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     

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.     

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).     

Stokes flow in an elastic tube—a large-displacement fluid-structure interaction problem

Viscous flow in elastic (collapsible) tubes is a large-displacement fluid-structure interaction problem frequently encountered in biomechanics. This paper presents a robust and rapidly converging procedure for the solution of the steady three-dimensional Stokes equations, coupled to the geometrically non-linear shell equations which describe the large deformations of the tube wall. The fluid and solid equations are coupled in a segregated method whose slow convergence is accelerated by an extrapolation procedure based on the scheme's asymptotic convergence behaviour. A displacement control technique is developed to handle the system's snap-through behaviour. Finally, results for the tube's post-buckling deformation and for the flow in the strongly collapsed tube are shown. © 1998 John Wiley & Sons, Ltd.     

Experimental and numerical study on a laminar fluid-structure interaction reference test case

With the rapid development of numerical codes for fluid-structure interaction computations, the demand for validation test cases increases. In this paper we present a comparison between numerical and experimental results for such a fluid-structure interaction reference test case. The investigated structural model consists of an aluminum front cylinder with an attached thin metal plate and a rear mass at the trailing edge. All the structure is free to rotate around the axle mounted in the center of the front cylinder. The model's geometry and mechanical properties are chosen in such a way as to attain a self-exciting periodical swiveling movement when exposed to a uniform laminar flow. Reproducibility of the coupled fluid-structure motion is the key criterion for the selection of the model in order to permit an accurate reconstruction of the results in the time-phase space. The Reynolds number of the tests varies up to 270 and within that range the structure undergoes large deformations and shows a strong nonlinear behavior. It also presents two different self-excitation mechanisms depending on the flow velocity. Hence, challenging tasks arise for both the numerical solution algorithm and the experimental measurements. To account for the two different excitation mechanisms observed on increasing the speed of the flow, results for two different velocities are considered: the first at 1.07 m/s (Re=140) and the second at 1.45 m/s (Re=195). The comparisons presented in this paper are carried out on the basis of the time trace of the front body angle, trailing edge coordinates, structure deformation and the time-phase resolved flow velocity field. They reveal very good agreement in some of the fluid-structure interaction modes whereas in others deficiencies are observed that need to be analyzed in more detail.     

Vortices in time-periodic shear flow

Vortices emerging in geophysical turbulence may experience deformations due to the non-uniform ambient flow induced by neighbouring vortices. At first approximation this ambient flow is modeled by a linear shear flow. It is well known from previous studies that the vortex may be (partially) destructed through removal of weak vorticity at the vortex edge—a process referred to as ‘stripping’. While most previous studies considered a stationary external shear flow, we have examined the behaviour of the vortex embedded in a linear shear flow whose strength changes harmonically in time. Aspects of the vortex dynamics and the (chaotic) transport of tracers have been studied by both laboratory experiments and numerical simulations based on a simple kinematical model.     

Study on fluid-structure interaction in liquid oxygen feeding pipe systems using finite volume method

The fluid-structure interaction may occur in space launch vehicles,which would lead to bad performance of vehicles,damage equipments on vehicles,or even affect astronauts’ health.In this paper,analysis on dynamic behavior of liquid oxygen (LOX) feeding pipe system in a large scale launch vehicle is performed,with the effect of fluid-structure interaction (FSI) taken into consideration.The pipe system is simplified as a planar FSI model with Poisson coupling and junction coupling.Numerical tests on pipes between the tank and the pump are solved by the finite volume method.Results show that restrictions weaken the interaction between axial and lateral vibrations.The reasonable results regarding frequencies and modes indicate that the FSI affects substantially the dynamic analysis,and thus highlight the usefulness of the proposed model.This study would provide a reference to the pipe test,as well as facilitate further studies on oscillation suppression.     

A modal analysis for the dynamic response of fluid-structure systems

In this paper a theory of modal analysis for the dynamic response of fluid-structure systems is presented. A pair of generalized eigenvalue equations with three real symmetric matrices and their relationships are derived from the finite element equations in the form of structural displacements and fluid velocity potential. Generalized orthogonality relations of modal vectors are then developed. The response of the system to external excitation is derived in closed form by modal expansion. Two examples of the solution are given for illustration.     

Incompressible low-speed-ratio flow in non-uniform distensible tubes

The fluid flow in distensible tubes is analysed by a finite element method based on an uncoupled solution of the equations of wall motion and fluid flow. Special attention is paid to the choice of proper boundary conditions. Computations were made for sinusoidal flow in a distensible uniform tube with the Womersley parameter α = 5, and a ratio between tube radius and wavelenth from 0·0001 to 0·5. The agreement between the numerical results and Womersley's analytic solution depends on the speed ratio between fluid and wave velocity, and is fair for speed ratios up to 0·05. The analysis of the flow field in a distensible tube with a local inhomogeneity revealed a marked influence of wave phenomena and wall motion on the velocity profiles.     

Added mass for fluid-structure vibration problems

The problem of computing the vibration modes of a structure vibrating in a fluid is examined with specific application to ship hulls. In particular, methods which take proper account of the three-dimensional nature of the water movements are described. Fluid singularities involving either a line doublet on the intersection of the water surface with the plane of symmetry or distributed sources on retracted boundaries are particularly effective at modelling the fluid flow and appear to give better numerical efficiencies than finite element or boundary element methods. The effects of the extra coefficients in the mass matrix arising from added mass on the various methods of eigensolution are discussed.     

A fractional nonlocal approach to nonlinear blood flow in small-lumen arterial vessels

Meccanica - The behavior of human blood flowing in arteries is still an open topic for its multi-phase nature and heterogeneity. In large arterial vessels the well-known Hagen–Poisueille law,...     

Immersed finite element method for fluid-structure interactions

In this paper, we present a detailed derivation of the numerical method, Immersed Finite Element Method (IFEM), for the solution of fluid-structure interaction problems. This method is developed based on the Immersed Boundary (IB) method that was initiated by Peskin, with additional capabilities in handling nonuniform and independent meshes and applying arbitrary boundary conditions on both fluid and solid domains. A higher order interpolation function is adopted from one of the mesh-free methods, the Reproducing Kernel Particle Method (RKPM), which relieves the uniformity constraint of fluid meshes. Two 2-D example problems are presented to illustrate the capabilities of the algorithm. The accuracy in the numerical analysis demonstrates that the IFEM algorithm is a reliable and robust numerical approach to solve fluid and deformable solid interactions.     

Numerical simulation of soft palate movement and airflow in human upper airway by fluid-structure interaction method

In this paper, the authors present airflow field characteristics of human upper airway and soft palate movement attitude during breathing. On the basis of the data taken from the spiral computerized tomography images of a healthy person and a patient with Obstructive Sleep Apnea-Hypopnea Syndrome (OSAHS), three-dimensional models of upper airway cavity and soft palate are reconstructed by the method of surface rendering. Numerical simulation is performed for airflow in the upper airway and displacement of soft palate by fluid-structure interaction analysis. The reconstructed three-dimensional models precisely preserve the original configuration of upper airways and soft palate. The results of the pressure and velocity distributions in the airflow field are quantitatively determined, and the displacement of soft palate is presented. Pressure gradients of airway are lower for the healthy person and the airflow distribution is quite uniform in the case of free breathing. However, the OSAHS patient remarkably escalates both the pressure and velocity in the upper airway, and causes higher displacement of the soft palate. The present study is useful in revealing pathogenesis and quantitative mutual relationship between configuration and function of the upper airway as well as in diagnosing diseases related to anatomical structure and function of the upper airway. The project supported by the National Natural Science Foundation of China (10672036, 10472025 and 10421002), the Natural Science Foundation of Liaoning Province (20032109). English text was polished by Yunming Chen.     

Laplace transform-boundary element coupling method for viscous fluid-structure impact analysis

Based on linearized 2-D Navier-Stokes equation, a Laplace transform-boundary element coupling method for viscous fluid-structure impact analysis is proposed. Under assumption of incompressibility for the fluid, the corresponding equivalent boundary integral equation in terms of the potential function and stream function is first established by Lamb's transform in the Laplace transform domain. It enables us to solve impact water problems in frequency domain by the boundary element method, in which the effect of viscous flow on the dynamic response can be taken into account. Then a complete solution of the problem under consideration in time domain is obtained by means of Durbin's formulas for the numerical inversion of the Laplace transform. Finally, a practical example is given to confirm the validity of the present method. Project supported by the National Defence Foundation of Science & Technology of China (No. J14. 8. 1. JW0515).     

A two-fluid model for pulsatile flow in catheterized blood vessels

The pulsatile flow of blood through a catheterized artery is analyzed, assuming the blood as a two-fluid model with the suspension of all the erythrocytes in the core region as a Casson fluid and the peripheral region of plasma as a Newtonian fluid. The resulting non-linear implicit system of partial differential equations is solved using perturbation method. The expressions for shear stress, velocity, flow rate, wall shear stress and longitudinal impedance are obtained. The variations of these flow quantities with yield stress, catheter radius ratio, amplitude, pulsatile Reynolds number ratio and peripheral layer thickness are discussed. It is observed that the velocity distribution and flow rate decrease, while, the wall shear, width of the plug flow region and longitudinal impedance increase when the yield stress increases. It is also found that the velocity increases, but, the longitudinal impedance decreases when the thickness of the peripheral layer increases. The wall shear stress decreases non-linearly, while, the longitudinal impedance increases non-linearly when the catheter radius ratio increases. The estimates of the increase in the longitudinal impedance are considerably lower for the present two-fluid model than those of the single-fluid model.