Propagation of large air pockets in ducts. Analytical and numerical approaches
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Applied Mathematical Modelling
Air cavity propagationGeyseringInterface dynamicsTwo phase-flowsContinuous finite elements
Molina, J., & Ortiz, P. (2022). Propagation of large air pockets in ducts. Analytical and numerical approaches. Applied Mathematical Modelling, 110, 633-662.
SponsorshipThis work was supported by the Grant #PID2020-115778GB-I00 funded by MCIN/AEI/10.13039/501100011033.; Open access charge was funded by Universidad de Granada / CBUA.
This paper presents analytical and numerical methods to compute intrusion of air pockets and geysering events in sewer systems. The theoretical approach, accomplished by a control volume analysis, takes into account gas expansion effects and free surface position to determine impulsion of water above the bubble. This analytical model is able to predict dynamics of single and consecutive elongated rising bubbles, revealing conditions that contribute to a sudden bubble decompression, and therefore to a severe geysering event. A non-oscillatory finite element method (NFEM) for fluid interface flows is the basis to construct the numerical model. The method assures positivity of phase function, reduces spurious momentum transfers between phases, and integrates a modified continuity equation to preserve mass under the weak compressibility assumption. Numerical simulations scrutinize conditions for emergence of air pockets in ducts, giving rise to simple solutions that provide the required flow rate to avoid the intrusion of cavities. Axisymmetric and complete three dimensional numerical models are used to perform rising Taylor bubbles and geysering experiments, to complement analytical results by giving precise flow details, in particular above the ground level.