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
收稿日期: 2014-04-18
修回日期: 2014-06-13
网络出版日期: 2014-06-16
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
Received date: 2014-04-18
Revised date: 2014-06-13
Online published: 2014-06-16
Supported by
National Natural Science Foundation of China (11072114); Science and Technology Innovation Foundation of Shanghai Aerospace (SAST201365)
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。
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 . DOI: 10.7527/S1000-6893.2014.0120
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.
[1] Liu X, Zhu D M, Lu M W, et al. h, p, hp adaptive meshless method for plane crack problem[J]. Chinese Journal of Theoretical and Applied Mechanics, 2000, 32(3): 308-318 (in Chinese). 刘欣, 朱德懋, 陆明万, 等. 平面裂纹问题的h, p, hp型自适应无网格方法的研究[J].力学学报, 2000, 32(3): 308-318.
[2] Chen S S, Liu Y H, Cen Z Z. Lower bound limit analysis by using the element-free Galerkin method with orthogonal basis[J]. Chinese Journal of Theoretical and Applied Mechanics, 2007, 39(5): 633-640 (in Chinese). 陈莘莘, 刘应华, 岑章志. 极限下限分析的正交基无单元Galerkin法[J]. 力学学报, 2007, 39(5): 633-640.
[3] Batina J. A gridless Euler/Navier-Stokes solution algorithm for complex two-dimensional application, AIAA-1993-0333[R]. Reston: AIAA, 1993.
[4] Sridar D, Balakrishnan N. An upwind finite difference scheme for meshless solvers[J]. Journal of Computational Physics, 2003, 189(1): 1-29.
[5] Chen H Q. An implicit gridless method and its applications[J]. Acta Aerodynamica Sinica, 2002, 20(2): 133-140 (in Chinese). 陈红全. 隐式无网格算法及其应用研究[J].空气动力学学报, 2002, 20(2): 133-140.
[6] Munikrishna N, Balakrishnan N. Turbulent flow computations on a hybrid Cartesian point distribution using meshless solver LSFD-U[J]. Computers & Fluids, 2011, 40(1): 118-138.
[7] Wang G, Ye Z Y, Jiang C Q, et al. Gridless method for Navier-Stokes equations with high Reynolds number[J]. Chinese Journal of Applied Mechanics, 2007, 24(3): 348-352 (in Chinese). 王刚, 叶正寅, 蒋超奇, 等. 高雷诺数下求解NS方程的无网格算法[J]. 应用力学学报, 2007, 24(3): 348-352.
[8] Cai X W, Tan J J, Zhang M, et al. Meshless least square method based on COP reconstruction for viscous flow simulation[J]. Journal of Nanjing University of Science and Technology, 2013, 37(6): 880-885 (in Chinese). 蔡晓伟, 谭俊杰, 张木, 等. 粘性流模拟中基于点云重构的最小二乘无网格法[J]. 南京理工大学学报, 2013, 37(6): 880-885.
[9] Launder B E, Spalding D B. Lectures in mathematical models of turbulence[M]. London: Academic Press, 1972.
[10] Yakhot V, Orzag S A. Renormalization group analysis of turbulence. I. basic theory[J]. Journal of Scientific Computing, 1986, 1(1): 3-51.
[11] Menter F R. Two-equation eddy-viscosity turbulence models for engineering applications[R]. AIAA Journal,1994, 32(8): 1598-1605.
[12] Liou M S. A further development of the AUSM+ scheme towards robust and accurate solutions for all speeds, AIAA-2003-4116[R]. Reston: AIAA, 2003.
[13] May G, Jameson A. Unstructured algorithm for inviscid and viscous flows embedded in a unified solver architecture: Flo3xx, AIAA-2005-0318[R]. Reston: AIAA, 2005.
[14] Haase W, Bradsma F, Elsholz E, et al. EUROVAL-an European initiative on validation of CFD codes notes on numerical fluid mechanics[M]//Notes on numerical fluid mechanics. Braunschweig, Wiesbaden: Vieweg, 1993.
[15] Harris C D. Two-dimensional aerodynamic characteristics of the NACA0012 airfoil in the Langley 8-foot transonic pressure tunnel, NASA-TM-81927[R]. Washington, D.C.: NASA, 1981.
[16] Cook P H, Donald M A, Firmin M C P. AerofoilRAE2822 pressure distribution, boundary layer and wake measurement, Report No. AR 138[R]. [S.l.]: AGARD, 1979.
[17] Michel D, Aftosmis M J, Berger M J, et al. Automatic hybird-cartesian grid generation for high-Reynolds number flows around complex geometries, AIAA-1999-0777[R]. Reston: AIAA, 1999.
[18] Medic G, Kalitzin G, Iaccarino G, et al. Adaptive wall functions with applications, AIAA-2006-3744[R]. Reston: AIAA, 2006.
[19] Peng S H, Eliasson P, Davidson L. Examination of the shear stress transport assumption with a low-Reynolds number k-ω model for aerodynamic flows, AIAA-2007-3864[R]. Reston: AIAA, 2007.
[20] Kral L D. Recent experience with different turbulence models applied to the calculation of flow over aircraft components[J]. Progress in Aerospace Sciences,1998, 34: 481-541.
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