Numerical Simulation of Water Pipeline Filling Events with Limited Ventilation

Water mains filling procedure follow certain maintenance operations that require the emptying of pipelines. These procedures are performed carefully in order to prevent air pocket formation, as such pockets may trigger damaging surges, as well impose blockages that reduce pipe conveyance. While previous research addressed the modeling of the pipeline filling events, the air phase within the conduits is in most cases either not included in the simulation, or its formulation is very simplified, not including air pressure gradients. This article presents an ongoing work which aims to couple a Two-Component Pressure Approach model to simulate water flow with a discretized model for air phase flow within the conduits based on the isothermal Euler equations. The proposed model includes improvements in source terms calculations, and the main goal is to create a modeling framework able to represent a diverse range of flow conditions in water mains. A test case, which is a modified version of the experimental setup presented by Trajkovic, et al. (1999) is used to present the preliminary results of the proposed model. INTRODUCTION Water mains are important components of the urban infrastructure designed to operate in pressurized flow mode, but under abnormal operational conditions air phase may be present within the conduits. Such conditions are more commonly observed during the filling and emptying of water mains, but may also occur following accidental water main ruptures, or when water demand exceeds supply, in which case the pipes act as reservoirs. In the process of reestablishing normal operational conditions, the air within the conduits is eliminated by air valves, located at selected points along the pipeline length. Yet, even with the air valves, the refilling process is often performed very cautiously due to the potentially damaging surges that may occur due to the air-water interactions during the filling event. Because of the uncertainties related to these interactions, the filling is generally performed slowly, and the restoring of normal pipeline conditions may take several hours, or even days, depending on the event that caused disruption of the distribution system. This flow interruption has major impacts in water consumers, and the ability to quickly and safely restore operational conditions in water mains is very much desirable. Numerical models represent a feasible way to minimize the uncertainties related to the air-water interactions during the filling process. Three dimensional, CFD packages are a possible solution, but considering the length of the pipeline systems, the flow unsteadiness, and the time scale of the filling events (up to several hours of unsteady flow conditions), these solutions are not practical yet. One dimensional, unsteady flow models would be an alternative, but they also have limitations. Current unsteady flow models in use by water work authorities, usually applied to assess waterhammer effects and closed pipe surges, usually assume homogeneous, single-phase flow conditions. By contrast, the refilling process has several flow portions in two-phase, stratified flow conditions, invalidating the use of those single phase models, as demonstrated by Vasconcelos and Marwell (2008). These stratified flows are observed during the transition between free surface and pressurized flows (Wright et al., 2008), and may be simulated by models that are able to handle this transition. Vasconcelos (2007) proposed an innovative method to simulate the filling of water mains using a flow regime transition model based on the Saint-Venant equations modified by the Two-component Pressure Approach (Vasconcelos et al., 2006). This model was in fact able to simulate the regions of stratified flow conditions during the refilling of water mains, but could not account for air pressurization as it was assumed ideal ventilation conditions. This hypothesis regarding air ventilation has its limitations, as demonstrated in the work by Vasconcelos et al. (2009). The actual filling of a 350-mm, 4.5 km long ductile iron water main was monitored, measuring flow rates and pressures at selected locations. Measurements were compared with the predictions by Vasconcelos (2007) model. Deviations between model and field measurements were significant for an initial configuration when ventilation conditions were limited. In a subsequent filling, with additional air valves, the predictions approached better field measurements, yet some discrepancies persisted, and were still attributed to air pressurization. While several important studies have addressed the effects of entrapped pockets in pressurized flows (Falvey, 1980; Estrada, 2007; Little et al. 2008; among others) the linking of those effects to one-dimensional numerical modeling is still limited. Among previous investigations related to this topic, one includes the works by Martin (1976), Li and McCorquodale (1999), Izquierdo et al. (1999) and Zhou, et al. (2002). These models rely on lumped inertia approach, assuming well defined airwater interfaces, which are not applicable to the expected conditions during gradual filling of long, sloped water mains. Recently, Vasconcelos and Wright (2009) and Leon, et al. (2009) proposed models that are based on the Saint-Venant equation and can also handle air pressurization in the context of the rapid filling of stormwater storage tunnels. Yet those models assume uniform air pressure within the air pocket, a condition that may not be realistic when the pocket length is very large, such as in the case of water main filling events. Finally, a model proposed by Arai and Yamamoto (2003) simulates the rapid filling of closed conduits using a discretized formulation for air phases. The 4-point, linear, implicit finite-difference scheme used to solve the flow is unconditionally stable, however is not adequate to simulate discontinuities such as bores due to numerical diffusion (Toro, 2001). In summary, the filling of water main represents a complex flow condition that may trigger serious operational problems. These fillings could be performed more rapidly if the uncertainties related to air-water interactions were reduced. Some numerical modeling efforts have aimed towards the description of these flows, but model limitations include the inability to handle air pressurization, the assumption that air pressure is uniform within the pocket or use. It is desirable to improve current modeling capabilities by coupling an unsteady, discretized flow solver to simulate the air phase during the filling process. OBJECTIVES This paper presents results of an ongoing investigation performed at Auburn University, aiming towards the improvement of the model proposed by Vasconcelos (2007) by adding the capability of dealing with pressurized air pockets. The simulation of air phase is performed by solving the isothermal Euler equations throughout the extent of the shrinking air pocket. Air pressurization is accounted in the unsteady water flow simulation by adding an additional term in the Saint-Venant equations, as described in Vasconcelos and Wright (2009). To test the model results, a series of hypothetical rapid filling flows is simulated based on the geometry of the experimental work presented by Trajkovic, et al. (1999). Key variables such as the effect of initial flow rates and ventilation sizes are systematically investigated. METHODOLOGY Mathematical Model The mathematical model which is the basis for the proposed approach is a modified version of the Saint-Venant equation which is able to simulate flow regime transition between free surface and pressurized flow regimes. The work by Vasconcelos and Wright (2009) is based on the Two-component Pressure Approach (Vasconcelos et al., 2006), further modified to incorporate air phase pressurization is presented in equations 1 and 2 in conservative divergent form: