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Choked and sonic flow 5

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robjoenz

Nuclear
Apr 23, 2008
1
The definition of choked flow is when a reduction in downstream pressure does not result in an increase in flow through an orifice. In the case of a tiny hole in a pipe if flow becomes sonic it will also be choked.

My question is... if you have choked flow does it necessarily mean you will have sonic flow? i.e. can choked flow exist for sub-sonic velocities?

Thanks,
Rob
 
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Yes, "choked flow" implies that the exhaust stream is initially moving at Mach 1.0. That velocity never lasts very long because of fluid friction and changing the momentum of surrounding gas molecules immediately begin slowing it down, but the velocity at the exit plane is Mach 1.0.

David

David Simpson, PE
MuleShoe Engineering
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Choked flow may occur with less than 1.0 mach number- if there are sharp angles then there can occur "oblique shock waves" when the average velocity thru the hole is less than the speed of sound.

For example, flow thru some control valves , such as a globe valve, implies sharp angles and changes of direction. This is described by the "ISA handbook of control valves" as when the Xt is greater than 0.1 . For a streamlined ball valve Xt=0.1, and no oblique shock waves form. For a typical globe valve, Xt=0.8 and oblique shock waves do form and choked flow will occur at a pressure ration less than critical. For a CCI drag valve , Xt=1.0, and no shock waves form and the flow is frictionally choked, not acoustically choked.

In the case of choked flow thru a hole in the pipe, the discharge coeficient is about Cd=0.82, but will vary according to the ratio of the hole diameter to the wall thickness of the pipe. So, based on 100% hoel area, it never reaches sonic velocity , but based on an apparent vena contracta or due to oblique shock waves it becomes choked.
 
If the process is other than adiabatic, say, isothermal the flow will not choke at Mach=1.

 
Wait a doggone minute here.

sailoday, can you provide an example of an isothermal flow in conditions described by choked flow (i.e., downstream pressure < upstream pressure * (2/(k+1))^(k/(k-1)))?

Davefitz, I've found that in the conditions you describe (i.e., standing shock waves downstream of the restricting element) that the pressure at the outlet of the restricting element is higher than the critical pressure from the equation above and the flow is not choked.

My experience says that if you satisfy the equation above, then the velocity will be 1.0 Mach at that exact point. If something downstream restricts the mass flow rate then pressure will increase at the restrictive element and the conditions for choked flow will no longer be satisfied.

David
 
sailoday28 and zdas04, isothermal choke flow may occur in longer pipe lines, that choke at some expansion.

But my understanding was always that Mach=1 in both cases, it is just that sonic velocity for isothermal flow is different from adiabatic flow.

 
After reviewing my copy of "The Dynamics and Thermodynamics of Compressible Fluid Flow" by Shapiro, the isothermal flow model falls apart at M = 1/k1/2, where an infinite heat transfer per unit length is needed to maintain a constant temperature. In reality when a subsonic isothermal flow approaches this limiting Mach Number, all fluid properties change rapidly with distance. Unless heat is transferred purposely, flow is likely to be more adiabatic than isothermal.

Good luck,
Latexman
 
Latexman (Chemical)
The original question was
My question is... if you have choked flow does it necessarily mean you will have sonic flow? i.e. can choked flow exist for sub-sonic velocities?
You clearly have chosen an excellent reference(Shapiro), however, choking can occur at other than M=1.
Regards

 
ronjoenz said:
if you have choked flow does it necessarily mean you will have sonic flow? i.e. can choked flow exist for sub-sonic velocities?

The velocity of sound is thermodynamically defined as a small compression wave moving adiabatically and frictionlessly through the medium. This is an isentropic process. If the actual flow process deviates from this, for example the flow is isothermal or there is significant friction or the flow is not adiabatic, it should not be surprising that choked flow can occur at velocities other than sonic.

If a = acoustic velocity (velocity of sound) and a' = the limiting velocity of isothermal flow, then a = a' x k1/2.

Good luck,
Latexman
 
In isentropic flow (adiabatic + small friction loss), just as isothermal flow, the mass velocity reaches a maximum when the downstream pressure drops to the point where the velocity becomes sonic at the end of the pipe (e.g., the flow is choked).

But given:
c = speed of sound
M = molecular weight
R = gas constant
v = spatial averaged velocity
T = constant temperature
1 = reference point 1
2 = reference point 2
* = sonic state

Under isothermal conditions, choked flow occurs when:
v2 = c = v2* = (R*T/M)^0.5

Under Adiabatic conditions (or locally isentropic), choked flow occurs when:
v2 = c = v2* = (k*R*T2/M)^0.5

Reference: Darby, R., Chemical Engineering Fluid Mechanics, marcel Dekker, 2001

"We don't believe things because they are true, things are true because we believe them."
"Small people talk about others, average people talk about things, smart people talk about ideas and legends never talk."
 
sheiko,

I have Ron Darby's book and I really don't agree with saying c = v2* = (R*T/M)^0.5 for isothermal flow. The speed of sound has a very precise thermodynamic definition:

c = (gc(dP/d[&rho;])S)1/2

One cannot calculate with 100% rigor the speed of sound of a medium in isothermal flow. This is due to the constant entropy constraint in the definition of the speed of sound. Isothermal and isentropic conditions are definitely not the same thing.

It's a good book, but being too loose with precise thermodynamic definitions makes this section a bit sloppy in my opinion.

Good luck,
Latexman
 
I would argue that the mathematics say that isothermal flow chokes at M<1 and the equations are consistent.

However, I would also argue that at the moment that an isothermal flow chokes, an infinite amount of heat is needed to be transferred into the gas in order to maintain the temperature of the gas. Since this is physically impossible, the temperature must change, and isothermal flow cannot exist in a choked state. I'd say the equations are physically meaningless at that point and so choked isothermal flow cannot happen in reality. Before you reach the choke point, any real system must always diverge from isothermal conditions.

Exactly how long the isothermal flow equations adequately describe a flow as its velocity builds up depends on the gas, but I'd say that it's pretty conclusive that they do not realistically describe choked flows.
 
Doh. How long the isothermal flow equations hold up depend on the state of the gas and the amount of heat that can get into the gas (i.e. surroundings), not just the state of the gas.

My apologies.
 
The isothermal equations work really well for a body moving in an infinate reservoir (fighter planes at Mach 3 may heat themselves up, but they don't change the temperature of the atmosphere a measurable amount). There are really no situations where the equations work when the fluid must reach this speed (instead of the body within the fluid).

David
 
Latexman (Chemical)

Your response of
"One cannot calculate with 100% rigor the speed of sound of a medium in isothermal flow."
Sound speed in isothermal flow is per the definition in your response
c = (gc(dP/d?)S)1/2 or
- with or without isothermal flow
c^2=gamma (dp/droh)isothermal
 
sailoday28,

Maybe I'm making too much of a big deal of the definition of sound speed being for isentropic conditions. What got me started was the equations in Darby's book:

c = (kRT2/M)1/2 for Adiabatic flow

and

c = (RT/M)1/2 for Isothermal flow

but

(kRT2/M)1/2 is not = (RT/M)1/2

A different symbol should have been used for the isothermal case or subscripts or something. It's confusing. Anyway, whether one uses c2 = (dP/drho)S or k(dP/drho)T they are calculating sound speed for isentropic conditions in both cases. I don't see how this has meaning to the limiting velocity for isothermal conditions which = c/k1/2 or (dP/drho)T (with no k in the equation).

Good luck,
Latexman
 
"Mass velocity" simply does not mean anything. The quantity you described is actually "mass flow rate". "Velocity" is a distance over a time in a direction ("speed" is a distance over a time). Mass per second does not meet the definition.

And, if the upstream pressure increases, then the velocity will increase AND the mass flow rate will increase. Sonic velocity is dependent on the media in which the sound is traveling--if the media becomes more dense then the speed of sound increases. In the equations you re-quoted above, the mass flow rate (that I've never seen given the designation "Q" before, but that is a quibble) will increase as the pressure increases--SO WILL THE VELOCITY. By the way the limiting equation that you included is the same one I posted in this thread three days ago.

The only thing special about choked flow is that as long as the pressures satisfy the limiting inequality the downstream pressure does not matter.

David
 
In the reference i mentionned in post dated 24 Apr 08 11:11 (Darby 2001) the mass velocity is the mass flux: G = m / A = rho*v, with:
m: mass flow rate
A: cross sectionnal area
rho: density
v: spatial averaged velocity

"We don't believe things because they are true, things are true because we believe them."
"Small people talk about others, average people talk about things, smart people talk about ideas and legends never talk."
 
zdas04,
I agree with you that there is no such thing as mass velocity. As you say you can have "mass flowrate" or velocity but not mass velcity. even the units quoted of kg/s are not "velocity" related.
 
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