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#

Sound Speed in Two Phase Medium

The gas flow in many industrial situations contains other
particles.
In actuality, there could be more than one speed
of sound for two phase flow.
Indeed there is double chocking phenomenon in two phase flow.
However, for homogeneous and under certain condition
a single velocity can be considered.
There can be several models that approached this problem.
For simplicity, it assumed that two materials are homogeneously mixed.
Topic for none homogeneous mixing are beyond the scope of this book.
It further assumed that no heat and mass transfer occurs between
the particles.
In that case, three extreme cases suggest themselves:
the flow is mostly gas with drops of the other phase (liquid or solid),
about equal parts of gas and the liquid phase, and liquid with
some bubbles.
The first case is analyzed.

The equation of state for the gas can be written as

The average density can be expressed as

where

is the mass ratio of the
materials.

For small value of
equation (3.40)
can be approximated as

where

is mass flow rate per gas flow rate.

The gas density can be replaced by equation (3.39)
and substituted into equation (3.41)

A approximation of addition droplets of liquid or dust (solid) results
in reduction of

and yet approximate equation similar to
ideal gas was obtained.
It must noticed that

.
If the droplets (or the solid particles) can be assumed to have the same
velocity as the gas with no heat transfer or fiction between the particles
isentropic relation can be assumed as

Assuming that partial pressure of the particles is constant and
applying the second law for the mixture yields

Therefore, the mixture isentropic relationship can be expressed as

where

Recalling that

reduces equation (

3.46)
into

In a way the definition of

was so chosen that effective
specific pressure heat and effective specific volumetric heat are

and

respectively.
The correction factors for the specific heat is not linear.

Since the equations are the same as before
hence the familiar equation for speed of sound can be applied
as

It can be noticed that

and

are smaller than
similar variables in a pure gas.
Hence, this analysis results in lower speed of sound compared to
pure gas.
Generally, the velocity of mixtures with large gas component
is smaller of the pure gas.
For example, the velocity of sound in slightly wed steam can be
about one third of the pure steam speed of sound.

Meta

For a mixture of two phases, speed of sound can be expressed as

where

is defined as

END META

** Next:** Isentropic Flow
** Up:** Speed of Sound
** Previous:** Speed of Sound in
** Index**
Created by:Genick Bar-Meir, Ph.D.

On:
2007-11-21