generalized transform technique for fluid-structural interaction during water hammer

unsteady flow in pipes may appear in certain circumstances and may cause undesired effects in industrial processes. the objective of this paper is to develop a new simulation model for the fluid–structure interactions (fsi) that occur in pipeline systems during water hammer. the mathematical formulation is based on water hammer equations, traditionally used in the literature, coupled with a standard beam formulation for the structure and implementing the generalized integral transform technique, gitt to treat the set of equations. the solution method is applied to a straight pipeline system subjected to axial impact load by a rapid valve closure and axial vibration of pipe, pressure and velocity of fluid are investigated. in the first step, the set of governing partial differential equations is transformed into a set of second-order differential equations in dimensionless form. in the second step the ideas in gitt approach to construct a hybrid analytical-numerical solution are implemented to obtain dynamic response of fsi during water hammer. by adopting a fourth-order eigenvalue problems and proposing eigenfunction expansions the transformed functions system results in the form of initial value problems. the explicit fourth-order runge-kutta and the implicit adams-bashforth-moulton scheme are used to treat the set of obtained coupled ordinary differential initial value problems. following the evaluation of time dependent variables, the analytical inversion formulas are recalled to recover the dimensionless functions for the velocity of fluid, the pressure and the axial displacement of the wall of pipe, v(x,t), p(x,t) and u(x,t). to illustrate the capability and efficiency of the proposed scheme, delft hydraulic benchmark (dhb) problem b is chosen to show the performance of the methodology. furthermore, the convergences behavior of solution is examined for increasing truncation orders and a perfect convergence is observed.