Sizing of orifice? 2

[ddkm]

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.

 

[Assumptions]

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)]

 

[Latexman]

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

 

[sailoday28]

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.

 

[Latexman]

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

 

[mbeychok]

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)
.

 

[Latexman]

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

 

[sailoday28]

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.

 

[mbeychok]

Latexman:

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

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:

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)
.

 

[Latexman]

mbeychok:

When I said:

. . . 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

 

[sailoday28]

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.

 

[ddkm]

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).

 

[ddkm]

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

Calculation:

P_cf/P₁ = {2/(k+1)} ^ {k/(k-1)}

where

P_cf = 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: P_cf = 41bar(A)


Comments?

 

[ddkm]

Milton:

Your explanation on the role of the g_c 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 g_c constant gives a final dimensionless value. And a value of unity at that!

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

And to think that literature (Perry) refers to it as a dimensional constant!</sub>

 

[katmar]

ddkm,

The value of g_c in US Customary units is not dimensionless. The combination ft.lb_m/s² is mass x acceleration and is equal to poundals. The units of g_c 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 g_c.

regards
katmar

 

[sailoday28]

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.

 

[ddkm]

k = C_p/C_v but I've not been able to find individual values of C_p and C_v. 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---

 

[Latexman]

I don't know where on the internet, but Crane Technical Paper 410 has a graph of Cp/Cv for steam versus absolute pressure. ddkm, you need a copy of this extremely valuable reference anyway, if you don't already have it. You can read about it here

http://www.cranevalve.com/tech.htm

and buy it here

http://store.vervante.com/c/v/category.html?pard=crane

for $36.

Good luck,
Latexman

 

[sailoday28]

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.

 

[ddkm]

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):


[blue]
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

[/blue]


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


---engineering your life---

 

[ddkm]

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---