Talk:Choked flow

From Wikipedia, the free encyclopedia

[edit] Mass flow rate of a gas is not limited under choked conditions

This article needs re-writing to make clear that: (a) the flow of a gas through a restriction attains a maximum linear velocity (i.e., m/s or ft/s) under choked conditions and that velocity cannot be increased by reducing the downstream pressure, but (b) the mass flow rate (i.e., kg/s or lb/s) is not limited under choked conditions ... it can still be increased by increasing the upstream pressure. That is easily shown by the equation for mass flow rate under choked conditions:

References:

• Handbook of Chemical Hazard Analysis Procedures, Appendix B, Federal Emergency Management Agency, U.S. Dept. of Transportation, and U.S. Environmental Protection Agency, 1989.

Handbook of Chemical Hazard Procedures

• "Risk Management Program Guidance For Offsite Consequence Analysis", U.S. EPA publication EPA-550-B-99-009, April 1999.  Guidance for Offsite Consequence Analysis

• "Methods For The Calculation Of Physical Effects Due To Releases Of Hazardous Substances (Liquids and Gases)", PGS2 CPR 14E, Chapter 2, The Netherlands Organization Of Applied Scientific Research, The Hague, 2005. PGS2 CPR 14E

[edit] Finished a complete revision

I just finished the complete revision of this article. - mbeychok 21:39, 18 March 2006 (UTC)

[edit] Some corrections

I clarified some of the terminology:

• there was confusion over upstream vs. ambient pressure

• It was not clear that choked flow occurs in fluids as well as ideal gases

• The equations deal with molecular ideal gases. Non-ideal gases have significant nonlinearities in the equation of state (ie they differ from the "PV=nRT" form, including higher powers of T, P, and V). In one place, real vs ideal was contrasted incorrectly -- the correct contrast is molecular vs. monatomic ideal gases.

I also generalized the discussion a bit -- Mbeychok's nice treatment dealt primarily with gas venting from a closed system, but choked flow holds for many more systems than just that.

Cheers, zowie 19:19, 23 March 2006 (UTC)

Zowie, thanks for your two lead-in paragraphs. I only see one problem with them and that is the use of the word "flow" without qualifying whether we are talking about volumetric flow (i.e., linear velocity times cross-secdtional area) or about mass flow. I believe that one cannot stress the point enough that "choked flow" pertains to the linear velocity or the volumetric flow rate, but not to the mass flow rate which can still be increased by increasing the upstream pressure ... at least, for gases. Do you think that you could perhaps add a sentence to your lead-in paragraphs stressing the distinction between volumetric flow rate and mass flow rates?

I have yet to find or read a clear presentation concerning choked liquid flows or to find any relevant, precise equations defining choked liquid flows.- mbeychok 01:29, 24 March 2006 (UTC)

No problem, thanks for the updates. There's a nice presentation here: [1]. In engineering circles single-phase choked fluid flow is often called "critical flow"; it might be easier to spot by that name (and, come to think of it, we should mention that in the article...) It's set by the same condition as choked gas flow -- zero pressure in the choke plane -- but as the motion is incompressible some of the terms are different.

Hmm... I might not understand what you mean about mass flow vs volumetric flow, since I'm used to thinking more about fluids than gases. By increasing the upstream pressure in a gas, you increase the sound speed, which in turn increases the linear flow rate in the choke plane -- isn't that the mechanism for increased rate if the upstream pressure is increased? Since KE = 1/2 mv^2, in the choke plane, all of the internal PE is converted to KE, and the PE is linear in the pressure, one should expect the flow rate to vary as the square root of the pressure, at constant density -- which is exactly what you have in your equations.

Cheers, zowie 05:17, 24 March 2006 (UTC)

I think our problem in one of semantics. I have been a practicing engineer for over 50 years and you're an astrophysicist. We simply don't speak the same language. So please bear with me as I try to clarify the difference between mass flow rate and volumetric flow rate. And also for the moment, let us forego using the word "fluid" and talk only of gases and liquids.

By mass flow rate, I mean gas mass per unit time (e.g., kg/s) and by volumetric flow rate, I mean gas volume per unit time (e.g., m³/s). By linear velocity (or speed), I mean distance per unit time (e.g., m/s).

Now, take another look at my opening comment on this talk page and also at the choked flow equation for a gas (which is one of the two equivalent forms I've presented in the choked flow article itself). When the ratio of upstream pressure to downstream pressure across a flow aperture is sufficient to cause choking, it is the gas linear velocity that becomes choked when that velocity reaches sonic velocity. When the linear velocity chokes, the volumetric flow rate also becomes choked because the volumetric velocity is simply the linear velocity multiplied by the area of the aperture (i.e., volume = area × velocity).

But the mass flow rate does not become choked!! As plainly shown in the choked flow equation for calculating the mass flow rate (in my opening comment), increasing the pressure will increase the mass flow rate even though the volumetric flow rate can not increase at choked conditions. Why? Primarily because increasing the pressure, increases the density of a gas and a higher gas density results in a higher mass flow rate without any change in the volumetric flow rate (e.g., mass flow rate = density × volume flow rate).

Why did I think this is important information to impart? Because over the years, I've encountered literally dozens of engineers who thought choked flow conditions limited their ability to increase the mass flow rate through their calibrated orifices and other flow control devices ... when, in fact, only the volumetric flow rate is limited.

Since the effect of pressure on the density of liquids is almost negligible (compared to the effect of pressure on gas density), the choked flow of liquids is probably very much different than that of gases. That is why I felt simply using the words "flow" and "fluids" isn't specific enough and we should always be very careful to make the distinction between "mass flow rate" and "volumetric flow rate" ... as well as between "compressible fluids" and "incompressible" fluids.

Please excuse me for being so long-winded and for perhaps dwelling on what is obvious to you, but I did want to get us talking the same language. - mbeychok 07:18, 24 March 2006 (UTC)

No, no, thank you for taking the time!

Hmmm... I had some more thought about gas pressure, and I think I've been wrong-headed about it. After all, in an ideal gas, zero pressure -> zero density -> zero mass flow, so I've apparently been thinking wrongly about the gas case. Even in the fluid case, "zero pressure" can't really be zero pressure since then you get a two-phase flow as the water boils, and the flow clearly isn't strictly choked then.

I think I've also been thinking something different than you as the definition of "choked" -- it seems obvious to me that changing the pressure upstream should change the flow rate; the surprising and interesting thing is that changing the pressure downstream doesn't change it, and I've been mentally labeling that condition "choked"! But now I understand, I think. Increasing gas pressure at uniform temperature doesn't increase the sound speed (which depends only on temperature and molecular mass), so the linear flow rate can't change as the pressure changes -- but the density changes, so the mass flow rate can vary. Yes?

I must apologize -- this is really quite far outside my realm of expertise, as you noticed, so I must defer to you on definitions and such. zowie 16:40, 24 March 2006 (UTC)

Yes, I think that we now understand each other much better. Under choked flow conditions, any further decrease of the downstream pressure will indeed not change the mass flow rate or the volumetric flow rate. However, increasing the upstream pressure will result in an increase in the mass flow rate. That is precisely what the choke flow equations are saying in their own language.

So, it would be kind of you if you would please emphasize that point in the opening paragraphs that you added ... and also emphasize the point that choked flow in gases is quite different from choked flow in liquids.

The reason that I did not write about choked flow in liquids is, quite frankly, that I lack enough knowledge about that aspect. I don't believe in reading a few books or articles and becoming an instant "expert". Perhaps, someone truly knowledgeable will add a section on that subject. - mbeychok

Okay, I updated the introduction. Is that suitable? Thanks again for taking the time to hash this out! zowie 18:48, 24 March 2006 (UTC)

In a word, yes. If you are ever in Newport Beach, California, I'd like to meet you. - mbeychok 19:16, 24 March 2006 (UTC)

I'd like that too. I live in Boulder, Colorado but I travel to California from time to time. Please look me up if you make it to the front range. zowie 20:11, 24 March 2006 (UTC)

[edit] Sailoday28, please furnish a citation

Greetings, Sailoday28: Please furnish a reference citation for the statement about choked isothermal flow occurring when the Mach number equals the square root of Cp/Cv. If you are not familiar with how to format a reference for a Wikipedia article, simply provide your reference just below here and I will format it and install it for you. If possible, an online reference would be preferable. Regards, - mbeychok 05:54, 14 February 2007 (UTC)

Ho=stagnation enthalpy, h=enthalpy, V=spec vol, U=velocity,

P=pressure, G=mass flux, gamma=cp/cv, a=sound speed, a^2=gammaRT

M=U/a

subscript 1 refers to upstream conditions

dHo=dQ and also dQ=dh-VdP

dU^2/2+dh = dQ = dh-VdP

dU^2/2 + VdP=0

For isothermal process and perfect gas:

dU^2/2 - RTdV/V = 0

Integrate U^2/2 - U1^2/2 - RT ln(V/V1) = 0

But U=GV, so (GV)^2 -(G1V1)^2 - 2RT ln(V/V1) = 0

Differentiate G wrt V and set=0 to maximize mass flux

2V(G^2)-2RT/V =0

But GV=u

U^2 = RT, M^2 = U/a)^2, M^2=RT/a^2 = RT/(gammaRT)

M^2=1/gamma

—The preceding unsigned comment was added by 69.140.39.229 (talk • contribs) 14 February (UTC).

Thanks, 69.140.39.229, whomever you may be, for the contribution of your derivation. But when I asked Sailoday28 for a reference, I meant a book, journal article or online article ... in other words, a verifiable, valid reference. This article still needs that. - mbeychok 19:30, 14 February 2007 (UTC)

Sailoday28 provided a valid reference on his Talk page in response to my request and I have now added the reference into this article. All is well. - mbeychok 05:17, 16 February 2007 (UTC)

[edit] Choked flow discussion.

Mbeychok. I think some discussion would help as to the focus of your original write up. I don't wish to take away all the good work that you have put into this article. As you have demonstrated, you are a good writer and probably can incorporate some comments of mine which I think are worthwhile. My email is sailoday_28@yahoo.com PS, The equations that looked like jibberish for isothermal flow were mine and thank you for straightening them out. Regards```` —The preceding unsigned comment was added by Sailoday28 (talk • contribs) 22:59, 22 February 2007 (UTC).

Sailoday28, I would be pleased to hear from you. Just go to my user page by clicking here ==>mbeychok. Then in the left hand frame scroll down to the link at "Email this user" and click on it. Be sure to include "Wiki email" in the subject so that it won't be deleted as spam. When I subsequently reply to you, then you will have my regular email address.

By the way, if you would just create a user page of your own, then your name would henceforth appear in blue rather than red. You could also automatically sign your comments on any Discussion page (as explained in the box at the top of this page) by simply typing 4 tildes at the end of your comments like this: ~~~~. As I think I said before, if you expect to do much on the Wikipedia, it is worth taking the time to at least learn how to create pages, how to edit them correctly, how to create internal Wiki links, and how to use Discussion pages. Regards, - mbeychok 23:47, 22 February 2007 (UTC)

Sailoday28: I sent you an email (at your Yahoo address) on Saturday, Feb 25th, discussing how we could collaborate on your suggestions ... and I am waiting of your reply. - mbeychok 19:41, 25 February 2007 (UTC)

[edit] Purpose of "choked" flow

If you agree that choked flow is that resulting from given upstream conditions to the point where downstream backpressue will not effect flow then you might want to rearrange article to different types of choked flow not necessarily in the following order: 1- choking due to the area change--ie venturi effect 2. adiabatic choking in pipes 3 isothermal choking 4-choking with heat addition to pipe

You have started with perfect gas using a Cd. Perhaps a real gas formulation such as a "Generalized" Beattie-Bridgeman or others could be included. By Generalized, I am refering to type of equation of state (EOS)which is reasonably accurate for a number of gases.

The EOS could also be applied to items 2, 3 and 4 above.

Give one example for each discussion.

Main focus for all of above would be for a non-condensing gas.

Regards Sailoday28 22:45, 23 February 2007 (UTC)