旋转坐标系下分区计算的LU隐式方法
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摘要
将隐式时间迭代方法应用于并行计算是CFD研究中的热点问题,研究发现LU-SGS格式在旋转坐标系下对分区边界比较敏感,对旋翼悬停状态进行分区并行计算时碰到了计算发散的问题。针对此问题,对基于LU分解的3种隐式时间迭代格式(LU-SGS、DP-LUR和HLU-SGS)进行了对比研究,设计了静止流场下的旋转网格算例对计算方法进行测试。结果表明,LU-SGS格式在网格边界采用简化处理方法,当边界的逆变速度增大时会引起数值误差放大,误差的不断积累导致计算发散。DP-LUR和HLU-SGS格式通过在边界单元采用雅克比迭代算法,能有效消除分区边界影响,使计算格式在大CFL数条件下保持稳定,其中HLU-SGS继承了LU-SGS迭代效率高的特点。在此基础上,采用并行化的LU隐式方法对Caradonna-Tung旋翼进行了并行计算,针对两套稀密程度不同的背景网格,在产生复杂分区边界的计算网格条件下,均获得了气动力和旋翼尾迹都充分收敛的流场。通过计算,分析了背景网格密度对预测气动力性能和捕捉尾迹流场的影响,计算结果与试验值吻合良好,验证了当前隐式计算方法适用于旋转坐标系并行计算,适合于推广至其他大规模并行分区的流场计算。
The application of implicit time iterative method to parallel computing is a hot issue in CFD research.It is found that LU-SGS scheme is sensitive to partition boundary in the rotating reference frame,and thus the problem of computational divergence is encountered in parallel calculation of the hovering rotor.To solve this problem,three implicit time iterative schemes based on LU decomposition(namely LU-SGS,DP-LUR,and HLU-SGS)are studied comparatively,and a rotating grid example is designed to test these calculation methods.Results show that as the LU-SGS scheme uses a simplified method to deal with boundary cells,numerical errors increases in proportion to the rotating speed and accumulation of errors leads to divergence of calculation.DP-LUR and HLU-SGS schemes can effectively eliminate the influence of partition boundaries by using Jacobian iterations in boundary cells,and both keep the scheme stable with large CFL number.HLU-SGS inherits the high efficiency of LU-SGS scheme.Parallel computations of the Caradonna-Tung rotor are then carried out by the three schemes,where coarse and fine background meshes are studied comparatively.Although complex partition boundaries are produced for parallel computation,fully converged results of the aerodynamic force and wake are obtained.The computation results are in good agreement with experimental data,showing that current implicit time stepping methods are applicable for parallel computation in rotating reference frame,and can be furtherly extended to other large scale parallel computations.
The application of implicit time iterative method to parallel computing is a hot issue in CFD research.It is found that LU-SGS scheme is sensitive to partition boundary in the rotating reference frame,and thus the problem of computational divergence is encountered in parallel calculation of the hovering rotor.To solve this problem,three implicit time iterative schemes based on LU decomposition(namely LU-SGS,DP-LUR,and HLU-SGS)are studied comparatively,and a rotating grid example is designed to test these calculation methods.Results show that as the LU-SGS scheme uses a simplified method to deal with boundary cells,numerical errors increases in proportion to the rotating speed and accumulation of errors leads to divergence of calculation.DP-LUR and HLU-SGS schemes can effectively eliminate the influence of partition boundaries by using Jacobian iterations in boundary cells,and both keep the scheme stable with large CFL number.HLU-SGS inherits the high efficiency of LU-SGS scheme.Parallel computations of the Caradonna-Tung rotor are then carried out by the three schemes,where coarse and fine background meshes are studied comparatively.Although complex partition boundaries are produced for parallel computation,fully converged results of the aerodynamic force and wake are obtained.The computation results are in good agreement with experimental data,showing that current implicit time stepping methods are applicable for parallel computation in rotating reference frame,and can be furtherly extended to other large scale parallel computations.
引文
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[16]张来平,马戎,常兴华,等.虚拟飞行中气动、运动和控制耦合的数值模拟技术[J].力学进展,2014,44(1):376-417.ZHANG L P,MA R,CHANG X H,et al.Review of aerodynamics/kinematics/fight-control coupling methods in virtual ight simulations[J].Advances in Mechanics,2014,44(1):376-417(in Chinese).
[17]CARADONNA F X,TUNG C.Experimental and analytical studies of a model helicopter rotor in hover:NASA TM 81232[R].Washington,D.C.:NASA,1981.
[18]SRINIVASAN G R,BAEDER J D,OBAYASHI S,et al.Flowfield of a lifting rotor in hover:A Navier-Stokes simulation[J].AIAA Journal,1992,30(10):2371-2378.
[19]MOHD N,BARAKOS G N.Computational aerodynamics of hovering helicopter rotors[J].Journal Mecanikal,2012,34(1):16-46.
[20]李震,张锡文,何枫.基于速度梯度张量的四元分解对若干涡判据的评价[J].物理学报,2014,63(5):1-7.LI Z,ZHANG X W,HE F.Evaluation of vortex criteria by virtue of the quadruple decomposition of velocity gradient tensor[J].Acta Physica Sinica,2014,63(5):1-7(in Chinese).
[21]EGEBERG T F.Onset and progressiong of vortical structures for a surface combatant at drift angles 0,10and 20degrees[D].Trondheim:Norwegian University of Science and Technology,2013.
[2]HARIHARAN N,EGOLF A,SANKAR L.Simulation of rotor in hover:Current state and challenges:AIAA-2014-0041[R].Reston,VA:AIAA,2014.
[3]ZHAO Q J,ZHAO G Q,WANG B,et al.Robust Navier-Stokes method of predicting unsteady flowfield and aerodynamic characteristics of helicopter rotor[J].Chinese Journal of Aeronautics,2018,31(2):214-224.
[4]朱国林,徐庆新.计算流体力学并行计算技术研究综述[J].空气动力学学报,2002,20(1):1-6.ZHU G L,XU Q X.Review on parallel computation technique on computational fluid dynamics[J].Acta Aerodynamica Sinica,2002,20(1):1-6(in Chinese).
[5]ROOSE D,DRIESSCHE R V,邹辉,等.并行计算机和计算流体力学并行算法[J].力学进展,1998,28(1):111-125.ROOSE D,DRIESSCHE R V,ZOU H,et al.Parallel computers and parallel algorithms for CFD[J].Advances in Mechanics,1998,28(1):111-125(in Chinese).
[6]WANG G,JIANG Y W,YE Z Y.An improved LU-SGS implicit scheme for high reynolds number flow computations on hybrid unstructured mesh[J].Chinese Journal of Aeronautics,2012,25(1):33-41.
[7]黄宇,阎超,袁武.适用于混合网格的改进雅可比迭代法及其应用[J].北京航空航天大学学报,2016,42(3):551-561.HUANG Y,YAN C,YUAN W.Improved Jacobi iterative method for hybrid grid and its application[J].Journal of Beijing University of Aeronautics and Astronautics,2016,42(3):551-561(in Chinese).
[8]WISSINK A M,LYRINTZIS A S,STRAWN R C.Parallelization of a three-dimensional flow solver for Euler ro-torcraft aerodynamics predictions[J].AIAA Journal,1996,34(11):2276-2283.
[9]LUO H,SHAROV D,BAUM J D.Parallel unstructured grid GMRES+LU-SGS method for turbulent flows:AIAA-2003-273[R].Reston,VA:AIAA,2003.
[10]OTERO E,ELIASSON P.Improving the performance of the CFD code edge using LU-SGS and line-implicit methods[C]∥CEAS 2013the International Conference of the European Aerospace Societies,2013.
[11]徐丽,杨爱明,丁珏,等.用隐式方法和WENO格式计算悬停旋翼跨声速无粘流场[J].计算力学学报,2010,27(4):607-612.XU L,YANG A M,DING Y,et al.Numerical simulation on the inviscid flowfield of transonic hovering rotor using implicit method and WENO schemes[J].Chinese Journal of Computational Mechanics,2010,27(4):607-612(in Chinese).
[12]叶舟,史勇杰,徐国华.耦合高效配平策略的旋翼气动特性分析方法[J].航空动力学报,2017,32(4):882-889.YE Z,SHI Y J,XU G H.Analytical method of rotor aerodynamic characteristics by coupling a high-efficiency trim strategy[J].Journal of Aerospace Power,2017,32(4):882-889(in Chinese).
[13]吴琪,招启军,林永峰,等.旋翼跨音速非定常黏性绕流的高效CFD模拟方法[J].南京航空航天大学学报,2015,47(2):212-219.WU Q,ZHAO Q J,LIN Y F,et al.Highly-efficient CFD method for predicting unsteady transonic viscous flow around rotor[J].Journal of Nanjing University of Aeronautics&Astronautics,2015,47(2):212-219(in Chinese).
[14]CHEN R F,WANG Z J.Fast,block lower-upper symmetric Gauss-Seidel scheme for arbitrary grids[J].AIAA Journal,2000,38(12):2238-2245.
[15]余婧,郝东,周铸,等.大规模多块结构网格并行任务负载平衡算法[C]∥第十七届全国计算流体力学会议,2017.YU J,HAO D,ZHOU Z,et al.Load balance algorithms of parallel task for large scale multi-block grids[C]∥The17th National CFD Conference,2017(in Chinese).
[16]张来平,马戎,常兴华,等.虚拟飞行中气动、运动和控制耦合的数值模拟技术[J].力学进展,2014,44(1):376-417.ZHANG L P,MA R,CHANG X H,et al.Review of aerodynamics/kinematics/fight-control coupling methods in virtual ight simulations[J].Advances in Mechanics,2014,44(1):376-417(in Chinese).
[17]CARADONNA F X,TUNG C.Experimental and analytical studies of a model helicopter rotor in hover:NASA TM 81232[R].Washington,D.C.:NASA,1981.
[18]SRINIVASAN G R,BAEDER J D,OBAYASHI S,et al.Flowfield of a lifting rotor in hover:A Navier-Stokes simulation[J].AIAA Journal,1992,30(10):2371-2378.
[19]MOHD N,BARAKOS G N.Computational aerodynamics of hovering helicopter rotors[J].Journal Mecanikal,2012,34(1):16-46.
[20]李震,张锡文,何枫.基于速度梯度张量的四元分解对若干涡判据的评价[J].物理学报,2014,63(5):1-7.LI Z,ZHANG X W,HE F.Evaluation of vortex criteria by virtue of the quadruple decomposition of velocity gradient tensor[J].Acta Physica Sinica,2014,63(5):1-7(in Chinese).
[21]EGEBERG T F.Onset and progressiong of vortical structures for a surface combatant at drift angles 0,10and 20degrees[D].Trondheim:Norwegian University of Science and Technology,2013.