Gas Choked Flow Prediction using Cp/Cv and Ma Number 1

[DoraeS]

I have a doubt which I tried to look up from internet but could not be clearly understood:

Cited from wikipedia, statement 1:
"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";

Cited from wikipedia, Statement 2:
"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".

I often heard ppl saying that when your downstream pressure of orifice/control valve is less than approx. 50% of upstream pressure, the flow will be choked. This is true when looking at statement 2 above. However, if we using Ma number formula and definition from statement 1 above, one can easily 'avoid' choked flow at downstream by increasing pipe size while having downstream pressure well below 50% of the upstream pressure still.

Can anyone help to explain to me whether these two statements are contradicting or not? What I am trying to convince myself is, Ma number to predict choked flow can be used for downstream piping system, in this case choked flow is a function of downstream pressure as well as downstream pipe size (and of course other properties); and Cp/Cv formula cited in statement 2 can be used to predict choked flow at the orifice nozzle throat only. Is my interpretation correct?

Thanks.

 

[Latexman]

However, if we using Ma number formula and definition from statement 1 above, one can easily 'avoid' choked flow at downstream by increasing pipe size while having downstream pressure well below 50% of the upstream pressure still.

A lot of times, piping is enlarged to lower pressure drop to avoid choking in the pipe, but the control element or device (safety valve, restriction orifice, etc.) remains the same size. Choking then occurs in the restricted device only, and the pressure drop in the pipe drops to < 50%. When the pipe is enlarged, the point at which choking occurs can shift to another point.

Good luck,
Latexman

 

[DoraeS]

Hi Latexman,
I have come across cases with enlarged downstream pipe size and in this case, even the pressure in the pipe is well below 50% of upstream pipe, the results from simulation tool is reported as "non choking".
E.g. Upstream pressure is 20 barg and across orifice, pressure at throat is 0.5 barg and at the end of downstream pipe it is 0 barg, the piping has been reported as "non choking".

Do you or does anyone have other opinions?

 

[Latexman]

The 50% rule of thumb applies to absolute pressures only. 1.5 bara at the beginning of the pipe and 1.0 bara at the exhaust < 50% pressure drop. I see no problem with it being called "non-choking".

Good luck,
Latexman

 

[Latexman]

I forgot to mention the % loss is referenced to the upstream pressure in the 50% rule of thumb.

Good luck,
Latexman

 

[DoraeS]

Hi Latexman,
I mean upstream pressure is 21 bara and downstream piping right at orifice is 1.5 bara and end of pipe is 1.0 bara.

 

[Latexman]

But you have an RO in the middle. That's kind of a discontinuity in the analysis of the upstream and downstream pipe! You have to break these three components of the problem into separate flow analysis. A pipe is not an RO is not a pipe. You need to look at the dP of each component to see if choking is an issue. You can have choking in 0 to 3 points, it depends.

Good luck,
Latexman

 

[Latexman]

"You need to look at the dP of each component to see if choking is an issue" may be somewhat misleading. What happens in the upstream pipe affects what happens in the RO, and both affect what happens in the downstream pipe. You need to integrate the system from beginning to end.

Good luck,
Latexman

 

[sailoday28]

Whether or not there is an orifice or venturi, flow will choke ---when for given fixed upstream stagnation temperature and pressure, there is no further increase in flow as downstream back pressure is decreased.

 

[Latexman]

Thanks sailoday, I should have said, "You can have choking in [red]1[/red] to 3 points, it depends.

Good luck,
Latexman

 

[hacksaw]

All this talk about RO's is risky as true "choked flow" only occurs for an adiabatic expansion such as with special flow nozzles.

 

[Latexman]

Yeah, the OP didn't specify thick walled orifice or thin walled orifice, so I took the most commonly believed route.

Good luck,
Latexman

 

[sailoday28]

hacksaw . Choked conditions can occur with other types of flow (ie. other than adiabatic). Isothermal is one example.

 

[sheiko]

llc0612,

The 50% rule of thumb breaks down when pipe friction becomes a factor. It cannot be used to predict the supply and discharge pressures necessary for sonic choking unless the piping has negligible friction loss. This rule of thumb is typically used to determine the critical pressure ratio for gas sonic velocity across a NOZZLE or an ORIFICE.





"We don't believe things because they are true, things are true because we believe them."

 

[davefitz]

it sounds like you may need to take a course in compressible flow, or at least study a textbook on the subject.

For a compressible fluid, the flow can be choked either acoustically ( fluid at speed of sound at flow area minimum) or frictionally choked ( see Fanno flow or Fanno curves).

For the case of multiple orifices in series, the flow chokes at the orifice whcih has minimum flow area.

 

[hacksaw]

Sailoday28,

didn't mean to imply that isothermal process was excluded, common issue in pipelines

like davefitz points out it is more than "just" a flow restriction involved

 

[sheiko]

davefitz,

You are right saying that "for a compressible fluid, the flow can be choked either acoustically ( fluid at speed of sound at flow area minimum) or frictionally choked (see Fanno flow or Fanno curves).", but i hope it is not consequent to my post. I just said that the 50% rule of thumb may only be applied to flow through NOZZLES or ORIFICES.

"We don't believe things because they are true, things are true because we believe them."