基于局部时均Navier-Stokes模型的分域计算方法

doi:10.3969/j.issn.1000-1093.2021.01.011

摘要/Abstract

摘要： 基于标准局部时均Navier-Stokes模型中控制参数f_k的取值特点，提出一种基于分域思想的计算方法。针对不同的流域采用不同的f_k值，实现在同一个计算流域设置不同湍流模型的效果。应用该方法分别计算绕方柱的单相流动和绕Clark-y水翼的非定常空化流动，并将计算结果与相应实验结果进行对比。结果表明：数值计算得到的方柱表面压力系数分布以及流场中不同截面处的速度分布均与实验结果吻合较好；新方法可以很好地捕捉到Clark-y水翼吸力面空穴形态随时间的演化过程，以及水翼升力系数随时间的波动规律。

关键词: 局部时均Navier-Stokes模型, 分域计算, 方柱绕流, 非定常空化

Abstract: A partially-averaged Navier-Stokes（PANS）method is proposed to calculate different regions of flow field with different values of f_k, which imposes the different turbulence models to be set at the same time. The proposed method is applied to simulate the single-phase flow around the two-dimensional square cylinder and the unsteady cavitating flows around Clark-y hydrofoil, respectively. The modified PANS model well predicts the pressure coefficient distributions on the surface of square cylinder and the velocity distribution at different sections of flow field. In addition, it can well capture the time evolutions of the cavities around the Clark-y hydrofoil and the fluctuation of lift coefficient of hydrofoil.

Key words: partially-averagedNavier-Stokesmodel, domaincomputing, flowaroundsquarecylinder, unsteadycavitatingflow

中图分类号:

TV131.3⁺2

罗倩，胡常莉. 基于局部时均Navier-Stokes模型的分域计算方法[J]. 兵工学报, 2021, 42(1): 100-107.

LUO Qian， HU Changli. Domain Computing Method Based on Partially-averaged Navier-Stokes Turbulence Model[J]. Acta Armamentarii, 2021, 42(1): 100-107.

参考文献

［1］季斌, 程怀玉, 黄彪, 等. 空化水动力学非定常特性研究进展及展望［J］. 力学进展, 2019, 49:428-479.
JI B, CHENG H Y, HUANG B, et al. Research progresses and prospects of unsteady hydrodynamics characteristics for cavitation［J］. Advances in Mechanics, 2019, 49: 428-479. (in Chinese)
［2］王建春, 吴乘胜, 王星, 等. 中等雷诺数方柱绕流的直接数值模拟及涡系分析［J］. 船舶力学, 2019, 23(8):893-905.
WANG J C, WU C S, WANG X, et al. Direct numerical simulation of medium Reynolds number flow past square cylinder and analysis of vortex structures［J］. Journal of Ship Mechanics, 2019, 23(8):893-905.(in Chinese)
［3］张显雄, 张志田, 张伟峰, 等. 五种湍流涡粘模型在二维方柱绕流数值模拟中的对比研究［J］. 空气动力学学报, 2018, 36(2): 339-349.
ZHANG X X, ZHANG Z T, ZHANG W F, et al. Comparison of five eddy viscosity turbulence models in numerical simulation of flow over a two-dimensional square cylinder［J］. Acta Aerodyna-mica Sinica, 2018, 36(2):339-349.(in Chinese)
［4］ LONG X P, LONG Y, LONG W T, et al. Some notes on numerical simulation and error analyses of the attached turbulent cavitating flow by LES［J］. Journal of Hydrodynamics, 2018, 30(2):369-372.
［5］ JI B, LONG Y, LONG X P, et al. Large eddy simulation of turbulent attached cavitating flow with special emphasis on large scale structures of the hydrofoil wake and turbulence cavitation interactions［J］. Journal of Hydrodynamics, 2017, 29(1):27-39.
［6］杨龙, 胡常莉, 罗倩. 不同攻角下绕平头回转体初生空化流动特性研究［J］. 兵工学报, 2020, 41(4):711-719.
YANG L, HU C L, LUO Q. Study of characteristics of inception cavitating flows around an axisymmetric blunt body at different angles of attack［J］. Acta Armamentarii, 2020, 41(4):711-719.
［7］ WANG B L, LIU Z H, LI H Y, et al. On the numerical simulations of vortical cavitating flows around various hydrofoils［J］. Journal of Hydrodynamics, Ser. B, 2017, 29(6): 926-938.
［8］ DENG R, GAO Z Y, LI Y L, et al. Development and research status of turbulence model［J］. Journal of Ship Mechanics, 2019, 23(3):360-376.
［9］ GIRIMAJI S S. Partially-averaged Navier-Stokes model for turbulence: a reynolds-averaged Navier-Stokes to direct numerical simulation bridging method［J］. Journal of Applied Mechanics, 2006, 73(3):413-421.
［10］ RAZI P, TAZRAEI P, GIRIMAJI S. Partially-averaged Navier-Stokes(PANS) simulations of flow separation over smooth curved surfaces［J］. International Journal of Heat and Fluid Flow, 2017, 66:157-171.
［11］王亦晓, 秦战生, 陈洋, 等. 基于PANS的轴流泵簸箕形进水流道水力特性［J］. 南水北调与水利科技, 2019, 17(6):201-208.
WANG Y X, QIN Z S, CHEN Y, et al. Study on the hydraulic characteristics of dustpan shaped inlet of an axial flow pump based on PANS［J］. South-to-North Water Transfers and Water Science & Technology, 2019, 17(6):201-208. (in Chinese)
［12］ BUSCO G, HASSAN Y A. Solution verification of PANS model for a PWR fuel assembly［J］. Nuclear Engineering and Design, 2019, 353:110231.
［13］刘跃, 管小荣, 徐诚. SAS与PANS模型在圆柱绕流中的应用比较［J］. 空气动力学学报, 2019, 37(4):530-540.
LIU Y, GUAN X R, XU C. Assessment of SAS and PANS models in simulations of flow over a circular cylinder［J］. Acta Aerodynamica Sinica, 2019, 37(4):530-540. (in Chinese)
［14］黄彪, 王国玉, 权晓波, 等. PANS模型在空化湍流数值计算中的应用［J］. 应用力学学报, 2011, 28(4): 339-343.
HUANG B, WANG G Y, QUAN X B, et al. Application of the partially-averaged Navier-Stokes method in computations of turbulent cavitating flows［J］. Chinese Journal of Applied Mechanics, 2011, 28(4): 339-343. (in Chinese)
［15］胡常莉, 王国玉, 陈广豪. 绕平头回转体空穴的发展及脱落特性研究［J］. 兵工学报, 2014, 35(1):88-95.
HU C L, WANG G Y, CHEN G H. Study of characteristics of unsteady cavitating flow around an axisymmetric blunt body［J］. Acta Armamentarii, 2014, 35(1):88-95.（in Chinese）
［16］ LUO X W, HUANG R F, JI B. Transient cavitating vortical flows around a hydrofoil using k-ω partially averaged Navier-Stokes model［J］. Modern Physics Letters B, 2016, 30(1):1550262.
［17］ ZHANG D S, SHI W D, PAN D Z, et al. Numerical simulation of cavitation shedding flow around a hydrofoil using partially-ave-raged Navier-Stokes model［J］. International Journal of Numerical Methods for Heat & Fluid Flow, 2015, 25(4):825-830.
［18］ HUANG R F, LUO X W, JI B. Numerical simulation of the transient cavitating turbulent flows around the Clark-y hydrofoil using modified partially averaged Navier-Stokes method［J］. Journal of Mechanical Science and Technology, 2017, 31(6):2849-2859.
［19］ HU C L, WANG G Y, CHEN G H, et al. A modified PANS model for computations of unsteady turbulence cavitating flows［J］. Science China Physics, Mechanics & Astronomy, 2014, 57(10): 1967-1976.
［20］ GIRIMAJI S S, ABDOL-HAMID K S. Partially averaged Navier Stokes model for turbulence: implementation and validation［C］∥Proceedings of the 43rd AIAA Aerospace Sciences Meeting and Exhibit. Reno, NV, US:AIAA, 2005.
［21］ LYN D A, EINAV S, RODI W, et al. A laser-doppler velocimetry study of ensemble-averaged characteristics of the turbulent near wake of a square cylinder［J］. Journal of Fluid Mechanics, 2006, 304:285-319.
［22］ NORBERG C. Flow around rectangular cylinders: pressure forces and wake frequencies［J］. Journal of Wind Engineering & Industrial Aerodynamics, 1993, 49(1/2/3):187-196.
［23］ MINGUEZ M, BRUN C, PASQUETTI R, et al. Experimental and high-order LES analysis of the flow in near-wall region of a square cylinder［J］. International Journal of Heat and Fluid Flow, 2011, 32(3):558-566.
［24］ TRIAS F X, GOROBETS A, OLIVA A. Turbulent flow around a square cylinder at Reynolds number 22000: a DNS study［J］. Computers & Fluids, 2015, 123: 87-98．
［25］ ZWART P J, GERBER A G, BELAMRI T. A two-phase flow model for predicting cavitation dynamics［C］∥Proceedings of the 5th International Conference on Multiphase Flow. Yokohama, Japan: ［s.n.］, 2004.
［26］ PENG X X, JI B, CAO Y T, et al. Combined experimental observation and numerical simulation of the cloud cavitation with U-type flow structures on hydrofoils［J］. International Journal of Multiphase Flow, 2016, 79:10-22.
［27］ WU Q, HUANG B, WANG G Y, et al. The transient characteristics of cloud cavitating flow over a flexible hydrofoil［J］. International Journal of Multiphase Flow, 2018, 99:162-173.
［28］李雨濛, 陈晖, 项乐, 等. 水翼非定常空化流动中湍流模型研究［J］. 火箭推进, 2019, 45(6):29-37.
LI Y M, CHEN H, XIANG L, et al. Study on turbulent model of unsteady cavitating flow around hydrofoil［J］. Journal of Rocket Propulsion, 2019, 45(6):29-37. (in Chinese)
［29］时素果, 王国玉, 王复峰, 等. 绕三维水翼云状空化现象的实验研究［J］. 应用力学学报, 2011, 28(2):105-110.
SHI S G, WANG G Y, WANG F F, et al. Experimental study on unsteady cavitation flows around three-dimensional hydrofoil［J］. Chinese Journal of Applied Mechanics, 2011, 28(2):105-110. (in Chinese)