Validation of Hyperbolic Model for Water-Hammer in Deformable Pipes

Abstract

A mathematical formulation is presented to describe the transient flow of homogeneous gas–liquid mixtures in deformable pipes. The mixture density is defined by an expression averaging the two-component densities where isothermal evolution of the gaseous phase is admitted. Instead of the void fraction, which varies with pressure, the gas–fluid mass ratio (or the quality), assumed to be constant, is used. By application of the conservation of mass and momentum laws, a nonlinear hyperbolic system of two differential equations is obtained for the two principal dependent variables, which are the fluid pressure and velocity. Consideration is given in this paper to the numerical solution of these equations by the method of characteristics and the finite difference conservative scheme. The finite difference scheme computes the pressure by using a Newton–Raphson iterative formula, where the pressure wave speed takes place explicitly. To verify the validity of the computed results, comparison has been made with those of the numeric-experimental example of Chaudry et al. “Analysis of Transient in Bubbly Homogeneous Gas–Liquid Mixtures,” 1990. ASME J. Fluids Eng., 112 , pp. 225–231. [S0098-2202(00)00301-1]