Critical flow through orifice plates 2

[zdarlight]

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.

 

[zdas04]

I think you must have misread something. You can get sonic flow through a thin orifice plate, but supersonic requires a divergent nozzle after the flow is choked. Compressible flow is funny. For incompressible flow (at speeds below 0.6 Mach a compressible fluid will exhibit the characteristics of incompressible flow), a divergent nozzle will reduce velocity (while increasing pressure). For compressible flow, a divergent nozzle increases the surface area of the constraining standing wave and increases velocity above 1.0 Mach.

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

 

[zdarlight]

It's a very funny thing indeed! The statement thats puzzling me is 'choked flow won't occur across a thin, shrp edged orifice plate'. My understanding is if there is nothing choking the flow AT the orifice, surely a choke will occur downstream? Also if there is no choke, whats stopping the flow from going supersonic....I understand the theory of converging/diverging nozzles and obviously comparing the diverging section to flow after orifice plate an orifice plate made me think 'no, this will not allow for control expansion, thus super sonic flow cannot occur' but the idea of there being no choke contradicts my thoughts if you know what i mean?

If I were to say to you an orifice plate should ALWAYS operate below critical conditions would you agree with me?

 

[Latexman]

In a thin, sharp edged orifice plate the vena contracta is not confined; it occurs downstream of the orifice plate. Since it is not confined it can be affected by changes downstream. Thus, if downstream pressure is reduced, flow is increased/velocity is increased/flow area of vena contracta expands.

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

 

[zdas04]

Latexman,
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

 

[zdarlight]

Thanks for the posts guys. But my question still kind of goes un-answered.

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?

 

[Latexman]

It doesn't choke in the classical sense with a thin plate orifice. If downstream pressure is further reduced beyond the "critical pressure ratio", flow increases.

Google Cunninhgham's 1951 paper on it.

Good luck,
Latexman

 

[zdarlight]

But for the example of a RO plate downstream pressure cannot be reduced beyond the critical pressure ratio? Because it is the RO plate itself that is inducing this pressure drop....yes?

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?

 

[Latexman]

I think your thinking may be limited by your particular situation. A device could be added downstream that reduces the pressure, and the flow would increase, so it's not technically choked. Choked flow is defined as a limiting condition which occurs when the mass flow rate will not increase with a further decrease in the downstream pressure while upstream pressure remains fixed.

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

 

[davefitz]

Below is a response I replied in 2004 in tis forum, which may be relevant:

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