2 replies to this topic

[Bonestein]

Hello All,

I’m attempting to calculate the maximum mass flow rate through a ½” diameter leak in a refrigerant line. Why? California Mechanical Code requires abatement of refrigeration machine room exhaust if there is a potential for the concentration of the accidentally released refrigerant exceeds 25% LEL or 50% IDLH. The exception to the abatement requirement requires approved exhaust plume calculations concluding such concentrations would not be possible.

I had two choices, prove that the machine room exhausted airflow would never exceed the 25% LEL or 50% IDLH or model the exhaust plume to determine the concentration of refrigerant at the adjacent property boundary. I decided to calculate the exhausted airflow through the ½” diameter leak. I calculated it by estimating the mass flow rate for choked flow (sonic flow).

The equation that was selected is the Rasouli and Williams source model (found on this website):

CD (A / V) (g R / M)^1/2 [(k - 1)/(2k)] k3/2 [2/(k + 1)]^a (T0 / P0^ b )^1/2 (t2 - t1) = P2^c- P1^c

By solving for pressure and varies times after initial discharge and assuming issetropic flow, I solve for corresponding temperature:

(T2 / T1) = (P2 / P1)^(k -1)/k

I solve for mass flow with the ideal gas law

W = P V M / R T

There’s one assumption that I’m not sure is valid and I’, hoping to get feedback. What is the source volume? Is the source volume the approximate volume of pipe and shell on both the high pressure side (downstream of the compressor and upstream of the expansion valve) and the low pressure side (downstream of the expansion valve and upstream of the compressor)?

If it’s only the high pressure side, do I assume the volume of saturated liquid refrigerant and the volume of saturated vapor are essentially equal?

Does anyone have any thoughts?

This is getting complicated.

Any input asides from requesting that I simply fudge it would be greatly appreciated!

[Art Montemayor]

Bones:

This is a very interesting, real-life problem that others besides myself probably want to comment on. However, I'm having a lot of problems trying to read and understand your post -- due primarily to the use of some font characters that are not liked by this website. For example, I can not interpret the identity of the leak diameter you write. I also believe you are using something else besides a normal apostrophe, since what appears to be the contraction "I'm" comes out garbled.

Can you furnish another copy of your text? I tried to edit your original text but it reads the same as it appears in this forum. If you have trouble typing the text in directly, you can send it to me at my personal email through this forum and I'll insert in into the forum, making sure it reads OK.

I think you are using the paper published by Milton Beychok in this website - which, in my opinion, is the correct thing to do. However, I have questions about what the nature of the presumed leak is. You don't state if it is liquid refrigerant (it would help to know the actual refrigerant - I don't think we're talking about NH3; or are we?) or the gas phase. It makes a difference - as you can read in Milton's paper. If you are leaking out liquid refrigerant, there is no sonic velocity in question. The maximum flowrate available with sonic (choke) flow is only obtainable with gaseous flow. Milton visits this forum regularly, as witnessed by his posts from time-to-time, and I'm sure he would love to give you his valued and expert comments. You couldn't get better, expert help from anyone else on this subject. But first, lets get the basic data in readable and understandable format. Let's try to get your post in good, specific and correct engineering English so that Milton and others can fully and correctly understand what it is that you are up against and what we can help you with.

Don't forget to get in touch with me via email if you have problems. I can help. I'll await your re-post or your response for help.

Art Montemayor
Spring, TX

[mbeychok]

I agree with Art Montemayor that you need to re-submit your posting and use fonts that are printable in this forum.

I would also make four other points:

(1) The Razouli and Williams model applies only to choked flow of a gas. It does not apply to either liquids or to flashing two-phase flow. In other words, if your refrigerant is ammonia or propane (for example), and you are leaking liquid ammonia or liquid propane, it will flash into two-phase flow and that cannot be handled by the Razouli and Williams model.

(2) If you are leaking gas, and want to use the Razouli and Williams model, I would strongly urge you to visit www.air-dispersion.com/feature2.html to read the updated version of my article.

(3) If you are leaking a liquified gas (such as ammonia or propane) which will flash into two-phase flow, then visit www.air-dispersion.com/source.html and select whether you want metric units or the customary USA units. Then select discharge of a "Flashing Of A Saturated Liquid". That will show you how to calculate the instantaneous initial flow of flashing liquid through the leak.

(4) Finally, if you are leaking a gas and want to simplify the work, I would suggest that you not use the Rasouli and Williams model. Instead, visit www.air-dispersion.com/source.html, select metric or USA units, and then select "Gas Discharge From a Pressurized Source". That will show you how to calculate the instantanous initial gas flow (either choked or non-choked) through the leak. That will be higher than the time-averaged flow rate you would get using Razouli and Williams. The higher instantaneous initial flow will be more conservative but much more easily calculated.