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Speed of sound in two-phase mixture?

Speed of sound in two-phase mixture?

Speed of sound in two-phase mixture?

(OP)
Guys do any of you know how to calculate the speed of sound in a two-phase mixture.  Specifically this is steam of 65% quality at 1100 psig.

Obviously this puts me waaaay out of ideal gas assumptions.  I can calc the c in the two phases but I am suspect of using a mass-wieghted average of the individual phase c, as one would do with enthalpy.

Any ideas?
Thanks!

Thanks!
Pete

RE: Speed of sound in two-phase mixture?

What kind of precision do you need?  For most of the problems that I need "c" of a 2-phase flow, I calculate each phase as though it were by itself and then use whichever one gives me the more conservative answer.  I figure that there are so many assumptions, estimates, and guesses in most of the things I do with two-phase flow that trying to be more rigorous with the speed of sound is outside the accuracy of the calculation--most two-phase flow calculations are only valid to within 30% anyway.

I had a boss once that said "you can lacquer a turd and make it all shinny and pretty, but it is still a piece of crap".  That may be too crass for this forum, but it has always meant to me that you shouldn't work any harder than the data will support.

David

RE: Speed of sound in two-phase mixture?

For a one component-homogeneous mixture
C^2  =-V^2 dP/dV(isentropic)         (1)
where C=sound speed, V=specific volume, P=pressure
Clearly,the specific volume,V and entropy, S should be known from
V=Vf+xVfg        (2)               where x is the quality
S=Sf +x Sfg       (3)

The specific volume may be shown to be from Classus-Claperon  (excuse spelling)
V=Vf + (S-Sf)dT/dP    (4)    Note S= constant


(Plot T vs P in the vicinity of your pressure and get first derivative.  You will also have to plot dT/dP to get the second derivate.)


dV/dP=dVf/dP + (S-Sf)d^2T/dP^2  -dT/dP(dSf/dP)   (5)

You now get dP/dv from (5) after a little graphical work.
Substitute in (1) and take the square root.

I have found it very interesting to try above for low quality steam water. See what happens as x approaches zero.

Regards







RE: Speed of sound in two-phase mixture?

Consult the manufacturers of doppler type ultrasonic flow sensors.  The doppler meters work best with some bubbles or particles in the stream.  However, I suspect that your two-phase steam application is a poor match for their data.

John

RE: Speed of sound in two-phase mixture?

I believe the original question was "to calculate the speed of sound"

By the way to get dT/dP , note that dT/dP=Sfg/Vfg.

To get the second derivative, get Sfg/Vfg at a small increment of pressure (or temp)above and below (equal encrements)that of 1100 psig.  That will give dT/dP at three points and numerically, one then obtains the second derivative.
Regards

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