Calculating the speed of sound in wet steam

[GerardLardner]

Does anyone have a method for calculating the speed of sound in wet steam?

The standard method works for dry or superheated steam, but breaks down rapidly at and below saturation temperature.

The 2015 paper by Šafařík, November, Jícha and Hackman "On the speed of sound in steam" shows a discontinuity in the speed vs dryness curves at about 0.98 dryness, but I do not know if that is supported by measurement.

[GerardLardner]

Sorry, spelling checker has mangled the names mentioned above. They should be Šafařík, Nový, Jícha, and Hajšman.

[ppal]

THE SPEED OF SOUND IN STEAM (asee.org)  - dont know wet or dry  

Sound Speed in Liquid‐Gas Mixtures: Water‐Air and Water‐Steam (illinois.edu)

But I guess you can search just like I did and this is not it!

and Chat GPT says

 And  Gemini AI says:

If you need a rough estimate, you might find references to the speed of sound in wet steam being around 10% lower than dry steam at similar conditions. However, this is a simplification and won't be accurate for all cases.

[terryhendicott]

Hi,

Your reference says no measured data is available?:  But there is one that has measurements of wet steam.

ON THE SPEED OF SOUND IN STEAM
Pavel Šafa?íka,?, Adam Novýb, David Jíchaa,b, Miroslav Hajšmanb

Papers [5, 6] provide much stimulation for further studies of the speed of sound in wet steam, because they deal with the propagation of waves in wet steam. However, no measured data have in fact been published.

[5, 6] are not this article:
Velocity of Sound Measurements in Wet Steam
R. E. Collingham and J. C. Firey

TY - JOUR
T1 - Velocity of Sound Measurements in Wet Steam
AU - Collingham, R. E.
AU - Firey, J. C.
Y1 - 1963/07/01
PY - 1963
DA - 1963/07/01
N1 - doi: 10.1021/i260007a005
DO - 10.1021/i260007a005
T2 - Industrial & Engineering Chemistry Process Design and Development
JF - Industrial & Engineering Chemistry Process Design and Development
JO - Ind. Eng. Chem. Proc. Des. Dev.
SP - 197
EP - 202
VL - 2
IS - 3
PB - American Chemical Society
SN - 0196-4305
M3 - doi: 10.1021/i260007a005
UR - https://doi.org/10.1021/i260007a005
ER -

[GerardLardner]

Hi, and thank you for your coments. I had read that paper in detail. It refers to a mathematical development of an earlier paper by the same authors as a pure numerical model, but the conclusions. section 5, notes "It should be pointed out here that no measured data are available for the speed of sound in wet steam, and there are also only limited theoretical resources". I am hoping someone knows of a newer resource which is compared to experimental data. Figure 4 in this paper shows a discontinuity in the velocity curves at a steam quality about 0.98; but it is not clear is any experimental data supports this obsrvation.

I have read the 1963 paper by Collingham and Firey, and the later 1966 paper by England, Firey and Trapp. on measurement of the speed of sound in wet steam. However, the method shows significant experimental issues that may be affecting their results. But, that said, I have not (yet) found newer experimental data.Maybe when I have read the paper by Kieffer it will be clearer, but that appears from the abstract to be another theoretical study.

[GerardLardner]

I should add there is one other paper that looks very promising: Zhang and others. "Experimental validation of sonic speed theory for wet steam", 2022. However, I have not been able to obtain a copy yet.

[GerardLardner]

Your first suggestion, https://coed.asee.org/wp-content/uploads/2020/08/8-The-Speed-of-Sound-in-Steam.pdf, I had read and implemented in Mathcad. As written in the paper, it is based on temperature rather than quality. I modified it to calculate the entropy based on p1 and quality rather than p1 and T1. When the quality is set to 1.0, the method exactly matches any other calculation; however, for quality below 0.999, the calculated speed of sound drops to 5 m/s; clearly unreasonable.

I had downloaded the second reference yesterday but, as I was writing around midnight (Irish time), I had not read it. I will read it later today.

[Eric_S]

Hi @GerardLardner , this is an interesting topic to me. I noticed that when I try to do velocity calls in my steam tables tool, it fails to find a velocity when I go into the wet region. However, I can make calls if I ask for the velocity just in the vapor component, but it's not clear to me that those numbers will be correct.

I thought of something, let me know what you think. You probably have tools that will find the nozzle critical or choking pressure given the inlet steam conditions. What if you were to find the available energy from the inlet down to the choking pressure, and then use the kinetic energy equation to solve for the velocity? If the water droplets are actually able to be a drag on the flow I guess the true number could be less than what you would calculate.

[GerardLardner]

It seems to me there is not yet an accepted understanding of the speed of sound in wet steam - or at least not an accepted means of calculating it that has been validated by measurement. The concept is touched on in a number of papers on steam turbines.

There is one recent paper that looks promising: Zhang, Wu, Li, Yang and Yang Experimental validation of sonic speed theory for wet steam. But Sagepub want £32 for it and I have no confidence it really addresses the question in the form I want. I may bite the bullet and buy it but the price seems larcenous for six or eight pages; I could buy a much more interesting novel for less than half that amount.

[GerardLardner]

Well, it looks like the paper by Zhang et al (https://doi.org/10.1177/09576509211058056) does validate the theory by V Petr Wave propogation in wet steam. (https://doi.org/10.1243/0954406041474237), at least to within their experimental error (+/-4%). Now I just have to get my head around it. Something to do during the Easter break 😁

[Eric_S]

Great news, thanks for the update, @GerardLardner I wonder if @ValeryOchkov has any thoughts about this topic?

[Eric_S]

@GerardLardner I was reading the abstract of the paper by Zhang et al, which I can read without buying the paper, and they refer to something called the frozen speed. Do you know what they mean by that? Thanks.

[GerardLardner]

No. I think I have seen it mentioned in some of the other papers I have skimmed through but I have not seen it defined. I assumed it was a common term.

[GerardLardner]

It appears that 'frozen' conditions in this sense means there is no heating or cooling at the wave, i.e. neither the moisture droplets are flashing nor the vapor condensing.

Conceptually I have difficulty with this simplification. Unless the timescale considered is very short, the pressure change in the acoustic wave should result in some degree of phase change. But the frozen wave concept allows the conditions to be explored assuming the mixture is isentropic.

[Eric_S]

Thanks @GerardLardner for this further explanation, it does help. 

[vnamboodheri]

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