Definition of Choking or Critcal Flow 3

[leongw]

Dear all,

I am looking for an explanation on the definition of choking or critical flow and what happen during choking or critical flow condition.

Appreciate if someone can assist.

Thank you.

 

[zdas04]

dcasto,
There is a point usually about 55% of upstream psia where raising pressure will decrease flow. That point is dependent on gas compostion. The 25% rule of thumb is there to ensure that the PSV exhaust never approaches the critical pressure.

David

 

[sailoday28]

mbeychok (Chemical)Please note that the choked flow web site that you reference should be corrected to state that the formulations for the isentropic equations are for steady state and upstream pressure should be "stagnation" pressure.

Also--For isothermal choked flow the choked velocity is different then the sound velocity- for isothermal choking Mach is not =1.

With reference to unsteady flows, such as an instantenous pipe rupture, the initial critical pressure ratio can be significantly higher than that of the steady state.

Regards

 

[AKL7]

All,

let me suggest to extend this discussion to multiphase flows.

Apart from correct definitions given above, choking as an effect will happen in gas, liquid and multiphase mixtures when flow velocity* will reach pressure wave propagation speed*.

Question is, how to describe choking criteria in multiphase flow as a function of Pin/Pout?

When in critical flow, how mass flow rate will behave as a function of Pin given that phase mass transfer and gas compressibility functions of pressure are known?

(*to be defined for multiphase flow as effective values depending on the flow regime)

 

[AKL7]

This is what I came up with so far, up for your comments:

If choking device is of venturi profile than Bernoulli with empirical corrections for frictions and turbulence could be used to describe flowing pressure profile across the device. Using that equation, Pin/Pout choking criteria could be defined for known effective velocity of pressure wave propagation in multiphase mixture.

However, when velocity of the flow approaches sound velocity through a choking device, there will be a static shock wave formed at the point of maximum acceleration/discharge. Bernoulli is linear and can not describe shock wave pressure profile. In fact one of the main assumptions in Bernoulli model is that flow is continuous. However, at the point where flow reaches velocity of sound flow exhibit phase "rapture" - flows upstream and downstream are hydraulically disconnected and therefore Bernoulli conservation law does not work. So, Bernoulli could not be used to build mass flow rate function of Pin in critical flow.

Very simple model could be used to predict pressure buildup upstream the choke when in sonic condition. Under assumption that sonic velocity is constant, volumetric flow rate at line condition that corresponds to sonic velocity through the choke will be maximum possible volumetric line condition flow rate. So, for given mass flow rate, at sonic condition, pressure upstream the choke will build up to the point when given flow rate at standard condition will be compressed to the max possible volumetric flow rate at line conditions as defined above.

At sonic conditions:
dQ(P)/dP = d(qline*density(P))/dP = qline*(density(P)/dP,

where qline = Vs*choke_flow_area

Now, of course dVs/dP is not zero, but how significant it is?

As far as I know VOS drops with a first droplets appearing in gas media increasing mixture density and then comes up when increasing amount of liquid start to effect compressibility of the system.

 

[AKL7]

Further on VOS in multiphase, would you guys believe that one will hear bell ring later in a rainy day than in a sunny day?

I think that multiphase sonic velocity will be equal to gas sonic velocity when there is a continuous gas phase in the flow and equal to liquid sonic velocity when there is a continuous liquid phase, sonic velocity below gas and liquid sonic velocity can only occur in slug flow when there is no either liquid or gas continuous phase and system still has compressibility of gas but already much higher effective density.

 

[dcasto]

zdas04, My point too. I had a header system that if every relief valve went off at once the header pressure would be almost 50% of "The worst case set point" back pressure. Mind you that most of the PSV's where thermal or fire case on a storage site over 1 mile square. The engineering firm was recommendeding we install an all new flare header to get below the 25%. Holy cow, the site was 40 years old and the header only has been used a few times (most old timers barely remember its use let alone people with less than 10 years on site). It was an up hill battle.

 

[sailoday28]

mbeychok (Chemical) 10 Jan 07 12:59
Artisi (Mechanical)

http://en.wikipedia.org/wiki/Choked_flow

Any papers that I have written for the ASME have been reviewed prior to acceptance for publishing by 3 of my peers. This is probably true for publications in other professional societies.
I don't believe that is true for the website referenced above.

Regards.