Monolithic approach to thermal fluid-structure interaction with nonconforming interfaces

This paper presents a monolithic approach to the thermal fluid-structureinteraction(FSI) with nonconforming interfaces.The thermal viscous flow is governedby the Boussinesq approximation and the incompressible Navier-Stokes equations.Themotion of the fluid domain is accounted for by an arbitrary Lagrangian-Eulerian(ALE)strategy.A pseudo-solid formulation is used to manage the deformation of the fluid do-main.The structure is described by the geometrically nonlinear thermoelastic dynamics.An efficient data transfer strategy based on the Gauss points is proposed to guarantee theequilibrium of the stresses and heat along the interface.The resulting strongly coupledset of nonlinear equations for the fluid,structure,and heat is solved by a monolithicsolution procedure.A numerical example is presented to demonstrate the robustness andefficiency of the methodology.     

Immersed boundary methods for fluid-structure interaction: A review

In this review, we introduce immersed boundary (IB) methods for fluid-structure interactions (FSIs) of rigid and elastic bodies. IB methods impose momentum forcing on an Eulerian mesh to satisfy boundary conditions on the interface between fluid and structure, which enables us to use a non-body conforming grid system for complex-shaped moving bodies. Imposition of the momentum forcing is performed directly through discrete delta function or indirectly through velocity reconstruction, by which IB methods have their own strengths and weaknesses to FSI problems of rigid and elastic bodies. To deal with FSI, IB methods using monolithic and partitioned (strong and weak coupling) approaches with different stability and cost have been suggested. Nevertheless, two important problems in FSI, cases of low density ratio of solid to fluid and high Reynolds number, have not been completely overcome by current IB methods in terms of the stability, accuracy and cost. These aspects are examined in this review.     

Waterhammer with fluid-structure interaction

The classical theory of waterhammer is a well-known and accepted basis for the prediction of pressure surges in piping systems. In this theory the piping system is assumed not to move. In practice however piping systems move when they are loaded by severe pressure surges, which for instance occur after rapid valve closure or pump failure. The motion of the piping system induces pressure surges which are not taken into account in the classical theory.In this article the interaction between pressure surges and pipe motion is investigated. Three interaction mechanisms are distinguished: friction, Poisson and junction coupling. Numerical experiments on a single straight pipe and a liquid loading line show that interaction highly influences the extreme pressures during waterhammer occurrences.Nomenclature A _f cross-sectional discharge area - A _t cross-sectional pipe wall area - c _f pressure wave speed in fluid - c _t axial stress wave speed in pipe wall - E Young's modulus for pipe wall material - e pipe wall thickness - f Darch-Weisbach friction coefficient - g gravitational acceleration - H fluid pressure head - h elevation of pipe - K _f fluid bulk modulus - P fluid pressure - R internal radius of pipe - T _c valve closure time - t time - u _r radial displacement of pipe - u _z axial displacement of pipe - u _z axial velocity of pipe - V fluid velocity - z distance along pipe - elevation angle of pipe - length of pressure wave - Poisson's ratio - _f fluid density - _t density of pipe wall material - t _z axial pipe stress - hoop stress     

A semi-implicit finite volume scheme for a simplified hydrostatic model for fluid-structure interaction

Simulating fluid-structure interaction problems usually requires a considerable computational effort. In this article, a novel semi-implicit finite volume scheme is developed for the coupled solution of free surface shallow water flow and the movement of one or more floating rigid structures. The model is well-suited for geophysical flows, as it is based on the hydrostatic pressure assumption and the shallow water equations. The coupling is achieved via a nonlinear volume function in the mass conservation equation that depends on the coordinates of the floating structures. Furthermore, the nonlinear volume function allows for the simultaneous existence of wet, dry and pressurized cells in the computational domain. The resulting mildly nonlinear pressure system is solved using a nested Newton method. The accuracy of the volume computation is improved by using a subgrid, and time accuracy is increased via the application of the theta method. Additionally, mass is always conserved to machine precision. At each time step, the volume function is updated in each cell according to the position of the floating objects, whose dynamics is computed by solving a set of ordinary differential equations for their six degrees of freedom. The simulated moving objects may for example represent ships, and the forces considered here are simply gravity and the hydrostatic pressure on the hull. For a set of test cases, the model has been applied and compared with available exact solutions to verify the correctness and accuracy of the proposed algorithm. The model is able to treat fluid-structure interaction in the context of hydrostatic geophysical free surface flows in an efficient and flexible way, and the employed nested Newton method rapidly converges to a solution. The proposed algorithm may be useful for hydraulic engineering, such as for the simulation of ships moving in inland waterways and coastal regions.     

流体与结构相互作用问题的FE-SPH耦合模拟

应用有限元(FE)-光滑粒子流体动力学(SPH)耦合法模拟了具有自由表面的不可压流体与结构的相互作用问题.流体和结构分别采用SPH法和有限元法同时求解,两者在交界面处的相互作用通过接触算法进行处理.为了避免隐式计算压力,通过引入人工压缩率,将不可压流体近似为人工可压缩流体.采用FE-SPH耦合法对弹性板在随时间变化的水压作用下的变形以及倒塌水柱冲击弹性结构两个问题进行了模拟.模拟结果与实验结果以及其他已有数值结果符合良好,说明FE-SPH耦合法用于流体与结构相互作用问题的模拟是可行和有效的.     

A new fluid-structure interaction analysis based on higher-order boundary elements

In strip theory analysis the vessel is represented by a series of 2D transverse sections. For 2D arbitrary-shaped sections either floating in the free surface or totally submerged, a higher-order boundary element analysis has been developed to permit determination of the associated radiation and diffraction velocity potentials. In this paper the formulation of the cited interaction problems is reworked to reflect the new capability of permitting curved boundary elements to represent the geometry and a higher-order functional behaviour of the unknown velocity potentials over that geometry. This is in direct contrast to the usual technique of using straight-line geometric panels and invariant behaviour of the required potentials over these simple panels. Applications to representative sections of floating ships and the fully submerged pontoon section of a semi-submersible are presented. Within these applications the results of the standard Frank close-fit technique, of linear panels and constant behaviour, are compared with different combinations of higher-order representations of the geometry and the determined velocity potentials. Conclusions regarding the advantages and limitations of the procedures developed are discussed.     

Hybrid algorithm for modeling of fluid-structure interaction in incompressible, viscous flows

The objective of this paper is to present and to validate a new hybrid coupling (HC) algorithm for modeling of fluid-structure interaction (FSI) in incompressible, viscous flows. The HC algorithm is able to avoid numerical instability issues associated with artificial added mass effects, which are often encountered by standard loosely coupled (LC) and tightly coupled (TC) algorithms, when modeling the FSI response of flexible structures in incompressible flow. The artificial added mass effect is caused by the lag in exchange of interfacial displacements and forces between the fluid and solid solvers in partitioned algorithms. The artificial added mass effect is much more prominent for light/flexible structures moving in water, because the fluid forces are in the same order of magnitude as the solid forces, and because the speed at which numerical errors propagate in an incompressible fluid. The new HC algorithm avoids numerical instability issues associated with artificial added mass effects by embedding Theodorsen’s analytical approximation of the hydroelastic forces in the solution process to obtain better initial estimates of the displacements. Details of the new HC algorithm are presented. Numerical validation studies are shown for the forced pitching response of a steel and a plastic hydrofoil. The results show that the HC algorithm is able to converge faster, and is able to avoid numerical instability issues, compared to standard LC and TC algorithms, when modeling the transient FSI response of a plastic hydrofoil. Although the HC algorithm is only demonstrated for a NACA0009 hydrofoil subject to pure pitching motion, the method can be easily extended to model general 3-D FSI response and stability of complex, flexible structures in turbulent, incompressible, multiphase flows.     

一种面向舰船结构毁伤的大变形流固耦合数值计算方法

水下爆炸导致舰船结构毁伤是一个复杂的非线性大变形流固耦合过程,高精度的流固耦合计算是获得高置信模拟结果的关键。基于浸没边界思想,本文提出一种面向大变形壳理论的流固耦合数值方法,可精确刻画流固耦合界面并高效求解流固界面约束方程。基于该方法,本文提出了完整的适用于水下爆炸舰船结构毁伤的大变形流固耦合数值计算方案,并基于大规模并行编程框架,研发形成适用于舰船结构毁伤的流固耦合大规模并行计算软件。与泰勒平板理论解和水下爆炸结构冲击响应实验数据等进行对比表明,本文方法可有效模拟大变形流固耦合工程问题,具备较高数值求解精度。在此基础上,完成了水下爆炸整船结构毁伤过程大规模数值模拟。该方法可有效应用于舰船毁伤等级评估,应用前景广阔。     

薄膜结构风致耦合作用数值初探

采用迭代耦合的数值方法,结合有限元离散,对典型马鞍面封闭式薄膜结构的风致耦合作用进行了模拟研究,并对结构风致振动特性以及流场对结构振动的影响进行了探讨.数值结果表明,结构的平均位移与边界条件、风荷载分布及结构的振动形式有关;而脉动位移则与风场的涡形、演化规律以及结构形式的关系明显.钝体膜结构上出现周期性脱落的漩涡.在极低的预应力条件下,由于漩涡与结构的相互作用,薄膜上的结构振动呈现"行波"效应,薄膜上各部分的振动特性有明显区别,气流分离、漩涡脱落强烈以及"行波"尾端鞭梢效应明显的区域,脉动位移幅值及其振动频率较大.     

流固耦合分析的载荷映射开放式软件架构设计

基于开放式工程与科学计算软件平台SiPESC设计实现了流固耦合分析流场载荷映射软件架构。软件的核心问题是解决计算流体力学(CFD)网格模型与计算结构力学(CSD)网格模型交互界面网格不匹配情况下的流-固载荷映射问题。软件采用插值方法将流场分析得到的物面载荷转换为结构分析的载荷边界条件。软件基于SiPESC平台的微核心+插件的开放式可扩展软件框架进行设计,依托SiPESC.ENGDBS工程数据库管理系统实现大规模数据管理。设计实现的软件框架提供了算法的灵活扩展接口与管理机制,可动态扩展新的插值算法,满足流固耦合分析需要的数据管理与数据转换需求。在该软件框架下,已实现了多种插值算法,并完成验证算例与工程算例的载荷数据转换。算例表明软件功能具备良好的工程适用性,为进一步开发与应用奠定基础。     

输液管道附加支承刚度优化设计

研究液固耦合效应作用下,两端铰支输液管道系统附加支承的刚度和位置优化设计。应用有限元分析方法,建立了输液管道液固耦合振动方程。为有效控制管道结构的振动,利用在管道结构上附(增)加支承的方法,提高输液管道系统的固有频率,预防系统可能发生强烈的耦合振动导致不稳定状态。提出了附加支承最小(临界)刚度的快速计算策略和途径,分别探讨分析了输液管道内液体的流速、附加支承的位置以及第一阶固有频率的目标值对最优支承刚度值的影响。     

流体-结构耦合问题的有限元并行计算研究

流体-结构耦合问题广泛存在于各种工程领域,本文采用ALE显式有限元法求解该类问题,并对该方法的并行性进行讨论。同时根据流体-结构耦合问题与ALE显式有限元的计算特点,在坐标递归分区方法的基础上设计并程序实现了基于流体-结构耦合均衡的分区算法。通过与坐标递归分区方法的计算结果相比较,对于流体-结构耦合问题的求解,耦合均衡并行分区方法具有更好的加速比和并行效率。     

On the role of (weak) compressibility for fluid-structure interaction solvers

In the present study, a weakly compressible formulation of the Navier-Stokes equations is developed and examined for the solution of fluid-structure interaction (FSI) problems. Newtonian viscous fluids under isothermal conditions are considered, and the Murnaghan-Tait equation of state is employed for the evaluation of mass density changes with pressure. A pressure-based approach is adopted to handle the low Mach number regime, ie, the pressure is chosen as primary variable, and the divergence-free condition of the velocity field for incompressible flows is replaced by the continuity equation for compressible flows. The approach is then embedded into a partitioned FSI solver based on a Dirichlet-Neumann coupling scheme. It is analytically demonstrated how this formulation alleviates the constraints of the instability condition of the artificial added mass effect, due to the reduction of the maximal eigenvalue of the so-called added mass operator. The numerical performance is examined on a selection of benchmark problems. In comparison to a fully incompressible solver, a significant reduction of the coupling iterations and the computational time and a notable increase in the relaxation parameter evaluated according to Aitken's Δ² method are observed.     

Mesh adaptation framework for embedded boundary methods for computational fluid dynamics and fluid-structure interaction

Embedded Boundary Methods (EBMs) are often preferred for the solution of Fluid-Structure Interaction (FSI) problems because they are reliable for large structural motions/deformations and topological changes. For viscous flow problems, however, they do not track the boundary layers that form around embedded obstacles and therefore do not maintain them resolved. Hence, an Adaptive Mesh Refinement (AMR) framework for EBMs is proposed in this paper. It is based on computing the distance from an edge of the embedding computational fluid dynamics mesh to the nearest embedded discrete surface and on satisfying the y⁺ requirements. It is also equipped with a Hessian-based criterion for resolving flow features such as shocks, vortices, and wakes and with load balancing for achieving parallel efficiency. It performs mesh refinement using a parallel version of the newest vertex bisection method to maintain mesh conformity. Hence, while it is sufficiently comprehensive to support many discretization methods, it is particularly attractive for vertex-centered finite volume schemes where dual cells tend to complicate the mesh adaptation process. Using the EBM known as FIVER, this AMR framework is verified for several academic FSI problems. Its potential for realistic FSI applications is also demonstrated with the simulation of a challenging supersonic parachute inflation dynamics problem.     

Design and fluid-structure interaction analysis for a microfluidic T-junction with chemo-responsive hydrogel valves

Due to the deformation ability even under small loads, hydrogels have been widely used as a type of soft materials in various applications such as actuating and sensing, and have attracted many researchers to study their behaviors. In this paper, the behavior of hydrogel micro-valves with reverse sensitivity to the p H inside a T-junction flow sorter is investigated. With the fluid-structure interaction(FSI) approach, the effects of various parameters such as the inlet pressure and the p H value...     

Coupled MPS-modal superposition method for 2D nonlinear fluid-structure interaction problems with free surface

In this paper, a coupled MPS-modal superposition method is developed for 2D nonlinear fluid-structure interaction problems. In this method, the rigid-body and relatively small elastic deformation are coupled together, which considers the mutual effect between them. The elastic deformation of the structure is represented by a mode superposition formulation, which is more efficient compared with FEM, regardless of the size of the structure. For 2D cases, if the first three modes are chosen to represent the flexible deformation of the structure, it only results in a 6×6 matrix equation to be solved. For the fluid motion, the modified Moving Particle Semi-implicit (MPS) method, which significantly reduces the fluctuation of pressure calculation of the original MPS method, is used.Two nonlinear problems, i.e. breaking-water-dam impacting a floating beam and flexible wedge slamming into the water are simulated to demonstrate the performance of the developed method. The numerical simulations show that this coupling model is capable of providing stable results that are generally in good agreement with the available experimental data. For the highly nonlinear case with very large rigid motions, the mutual effect between elastic deformation and rigid motions could accumulate to a relatively remarkable level shown by the curves of trajectories or acceleration history of the body mass centre. This also indicates the importance of mutual effect to analyse highly nonlinear FSI problems with large rigid-body motions and relatively small flexible deformation.     

Adaptive mesh refinement for simulating fluid-structure interaction using a sharp interface immersed boundary method

In this article, adaptive mesh refinement (AMR) is performed to simulate flow around both stationary and moving boundaries. The finite-difference approach is applied along with a sharp interface immersed boundary (IB) method. The Lagrangian polynomial is employed to facilitate the interpolation from a coarse to a fine grid level, while a weighted-average formula is used to transfer variables inversely. To save memory, the finest grid is only generated in the local areas close to the wall boundary, and the mesh is dynamically reconstructed based on the location of the wall boundary. The Navier-Stokes equations are numerically solved through the second-order central difference scheme in space and the third-order Runge-Kutta time integration. Flow around a circular cylinder rotating in a square domain is firstly simulated to examine the accuracy and convergence rate. Then three cases are investigated to test the validity of the present method: flow past a stationary circular cylinder at low Reynolds numbers, flow past a forced oscillating circular cylinder in the transverse direction at various frequencies, and a free circular cylinder subjected to vortex-induced vibration in two degrees of freedom. Computational results agree well with these in the literature and the flow fields are smooth around the interface of different refinement levels. The effect of refinement level has also been evaluated. In addition, a study for the computational efficiency shows that the AMR approach is helpful to reduce the total node number and speed up the time integration, which could prompt the application of the IB method when a great near-wall spatial resolution is required.     

The fluid-structure interaction between a tensioned elastica and a flotation guide

Fluid-structure interaction between a flotation-guide and a tensioned elastic beam was investigated theoretically and experimentally. The work is inspired by manufacturing of thin flexible materials such as paper, foils and tape, collectively known as web. The mechanics of the web was modeled as an elastica beam, and solved in a Eulerian reference system by using the finite element method. The fluid mechanics in the beam/flotation-guide interface was modeled with two different fluid mechanics approaches with and without height averaging of the flow variables. The fluid models were solved with a finite volume approach. A stacked, iterative coupling algorithm was used to obtain coupled solutions. Experiments were performed to verify the two FSI models. The experiments showed that the supply pressure inside the flotation-guide must be at least equal to the belt-wrap pressure of the web for flotation to occur, as expected. The effects of large web deformations and using the height-averaged fluid model were analyzed by varying design parameters such as web wrap angle, flotation-guide radius, supply pressure, and the distribution of the pressure supply holes. This work showed that the height-averaged fluid mechanics model fails to predict the two-dimensional flow near the exit regions, which develops for cases where the web-reverser clearance tends to have large diverging variations. It was also shown that in order to keep the applied web tension at a constant level, the arc length of the web between the supports must change.     

Pressure pulses in fluid filled distensible tubes

Summary By comparing experimental records with model solutions we are led to propose a dispersion relation governing the propagation of pressure pulses in fluid filled distensible tubes. This relation contains a single undetermined parameter having the dimension of time. We show how this parameter may be interpreted and obtain an estimate of its value. Some comments concerning the speed of propagation of pressure waves in the haemodynamics contest are made.

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Sommario Si considera la propagazione di onde di pressione in tubi distensibili riempiti di fluido. Dal confronto delle registrazioni sperimentali con le soluzioni teoriche si propone una semplice relazione di dispersione che contiene un singolo parametro indeterminato avente le dimensioni di un tempo. Si mostra come interpretare tale parametro e come stimare il suo valore. Si conclude con alcune considerazioni sulla velocità di propagazione delle onde di pressione nell'ambito emodinamico.

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This work has been realized within a bilateral project supported by the Italian Research Council (CNR) and the Natural Scinces and Engineering Research Council of Canada (NSERC).