工程力学 ›› 2016, Vol. 33 ›› Issue (12): 21-30.doi: 10.6052/j.issn.1000-4750.2015.05.0385

• 基本方法 • 上一篇    下一篇

基于k-kL两方程湍流模式的尺度自适应模拟

李钊, 陈海昕, 张宇飞   

  1. 清华大学航天航空学院, 北京 100084
  • 收稿日期:2015-05-07 修回日期:2015-08-24 出版日期:2016-12-25 发布日期:2016-12-25
  • 通讯作者: 陈海昕(1974-),男,陕西人,教授,博士,主要从事空气动力学、计算流体力学研究(E-mail:chenhaixin@tsinghua.edu.cn). E-mail:chenhaixin@tsinghua.edu.cn
  • 作者简介:李钊(1986-),男,河南人,博士,主要从事计算流体力学研究(E-mail:lizhao08@mails.tsinghua.edu.cn);张宇飞(1983-),男,四川人,讲师,博士,主要从事气动设计、计算流体力学研究(E-mail:zhangyufei@tsinghua.edu.cn).
  • 基金资助:
    国家973项目(2014CB744801);国家自然科学基金项目(11102098,11372160)

SCALE ADAPTIVE SIMULATION BASED ON A K-KL TWO-EQUATION TURBULENCE MODEL

LI Zhao, CHEN Hai-xin, ZHANG Yu-fei   

  1. School of Aerospace Engineering, Tsinghua University, Beijing 100084, China
  • Received:2015-05-07 Revised:2015-08-24 Online:2016-12-25 Published:2016-12-25

摘要: k-kL两方程模式是一种对湍动能积分尺度输运方程模化的新型湍流模式,具有尺度自适应模拟的特性,能够在统一的表达形式下对流动进行定常和非定常数值模拟。引入可实现性修正,在二维零压力梯度平板边界层中验证其影响,进而选择典型流动的标准算例对这一模式进行较为全面的评估。通过三维CRM翼身组合体绕流算例验证了该模式应用于工程问题的实用性,并考察了网格密度对计算精度的影响。在周期山的三维非定常计算中,k-kL模式能够较好分辨流场中丰富的涡结构,准确捕捉流动大规模分离区的位置和形状,统计平均的表面摩擦力分布和速度场与实验和大涡模拟结果符合良好。上述计算展示了k-kL两方程模式在定常和非定常计算中的流动预测能力和工程应用潜力。

关键词: 计算流体力学, k-kL湍流模式, 尺度自适应模拟, 雷诺平均Navier-Stokes方程, 非定常流动分离

Abstract: The two-equation k-kL turbulence model is based on the transportation equations of turbulent kinetic energy and the integral scale. It is characterized by the capacity of the scale-adaptive simulation, and thus the satisfactory prediction performance in both steady and unsteady flow simulations under a unified form. The present study aims at a comprehensive assessment of this model through classical flow test cases. A two-dimensional zero-pressure-gradient boundary layer case is used to validate the currently introduced realizable correction of this model. Steady computations of the three-dimensional CRM wing/body show its engineering applicability compared with the SA model and the SST model. A grid convergence study is included. In the unsteady computations with the k-kL model, massive separation flows over the periodic hills are well predicted with rich vortical structures. The time-averaged friction distribution and the velocity field are in good agreement with the experimental data and the previous Large Eddy Simulation results. All above demonstrates the advantage and potential of this turbulence model in both steady and unsteady flow simulations.

Key words: computational fluid dynamics, k-kL turbulence model, scale-adaptive simulation, Reynolds averaged Navier-Stokes equation, unsteady flow separation

中图分类号: 

  • V211.3
[1] 王兵, 张会强, 王希麟. 亚格子尺度湍流特性研究[J]. 工程力学, 2006, 23(2):47-51. Wang Bing, Zhang Huiqiang, Wang Xilin. On sub-grid scale turbulence characteristics[J]. Engineering Mechanics, 2006, 23(2):47-51. (in Chinese)
[2] 郭涛, 张涛, 赵威. 基于LES的直管流致振动分析[J]. 工程力学, 2012, 29(10):340-346. Guo Tao, Zhang Tao, Zhao Wei. Flow-induced vibration analysis of straight pipe based on LES[J]. Engineering Mechanics, 2012, 29(10):340-346. (in Chinese)
[3] 王晓玲, 孙蕊蕊, 敖雪菲, 等. 大涡模拟在旋流沉砂池中的应用研究[J]. 工程力学, 2013, 30(8):155-162. Wang Xiaoling, Sun Ruirui, Ao Xuefei, et al. Large eddy simulation on vortex grit chamber for sandstone wastewater treatment[J]. Engineering Mechanics, 2013, 30(8):155-162. (in Chinese)
[4] 薛大文, 陈志华, 孙晓晖, 等. 翼型绕流分离的微楔控制[J]. 工程力学, 2014, 31(8):217-222. Xue Dawen, Chen Zhihua, Sun Xiaohui, et al. Micro-ramp control of the boundary separation induced by the flow past an airfoil[J]. Engineering Mechanics, 2014, 31(8):217-221. (in Chinese)
[5] Spalart P R. Detached-eddy simulation[J]. Annual Review of Fluid Mechanics, 2009, 41(1):181-202.
[6] Slotnick J, Khodadoust A, Alonso J, et al. CFD vision 2030 study:a path to revolutionary computational aerosciences[M]. Virginia US:NASA, 2014:1-51.
[7] Menter F R, Egorov Y. The scale-adaptive simulation method for unsteady turbulent flow predictions. Part 1:theory and model description[J]. Flow, Turbulence and Combustion, 2010, 85(1):113-138.
[8] Egorov Y, Menter F R, Lechner R, et al. The scale-adaptive simulation method for unsteady turbulent flow predictions. Part 2:Application to complex flows[J]. Flow Turbulence and Combustion, 2010, 85(1):139-165.
[9] Fröhlich J, von Terzi D. Hybrid LES/RANS methods for the simulation of turbulent flows[J]. Progress in Aerospace Sciences, 2008, 44(5):349-377.
[10] 白俊强, 王晨, 张扬. 一种基于冯卡门尺度的湍流模式在模拟稳态和非稳态问题中的应用[J]. 工程力学, 2014, 31(11):39-45. Bai Junqiang, Wang Chen, Zhang Yang. Application of a turbulence model based on von Karman length scale in steady and unsteady flow simulation[J]. Engineering Mechanics, 2014, 31(11):39-45. (in Chinese)
[11] 杜磊, 宁方飞. 高亚临界雷诺数圆柱绕流的尺度自适应模拟[J]. 力学学报, 2014, 46(4):487-496. Du Lei, Ning Fangfei. Scale adaptive simulation of flows around a circular cylinder at high sub-critical Reynolds number[J]. Chinese Journal of Theoretical and Applied Mechanics, 2014, 46(4):487-496. (in Chinese)
[12] 王翔宇, 李栋. SST-SAS在小分离流动数值模拟中的表现测试[J]. 西北工业大学学报, 2014, 32(3):337-340. Wang Xiangyu, Li Dong. Behavior of SST-SAS for mild airfoil trailing-edge separation[J]. Journal of Northwestern Polytechnical University, 2014, 32(3):337-340. (in Chinese)
[13] 高瑞泽, 徐晶磊, 赵瑞, 等. XY-SAS模型对于分离流动的性能分析[J]. 北京航空航天大学学报, 2010, 36(4):415-419. Gao Ruize, Xu Jinglei, Zhao Rui, et al. Evaluation of XY-SAS model for separated flows[J]. Journal of Beijing University of Aeronautics and Astronautics, 2010, 36(4):415-419. (in Chinese)
[14] 徐晶磊, 阎超. 一个一方程scale-adaptive simulation模型的构造[J]. 气体物理, 2010, 5(1):79-82. Xu Jinglei, Yan Chao. A one-equation scale-adaptive simulation model[J]. Physics of Gases, 2010, 5(1):79-82. (in Chinese)
[15] 张扬, 白俊强, 华俊, 等. 基于卡门尺度和滤波方法的SST方程改进[J]. 力学学报, 2013, 45(3):442-446. Zhang Yang, Bai Junqiang, Hua Jun, et al. Improvement and assessment of the SST equation based on Karman scale and filter[J]. Chinese Journal of Theoretical and Applied Mechanics, 2013, 45(3):442-446. (in Chinese)
[16] 白俊强, 张扬, 徐晶磊, 等. 新型单方程湍流模型构造及应用研究[J]. 航空学报, 2014, 35(7):1804-1814. Bai Junqiang, Zhang Yang, Xu Jinglei, et al. Construction and its application of a new one-equation turbulence model[J]. Acta Aeronautica et Astronautica Sinica, 2014, 35(7):1804-1814. (in Chinese)
[17] Abdol-Hamid K S. Assessments of a turbulence model based on Menter's modification to Rotta's two-equation model[J]. Grapevine, TX, US, 51st AIAA Aerospace Sciences Meeting, 2013.
[18] Decaix J, Goncalvès E. Time-dependent simulation of cavitating flow with k-l turbulence models[J]. International Journal for Numerical Methods in Fluids, 2012, 68(8):1053-1072.
[19] Davidson L. Evaluation of the SST-SAS model:channel flow, asymmetric diffuser and axisymmetric hill[C]. Egmond aan Zee, The Netherlands:European Conference on Computational Fluid Dynamics (ECCOMAS CFD), 2006.
[20] Lincke A. Verification and validation of von Karman length scale for identification of turbulent structures[M]. Gottingen German:DLR, 2009:29-62.
[21] Xu J, Hu N, Gao G. A high-fidelity turbulence length scale for flow simulation[C]//Berlin German:Progress in Hybrid RANS-LES Modelling, Springer, 2011:141-145.
[22] Chen H X, Fu S, Li F W. Navier-Stokes simulations for transport aircraft wing/body high-lift configurations[J]. Journal of Aircraft, 2003, 40(5):883-890.
[23] Chen H X, Huang X D, Shi K, et al. A computational fluid dynamics study of circumferential groove casing treatment in a transonic axial compressor[J]. Journal of Turbomachinery-Transactions of the ASME, 2014, 136(3):31003.
[24] 张宇飞, 陈海昕, 符松, 等. 一种实用的运输类飞机机翼/发动机短舱一体化优化设计方法[J]. 航空学报, 2012, 33(11):1993-2001. Zhang Yufei, Chen Haixin, Fu Song, et al. A practical optimization design method for transport aircraft wing/nacelle integration[J]. Acta Aeronautica et Astronautica Sinica, 2012, 33(11):1993-2001. (in Chinese)
[25] Wang Q J, Ren Y X, Sun Z S, et al. Low dispersion finite volume scheme based on reconstruction with minimized dispersion and controllable dissipation[J]. Science China Physics Mechanics & Astronomy, 2013, 56(2):423-431.
[26] Shima E, Kitamura K. Parameter-free simple low-dissipation AUSM-family scheme for all speeds[J]. AIAA Journal, 2011, 49(8):1693-1709.
[27] Spalart P R, Allmaras S R. A one-equation turbulence model for aerodynamic flows[C]. Reno, NV, US:30th Aerospace Sciences Meeting and Exhibit, 1992.
[28] Menter F R. Two-equation eddy-viscosity turbulence models for engineering applications[J]. AIAA Journal, 1994, 32(8):1598-1605.
[29] Wilcox D C. Formulation of the k-w turbulence model revisited[J]. AIAA Journal, 2008, 46(11):2823-2838.
[30] Rumsey C. Turbulence modeling resource[DB]. http://turbmodels. larc.nasa.gov/. 2014-08-06.
[31] Rivers M. Common research model[DB]. http://commonresearchmodel.larc.nasa.gov/.2012-02-10.
[32] Levy D W, Laflin K R, Tinoco E N, et al. Summary of data from the fifth computational fluid dynamics drag prediction workshop[C]. Grapevine, TX, US:51st AIAA Aerospace Sciences Meeting, 2013.
[33] Park A, Laflin K R, Chaffin M S, et al. CFL3D, FUN3D, and NSU3D contributions to the fifth drag prediction workshop[C]. Grapevine, TX, US:51st AIAA Aerospace Sciences Meeting, 2013.
[34] ERCOFTAC. 2D periodic hill flow[DB]. http://qnet-ercoftac.cfms.org.uk/w/index.php/UFR_3-30.2013-07-25.
[35] Fröhlich J, Mellen C P, Rodi W, et al. Highly resolved large-eddy simulation of separated flow in a channel with streamwise periodic constrictions[J]. Journal of Fluid Mechanics, 2005, 526(3):19-66.
[36] Breuer M, Peller N, Rapp C, et al. Flow over periodic hills-numerical and experimental study in a wide range of Reynolds numbers[J]. Computers & Fluids, 2009, 38(2):433-457.
[37] Rapp C, Manhart M. Flow over periodic hills:an experimental study[J]. Experiments in Fluids, 2011, 51(1):247-269.
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