Numerical Modeling of Transient Flow in Pipe With Taking Into Account Fluid-Structure Interaction

In hydraulic transient or waterhammer phenomena, it is well known that, the acoustic celerity is strongly influenced by both the elasticity of the pipe material and the fluid [1]–[3]. In actuality, by exchange of momentum between the two mediums, the deformation of pipe causes longitudinal stress waves to propagate along the pipe wall at celerity greater than that of waterhammer acoustic wave. Such fluid structure interaction, is reported by several investigations[2] dealt with different levels of difficulty depending on the number of equations to be solved. The present work is a simplified case based on a four equations including, through the Poisson's ratio of pipe material, fluidstructure interaction model. The derivation of basic equations is based on conservation laws of mass, momentum and energy for both the fluid and pipe material. The set equations obtained are solved numerically by the method of characteristics. The average pressure across a right sections of pipe and velocity displacement of pipe wall are computed at each time. The results obtained are in agreement with those found the literature [4]. This study highlights , against the classical theory of waterhammer, the significant effects of the fluid-structure interaction on the pressure oscillations generated by the waterhammer phenomena resulting from fast closure of valve