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.
Highlights
The ground level water and rainfall amounts are conducted through below-grade closed conduit systems, in which the flow regime is mostly a free surface flow
The undertaken Shock-Fitting approach includes the rigid column model, applied to the upstream pressurized flow, in which the relevant governing equations are solved using the implicit backward Euler scheme and the Saint-Venant equations set applied to the downstream free surface flow, which is solved by the method of characteristics (MOC)
The results of the Shock-Fitting approach, hereafter called RCSV representing the rigid column model applied to the pressurized flow and the Saint-Venant equations applied to the free surface flow, is compared to the experimental data of Hatcher et al (2015), called EXP, as well as their numerical solutions calculated by the rigid column model, called RC, and the modified Saint-Venant equations solved by MOC method, called modified Saint-Venant equations set (MSV)
Summary
The ground level water and rainfall amounts are conducted through below-grade closed conduit systems, in which the flow regime is mostly a free surface flow. The two-components pressure approach (TPA), an alternative to the Preissmann slot, was proposed by Vasconcelos et al (2006) and further studied by Vasconcelos and Wright (2007) and Vasconcelos and Marwell (2011) to overcome the inability of the Preissmann slot model in calculating subatmospheric pressures. This approach can capture the relevant experimental data with a good agreement; it is subject to oscillatory behaviors, in presence of high pressure wave speeds (Bousso et al 2013). The main disadvantages of these models are that they are expensive and difficult to implement
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