Investigation and implementation of a 1-D water hammer numerical model with liquid column separation

Abstract

Over the years, many advances have been made in the numerical prediction and simulation of hydraulic transients. This is especially true for water hammer with liquid column separation. The open literature presents numerous research articles, numerical models, and experiments on hydraulic transients. However, even with these advancements and mathematical tools, water hammer with liquid column separation are still hydraulic transients often overlooked by design and process engineers. This may lead to equipment damage and downtime of plants and catastrophic, and sometimes even fatal, consequences. The hydraulic transient causes highpressure pulses in the pipe system much higher than the operating and water hammer pressures. The open literature showed that the most popular numerical model for predicting and simulating water hammer with liquid column separation is the discrete gas cavity model (DGCM). Unfortunately, the open literature lacks information on implementing the DGCM model, especially regarding the free gas volume weighing factor’s effect on the grid and time step independenceand the proper value for the weighing factor when conducting simulations. Many researchers present conflicting proposed values for the weighing factor in the literature. This study aims to address the gap in the literature by implementing the DGCM model into the EES software package, conducting a sensitivity analysis of the weighing factor, and comparing experimental results with simulation results for various weighing factor values. The sensitivity analysis of the weighing factor gives insight into the effect of different weighing factors on the grid and time step independence of the DGCM numerical model. The purpose of the comparison of the experimental and simulation results is to establish whether a baseline value for the weighing factor exists or if the weighing factor is system-dependent. The sensitivity analysis results revealed that as the weighing factor value increased from 0.5 to 1, the grid and time step size for independence increased. This led to the conclusion that for higher values of the weighing factor, grid and time step independence was reached at a larger grid and time step size. If a weighing factor of 1 was used, the larger grid and time step size led to a shorter simulation time. The comparison between the experimental and simulation results revealed that as the weighing factor value increased from 0.5 to 1, better comparisons were obtained with the experimental results, and numerical stability increased. In conjunction with the sensitivity analysis results, thisled to the conclusion that a weighing factor of 1 is strongly recommended for lower simulation time, higher numerical stability, and improved accuracy.