Application of two-component pressure approach and Harten–Lax–van Leer (HLL) solver to model transient flow with regard to air entrapment

Abstract

Abstract Water distribution systems are basically designed to convey pressurized flow; however, in some situations such as the intermittent operation of the system, the network may experience a transition between free-surface and pressurized flow. On the other hand, combined sewer systems, designed basically for free-surface flow, may undergo pressurization due to extreme rainfalls. During transient flow, free-surface flow changes into a pressurized flow (and vice versa) which could be accompanied by intensive transient pressures causing structural damages to the system. In a pipe filling process, the existing air can be entrapped due to improper ventilation, intensifying the transient pressures in some cases. In this paper, the two-component pressure approach (TPA) and a Harten–Lax–van Leer Riemann solution are applied to model transient flow. The model is validated by comparing its results with the analytical solution of three simple examples, and then the model with an air chamber as the downstream boundary is used to simulate a literature experimental setup that includes air pocket entrapment. As the volume of the air pocket decreases, the errors of the model increase due to the inherent deficiency of the one-dimensional model. Furthermore, it is recommended to limit the Courant number to 0.5 for high acoustic wave speeds.