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Research Papers: Fundamental Issues and Canonical Flows

# The Virtual Mass Theory of a Taylor Bubble Rising in Vertical Pipes

[+] Author and Article Information
Abdullah Abbas Kendoush

Department of Nuclear Engineering Technology,
Augusta Technical College,
Augusta, GA 30906
e-mail: akendoush@augustatech.edu

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received February 17, 2017; final manuscript received November 5, 2017; published online January 9, 2018. Assoc. Editor: Oleg Schilling.

J. Fluids Eng 140(5), 051202 (Jan 09, 2018) (6 pages) Paper No: FE-17-1103; doi: 10.1115/1.4038663 History: Received February 17, 2017; Revised November 05, 2017

## Abstract

Analytical solutions were obtained for the virtual mass of a Taylor bubble rising in a liquid confined by a circular pipe under transient conditions. The solution of the virtual mass coefficient was based on potential inviscid flow. The present solution is applicable to low viscosity liquids and to Capillary number ($Ca)<0.005$. The virtual mass solution showed dependence on bubble geometry. The present solution was validated by comparison with the available numerical solutions and experimental data of other investigators.

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Topics: Bubbles , Pipes
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## Figures

Fig. 1

The two types of Taylor bubbles rising in (a) highly viscous liquid and (b) less viscous liquid

Fig. 2

Partitions of the various flow regions around the Taylor bubble

Fig. 3

The variation of the virtual mass coefficient with the geometrical ratio of the Taylor bubble

Fig. 4

The variation of the virtual mass coefficient of the Taylor bubble with the volume fraction

Fig. 5

Comparison with Wang and Tong's [26] numerical solution (continuous line) and present solution Eq. (34) (dashed line)

Fig. 6

Comparison of the present solution (Eq. (38)) (--- - ---), with the experimental data of Talvy et al. [34] (□), the experimental correlation of Moissis and Griffith [35] (-----), and the experimental correlation of Pinto and Campos [9] (-- -- --)

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