Estimation of Maximum Overshoot of High-Frequency Pressure Oscillation Excited by Step Pressure Load in Thin-Walled Liquid-Filled Pipe

Abstract Instantaneous step water hammer in liquid-filled pipes could excite high-frequency vibration of the pipe wall, and rapid expansion and contraction of the pipe wall could induce high-frequency pressure oscillation. The oscillating pressure may exceed the classical Joukowsky value, posing additional risk to the operational safety of pressurized pipelines. This study established a numerical model for one-dimensional liquid-filled pipe with fluid–structure interaction and radial inertia of pipe considered, in which the governing equations of liquid and pipe are discretized and solved by the coupling of the method of characteristics and the finite difference method, respectively. The established model is validated by the classical thin-walled Delft and Skalak’s infinitely long tube cases, and the high-frequency pressure oscillation tailing step pressure load is captured in both validation cases. Theoretical analysis is conducted for both the impact and free-vibration stages, and a formula for estimating the maximum pressure overshoot is derived. Based on the theoretical analysis and simulation results of the Delft and Skalak cases, a maximum relative pressure overshoot of approximately 30% is observed. This value is obtained under the conditions investigated in this study and may serve as a conservative estimate for similar thin-walled pipe systems. The influence of several systematic parameters on the maximum overshoot is investigated, and the results indicate that maximum overshoots under different systematic parameters are all less than 30%, and the maximum error in the estimated maximum overshoot is less than 23%.