Frequency Domain Analysis of Water Hammer with Fluid-Structure Interaction in Viscoelastic pipe

In this research, Fluid-Structure Interaction (FSI) including transient flow in a viscoelastic (VE) pipe has been studied in frequency domain. The main purpose was to investigate water hammer problem using extended Transfer Matrix Method (TMM) in a typical reservoir-viscoelastic pipe-valve system. One of the generally expected advantage of frequency domain analysis is that the integral form of equations in time domain would be transformed to algebraic form. Here it would be more beneficial to utilize frequency domain methods since convolution integral which appears in viscoelastic models in time domain will also be vanished. TMM has been adopted to the transient flow in a VE pipe to derive field matrix where a non-oscillating valve is considered as boundary condition. The generalized Kelvin-Voigt model was used to simulate the viscoelastic behavior of the pipe wall. The proposed model has been explored to solve two well-known case studies of FSI in frequency domain. Results of both cases confirm good agreement between analytical and experimental data. To investigate the simultaneous effects of viscoelasticity and FSI in frequency domain a sample problem has been analyzed. Results for different conditions including interactional and non-interactional system together with both viscoelastic and elastic pipe material have been illustrated and compared. Also a comparison among 3-element, 5-element and higher order Kelvin-Voigt models has been performed based on which one may deduce the appropriateness of 3-element model.