1. Lecture 16
Multiphase flows
Part 1

2. Mixture of different phases
Gas
Liquid
Solid

3. Four categories of multiphase flows
Gas-liquid or liquid-liquid flows
Gas-solid particle flows
Liquid-solid flows
Three-phase flows

4. Gas-liquid or liquid-liquid flows
A bubble flow: this is a flow of individual gaseous or liquid bubbles in a continuous fluid
A droplet flow: this is a flow of discrete liquid droplets in a continuous gas
A slug flow: this is a flow of large bubbles in a continuous liquid

5. Examples

6. Gas-solid flows
A particle-laden flow: this is a flow of discrete particles in a continuous gas
Pneumatic transport. It is used to move various bulk materials and piece goods through transport communications using the energy of a gaseous carrier medium (air, steam, various gases).
A fluidised bed. This consists of a vessel containing particles, into which a gas is introduced through a distributor

7. Examples

8. Fluid and solid flows
A slurry flow: this flow is a transfer of particles in the liquid
Hydrotransport: this describes densely distributed solid particles in a continuous liquid.
Sedimentation: This describes a tall column initially containing a uniform dispersed mixture of particles. At the bottom, the particles will slow down and form a sludge layer. At the top, a clear interface will appear, and in the middle a constant settling zone will exist.

9. Three-phase flows are combinations of other flow modes listed in the previous sections.

10. Dispersed phase and continuous phase
A dispersed phase is a phase in a two-phase system that consists of finely divided particles (as colloidal particles), droplets, or bubbles of one substance distributed through another substance - the continuous phase.

11. Two distinct multiphase flow models
In trajectory models (Lagrangian Particle Tracking multiphase models), the motion of the disperse phase is assessed by following either the motion of the actual particles or the motion of larger, representative particles. The details of the flow around each of the particles are subsumed into assumed drag, lift and moment forces acting on and altering the trajectory of those particles. The thermal history of the particles can also be tracked if it is appropriate to do so.

12. Two-fluid models or Eulerian-Eulerian multiphase models, the disperse phase is treated as a second continuous phase intermingled and interacting with the continuous phase. Effective conservation equations (of mass, momentum and energy) are developed for the two fluid flows; these included interaction terms modeling the exchange of mass, momentum and energy between the two flows

13. Eulerian-Eulerian Multiphase vs. Particle Transport
Advantages of Eulerian-Eulerian multiphase models
Disadvantages of Eulerian-Eulerian multiphase models
Complete global information for the particle phase is available
Expensive if many sets of equations are used; that is, if there are many particle sizes. However, the homogeneous MUSIG model is an Eulerian- Eulerian model that uses a single velocity field for multiple size groups.
Applicable for wide range of volume fractions
Knowledge of the diffusion coefficients is incomplete
Relatively cheap for one additional set of equations
Difficult to get accuracy over a range of particle sizes for combustive flows
Turbulence is included automatically
When there is phase change, the particle diameter must be user-specified rather than calculated automatically by the model. This can decrease accuracy. (The droplet condensation model is an exception.)

14. Advantages and Disadvantages of Particle Transport
Advantages Particle Tracking multiphase models
Disadvantages Particle Tracking multiphase models
Complete information on behavior and residence time of individual particles is available.
Expensive if a large number of particles have to be tracked.
Relatively cheaper for wide range of particle sizes.
Very expensive to include turbulence.
Better detail for mass and heat transfer.
Essentially only possible as a post- process for a large number of particles.
More flexible when there is a significant size distribution leading to different particle velocities. (In Eulerian- Eulerian Multiphase, a momentum equation must be solved for each representative size which becomes very expensive.)
Restricted to low particle volume fractions.

15. Mathematical modeling of multiphase flows
The mathematical model includes conservation equations for the gas and particles: conservation equations for mass, momentum, and total energy.
The equations for the gas and solid particles are written in the complex formulation of Lagrange-Euler.
The mutual influence of gas and particles is taken into account.
The solution of the equations for the gas and particles is performed jointly in a unified system.

16. For each group of particles (α=1,2,
For each group of particles (α=1,2,...L), the equations describing the motion of the particles include

20. Henderson formula for the drag coefficient

22. Nusselt criterion

23. Gas phase equations