The Basics of Two-Phase Flow
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My goal for this lecture is to lay down basic terminology for two-phase
flow, and give a feeling for what various void fractions represent.
Processes in power systems involve various forms of two-phase
and it is specially important when dealing with accident scenarios in
nuclear power plants. If you are going to work in this field you need
to understand the basic terminology (jargon).
Two Stages of Science
1. Description and Classification (Organization)
- Reflected in basic Flow regime maps for two-phase flow
- Also seen in two-phase heat transfer with the boiling curve
2. Predictive Theories
- Kaye Lathrop once identified three phases in the history of
There are three historical phases in the development of
theoretical science. The first beginning at the dawn of history, and
only fading in recent years is "back-of-the-envelop science". All
predictions were made with hand calculations. The next phase, "science
by computer," began in the 1950's with the advent of useful
programmable computers. The third and terminal phase of science became
noticeable a couple decades ago. It is "science by view graph," and has
probably been driven by the dominance of government funding of
- Theories that produce useful results with hand calculations are
only useful for very simple problems
- Most systems of interest to us are so complex that they need
computers to carry out the calculations
- Computers don't recognize differential equations
- A layer of numerical models for the differential equations must
Three Tasks of Numerical Simulation
- Understand the Predictive Theories of Real World relevant to what
you need to simulate
- Create a Virtual World on the computer that mimics the desired
portion of the real world
- Quantify Differences Between the Real and Virtual Worlds
- Permits clearer and more concise discussions
- Great for job security
- Key terms (see the list of acronyms
- Subscripts l or script l (liquid), g (gas), v (vapor), m
(mixture), s (saturation), w (wall), I (interface)
- Void fraction ( Greek letter alpha)
- mean density
- mean velocity
- relative velocity
- phasic volumetric flows or fluxes
- phasic mass flows or fluxes
- saturation temperature and saturation pressure
- Quality (x)
- mass quality = vapor mass/ total mass
- flow quality = vapor flow / total flow
- equilibrium quality x = (htot-hls)/(hgs-hls)
here h is the
Simple Two-Phase Flow Regimes
- Consider horizontal and vertical pipes, most research
characterizes either horizontal or vertical flow, although some is
available for inclined pipes.
- Flow regimes are frequently plotted on void fraction vs.
mass flux (kg/m**2/s) axes.
- Above 2700 kg/m2s the regime is also called "churn
- Slug flow can exist
roughly in the void fraction range from 0.3 through 0.5 with mass flow
< 2000.. This is
basically flow where the bubble diameter reaches the pipe
diameter. Important scaling issues occur here. Smaller
scale experiments can go into slug flow regimes that would not be seen
in a full reactor coolant pipe.
- There is an additonal flow regime for horizontal pipes.
- What is the flow like in a culvert under a road or a sewer
- This is horizontally stratified flow, and the conditions for
transfer between this regime and standard bubbly or droplet flow are in
part related to the Froude number (F=sqrt(V**2/(gD)). This is basically
the square root of the ratio of specific kinetic energy to specific
gravitational potential energy.
- When we add the complication of heated walls later, more will
have to be said about flow regimes.
Physical Feel for void fractions (see my sample void calculations)
- What do you think is the void fraction in a heavy rain
Can you think of a way to estimate the void fraction? Think about the
distance at which you can no longer see anything. As you look through a
volume of air that has a cross sectional area A (area of your iris
opening) and viewing length l, the area blocked by rain drops is
roughly equal to the product of the number density of drops, the
viewing volume, and the projected area of one average drop (pi times
the drop radius squared). The maximum range of vision is approximately
at the point where this blocked area equals A.
- To get what we want, first we calculate number density as a
function of alpha and r. Substitute this in the above equation. and
solve for void as a function of l and r.
- In a heavy rain I can't see much past my front fence line
which is about 1000 feet away. For lack of a better guess lets take
1/4" drops. We get a void fraction of 0.999972.
- Rearrange the final equation to get visibility as a function
of void and r. What does this tell you about fog?
- Calculate void fraction with bubbles just touching. It is
- Calculate void fraction where droplets have a surface
separation of one diameter. If you assume the drops are equal size and
centered in a uniform cubic lattice, the answer is 0.935.
- Uniform droplets will have a surface separation of 1.279
diameters when the void fraction is 0.75.
Maintained by John Mahaffy : firstname.lastname@example.org