Speed of sound in two-phase mixture?

[KernOily]

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

 

[zdas04]

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

 

[sailoday28]

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

 

[jsummerfield]

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

 

[sailoday28]

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