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Research Papers: Multiphase Flows

The Phenomenon of Bubbles Negative Relative Velocity in Vertical Bubbly Jets

[+] Author and Article Information
Jamel Chahed

University of Tunis El Manar,
National Engineering School of Tunis,
BP N°37, Le Belvedere,
Tunis 1002, Tunisia
e-mail: jamel.chahed@enit.rnu.tn

Aroua Aouadi

University of Tunis El Manar,
National Engineering School of Tunis,
BP N°37, Le Belvedere,
Tunis 1002, Tunisia
e-mail: aroua.aouadi@gmail.com

Mariem Rezig

University of Tunis El Manar,
National Engineering School of Tunis,
BP N°37, Le Belvedere,
Tunis 1002, Tunisia
e-mail: rezig.mariem@gmail.com

Ghazi Bellakhal

University of Tunis El Manar,
National Engineering School of Tunis,
BP N°37, Le Belvedere,
Tunis 1002, Tunisia
e-mail: ghazi.bellakhal@enit.rnu.tn

1Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received December 14, 2015; final manuscript received May 31, 2016; published online August 11, 2016. Assoc. Editor: Mark R. Duignan.

J. Fluids Eng 138(12), 121301 (Aug 11, 2016) (11 pages) Paper No: FE-15-1921; doi: 10.1115/1.4033842 History: Received December 14, 2015; Revised May 31, 2016

Many experiments demonstrate that the bubble relative (slip) velocities in vertical turbulent sheared bubbly flows are significantly lower than those in quiescent infinite fluid. Moreover, vertical bubbly jet experiments performed by Sun and Faeth (1986, “Structure of Turbulent Bubbly Jets-1. Methods and Centerline Properties,” Int. J. Multiphase Flow, 12(1), pp. 99–114) indicate that bubble slip velocities have negative values in the high sheared zone near the injector. The present analysis shows that the phenomenon of the slip velocity inversion is associated with the effect of the turbulent part of the interfacial force. A new formulation of the turbulent contribution of the added mass force is proposed. This formulation is analyzed using the vertical bubbly jet experimental data. The results provide evidence that the turbulent contribution of the added mass force is at the origin of the slip velocity reduction and could explain the appearance of the negative values observed in bubbly jet experiments. As a whole, the turbulent contribution of the added mass force which comprises two terms (a nonlinear turbulent term and a convective acceleration term associated to the drift velocity) opposes the action of the gravity and their effect may be high enough to produce negative slip velocities. Taken separately, the two turbulent terms cannot explain the reversal and the reduction of slip through the entire section in the near injection zone of the bubbly jet. The combined effect of the two turbulent terms makes it possible to reproduce slip velocity profiles as observed in the near injection zone.

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References

Figures

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Fig. 1

Schematic diagram of the vertical bubbly jet

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Fig. 2

Mean slip velocity of the bubbles (case 1). Experimental data from Ref. [31]: solid symbols for bubble averaging; open symbols for time averaging.

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Fig. 7

Average longitudinal slip velocity (case 1, x/d = 8). Lines: calculation results (effect of the turbulent nonlinear term from the added mass force). Symbols: experimental data from Ref. [31].

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Fig. 6

Average longitudinal slip velocity (case 1, x/d = 8). Lines: calculation results (effect of the average part of the added mass force). Symbols: experimental data from Ref. [31].

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Fig. 9

Average longitudinal slip velocity (case 1, x/d = 8). Lines: calculation results (adjustment of the turbulent contribution of the added mass force). Symbols: experimental data from Ref. [31].

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Fig. 5

Turbulent shear stress profiles (case 1). Symbols: experimental data from Ref. [31]; lines: polynomial fittings.

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Fig. 4

Normalized void fraction profiles (case 1). Symbols: experimental data from Ref. [31]; lines: exponential fittings.

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Fig. 3

Average liquid velocity profiles (case 1). Symbols: experimental data from Ref. [31]; lines: exponential fittings.

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Fig. 8

Average longitudinal slip velocity (case 1, x/d = 8). Lines: calculation results (effect of the added mass force related to the acceleration due to the drift velocity). Symbols: experimental data from Ref. [31].

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Fig. 10

Average longitudinal slip velocity (case 1). Lines: calculation results (adjustment of the turbulent contribution of the added mass force). Symbols: experimental data from Ref. [31] (solid symbols for bubble averaging; open symbols for time averaging).

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Fig. 11

Average longitudinal slip velocity (case 2). Lines: calculation results (adjustment of the turbulent contribution of the added mass force). Symbols: experimental data from Ref. [31] (solid symbols for bubble averaging; open symbols for time averaging).

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Fig. 12

Average longitudinal slip velocity (case 3). Lines: calculation results (adjustment of the turbulent contribution of the added mass force). Symbols: experimental data from Ref. [31] (solid symbols for bubble averaging; open symbols for time averaging).

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