Lecture notes on multiphase flow fundamentals @Kobe University

Contents

• 1. Local instantaneous equations
  • 1.1. Governing equations
  • 1.2. Jump conditions
  • 1.3. Interface tracking
• 2. Void fraction
  • 2.1. Averaged quantities
  • 2.2. Drift-flux model
• 3. Two-phase pressure drop
  • 3.1. Global balance in steady upward flow
  • 3.2. Frictional pressure drop: Homogeneous model
  • 3.3. Frictional pressure drop: Lockhart-Martinelli correlation
• 4. Annular flow
  • 4.1. Upward co-current annular flow
  • 4.2. Counter-current annular flow
  • 4.3. Counter-current limitation
• 5. Averaged equations
  • 5.1. Averaging basic equations
  • 5.2. Interfacial momentum transfer
• 6. Analysis of bubble rise motion
  • 6.1. Dimensionless groups
  • 6.2. Bubble velocity correlations
  • 6.3. Shape deformation
• 7. Virtual mass
• 8. Drag force acting on spherical body
  • 8.1. Drag acting on a solid sphere in Stokes flow (LL)
  • 8.2. Drag acting on a fluid sphere in Stokes flow
  • 8.3. Drag acting on a spherical bubble at high \(Re\)
• 9. Vorticity-related problems
  • 9.1. Drag acting on a solid sphere in Stokes flow (GKB)
  • 9.2. Drag-enstrophy relation
  • 9.3. Drag-vorticity relation
  • 9.4. Lift acting on spherical body in inviscid flow with weak shear
  • 9.5. Basset (history) force on a solid sphere in Stokes flow
• 10. Deformed bubbles
  • 10.1. Large bubbles in liquid
  • 10.2. Wave analogy for bubble rise velocity
  • 10.3. Lift reversal
• 11. Taylor bubble: bullet-shaped bubbles in pipe
  • 11.1. Order-of-magnitude analysis for bubble velocity
  • 11.2. Lubrication of liquid film
  • 11.3. Bretherton problem
• 12. Contaminated system
  • 12.1. Isotherm and surfactant kinetics
  • 12.2. Surfactant transport
  • 12.3. Contaminated drops in Stokes flow
  • 12.4. Bretherton problem with surfactant

Appendix

• Mathematics tips
  • Some useful identities
  • Polar and axial vectors
  • Biot-Savart law
  • \(\nabla^{2} (1/r)\) behaves as Dirac’s delta
• Fluid mechanics fundamentals
  • Continuity and NS equations in polar coordinate systems
  • Viscous dissipation
  • Potential flow about sphere
  • Water wave of infinitesimal amplitude
  • Vorticity equation
  • Helmholtz’s law
  • Vorticity in terms of drift function
  • Biot-Savart field by uniform line vorticity

References

• References