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一种跨声速定常流场求解加速方法

乔磊 白俊强 邱亚松 华俊 张扬

乔磊, 白俊强, 邱亚松, 等 . 一种跨声速定常流场求解加速方法[J]. 北京航空航天大学学报, 2018, 44(3): 470-479. doi: 10.13700/j.bh.1001-5965.2017.0216
引用本文: 乔磊, 白俊强, 邱亚松, 等 . 一种跨声速定常流场求解加速方法[J]. 北京航空航天大学学报, 2018, 44(3): 470-479. doi: 10.13700/j.bh.1001-5965.2017.0216
QIAO Lei, BAI Junqiang, QIU Yasong, et al. High-efficiency solving method for steady transonic flow field[J]. Journal of Beijing University of Aeronautics and Astronautics, 2018, 44(3): 470-479. doi: 10.13700/j.bh.1001-5965.2017.0216(in Chinese)
Citation: QIAO Lei, BAI Junqiang, QIU Yasong, et al. High-efficiency solving method for steady transonic flow field[J]. Journal of Beijing University of Aeronautics and Astronautics, 2018, 44(3): 470-479. doi: 10.13700/j.bh.1001-5965.2017.0216(in Chinese)

一种跨声速定常流场求解加速方法

doi: 10.13700/j.bh.1001-5965.2017.0216
基金项目: 

国家自然科学基金 11502211

国家自然科学基金 11602199

详细信息
    作者简介:

    乔磊  男, 博士研究生。主要研究方向:计算流体力学

    白俊强  男, 博士, 教授, 博士生导师。主要研究方向:飞行器设计、设计空气动力学、非定常空气动力学、工程湍流模拟

    邱亚松  男, 博士, 助理工程师。主要研究方向:飞行器气动设计、计算流体力学与降阶方法

    华俊  男, 博士, 教授, 博士生导师。主要研究方向:飞行器气动设计、机翼防冰系统数值模拟、计算流体力学与控制系统耦合

    张扬  男, 博士研究生。主要研究方向:工程湍流模拟、流动控制

    通讯作者:

    邱亚松, E-mail: qiuyasong@nwpu.edu.cn

  • 中图分类号: V221.3

High-efficiency solving method for steady transonic flow field

Funds: 

National Natural Science Foundation of China 11502211

National Natural Science Foundation of China 11602199

More Information
  • 摘要:

    跨声速定常流场的隐式求解相当于使用牛顿迭代法求解一个非线性方程组。为满足牛顿迭代收敛性的要求,通常需要对所求解问题进行全局化处理。在同伦延拓的框架内,提出了一种基于拉普拉斯算子的方程延拓方法,提高了定常流场隐式求解收敛速度。针对定常流场通常初始化为均匀来流的特点,一方面利用拉普拉斯算子的椭圆性加快边界条件信息向流场内部的传播,另一方面利用拉普拉斯算子的线性和正定性改善延拓问题的正则性,综合两者增加拟牛顿算法的稳定性,提高可用CFL数,最终达到提高流场求解效率的目的。由于流场问题的复杂性和非线性,难以通过理论分析得出先验的最优非线性求解策略。因此,通过无黏NACA0012翼型、湍流RAE2822翼型和三维ONERA M6机翼等算例的数值实验,研究了拉普拉斯项参数对收敛效率的影响,给出了效率较优的参数组合,验证了本文方法在跨声速情况下相对于经典伪时间推进法可以节约20%以上的CPU计算时间。

     

  • 图 1  无黏NACA0012翼型算例的计算网格

    Figure 1.  Computational grid of invicid NACA0012 airfoil test case

    图 2  无黏NACA0012翼型算例升力系数、阻力系数及残差收敛曲线

    Figure 2.  Lift coefficient, drag coefficient and residual convergence history of invicid NACA0012 airfoil test case

    图 3  无黏NACA0012翼型算例的表面压力系数分布

    Figure 3.  Surface pressure coefficient distribution of invicid NACA0012 airfoil test case

    图 4  湍流RAE2822翼型算例的计算网格

    Figure 4.  Computational grid of turbulent RAE2822 airfoil test case

    图 5  湍流RAE2822翼型算例升力系数、阻力系数及残差收敛曲线

    Figure 5.  Lift coefficient, drag coefficient and residual convergence history of turbulent RAE2822 airfoil test case

    图 6  湍流RAE2822翼型算例的表面压力系数分布

    Figure 6.  Surface pressure coefficient distribution of turbulent RAE2822 airfoil test case

    图 7  三维ONERA M6机翼算例的计算网格

    Figure 7.  Computational grid of 3D ONERA M6 wing test case

    图 8  三维ONERA M6机翼算例升力系数、阻力系数及残差收敛曲线

    Figure 8.  Lift coefficient, drag coefficient and residual convergence history of 3D ONERA M6 wing test case

    图 9  三维ONERA M6机翼算例表面压力系数分布

    Figure 9.  Surface pressure coefficient distribution of 3D ONERA M6 wing test case

    表  1  无黏NACA0012翼型算例的延拓参数和收敛效率

    Table  1.   Continuation parameters and convergence efficiency of invicid NACA0012 airfoil test case

    算例 CFL0 cLP0 n t/s 相对时间节约/%
    PTM1 6 152 38.79 -28.2
    PTM2 8 109 30.25 0
    LPTM1 20 5×10-2 67 25.77 14.8
    LPTM2 20 5×10-3 66 22.07 27.0
    LPTM3 20 1×10-3 64 22.50 25.6
    LPTM4 20 5×10-4 62 21.37 29.4
    LPTM5 10 5×10-5 92 25.56 15.5
    下载: 导出CSV

    表  2  湍流RAE2822翼型算例的延拓参数和收敛效率

    Table  2.   Continuation parameters and convergence efficiency for turbulent RAE2822 airfoil test case

    算例 CFL0 cLP0 n t/s 相对时间节约/%
    PTM1 3 94 51.00 -20.4
    PTM2 4 78 42.37 0
    LPTM1 8 5×10-4 55 36.86 13.0
    LPTM2 8 5×10-5 52 31.43 25.8
    LPTM3 8 1×10-5 56 33.25 21.5
    LPTM4 8 5×10-6 57 32.80 22.6
    LPTM5 6 5×10-7 65 36.52 13.8
    下载: 导出CSV

    表  3  ONERA M6机翼算例的延拓参数和收敛效率

    Table  3.   Continuation parameters and convergence efficiency for 3D ONERA M6 wing test case

    算例 CFL0 cLP0 n t/s 相对时间节约/%
    PTM1 3 80 8 864.73 -12.5
    PTM2 4 66 7 877.23 0
    LPTM1 10 5×10-4 48 7 167.50 9.0
    LPTM2 10 5×10-5 42 6 231.59 20.9
    LPTM3 10 1×10-5 43 6 074.64 22.9
    LPTM4 10 5×10-6 45 6 154.65 21.9
    LPTM5 5 5×10-7 58 7 190.52 8.7
    下载: 导出CSV
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出版历程
  • 收稿日期:  2017-04-10
  • 录用日期:  2017-07-07
  • 刊出日期:  2018-03-20

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