Analysis for Water Hammer considering the effect of Fluid Structure Interaction in Straight Pipes.

Abstract

Water hammer is a serious problem in flow pipelines of nuclear power plant as fluid structure interaction significantly affects the response of pipe components and performance of such plants as a whole. This phenomenon is basically observed when there is sudden increase in flow velocity, abrupt change in cross section and if the flow is forced fully to stop. The purpose of this study is to use a finite element approach for studying such a highly nonlinear problem in order to investigate the effect of fluid structure interaction (FSI) in pipe lines. In this study, the transient water hammer problem is attempted by considering the effect of all three Poisson, friction and junction couplings. The continuity and momentum equations are written in terms of pressure and velocity of the flow. Along with this the pipe-structural equations in axial direction is considered. Compared to conventional water hammer relations, present work accounts the Poisson coupling as an important term in the fluid dynamic equations. The complete interaction of fluid and pipe comes with boundary condition, which is taken as gradual valve closure. There are various solution approaches such as method of characteristics (MOC), finite element-MOC mixed method as well as finite element approach alone. In present work, finite element approach is employed to mesh the fluid and solid regions. In FEM method two kind of formulation has been done to account for symmetric matrix formulation and shape function used in determining the mass stiffness and damping matrix element. This kind of formulation uses velocity potential () and hydrostatic pressure (p) as unknowns in fluid domain and axial displacement (u) as unknown in solid domain. A MATLAB code has been written to calculate result for Finite element formulation by solving the nonlinear second-order differential equations using Newmark-beta scheme.