International Journal of Modern Trends in Engineering and Research e-issn No.: , Date: April, 2016

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1 International Journal of Modern Trends in Engineering and Research e-issn No.: , Date: 8-30 April, 016 Numerical Analysis of Fluid Flow Induced Vibration of Pipes A Review Amol E Suradkar 1 Shubham R Suryawanshi 1 Department of Mechanical Engineering, MET s BKC IOE, Nasik, amolsuradkar05@gmail.com Department of Mechanical Engineering, MET s BKC IOE, Nasik, shubhamsuryawanshi55@gmail.com Abstract- The current research paper deals with the effects of vibration due to internal fluid flow in a pipeline. The flow of a fluid through a pipe can impose pressures on the walls of the pipe causing it to deflect under certain flow conditions. The deflection of the pipe may lead to structural instability of the pipe. Mathematical model of pinned pinned pipe carrying fluid has been developed. The partial differential equation of motion governing the lateral vibrations of the pipe is employed to develop the stiffness matrices corresponding to two of the terms of the equations of motion. The Equation of motion includes a mixed-derivative terms. As for boundary condition, namely simplysupported pipe is considered.. Keywords- Structural instability, flow induced vibration, Mathematical model, Stiffness matrix, Structural inertia. I. INTRODUCTION Vibration and noise problems due to fluid flow occur in many industrial plants. This obstructs smooth plant operation. This leads to significant maintenance and repair costs. Flow-related vibration phenomena are generally known as flow-induced vibrations (FIV). The term flow-induced vibration and noise (FIVN) is used when flow-induced noise is present. It is fairly evident that the fluid force acting on an obstacle in flow will vary due to the flow unsteadiness and that the varying force, in turn, may cause vibration of the obstacle. In case of piping connected to reciprocating fluid machines, for example, the oscillating (fluctuating) flow in the piping generates excitation forces causing piping vibration. Flow induced vibration of pipes has been a subject of considerable research in the last four decades. By using the flow induced vibration we can develop electromagnetic energy. In the oil field development and production, fluid flow is an extremely important parameter which determines the transmission characteristics of the oil production structural failure due to flow induced vibration is a common problem affecting performance and reliability of heat exchangers. Under certain conditions fluid flow inside a pipe can initiate vibrations of the pipe. If the vibration intensity is large enough pipes can strike against each other or against their supports causing structural fatigue or complete failure. Flow induced vibration also occur in transcontinental oil pipelines causing damage of support structure or cracks of the pipelines leading to costly shut down. As the pipes are widely used in many industrial fields, flow-induced vibration analysis of pipes conveying fluid has been one of the attractive subjects in structural dynamics. It is well known that pipeline systems may undergo divergence and flutter types of instabilities generated by fluid-structure All rights Reserved 1058

2 Volume 3, Issue 4, [April 016] Special Issue of ICRTET 016 In many situations where machines are operating and fluids are transported. Pipe system are responsible for the transmission of noise, e.g. in buildings, ships, power plants, process plants, etc. Excessive vibrations may lead to fatigue and cause damage to vital parts of installations. Fluid pulsations may also cause incorrect reading of flow meters and other control devices and the wastage of money and time also.the monitoring of pulsations or vibrations can be valuable to diagnose those problems. So that there is a scope to investigate the response of a structure due to combined loading of fluid, fluid inertia and structural inertia. Hence in the present study an attempt will be made to investigate the factors influencing flow induced vibration. II. LITERATURE REVIEW Determination of flow induced vibration of pipelines due to an internal flow becomes a subject of considerable importance. Literature reflects studies related to flow induced vibrations in the last four decades. On the basis of aim and objective the literature review is as follows, The fast Fourier transform FFT is used to investigate the structural dynamic characteristics and the internal fluid transient properties. The wave characteristics, divergence stability and dynamics of the viscous elastic pipelines conveying internal flow are examined by Lee et al.[1] using the spectral element method. Small perturbations with respect to the steady state values of inner fluid velocity and pressure is considered to make the governing equations to be linear. In the spectral element model the governing differential equation of motion is transformed into the frequency-domain by using the discrete Fourier transformation theory. The internal flow velocity at which the divergence instability occurs is derived in an analytical form. A spectral element model is developed by Lee and Park [] for the uniform straight pipelines with an internal unsteady fluid. Four coupled pipedynamics equations are derived in terms of the transverse displacement, the axial displacement, the fluid pressure and velocity and then liberalized them. We consider steady-state flow-induced vibration problem in pipe conveying an internal flow with constant velocity. The self-excited flexural vibration of a pipe due to an internal flow with constant velocity was investigated by Biswas and Ahmed [3]. Afterward, Gorman et al. [4] included the effects of radial shell vibration and initial axial tension on Lee s pipe-dynamics model. Most of the earlier studies are related to investigations about inner transient flow with time-varying velocity, which are reviewed at first here. Coupled pipedynamics equations for the axial, radial, and lateral vibrations of the pipeline as well as for the transients of unsteady internal fluid pressure and velocity were the subject of studies by Lee and Kim [5] and Lee et al.[6].the first attempt in flow-induced vibration study was done by Ashley and Havilland [7].The practical vibration problems of heat exchanger tubes in power plants and nuclear reactors were the subject of many studies as other aspects of this field. The finite elements models and also other numerical methods are frequently used for these studies. For want of space, we review the studies which are only based on the analytical methods. III. MATHEMATICAL MODELING.1 Equations of Motion for Flow Consider a pipe of length L, modulus of elasticity E, and its transverse area moment I. A fluid flows through the pipe at pressure p and density at a constant velocity v through the internal pipe crosssection of area A. As the fluid flows through the detecting pipe it is accelerated, because of the changing curvature of the pipe and the lateral vibration of the pipeline. The vertical component All rights Reserved 1059

3 Volume 3, Issue 4, [April 016] Special Issue of ICRTET 016 fluid pressure applied to the fluid element and the pressure force F per unit length applied on the fluid element by the tube walls oppose these accelerations. Referring to figures (.1) and (.), balancing the forces in the Y direction on the fluid element for small deformations, gives / y x t x F A( ) A( ) (.1) Figure.1: Pinned-Pinned Pipe Carrying Fluid Figure.: Pipe Carrying Fluid, Forces and Moments acting on Elements (a) Fluid (b) Pipe. Finite Element Model Consider a pipeline span that has a transverse deflection Y(x, t) from its equilibrium position. The length of the pipe is L, modulus of elasticity of the pipe is E, and the area moment of inertia is I. The density of the fluid flowing through the pipe is ρ at pressure p and constant velocity through the internal pipe cross section having area A. Flow of the fluid through the deflecting pipe is accelerated due to the changing curvature of the pipe and the lateral vibration of the pipeline. From the previous section we have the equation of motion for free vibration of a fluid converting pipe: 4 EI y A y A y M y 0 4 t x x t t (.) The Element stiffness matrix for a beam element is given All rights Reserved 1060

4 Volume 3, Issue 4, [April 016] Special Issue of ICRTET 016 [ K 1 6l 1 6l EI 6l 4l 6l l ] 3 l 1 6l 1 6l 6l l 6l 4l e (.3).3 Matrix Formation In order to form a Global Matrix, we start with a 6x6 null matrix, with its six degrees of freedom being translation and rotation of each of the nodes. So our Global Stiffness matrix looks like this: KGlobal (.4) We shall now build the global stiffness matrix by inserting element 1 and element of element stiffness matrix into the global stiffness matrix. We get, 1 6l 1 6l 0 0 6l 4l 6l l 0 0 EI 1 6 l (1 1) ( 6l 6 l) 1 6l KGlobal 3 (.5) l 6l l ( 6l 6 l) (4l 4 l) 6l l l 1 6l l 6l 0 When the boundary conditions are applied to a simply supported pipe carrying fluid, the 6x6 Global Stiffness Matrix formulated in eq (.5) is modified to a 4x4 Global Stiffness Matrix. It is as follows; Y 1 X L Figure 3.1: Representation of Simply Supported Pipe Carrying All rights Reserved 1061

5 Volume 3, Issue 4, [April 016] Special Issue of ICRTET 016 K Global 4l 6l l 0 EI 6 l (1 1) ( 6l 6 l) 6l 3 l l ( 6l 6 l) (4l 4 l ) l 0 6l l 4l (.6) Since the pipe is supported at the two ends the pipe does not deflect causing its two translational degrees of freedom to go to zero. Hence we end up with the Stiffness Matrix shown above. IV. SUMMARY This paper deals with the numerical analysis of flow induced vibration in pipes considering the effects of vibrations due to flow in a pipeline. Finite Element model for a pipe is studied and developed it for vibration analysis of a Pipe Carrying Fluid. And, then implemented the above developed model to Simply Supported Pipe configuration which Carries Fluid. REFERENCES [1] Evans Robert P., Flow rate measurements using flow induced pipe vibration,asme,j. Fluids Eng.16() pp.80-85,004. [] Faal R. T., Derakhshan D., Flow-Induced Vibration of Pipeline on Elastic Support, The Twelfth East Asia- PacifiC Conference on Structural Engineering and Construction, Procedia Engineering 14, pp , 011. [3] Gohela Hardik R, Shahb Balkrushna A, Lakdawala Absar M,Numerical Investigation of Flow Induced Vibration for the Triangular Array of Circular Cylinder,Chemical, Civil and Mechanical Engineering Tracks of 3rd Nirma University International Conference (NUiCONE-01) Procedia Engineering 51,pp , 013. [4] Iyan Grant, Flow Induced Vibration in Pipes, A Finite Element Approach, 006 [5] Liu Long, Flow-Induced Vibration Analysis of Supported Pipes Conveying Pulsating Fluid Using Precise Integration Method, Mathematical Problems in Engineering,,pp , 010. [6] Marakala Narasimha, Investigated Combined Effect of Fluid and Thermal Induced Vibration on Vertical Thin Slender Tube experimentally and theoretically,iosr, pp ,,008. [7] Vasilyev Peter, Fromzel Leonid,Analytical Study of Piping Flow-induced Vibration. Example of Implementation,Transactions of the 17th International Conference on Structural Mechanics in Reactor Technology (SMiRT 17) Prague,,pp.17, 003. [8] Ying Shang, Optical fiber fluid flow monitoring system based on flow induced vibration,ieee,009. F : Pressure Force in newton (N) : Density in kg/m 3 A : cross sectional area of pipe in inches L : Length of pipe in (m) Y : Direction of fluid element in m E : Modulus of Elasticity in N/m I : Moment of Inertia in kg.m V : velocity in m/s M : Mass in kg All rights Reserved 106

Flow-Induced Vibration of Pipeline on Elastic Support

Available online at www.sciencedirect.com Procedia Engineering () 986 99 The Twelfth East Asia-Pacific Conference on Structural Engineering and Construction Flow-Induced Vibration of Pipeline on Elastic