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.