Effect of Bath Depth and Nozzle Geometry on Spout Height in Submerged Gas Injection at Bottom

  • Junbing Xiao
  • Hongjie YanEmail author
  • Liu Liu
  • Felix Möller
  • Zhiwen Hu
  • Sebastian Unger


Spout height is a widely used parameter to quantitatively analyze the performance of the submerged gas injection in industrial applications. However, the effect of bath depth and nozzle geometry on spout height in submerged gas injection is still unclear. In this work, the effect of bath depth and nozzle geometry on spout height in submerged gas injection at bottom was experimentally investigated. Circular-shaped, three-leaf-shaped, four-leaf-shaped, and four-flower-shaped nozzles were used for this study. Spout height was extracted from the images captured by high-speed camera and analyzed by digital image processing. The results indicate that the effect of nozzle geometry on spout height is as important as gas flow rate and bath depth. Through dimensional analysis, predictive correlations of spout height from circular shape and four-leaf shape were developed with dimensionless bath depth and a modified Froude number using orifice perimeter and opening area as characteristic parameters. Experimental data were compared with the correlations from literature and good agreement was found.

List of Symbols

A, a, B, b, c, d, e, f, j, k, l

Symbols (dimensionless)


Constants (dimensionless)


Orifice opening area (m2)


Constants (dimensionless)


Constants (dimensionless)


Nozzle diameter without internal geometry (m)


Gravitational acceleration (m/s2)


Spout height (m)


Bath depth (m)


Instantaneous spout height from image i (m)

\( \bar{h} \)

Time-averaged spout height (m)

\( \bar{h}_{\text{d}} \)

Depth-averaged spout height (m)


Mean spout height (m)


Index for bath depth (dimensionless)


Unknown constants (dimensionless)


Independent physical unit (m)


Orifice perimeter (m)


Independent physical unit (kg)


Error due to the first source (m)


Error due to the second source (m)


Total uncertainties of measured spout height (Percent)


Gas flow rate (m3/s)


Independent physical unit (s)


Vessel width (m)

Greek Letters


Opening ratio (dimensionless)


Gas density (kg/m3)


Liquid density (kg/m3)


Kinematic viscosity (m2/s)


Deviation for analyzing the influence of bath depth on spout height (dimensionless)


Deviation or analyzing the influence of nozzle geometry on spout height (dimensionless)

Latin Letters


Number (dimensionless)



This work was financially supported by the National Natural Science Foundation of China (No. 51676211), Key R&D Plan of Hunan Province of China (No. 2017SK2253), and Fundamental Research Funds for the Central Universities of Central South University (No. 2015zzts044). One of the authors (J. XIAO) gratefully acknowledges the financial support from China Scholarship Council. The authors appreciate the help from Mr. Alexander Döß in this manuscript.

Conflict of interest

The authors declare that they have no conflicts of interest to this work.


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Copyright information

© The Minerals, Metals & Materials Society and ASM International 2019

Authors and Affiliations

  • Junbing Xiao
    • 1
  • Hongjie Yan
    • 1
    Email author
  • Liu Liu
    • 1
  • Felix Möller
    • 2
  • Zhiwen Hu
    • 1
  • Sebastian Unger
    • 2
  1. 1.School of Energy Science and EngineeringCentral South UniversityChangshaChina
  2. 2.Institute of Fluid DynamicsHelmholtz-Zentrum Dresden-RossendorfDresdenGermany

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