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)

**Maintained by John
Mahaffy
: jhm@psu.edu**