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Choke Flow - Restriction Orifice Plate

03/26/2009 7:20 PM

Dear everyone,

Hi, this is YTAhn i am woring in Offshore industry. I have one issue regarding Choke flow of Restrction Orifice Plate. I have to make pressure drop 130.5 Bar where inlet pressure is 134.4 Barg. However, my vendor says flow starts choking at DP 73.4 bar.

  1. What is expected problem at choked flow?
  2. How can i solve the problem?
  3. Why is restriction orifice used? for control flow rate or make pressure drop at discharge line.

Your reply on this subject will be highly appreciated.

Best regards

YTAhn

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#1

Re: Choke flow of Restriction Orifice Plate

03/27/2009 2:05 AM

Hi there.

Maybe this will help:

Choked flow

Choked flow of a fluid is a fluid dynamic condition caused by the Venturi effect. When a flowing fluid at a certain pressure and temperature flows through a restriction (such as the hole in an orifice plate or a valve in a pipe) into a lower pressure environment, under the conservation of mass the fluid velocity must increase for initially subsonic upstream conditions as it flows through the smaller cross-sectional area of the restriction. At the same time, the Venturi effect causes the static pressure to decrease. Choked flow is a limiting condition which occurs when the mass flow rate will not increase with a further decrease in the downstream pressure environment while upstream pressure is fixed.

For homogeneous fluids, the physical point at which the choking occurs for adiabatic conditions is when the exit plane velocity is at sonic conditions or at a Mach number of 1.[1][2][3] It is most important to note that the mass flow rate can still be increased by increasing the upstream stagnation pressure, or by decreasing the upstream stagnation temperature.

The choked flow of gases is useful in many engineering applications because the mass flow rate is independent of the downstream pressure, depending only on the temperature and pressure on the upstream side of the restriction. Under choked conditions, valves and calibrated orifice plates can be used to produce a particular mass flow rate.

If the fluid is a liquid, a different type of limiting condition (also known as choked flow) occurs when the Venturi effect acting on the liquid flow through the restriction decreases the liquid pressure to below that of the liquid vapor pressure at the prevailing liquid temperature. At that point, the liquid will partially flash into bubbles of vapor and the subsequent collapse of the bubbles causes cavitation. Cavitation is quite noisy and can be sufficiently violent to physically damage valves, pipes and associated equipment. In effect, the vapor bubble formation in the restriction limits the flow from increasing any further.[4][5]

Contents

[hide]

[edit] Mass flow rate of a gas at choked conditions

All gases flow from upstream higher stagnation pressure sources to downstream lower pressure sources. There are several situations in which choked flow occurs, such as: change of cross section (as in a convergent-divergent nozzle or flow through an orifice plate), Fanno flow, isothermal flow and Rayleigh flow.

[edit] Choking in change of cross section flow

Assuming ideal gas behavior, steady state choked flow occurs when the ratio of the absolute upstream pressure to the absolute downstream pressure is equal to or greater than [ ( k + 1 ) / 2 ] k / ( k - 1 ), where k is the specific heat ratio of the gas (sometimes called the isentropic expansion factor and sometimes denoted as γ ).

For many gases, k ranges from about 1.09 to about 1.41, and therefore [ ( k + 1 ) / 2 ] k / ( k - 1 ) ranges from 1.7 to about 1.9 ... which means that choked flow usually occurs when the absolute source vessel pressure is at least 1.7 to 1.9 times as high as the absolute downstream pressure.

When the gas velocity is choked, the equation for the mass flow rate in SI metric units is: [1][2][3][6]

=

where the terms are defined in the table below. If the density ρ is not known directly, then it is useful to eliminate it using the Ideal gas law corrected for the real gas compressibility:

=

so that the mass flow rate is primarily dependent on the cross-sectional area A of the hole and the upstream pressure P, and only weakly dependent on the temperature T. The rate does not depend on the downstream pressure at all. All other terms are constants that depend only on the composition of the material in the flow. Although the gas velocity reaches a maximum and becomes choked, the mass flow rate is not choked. The mass flow rate can still be increased if the upstream pressure is increased.

where:

=

mass flow rate, kg/s

C

= discharge coefficient, dimensionless (usually about 0.72)

A

= discharge hole cross-sectional area, m²

k

= c

p/cv of the gas

cp

=

specific heat of the gas at constant pressure

cv

= specific heat of the gas at constant volume

ρ

= real gas density at P and T, kg/m³

P

= absolute upstream stagnation pressure, Pa

M

= the gas

molecular mass, kg/kmole (also known as the molecular weight)

R

=

Universal gas law constant = 8314.5 (N·m) / (kmole·K)

T

= absolute gas temperature, K

Z

= the gas compressibility factor at P and T, dimensionless

The above equations calculate the steady state mass flow rate for the stagnation pressure and temperature existing in the upstream pressure source.

If the gas is being released from a closed high-pressure vessel, the above steady state equations may be used to approximate the initial mass flow rate. Subsequently, the mass flow rate will decrease during the discharge as the source vessel empties and the pressure in the vessel decreases. Calculating the flow rate versus time since the initiation of the discharge is much more complicated, but more accurate. Two equivalent methods for performing such calculations are explained and compared online.[7]

The technical literature can be very confusing because many authors fail to explain whether they are using the universal gas law constant R which applies to any ideal gas or whether they are using the gas law constant Rs which only applies to a specific individual gas. The relationship between the two constants is Rs = R / M.

Notes:

  • For a monatomic ideal gas, Z = 1 and ρ is the ideal gas density.
  • kmole = 1000 moles = 1000 gram-moles = kilogram-mole

[edit] Thin-plate orifices

The flow of real gases through thin-plate orifices never becomes fully choked. The mass flow rate through the orifice continues to increase as the downstream pressure is lowered to a perfect vacuum, though the mass flow rate increases slowly as the downstream pressure is reduced below the critical pressure.[8] Cunningham (1951) first drew attention to the fact that choked flow will not occur across a standard, thin, square-edged orifice.[9] [10]

[edit] Minimum pressure ratio required for choked flow to occur

The minimum pressure ratios required for choked conditions to occur (when some typical industrial gases are flowing) are presented in Table 1. The ratios were obtained using the criteria that choked flow occurs when the ratio of the absolute upstream pressure to the absolute downstream pressure is equal to or greater than [ ( k + 1 ) / 2 ] k / ( k - 1 ) , where k is the specific heat ratio of the gas. The minimum pressure ratio may be understood as the ratio between the upstream pressure and the pressure at the nozzle throat when the gas is traveling at Mach 1; if the upstream pressure is too low compared to the downstream pressure, sonic flow cannot occur at the throat.

Table 1

Gas k = c

p/cv

Minimum
P

u/Pd
required for
choked flow

Hydrogen1.4101.899
Methane1.3071.837
Propane1.1311.729
Butane1.0961.708
Ammonia1.3101.838
Chlorine1.3551.866
Sulfur dioxide1.2901.826
Carbon monoxide1.4041.895

This should answer your three questions

Regards,

Craig

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#2
In reply to #1

Re: Choke flow of Restriction Orifice Plate

03/27/2009 11:29 AM

GA!

And goodnes what an answer!

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#3
In reply to #2

Re: Choke flow of Restriction Orifice Plate

03/27/2009 4:00 PM

Oh c'mon! Anyone can copy and paste from WIKI, though I have no doubt that craigza knows a lot of this stuff from what I've seen of his other posts.

I can't believe how some posts get GAs - like this one (totally surprising and undeserved) and some great ones don't.

Oh well such is life at CR4 - we don't revolve around GAs, but the interesting content that is found here.

Mike

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#5
In reply to #2

Re: Choke flow of Restriction Orifice Plate

03/28/2009 5:36 AM

Hi, edignan!

Perhaps you should have awarded your GA to Wikipedia.

Mark

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#4
In reply to #1

Re: Choke flow of Restriction Orifice Plate

03/28/2009 5:34 AM

Hi, craigza!

You could have just given the link to this Wikipedia article and let the OP look it up himself.

Mark

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#6
In reply to #1

Re: Choke flow of Restriction Orifice Plate

03/28/2009 12:08 PM

Hi Craig

Really it's a great effort from you, Thnx & with my regards

Amr

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#7
In reply to #6

Re: Choke flow of Restriction Orifice Plate

03/28/2009 1:06 PM

Hi, Joker!

Welcome to CR4! You have a great sense of humour, and I'm looking forward to seeing more posts from you in here in the future.

Mark

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#8
In reply to #1

Re: Choke flow of Restriction Orifice Plate

03/28/2009 7:28 PM

Good Answer, that should cover a multitude of questions.

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#9

Re: Choke Flow - Restriction Orifice Plate

03/29/2009 10:26 PM

Thanks for your response. I noted choked flow effects are as below. 1. Gas : to make constant mass flow rate. 2. Liquid : Flash and Cavitation can be occured. Then, how can i use restriction orifice plate? For Gas, i should make required differential pressure (discharge pressure) considering flow rate. It means, flow can not be passed via orifice plate well. Required Flow rate is not achieved at downstream of orifice plate. Am i right? For Liquid, Flashing and cavitation will make noise and erroision to the downstream. Shall i make acoustic insulation on pipe to prevent noise? or to include more Restriction Orifice Plate to make differential pressure by degrees? I am still confusing. Please help me. I will be waiting for your response. Thanks, Best Regard YTAhn

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Anonymous Poster
#10

Re: Choke Flow - Restriction Orifice Plate

03/30/2009 12:38 AM
  1. What is expected problem at choked flow?

Choked flow is a condition, wherein the desired flow rate is not available even though there is press. drop in general terms.

  1. How can i solve the problem?

choked condition can be avoided by dividing the required pressure drop in multiples stages, so that press. drop across each stage doesnot exceed the choked press. drop.

  1. Why is restriction orifice used? for control flow rate or make pressure drop at discharge line.

This needs to be answered by your own self checking the application. If it is like release to flare / discharge system, then may be the press. drop is essential, so even if the release happens at a lower rate, then you can allow the same.

However if there is relevance of ensuring that the relieving rate is important (eg. depressurisation of reactors etc) then we need to ensure that the press. drop happens alongwith desired flow, by using multi stage / multi hole orifices. Suppliers of restriction orifice assembly would provide you the requisite details depending on the application.

As such I am not aware of any global standard, which addresses the above, however if other users are aware, then they may please add from their side.

regards

PS : do provide a feedback on the above since this is my first resposne on CR4

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#15
In reply to #10

Re: Choke Flow - Restriction Orifice Plate

09/21/2015 8:04 PM

can you provide any reference for multi-hole orifice sizing and noise claculation?

Thanks

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#11

Re: Choke Flow - Restriction Orifice Plate

03/30/2009 2:21 AM

Hi all,

Yes it was a copy and paste from wiki. The point is that it answers the problem. :)

If the person did not know about wikipedia before this - he certainly does now. As you will note - I did not delete or remove any of the wiki references or links.

I also want to state - that if I did not know that the answer was correct - I would not have used it as a reference.
Anyways - have a great day all. Another week at the office.

Cheers

Craig

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#12

Re: Choke Flow - Restriction Orifice Plate

03/30/2009 8:29 PM

Dear Everyone,

Thanks for your kindly response.

I noted what is choked flow.

Thanks,

Best Regards YTAhn

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Anonymous Poster
#13
In reply to #12

Re: Choke Flow - Restriction Orifice Plate

12/20/2009 10:12 AM

hi.

I think you should use à multi-RO system

if you have P1 --> P2

try : P1-->P1* by the first orifie then P1*-->P2 by the second orifice.

tis method is used when p1/p2 is importante.

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#14

Re: Choke Flow - Restriction Orifice Plate

03/04/2013 11:28 AM

Dear YTAhn,

Is the fluid is COMRESSIBLE or NON-COMPRESSIBLE.?

The COMRESSIBLE or NON-COMPRESSIBLE character of the fluid has great impact on the Flow.

DHAYANANDHAN.S

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