Linearized Solution for Rapid Filling of Horizontal Pipe with Entrapped Air

Abstract

Rapid filling of a horizontal pipe with an entrapped air pocket has attracted significant attention as overpressurization induced by air compression may cause safety concerns. This study developed a linearized model for a rapidly filling horizontal pipe, by using a Jacobian linearization around the equilibrium point of the nonlinear system. The analytical expressions explicitly show the relationship between the characteristics of pressure oscillation and parameters including the driving head, the length of the water column, the length of the entrapped air pocket, the location of the equilibrium point, and the polytropic exponent. The oscillation frequency increases with the driving head whereas it decreases with the length of the air pocket. The obtained analytical solution compares well with the rigid-column model for a limited range, and it is improved by means of introducing power-law fitting for general cases. The linearization method also can be used in other cases, such as rapid filling in a horizontal pipe with the entrapped air pocket above an initial water layer or in slope/vertical pipes.