Choked Flow in valve 2

[nalasimbha]

Hi,

I would like to know if choked flow can occur in a valve even if the velocity of air passing through the valve has not reached Mach 1.

Also how will I determine is the flow is choked or not, given I know the upstream and downstream pressures.

Thank you

 

[ione]

Chocked flow implies velocity is at sonic value, that is at Mach number of 1.

Take a look to the Venturi’s effect: it could be useful.

The link below is helpful for your second question

http://www.engineeringtoolbox.com/flow-coefficients-d_277.html

 

[zdas04]

If downstream pressure is less than

P(crit)=P(upstream)*(2/(k+1))^(k/(k-1)

Then the flow is critical and velocity is 1.0 M. For air this works out to 0.528 times upstream pressure (in absolute units). For typical natural gas (i.e., k=1.28) it is 0.549 times upstream pressure.

David

 

[nalasimbha]

Thank you for your replies. I have air coming in at 200 psi and the outlet pressure is 100 psi. The velocity through the valve is not sonic. Will the valve choke? I do realise that P* is 0.528 and Po/Pi = 0.5. Kindly clarify

 

[ione]

Nalhasimba,
The correlation reported by zdas04 is absolutely right and gives a precise value for the choked flow. I’d just add that “k” is the ratio of the specific heats

k = cp / cv

cp= specific heat capacity for the gas in a constant pressure process [kJ/(kg K)]

cv =specific heat capacity for the gas in a constant volume process [kJ/(kg K)]

k (very) slightly varies with temperature.

 

[zdas04]

If the air is at 200 psig (NEVER say "200 psi" on eng-tips.com, it means nothing and makes it harder for people to help you) and you are at sea level then P(up) = 214.7 psia and P(crit)=113.36 psia=98.66 psig. As long as the exhaust pressure is less than 98.666 psig then you will have critical flow and velocity will be 1.0 M.

Now if the values you gave were psia then P(crit)=105.6 psia=90.9 psig so with 100 psia downstream you are choked and velocity =1.0M

David

 

[ione]

Nalhasimba,

When approaching chocked flow problems and related topics (i.e. flow coefficient Cv), always use absolute values for pressures.

 

[JimCasey]

Being choked is neither bad or unusual for a valve. If the ratio of (absolute) pressures :inlet/outlet is greater than ~2, then the flow is choked.



Choked does not mean that the flow stops.
Choked does not mean that you can't get any additional flow through the valve. Just open the valve more and you'll have more flow.
It really only means that the actual capacity is less than that predicted by the noncritical Cv equation. Once the deviation of the measured flow less than the predicted flow exceeds 2% the flow is said to have choked.
Another thing that happens is if the flow is choked and tnothing else changes, it is possible to lower the downstream pressure additionally wouthout affecting the flowrate.
Once the flow is choked: the math changes and you use a different equation. Any manufacturer's sizing software is going to address this and automatically shift to the compressible flow routine. The compressible flow routine has 15 variables. It is not fun. If you are sizing valves by pencil, paper, and calculator you have too much free time.

 

[nalasimbha]

Thank you everyone for your response. I got a air valve sized up by a sales guy for the following conditions.

114.7 psia upsteam
14.7 psia downstream

The Mach number through the sized up valve is 0.85.

Pressure ratio: 114.7/14.7 = 7.8

Choked flow occurs when mach no is 1. But in this case mach number through the valve is less that 1. Can choked flow still occur @ M=0.85? I get the math and know what happens during choked flow.

In this case things look contradicting and I am a little confused.

Thank you

 

[ione]

How have you computed the Mach number?

 

[ione]

It’s definitely a choked flow application.

You have (or should have ) the Cv of the valve and so you can calculate your gas flow rate.
I use Kv instead of Cv as I am more familiar with (Kv = 0.853 *Cv)

Q = 480.4 * Kv * SQRT[(deltaP*Pd)/(T*rhorel)]

Where:

Q = gas flow rate, normal cubic meter per hour
Pd = outlet gas absolute pressure (bara)
deltaP = pressure difference (bar)
T = gas absolute temperature (K)
rhorel = gas density compared to air (in this case = 1)


At this point you can calculate your gas speed

V = 1.222 * (Q*T)/(Pd*D^2)

where:

V = gas speed (m/s)
Q = gas flow rate, normal cubic meter per hour
T = gas absolute temperature (K)
Pd = outlet gas absolute pressure (bara)
D = internal valve diameter (mm)

Then you can calculate M = V/u (with u speed of sound in the medium)

 

[zdas04]

With a discharge to atmosphere, your salesman (or his program) is simply wrong. Sorry, but the arithmetic works out to Mach 1.0 and a program that disagrees with that is wrong.

David

 

[nalasimbha]

Correct me if I am wrong.

Pdownstream = 14.7 psia
Critical pressure ratio for air = 0.528

Pupstream = 14.7 / 0.528 = 27.8 psia

Hence the flow must be choked if the upstream is at 27.8 psia and the outlet is at 14.7 psia.

However increasing upstream pressure will increase the mass flow rate as the density increases and hence mass flow increases. Based on this if I increase the upstream pressure to 100 psia I should be able to get higher mass flow.

I do appreciate the time you are taking to clarify my question.

In regards to mach number of 0.85, i didn't calculate it. I was given to me by the sales guy.

 

[zdas04]

It is not a good idea to work this problem backwards, you end up with odd velocities. Start with the upstream pressure (114.7 psia) and apply the critical flow equation and the maximum downstream pressure that will give you sonic flow is 60.56 psia. Any pressure less than that number will give you exactly the same mass flow rate, velocity, and volume flow rate.

In your example, 27.8 psia upstream of an exhaust to atmosphere would give you choked flow, but since the upstream pressure is so much lower, the mass flow rate, velocity, and volume flow rate would be a fraction of their values at 114.7 psia upstream.

With regard to your salesman telling you that the velocity was less than Mach 1.0 there is a time that that number would be right--if the valve configuration forced a pressure drop between the valve seat ant the actual exhaust then you would never see pressure below critical until the exit plane of the exhaust pipe. This could happen if there is a lengthy tail pipe or a tortuous path through the valve. In this case, the pressure immediately downstream of the valve seat could be slightly higher than 60.56 psia, and the remainder of the pressure drop is taken incrementally through the ports and down the tail pipe. If that happened then you could be a a fraction of Mach 1.0, but I've never seen a valve with that much pressure drop after the seat.

 

[ione]

nalasimbha,

Please take a look to the link below: you'll find the undeniable mathematical evidence that for chocked flow (assuming air as an ideal gas) the Mach number must be equal to 1.

http://wins.engr.wisc.edu/teaching/mpfBook/node18.html

There must be something wrong with the program that calculated M=0.85

 

[JLSeagull]

I cannot believe that anyone here would doubt the information provided by a salesperson or her software.

One of those manufacturers also claims that the velocity in the vena contracta is not important for valve wear.

 

[davefitz]

In the case of CCI Self valves, considering the stacked discs and the engineered change of area as the fluid passes thru the stacks, one can have Pi/Po = 7.5 :1 and not have acoustically choked flow . The flow is frictionally choked instead. ( Xt=1.0)

The above postings that correlate (acoustically) choked flow with a critical pressure ratio and ratio of specific heats are at best describing the choking that occurs across a simple ball valve. Any other valve with complex internal geomety will experience "oblique shock waves" at a pressure ratio less than the acoustic limit, and such typical valevs ould have their choked or critical flow computed using the ISA method , which includes the factors Cv, Xt, ratio of specific heats, etc.

 

[ione]

davefitz,

Thanks for your contribution to this thread: you have added a new point of view.

Anyhow I consider that our attention should be focused on what “choked” is referred to.
The adjective “choked” (IMO) should be more properly referred to a particular fluid velocity than to flow (mass) as this condition defines an upper limit for the velocity and not for flow (mass). In choked conditions, the mass flow rate could be anyway be increased as upstream absolute pressure is increased (density increases). So if we are talking about choked condition, this should imply M=1.

 

[nalasimbha]

Thank you everyone for your inputs and clarifying my question.

 

[zdas04]

I'm not sure where this error in people's thinking is coming from, but the speed of sound is NOT a physical constant. It is a function of fluid density. So if you increase upstream pressure, the speed of sound increases. If you decrease upstream pressure, the speed of sound decreases. Consequently, the REASON that mass flow rate will increase with increasing velocity is BECAUSE the velocity increased. Several posts above have tried to make a distinction between velocity (as a constant) and mass flow rate (as an unrelated variable) and that distinction is not correct.

The definition of "Choked flow" above is correct. Our interpretation of it is often flawed. The "upstream" and "downstream" pressures refer to adjacent points across a single restriction. A valve with 5 pressure drops that has a large enough pressure drop across the entire valve to be choked could easily never have a single pair of adjacent points that satisfy the conditions for choked flow so you never get to Mach 1.0.

The OP said he had a "valve" and we all assumed it was a simple globe valve with a single restriction. If that assumption was correct then the discussion above is on point. If that assumption was not correct then maybe the OP is in a better position now to understand what his vendor is telling him.

David