On the two-dimensional characteristics of laminar fluid transients in viscoelastic pipes

A two-dimensional numerical model is developed to study the behavior of laminar fluid transients in viscoelastic pipes. The present procedure couples a two-dimensional water hammer model with a single element Kelvin-Voigt model, where the latter is used to simulate the viscoelastic behavior of the pipe wall. The method of lines is implemented in the present study, where second-order accurate central difference expressions are used for the discretization of the spatial terms and the classical fourth-order accurate Runge-Kutta method is used for integrating the discretized equations in time. Through the present numerical results and dimensional analysis of the governing equations, a non-dimensional parameter is identified which governs the effect of pipe wall viscoelasticity on the fluid transient. The identified parameter shows that the effect of pipe wall viscoelasticity is more pronounced in the case of longer pipes with bigger diameters and larger wave speeds. Moreover, a parametric study is carried out to identify the effect of the non-dimensional parameter on the various characteristics of the fluid transient and on the pipe instantaneous and retarded strain components.