Critical flow through orifice plates
Critical flow through orifice plates
(OP)
Hello all, I'm new to this so bare with me.
I have recently started working for an instrumentation company and after briefly reviewing the orifice plate calc software I've been left puzzled.
I've read that supersonic flow is acheiveable through a thin plate orifice. This i can grasp but i can find little literature explain what happens after this. It is my understanding that a shock must occur at some location downstream, which I assume isnt ideal for the system. So what Id like to know is what are the effects and implications of inducing a supersonic flow through an orifice? Or indeed if anyone could shed some light what on exactly is going to happen downstream then i'd muchly appreciate it.
Also in the R.W.Miller flow handbook an orifice plate of 1<t/d<6 criterion is described. The idea of the thicker plate to induce a choke at the orifice so flow remains subsonic. Would I be right in saying that my critical pressure value at this point would be equal to p2 downstream? Or some function of it?
As you can probably tell I'm rather confused about the whole scenario. If anyone has any links, texts, views....anything they think could help me 'get the ball rolling' I'd really appreciate it
Thanks.
I have recently started working for an instrumentation company and after briefly reviewing the orifice plate calc software I've been left puzzled.
I've read that supersonic flow is acheiveable through a thin plate orifice. This i can grasp but i can find little literature explain what happens after this. It is my understanding that a shock must occur at some location downstream, which I assume isnt ideal for the system. So what Id like to know is what are the effects and implications of inducing a supersonic flow through an orifice? Or indeed if anyone could shed some light what on exactly is going to happen downstream then i'd muchly appreciate it.
Also in the R.W.Miller flow handbook an orifice plate of 1<t/d<6 criterion is described. The idea of the thicker plate to induce a choke at the orifice so flow remains subsonic. Would I be right in saying that my critical pressure value at this point would be equal to p2 downstream? Or some function of it?
As you can probably tell I'm rather confused about the whole scenario. If anyone has any links, texts, views....anything they think could help me 'get the ball rolling' I'd really appreciate it
Thanks.





RE: Critical flow through orifice plates
The thicker the restricting orifice plate is, the larger percentage of the pressure drop is permanent(which is one of the criteria for achieving choked flow through an orifice). For a plate used in square-edged orifice measurement, the permanent pressure drop is a function of the beta ratio and for large beta ratios the permanent pressure drop is pretty small.
David
RE: Critical flow through orifice plates
If I were to say to you an orifice plate should ALWAYS operate below critical conditions would you agree with me?
RE: Critical flow through orifice plates
A thick plate orifice that physically confines the vena contracta by it's orifice area chokes the flow because the vena contracta cannot be expanded beyond the orifice diameter.
Good luck,
Latexman
RE: Critical flow through orifice plates
That is a clear an explanation of that phenomenon as I've ever seen. Thank you.
Zdarlight,
The highest velocity I saw when I was studying the AGA/API/ANSI database that they used to develop the discharge and expansion coefficients was about 0.2 Mach. Gas flow at that velocity acts as an incompressible flow and is way subsonic. The highest velocity I've ever calculated in an orifice meter has been well below 0.1 Mach. At those velocities, Bernoulli's equation is perfectly valid (even if you have to tweak it for real-world exit conditions if you want the extreme repeatability and tiny uncertainty required for custody transfer).
David
RE: Critical flow through orifice plates
I totally agree with what your saying about the vena contracta in for a thin plate flow being allowed to expand due to the lack of a control boundary at the point. But, what happens then?
Think about it, a flow reaches critical conditions but nothing can choke it. What happens to that flow then? Choking is what keeps a flow from going super sonic in most practical applications (nozzles, pipework).
Do you see the point I'm trying to make?
RE: Critical flow through orifice plates
Google Cunninhgham's 1951 paper on it.
Good luck,
Latexman
RE: Critical flow through orifice plates
And would you agree with me if I said the mass flowrate through the system would indeed increase beyond the critical condition, but due to the vena contracta diameter gradually increasing, and the VC moving closer to a plate, although the mass flow rate is increasing, the actually velocity of flow will not?
So yes FLOW will increase, but velocity will not increase past sonic. And this will carry on until plate thickness is insufficient to prevent bending, bringing plate criterion to 1<t/d<6 and thus a choke will now occur anyway.....Am I correct now orrrrrr?
RE: Critical flow through orifice plates
Increase beyond the critical condition? No. You can certainly calculate the critical pressure, but for a thin plate orifice it's not really technically correct as a point where choking starts. Yes, there are different mechanisms at play above the critical pressure compared to below the critical pressure. For a thin plate orifice the critical pressure is more of an inflection point on the flow curve, than it is the onset of choking.
Now, I will say, using the assumption that a thin plate orifice chokes at the critical pressure may not be too bad of an assumption in some cases. It may be pretty close and it depends if that is "good enough" for what you are doing. However, it's not technically correct.
Look at Wikipedia's two articles on orifice plate and choked flow. That may help.
Good luck,
Latexman
RE: Critical flow through orifice plates
I found a useful reference from the RW Miller handbook. Try A.J. Ward-Smith "Critical Flowmetering: The Characteristics of cylindrical nozzles with Sharp Upstream edges" Int J Heat Fluid Fl vol 1 No 3 pp 123-132 1979
In my case I needed to predict the flow vs pressure characteristic of a condenser sparger pipe, inlet P of about 100 psia, outlet P about 2 psia, 0.75" dia holes in a 0.25" thk rolled plate ( t/d= 0.33)
Per Ward-Smith, the choked compressible flow Cd is a function of the t/d ratio. As follows:
sharp edge, t/d= 0, Cd = 1.0
thin plate (0<t/d<1)Cd varies smoothly from 1 to 0.81 as function of t/d.
thick plate ( 1<t/d<7) Cd = 0.81 constant
very thick plate (t/d > 7) Cd less tahn 0.81 per Fanno friction
Tremendous difference compared to standard non choked sharp edge Cd of 0.64