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.