Characteristics for choked flow accross a standard orifice

[gubau]

Hi all

I have 3 pressure vessels A,B and C. A 25mm internal diameter pipe connects A & B as well as B & C. I have installed a standard square edged British Orifice (BS1042) ,or similarly ISO5167-1 square edged orifice, in the middle of the two pipes. The length of the 25mm internal diameter pipes are 500mm. The diameter of the orifice plate is 5mm. I would like to obtain the pressure ratio Po/P2 versus the dimensionless mass flow (mdot*square(To))/Po for the choked flow region accross these orifices. The pressures of the tanks are typically A=5Barg, B=vacuum and C=8Barg. Air is used. Does this data exist anywhere ? Is it possible to analytically calculate this behaviour ?

Thanks
Günther

 

[davefitz]

The classical solution (perfect gas) for 2 or more orifices of same diameter in series is that the choking occurs at the final orifice. If the orifices have a different diameter, then it chokes at the smallest flow area. Unless of course one has frictional choking in the long run of pipes. ( Fanno curves)

The method of solution would be to work backwards from the exhaust to inlet. Assume choked at the final exhaust, and calculate the Pi/Po ratio for the final pipe run using :

sum(fL/d)=(1-M2)/r/M2+(r+1)/2/r*Ln{(1+r)*M2/(2+(r-1)*M2)}
and
Pi/Po= SQRT{(r+1)/(2+(r-1)*M2)} /M
M= inlet mach no, r= Cp/Cv, L=length, D= in dia, etc.
M2= M*M

If the Pi/Po ratio is less than the ratio of areas
A0*SQRT(Cd) / Ap then the flow is frictionally choked in the pipe run, but if larger, than the flow is choked in the orifices.

The Cd for a choked square edged orifice is per A.J. Ward-Smith, "Critical Flowmetering:The characteristics fo cylindrical nozzles with sharp upstream edges" int j heat fluid fl, vol1 no 3 pp 123-132, 1979, viz:
Cd = 1.0 for t/d = 0( sharp edge)
Cd varies from 1 t= 0.81 as t/d vaires from o to 1
Cd= 0.81 for 1<t/d<7
Cd less than 0.81 for t/d > 7 per Fanno friction
t= orifice plate thickness, d= orifice dia.