Calculating Column Separation in Conduit Systems Using an Innovative Open Channel Based Model

Abstract

An innovative numerical model called the Modified Two-Component Pressure Approach (MTPA) is proposed to better capture the physics of column separation in conduit systems. Based on the Two-Component Pressure Approach (TPA), the MTPA calculates both cavitating and pressurized flow using a single set of equations that governs unsteady flow in open channel flow. As opposed to shock-fitting-based models, in which a complex algorithm is needed to keep track of the interfaces separating the cavitating and liquid zones, the proposed model can capture both flow phases automatically. The first-order Godunov type finite volume method is utilized to numerically solve the equations. A customized Harten, Lax and Van Leer (HLL) Riemann solver is employed to calculate the fluxes at the computational cell boundaries and to dissipate potential post-shock oscillations generated when the cavity is collapsed and the open channel flow beneath the cavity is switched back to pressurized flow. The numerical results are shown to be in good agreement with both experimental data and the results obtained from the Discrete Gas Cavity Model (DGCM). A hypothetical test case is also presented to demonstrate the unique feature of the proposed model, which is the ability to simultaneously account for waterhammer, cavitation, and open channel flow regimes, a feature making the model even superior to the DGCM. Several numerical approaches are available to successfully calculate the induced waterhammer pressures following column separation. Existing 1D models based on these numerical approaches can help engineers quantify the impacts of column separation and design measures to protect the pipe system against this phenomenon. Nevertheless, most of the existing models used in the industry exclusive work with pipe systems that remain fully pressurized during transient flow. However, column separation may occur in pipe systems carrying concurrent open channel and pressurized flows. Examples of such systems and operating conditions are sewer conveyance and pipe system collection, intermittent water distribution systems, pump power failure in self-draining pumped pipelines, and pipeline filling and draining. To fill part of this gap, this paper presents a numerical open channel-based 1D model that can treat concurrent transient open channel, pressurized flow, and column separation. The model is validated using experimental data, numerical results from other models, and a hypothetical example. The results reveal that the model is accurate enough to be used in practical applications. The model can also calculate the shape and spread of vapor cavities across the pipe system, a feature that makes the proposed model superior to counterpart models.