Finite volume method; Homogeneous Equilibrium Model; Preissmann slot; Local Instant Formulation; Air-entrainmen; Hydraulic engineering; Ecoulement; Transport d'air; Hydraulique
Abstract :
[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.
Research center :
Aquapôle - ULiège
Disciplines :
Civil engineering
Author, co-author :
Kerger, François
Erpicum, Sébastien ; Université de Liège - ULiège > Département Argenco : Secteur MS2F > Hydraulique génér., const. hydraul. et méc. des fluides
Dewals, Benjamin ; Université de Liège - ULiège > Département Argenco : Secteur MS2F > Hydrodynamique appl. et constructions hydrauliques (HACH)
Archambeau, Pierre ; Université de Liège - ULiège > Département Argenco : Secteur MS2F > Hydrodynamique appl. et constructions hydrauliques (HACH)
Pirotton, Michel ; Université de Liège - ULiège > Département Argenco : Secteur MS2F > Hydrodynamique appl. et constructions hydrauliques (HACH)
Language :
English
Title :
1D unified mathematical model for environmental flow applied to steady aerated mixed flows
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