面向非结构混合网格高精度阻力预测的梯度求解方法
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摘要
针对非结构混合网格的特点,通过改进传统的Green-Gauss梯度求解方法,提出了一种可提高非结构混合网格黏性计算精度的节点型Green-Gauss梯度求解方法。利用改进后的方法,完成了DLR-F4翼身组合体算例的计算和对比分析。改进后的梯度求解方法残差收敛更好,下降量级更多,阻力系数和试验吻合更好,激波区域压力分布和分离区域流场细节的模拟更精确,说明改进后的梯度求解方法有效提高了程序的鲁棒性和阻力预测精度,验证了方法的有效性。采用改进后的方法对第5届AIAA阻力预测研讨会的通用研究模型(CRM)进行了详细的模拟分析,结果表明:改进的梯度求解方法更加适用于非结构混合网格的黏性计算,计算精准度达到国际同类CFD软件水平,进一步验证了改进方法的可靠性。
Based on the characteristics of the unstructured hybrid grid,a new gradient calculation method named node-based Green-Gauss is presented by improving the original Green-Gauss method.To validate the new method,a numerical simulation of the DLR-F4 wing-body configuration is performed.The numerical results are analyzed and compared with that of the original Green-Gauss method.The results indicate that better residual convergence and more order of magnitude decrease can be obtained with the new method,the drag coefficients show a good agreement with experiment results,and the pressure distributions in the shock wave and separation region can be computed more accurately.It is found that the new method has excellent drag prediction accuracy and more robustness.Moreover,the Common Research Model(CRM)adopted in the 5 th AIAA Drag Prediction Workshop is studied by using the method proposed.The results demonstrate that the new method is much more suitable for computation of viscosity of the unstructured hybrid grid,and the accuracy reaches the same level of famous CFD software.All of this further verify the drag prediction accuracy of the new method.
Based on the characteristics of the unstructured hybrid grid,a new gradient calculation method named node-based Green-Gauss is presented by improving the original Green-Gauss method.To validate the new method,a numerical simulation of the DLR-F4 wing-body configuration is performed.The numerical results are analyzed and compared with that of the original Green-Gauss method.The results indicate that better residual convergence and more order of magnitude decrease can be obtained with the new method,the drag coefficients show a good agreement with experiment results,and the pressure distributions in the shock wave and separation region can be computed more accurately.It is found that the new method has excellent drag prediction accuracy and more robustness.Moreover,the Common Research Model(CRM)adopted in the 5 th AIAA Drag Prediction Workshop is studied by using the method proposed.The results demonstrate that the new method is much more suitable for computation of viscosity of the unstructured hybrid grid,and the accuracy reaches the same level of famous CFD software.All of this further verify the drag prediction accuracy of the new method.
引文
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[20]ANDREW W C,ANDREW J D.Towards accurate flow predictions using unstructured meshes:AIAA-2009-3650[R].Reston,VA:AIAA,2009.
[21]张耀冰.运输机气动特性混合网格数值模拟研究[D].绵阳:中国空气动力研究与发展中心,2014.ZHANG Y B.Numerical simulation of transport aircraft's aerodynamic characteristics using mixed grid[D].Mianyang:China Aerodynamics Research and Development Center,2014(in Chinese).
[22]BLAZEK J.Computational fluid dynamics:Principles and applications[M].Oxford:Elsevier Science Ltd.,2001:129-179.
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[24]REDEKER G.DLR-F4wing body configuration,in Chapter B of a selection of experimental test cases for the validation of CFD codes:AGARD-1994-AR-303[R].Paris:AGARD,1994.
[25]SHAHYAR Z P,NEAL T F.Assessment of the unstructured grid software TetrUSS for drag prediction of the DLR-F4 configuration:AIAA-2002-0839[R].Reston,VA:AIAA,2002.
[26]TINOCO E,LEVY D.DWP 5summary of participant data[C]∥5th CFD Drag Prediction Workshop.Reston,VA:AIAA,2012.
[27]李钊,陈海昕,张宇飞.基于广义Richardson外插方法的阻力预测精度分析[J].航空学报,2015,36(7):2105-2114.LI Z,CHEN H X,ZHANG Y F.Accuracy analysis of drag prediction based on generalized Richardson extrapolation[J].Acta Aeronautica et Astronautica Sinica,2015,36(7):2105-2114(in Chinese).
[2]LEVY D W,ZICKUHR T,VASSBERG J C,et al.Summary of data from the first AIAA CFD drag prediction workshop:AIAA-2002-0841[R].Reston,VA:AIAA,2002.
[3]LAFLIN K R,KLAUSMEYER S M,ZICKUHR T,et al.Summary of the second AIAA CFD drag prediction workshop[J].Journal of Aircraft,2005,42(5):1165-1178.
[4]VASSBERG J C,TINOCO E N,MANI M,et al.Summary of the third AIAA CFD drag prediction workshop[J].Journal of Aircraft,2008,45(3):781-798.
[5]VASSBERG J C,TINOCO E N,MANI M,et al.Summary of the fourth AIAA CFD drag prediction workshop:AIAA-2010-4547[R].Reston,VA:AIAA,2010.
[6]SLOTNICK J,KHODADOUST A,ALONSO J,et al.CFD vision 2030study:A path to revolutionary computational aerosciences:NASA/CR-2014-218178[R].Washington,D.C.:NASA,2014.
[7]BARTH T J.An overview of combined uncertainty and a posteriori error bound estimates for CFD calculations:AIAA-2016-1062[R].Reston,VA:AIAA,2016.
[8]王运涛,孟德虹,孙岩,等.DLR-F6/FX2B翼身组合体构型高精度数值模拟[J].航空学报,2016,37(2):484-490.WANG Y T,MENG D H,SUN Y,et al.High-order accuracy numerical simulation of DLR-F6/FX2B wing-body configuration[J].Acta Aeronautica et Astronautica Sinica,2016,37(2):484-490(in Chinese).
[9]JOHNSON F T,TINOCO E N,YU N J.Thirty years of development and application of CFD at Boeing Commercial Airplanes,Seattle[J].Computer and Fluid,2005,34(10):1115-1151.
[10]张健,邓有奇,李彬,等.一种适用于三维混合网格的GMRES加速收敛新方法[J].航空学报,2016,37(11):3226-3235.ZHANG J,DENG Y Q,LI B,et al.A new method to accelerate GMRES’s convergence applying to three-dimensional hybrid grid[J].Acta Aeronautica et Astronautica Sinica,2016,37(11):3226-3235(in Chinese).
[11]徐嘉,刘秋洪,蔡晋生,等.基于隐式嵌套重叠网格技术的阻力预测[J].航空学报,2013,34(2):208-217.XU J,LIU Q H,CAI J S,et al.Drag prediction based on overset grids with implicit hole cutting technique[J].ActaAeronautica et Astronautica Sinica,2013,34(2):208-217(in Chinese).
[12]王运涛,李松,孟德虹,等.梯形翼高升力构型的数值模拟技术[J].航空学报,2014,35(12):3213-3221.WANG Y T,LI S,MENG D H,et al.Numerical simulation technology of high lift trapezoidal wing configuration[J].Acta Aeronautica et Astronautica Sinica,2014,35(12):3213-3221(in Chinese).
[13]康忠良,阎超.适用于混合网格的约束最小二乘重构方法[J].航空学报,2012,33(9):1598-1605.KANG Z L,YAN C.Constrained least-squares reconstruction method for mixed grids[J].Acta Aeronautica et Astronautica Sinica,2012,33(9):1598-1605(in Chinese).
[14]LEVY D W,CHAN M S.Comparison of viscous grid layer growth rate of unstructured grids on CFD drag prediction workshop results:AIAA-2010-4671[R].Reston,VA:AIAA,2010.
[15]MAVRIPLIS D J.Viscous flow analysis using aparallel unstructured multigrid solver[J].AIAA Journal,2000,38(11):2067-2076.
[16]ALLMARAS S R,BUSSOLETTI J E.Algorithm issues and challenges associated with the development of robust CFD codes[R].New York:Springer,2009:1-19.
[17]TINOCO E N,BOGUE D R,KAO T J,et al.Progress toward CFD for full flight envelope[J].The Aeronautical Journal,2005,109(1100):451-460.
[18]EMRE S,CHRISTOPH B.Gradient calculation methods on arbitrary polyhedral unstructured meshes for cell-centered CFD solvers:AIAA-2014-1440[R].Reston,VA:AIAA,2014.
[19]SHIMA E,KITAMURA K,HAGA T.Green-Gauss/weighted-least-squares hybrid gradient reconstruction for arbitrary polyhedral unstructured grids[J].AIAA Journal,2013,51(11):2740-2747.
[20]ANDREW W C,ANDREW J D.Towards accurate flow predictions using unstructured meshes:AIAA-2009-3650[R].Reston,VA:AIAA,2009.
[21]张耀冰.运输机气动特性混合网格数值模拟研究[D].绵阳:中国空气动力研究与发展中心,2014.ZHANG Y B.Numerical simulation of transport aircraft's aerodynamic characteristics using mixed grid[D].Mianyang:China Aerodynamics Research and Development Center,2014(in Chinese).
[22]BLAZEK J.Computational fluid dynamics:Principles and applications[M].Oxford:Elsevier Science Ltd.,2001:129-179.
[23]SAXENA S K,MANOJ T N.Implementation and testing of Spalart Allmaras model in a multi-block code:AIAA-2002-0835[R].Reston,VA:AIAA,2002.
[24]REDEKER G.DLR-F4wing body configuration,in Chapter B of a selection of experimental test cases for the validation of CFD codes:AGARD-1994-AR-303[R].Paris:AGARD,1994.
[25]SHAHYAR Z P,NEAL T F.Assessment of the unstructured grid software TetrUSS for drag prediction of the DLR-F4 configuration:AIAA-2002-0839[R].Reston,VA:AIAA,2002.
[26]TINOCO E,LEVY D.DWP 5summary of participant data[C]∥5th CFD Drag Prediction Workshop.Reston,VA:AIAA,2012.
[27]李钊,陈海昕,张宇飞.基于广义Richardson外插方法的阻力预测精度分析[J].航空学报,2015,36(7):2105-2114.LI Z,CHEN H X,ZHANG Y F.Accuracy analysis of drag prediction based on generalized Richardson extrapolation[J].Acta Aeronautica et Astronautica Sinica,2015,36(7):2105-2114(in Chinese).