Godunov-Type Solutions with Discrete Gas Cavity Model for Transient Cavitating Pipe Flow

Abstract

To simulate transient cavitating pipe flow, the discrete gas cavity model (DGCM) is combined with first-order and second-order finite-volume method (FVM) Godunov-type schemes. The earlier discrete vapor cavity model (DVCM) and DGCM based on the method of characteristics (MOC) are known to produce unrealistic pressure spikes. The new FVM-DGCM extends the previously developed FVM-DVCM through the introduction of a very small amount of free gas at the middle of each computation cell. Importantly, a pressure adjustment procedure is proposed to establish the relation between the cavity and the halves of the reach. Predictions of FVM-DGCM are compared with those of FVM-DVCM and MOC-DGCM and with experimental data. Results show that the proposed model reproduces the experimental pressure histories considerably better than the other two models. In particular, it produces fewer spikes, but—as in the old models—the first pressure peak due to cavity collapse is predicted much better than the subsequent peaks. The second-order FVM-DGCM is found to be accurate and robust, even for Courant numbers significantly less than 1.