Choked Flow Critical Area Question
Choked Flow Critical Area Question
(OP)
Hi All,
I'm a pretty new engineer a couple years out of college. The topic of choked flow keeps coming up at my job so I've bought a couple compressible flow books and am attempting to educate myself. Currently browsing through Compressible Fluid Flow by Saad (if you have any other recommendations, please let me know). In the section discussing mass flow, Saad shows that the maximum mass flow occurs when Mach Number = 1 and minimum flow area. The minimum flow area is A* the cross sectional area at M = 1. He goes on to define a ratio A(actual)/A* and states that this value can never be less than 1.
What does this mean? If A* at M = 1 is defined as 5 in2, what would happen if A = 3 in2? It seems to imply this can't physically happen so I'm confused.
Thanks for your time
I'm a pretty new engineer a couple years out of college. The topic of choked flow keeps coming up at my job so I've bought a couple compressible flow books and am attempting to educate myself. Currently browsing through Compressible Fluid Flow by Saad (if you have any other recommendations, please let me know). In the section discussing mass flow, Saad shows that the maximum mass flow occurs when Mach Number = 1 and minimum flow area. The minimum flow area is A* the cross sectional area at M = 1. He goes on to define a ratio A(actual)/A* and states that this value can never be less than 1.
What does this mean? If A* at M = 1 is defined as 5 in2, what would happen if A = 3 in2? It seems to imply this can't physically happen so I'm confused.
Thanks for your time





RE: Choked Flow Critical Area Question
If you mean something else, you'll have to be more clear. Attach a sketch.
Good luck,
Latexman
Technically, the glass is always full - 1/2 air and 1/2 water.
RE: Choked Flow Critical Area Question
I'm having trouble understanding choked flow in general, so any guides or references you could point me to would be appreciated.
Thanks
RE: Choked Flow Critical Area Question
Good luck,
Latexman
Technically, the glass is always full - 1/2 air and 1/2 water.
RE: Choked Flow Critical Area Question
RE: Choked Flow Critical Area Question
When choked (M = 1), downstream pressures cannot be transmitted upstream to affect mass flow. Pressure wave travel at sonic speed. Since sonic speed exists at A*, pressure waves cannot get past A*.
Good luck,
Latexman
Technically, the glass is always full - 1/2 air and 1/2 water.
RE: Choked Flow Critical Area Question
One more question, if you don't mind. With regards to pressure drop in a pipe after it becomes choked flow, what would be the best approach to calculate it in your opinion? I've come across some things saying the pressure in pipe after it becomes choked can't fall below P* while others seem to imply only the region directly downstream of the shock is P* and frictional losses are calculated as they usually are.
RE: Choked Flow Critical Area Question
Directly downstream of the shock is the backpressure created from that point to the exit. A lot of times I've heard folks say to calculate this pressure drop backwards - from exit to choke point.
Good luck,
Latexman
Technically, the glass is always full - 1/2 air and 1/2 water.
RE: Choked Flow Critical Area Question
With a tail pipe longer than about 8 times the tailpipe diameter it gets a lot messier. Let's say that we have a SG 0.6 gas at 10,000 psia upstream of an atmospheric vent with a tail pipe. Critical pressure is 5457 psia (using k=1.3) which is a fair bit above atmospheric pressure, so you would expect a second standing wave in the pipe, and a third, etc. The only way I've ever been able to match physical system performance with a tail pipe on my blowdown has been to use the critical pressure relative to atmospheric pressure (e.g., 27 psia at sea level). This is a much smaller mass flow rate than you would get using the system flow rate, but when I've used the system pressure I've predicted blowdown times that were far shorter than we saw in the field.
Once you have a mass flow rate that you believe, you can calculate flowrates a pressure drops throughout the system.
David Simpson, PE
MuleShoe Engineering
In questions of science, the authority of a thousand is not worth the humble reasoning of a single individual. ùGalileo Galilei, Italian Physicist
RE: Choked Flow Critical Area Question
RE: Choked Flow Critical Area Question
Field measurements have matched my conceptual model in dozens of system blowdowns. If (with a tailpipe) I use a critical pressure bulked up from local atmospheric pressure I generally can project a blowdown time within a few minutes of actual. If I use system pressure and recalculate upstream pressure every second I predict blowdown times that are 5-10% of actual.
David Simpson, PE
MuleShoe Engineering
In questions of science, the authority of a thousand is not worth the humble reasoning of a single individual. ùGalileo Galilei, Italian Physicist
RE: Choked Flow Critical Area Question
Attached is a quick sketch of the tailpipe of the scenario you described, with some fittings added. I'm imagining you start just inside the pipe end at 27 psia (last wave). Then you march up the pipe, adding back any pipe friction/fitting losses until you build up to the next shock wave?
I believe in this situation mass flow must be same all throughout the tailpipe, but the velocity changes significantly after each of those shock waves which drops the pressure. Or am I going about it the wrong way?
RE: Choked Flow Critical Area Question
Yes.
No.
Good luck,
Latexman
Technically, the glass is always full - 1/2 air and 1/2 water.
RE: Choked Flow Critical Area Question
27 psia is the pressure upstream the last shock wave, just inside the pipe. How do you determine where the other shock waves are? In other words, how do you know it doesn't just go from 14.7-> 27-> 50-> 92-> 169-> 310 psia, etc, up to 5,457, in consecutive shock waves? What determines the spacing?
Thanks for all your help
RE: Choked Flow Critical Area Question
Let's say that your blowdown was in the middle of a multi-mile line. Among a million other things that you don't know, you have no valid way to apportion the flow from the left and the flow from the right. And if you were able to fix it at a point in time, it would change in the next milisecond.
My technique is to:
- Determine mass flow rate out the end of the pipe with critical pressure on the upstream and of the tailpipe and atmospheric pressure immediately after the shock wave.
- Assume pressure at the trunk (on the tailpipe side) is at critical for the system pressure (gives you a dP down the tail pipe, but be really careful trying to pretend that velocities in this transonic region mean anything with regard to pressure drops or friction).
- Jump to the head(s) of the pipe and measure the pressure(s)
- Use some method to apportion the mass flow rate that is leaving the system to the various flow paths (I use percent of total pipe volume for my first iteration, you have to use something)
- Using the mass flow rate (converted to volume flow rate at standard conditions) to convert the upstream pressure to a system pressure at the hole.
- Do that for each leg and when you don't get the same value for pressure at the outlet from the various legs, tweak the relative flow rates until you do.
- Then move the clock ahead a few seconds and do it again.
- Repeat until you reach your target conditions (I do this to estimate blowdown times, I can't think of another reason to do it).
It is really ugly, non-theoretical, empirical, and cumbersome. You really have to have a good reason to put yourself through it. I wrote a MathCAD program to do all the picky iterations and friction factor calculations so it doesn't hurt quite as bad as it used to, but it still is a pain and it only gets you to the start of the transonic exit region. I've never found a good way to do any calcs in the transonic region at all, so I typically guess a duration to 0.6 Mach. Once exit velocity drops below 0.6 Mach, you can go back to incompressible math and get closer to theoretical activities.I have never found many people who were all that interested in working with compressible flow within a pipe. Everything I've ever done with it has started with aerospace calcs and tweaked them to work in a pipe. I never published my tweaks because I never found anyone who cared enough for it to be worth the effort.
David Simpson, PE
MuleShoe Engineering
In questions of science, the authority of a thousand is not worth the humble reasoning of a single individual. ùGalileo Galilei, Italian Physicist
RE: Choked Flow Critical Area Question
Ted
RE: Choked Flow Critical Area Question
Wow. I knew compressible flow was infinitely uglier than incompressible flow but I didn't know we couldn't analyze so much of it in a pipe. This came about from not fully understanding the compressible flow software we have and trying to educate myself to hopefully explain what it was doing. But that sounds unlikely now haha.
Hydtools,
Thanks! I'll definitely go through that.
RE: Choked Flow Critical Area Question
David Simpson, PE
MuleShoe Engineering
In questions of science, the authority of a thousand is not worth the humble reasoning of a single individual. ùGalileo Galilei, Italian Physicist
RE: Choked Flow Critical Area Question
See attached article. Quite interesting although a bit of a departure from your original question. It does illustrate a lot of the phenomena explained by zdas04.
http://www.aft.com/documents/AFT-CE-Gasflow-Reprin...
RE: Choked Flow Critical Area Question
Thanks for the article. I've actually come across that one before and it's very helpful.