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# Multistage restriction orifice calculation

## Multistage restriction orifice calculation

(OP)

Hi all,

In our case, we must design a multistage device, wich includes 3 restriction orifices in series. Is there any difference between multistage and simple restriction orifice calculation? I've seen some links about this theme but unfortunately I don't have access to that ones.
I've been calculating that device orifice by orifice, using intermediate pressures and pressure loss, but results aren't still those I hoped to be.

### RE: Multistage restriction orifice calculation

Its an iterative calc changing the intermediate pressures and specific volume (assumes vapor calc) until the mass rate through each is identical.

### RE: Multistage restriction orifice calculation

(OP)
Hi! Thanks for your answer. This is what I tried at the first step, but I had to compare that results with other ones calculated as a multistage assembly and they didn't really match...
Does anybody know how to calculate a multistage restriction orifice device?

### RE: Multistage restriction orifice calculation

take into account that some free length befor and after the orrifice is needed to ensure propper operation. Why go for a multi stage device anyway?

### RE: Multistage restriction orifice calculation

(OP)
we already use some pipe diameters before and after the RO (restriction orifice).
the multistage device is used because we need to decrease pressure from 40 to 5 bar. this kind of devices are used to gradually decrease pressure

### RE: Multistage restriction orifice calculation

So once implemented the series of RO's did not sort the pressure drop you wished? This might be the case if the RO's are placed to close together. trailing the RO the flow patern peaks in the center of the pipe (radial flow distribution is normally parrabolic but can show more of a gauscurve-like behaviour for several meters depending on velocity). When placing an other RO in this disturbance, it is less effective (gas mass facing the plate of the RO is smaller). I found  that reducing pipe size after the first RO and so-on(increacing velocity ==> Reinolds) deminishes this effect. Also, tuning becomes easier.

### RE: Multistage restriction orifice calculation

The article is still available to anyone who needs it and I still get the occasional request for it.

Essentially, you start at the back and determine the maximum dP you can take across an orifice to avoid cavitation and then use that pressure as the outlet pressure for the next orifice and so on up the line.

### RE: Multistage restriction orifice calculation

If the fluid is a compressible gas with choked conditions , the flow thru the system will be choked flow based on the orifice that has the smallest diameter. If they all have exactly the same ID, then just assume the flow is choked across the final one.

The purpose for multiple orifices is to reduce noise , and to provide a backup orifice when the final orifice erodes down. The use of multiple orifices of exactly the same diameter will not change the flow vs upstream pressure correlation unless you have sufficient number to cause "frictional choking", .

The calculation of choked flow thru a series of orifices is a classical problem in compressible flow theory, and under the assumption of a "perfect gas" , the choked mass flowrate ( of W/A vs Pi/Po ) is only a function of the orifice that has the smallest area.

If the fluid is erosive, then it is best to either use a  SS "capillary tube" or one of the engineered velocity controlled multiple stage devices, such as the CCI flow restricotr .

### RE: Multistage restriction orifice calculation

For sizing a system to give a specified flow, I think you just chose a low noise pressure profile (dP/P for each plate) first, and then size each orifice sequentially. No itteration is required.

Itteration should only be required for a flow calculation- i.e. to find the flow through a system of known orifice sizes and boundary pressure conditions. This can be done by choosing flows (start low and work up) until the outlet pressure from the last orifice equals the boundary condition.

That's my opinion anyway.

best wishes,
sshep

### RE: Multistage restriction orifice calculation

for the standard solution to the classical problem of multiple orifes, see example 6.3 of"compressible Fluid Dynamics" by philip thompson 1972 first edition.

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