流体—结构耦合数值方法研究及其应用
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摘要
在海洋、船舶、航空、水利、化工和核动力等工程领域中,都会遇到流体和结构相互作用的耦合问题,其中,非线性动态流固耦合问题是目前学术界和工程界最具挑战性的研究内容之一。随着计算机硬件水平和流固耦合数值计算方法的发展,如何利用现代数值方法,深入研究非定常流场对结构的激振作用,对于避免流体诱发的共振从而提高结构的可靠性和安全性具有重要意义。本文基于流固弱耦合交错算法,分别应用大型通用有限元分析软件FLUENT和MARC对耦合系统进行离散求解,其主要工作包括:
1.对于流体—结构耦合系统的结构部分,本文给出了基于几何大变形非线性增量有限元模型,并讨论了在MARC软件中采用大变形理论时,力跟随和力不跟随对结构计算结果的影响。
2.对于流体—结构耦合系统的流体部分,本文建立了基于ALE描述的N-S流体有限体积控制方程,并引入动网格法来保证结构大变形后流体网格的质量,避免流体网格出现畸变。最后,在FLUENT中以鱼类行波运动为算例进行动网格计算,验证了所采用方法的有效性和正确性。
3.引入流体和结构在耦合界面上的协调条件,建立了非线性流体—结构耦合计算模型,采用基于FLUENT和MARC软件的弱耦合交错计算方法,并寻找合适的插值函数,通过两软件的二次开发功能,给出了耦合界面不匹配网格间运动和载荷传递的方法,编程实现流体—结构的耦合计算。
4.以两个具有广泛工程背景的算例对所建立起来的耦合方法进行深入分析。首先研究了单自由度弹性支撑方柱的涡致振动问题,捕获了涡致振动的“锁定”、“拍”等现象,验证了所建立的耦合方法的可行性。然后重点分析了处于静止方柱尾迹结构内的柔性悬臂梁涡致振动问题,讨论了交错耦合计算时间步长、雷诺数、结构几何非线性模型对悬臂梁响应的影响。
The interaction of fluid flow and flexible solid structures is frequently encountered in many areas of civil, mechanical, marine, aerospace, chemical and nuclear power engineering. As one of those interaction problems, nonlinear dynamic fluid-structure interaction has become one of the most challenging research issues in academic and engineering field at present. With the development of computational resource and fluid-structure computational methodologies, how to adapt modern numerical method to deeply study the influence of structure vibration on fluid flied is of great significance to avoid the fluid-induced resonance and improve the reliability and security of the structures. In this thesis, a weak dynamic nonlinear fluid structure interaction staggered numerical simulation method is put forward and established, and is verified by several real examples through general-purpose finite element program MARC and FLUENT. The main works of this thesis are listed as follows:
1. For the structure region of the fluid-structure interaction system, the incremental nonlinear finite element model is introduced based on large geometric deformation. Meanwhile, it is applied in the vibration problem of a flexible cantilever beam to discuss the effect of non-follow force model and follow force model to the structure responses.
2. For the fluid region of the fluid-structure interaction system, the N-S equations with Arbitrary Lagarian-Eulerian(ALE) description are adopted to exactly describe the fluid boundary movement of FSI system. Also, the dynamic mesh method is introduced to maintain good element shapes of the fluid. Then, taking the fish-like swimming foils as a calculation example, the validity of ALE method and dynamic mesh method is verified.
3. Through the compatible conditions on the boundary between the fluid and structure, a weak coupled nonlinear dynamic fluid-structure interaction model is set up. In this model, the solid region is solved with code MARC, while the fluid region is simulated with code FLUENT. To realize the data transmission between the two softwares, the user defined functions of both softwares are developed and compiled. At the same time, the data transmission methods of movements and loads between the non-matching discrete meshes of fluid and structure on the interaction surfaces are given.
4. As the application of methods and models mentioned above, firstly, the elastic-mounted square rectangular free oscillation problem is present. The results show that, when oscillation frequencies of the rectangular are in a certain range, the "lock-in" phenomenon, a kind of nonlinear fluid-structure interaction resonance phenomenon, and "beat" phenomenon will appear. Secondly, the flow-induced vibration problem of a flexible cantilever beam is analyzed in details. And the effects of staggered coupled time step sizes, structure nonlinear finite element models and Renault number to the responses of the cantilever beam are investigated respectively.
1.对于流体—结构耦合系统的结构部分,本文给出了基于几何大变形非线性增量有限元模型,并讨论了在MARC软件中采用大变形理论时,力跟随和力不跟随对结构计算结果的影响。
2.对于流体—结构耦合系统的流体部分,本文建立了基于ALE描述的N-S流体有限体积控制方程,并引入动网格法来保证结构大变形后流体网格的质量,避免流体网格出现畸变。最后,在FLUENT中以鱼类行波运动为算例进行动网格计算,验证了所采用方法的有效性和正确性。
3.引入流体和结构在耦合界面上的协调条件,建立了非线性流体—结构耦合计算模型,采用基于FLUENT和MARC软件的弱耦合交错计算方法,并寻找合适的插值函数,通过两软件的二次开发功能,给出了耦合界面不匹配网格间运动和载荷传递的方法,编程实现流体—结构的耦合计算。
4.以两个具有广泛工程背景的算例对所建立起来的耦合方法进行深入分析。首先研究了单自由度弹性支撑方柱的涡致振动问题,捕获了涡致振动的“锁定”、“拍”等现象,验证了所建立的耦合方法的可行性。然后重点分析了处于静止方柱尾迹结构内的柔性悬臂梁涡致振动问题,讨论了交错耦合计算时间步长、雷诺数、结构几何非线性模型对悬臂梁响应的影响。
The interaction of fluid flow and flexible solid structures is frequently encountered in many areas of civil, mechanical, marine, aerospace, chemical and nuclear power engineering. As one of those interaction problems, nonlinear dynamic fluid-structure interaction has become one of the most challenging research issues in academic and engineering field at present. With the development of computational resource and fluid-structure computational methodologies, how to adapt modern numerical method to deeply study the influence of structure vibration on fluid flied is of great significance to avoid the fluid-induced resonance and improve the reliability and security of the structures. In this thesis, a weak dynamic nonlinear fluid structure interaction staggered numerical simulation method is put forward and established, and is verified by several real examples through general-purpose finite element program MARC and FLUENT. The main works of this thesis are listed as follows:
1. For the structure region of the fluid-structure interaction system, the incremental nonlinear finite element model is introduced based on large geometric deformation. Meanwhile, it is applied in the vibration problem of a flexible cantilever beam to discuss the effect of non-follow force model and follow force model to the structure responses.
2. For the fluid region of the fluid-structure interaction system, the N-S equations with Arbitrary Lagarian-Eulerian(ALE) description are adopted to exactly describe the fluid boundary movement of FSI system. Also, the dynamic mesh method is introduced to maintain good element shapes of the fluid. Then, taking the fish-like swimming foils as a calculation example, the validity of ALE method and dynamic mesh method is verified.
3. Through the compatible conditions on the boundary between the fluid and structure, a weak coupled nonlinear dynamic fluid-structure interaction model is set up. In this model, the solid region is solved with code MARC, while the fluid region is simulated with code FLUENT. To realize the data transmission between the two softwares, the user defined functions of both softwares are developed and compiled. At the same time, the data transmission methods of movements and loads between the non-matching discrete meshes of fluid and structure on the interaction surfaces are given.
4. As the application of methods and models mentioned above, firstly, the elastic-mounted square rectangular free oscillation problem is present. The results show that, when oscillation frequencies of the rectangular are in a certain range, the "lock-in" phenomenon, a kind of nonlinear fluid-structure interaction resonance phenomenon, and "beat" phenomenon will appear. Secondly, the flow-induced vibration problem of a flexible cantilever beam is analyzed in details. And the effects of staggered coupled time step sizes, structure nonlinear finite element models and Renault number to the responses of the cantilever beam are investigated respectively.
引文
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[6]Ergin,A.,Ugurlu,B.,Linear vibration analysis of cantilever plates partially submerged in fluid.Journal of Fluids and Structures.2003,17:927-939.
[7]Lam K.Y.,Wang Q.X,Zong Z,A nonlinear fluid-structure interaction analysis of a near-bed submarine pipeline in a current.Journal of Fluids and Structures,2002,16:1177-1191.
[8]王少波,刘元杰,梁醒培.弹性板在粘性流体中的耦合振动分析.机械工程学报.2004,40(7):63-66.
[9]谌勇,张军,汪玉,唐平.流体介质中圆板受冲击载荷时的弹塑性非线性动力响应.振动与冲击.2005,24(5):30-34.
[10]Gluck M.,Breuer M.,Durst F.,Halfmann A.,Rank E.Computation of wind-induced vibrations of flexible shells and membrane structures.Journal of Fluids and Structures.2003,17:739-765.
[11]Slone A.K.,Pericleous K.,Bailey C.,Cross M.Dynamic fluid-structure interaction using finite volume unstructured mesh procedures.Computers and Structures.2002,80:371-390.
[12]Zhang H.,Zhang X.,Ji S.,Guo Y.,Ledezma G.,Elabbasi N.Recent development of fluid-structure interaction capabilities in the ADINA system.Computers and Structures.2003,81:1071-1085.
[13]Namkoong K,Choi H.G.,Yoo J.Y.Computation of dynamic fluid-structure interaction in two-dimensional laminar flows using combined formulation.Journal of Fluids and Structures.2005,20:51-69.
[14]Park K,Felippa C,DeRuntz J.Stabilization of staggered solution procedures for fluid-structure interaction analysis.Computational methods for fluid-structure interaction problems.ASME,1977,AMD-vol.26.
[15]戴大农.流固耦合系统动力分析的若干基本问题与数值方法.博士学位论文.清华大学工程力学系,1988.
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[17]Westergarrd H.M.Water pressures on dams during earthquakes.Trans.Amer.Soc.Civ.Eng.1933,98:418-433
[18]田野正.地震力对重力坝的影响,水利译丛,第三期,1957.
[19]小坪清真.不规则地震力所引起坝上的动水压力,水利译丛,第九期,1958.
[20]钱令希,邱大洪.利用电模拟法计算挡水坝在满库时的自振频率.土木工程学报,1958,5(2):12-18.
[21]刘恢先,王孝信.挡水坝地震荷载,地震工程研究报告集,第一集,1962:140-153.
[22]郑哲敏.平板在流体作用下的振动.力学学报,1958,2(1):11-16.
[23]郑哲敏等.悬臂梁在一侧受有液体作用下的振动.力学学报,1959,3(2):111-119.
[24]王前信,王孝信.在不规则地震作用下刚性坝面动水压力的探讨,地震工程研究报告集,第一集,1962:153-161.
[25]王前信,王孝信.悬臂梁在一侧有水时的自振特性与地震荷载,地震工程研究报告集,第一集,1962:161-172.
[26]居荣初,黄振平,杜瑞明.水中圆柱体结构的自由振动,地震工程研究报告集,第一集,1962:173-181.
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