Abstract
The accurate prediction of self-aerated flow is not always easy to obtain, particularly if the computational performance is the main concern. Two-fluid formulation is suitable to simulate the dispersed air in a continuous water phase (e.g. bubbly flows) in a fine mesh, whereas the interface tracking methods are used for sharp interfaces with two continuous and contiguous phases (e.g. free-surface flows). Several approaches have emerged to combine both methods; however all found a gap in the transition between resolved and unresolved scales of air at the interface. Including a source term that predicts the self-aeration process is viewed as a promising step to overcome such difficulty. In this work, we added to the volume-of-fluid formulation an extra advection-diffusion equation connected to a source of air at the free surface to simulate the dispersed bubble phase. One-way coupling and two-way coupling versions of this model are tested along with sensitivity tests to show the accuracy of the new source term that does not require calibration. The location of the aeration is analysed and investigated. Results are obtained in terms of free-surface flow depths, air–concentration profiles and velocity fields and compared to experimental data acquired in a scaled stepped spillway model with good agreement. The free-surface given by the air-entrainment model is in good agreement in both non-aerated and aerated zone of the spillway.
Funding statement: This study had the support of FCT (Portuguese Foundation for Science and Technology) through the Projects UID/MAR/04292/2013 and Grant SFRH/BD/85783/2012, financed by MEC (Portuguese Ministry of Education and Science) and FSE (European Social Fund), under the programs POPH/QREN (Human Potential Operational Programme from National Strategic Reference Framework) and POCH (Human Capital Operational Programme) from Portugal2020.
Acknowledgements
Pedro Lopes would like to acknowledge the facilities provided during a period of 3 months in 2014 as visiting student at FH-Aachen, Germany, from which the experimental results were obtained. All the numerical results here showed were performed in the Centaurus Cluster of the Laboratory for Advanced Computing of University of Coimbra, Portugal.
References
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