,验证了所提算法的有效性,并拓展了无网格方法求解湍流流动的途径。

关键词: 无网格法, 湍流, 点云重构, 移动最小二乘, 各向异性点云

Abstract:

In the present paper, the moving least square meshless method is used to solve Reynolds-averaged Navier-Stokes equations with RNG (Re-Normalisation Group) k-ε turbulence model. The flux is calculated by AUSM (Advection Upstream Splitting Method)⁺-up scheme; the moving least square method with cloud of points reconstruction technology, which can obtain good results from highly anisotropic cloud of points, is adopted to fit the spatial derivative, and the third order SSP (Strong Stability Preserving) Runge-Kutta scheme is used for the time advance to solve the discrete format control equation. Based on this, the subsonic and transonic viscous flow field around NACA0012 and RAE2822 airfoils is simulated. According to the numerical simulation results, the pressure coefficient distribution curves of the airfoil surface and the Mach number contours are presented, and the mean velocity profiles of the boundary layer at different locations are also investigated. The simulation results produced by the present work show a good agreement with the experiment results as well as other numerical simulation results, which means the method proposed in the present paper can successfully simulate the subsonic and transonic viscous flow around airfoil and also verify the effectiveness of the algorithm. What's more, the present work can also expand the way of meshless method to solve the turbulent flow.

Key words: meshless method, turbulent, cloud of point reconstruction, moving least square, anisotropic cloud of points

中图分类号:

V211.3

王园丁, 谭俊杰, 蔡晓伟, 任登凤, 马新建. 无网格法耦合RNGk-ε湍流模型在亚、跨声速翼型黏性绕流中的数值模拟[J]. 航空学报, 2015, 36(5): 1411-1421.

WANG Yuanding, TAN Junjie, CAI Xiaowei, REN Dengfeng, MA Xinjian. Numerical simulation of subsonic and transonic viscous flow around airfoil using meshless method coupled with RNG k-ε turbulent model[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2015, 36(5): 1411-1421.

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E-mail：hkxb@buaa.edu.cn

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主管单位：中国科学技术协会主办单位：中国航空学会北京航空航天大学

无网格法耦合RNGk-ε湍流模型在亚、跨声速翼型黏性绕流中的数值模拟

Numerical simulation of subsonic and transonic viscous flow around airfoil using meshless method coupled with RNG k-ε turbulent model

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