薄壁结构流固耦合数值模拟及计算方法研究
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摘要
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。采用现代数值方法,深入研究结构振动对流场的影响以及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。本论文从理论角度,提出一种基于压力泊松方程的整体积分紧耦合算法和基于LES流体求解器的预估-校正同步迭代强耦合算法,给出了相关的数值算例,并通过与其它文献计算结果的比较,验证了该方法的有效性和准确性。论文共计六章,其主要研究内容及学术贡献如下：
首先,构建了流体-结构耦合系统的流体动力学模块和三维固体非线性有限元动力分析模块。结合尺度相似模型和Smagorinsky模型,借鉴动态亚格子模型的构造方法,推导出亚格子动能ksgs满足的输运方程,发展了一种新的一方程混合动态亚格子应力模型。在该模型中,亚格子动能的平方根ksgs1/2作为混合模型中涡粘性部分的速度尺度,并在ksgs的输运方程中包含一些附加的尺度相似部分,较以往的混合模型有较大的提高,既能反映实际的湍流涡结构特征,又具有适当的湍动能耗散特性。有限体积法用来离散大涡模拟的控制方程,SIMPLEC算法实现压力和速度耦合变量的分离求解,TDMA解法用于求解大型离散代数方程组,构建基于LES的CFD求解器。通过2个数值算例考核表明,一方程混合动态亚格子模型不仅具有良好的捕捉湍流涡结构特征能力,而且具有良好的反映小尺度涡结构湍动能耗散的能力,采用的数值方法具有较好的计算收敛性和非定常流动描述能力,同时将数值计算结果与试验结果进行了对比分析,两者较吻合,证明本文建立的CFD求解器是可靠的。基于几何非线性有限元的基本思想,利用非线性的位移-应变几何关系和线弹性的材料本构关系,建立几何非线性的三维实体有限元动力分析模型,采用Newmark-β隐式时间积分格式离散时间项,离散后的代数方程组采用修正的Newton-Raphson迭代方法进行求解,构建CSD求解器。
其次,建立了基于LES流体求解器的同步迭代强耦合算法。采用提高的弹簧光滑法来更新流体网格,选择满足动态网格几何守恒定律的流体时间积分方法,以消除额外的数值寄生振荡及计算不稳定性。将基于能量守恒的一致插值方法用于非一致界面离散网格的信息交换,以保持耦合系统的能量守恒,并有机地耦合上述的CFD、CSD和流场网格更新三大计算模块,同时在每个时间步内引入预估-校正子迭代程序,让流体与固体模块在时间上整体向前推进,实现同步迭代强耦合算法。采用该方法数值模拟了水轮机导水机构内活动导叶的水弹性振动特性,探讨了流体激振可能诱发的结构共振现象,得到许多具有实际工程价值的结论。
再次,建立了基于压力泊松方程的整体积分紧耦合算法。采用非线性有限元增量法,引入耦合界面位移和应力协调条件,建立非线性动态流体-结构耦合整体有限元模型。通过预估-校正多步迭代格式,实现整体耦合系统的时间推进。在每一个时间步内,基于流体压力泊松方程,求解与流体控制方程一致的等价耦合动量方程直接得到耦合系统的解,而避免直接求解大型耦合系统方程有效地降低了耦合系统求解的自由度。最后采用该方法数值模拟了处于静止方柱尾迹涡结构内的柔性悬臂梁非线性大变形流固耦合振动问题,捕捉到了一些重要的涡激振动现象,得到与其它文献较一致的计算结果,证明该耦合方法的正确性。
最后,对考虑动态流固耦合效应的流激振动问题进行试验研究
刚性方柱放置在试验模型槽道正中央,弹性薄板的一端固定在方柱尾端,弹性薄板上、下端和另一端自由,在弹性板表面上布置一支LL-072-25A型压力传感器和一支DH-201型加速度传感器。上游方柱绕流形成周期性涡脱落,诱发下游弹性薄板的水弹性振动。采用两套独立运作的测试系统,即DH-5935N动态信号测试分析系统,测试流固耦合振动弹性板上代表点的压力和板的加速度,利用全三维的粒子测速仪PIV系统测试流场速度分布,两套独立运作的测试系统在时间上保持同步,既得到流场动态分布特性和弹性板近壁区涡结构演化过程,又同时得到结构涡激振动信息。对试验结果进行全面深入地分析,进一步验证和指导流固耦合数值模型。
Nonlinear dynamic fluid-structure interaction (FSI) is one of the most challenging research issues in academic and engineering fields. A study of the mutual influences between the structure vibration and the flow field by using the state-of-the-art numerical methods is of great significance to avoid the flow-induced resonance of a structure in fluid, and it is quite important to improve the reliability and safety of the structure designs. In this dissertation, a monolithicly coupled model based on the pressure Possion equation (PPE) and a closely coupled model based on the large eddy simulation (LES) solver are presented and verified by several numerical examples. The dissertation is generally outlined into 6 chapters. The main contributions are stated as following.
Firstly, a fluid flow and a structure dynamics solvers are constructed, respectively. For the fluid numerical model in the FSI system, a dynamically mixed one-equation subgrid-scale (SGS) model is modeled on the scale-similarity model and Smagorinsky eddy-viscosity model. In the proposed SGS model, the square root of the SGS kinetic energy,(?), is used to obtain the velocity scale for the eddy-viscosity to be applied in the model. The modeled ksgs equation is derived and some of the additional scale-similarity parts are incorporated to compare the ksgs equation with the previous studies. It shows that the suggested model has the capability of capturing the details of the flow structures and the dissipation of the turbulent kinetic energy. Finite volume method (FVM) is used to be discrete of the LES governing equations. The SIMPIEC algorithm is applied to solve of the coupled equation of the velocity and pressure. Tri Diagonal Matrix Algorithm (TDMA) is adopted to solve the algebraic discrete equations. For the structure numerical model in the FSI system, a nonlinear relation between strain and displacement and a linear elastic model are used respectively, and a three dimensional nonlinear finite element model for the structure dynamics is thus constructed. A Newmark-βimplicit time integration algorithm is used, and the Newton-Raphson iterative scheme is adopted to solve the algebraic equations.
Secondly, a closely coupled approach is constructed based on the LES flow solver. A moving mesh algorithm based on smooth spring analogy is used and a geometrically conservative implicit numerical scheme for the flow computations on the moving mesh is established. A load and motion transfer algorithm with non-matching discrete interface based on the momentum and energy conservation is introduced. It paves a coupling way to use the different solvers for the fluid, the structure and the mesh motion models for the complex nonlinear FSI problems. As an example, the hydro-elasticity vibration of the guide vane of a Francis hydro turbine is simulated. Three different materials for this guide vane are adopted respectively in this working example. The different dynamic behaviors of the fluid and the structure are discussed in detail. The numerical results show the validity of the proposed approach.
Thirdly, a monolithic approach based on the fluid pressure Poisson equation (PPE) and predictor-multi-corrector algorithm (PMA) is created to solve the interactions between incompressible viscous fluid and an elastic body. The PPE is derived so as to be consistent with the coupled equations for the FSI system. Based on this approach, the fluid pressure is implicitly derived to satisfy the incompressibility constraint, and the other unknown variables are explicitly derived. In the consistent fluid equation, the momentum and the continuity equations are included in the same fluid domain. A consistent fluid equation is established by the substructure procedure for the structural equation to reduce degrees of freedoms (DOFs) in the structural domain. To demonstrate the performance of the proposed approach, a working example, a beam immersed in the incompressible fluid, is simulated. The results show that the approach developed is a powerful tool in solving the FSI problems of the flexible structures.
Finally, we have performed an experiment on the vibration of an elastic thin plane due to being induced by the vortex shedding of the flow through a square body. The fixed square rigid body is submerged in the incompressible fluid and a thin elastic plane is attached to the rigid body in the centre of the downstream face. The pressure sensor that is manufactured by Kulite company, LL-072-25A, was mounted on the surfaces of the elastic plane, and a acceleration sensor provided by DongHua company, DH-201 is embedded in the free end of the elastic plane. The vortices, which separate from the corners of the rigid body, generate a lift force which excites oscillation of the thin elastic plane. Two independent measuring systems, are used in experiment. One is the dynamical test system to pick up the signals from the sensors, and other is of a 3D particle image velocimetry (PIV) to measure the flow fields. The measurements obtain findings on the vibration induced by the vortex shedding and the evolution of the vortex near the vibrating wall surfaces.
首先,构建了流体-结构耦合系统的流体动力学模块和三维固体非线性有限元动力分析模块。结合尺度相似模型和Smagorinsky模型,借鉴动态亚格子模型的构造方法,推导出亚格子动能ksgs满足的输运方程,发展了一种新的一方程混合动态亚格子应力模型。在该模型中,亚格子动能的平方根ksgs1/2作为混合模型中涡粘性部分的速度尺度,并在ksgs的输运方程中包含一些附加的尺度相似部分,较以往的混合模型有较大的提高,既能反映实际的湍流涡结构特征,又具有适当的湍动能耗散特性。有限体积法用来离散大涡模拟的控制方程,SIMPLEC算法实现压力和速度耦合变量的分离求解,TDMA解法用于求解大型离散代数方程组,构建基于LES的CFD求解器。通过2个数值算例考核表明,一方程混合动态亚格子模型不仅具有良好的捕捉湍流涡结构特征能力,而且具有良好的反映小尺度涡结构湍动能耗散的能力,采用的数值方法具有较好的计算收敛性和非定常流动描述能力,同时将数值计算结果与试验结果进行了对比分析,两者较吻合,证明本文建立的CFD求解器是可靠的。基于几何非线性有限元的基本思想,利用非线性的位移-应变几何关系和线弹性的材料本构关系,建立几何非线性的三维实体有限元动力分析模型,采用Newmark-β隐式时间积分格式离散时间项,离散后的代数方程组采用修正的Newton-Raphson迭代方法进行求解,构建CSD求解器。
其次,建立了基于LES流体求解器的同步迭代强耦合算法。采用提高的弹簧光滑法来更新流体网格,选择满足动态网格几何守恒定律的流体时间积分方法,以消除额外的数值寄生振荡及计算不稳定性。将基于能量守恒的一致插值方法用于非一致界面离散网格的信息交换,以保持耦合系统的能量守恒,并有机地耦合上述的CFD、CSD和流场网格更新三大计算模块,同时在每个时间步内引入预估-校正子迭代程序,让流体与固体模块在时间上整体向前推进,实现同步迭代强耦合算法。采用该方法数值模拟了水轮机导水机构内活动导叶的水弹性振动特性,探讨了流体激振可能诱发的结构共振现象,得到许多具有实际工程价值的结论。
再次,建立了基于压力泊松方程的整体积分紧耦合算法。采用非线性有限元增量法,引入耦合界面位移和应力协调条件,建立非线性动态流体-结构耦合整体有限元模型。通过预估-校正多步迭代格式,实现整体耦合系统的时间推进。在每一个时间步内,基于流体压力泊松方程,求解与流体控制方程一致的等价耦合动量方程直接得到耦合系统的解,而避免直接求解大型耦合系统方程有效地降低了耦合系统求解的自由度。最后采用该方法数值模拟了处于静止方柱尾迹涡结构内的柔性悬臂梁非线性大变形流固耦合振动问题,捕捉到了一些重要的涡激振动现象,得到与其它文献较一致的计算结果,证明该耦合方法的正确性。
最后,对考虑动态流固耦合效应的流激振动问题进行试验研究
刚性方柱放置在试验模型槽道正中央,弹性薄板的一端固定在方柱尾端,弹性薄板上、下端和另一端自由,在弹性板表面上布置一支LL-072-25A型压力传感器和一支DH-201型加速度传感器。上游方柱绕流形成周期性涡脱落,诱发下游弹性薄板的水弹性振动。采用两套独立运作的测试系统,即DH-5935N动态信号测试分析系统,测试流固耦合振动弹性板上代表点的压力和板的加速度,利用全三维的粒子测速仪PIV系统测试流场速度分布,两套独立运作的测试系统在时间上保持同步,既得到流场动态分布特性和弹性板近壁区涡结构演化过程,又同时得到结构涡激振动信息。对试验结果进行全面深入地分析,进一步验证和指导流固耦合数值模型。
Nonlinear dynamic fluid-structure interaction (FSI) is one of the most challenging research issues in academic and engineering fields. A study of the mutual influences between the structure vibration and the flow field by using the state-of-the-art numerical methods is of great significance to avoid the flow-induced resonance of a structure in fluid, and it is quite important to improve the reliability and safety of the structure designs. In this dissertation, a monolithicly coupled model based on the pressure Possion equation (PPE) and a closely coupled model based on the large eddy simulation (LES) solver are presented and verified by several numerical examples. The dissertation is generally outlined into 6 chapters. The main contributions are stated as following.
Firstly, a fluid flow and a structure dynamics solvers are constructed, respectively. For the fluid numerical model in the FSI system, a dynamically mixed one-equation subgrid-scale (SGS) model is modeled on the scale-similarity model and Smagorinsky eddy-viscosity model. In the proposed SGS model, the square root of the SGS kinetic energy,(?), is used to obtain the velocity scale for the eddy-viscosity to be applied in the model. The modeled ksgs equation is derived and some of the additional scale-similarity parts are incorporated to compare the ksgs equation with the previous studies. It shows that the suggested model has the capability of capturing the details of the flow structures and the dissipation of the turbulent kinetic energy. Finite volume method (FVM) is used to be discrete of the LES governing equations. The SIMPIEC algorithm is applied to solve of the coupled equation of the velocity and pressure. Tri Diagonal Matrix Algorithm (TDMA) is adopted to solve the algebraic discrete equations. For the structure numerical model in the FSI system, a nonlinear relation between strain and displacement and a linear elastic model are used respectively, and a three dimensional nonlinear finite element model for the structure dynamics is thus constructed. A Newmark-βimplicit time integration algorithm is used, and the Newton-Raphson iterative scheme is adopted to solve the algebraic equations.
Secondly, a closely coupled approach is constructed based on the LES flow solver. A moving mesh algorithm based on smooth spring analogy is used and a geometrically conservative implicit numerical scheme for the flow computations on the moving mesh is established. A load and motion transfer algorithm with non-matching discrete interface based on the momentum and energy conservation is introduced. It paves a coupling way to use the different solvers for the fluid, the structure and the mesh motion models for the complex nonlinear FSI problems. As an example, the hydro-elasticity vibration of the guide vane of a Francis hydro turbine is simulated. Three different materials for this guide vane are adopted respectively in this working example. The different dynamic behaviors of the fluid and the structure are discussed in detail. The numerical results show the validity of the proposed approach.
Thirdly, a monolithic approach based on the fluid pressure Poisson equation (PPE) and predictor-multi-corrector algorithm (PMA) is created to solve the interactions between incompressible viscous fluid and an elastic body. The PPE is derived so as to be consistent with the coupled equations for the FSI system. Based on this approach, the fluid pressure is implicitly derived to satisfy the incompressibility constraint, and the other unknown variables are explicitly derived. In the consistent fluid equation, the momentum and the continuity equations are included in the same fluid domain. A consistent fluid equation is established by the substructure procedure for the structural equation to reduce degrees of freedoms (DOFs) in the structural domain. To demonstrate the performance of the proposed approach, a working example, a beam immersed in the incompressible fluid, is simulated. The results show that the approach developed is a powerful tool in solving the FSI problems of the flexible structures.
Finally, we have performed an experiment on the vibration of an elastic thin plane due to being induced by the vortex shedding of the flow through a square body. The fixed square rigid body is submerged in the incompressible fluid and a thin elastic plane is attached to the rigid body in the centre of the downstream face. The pressure sensor that is manufactured by Kulite company, LL-072-25A, was mounted on the surfaces of the elastic plane, and a acceleration sensor provided by DongHua company, DH-201 is embedded in the free end of the elastic plane. The vortices, which separate from the corners of the rigid body, generate a lift force which excites oscillation of the thin elastic plane. Two independent measuring systems, are used in experiment. One is the dynamical test system to pick up the signals from the sensors, and other is of a 3D particle image velocimetry (PIV) to measure the flow fields. The measurements obtain findings on the vibration induced by the vortex shedding and the evolution of the vortex near the vibrating wall surfaces.
引文
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