Investigation of Air Pocket Behavior in Pipelines Using Rigid Column Model and Contributions of Time Integration Schemes

Abstract

This paper studies the air pressurization problem caused by a partially pressurized transient flow in a reservoir-pipe system. The purpose of this study is to analyze the performance of the rigid column model in predicting the attenuation of the air pressure distribution. In this regard, an analytic formula for the amplitude and frequency will be derived, in which the influential parameters, particularly, the driving pressure and the air and water lengths, on the damping can be seen. The direct effect of the driving pressure and inverse effect of the product of the air and water lengths on the damping will be numerically examined. In addition, these numerical observations will be examined by solving different test cases and by comparing to available experimental data to show that the rigid column model is able to predict the damping. However, due to simplified assumptions associated with the rigid column model, the energy dissipation, as well as the damping, is underestimated. In this regard, using the backward Euler implicit time integration scheme, instead of the classical fourth order explicit Runge–Kutta scheme, will be proposed so that the numerical dissipation of the backward Euler implicit scheme represents the physical dissipation. In addition, a formula will be derived to calculate the appropriate time step size, by which the dissipation of the heat transfer can be compensated.

A Modified Shock Tracking–Capturing Finite-Volume Approach for Transient Mixed Flows in Stormwater Systems

“…Therefore, it was shown that this shockfitting approach can improve overpredicted peak values and it can predict the attenuation behavior observed in the solutions. In addition, Rokhzadi and Fuamba (2021) analyzed the contribution of numerical dissipation on the RC model's ability to solve the air pocket entrapment problem in transient flows. They showed that the time step size directly controls the numerical dissipation of implicit schemes.…”