EI、Scopus 收录
中文核心期刊

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

k-ω SST湍流模式三维激波分离流动修正

杜一鸣 高正红 舒博文 邱福生 宋辰星

杜一鸣, 高正红, 舒博文, 邱福生, 宋辰星. k-ω SST湍流模式三维激波分离流动修正. 力学学报, 2022, 54(6): 1485-1501 doi: 10.6052/0459-1879-22-065
引用本文: 杜一鸣, 高正红, 舒博文, 邱福生, 宋辰星. k-ω SST湍流模式三维激波分离流动修正. 力学学报, 2022, 54(6): 1485-1501 doi: 10.6052/0459-1879-22-065
Du Yiming, Gao Zhenghong, Shu Bowen, Qiu Fusheng, Song Chenxing. Three-dimensional shock separated flow corrections doi: 10.6052/0459-1879-22-065
Citation: Du Yiming, Gao Zhenghong, Shu Bowen, Qiu Fusheng, Song Chenxing. Three-dimensional shock separated flow corrections doi: 10.6052/0459-1879-22-065

k-ω SST湍流模式三维激波分离流动修正

doi: 10.6052/0459-1879-22-065
详细信息
    作者简介:

    邱福生, 教授, 主要研究方向: 飞行器设计及飞行动力学. E-mail: qfsmaple@163.com

  • 中图分类号: O354

THREE-DIMENSIONAL SHOCK SEPARATED FLOW CORRECTIONS OF k-ω SST MODEL

  • 摘要: “激波−边界层分离”是航空气动领域的典型湍流非平衡流动问题, 准确模拟激波分离对于跨声速飞行器气动性能评估和优化设计具有重要意义. 然而传统涡黏性湍流模式中涡黏性系数的定义方式并不适用于非平衡流动, k-ω SST湍流模式为此引入的Bradshaw假设在应用于三维强逆压梯度和较大分离流动时反而限制了雷诺应力的生成, 导致包括k-ω SST在内的常用涡黏性湍流模式均无法对此类流动进行准确模拟. 同时, 现有的非线性雷诺应力本构关系也并不能有效提高模拟精度. 为此, 针对k-ω SST模式分别提出了基于Bradshaw假设和基于长度尺度的两种激波分离流动修正方法. 前者通过提高Bradshaw常数的方式放宽了对雷诺应力生成的限制, 后者则从湍流长度尺度概念出发, 利用混合长度理论、湍动能生成/耗散之比和一种新定义的长度尺度之比构造了ω方程耗散项修正函数, 提高了模式在三维激波分离流动中的建模长度尺度. 两种方法对ONERA M6机翼跨声速大攻角流动均能得到较雷诺应力模式更好的模拟结果. 进一步的雷诺应力分析表明, 三维激波分离流动中“主雷诺应力分量”的概念不再成立, 各雷诺应力分量大小接近. 网格收敛性分析、对其他攻角状态的验证以及湍流平板边界层壁面律验证进一步确认了所提出的两种修正方法的合理性、有效性和通用性.

     

  • 图  2  RAE2822翼型计算网格

    Figure  2.  Computational grid of RAE2822 airfoil

    图  1  计算压力系数和摩擦系数分布与实验的对比

    Figure  1.  Comparison of computed pressure and skin friction coefficients distribution with experiment

    图  3  ONERA M6机翼形状与模式参数

    Figure  3.  Shape and parameter of ONERA M6 wing

    图  4  ONERA M6计算网格

    Figure  4.  Computational grid of ONERA M6 wing

    图  5  小攻角状态计算压力分布与实验的对比

    Figure  5.  Comparison of computed pressure distribution with experiment at small angles of attack

    图  6  表面压力分布与极限流线对比

    Figure  6.  Comparison of surface pressure distribution and limited streamline pattern

    图  7  α = 6.06°状态计算压力分布与实验的对比(非线性模式与RSM、SST和BSL模式)

    Figure  7.  Comparison of computed pressure distribution with experiment at α = 6.06° (nonlinear models with RSM, SST and BSL models)

    图  8  α = 6.06°状态网格收敛性对比

    Figure  8.  Comparison of grid convergence at α = 6.06°

    9  α = 6.06°状态计算压力分布与实验的对比(修正方法与RSM、SST和BSL模式对比)

    9.  Comparison of computed pressure distribution with experiment at α = 6.06° (correction methods with RSM, SST and BSL models)

    图  10  表面压力分布与极限流线对比(修正方法)

    Figure  10.  Comparison of surface pressure distribution and limited streamline pattern (correction methods)

    图  11  采用FPD修正的压力分布与其他结果的对比

    Figure  11.  Comparison of FPD-fixed pressure distribution with other results

    图  12  采用FPD修正的截面湍动能生成/耗散之比

    Figure  12.  Sectional contour of Pk/Dk using FPD correction

    图  13  y/b = 90%截面前缘及分离前湍动能生成/耗散之比

    Figure  13.  Pk/Dk contour at leading edge and before separation of y/b = 90% section

    14  对修正函数FPD进行限制前后的湍流量计算结果对比

    14.  Comparison of the computed turbulence variables before and after limiting the modified function FPD

    图  15  α = 6.06°状态两种修正方法的网格收敛性对比

    Figure  15.  Grid convergence comparison of two corrections at α = 6.06°

    16  两种修正方法应用于其他攻角状态的计算压力分布对比

    16.  Computed pressure distribution comparison of two corrections at other angles of attack

    16  两种修正方法应用于其他攻角状态的计算压力分布对比(续)

    16.  Computed pressure distribution comparison of two corrections at other angles of attack (continued)

    图  17  不同流动中雷诺应力分量的对比

    Figure  17.  Comparison of Reynolds-stress component for different flows

    图  18  湍流平板边界层计算网格

    Figure  18.  Computational grid of turbulent boundary layer of flat plate

    图  19  不同方法的壁面律曲线与实验数据和理论值的对比

    Figure  19.  Computational wall-function law by different methods comparing with experimental and theoretical data

    表  1  ONERA M6机翼计算状态

    Table  1.   Computation conditions of ONERA M6 wing

    MaRe/106α/(°)
    0.84[31]14.6 (root) [31]3.06
    6.06
    0.835911.81 (M.A.C.)4.08
    0.844711.78 (M.A.C.)5.06
    下载: 导出CSV
  • [1] Wilcox DC. Turbulence Modeling of CFD, 3rd edition. California: DCW Industries Inc, 2006
    [2] Rumsey CL, Ying SX. Prediction of high lift: review of present CFD capability. Progress in Aerospace Sciences, 2002, 38(2): 145-180 doi: 10.1016/S0376-0421(02)00003-9
    [3] Slotnick J, Khodadoust A, Alonso J, et al. CFD vision 2030 study: a path to revolutionary computational aerosciences. NASA/CR-2014-218178
    [4] 阎超, 屈峰, 赵雅甜等. 航空航天CFD物理模型和计算方法的述评与挑战. 空气动力学学报, 2020, 38(5): 829-857 (Yan Chao, Qu Feng, Zhao Yatian, et al. Review of development and challenges for physical modeling and numerical scheme of CFD in aeronautics and astronautics. Acta Aerodynamica Sinica, 2020, 38(5): 829-857 (in Chinese) doi: 10.7638/kqdlxxb-2020.0072

    Yan Chao, Qu Feng, Zhao Yatian, et al. Review of development and challenges for physical modeling and numerical scheme of CFD in aeronautics and astronautics. Acta Aerodynamica Sinica, 2020, 38(5): 829-857(in Chinese) doi: 10.7638/kqdlxxb-2020.0072
    [5] Kato M, Launder BE. The modelling of turbulent flow around stationary and vibrating square cylinders//9th Symposium on Turbulent Shear Flows, Kyoto, Japan, 1993
    [6] Townsend AA. Equilibrium layers and wall turbulence. Journal of Fluid Mechanics, 1961, 11(1): 97-120 doi: 10.1017/S0022112061000883
    [7] Prandtl L. Bericht über untersuchungen zur ausgebildeten turbulenz. Journal of Applied Mathematics and Mechanics, 1925, 5(21): 136-139
    [8] Coakley TI. Turbulence modeling methods for the compressible Navier-Stokes equations. AIAA-83-1693
    [9] Johnson DA, King LS. A mathematically simple turbulence closure model for attached and separated turbulent boundary layers. AIAA Journal, 1985, 23(11): 1684-1692 doi: 10.2514/3.9152
    [10] Bradshaw P, Ferriss DH, Atwell NP. Calculation of boundary layer development using the turbulent energy equation. Journal of Fluid Mechanics, 1967, 28(3): 593-616 doi: 10.1017/S0022112067002319
    [11] Townsend AA. The Structure of Turbulent Shear Flow, 2nd edition. Cambridge: Cambridge University Press, 1976
    [12] Menter FR. Improved two-equation k-ω turbulence models for aerodynamic flows. NASA/TM-103975, 1992
    [13] Menter FR. Two-equation eddy-viscosity turbulence models for engineering applications. AIAA Journal, 1994, 32(8): 1598-1605 doi: 10.2514/3.12149
    [14] Schmitt V, Charpin F. Pressure distributions on the ONERA-M6-Wing at transonic Mach tumbers. AGARD-AR-138, 1979
    [15] Spalart PR, Allmaras SR. A one-equation turbulence model for aerodynamic flows. AIAA-92-0439
    [16] 聂胜阳, 高正红, 黄江涛. 微分雷诺应力模型在激波分离流中的应用. 空气动力学学报, 2012, 30(1): 52-56 (Nie Shengyang, Gao Zhenghong, Huang Jiangtao. Differential Reynolds stress model for shock and separated flow. Acta Aerodynamica Sinica, 2012, 30(1): 52-56 (in Chinese) doi: 10.3969/j.issn.0258-1825.2012.01.009

    Nie Shengyang, Gao Zhenghong, Huang Jiangtao. Differential Reynolds stress model for shock and separated flow. Acta Aerodynamica Sinica, 2012, 30(1): 52-56 (in Chinese) doi: 10.3969/j.issn.0258-1825.2012.01.009
    [17] Cécora RD, Eisfeld B, Probst A, et al. Differential Reynolds stress modeling for aeronautics. AIAA-2012-0465
    [18] Lee-Rausch EM, Rumsey CL, Eisfeld B. Application of a full Reynolds stress model to high lift flows. AIAA-2016-3944
    [19] 舒博文, 杜一鸣, 高正红等. 典型航空分离流动的雷诺应力模式数值模拟. 航空学报, 2022, 43(10): 126385 (Shu Bowen, Du Yiming, Gao Zhenghong, et al. Numerical simulation of Reynolds stress model of typical aeronautic separated flow. Acta Aeronautica et Astronautica Sinica, 2022, 43(10): 126385 (in Chinese)

    Shu Bowen, Du Yiming, Gao Zhenghong, et al. Numerical simulation of Reynolds stress model of typical aeronautic separated flow. Acta Aeronautica et Astronautica Sinica, 2022, 43(10): 126385 (in Chinese)
    [20] Li HR, Zhang YF, Chen HX. Optimization of supercritical airfoil considering the ice-accretion effects. AIAA Journal, 2019, 57(11): 4650-4669 doi: 10.2514/1.J057958
    [21] Li HR, Zhang YF, Chen HX. Aerodynamic prediction of iced airfoils based on modified three-equation turbulence model. AIAA Journal, 2020, 58(9): 3863-3876 doi: 10.2514/1.J059206
    [22] Rumsey CL, Vatsa VN. Comparison of the predictive capabilities of several turbulence models. Journal of Aircraft, 1995, 32(3): 510-514 doi: 10.2514/3.46749
    [23] Frink NT. Assessment of an unstructured-grid method for predicting 3-D turbulent viscous flows. AIAA-1996-0292
    [24] Bradshaw P, Perot JB. A note on turbulent energy dissipation in the viscous wall region. Physics of Fluids A: Fluid Dynamics, 1993, 5(12): 3305 doi: 10.1063/1.858691
    [25] NPARC Alliance Verification and Validation Archive, available at: https://www.grc.nasa.gov/WWW/wind/valid
    [26] Cook PH, McDonald MA, Firmin MCP. Aerofoil RAE2822-pressure distributions, and boundary layer and wake measurements. AGARD AR 138, 1979
    [27] Krist SL, Biedron RT, Rumsey CL. CFL3 D user’s manual-ver. 5.0 (2nd edition). NASA/TM-1998-208444
    [28] Hellstrom T, Davidson L, Rizzi A. Reynolds stress transport modelling of transonic flow around RAE2822 airfoil. AIAA-94-0309
    [29] Menter FR, Kuntz M, Langtry R. Ten years of industrial experience with the SST turbulence model. Turbulence, Heat and Mass Transfer, 2003, 4: 625-632
    [30] Togiti V, Eisfeld B. Assessment of g-equation formulation for a second-moment Reynolds stress turbulence model. AIAA-2015-2925
    [31] Turbulence Modeling Resource, NASA Langley Research Center, available at: https://turbmodels.larc.nasa.gov
    [32] Rodi W. A new algebraic relation for calculating the Reynolds stresses. Journal of Applied Mathematics and Mechanics, 1976, 56(S1): T219-T221
    [33] 陈懋章. 黏性流体动力学基础. 北京: 高等教育出版社, 2002

    Chen Maozhang. Fundamental of Viscous Fluid Dynamics. Beijing: Higher Education Press, 2002(in Chinese)
    [34] Rumsey CL, Gatski TB. Recent turbulence model advances applied to multielement airfoil computations. Journal of Aircraft, 2001, 38(5): 904-910 doi: 10.2514/2.2850
    [35] Spalart PR. Strategies for turbulence modelling and simulation. International Journal of Heat and Fluid Flow, 2000, 21: 252-263 doi: 10.1016/S0142-727X(00)00007-2
    [36] Mani M, Babcock DA, Winkler CM, et al. Predictions of a supersonic turbulent flow in a square duct. AIAA-2013-0860
    [37] Rumsey CL, Carlson JR, Pulliam TH, et al. Improvements to the quadratic constitutive relation based on NASA juncture flow data. AIAA Journal, 2020, 58(10): 4374-4384
    [38] 杜一鸣. 涡黏性湍流模式修正与三维边界层转捩预测方法研究. [博士论文]. 西安: 西北工业大学, 2021

    Du Yiming. Research on modification of RANS eddy-viscosity turbulence model and prediction method of three-dimensional boundary-layer transition. [PhD Thesis]. Xi’an: Northwestern Polytechnical University, 2021 (in Chinese)
    [39] Georgiadis NJ, Yoder DA. Recalibration of the Shear Stress Transport Model to improve calculation of shock separated flows. AIAA-2013-0685
    [40] Georgiadis NJ, Rumsey CL, Huang GP. Revisiting turbulence model validation for high-Mach number axisymmetric compression corner flows. AIAA-2015-0316
    [41] Erb A, Hosder S. Uncertainty analysis of turbulence model closure coefficient for shock wave-boundary layer interaction simulations. AIAA-2018-2077
    [42] Kolmogorov AN. Equations of turbulent motion of an incompressible fluid. Izvestia Academy of Sciences, USSR, Physics, 1942, 6: 56-58
    [43] Hellsten A, Laine S. Extension of the k-ω-SST turbulence model for flows over rough surfaces. AIAA-97-3577
    [44] Wieghardt K, Tillman W. On the turbulent friction layer for rising pressure. NACA-TM-1314, 1951
  • 加载中
图(22) / 表(1)
计量
  • 文章访问数:  575
  • HTML全文浏览量:  224
  • PDF下载量:  139
  • 被引次数: 0
出版历程
  • 收稿日期:  2022-02-10
  • 录用日期:  2022-04-06
  • 网络出版日期:  2022-04-07
  • 刊出日期:  2022-06-18

目录

    /

    返回文章
    返回