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Multiphase Flows

A Two-Way Coupled Polydispersed Two-Fluid Model for the Simulation of Air Entrainment Beneath a Plunging Liquid Jet

[+] Author and Article Information
Jingsen Ma

 Center for Multiphase Research, Rensselaer Polytechnic Institute, Troy, NY 12180jingsen.ma@gmail.com

Assad A. Oberai1

 Center for Multiphase Research, Rensselaer Polytechnic Institute, Troy, NY 12180oberaa@rpi.edu

Donald A. Drew

 Center for Multiphase Research, Rensselaer Polytechnic Institute, Troy, NY 12180drewd@rpi.edu

Richard T. Lahey

 Center for Multiphase Research, Rensselaer Polytechnic Institute, Troy, NY 12180laheyr@rpi.edu

1

Address all correspondence to this author.

J. Fluids Eng. 134(10), 101304 (Sep 28, 2012) (10 pages) doi:10.1115/1.4007335 History: Received March 01, 2011; Revised May 29, 2012; Published September 27, 2012; Online September 28, 2012

Plunging liquid jets are commonly encountered in nature and are widely used in industrial applications (e.g., in waterfalls, waste-water treatment, the oxygenation of chemical liquids, etc.). Despite numerous experimental studies that have been devoted to this interesting problem, there have been very few two-phase flow simulations. The main difficulty is the lack of a quantitative subgrid model for the air entrainment process, which plays a critical role in this problem. In this paper, we present in detail a computational multiphase fluid dynamics (CMFD)-based approach for analyzing this problem. The main ingredients of this approach are a comprehensive subgrid air entrainment model that predicts both the rate and location of the air entrainment and a two-fluid transport model, in which bubbles of different sizes are modeled as a continuum fluid. Using this approach, a Reynolds-averaged Navier Stokes (RaNS) two-way coupled two-phase flow simulation of a plunging liquid jet with a diameter of 24 mm and a liquid jet velocity around 3.5 m/s was performed. We have analyzed the simulated void fraction and bubble count rate profiles at three different depths beneath the average free surface and compared them with experimental data in literature. We observed good agreement with data at all locations. In addition, some interesting phenomena on the different movements of bubbles with different sizes were observed and discussed.

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Copyright © 2012 by American Society of Mechanical Engineers
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Figures

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Figure 1

Schematic diagram of experimental setup [(40),41]

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Figure 2

Computational domain and mesh, where the dark horizontal surface represents the free surface

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Figure 3

Distribution of the kernel of the entrainment source strength, k(∂un/∂n), for the plunging jet problem with uj = 3.5 m/s: (a) slice through center of the jet, where the white line represents the free surface; (b) three-dimensional view of the free surface

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Figure 4

A typical snapshot of void fraction distribution

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Figure 5

A comparison of void fraction contours predicted by: (a) two-way coupling simulation with turbulent dispersion model turned on; (b) two-way coupling simulation with the turbulent dispersion model inactive; (c) one-way coupling with the turbulent dispersion model turned on; (d) one-way coupling with the turbulent dispersion model inactive

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Figure 6

Temporally and circumferentially averaged void fraction profiles at 0.8 Dj (top), 1.2 Dj (middle), 2.0 Dj (bottom). Interested readers are referred to our previous work [36] for a comparison with monodispersed, one-way coupled results.

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Figure 7

Temporally and circumferentially averaged bubble count rate profiles at 0.8 Dj (top), 1.2 Dj (middle), 2.0 Dj (bottom)

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Figure 8

Void fraction contours for bubbles with diameters of 1 mm (top), 5 mm (middle), 9 mm (bottom), predicted by two-way coupling modeling, with turbulent dispersion model being inactive

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Figure 9

Comparison of void fraction profiles for bubbles with diameters of 1 mm, 5 mm, 9 mm, predicted by two-way coupling modeling, with turbulent dispersion model being inactive

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