wet steam thru orifice 6

[sailoday28]

Sizing of orifice?
Reference thread124-139392

Why would engineers use a perfect gas formulation to determine flow rate of saturated steam (inital state) that will pass through an orifice?

 

[FredRosse]

Engineers use the perfect gas equation for saturated steam flow because it is so very much more simple than real wet steam solutions, and it is sufficiently accurate (at high steam quality) for 99% of the problems encountered.

 

[sailoday28]

What is the basis for accurate for 99% of the problems.---If gamma used is approximately 1.3 and wet steam gamma at high quality is in the neighborhood of 1.1.??

 

[Latexman]

Because they have a tool already in hand that solves the perfect gas case. Then they can put steam traps on vertical piping drops ("dry leg") to carry the condensate away.

Good luck,
Latexman

 

[sailoday28]

Latexman (Chemical)
But then again the traps may be unecessary as the orifice flow expands to lower pressure and lower velocity. And the upstream flow in now superheated. Is that the dry leg that you are jesting about?
However, they will have calculated wrong flows based on wrong assumptions.

Two phase single component flow is an interesting and much studied topic. Steam water mixture flow in pipes , nozzles and orifices is a major design concern in nuclear power plants.
In particular, high energy lines breaks, especially with choked flow.

 

[Latexman]

I wasn't jesting. Steam lines usually have a small bore tee at the lowest elevation of the pipe at some interval to remove condensate. For horizontal steam lines this small bore tee enters the bottom of the steam line. This small bore pipe is run to a convenient maintenance elevation, usually near ground level, and a steam trap installed. The name these vertical condensate removal lines are commonly called in the chemical industry in North America is a "dry leg". They get the heaviest use on cold start-ups.

You are correct. At about 450 psig, sat'd steam has an inflection point on the P vs. H curve. Sat'd steam at 450 psi or lower whose pressure is isenthalpically reduced will become superheated. However, sat'd steam whose pressure is isenthalpically reduced to 450 psi or higher will become two phase.

Good luck,
Latexman

 

[katmar]

I'm with Latexman on this one. It's a case of horses for courses. If you are designing for two phase flow at 450 psi in a nuclear power station then by all means use the best tools available. But if you are designing a flow controller to a simple reboiler at 150 psi then an ideal gas calculation is all that is needed.

Take a typical case and vary gamma over the range 1.1 to 1.4 and see how it affects the calculated flowrate. It will be a fraction of a percent. This is plenty accurate enough in an ordinary chemical plant. We have been doing it this way for over 50 years and these plants have been running safely and profitably.

The presence of liquid water will have a bigger effect via the actual density of the two-phase fluid, but as long as reasonable precautions are taken to trap the lines (as stated by Latexman) it is good enough for ordinary calculations.

 

[25362]

As a possible answer to the question by sayloday28, if I'm not mistaken, the formula for mass flow rates on chocked flow through orifices shows dependency on

(k^0.5)[2[÷](k+1)] ^(k-1)/2k-2)​

The errors by using k=1.3 vs k=1.1 is about 5%, considered by many as sufficiently accurate for chemical engineering calculations.

 

[mbeychok]

Latexman, Katmar, 25362 and Fred Rosse:

If you will all remember when this subject was first discussed in Thread124-139392 in the Chemical Plant Design & Operations Forum, it finally ended after 44 messages had discussed it at great length. In the 43rd message, I said:

"Wow! This thread has taken on a life of its own and seems to go on forever.

Back in the 1950's, when we didn't even have electronic calculators (much less computers), we developed process flow sheets, heat and material balances, and equipment specs for complete refineries in 3-5 months using slide rules. If we developed a Ph.D. thesis every time we sized a restriction orifice, it would have taken us 3-5 years or even more.

And some of those refineries are still operating and operating well."

Then Sailoday decided to start it all over again in this "Heat Transfer & Thermodynamics Engineering Forum". All of you are saying what I was trying to say in the quote above which is that sizing a restriction orifice does not warrant the same effort as required for a Ph.D. thesis. There is a great deal of difference between practical engineering and theoretical research. Process plants would never get designed if we put that much effort into every facet of a plant design. So I repeat, refineries designed and built by practical engineers in the 1950's are still operating in 2005 and operating well.

Milt Beychok

Milton Beychok
(Contact me at www.air-dispersion.com)
.

 

[sailoday28]

25362 (Chemical)Correct me if I'm wrong. For an ideal gas const k, the choked flow mass flux is proportional to
(2/k+1)^[(k+1)/2/(k-1)]

In the power industry, I have been used to using the most appropriate formula to determne prediction of results. Then, I would hope for the actual results to be within an acceptable range.
The fact is -if for the past 50 years, a gamma for two phase high quality steam is approximated with 1.3, what would be used for Fanno line calcs when the flow is two phase?
Must one look in Crane to get a formula to calculate a result when
-- Past editions of the ASME steam tables have graphs illustrating choked mass flux vs source conditions. The only stipulation is that the flux is for homogeneous flow.

With regard to trapping condensate, I agree that other factors such as start up must be considered.
Condensation at other than start up is also dependent upon the ambient temp and insulation of piping.

 

[25362]

For choked conditions, gas mass flowrate estimation formulas, see

http://www.air-dispersion.com/msource.html#Gas Discharge

 

[ddkm]

The formula for the mass flowrate (choked) is:

Qm (choked)= Co A Po SQRT[ (kM/RT_o) [2/(k+1)]^{[(k+1)/(k-1)]} ]


which is proportional to:

SQRT [ k [2/(k+1)]^{[(k+1)/(k-1)]} ]

i.e. k^0.5 [2/(k+1)]^{[(k+1)/2(k-1)]} ]


So, both of you are not quite right.

---engineering your life---

 

[ddkm]

Substituting for k=1.3 and k=1.1, the variation is then about 6% (for the choked mass flowrate).

---engineering your life---

 

[sailoday28]

25362 (Chemical)Correct me if I'm wrong. Your formula for the proportionallity of the flow, except for a typo in the exponent is correct. I based my derivation on the stagnation condtions being the same for both perfect gas gammas. Multiplying my forumula (where I previously cancelled out Ao (sound speed)= sqrt(gammar R To) will yield your result

 

[25362]

At 76 bara, Cp/Cv = 1.97 !! for saturated steam. Am I right ?

 

[sailoday28]

I have a little problem in defining Cp/Cv on the saturation line. Cp is dh/dt at const press.
On the sat line taking a derivative with respect to temp at const pressure doesn't work, unless the derivative is taken with the pressure slightly higher than the sat pressure. Same goes for Cv.

Cp and Cv cannot be defined in the 2 phase region.

My misplaced copy of the 1936 Keenan and Keyes Steam Tables gives a discussion of C' and C", which are specific heats specifically on the sat line. the prime for sat liq. and double prime for sat vapor.

From my 1985ish NBS/NRC Steam Tables Haar, Gallagher and Kell, I can estimate that the isentropic exp coef,, (Cp/Cv) at 55 bars and 180 bars approx 1.27. No intermediate values are given.
Note again, these values are really in a region where an equation of state can be given.

 

[25362]

Sayloday28, have a look at the NIST chemistry WebBook tables and you'll find the values for Cp and Cv for (liquid) water as well as for saturated and superheated steam.

 

[sailoday28]

I don't doubt your reference to NIST. However, I would like to know what is meant by the definition of Cp. Is the limit of the derivative of enthalply with respect to temp at const temp good in only one direction? If that is how it is used, then the users should be aware of it.

Does the derivative of a property when entering a two phase region have any significant affect? You bet. Consider the sound speed of liquid water. It is relatively high. At x=0, sound speed can be radically different and relatively small. This is the result of taking dp/drho on an isentrope from two different directions.

 

[Latexman]

Sailoday,

When you continued this thread over here I had a feeling you wanted to discuss something. I have difficulty understanding Cp/Cv on the saturation line too, also in the two phase region. With 2 phases present there is one less degree of freedom, so the independence between temperature and pressure that a gas enjoys is lost. The pressure (vapor pressure) is dependent on temperature. So, if pressure is to be held constant to get a Cp, then temperature must be constant. Since Cp = dH/dT, Cp becomes indeterminant. Likewise with Cv. I wonder, can Cp/Cv be determined using L'Hopital's rules?


Good luck,
Latexman

 

[sailoday28]

My reason for continuing the thread here was hopefully to find others who would reinforce use of available data to determine mass flux for choked flow of saturated steam.
In addition to the ASME steam tables, there is also Napiers rule. I have not compared its accuracy with that of the ASMEs results.
With regard to Cp/Cv, L'Hopitals rule would only apply to 0/0 etc.
For two phase, Cp and Cv have no meaning.
The isentropic exponent, gamma, which seems to be about 1.1 for sat steam simply relates pressure and spec. volume on an isentrope.
I do not know the validity of the 1.1 for pressure ratios involving choked flow. If fact, the formulas used for choked flow of a perfect gas, generally use a constant gamma. If large temp changes occur during gaseous choked flow, one should check validity and impact of the gamma dependency on temp. That in addition to the validity of using a perfect gas.
The calc for sound speed, (which depends on gamma)whether in the superheated or high quality region does not show a severe discontinuity. For subcooled water, the isentropic expansion to the low quality regions, does show a radical change (slowdown)in the sound speed.
Regards