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Technical Brief

# On the Ideal Grid Resolution for Two-Dimensional Eulerian Modeling of Gas–Liquid Flows

[+] Author and Article Information
Robert Picardi, Lei Zhao

Department of Mechanical Engineering (MC 0238),
Virginia Polytechnic Institute and State University,
Goodwin Hall, Room 210,
Blacksburg, VA 24061

Francine Battaglia

Fellow ASME
Department of Mechanical Engineering (MC 0238),
Virginia Polytechnic Institute and State University,
Goodwin Hall, Room 227,
Blacksburg, VA 24061
e-mail: fbattaglia@vt.edu

1Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received January 10, 2016; final manuscript received April 19, 2016; published online July 15, 2016. Assoc. Editor: Samuel Paolucci.

J. Fluids Eng 138(11), 114503 (Jul 15, 2016) (6 pages) Paper No: FE-16-1017; doi: 10.1115/1.4033561 History: Received January 10, 2016; Revised April 19, 2016

## Abstract

A study was performed to investigate the interesting observation that when using an Eulerian–Eulerian model to simulate a bubble column flow in two dimensions, accuracy did not always increase with increasing grid resolution. A correlation was found between the characteristic bubble diameter numerically specified and grid size, which identified a threshold where results lose physical meaning. An ideal relationship between grid size and bubble diameter was determined to optimize grid resolution and retain accuracy. The two-dimensional (2D) Eulerian model was validated using the experimental data of Rampure et al. (2003, “Modelling of Gas-Liquid/Gas-Liquid-Solid Flows in Bubble Columns: Experiments and CFD Simulations,” Can. J. Chem. Eng., 81(3–4), pp. 692–706). Further studies demonstrated that grid resolution could be increased to improve the numerical accuracy for three-dimensional (3D) simulations of the bubble column. The novel contributions of this study will show that the ratio of bubble diameter-to-grid cell size should equal $1/2$ for the 2D simulations.

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## Figures

Fig. 1

Two-dimensional geometry (or centerplane) of a bubble column

Fig. 2

Air volume fraction profiles at (a) y = 0.15 m and (b) y = 0.65 m for the 2D grid resolution study (db = 0.5 cm)

Fig. 3

Sketch of a computational grid cell, depicting the ideal bubble diameter-to-cell size relationship

Fig. 4

Air volume fraction profiles at y = 0.15 m for different grid resolutions when (a) db = 0.5 cm, (b) db = 0.35 cm, and (c) db = 0.2 cm. The ideal case for each scenario is denoted by the solid (red) line.

Fig. 5

Instantaneous air volume fraction contours for grid resolutions of (a) 15 × 150, (b) 30 × 300, and (c) 60 × 600 with db = 0.5 cm

Fig. 6

Air volume fraction profiles at (a) y = 0.15 m and (b) y = 0.65 m for the 3D grid resolution study (db = 0.5 cm)

Fig. 7

Air volume fraction profiles at (a) y = 0.15 m and (b) y = 0.65 m for the 2D and 3D cases (db = 0.5 cm)

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