[en] Finite volume method ; Homogeneous Equilibrium Model ; Preissmann slot ; Local Instant Formulation ; Air-entrainmen ; Hydraulic engineering
[fr] Ecoulement ; Transport d'air ; Hydraulique
[en] Hydraulic 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.
Aquapôle - AQUAPOLE
Fonds de la Recherche Scientifique (Communauté française de Belgique) - F.R.S.-FNRS