1D unified mathematical model for environmental flow applied to steady aerated mixed flows

Abstract

a b s t r a c tHydraulic models available in literature are unsuccessful in simulating accurately and efficiently environmental flows characterized by the presence of both air-water interactions and free-surface/pressurized transitions (aka mixed flows). The purpose of this paper is thus to fill this knowledge gap by developing a unified one-dimensional mathematical model describing free-surface, pressurized and mixed flows with air-water interactions. This work is part of a general research project which aims at establishing a unified mathematical model suitable to describe the vast majority of flows likely to appear in civil and environmental engineering (pure water flows, sediment transport, pollutant transport, aerated flows. . .). In order to tackle this problem, our original methodology consists in both time-and spaceaveraging the Local Instant Formulation, which includes field equations for each phase taken separately and jump conditions, over a flow cross-section involving a free-surface. Subsequently, applicability of the model is extended to pressurized flows as well. The first key result is an original 1D Homogeneous Equilibrium Model which describes two-phase free-surface flows. It is proven to be fundamentally multiphase, to take into account scale heterogeneities of environmental flow and to be very easy to solve. Next, applicability of this free-surface model is extended to pressurized flows by using the classical Preissmann slot concept. A second key result here is the introduction of an original negative Preissmann slot to simulate sub-atmospheric pressurized flows. The model is then closed by using constitutive equations suitable for air-water flows. Finally, this mathematical model is discretised by means of a finite volume scheme and validated by comparison with experimental results from a physical model in the case of a steady flow in a large scale gallery.

A semi‐implicit numerical model for urban drainage systems

“…Pressurized or partially pressurized flows are often solved by introducing the so‐called Preissmann slot . Implementing the Preissmann slot technique has the advantage of using only one flow type (free surface flow) throughout the whole system and of being able to approximate the piezometric head when and where any section pressurizes . Nevertheless, the Preissmann slot is an artifice that unavoidably alters the physics of the problem, resulting into several side effects such as incorrect propagation speed that will hamper accuracy significantly in for instance dynamically controlled pipe network systems .…”

Analysis of Unsteady Friction Models Used in Engineering Software for Water Hammer Analysis: Implementation Case in WANDA

“…In water distribution systems, the source of transient events may be related to valve maneuvers, pump trips, load acceptance, or rejection of turbines [4]. Therefore, researchers, water utilities, and engineers are interested in understanding the nature, generation, and propagation of water hammer waves [5][6][7].…”

Suppress Numerical Oscillations in Transient Mixed Flow Simulations with a Modified HLL Solver

“…To simplify this question, we can reduce the number of governing equations by adopting one set of governing equations for both flow conditions. Based on this idea, the Preissmann slot model (PSM) is proposed by Cunge [11] and it has been adopted by many researchers and commercial software packages for its simplicity and accuracy [12][13][14][15][16][17][18]. The gradient of piezometric head at the interface between two flow regimes are very steep which forms a discontinuity in flow, therefore the governing equations are normally discretized using the state-of-art finite volume method for it admits discontinuous solutions [19].…”