Frequency response of water hammer with fluid-structure interaction in a viscoelastic pipe

Abstract

Fluid-structure interaction (FSI) during water hammer in a viscoelastic (VE) pipe is studied in the frequency domain. The main aim is to investigate pressure and stress waves using Transfer Matrix Method (TMM) in a typical reservoir-VE pipe-valve (RPV) system. Both major coupling mechanisms namely Poisson and junction are taken into account. The generalized Kelvin-Voigt model simulates VE behavior during water hammer, which is generated by a quick closing/opening of downstream valve. The effect of viscoelasticity is modeled by Volterra integrals (in time) which are written as the products of transforms of the creep function and pressure (or stress) in the Laplace domain. The developed formulation is adopted to solve two well-known FSI problems from literature, and both demonstrate favorable agreement with available analytical and experimental data. To investigate the sole/simultaneous effect of Poisson and/or junction coupling and viscoelasticity, a hypothetical case study is considered and the corresponding results are closely investigated. The robust performance of the Transfer Matrix Method (TMM) allows for deducing the drop of pressure amplitudes due to viscoelasticity, frequency shift of Poisson coupling, and remarkable discrepancy of odd frequencies (relative to classical model) induced by junction coupling. This research is of crucial importance when frequency-response-based methods are utilized for defect detection of unrestrained pipes.