Transverse Flow of Periodic Pressure Waves in Vessel

Communications in Numerical Methods in Engineering, 2006

Numerical procedure for the analysis of fluid flow in a tube performing transverse oscillations is developed. The formulation of the problem is presented in differential equation form and a finite element model is developed leading to the first-order matrix differential equation. The fluid flow model incorporates transverse oscillation of the boundary through the convective inertia terms. Modal decomposition of the solution is performed and a technique for numerical solution of the finite element problem incorporating parametric vibrations is developed. Numerical results provide insight into the problem of fluid flow control by transverse vibrations of the tube.

International journal of pressure vessels and piping, 2005

The paper gives a bibliographical review of finite element methods(FEMs) applied for the analysis of pressure vessel structures/components and piping from the theoretical as well as practical points of view. This bibliography is a new addendum to the Finite elements in the analysis of pressure vessels and piping-a bibliography [1][2][3]. The listings at the end of the paper contain 856 references to papers and conference proceedings on the subject that were published in 2001-2004. These are classified in the following categories: linear and nonlinear, static and dynamic, stress and deflection analyses; stability problems; thermal problems; fracture mechanics problems; contact problems; fluid-structure interaction problems; manufacturing of pipes and tubes; welded pipes and pressure vessel components; development of special finite elements for pressure vessels and pipes; finite element software; and other topics. q † linear and nonlinear, static and dynamic, stress and deflection analyses (STR) † stability problems (STA) † thermal problems (THE) † fracture mechanics problems (FRA) † contact problems (CON) † fluid-structure interaction problems (FLU) † manufacturing of pipes and tubes (MAN) † welded pipes and pressure vessel components (WEL) † development of special finite elements for pressure vessels and pipes (ELE) † finite element software (SOF) † other topics (OTH)

Communications in Numerical Methods in Engineering, 2004

A modiÿed ÿnite element method is proposed to solve the unsteady pipe ow equations. This approach yields a six-point implicit scheme with two weighting parameters. An accuracy analysis carried out using the modiÿed equation approach showed that the proposed scheme has higher accuracy compared to other methods. A comparison of experimental data and the results of numerical solution showed that the required damping and smoothing of a pressure wave can be obtained when numerical di usion is produced by the applied method. It suggests that the physical dissipation process observed in the water hammer phenomenon is not represented properly in its mathematical model. Therefore, the classical system of water hammer equations seems to be incomplete.

Port-Said Engineering Research Journal, 2013

Pressure vessels are wildly used in many fields, such as chemical, petroleu m, military industries as well as in nuclear power plants. Pressure vessels should be designed with great care because rupture of pressure vessel may cause catastrophic accident. The common problem to the pressure vessel's designer is the accurate evaluation of stresses due to the applied mechanical and /or thermal loads. The finite element method FEM is one of the nu merical stress analysis for many subjects. In this paper a complete stress analysis through the wall of pressure vessel under the effect of constant and cyclic loading is presented. Hoop, radial, axial and effective stresses for cylindrical pressure vessels have been evaluated analytically as well as using the program package ANSYS as a nu merica l fin ite element method. A comparison between the analytical and numerical solution is presented, and it is found a good agreement between them.

International Journal of Fluid Power, 2009

A very compact description of viscid wave propagation in straight transmission lines with a circular cross section in frequency domain by a transcendental transfer matrix is known since several decades. The corresponding research results show that fluid friction is limited to small dynamic boundary layers whereas the remaining fluid domain exhibits practically no friction effect and has bulk flow characteristics. An explanation how this boundary layer transfers its dissipative effect to the bulk flow has been given by Gittler et al. using asymptotic expansion techniques. They found that the effect of the boundary layer on the bulk flow in the centre is given by radial velocity components. The authors have shown that the findings of Gittler et al. are generally valid in the 3D case exploiting matched asymptotic expansions. In this paper these results are developed further to exploit this dynamical boundary layer theory for an efficient Finite Element (FE) computation of viscid waves. Standard acoustic elements without viscosity as available in many FE codes combined with frequency dependent acoustic boundary conditions can be used to simulate 3D viscid wave propagation in frequency domain. Comparison with the analytical transmission line theory shows the validity and wide applicability of this approach. It is much more efficient than a direct resolution of the viscid boundary layer by a fine FE grid.

Mathematical Analysis and Applications, 2019

In the last decades, the finite element method (FEM) in fluid mechanics applications has gained substantial momentum. FE analysis was initially introduced to solid mechanics. However, the progress in fluid mechanics problems was slower due to the non-linearities of the equations and inherent difficulties of the classical FEM to deal with instabilities in the solution of these problems. The main goal of this review is to analyze FEM and provide the theoretical basis of the approach mainly focusing on parabolic type of problems applied in fluid mechanics. Initially, we analyze the basics of FEM for the Stokes problem and we provide theorems for uniqueness and error estimates of the solution. We further discuss FE approaches for the solution of the advection–diffusion equation such as the stabilized FEM, the variational multiscale method, and the discontinuous Galerkin method. Finally, we extend the analysis on the non-linear Navier–Stokes equations and introduce recent FEM advancements.

Universal Journal of Mechanical Engineering, 2015

The transverse of free vibration of pipes conveying fluid has been examined by using Euler-Bernoulli beam theory to show the effect of varied boundary conditions on pipes dynamic behaviors. The equation of motion of the pipe conveying fluid is obtained with a new approach with the assumptions of ideal fluid, which moves in the vertical direction with pipe and the pipe makes small oscillations, by Hamilton's variation principle. The flow in the pipe was modeled by considering well-known Euler equation. The dimensionless equations are solved for two different set of non-classical boundary conditions. The natural frequency equations and the critical flow velocity equations are obtained and the relation between the mass ratio and vibration frequency is examined by solving the differential equations. The values of natural frequencies caused by the fluid velocity are presented graphically.

Continuum Mechanics and Thermodynamics, 2010

The combined methodology of boundary integral equations and finite elements is formulated and applied to study the wave propagation phenomena in compound piping systems consisting of straight and curved pipe segments with compact elastic supports. This methodology replicates the concept of hierarchical boundary integral equations method proposed by L.I. Slepyan to model the time-harmonic wave propagation in wave guides, which have components of different dimensions. However, the formulation presented in this paper is tuned to match the finite element format and, therefore, it employs the dynamical stiffness matrix to describe wave guide properties of all components of the assembled structure. This matrix may readily be derived from the boundary integral equations, and such a derivation is superior over the conventional derivation from the transfer matrix. The proposed methodology is verified in several examples and applied for analysis of periodicity effects in compound piping systems of several alternative layouts.

Journal of Vibroengineering, 2016

The finite element model of transient pressure pulse propagation in a pipeline is presented in the form of the standard structural dynamic equation, which combines steady flow analysis for obtaining the initial conditions of the flow in the form of pressures and flow rates and non-linear dynamic analysis by using explicit numerical integration techniques. Three options of simplification of governing equation set have been analyzed. At low values of steady flow speed many non-linear and convection terms could be omitted, while at the flow speeds comparable with the wave propagation speed the full equation system has been analyzed. The full equation system analysis involves the techniques ensuring corrections of the initial conditions and of the nodal flow rate balance. The investigated pipelines may contain large number of branches and loops. Parts of large pipelines are analyzed as separate sub-models by employing non-reflecting boundary conditions at the cut boundaries. Properties ...

2005

Consider a fully developed, time-periodic motion of a Navier-Stokes fluid in an infinite straight pipe of constant cross section Ω (time-periodic Poiseuille flow). In this note we show that the axial pressure gradient and the flow rate associated to this motion are uniquely connected through a very simple relation involving parameters depending only on Ω and, therefore, independent of the particular velocity field. One immediate and important consequence of this property is that it allows for a very elementary proof of existence of time-periodic Poiseuille flow under a given flow rate. . 35Q30, 76D03, 76D05.