Comparing Unsteady Modeling Approaches of Surges Caused by Sudden Air Pocket Compression

Abstract

The entrapment and compression of air in closed conduits is a relevant problem in pipeline systems that experience unsteady flow regimes. Severe surging resulting from large air compressibility leads to failures, structural damage and other operational issues.Various studies have been performed on the topic, most of which simplified the flow equations by adopting a lumped inertia approach to simulate the unsteady water flow, an implementation of the ideal gas law, momentum equation and air-water continuity equations. The modeling benefits of a discretized approach, such as the method of characteristics (MOC), to simulate the water phase have not been sufficiently investigated. To address this knowledge gap, this paper compares an MOC and a lumped inertia model in adverse pipe slope conditions involving sudden air pocket compression caused by the closure (partial or total) of a downstream knife gate valve. In laboratory experiments air pressures and flow rates were measured during various sudden air compression events, serving to assess the accuracy of each modeling approach. Results of the comparison indicate that the two hydraulic models have comparable accuracy for partial valve closure cases. For total valve closures, the models are comparable for smaller surge events but significantly diverge when maximum H/D values exceed 60 to 80. This feature did not depend on the pipe L/D ratio for the proposed experiments, but the magnitude of error was affected by this ratio, specifically when the air pocket volume was less than unity. Additional experiments are needed to better assess the effects of the pipeline L/D ratio and other geometrical parameters, such as slope, on peak surge predictions.

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

“…For this purpose, a closed conduit transient flow will be solved by a Shock-Fitting approach and solutions will be compared to the solutions of the rigid column model and the modified Saint-Venant equations as well as the experimental data of Hatcher et al (2015). 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).…”

“…1). Following the experiment of Hatcher et al (2015), the pipeline diameters are set as D ¼ 53 mm and 102 m with the total length L t ¼ 10.7 m and L t ¼ 12 m and adverse slopes S ¼ 2% and S ¼ 1.3%, respectively. The pipe material is clear PVC with Manning roughness coefficient n ¼ 0.009.…”

“…where H a is the air pocket absolute pressure head and V u and L u are the velocity and the length of the pressurized water column, respectively. The parameters f and K loss are the Darcy friction factor and the summation of the local loss coefficients, respectively, which are assumed constant with given values f ¼ 0.025 and K loss ¼ 2.9, similar to Hatcher et al (2015) and Vasconcelos and Leite (2012). Note that this friction factor value, in the Moody diagram, corresponds to a fully turbulent flow with the relative pipe roughness ε ¼ 0.002.…”

“…Note that the upstream pressure head (H u ) is assumed to be constant and is calculated using the steady state condition as subsequently explained. Following Vasconcelos and Leite (2012) and Hatcher et al (2015), the air absolute pressure head (H a ) is calculated using a polytropic process as…”

“…Vasconcelos and Leite (2012), by using the RC model, experimentally and numerically investigated air pocket entrapments, caused by completely and partially closing a gate valve at the downstream. Subsequently, Hatcher et al (2015) studied the same problem, experimentally and numerically, using the RC model as well as the modified Saint-Venant equations set (MSV). Both models predicted the solutions with reasonable tolerance of accuracy, except for the total valve closure in which both models significantly overestimated peak values as well as these models were unable to predict attenuation behaviors attributed to these transient flows.…”