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

 

[JimCasey]

>>the speed of sound is NOT a physical constant. It is a function of fluid density. <<

My Marks Handbook shows the calculation for the Spped of sound in air as V=49.1 * Sqrt T
V is in fps, T is in degrees R

No density parameter there....


Aircraft experience sonic flight more easily at higher altitudes because the air is cooler, thus Mach1 is slower. Certainly intertial effects diminish due to less dense air at higher altitudes to let a plane go faster with less thrust.



ione is right. Increase the upstream pressure and you'll increase the mass flow rate thru a fixed restriction. If the flow is choked it will be independent of the downstream pressure

 

[PaoloPemi]

speed of sound is related to density,
c^2 = dp / drho
where c is speed of sound, p pressure and rho density

a decent software for control valves design / rating should evaluate the speed of sound at outlet conditions, I use this (free) tool

http://www.prode.com/en/valves.htm

however most manufacturers provide this kind of software with the FL, XT etc. coefficients required by ISA/ISO codes.

 

[PaoloPemi]

speed of sound is related to density,
c^2 = dp / drho
where c is speed of sound, p pressure and rho density

a decent software for control valves design / rating should evaluate the speed of sound at outlet conditions, I use this (free) tool

http://www.prode.com/en/valves.htm

however most manufacturers provide this kind of software with the FL, XT etc. coefficients required by ISA/ISO codes.

 

[zdas04]

JimCasey,
Careful with that simplification. It comes from

c^2=k*g*R(gas)*T

Starting with air and assuming that "k" is not a function of pressure and adding some unit conversions gets you to the constant you mentioned. In that single case your equation works fine.

The equation does come from dP/drho at constant entropy like PaoloPemi said, but if you note that P/rho=RT then you see where the pressure term falls out.

I've just spent a half hour in MathCad tweaking numbers and I keep reaching the same conclusion that several of you have come to--changing pressure at constant temperature does not change sonic velocity, but it does change mass flow rate. I'm not sure I know how to get my mind around this, but I'm working on it. I do know that I was wrong and several of you were right.

David

 

[ione]

David,

We have always to speak about “speed of sound in a medium” and not generically about “speed of sound”. It is the velocity the wave (sound) travels in a medium and so it varies with the medium properties. But in the assumptions of the posts above (those which led to M = 1 in choked conditions), air is always considered as an ideal gas. For an ideal gas and at a constant temperature, pressure has no effect on the speed of sound, because pressure and density have counterbalancing effects.

 

[PaoloPemi]

when sizing/rating a control valve one has to figure out values for Xt, Fl and other parameters mentioned in standards, in general it's better to leave this responsability to manufacturers...
At low pressures (as those mentioned in previous posts) the influence of pressure is limited, using Prode Properties (but other tools should give similar values) I calculated speed of sound in air with PR and SRK models

Air Mol. comp.
N2 0.78082
O2 0.2095
Ar 0.0093
Co2 0.00038

Press. 14.7 Psi.a
T (F) PR m/s SRK m/s
0 320.41 320.55
20 327.32 327.46
40 334.08 334.21
60 340.69 340.82
80 347.17 347.29
100 353.52 353.64
120 359.75 359.86
140 365.86 365.96
160 371.86 371.96
180 377.75 377.84


Press. 114.7 Psi.a
T (F) PR m/s SRK m/s
0 320.24 321.34
20 327.36 328.41
40 334.30 335.30
60 341.07 342.02
80 347.68 348.59
100 354.15 355.02
120 360.48 361.31
140 366.68 367.48
160 372.75 373.52
180 378.71 379.45

in this range of pressures and temperatures the assumption of ideal gas should not give too bad results.

 

[ione]

To better explain:

For the flow rate:

Q = rho*v*A

Where:
Q = flow rate
rho = fluid density
v = fluid velocity
A = cross sectional area

As you increase upstream absolute pressure the fluid density increases accordingly thus leading to mass flow rate increase, and this happens independently from the downstream absolute pressure.

At the same time, considering air as an ideal gas and for isentropic process

p/(rho^k) is constant during an isentropic process

(dp/drho)isentropic = k*(p/rho) = k*R*T

Where:

k = ratio of specific heats
p = pressure
R = gas constant
T = absolute gas temperature

From the speed of sound c definition


c^2 = dp/drho => c = SQRT (k*R*T)

So at constant temperature c is constant (for a specific medium)

 

[davefitz]

Its been over 25 yrs since I took the compressible fluid mech course, but the speed of sound is related to the mean molecular transverse velocity, which is proportional to the absolute temperature to some power. Molecular weight is also involved in the relationship, which makes it appear that density is involved, but the density is not the driver- its the speed of the speed of the molecules as they bounce around.

 

[ione]

A mistake in my previous post.
The molar mass M (kg/mol) of the medium enters the formula for the speed of sound (ideal gas and isentropic process):

c = SQRT (k*R*T/M)

Anyhow this doesn’t change how things are: for ideal gas and isentropic process the sound of speed is constant at constant temperature (independently from the pressure).

 

[JimCasey]

Back to the question,
The Salesman's software probably has the inside diameter of the pipe imbedded as a table. It is reporting the velocity downstream in either the body or in the pipe. The velocity thru the vena contracta or even thru the trim annulus will be sonic. With 0.85M downstream, it's likely to be quite noisy, too.

 

[jean33]

a important factor to consider is the noise due to flashing / cavitation / critical flow, we had a control valve that under certain conditions did produce a lot of noise, the plug had to be replaced at regular intervals and at last we decided to replace the valve. Unfortunately the manufacturer's software wasn't able to predict the problem.