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Sizing of orifice?
2

Sizing of orifice?

Sizing of orifice?

(OP)
Hello all. I'm a newbie here, searching for opinions on orifice sizing.

For a vapor through a hole (in this case, saturated steam), I was recommended the following equation (from Crowl/Louvar):


Qm (choked)
   = Co A Po SQRT{(k gc M / Rg To)*(2/k+1)^[(k+1)/(k-1)]}

(Equation is provided in the old units, not SI)
                
Then you vary the orifice diameter - which changes the cross sectional area A - and thus, changes the maximum flow Qm (choked). Keep varying the diameter til you get the max flow that is required.

Is this correct? I'm asking because I'm getting a very low calculated result compared to the expected result. Example I'm getting only 11kg/hr instead of, say, 1100kg/hr.

RE: Sizing of orifice?

ddkm:

Your equation has an extra g in it. This is the correct version for the indicated USA engineering units:

Qm (choked)
   = Co A Po SQRT{(k gc M / R To)*(2/k+1)^[(k+1)/(k-1)]}

where:
Qm = lb/s
Co = discharge coefficient = approximately 0.72
A = ft2
gc = gravitational conversion constant = 32.17 ft/s2
k = cp / cv of the gas
M = molecular weight of the gas
R = 1545.3 (ft-lb) / (lbmol)(°R)
Po = absolute upstream gas pressure, lb/ft2
To = upstream gas temperature, °R

(Note that the pressure is in pounds per square foot rather than  pounds per square inch)
---------------------------------------------------------
And here is the same equation for the indicated SI units:

Qm (choked)
   = Co A Po SQRT{(k gc M / R To)*(2/k+1)^[(k+1)/(k-1)]}

where:
Qm = kg/s
Co = discharge coefficient = approximately 0.72
A = m2
gc = gravitational conversion constant = 1 (kg-m) / (N-s2)
k = cp / cv of the gas
M = molecular weight of the gas
R = 8314.5 (Pa)(m3) / (kgmol)(°K)
Po = absolute upstream gas pressure, Pascals
To = upstream gas temperature, °K
----------------------------------------------------------
I hope this helps you,

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

RE: Sizing of orifice?

ddkm:

I'm at home and my references are at the office, but I'll take a stab at it.  Is Rg a gas constant that is specific to a certain gas?  In other words, it has the molecular weight built into it.  If so, I don't see why you'd need M in the equation.

Good luck,
Latexman

RE: Sizing of orifice?

ddkm:

Oh yeah, give us your data to look at.  That may spark an idea in someone.

Also the term you wrote as (2/k+1) is most clearly written as (2/(k+1)).

Good luck,
Latexman

RE: Sizing of orifice?

(OP)
Wow, you guys are really fast and helpful. Let's keep the momentum.


Mbeychok:
The equation is virtually the same. The universal gas constant was quoted as Rg, where g is a subscript. (i don't know how to do a subscript in the text).

More importantly, your comment of:  "the pressure should be in lb/ft2 instead of lb/in2" is precisely the missing link! Darn, I hate (sorry) to use the non-SI units and again, here it has caused me some calculation error. I've redone the calculation and the result looks much more reasonable! I'll show the calc in the next reply.

Even better, you have attached an SI-unit equivalent of the equation, which I was looking for. I half-suspected that it would be virtually the same, with the exception of gc and R constants. In particular, I was doubtful that we could just replace the gc as 1 for the SI units. But thanks anyway.

RE: Sizing of orifice?

(OP)
Latexman:

- Thanks for the heads-up: yeah, it should be 2/(k+1)

- I think the M (molecular weight) is necessary because the PV=nRT equation applies to a molar basis (i.e. where "n" is represented and R is quoted as 8.314J/molK). As such, since we need the calculation of the max flow to be on a mass basis, therefore the M comes into play.
Alternatively, we could look at n=m/M which gives PV=mRT/M and somehow this equation must have been fitted into another equation.

RE: Sizing of orifice?

(OP)
Let's look at the calculation I've done:


I'm trying to size an orifice for a high-pressure steam line with the purpose of restricting the flow (for safety reasons).

Data is as follows:
Steam supply
P = 75barG
T = 291ºC (saturated steam, extrapolated from tables)
k = Cp/Cv = 1.28 (I've used 1.28 based on someone else's data.  It's usually around this figure or up to 1.35, I think)
M = 18 for Steam (H2O)

For the coeff of discharge, I've used 0.61 as the book recommends this number for sharp-edged orifices (although we are dealing with annular orifices here) so:
Co = 0.61

Objective is to restrict the flow to a maximum of 1700kg/hr.


Solution:
=========

Using the equation and converting to non-SI units, we get:

Co    =    0.61                    
d    =    0.01    m    =    0.0328084    ft
A    =            =    0.000845396    ft2
Po    =    75    bar(G)            
    =    76.00    bar(A)    =    1102.2888    psia
                =    158729.5872    lb/ft2
k    =    1.28                    
gc    =    32.17    ft lbm/lbf s2                
M    =    18.00                    
Rg    =    1545    ft lbf/lbmole ºR                
To    =    291.00    ºC    =    1015.8    ºR


Note:  Using a spreadsheet, I've varied the diameter of the orifice to compute the Qm (choked).  With a figure of 10mm or 0.01m for the , this gives a Qm (choked) of about 1.043lb/s or 1704kg/hr.

Any comments?

RE: Sizing of orifice?

ddkm:

Yes, Crane Technical Paper 410 has a section of gas properties that uses Rg as a gas constant that is specific to a certain gas.  As you indicated, instead of PV=nRT they use PV=mRgT where Rg = R/M.

To learn how to use subscripts and lots of other neat stuff, click on "Process TGML" above the "Submit Post" button.

Good luck,
Latexman

RE: Sizing of orifice?

(OP)
Latexman: Thanks.

Wow, "process TGML" to do some kind of formatting. Well, as long as it gets the job done.

Latexman: Any comments on the calculation shown? I've used Co of 0.61, whereas Mbeychok had used 0.72. It may make some difference to the computed result, so just wondering what is the basis for the difference?

RE: Sizing of orifice?

(OP)
Using the SI equivalent, I've redone the calculation as follows:

Co    =    0.61
    
d    =    0.01    m
        
A    =    7.85398E-05    m2
            
Po    =    75    bar(G)
        
    =    76.00    bar(A)    =    7601325    Pa
            
k    =    1.28

gc    =    1    kgm/Ns2
                            
M    =    18.00
                            
Rg    =    8314    J/kg-mol K
    
To    =    291.00    ºC    =    564.00    K


Solution:
========
The only difference in the basic equation between the two non-SI and SI equations are the values of gc and R, where gc = 1 and R = 8314 (adjusted for kg-mol instead of the usual g-mol units) in the "SI" units. Therefore, using virtually the same equation and orifice diameter of 10mm, I get:

Qm (choked) = 0.4735 kg/s   i.e.  1704 kg/hr (same answer)


Thanks a lot, guys. This has been really helpful and given a higher level of confidence to my calc. Hope you guys were enlightened too.

RE: Sizing of orifice?

ddkm:

Having done the same cross-checking (by using the equation in USA units and the equation in metric units) at least a hundred times in the last few years, I know that the two equations I gave you in my earlier response provide equivalent answers. I am glad to see that you found that out as well.

I have only one other comment. There are those who would say that C, the coefficient of friction, should be much higher than my 0.72 ... which I chose as being conservative. Therefore, I question your use of C = 0.61.  What it really boils down to is how important accuracy is to you.  If the mass flow through the orifice size you selected turns out to be higher than you calculated by using 0.61, will it be detrimental to what you are trying to do? Only you can answer that question.

With best regards,

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

RE: Sizing of orifice?

(OP)
mbeychok:  yeah, found that out by actually doing the calculation itself. It's just that I couldn't imagine that the gc could so conveniently equate to 1.0 in the SI (metric) environment. When something looks too easy, well, you easily get doubts.

For the question on value of Co, obviously it could be critical since the calculation is done on purposes of safety. I guess I'll look around for more interpretation of this coefficient.

By the way, how is it that you call it coeff of friction? In the literature, they simply call it "discharge coeff"

RE: Sizing of orifice?

ddkm:

I got about the same answer with your numbers.

Perry's Handbook speaks to flow coefficients of annular orifices and has references.

Good luck,
Latexman

RE: Sizing of orifice?

ddkm:

My copy of Perry's is the 6th edition and the pages I will cite in this message are from that edition.

(1) Page 5-3 defines the gravitational conversion constant gc (which Perry's calls the dimensional constant) to be 1 (kg-m)/(N-s2).

(2) Page 5-3 also correctly makes a distinction between the gravitational conversion constant gc and the local gravitational acceleration g.  That is needed because some equations (other than the choked flow equation we are discussing) involve both gc and g.  

In the SI metric units, gc = 1 (kg-m)/(N-s2) and g = 9.807 m/s2.  In the customary USA units, both gc and g have the same numeric value of 32.17 ft/s2.

(3) Page 5-16 discusses the case of critical flow (i.e., choked flow) through a square-edged or sharp-edged orifice.  It states that if the pressure ratio r, which Perry's defines as P2/P1, is at the critical pressure pressure ratio of rc (i.e., at choked flow), then the discharge coefficient is "about 0.75".  Perry's also states that if the downstream pressure P2 drops below that corresponding to the critical pressure ratio, the coefficient of discharge will increase ... and as rc approaches zero, the coefficient of discharge increases to "about 0.84".

(4) I would like to encourage you to use R (without any subscript) and to [b]always make sure to define it as the universal gas constant. That is because many authors in the technical literature often use a gas constant that is only applicable to a specific gas molecular weight. I call that specific gas constant Rs where the subscript s denotes "specific".  As pointed out by Latexman, Rs = R/M. Unfortunately, those same authors often do not explain which gas constant they are using and that leads to much confusion.

(5) You might find it useful to visit www.air-dispersion.com/msource/html and read the section on "Gas Discharge To The Atmosphere From A Pressurized Source Vessel" using SI metric. The same section is available in the customary USA units at www.air-dispersion.com/usource/html.

Please excuse me for being so long-winded but I thought you might find the above to be useful.

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

RE: Sizing of orifice?

FYI
For those use the Qm choked equation , American units

The the product PoA in the referenced formula has to be in lbs units.  Po can be psia as long as A is in square inches.

Also note, that Po has to be stagnation and not static upstream pressure and more important

The referenced formulas are for perfect gas, constant specific heats.
For choked flow of saturated steam, which will pass thru wet states, I would refer to the graphs for choked flow that are illustrated in the ASME steam tables (at least they were illustrated in the past)

RE: Sizing of orifice?

ddkm:

If there is significant pipe and fittings in the high-pressure steam line, that can restrict the flow too, especially if the velocity in the pipe is quite high during maximum flow.  Some folks like to ignore the piping when sizing a restriction orifice, but I've seem a few cases when you can't.

For reason #3 in Milton Beyckok's post above and to make the flow restriction a little more difficult to change in the field, the last flow restriction I put in was a spool piece with a reducer, 1 foot length of smaller piping and an expander.  This acted as a "thick plate orifice" and once the critical pressure ratio was reached, the flow did not increase if downstream pressure decreased further.

Good luck,
Latexman

RE: Sizing of orifice?

Forgive me if this comes across as a bit of a rant, but one of my buttons has been pressed here.

ddkm has expressed surprise that the value of gc turns out to be exactly 1.0 in SI units. We need to look at this in more detail because the units are even more surprising than the value.

mbeychok has quoted from Perry that the units of gc in SI units are (kg.m)/(N.s2). But N is the unit of force, and force is mass x acceleration, so we could express N as kg.m/s2. These units all cancel out and low and behold, not only does gc have a value of 1.0, but it is dimensionless!

What is the point of including a factor that has a value of 1.0, and has no units???

This is a perfect example of the problems involved in converting an equation from one set of units to another, which was described by zdas04 in thread378-134079. The problem here is that the SI equation referenced by mbeychok has been derived by converting the Customary Units equation, instead of from first principles.

I have found that very few engineers really understand what gc actually is.

In the English system of units (also known as the foot-pound-second system) the unit of mass is the pound, and the unit of force is the poundal.

In the British Engineering system of units the unit of mass is the slug and the unit of force is the pound force.

Unfortunately in the US Customary system of units they have used the unit of mass (i.e. the pound) from the English set of units and the unit of force (i.e. the pound force) from the British Engineering system of units.

But
   1 pound force = 32.17 poundals, and
   1 slug = 32.17 pounds (mass)

So, if you mix these systems of units you have to include a conversion factor, which is the origin of the much misunderstood gc. It is ONLY in US Customary units that there is any need for gc and in every other consistent set of units the need for gc simply does not exist.

RE: Sizing of orifice?

katmar (Chemical)states".....So, if you mix these systems of units you have to include a conversion factor, which is the origin of the much misunderstood g."
Which leads misunderstanding and use of lbs in force and mass.  I have called the British system, the American system.   Weren't the Brits smart enough to stop using it?
I believe those of us in the US are the only ones still using a complicated system.

 Go SI

RE: Sizing of orifice?

katmar:

In principle, I agree wholeheartedly with you. If you will take a few minutes to visit www.air-dispersion.com/msource.html and read the section on Gas Discharge To The Atmosphere From a Pressurized Source, you will see that I have indeed excluded the gc from the SI equation for choked flow.

But, like it or not, this forum and many similar ones still have participation from a great many older engineers who live in the USA and who still do not use the SI metric system. That is why the originator of this thread obtained the choked flow equation (that used USA units) from the textbook written by Crowl and Louvar who are professors in USA universities.  

Until the day that the USA finally decides to go fully metric, we have to face the fact that people will have to cope with conversion of units from one system to another. I might add that we will also have to cope with the fact that, even in the metric countries, some people express pressure in Pascals, some use kg/cm2, and some use bars.

Milton Beychok

RE: Sizing of orifice?

Milton,

I meant no offense to you, and I apologise unreservedly if I came across as giving that impression.  I have the huge advantage of having been educated and employed in South Africa over the last forty + years, during which time we moved from English units to Metric units and finally to SI units.  I believe this has given me a perspective that would be hard to obtain for an engineer operating "inside" the old system, or even for an engineer who has grown up "metric" in Europe.

I still believe that it is an abomination that a book like Perry lists gc with the units given above.  Their mistake perpetuates the lack of understanding amongst practising engineers.  I appreciate the fact that people like you are able to overcome the habits of the past, in the way that you have given this formula without the gc in the SI version. It is time mainstream engineering caught up.

In some ways the Europeans have it worse than the Americans because with their "metric" systems they were always halfway there, and it seems this gave them even less motivation to drop the old ways than the Americans. As you say, the Europeans still use a variety of units, and that is probably why over 100 people download my Uconeer units conversion program every day.

The SI system is a quantum advance over the metric system (actually there were several metric systems) and I welcome the progress, slow as it is, that is being made in accepting this excellent tool.  An indication that progress is being made is that I see in my web logs that people get to the Uconeer web site by typing "How many inches in a foot" into Google. Hard to believe, but some people do not know this anymore!

regards
Harvey

RE: Sizing of orifice?

Orifice Sizing
I used the method given in Flow Measurement Engineering Handbook in Chapter 13.(Third Edition). My values differ by the difference in the discharge coefficient that have been used. The method is for a plate with d<thickness<6d.

The fly in the ointment for me is the assumption that we have a ideal/perfect/real gas. Looking into it a bit I calculated the total throat temperature to be about 120F lower than the upstream conditions and have to wonder how many phases are present. I would want to make sure that any errors would be on the safe side.

Units/Dimensions
A good reference for handling units that I found is given in Fluid Mechanics for Chemical Engineers by de Nevers in Chapter 1.(Second Edition) As is pointed out the units are even today being muddled, when if a typical person in Europe is asked how much they weigh he might well respond 80 kilos. When the correct SI answer would be 784.6 newtons.
So it seems to me that no matter what units that one uses, the language seems to silently lead us astray.
The approach taken in the above text for conversion is to multiply things by 1[ ie. 12 in = 1ft; 1 = 12in/ft or 1 = ft/(12in)]

RE: Sizing of orifice?

Annular orifices are used for gases with entrained liquids or solids and for liquids with a small amount of gases present.  When I saw he specified an annular orifice, I assumed he knew he'd have two phases, especially when he goes to start-up a cold steam line.

Good luck,
Latexman

RE: Sizing of orifice?

I believe we have wandered away from the original question and are focused on units which should not be a problem for engineers.  I see this mainly as a problem for undergraduates.

The original question relates to saturated vapor.This flow  will go two phase thru an orifice, yet our resposes (in addition to the system of units) relate to an equation for a perfect gas, with constant specific heat.

We have defined k=Cp/Cv---What is Cp or Cv in the two phase region?
 An isentropic expansion coef, gamma,however, may be approximated for a short expansion from the saturated state.  Plot p vs v (on log-log )for isentropic expansion and an equivalent gamma may be obtained.
Again, I suggest going to the (perhaps past) ASME steam tables, which willl provide critical or choked mass flux versus upstream conditions.

RE: Sizing of orifice?

I believe the original poster has his question answered and there is a tiny bit of one-up-man-ship going on.

Cp or Cv or Cp/Cv for a perfect gas in the two phase region is rubbish, because the presence of the liquid proves the gas is not a gas, but a vapor, and the vapor's properties will throw things off a little and the liquid's properties will throw things off a lot.  If you try to include the gas or vapor and the liquid in the derivations it'll get so complicated that it bogs down the average engineer and he has to consult with someone with a triple PhD in the subject to make progress.  So, what to do?  Apply the best "model" that you can and add details and conservatism to deal with the realities.

ddkm has done a good job of this IMO.  Apply the ideal gas orifice equation and deal with the condensate with an annular orifice.  The only additional advice I would give him is provide some "dry legs" with steam traps to take the the condensate out of the picture as quickly as you can.  Ddkm are you listening?  You can readily estimate the max.  condensate you have to deal with by using the steam tables or a Mollier diagram for water.

Engineering is like a sport, you have to have a game plan!  A game plan has 3 components.  The components are - "the plan", "the back-up plan", and "the emergency plan".  Why?  Because (in polite terms), stuff happens!

Good luck,
Latexman

RE: Sizing of orifice?

sailoday28:

I agree with Latexman that we have probably gnawed all of the meat off of this bone.

But I must point out that the the expansion of a gas through a restriction orifice is not an isentropic expansion.  It is an isenthalpic expansion. If I look at 76 bara saturated steam on my Mollier diagram and if that steam undergoes an isenthalpic expansion to a downstream pressure of about 6 bara or lower, the steam will still be saturated or actually have some superheat at the downstream pressure. In other words, the formation or non-formation of condensate will depend upon the orifice downstream pressure.

Milt Beychok

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

RE: Sizing of orifice?

mbeychok:

When I checked ddkm's numbers in my handy dandy compressible gas program, I recall the pressure at the orifice being around 41 bara.  At that point, due to the shape of the enthalpy vs. pressure diagram I'm looking at in Perry's 5th Edition, it's slightly in the two phase region.  Agreed, if the pressure drops lower isenthalpically, it eventually becomes superheated, but first it condenses more, then re-saturates, and finally superheats, all due to the shape of the curve.  But, is the pressure downstream of the orifice going to drop?  I don't think so.  There will be pressure recovery coming out of the vena contracta as the kinetic energy (velocity) is converted to potential energy (pressure).  The permanent pressure drop of the orifice will determine where the final pressure ends up downstream of the orifice, and it looks like that will be slightly in the two phase region.

Granted, I'm quickly integrating the results from an ideal gas, constant Cp/Cv, isenthalpic model with real data (the H vs. P diagram) in my mind.  Is it an ideal gas?  No.  Is Cp/Cv constant?  No way.  Is it 100% isenthalpic?  I doubt it, but I think you are right it is closer to that than isentropic.  I also wonder if we would be so far off if we treated it as isentropic that it wouldn't work in reality?  I doubt it.

Once we pick the best model or our favorite model or the one we have a handy dandy program for, the reality of whats happening in the process must be integrated into the design.

Good luck,
Latexman

RE: Sizing of orifice?

If one assumes the piping around the orifice to be well insulated, then the process is adiabatic.

If one assumes the orifice losses as negligible, then the adiabatic procees to the vena-contraca is isentropic. And KE changes must be accounted for. Flow, if choked is easily calculated, if pv^n is know for that process, two phase or not.
If one accounts for orifice losses, and flow is choked, then one uses a modified isentropic flow calc which should include the orifice coef.  The orifcie Cd is related to actual flow to ideal(isentropic) flow thru the choking point.  Calculate isentropic flow and then multiply by the Cd.
With choked flow and a known back pressure one may then obtain the downstream fluid properties.
If my memory serves me right, I believe the equivalent gamma for sat steam folllowing an isentrope follows  approx PV^1.1=constant.  
I would further emphasize, that the choked flow equations used earlier in this discussion for perfect gas ,const gamma, should include upstream pressure and temp as total or stagnation conditions, not static.
If the Chem Engineers Hand Book uses static, they are wrong.
On another symposium, I included, MdGraw-Hill response to the error used in the choked flow equation in the Mechanical Engineers HandBook.  McGraw-Hill advised that the next edition would be corrected.

RE: Sizing of orifice?

Latexman:

Let's first look at one of ddkm's postings:

Quote:

ddkm (Chemical) 9 Nov 05 22:41  
Let's look at the calculation I've done:

I'm trying to size an orifice for a high-pressure steam line with the purpose of restricting the flow (for safety reasons).

Data is as follows:
Steam supply
P = 75barG
T = 291ºC (saturated steam, extrapolated from tables)
As you can see his steam supply is at 75 bara not 41 bara. And as we know from all of the the foregoing postings, he was looking at an orifice to let that steam down to some lower pressure such that the flow would be at choked conditions. Therefore, his pressure downstream of the orifice would have to be about one-half or less of the upstream pressure ... that is, 38 bara or less. In effect, he has some quite high pressure steam and he is letting it down to a lower pressure.   

Now let's look at your last post:

Quote:

But, is the pressure downstream of the orifice going to drop?  I don't think so.  There will be pressure recovery coming out of the vena contracta as the kinetic energy (velocity) is converted to potential energy (pressure).  The permanent pressure drop of the orifice will determine where the final pressure ends up downstream of the orifice, and it looks like that will be slightly in the two phase region.
I don't understand what you are saying. The pressure downstream of the orifice is fixed by the overall system and not by what happens in or around the orifice. We have established that the downstream pressure is 38 bara or lower. No matter what energy changes occur during the path from the upstream pressure to the downstream pressure, if the flow is choked then the downstream pressure must be and is 38 bara or lower.

I agree that the path between the upstream 76 bara pressure and the downstream 38 bara or lower does involve first an isentropic drop in pressure and enthalpy ... and then there is an isobaric recovery of enthalpy until it reaches the original enthalpy. The net result is that the downstream enthalpy is the same as the upstream enthalpy, thus the overall expansion through the orifice is isenthalpic.

As I said before, when I look at this on my Mollier diagram, if the downstream pressure is about 6 bara or less, the downstream steam will still be saturated or even somewhat superheated.

Latexman, this is exactly what happens as steam flows through any steam pressure letdown station ... the expansion is isenthalpic. In fact, many steam pressure letdown stations include a desuperheater for the downstream steam.

If the upstream steam pressure were routed through a nozzle discharging into a turbine, where the steam then drove the turbine, the steam expansion would then be isentropic because work was extracted from the steam. In the case we are talking about in this thread, no work is being extracted from the steam and I repeat that the expansion is isenthalpic.

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

RE: Sizing of orifice?

mbeychok:

When I said:

Quote:

. . . I recall the pressure at the orifice being around 41 bara.

I meant literally at the orifice.  Technically speaking, I should have said at the vena contracta which is about half a pipe diameter downstream of the orifice.

So, yes, I knew the supply pressure was 76 bara.  I used Cp/Cv = 1.28 given by ddkm, and my program estimated the critical pressure ratio at 0.54.  That’s how I got 41 bara at the orifice.

Ddkm’s scenario could be that the pressure or flow control system further down stream of the restrictive orifice failed wide open.  It could also be he has a PSV that is too small if the steam flow rate exceeds 1700 kg/hr and something else is going on.  And if this something else is not going on, things run along smoothly and there isn’t a failed open control.  It could be many other things.  We don’t know exactly what’s going on.  My assumption was that for whatever happens further downstream of the orifice in the scenario it does not significantly pull the pressure down past the fully recovered pressure of the orifice.  Based on this, the part you didn’t understand all happens 4 to 8 pipe diameters downstream of the orifice if what is further downstream doesn’t significantly pull the pressure down past the fully recovered pressure of the orifice.  It’s a textbook description of what goes on as a gas flows through an orifice run for measuring flow.

I've sized restrictive orifices for scenarios that went either way, the downstream pressure was pulled way down and it wasn't.  It doesn't affect the sizing of the orifice, but in this case it does affect the downstream pressure drop calculations (one phase or two) or how the phases could be handled.  For example, if it stayed in the two phase region for any appreciable time and/or length of pipe, and depending on the layout of said pipe, the condensate may have to be removed as it condenses or it could accumulate in some low spot and cause all kinds of problems, like slugging, water hammer, piping erosion, etc.

Good luck,
Latexman

RE: Sizing of orifice?

mbeychok You have stated
"In the case we are talking about in this thread, no work is being extracted from the steam and I repeat that the expansion is isenthalpic."

If the piping in the vicinity of the orifice is well insulated, the flow is adiabatic. Now, if the velocity up and downstream of the orifice does not change, then isenthalpic applies.  Have you checked the velocities?
Of course the velocities will have to change.  If the change is small, then you can state that the process is approximately isenthalpic.

RE: Sizing of orifice?

(OP)
Wow, I was away from my computer for a few days and this topic has grown really large! Thanks for all the valuable input and side-topics. I'm still trying to read them in detail.

Maybe I'll respond to the latest ones first, maybe it's easier this way.

Latexman: You guessed correctly. The orifice is purely for FLOW restriction.   The inevitable pressure drop across the orifice is what is not preferred. The flow restriction is due to the fact that the vessel has indeed a PRV which has a discharge capacity of only 1700kg/hr.

Also, based on the critical pressure ratio, the fully recovered pressure (Is this the correct term?) after the orifice should be 41bar(A).

RE: Sizing of orifice?

(OP)
Sorry, what I meant is maximum pressure after the orifice should be 41bar(A) or less to sustain the critical flow assumption.

Calculation:

Pcf/P1    =    {2/(k+1)} ^ {k/(k-1)}

where

Pcf    = critical flow throat pressure
P1    = upstream relieving pressure
k    = ratio of the heat capacities (Cp/Cv) for any ideal gas

Using k=1.28  and P1=76bar(A):

We get:   Pcf = 41bar(A)


Comments?

                

RE: Sizing of orifice?

(OP)
Milton:

Your explanation on the role of the gc constant in the context of the SI and non-SI environment makes a whole lot of sense and very very useful to the core discussion here. After reading through it, I also agree that this constant functions purely for conversion between the different systems and does nothing else.

But for those who do not have the benefit of reading your explanation, when they are first introduced to the equations in the literature, they would be confused.

As katmar has pointed out rightly, restructuring the SI units in the gc constant gives a final dimensionless value. And a value of unity at that!

Furthermore, if you restructure the nonSI units in the gc constant (32.17 ft lbm/lb[sub]f[/ sup]s2, the final value is also dimensionless!

And to think that literature (Perry) refers to it as a dimensional constant!

RE: Sizing of orifice?

ddkm,

The value of gc in US Customary units is not dimensionless. The combination ft.lbm/s2 is mass x acceleration and is equal to poundals. The units of gc are therefore the ratio of poundals per pound force, and as I stated earlier this conversion factor is 32.17.

Where do the "pound force" units appear?  Again, this is a bad practice that has become accepted by users of US Customary units.  The units of pressure, which are given as "pounds per square foot" should be given as "pounds force per square foot".  This is where the mixed units creep in unnoticed, and create the need for gc.

regards
katmar

RE: Sizing of orifice?

What is the basis for gamma or k= 1.28 for the expansion of saturated steam undergoing an expansion thru a wet state?


I believe the original question should have been placed on the thermodynamics forum.  

 

RE: Sizing of orifice?

(OP)
k = Cp/Cv  but I've not been able to find individual values of Cp and Cv. So far, the data available just states "heat capacities" or "specific heat".

What I've noticed is that some worked examples I've read from literatures, normally associates the k of steam to be around the value of 1.28-1.35.

Anyone know an internet link where we can find the actual values?

---engineering your life---

RE: Sizing of orifice?

There is no way to get a Cp or Cv for two phase steam water mixtures.  You may however plot the isentropic process starting with saturated vapor and get a relation of pressure to specific volume.  That relation will yield something like pv^1.1 is a constant.

RE: Sizing of orifice?

(OP)
As an update, I couldn't find anything useful in Perry, but over the internet, so far I found this LINK, which basically gives only at temperature of 300K.

As example, for steam at 300K (hope it's readable):



Material Properties of Perfect Gases (PG-Model) (at 300 K)

Gas Formula Molar Mass Gas constant Spec. Heat at Const. Press. Spec. Heat at Const. Vol. Spec. Heat Ratio   

Steam H2O 18.015 0.4615 1.8723 1.4108 1.327  
    



Basically, k for steam is about 1.327 at 300K.

---engineering your life---

RE: Sizing of orifice?

(OP)
Milton/katmar:

Another question.  What would be the equation to use for calculating the maximum flow for non-critical flow?   I can't find this in Crowl/Louvar.

Will I find it in your website, Milton?   Anyway, I'll be reading it tonight, hopefully I'll find something.

Thanks.

---engineering your life---

RE: Sizing of orifice?

ddkm
Flow thru the orifice thru its exit prior to expansion to the larger down stream piping is two phase. The ratio of specific heats has no meaning unless the flow is in a metastable condition.  That condition is possible however, in a metastable condition, a shock/discontinuity to two phase normally occurs.

RE: Sizing of orifice?

ddkm,

You cannot really define a maximum flow for non-critical conditions. For a fixed upstream pressure the flow will increase as the downstream pressure decreases, until the choked condition is reached.

There must be hundreds of references on the internet, and in any standard fluids books you can lay your hands on (or even Perry), that will give you the necessary formula. But be aware that there will be two types of formulas. One is for using an orifice for metering flows, and the other is for so-called restriction orifices. In a metering application the pressure drop is basically the drop from the upstream pressure to the vena contracta, whereas in a restriction orifice you are looking at the overall pressure drop to a few pipe diameters downstream from the orifice.

There are a few computer programs that will give you the k value for steam at various temperatures and pressures. Googling for "Water and Steam Properties" will take you there. I can't comment on what Sailoday28 has said - when it comes to discontinuous metastable shocks I am lost.

RE: Sizing of orifice?

In the metastable state the fluid stays as a single phase.
For example, in the depressurization of sat steam thru a ventui or nozzle, it has been observed that the steam will not go two phase as the pressure drops. Then at a certain point along the axis of the nozzle two phase suddenly apprears. This is a discontinuity in the flow. What has been approximately an isentropic proscess yields a shock and entropy increase.  That process has been observed/measured in nozzles of steam turbines.

A similar result is in steam traps.  Sat water flows thru the trap. In the process where flashing should start, the water stays single phase.-Then suddely flashes. The result is higher than normally calculated flows for the trap.

RE: Sizing of orifice?

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.

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

RE: Sizing of orifice?

I hope you are not comparing the responses to Thesis material.  This topic thread should be on the thermodynamics forum.

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