Restriction Orifice Plate calculation - Help

[lpfaustini]

Dear fellows,

I could use some help involving restriction orifice plate (square-edge) according to RW.Miller calculations.

Datasheet specifies:
gas/vapor
Upstream pressure (pf1) 22bar
Pressure drop (delta p) 20bar
Inlet temperature (Tf1) 40°C
Compressibility factor (Z) 0.93
Specific heat ratio (k) 1.35
Pipe inside diameter (D) 161mm
Bore diameter (d) 51.75mm
Molar mass (Mgas) 27.77
Dinamic viscosity (mi) 0.013 cP
Plate thickness (tmin) 15mm
Mass flow (q) 47,047kg/h.

Restriction orifice calculations are on section 13(choked/critical flow), am I right ? So, for square-edged orifice plate, plate thickness must be greater than d and 6d (d= bore diameter) and thickness-to-bore ratio must be between 1 and 6. It occurs that the results are out of these values. Am I correct to suppose this is not a restriction plate but a flow-meter orifice plate? If so, ISO 5167 says we cannot calculate flow meter orifice plate if pressure ratio is less than 0.75 and the result is giving me 0.02. Am I lost?

Thanks in advance,
Luiz

 

[casflo]

With this thickness the plate has no critical conditions. Use the Crane Technical Paper No. 410 to calculate the restriction orifice. Look for the Crane in Google. You will find some free old edition.
casflo

 

[lpfaustini]

Hi casflo, thanks

When I said it's not critical flow, the client said: "Orifice shall be used and calculated as Restriction orifice, not a flow meter"

Using Crane, am I looking to the right calculations?

 

[casflo]

If you use the Crane, you can do the right calculations. For example in the edition of the year 1988 see in the page A-20 the flow coefficient C for restriction orifices and for nozzles. The nozzles may be assimilated to the calculation as a flow meter. As the fluid is a gas, you must know its specific heats in order to choose the appropiated expansion factor Y in the page A-21.

 

[lpfaustini]

Casflo,

Unfortunately I could not pick up the right value of expansion factor Y as dp/p1 (=22/22.5=0.97) falls out of the graphic area. Same for the Reynolds Number and discharge coefficient. I think my client doesn't know what is asking, because according to ISO 5167 for orifice plates, in order to continue the calculations, P2/P1 must be greater than 0.75.

I already warned the client about this, but he said "Orifice shall be used and calculated as Restriction orifice, not a flow meter"

 

[davefitz]

Below is a response I replied in 2004 in this forum, which may be relevant to critical flow through thick , square edged restriction orifices:

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

"Nobody expects the Spanish Inquisition!"

 

[ruifilho]

Lpfaustini
I made same quickly calculations with your data:
P1 = 22 bar
Delta P = 20 bar
Pipe diameter = 161 mm
Orifice diameter = 51,75 mm
With this orifice diameter the flow will be critical and the orifice outlet pressure will be around 11,8 bar and the orifice delta P around 10,2 bar.
Then, deltaP/P1 = 10,2/22 = 0,463; with this value, from Crane you have Y = 0,845 and assuming the flow is turbulent, we have C = 0,6.
With the equation 3-22 from Crane we get a mass flow around 28,000 kg/h.
Conclusion with this orifice diameter you will have critical flow and will not get the mass flow wanted of 47,047 kg/h.

 

[SNORGY]

I see a noise problem coming here. That's going to create more trouble for you than the dP ever will.

Not that I've ever overlooked *that* before...