Mathematical Model and Numerical Analysis of Hydraulic Shock Attenuation by a Damper in Pipeline Transportation Systems

This study presents a computationally efficient quasi-one-dimensional mathematical model based on the traveling wave method to investigate hydraulic shock attenuation using a gas-hydraulic damper in pipeline systems. Unlike conventional models, this formulation accounts for fluid compressibility and incorporates a non-linear boundary condition strictly satisfying gas mass conservation within the damper. The model was successfully validated against a MATLAB 2024 Simulink benchmark, demonstrating a maximum pressure amplitude discrepancy of only 5–8%. A parametric analysis evaluated the effects of damper volume, initial gas pressure, and pipe diameter on surge suppression. Results show that insufficient damper volume causes extreme negative pressure drops, risking severe cavitation and fluid column separation. Conversely, excessive volume induces “over-damping,” undesirably increasing system inertia and delaying steady-state recovery. Crucially, scaling analysis reveals that a damper optimized for a specific pipe diameter loses efficacy in larger pipes, as the flow’s kinetic energy scales with the diameter’s square. This model provides a robust, precise computational tool for the optimal and safe design of pipeline networks.