A robust two-equation model for transient-mixed flows

Abstract

A finite volume model was built upon earlier work with the aim of simulating free surface flows, pressurized flows and their simultaneous occurrence (mixed flows) in single-liquid and two-phase flow conditions (entrapment and release of air pockets). The model presented herein is based on a two-governing equation model. Three main contributions are presented herein, namely: (1) the ability of the proposed model to simulate mixed flows without restriction of the flow type in the free surface region (e.g., supercritical flow), (2) extension of our single-phase flow model for simulating the entrapment and release of air pockets, and (3) formulation of an approach for handling numerical instabilities that may occur during numerical pressurization of the flow. The model presented herein is robust and simulates any transient-mixed flow condition for realistic pressure wave celerities.

Optimizing Intermittent Water Supply in Urban Pipe Distribution Networks

“…The Preissman slot approach has been used, for example, by Trajkovic et al [32], who compared the model with experimental data; by Kerger et al [16], who implemented an exact Riemann solver and introduced a "negative slot" modification to handle subatmospheric pressure; by León et al, [22], who allowed the pressure wave speed to vary slightly; and by Borsche and Klar [1], who used a hexagonal cross-section to simplify the area-height relationship. Other transient flow models for air and water in single pipes include a "two-component pressure" approach [37,34]; a single-equation model with a modified pressure term [3,4]; a two-component model [23]; and a three-phase model accounting for air, air-water mixture, and water [15].…”

“…In practice, the slot width T s is a parameter chosen to set the value of pressure wave speed a, which may range from 20-1250 m/s [37] depending on practical context and numerical constraints. In each pipe, the governing equations for A and Q are the de St. Venant equations for free-surface flow [16,23], where L is the length of the pipe, T is the duration of the study period, and…”

“…For sewer flow, Sanders [30] presents a network implementation of the two-component pressure approach (TPA) of Vasconcelos [37]. The modeling for ITM was published by León in [23]. Urban water drainage is coupled to free surface flow by Borsche and Klaar [1].…”

Three-phase bi-layer model for simulating mixed flows

“…However, no model integrates the effect of both air-entrainment and air-entrapment in transient mixed flows. In addition, all shock-capturing models are known to develop posttransition oscillations (Politano et al 2007, Leon et al 2010). This problem is linked to the rapid variation of the pressure wave celerity at the transition ).…”

“…First, an overpressure term is added in the TPA model to account for the pressurization of the air pocket above the free surface (Vasconcelos et al 2006). Leon et al (2010) proposed similarly a two-equation model that adequately simulates the entrapment and release of air. They added equations describing steady free-surface flows by the ideal gas law.…”