Shock-Fitting Approach for Calculating Air Pocket Entrapment Caused by Full Obstruction in Closed Conduit Transient Flow

Abstract

This paper studies the ability of a Shock-Fitting approach in computing air pocket entrapments in a closed conduit transient flow, caused by suddenly blocking the downstream end. The flow is pressurized at the upstream, which detaches from the wall somewhere at the downstream after which a free surface flow develops. In this Shock-Fitting approach a pressurized flow is simulated by the rigid column model and the free surface flow is simulated by the Saint-Venant equations set. A transient region, which is characterized by the speed of the discontinuity, links these two flow regimes. The relevant governing equations of the rigid column model and the transient region are solved using the backward Euler temporal scheme and the Saint-Venant equations set is solved using the method of characteristics. It was found that this Shock-Fitting approach is able to predict the attenuation behavior as well as to calculate the flow variables more efficiently than the rigid column model and the modified Saint-Venant equations. By means of a linear stability analysis, it was shown that these improvements are provided by the speed of discontinuity in the transient region and the pressurized water column length.

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

“…Recently, the backward Euler implicit scheme has been used in [13] to simulate the dynamics of the entrapped air pocket using the 3D Navier-Stokes equation and the volume of fluid (VOF) method. In addition, Rokhzadi and Fuamba [14] proposed using the backward Euler implicit scheme to solve a similar problem by a shock-fitting approach.…”

“…Rokhzadi and Fuamba [14], for problems with small ratios of the reservoir pressure to the atmospheric pressure, used a shock-fitting approach, which is a combination of the RC model and the Saint-Venant equations. Rokhzadi and Fuamba proposed using the BE scheme instead of the 4th-RK scheme.…”

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

“…In addition, this method is able to automatically handle the supercritical conditions that may occur in the free-surface flow zone because interface fluxes are calculated by solving a Reimann problem (León et al 2010). Rokhzadi and Fuamba (2020), using the shock-fitting approach, which is a combination of the RC model and the Saint-Venant equations, calculated an air pocket entrapment problem in a partially pressurized transient flow. They showed that, compared to the fourth-order Runge-Kutta explicit time integration scheme, the dissipation property of the backward Euler implicit scheme can take the extra energy, which is left due to the RC model assumptions (Malekpour and Karney 2014) as well as due to neglecting the heat transfer process between the air and pipe wall (Lee 2005).…”