一种模拟动边界绕流的锐利界面浸入边界法

郭涛; 张晋铭; 张纹惠; 王文全

doi:10.11883/bzycj-2022-0342

一种模拟动边界绕流的锐利界面浸入边界法

doi: 10.11883/bzycj-2022-0342

郭涛^1,,
张晋铭¹,
张纹惠^{1, 3},
王文全^2, ,

1.
昆明理工大学建筑工程学院，云南昆明 650500
2.
四川大学水力学与山区河流开发保护国家重点实验室，四川成都 610065
3.
中国能源建设集团云南省电力设计院有限公司，云南昆明 650051

基金项目: 国家自然科学基金（51969009，52179087，52069010）

详细信息

作者简介:
郭　涛（1983－　），男，博士，副教授，guotaoj@126.com

通讯作者:
王文全（1977－　），男，博士，教授，wwqquan@126.com

中图分类号: O351
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- 文章访问数: 334
- HTML全文浏览量: 301
- PDF下载量: 41
- 被引次数: 0
出版历程
- 收稿日期: 2021-08-16
- 修回日期: 2022-08-25
- 网络出版日期: 2022-08-25
- 刊出日期: 2022-09-09

A sharp-interface immersed boundary method for simulating flows around bluff body with moving boundary

GUO Tao^1
,,
ZHANG Jinming¹,
ZHANG Wenhui^{1, 3},
WANG Wenquan^{2
, ,}

1.
Faculty of Civil Engineering and Mechanics, Kunming University of Science and Technology, Kunming 650500, Yunnan, China
2.
State Key Laboratory of Hydropower and Mountain River Engineering, Sichuan University, Chengdu 610065, Sichuan, China
3.
China Energy Engineering Group Yunnan Electric Power Design Institute Co., LTD., Kunming 650051, Yunnan, China

摘要

摘要: 为避免复杂贴体网格的更新和畸形对动边界流场计算效率、精度的影响，以充分掌握结构场的受力特性，采用一种改进的锐利界面（sharp-interface）浸入边界法模拟具有动边界绕流的流动问题。该方法将计算域中的固体视为流体，固体边界离散为若干个拉格朗日网格点，通过在界面单元处插值重构流动参数（速度），将其直接作为流动求解器的边界条件，由此来反映固体边界的影响。即通过构造“虚拟点—受力点—垂足点”的计算结构，借助双线性插值得到虚拟点的速度，再通过强制满足固体边界的无滑移条件计算出受力点的速度，以此为边界条件，最终求解基于浸入边界法的耦合系统方程，实现复杂动边界的流动数值模拟。采用C++编写该浸入边界法的数值程序，以单圆柱绕流为验证算例，通过与文献和实验结果的对比，验证了该方法的准确性和可靠性。在此基础上，对主动运动椭圆柱绕流问题进行了精细计算，探讨了不同轴长比(A_R)、不同攻角($ \theta $)下的椭圆柱对尾涡结构分布特征和水力不稳定现象的影响。捕捉到了反对称S型、“P+S” Ⅰ型、“P+S” Ⅱ型尾涡脱落模态，漩涡强度、涡脱频率和升阻比随A_R和$ \theta $的变化规律，以及确定了升阻比临界攻角(25°)。
- 锐利界面 /
- 浸入边界法 /
- 圆柱绕流 /
- 椭圆柱绕流 /
- 轴长比 /
- 涡脱频率 /
- 升/阻力系数
Abstract: When the structural wall moves over a fixed grid, the structure coverage will change, resulting in many dead and emerging elements. To avoid the influence of malformation and reconstruction of body-fitted grids on the calculation efficiency and accuracy of the fluid-structure interaction problems with coupled boundary movement on the fixed grid, an improved numerical method for describing the interaction between an immersed rigid body and fluid based on a sharp-interface is proposed. In this method, both the fluid and solid are regarded as pure fluid domains in the whole computational domain, and the solid boundary is divided into several Lagrangian grid points. The flow parameter or velocity is reconstructed by interpolation at the interface element, which is then directly used as the boundary condition of the flow field, thus reflecting the influence of the wall boundary conditions. The method constructs the calculation structure of “virtual point, force point and vertical foot point”, and the velocity of the virtual point is obtained by bilinear interpolation. Then, the velocity of the force point is calculated by forcing the solid boundary to meet the no-slip condition, and the equations of the coupling system based on the immersion boundary method are finally solved to realize the numerical simulation of the flow with a complex moving boundary. The numerical program for this immersed boundary method is established using C++, then the accuracy and reliability of the proposed method are validated by comparison with the literature and experimental results of the basic numerical example of flow around a cylinder. Furthermore, the effects of the structural shape and the angle of attack on the trailing vortex structure, the vortex shedding frequency, and the lift/ coefficient characteristics of the flow around the elliptical cylinder have been analyzed. The anti-symmetric S-type, “P+S” Ⅰ-type and “P+S” Ⅱ-type trailing vortex shedding modes, as well as the variation laws of the vortex structure size, vortex shedding frequency and lift-drag coefficients ratio with axis ratio and angle of attack, are captured. The critical angle of attack (25°) corresponding to the maximum lift-drag ratio is determined as 25°.
- sharp-interface /
- immersed boundary method /
- flow around circular cylinder /
- flow around elliptical cylinders /
- axis ratio /
- vortex shedding frequency /
- lift and drag coefficients

HTML全文

图 1 固体边界处理

Figure 1. Treatment of the solid boundary

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图 2 整体计算域及边界条件

Figure 2. Computational domain and boundary conditions

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图 3 流向速度分布

Figure 3. Isolines of velocity

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图 4 一个周期内尾迹涡的演化

Figure 4. Isolines of vorticity against time

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图 5 升力、阻力系数时程曲线

Figure 5. Variations of the lift and drag coefficients with time

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图 6 椭圆柱绕流计算模型

Figure 6. Computational model of flow around an elliptical cylinder

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图 7 一个周期内椭圆柱的瞬时攻角变化曲线

Figure 7. Changes of the instantaneous angle of attack of the elliptical cylinder within a period

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图 8 平均阻力系数、最大升力系数随轴长比的变化

Figure 8. Variation of lift and drag coefficients with axis ratio

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图 9 涡脱频率随轴长比的变化

Figure 9. Variation of vortex shedding frequency with axis ratio

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图 10 不同轴长比下的流线图

Figure 10. The instantaneous streamlines with different axis ratio

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图 11 不同轴长比工况下的瞬时涡量

Figure 11. Variation of instantaneous vorticity with axis ratio

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图 12 不同攻角对升、阻力系数的影响

Figure 12. Variations of lift and drag coefficients with angle of attack

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图 13 不同攻角下的瞬时压力场

Figure 13. Instantaneous pressure fields at different angles of attack

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图 14 不同攻角对涡脱频率的影响

Figure 14. Variation of vortex shedding frequency with angle of attack

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图 15 不同攻角下的瞬时涡量图

Figure 15. Variation of the instantaneous vorticity with the angle of attack

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图 16 不同攻角下的涡脱落模态示意图

Figure 16. The diagram of vortex modes at different angles of attack

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表 1 本文结果与其他文献结果的对比（$Re =300$）

Table 1. The results comparison of average drag coefficients and Strouhal number at $Re=300 $

算例平均阻力系数$ \overline {{c_{{\rm{D}}} }} $ $ {S_{\rm{t}}} $

文献[16] 1.24 0.215
文献[29] 1.27 0.21
文献[30] 1.40 0.20
本文 1.36 0.208

下载: 导出CSV

参考文献(30)

[1]	李仁年, 赵振希, 李德顺, 李银然, 陈霞, 于佳鑫. 风沙对风力机翼型绕流及其气动性能的影响 [J]. 农业工程学报, 2018, 34(14): 205–211; 303. DOI: 10.11975/j.issn.1002-6819.2018.14.026. LI R N, ZHAO Z X, LI D S, et al. Effect of wind sand on flow around airfoil wind turbine and its aerodynamic performance [J]. Transactions of Chinese Society of Agricultural Engineering, 2018, 34(14): 205–211; 303. DOI: 10.11975/j.issn.1002-6819.2018.14.026.
[2]	贲安庆, 窦华书. 可压缩机翼绕流的数值模拟及其稳定性分析 [J]. 浙江理工大学学报, 2015, 33(9): 675–681. BEN A Q, DOU H S. Numerical simulation of compressible flow around the airfoil and its stability analysis [J]. Jounal of Zhejiang Sci-Tech University, 2015, 33(9): 675–681.
[3]	刘雄, 梁湿. 风力机翼型在复合运动下的动态失速数值分析 [J]. 工程力学, 2016, 33(12): 248–256. DOI: CNKI:SUN:GCLX.0.2016-12-030. LIU X, LIANG S. Numerical investigation on dynamic stall of wind turbine airfoil undergoing complex motion [J]. Engineering Mechanics, 2016, 33(12): 248–256. DOI: CNKI:SUN:GCLX.0.2016-12-030.
[4]	KOIRALA R, NEOPANE H P, ZHU B S, et al. Effect of sediment erosion on flow around guide vanes of Francis turbine [J]. Renewable Energy, 2019, 136: 1022–1027. DOI: 10.1016/j.renene.2019.01.045.
[5]	LI W Z, WANG W Q, YAN Y, et al. Effects of pitching motion profile on energy harvesting performance of a semi-active flapping foil using immersed boundary method [J]. Ocean Engineering, 2018, 163(9): 94–106. DOI: 10.1016/j.oceaneng.2018.05.055.
[6]	郝栋伟, 张立翔, 王文全. 流固耦合S-型自主游动柔性鱼运动特性分析 [J]. 工程力学, 2015, 32(5): 13–18. HAO D W, ZHANG L X, WANG W Q. Swimming patterns of an S-type self-propelled flexible fish in fluid-structure interaction [J]. Engineering Mechanics, 2015, 32(5): 13–18.
[7]	向锦武, 孙毅, 申童, 李道春. 扑翼空气动力学研究进展与应用 [J]. 工程力学, 2019, 36(4): 8–23. XIANG J W, SUN Y, SHEN T, et al. Research progress and application of flapping wing aerodynamics [J]. Engineering Mechanics, 2019, 36(4): 8–23.
[8]	BOWERS A. Model tests showed aerodynamic instability of Tacoma narrows bridge [J]. Journal of Franklin Institute, 1941, 231(5): 470–470.
[9]	颜大椿. 湍流、风工程和虎门大桥的风振 [J]. 力学与实践, 2020, 42(4): 523–525. YAN D C. Turbulence, wind engineering and wind vibration of Humen Bridge [J]. Mechanics in Engineering, 2020, 42(4): 523–525.
[10]	PESKIN C S. Flow patterns around heart valves: a numerical method [J]. Journal of Computational Physics, 1972, 10: 252–271. DOI: 10.1016/0021-9991(72)90065-4.
[11]	GOLDSTEIN D, HANDLER R, SIROVICH L. Modeling a no-slip flow boundary with an external force field [J]. Journal of Computational Physics, 1993, 105(2): 354–366. DOI: 10.1006/jcph.1993.1081.
[12]	JAMALUDIN M J. Combined immersed boundaries/ B-spline methods for simulations of flow in complex geometries [J]. Annual Research Briefs, Center for Turbulence Research, 1997, 161(1): 317–327.
[13]	FADLUN E A, VERZICCO R, ORLANDI P, et al. Combined immersed-boundary finite-difference methods for three-dimensional complex flow simulations. [J]. Journal of Computational Physics, 2000, 161(1): 35–60. DOI: 10.1006/jcph.2000.6484.
[14]	LE D V, KHOO B C, LIM K M. An implicit-forcing immersed boundary method for simulating viscous flows in irregular domains [J]. Computer Methods in Applied Mechanics and Engineering, 2008, 197(25): 2119–2130. DOI: 10.1016/j.cma.2007.08.008.
[15]	WU J, SHU C. Implicit velocity correction-based immersed boundary-lattice Boltzmann method and its applications [J]. Journal of Computational Physics, 2009, 228(6): 1963–1979. DOI: 10.1016/j.jcp.2008.11.019.
[16]	王文全, 张国威, 闫妍. 模拟复杂流动的一种隐式直接力浸入边界方法 [J]. 工程力学, 2017, 34(2): 28–33; 93. DOI: 10.6052/j.issn.1000-4750.2015.07.0600. WANG W Q, ZHANG G W, YAN Y. An implicit direct force immersed boundary method for simulating complex flow [J]. Engineering Mechanics, 2017, 34(2): 28–33; 93. DOI: 10.6052/j.issn.1000-4750.2015.07.0600.
[17]	Uhlmann M. An immersed boundary method with direct forcing for the simulation of particulate flows [J]. Journal of Computational Physics, 2005, 209(2): 448–476. DOI: 10.1016/j.jcp.2005.03.017.
[18]	LAI M C, PESKIN C S. An immersed boundary method with formal second-order accuracy and reduced numerical viscosity [J]. Journal of Computational Physics, 2000, 160(2): 705–719. DOI: 10.1006/jcph.2000.6483.
[19]	郭涛, 郝栋伟, 李明华, 等. 基于浸入边界法研究超弹性红细胞在剪切流中的运动特性 [J]. 医用生物力学, 2015, 30(3): 243–248. DOI: 10.3871/j.1004-7220.2015.03.243. GUO T, HAO D W, LI M H, et al. Motion characteristics on hyper-elastic red cells in shear flow based on immersed boundary meth [J]. Journal of Medical Biomechanics., 2015, 30(3): 243–248. DOI: 10.3871/j.1004-7220.2015.03.243.
[20]	SOTIROPOULOS F, YANG X. Immersed boundary methods for simulating fluid-structure interaction [J]. Progress in Aerospace Sciences, 2014, 65(5): 1–21. DOI: 10.1016/.j.paerosci.2013.09.003.DOI:.
[21]	MOHAMMADI M H, SOTIROPOULOS F, BRINKERHOFF J. Moving least squares reconstruction for sharp interface immersed boundary methods [J]. International Journal for Numerical Methods in Fluids, 2019, 90(20): 57–80. DOI: 10.1002/fld.4711.
[22]	郭涛,张纹惠,王文全,等. 基于IBM法的低雷诺数下涡激振动高质量比效应的研究 [J]. 工程力学, 2022, 39(3): 222–232. DOI: 10.6052/j.issn.1000-4750.2021.07.0566. GUO T, ZHANG W H, WANG W Q, et al. Effects of high mass and damping ration on VIV of a circular cylinder with low Reynolds number based on IBM [J]. Engineering Mechanics, 2022, 39(3): 222–232. DOI: 10.6052/j.issn.1000-4750.2021.07.0566.
[23]	XIE F T, QU Y G, ISLAM M A, et al. A sharp-interface Cartesian grid method for time-domain acoustic scattering from complex geometries [J]. Computers and Fluids, 2020, 202: 104498. DOI: 10.1016/j.compfluid.2020.104498.
[24]	YOUSEFZADEH M, BATTIATO I. High order ghost-cell immersed boundary method for generalized boundary conditions [J]. International Journal of Heat and Mass Transfer, 2019, 137(7): 585–598. DOI: 10.1016/j.ijheatmasstransfer.2019.03.061.
[25]	BRADY P T, LIVESCU D. Foundations for high-order, conservative cut-cell methods: stable discretizations on degenerate meshes [J]. Journal of Computational Physics, 2021, 426: 109794. DOI: 10.1016/j.jcp.2020.109794.
[26]	MONASSE L, DARU V, MARIOTTI C, et al. A conservative coupling algorithm between a compressible flow and a rigid body using an embedded boundary method [J]. Journal of Computational Physics, 2012, 231(7): 2977–2994. DOI: 10.1016/j.jcp.2012.01.002.
[27]	张和涛, 宁建国, 许香照, 等. 一种强耦合预估-校正浸入边界法 [J]. 爆炸与冲击, 2021, 41(9): 094201. DOI: 10.11883/bzycj-2021-0129. ZHANG H T, NING J G, XU X Z, et al. A strong coupling prediction-correction immersed boundary method [J]. Explosion and Shock Waves, 2021, 41(9): 094201. DOI: 10.11883/bzycj-2021-0129.
[28]	胡建伟, 汤怀民. 微分方程数值方法[M]. 2 版. 北京: 科学出版社, 2007: 79–105.
[29]	BALARAS E. Modeling complex boundaries using an external force field on fixed Cartesian grids in large-eddy simulations [J]. Computers & Fluids, 2004, 33(3): 375–404. DOI: 10.1016/S0045-7930(03)00058-6.
[30]	SCHLICHING H. Boundary-layer theory [M]. New York: Mcgraw-Hill Book Company, 1979: 19–21.