Does orifice diameter affect critical pressure when testing for choked flow? 2

Does orifice diameter affect critical pressure through a converging nozzle, or is it entirely dependent on the ratio of inlet and outlet pressure? (assume Isentropic flow of air). References from other forum posts listed at the bottom.

I've seen many references for testing for choked flow using the following equation that depends only on pressure, not orifice diameter. Assuming dry air (k = 1.4), this works out to P/Po < .5283 for sonic flow (M=1) to occur.

Does orifice diameter have any effect on this? For example, if I enlarged the orifice to 99% on the inlet pipe diameter, wouldn't sonic flow cease to occur?

The formula for mass flow seems to reinforce that orifice area only scales the mass flow, with no effect on when max flow peaks (i.e. at sonic speeds, M = 1).

Am I thinking of this correctly? What gives?


Posts from other forums regarding choked flow:
[faq798-1196]
[faq1203-1293]

Other guides on sonic flow I have studied but had a hard time digesting.
[

http://highered.mcgraw-hill.com/sites/dl/free/0072938447/367579/Ch9_sample.pdf

]
[

http://www.engr.ipfw.edu/~renie/ME301 Page/ch16.pdf

]

Thanks in advance for straightening me out!

 

[zdas04]

Velocity is choked, mass flow rate is not. As long as downstream pressure is less than P[sub]choked[/sub] (I find that thinking of it as a ratio leads to mistakes, I always put upstream pressure on the right side of the equation) then you will have choked flow.

The NASA equation understates the effect of the transition from pipe flow to unconstrained flow and overstates flow, but the implication that sonic velocity is not a function of either hole size or how far the upstream pressure is above choked flow is correct.



David Simpson, PE
MuleShoe Engineering

"Belief" is the acceptance of an hypotheses in the absence of data.
"Prejudice" is having an opinion not supported by the preponderance of the data.
"Knowledge" is only found through the accumulation and analysis of data.
The plural of anecdote is not "data"

 

[erk1313]

Thank you for the quick and thoughtful confirmation. Still seems odd that you could achieve sonic velocity through a 4" hole with inlet pressure of 25psia to 14.7 psia.

 

[zdas04]

Try it sometime, but hold your ears, it is the same dBA as 10,000 psig upstream.

David Simpson, PE
MuleShoe Engineering

"Belief" is the acceptance of an hypotheses in the absence of data.
"Prejudice" is having an opinion not supported by the preponderance of the data.
"Knowledge" is only found through the accumulation and analysis of data.
The plural of anecdote is not "data"

 

[Latexman]

You just have to have a reservoir, compressor, turbine, blower, rocket engine, etc. big enough to keep up. The F-1 engine on the Saturn V has about a 3 feet diameter opening at the throat.

Good luck,
Latexman

Technically, the glass is always full - 1/2 air and 1/2 water.

 

[sailoday28]

ZDS04
Sorry. But Choked flow occurs when the mass flow will not increase as back pressure is lowered. AND upstream conditions are fixed.
Regards

 

[zdas04]

Sailoday28,
Sorry, but you are quite wrong. Choked flow occurs when VELOCITY will not increase when either downstream pressure is lowered or upstream pressure is raised. Fixed upstream pressure is not a requirement.

Think about it. You have a system at 10,000 psig blowing down to atmosphere. The velocity will stay at Mach 1.0 until upstream pressure gets to some number around 15 psig, and then further decreases in upstream pressure will reduce velocity.

Since mass flow rate is ρ*V*A, as pressure drops (with constant V and A), the mass flow rate will drop.

The only requirement for choked flow is that downstream pressure is less than P[sub]choked[/sub]

David Simpson, PE
MuleShoe Engineering

"Belief" is the acceptance of an hypotheses in the absence of data.
"Prejudice" is having an opinion not supported by the preponderance of the data.
"Knowledge" is only found through the accumulation and analysis of data.
The plural of anecdote is not "data"

 

[erk1313]

That is my understanding as well. Increasing inlet pressure will increase mass flow, but not velocity (M). Thanks for the helpful posts... perhaps some time I will be faced with the challenge of a 3ft diameter jet engine and will put this to the test!

 

[zdas04]

I did a blowdown once through the barrel on a 14-inch pig receiver. It was quite exciting.

David Simpson, PE
MuleShoe Engineering

"Belief" is the acceptance of an hypotheses in the absence of data.
"Prejudice" is having an opinion not supported by the preponderance of the data.
"Knowledge" is only found through the accumulation and analysis of data.
The plural of anecdote is not "data"

 

[BigInch]

Knock the valve off a scuba tank sometime.

Independent events are seldomly independent.

 

[sailoday28]

zds04
Consider a perfect gas with constant specific heats undergoing an isentropic process.
Energy equation ao^2= a^2 + (gamma-1)/2 *u^2
where a= sound speed u= local velocity and subscript o stagnations coditions

For isentropic process (rho/rhoo)= (a/ao)^(2/(gamma-1))
Substitute G/rho for u in the energy equation where G is the mass flus
Differentiate the energy equation with respect to G
and you will get a/ao=2/(gamma-1) after setting derivate wrt G =0
Substitute a/ao into energy equation yielding Mach=1.
Pressure relation could have been substituted for a. See next sentence.
p/po=(a/ao)^((2gamma/(gamma-1)) ie pv^gamma =constant Substitute for a/ao will yield critical pressure ratio

In other words for steady flow M=1 when mass flux is a max.

I did the above in haste and there can be an algebraic error, however I know from my basic days in engineering that choked flow occurs when lowering back pressure will not increase the mass flow

Regards

 

[BigInch]

Heading off any potential arguments, NASA would appear to agree that mass flow rate does not increase at choked flow conditions, per the graphics in the OP, however it also appears elementary that when steady state mass flow at choked conditions is reached, the velocity at any point in the system would also be at a constant maximum.

Independent events are seldomly independent.

 

[ione]

This is how I see it.

I agree that the parameter which is choked (limited, constrained) is velocity, I agree as well that you can increase mass flow, but not acting on downstream pressure.
At choked condition the mass flow rate Q is given by:

Q = C*A *SQRT[(kM/ZRT)*(2/(k+1))^((k+1)/(k-1))]

Q = mass flow rate
C = discharge coefficient
A = orifice hole area
k = gas cp/cv = ratio of specific heats
ρ = real gas density, at upstream P and T
P = absolute upstream pressurE
M = gas molecular weight
R = Universal Gas Law constant
T = gas temperature
Z = the gas compressibility factor at P and T

So Q is independent from downstream pressure.

What I consider flawed in David’s line of reasoning is:

“Since mass flow rate is ρ*V*A, as pressure drops (with constant V and A), the mass flow rate will drop”

“A” is not constant at vena contracta if you vary downstream pressure. So the velocity is limited (choked) at M=1, but you can in any case increase Q increasing the upstream pressure.

 

[zdas04]

A is constant with time, not position.

David Simpson, PE
MuleShoe Engineering

"Belief" is the acceptance of an hypotheses in the absence of data.
"Prejudice" is having an opinion not supported by the preponderance of the data.
"Knowledge" is only found through the accumulation and analysis of data.
The plural of anecdote is not "data"

 

[ione]

David,
I thought, but I might be wrong, in your post dated back 26 Sep 13 18:55 you meant that A was the area at vena contracta. Now if you change the downstream pressure (change with time) A is not constant anymore with time, but it will rather increase as density ρ, at downstream conditions, will decrease.
So I firmly agree with you that "The only requirement for choked flow is that downstream pressure is less than Pchoked", but when choked flow condition is satisfied, any further decrease in downstream pressure won't produce any increase of mass flow (and I think this what Sailoday28 was saying, or at least this is how I have interpreted his/her post). When choked flow condition is satisfied the only way to increase mass flow is to act on upstream condition (i.e. increase upstream pressure).

 

[sailoday28]

ione
A can vary. In my formulation, I use G, which is the mass flux or W/A.
Regards