One-Dimensional Compressible Solution for Transient Cavitating Pipe Flow

Fluid transient phenomena involving pressure wave propagation have often been studied and solved with the method of characteristics. Only recently has the finite-volume method (FVM) been proposed and implemented to solve the transient fluid flows for a one-dimensional water-hammer–based analysis. The use of the FVM permits the introduction of new solution algorithms and, at the same time, deals with more general conditions, including multiphase flow and cavitation. The research presented in this paper investigates improvements to the solution methods for one-dimensional flow simulation with compressibility and multiphase liquid-gas flows induced by cavitation in which the gas phase consists of two distinct components: noncondensible gas and vapor. The effects of the second phase and the compressibility play an essential role in the density and, consequently, the speed of sound variation in the flow, and accounting for these provide a more accurate prediction of pressure wave propagation. The simulations carried out were second-order accurate in time and space by using the monotonic upwind scheme for conservative laws (MUSCL). The total variation diminishing (TVD) strategy was also implemented for stability reasons. To consider the second phase, a variation of the discrete gas and vapor cavity model was used. In conclusion, a comparison with experimental data, similar algorithm approaches, and the classical method of characteristics indicate a more effective approach for the simulation of pressure-wave propagation for compressible conditions.