基于Helmholtz速度分解的黏势流耦合方法

上海交通大学学报（自然版） ›› 2016, Vol. 50 ›› Issue (01): 103-109.

基于Helmholtz速度分解的黏势流耦合方法

赵骥，朱仁传，缪国平

(上海交通大学船舶海洋与建筑工程学院, 海洋工程国家重点实验室, 上海 200240)

收稿日期:2015-01-13 出版日期:2016-01-29 发布日期:2016-01-29
基金资助:
国家重点基础研究发展计划（973）项目（2014CB046203），国家自然科学基金资助项目（51579147；51479117）

Approach of Viscous/Potential Flow Based on Helmholtz Velocity Decomposition

ZHAO Ji,ZHU Renchuan,MIAO Guoping

(State Key Laboratory of Ocean Engineering, School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiaotong University, Shanghai 200240, China)

Received:2015-01-13 Online:2016-01-29 Published:2016-01-29

摘要/Abstract

摘要： 摘要：针对NavierStokes(NS)方程，根据Helmholtz速度分解，将流场速度分解为势流部分和非势流部分，剥离势流部分后得到黏势流耦合的变形NS方程.变形NS方程求解的是非势流部分速度分量，其在远场的影响较弱，故较传统计算流体动力学（CFD）方法求解NS方程计算区域小，计算效率较高.以圆柱绕流为例，势流部分速度分量采用解析解，并在OpenFOAM平台内实现了变形NS方程的黏势流耦合计算.对不同雷诺数下圆柱绕流进行了计算模拟，并将耦合方法计算获得的流场中的速度、压力，与文献中的试验及传统CFD等计算的结果进行仔细比较和分析，相关结果吻合良好.研究表明，该方法适用于层流和湍流模型的计算模拟，为改善黏流计算效率提供了新的途径.

关键词: 黏势流耦合, OpenFOAM, 变形NS方程, Helmholtz分解, 圆柱绕流

Abstract: Abstract： According to Helmholtz velocity decomposition, a modified NavierStokes(NS) equation was obtained by decomposing the velocity into the potential flow component and the remaining one. The solution to the modified NS equation was only for the remaining velocity component which vanished in the far field. It was highly efficient to solve the modified NS equation due to the request of small computation domain. Such viscous/potential flow solver was developed on the platform of open source software OpenFOAM. The flows around a cylinder were simulated by the present method in which the analytical formula was taken as the solution to the potential flow. The calculations of the flow around a cylinder at different Reynolds numbers and the comparison of the results with the ones obtained by using the conventional computational fluid dynamics method and the experiment data were conducted. The results agree well, which indicates that the present method is suitable to solve both laminar and turbulence flow and it can improve the computational efficiency.

Key words: potential/viscous, OpenFOAM, modified NS equation, Helmholtz, flow around a cylinder

中图分类号:

U 661.3

赵骥，朱仁传，缪国平. 基于Helmholtz速度分解的黏势流耦合方法[J]. 上海交通大学学报（自然版）, 2016, 50(01): 103-109.

ZHAO Ji,ZHU Renchuan,MIAO Guoping. Approach of Viscous/Potential Flow Based on Helmholtz Velocity Decomposition[J]. Journal of Shanghai Jiaotong University, 2016, 50(01): 103-109.

参考文献

［1］DINH Q V, GLOWINSKI R, PRIAUX J, et al. On the coupling of viscous and inviscid models for incompressible fluid flows via domain decomposition［C］//First International Symposium on Domain Decomposition Methods for Partial Differential Equations. Philadelphia: SIAM, 1988: 350369. ［2］HAMILTON J A.Viscousinviscid matching for wavebody interaction problems［D］. Berkeley： University of California, 2002. ［3］ZHANG Yi, PESZYNSKA M, YIM S C. Coupling of viscous and potential flow models with free surface for near and far field wave propagation［J］. International Journal of Numerical Analysis and Modeling, Series B, 2013,3(3): 256282. ［4］KRISTIANSEN T, FALTINSEN O M. Gap resonance analyzed by a new domaindecomposition method combining potential and viscous flow［J］. Applied Ocean Research, 2012，34:198208. ［5］KUNHO K, SIRVIENTE A I, BECK R F. The complementary RANS equations for the simulation of viscous flows ［J］. International Journal for Numerical Methods in Fluids, 2005,48(2):199229. ［6］HELMHOLTZ H. On integrals of the hydrodynamical equations, which express vortexmotion［J］. Nelin.dinam, 2006, 33:473507. ［7］SHAO Yanlin. Numerical potentialflow Studies on weaklynonlinear wavebody interactions with/without small Forward Speeds［D］. Norway: Norwegian University of Science and Technology, 2010:4344. ［8］STLBERG E, BRGER A, LTSTEDT P, et al. High order accurate solution of flow past a circular cylinder［J］. Journal of Scientific Computing, 2006, 27（13）:431441. ［9］POSDZIECH O, GRUNDMANN R. A systematic approach to the numerical calculation of fundamental quantities of the twodimensional flow over a circular cylinder［J］. Journal of Fluids and Structures, 2007,23(3):479499. ［10］KRAVCHENKO A G, MOIN P. Numerical studies of flow over a circular cylinder at Re=3 900［J］. Physics of Fluids, 2000,12(2):403417.

[1]	郭海鹏, 邹早建, 李广年. 基于OpenFOAM的螺旋桨紧急倒车工况数值模拟[J]. 上海交通大学学报, 2023, 57(2): 168-176.
[2]	郭志远, 虞培祥, 欧阳华. 基于大涡模拟的圆柱绕流剪切层不稳定性[J]. 上海交通大学学报, 2021, 55(8): 924-933.
[3]	田康, 张尧, 李金龙, 张新曙, 尤云祥. 基于OpenFOAM几何流体体积方法的波浪数值模拟[J]. 上海交通大学学报, 2021, 55(1): 1-10.
[4]	马哲，周婷，孙家文，房克照，翟钢军. 基于改进质量源造波方法的非线性波数值模拟[J]. 上海交通大学学报, 2020, 54(1): 60-68.
[5]	欧珊，毛筱菲，刘祖源，黄天奇，余泽爽. 基于OpenFOAM的破损船舶横摇阻尼[J]. 上海交通大学学报（自然版）, 2019, 53(3): 305-314.
[6]	孔丹雅, 马哲, 王胤, 翟钢军. 二维重力式采样器触地姿态及采样率分析[J]. 海洋工程装备与技术, 2018, 5(增刊): 172-176.
[7]	蒋科, 张德华, 戚昱, 苏仰旋, 赵毅, 田润红. 亚临界雷诺数条件下圆柱绕流特性研究[J]. 海洋工程装备与技术, 2017, 4(1): 37-42.
[8]	杨春蕾，朱仁传，缪国平，范菊. 一种对船桨干扰问题的黏势流耦合求解方法[J]. 上海交通大学学报（自然版）, 2014, 48(12): 1795-1801.
[9]	尹纪富,尤云祥,李巍,胡天群. 电磁力控制圆柱体三维绕流场的脱体涡模拟[J]. 上海交通大学学报（自然版）, 2014, 48(02): 244-251.
[10]	陈薛浩, 朱志夏. 基于Fluent的海底管线附近流场分析[J]. 上海交通大学学报（自然版）, 2012, 46(03): 458-462.