ME 523

Numerical Solutions Applied To Heat Transfer And Fluid Mechanics Problems

# Computational Modeling of Multi-Phase Flow.

. Since we are closing the semester with various special topics, I want to cover one close to my heart.  Single phase CFD is considered a mature field, although people will continue to argue about turbulence models for decades, and computers will permit increasing detail in nodalization of applications.  Multi-phase CFD or Computational Multi-phase Fluid Dynamics (CMFD) is still in its infancy.  People can do a reasonable job modeling highly dispersed bubbly or droplet flow, but covering a full range of flow regimes is still a major challenge.  Even for dispersed flows more data is needed on turbulence, and much more work required developing turbulence models.  If CFD interests you, you will find interesting problems in CMFD for the rest of your professional career.

If you are wandering into the area of multi-phase flow, you need to know some jargon.
• Void Fraction:  Fraction of a given volume of space occupied by gas
• Mean density:  Total mass of all phases in a given volume divided by  that volume
• Mean velocity:  Total mass flux  divided by  mean density
• Quality (x)
• mass quality: gas mass in a volume divided by total mass in the volume
• flow quality:  gas mass flow divided by total mass flow
• equilibrium quality:  difference between total enthalpy and saturation liquid enthalpy divided by the difference between saturation vapor enthalpy and saturation liquid enthalpy
The first thing that you need to know about computational modeling of multi-phase flow is that numerical methods which function for single phase flow may not function well or at all for multi-phase flows.  First order upwind methods are still the primary approach in my world, and not because people haven't tried higher order approaches.

Other considerations are:
• Pay attention to the saturation temperature and pressure when selecting perturbations of independent variables to generate a numerical Jacobian.
• You will need to evaluate source terms associated with phase change implicitly
• Loose coupling of mass and energy equations seen in methods such as SIMPLE will work poorly or not at all
• It will be necessary to implement a sub-grid method to follow interfaces between phases (see this discussion of level tracking and water packing)

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Maintained by John Mahaffy : jhm@psu.edu