Elastic Water Column Modelling of an Undulating Pipeline Profile with Entrapped Air

Emptying pressurised pipelines with undulating profiles can generate subatmospheric pressure conditions that compromise structural integrity, particularly when no air admission valve is considered. One-dimensional models for this transient event have so far relied on the Rigid Water Column (RWC) assumption, which neglects the elasticity of the liquid phase and the deformability of the pipe walls. This study applies an Elastic Water Column Model (EWCM) to the emptying of pipelines with an undulating profile, in which the Method of Characteristics is applied on two independent moving grids coupled through a single entrapped air pocket governed by a polytropic law. The model is validated against nine configurations, each recorded twice, in a laboratory facility whose two branches rise at 30° to a common high point, forming an inverted V. The configurations cover symmetric air pockets under 6% and full valve opening, and asymmetric air pocket distributions under full opening. The EWCM predicts the minimum pressure with a mean absolute error of 0.21%, against 0.27% for the rigid formulation, and both remain below the scatter between experimental repetitions. The governing parameter depends on the valve opening level: under full opening, the shape of the valve manoeuvre dominates, whereas under a restrictive 6% opening, it leaves the minimum pressure unchanged and the polytropic exponent becomes the largest effect. The wave speed is negligible throughout. The ratio between the acoustic and mass-oscillation time scales, obtainable in closed form, remains between 0.014 and 0.028 across the configurations tested, with the divergence between the two formulations increasing with it.