Extension of the EMMS Model to Gas-Liquid Systems

  • Jinghai Li
  • Wei Ge
  • Wei Wang
  • Ning Yang
  • Xinhua Liu
  • Limin Wang
  • Xianfeng He
  • Xiaowei Wang
  • Junwu Wang
  • Mooson Kwauk
Chapter

Abstract

The Dual-Bubble-Size (DBS) model is an extension of the energy minimization multiscale (EMMS) approach for gas-liquid systems. The system is resolved into a liquid phase, small bubbles and large bubbles, and is jointly dominated by two movement tendencies; i.e., those of the small and large bubbles. A stability condition is formulated to reflect the compromise between these dominant mechanisms, offering another constraint in addition to mass and momentum conservation equations. The DBS model can theoretically predict the regime transition in bubble columns and physically explain the macro-scale evolution of flow structures through the jump change in the global minimum of the micro-scale energy dissipation changing from one point to another within the model space of the structure parameters. The DBS model is found to be an intrinsic model for gas-liquid systems in contrast to the models for single, triple, and multiple classes of bubble. A new model for the ratio of drag coefficient to bubble diameter, that is, the EMMS drag, is then integrated into the Eulerian-Eulerian computational fluid dynamics (CFD) models. The resulting improved prediction demonstrates the ability of the DBS model to reveal the multiscale nature and complexity of gas-liquid systems.

Keywords

Bubble column Computational fluid dynamics Mesoscale Meso-scale Multiphase flow Multiscale Multi-scale Stability condition 

Notation

CD

Drag coefficient for a bubble in a swarm, dimensionless

CD0

Drag coefficient for a bubble in a quiescent liquid, dimensionless

CD,p

Drag coefficient for a particle in multi-particle systems, dimensionless

cf

Coefficient of surface area increase, \( c_{\text{f}} = f_{\rm BV}^{2/3} + (1 - f_{\rm BV} )^{2/3} - 1 \), dimensionless

db

Bubble diameter, m

dL

Bubble diameter of large bubbles, m

dS

Bubble diameter of small bubbles, m

Eo

Eötvos number, dimensionless

fb

Volume fraction of gas phase, dimensionless

fL

Volume fraction of large bubbles, dimensionless

fS

Volume fraction of small bubbles, dimensionless

fBV

Breakup ratio of daughter bubble to its mother bubble, dimensionless

g

Gravitational acceleration, m/s2

Nbreak

Rate of energy consumption due to bubble breakage and coalescence per unit mass, m2/s3

Nsurf

Rate of energy dissipation due to bubble oscillation per unit mass, m2/s3

Nturb

Rate of energy dissipation in turbulent liquid phase per unit mass, m2/s3

Nst

Rate of energy dissipation for suspending and transporting particles per unit mass, m2/s3

NT

Total rate of energy dissipation

Pb

Bubble breakup probability, dimensionless

Ug

Superficial gas velocity, m/s

Ug,L

Superficial gas velocity for large bubbles, m/s

Ug,S

Superficial gas velocity for small bubbles, m/s

Ul

Superficial liquid velocity, m/s

Vrel

Relative velocity between gas and liquid, m/s

Greek Letters

εl

Volume fraction of liquid, dimensionless

λ

Character size of eddy, m

μ

Viscosity, Pa·s

ρ

Density, kg/m3

σ

Surface tension, N/m

ω

Collision frequency, 1/s

Subscripts

b

Bubble

g

Gas

l

Liquid

L

Large bubble

p

Particle

S

Small bubble

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Jinghai Li
    • 1
  • Wei Ge
    • 1
  • Wei Wang
    • 1
  • Ning Yang
    • 1
  • Xinhua Liu
    • 1
  • Limin Wang
    • 1
  • Xianfeng He
    • 1
  • Xiaowei Wang
    • 1
  • Junwu Wang
    • 1
  • Mooson Kwauk
    • 1
  1. 1.Institute of Process EngineeringChinese Academy of SciencesBeijingPeople’s Republic of China

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