Water Practice and Technology (Jun 2024)
Numerical modeling and simulation of water hammer phenomena using the MacCormack method
Abstract
Water hammer refers to pressure fluctuations caused by changes in fluid speed in hydraulic systems. This research proposes a model using the MacCormack method to study and control water hammer, specifically focusing on managing valve closure to reduce shock wave pressure during transient flow. Numerical simulations compare linear and quadratic closure laws for both rapid and gradual valve closure, with the goal of identifying the optimal laws. The findings show that with faster closure times, the overpressure at the valve section decreases linearly in the second quarter of the return period (t4). The application of the quadratic law results in reduced pressures at the valve compared to the linear law, with a maximum pressure difference of 0.05 bar between the highest and lowest values. When searching for the optimal valve closure law to mitigate overpressure, it is found that the exponent ‘m’ falls within the range of 1.117–1.599. As the slow closing time increases gradually, the range of variation for ‘m’ decreases. Furthermore, in the case of underpressure prevention, the exponent ‘m’ ranges from 0.95 to 1.419, and the range of ‘m’ remains relatively constant with the increase in closing time. HIGHLIGHTS The MacCormack method is used for simulating the transient flow in a long-distance buried pipe.; During a rapid closure, the quadratic law results in lower pressures compared to the linear law.; For a slow closure, the quadratic law leads to higher overpressure and higher underpressure compared to the linear law.; For each slow closure time, two optimal valve closure laws are deduced; the first one generates the minimum overpressure while the second one generates the minimum depression.; Unlike depression protection, the optimal law range for overpressure protection clearly decreases as the closure time increases.;
Keywords
