Multiple Choking Points in FANNO flow?

[rjw57]

I am struggling with something I have not done for some time. I am looking at a text on FANNO flow which describes how to combine loss coefficients for a series of piping components. The example is simple in that it starts with a pipeline that is larger than the downstream pipe and has a simple reduction from one pipe size to the next. I am trying to complete calculations for an application where a gas reservoir is pressurizing a vacuum vessel. I am certain that choked flow will occur. Here is my question: if I were to have a pipe arrangement of the following series of sizes 3">0.25">3">0.25">3" which are relatively short (hence my FANNO flow assumption) would it be possible that there would be multiple choke points should the pressure difference be adequate? (yes I realize this is an unrealistic setup, however, it is only to clarify my question). It seems intuitively obvious to me that this could occur, but I need to know if anyone can see why not.

Thanks
Bob

 

[LSThill]

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[PDF] Fanno Flow - Thermodynamics File Format: PDF/Adobe Acrobat - Quick View
change mass flux: new Fanno line. – friction alone can not allow flow to .... Fanno Flow Property Changes. • Summarize results in terms of reference ...

http://www.ae.gatech.edu/people/bzinn/.../fannoflow.pdf

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Fanno Flow - Compressible Flow Free Textbook An adiabatic flow with friction is named after Ginno Fanno a Jewish engineer. This model is the second pipe flow model described here. ...

http://www.potto.org/gasDynamics/node138.php

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Read OnLine - Compressible Flow Free Textbook The Approximation of the Fanno Flow by Isothermal Flow · More Examples of Fanno Flow · The Table for Fanno Flow · Rayleigh Flow ...

http://www.potto.org/gasDynamics/gasDynamics.php

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[luvz2flyalot]

Hey Bob,
Assuming one flow path, continuity dictates that the pressure in the most downstream vena contracta will be the lowest, hence this velocity will be higher than the other two 0.25" dia sections. So this will be the one and only choke point. I suppose theoretically with no total pressure loss you might see a choke point at each section, but in the real world never.
Richard

 

[ione]

Fanno flow is characterized by an adiabatic flow in a CONSTANT section conduit, where friction effects are taken into account. As the flow evolves adiabatically entropy must increase, because of friction caused by shear forces, until a maximum is reached. This maximum occurs for M=1 (M=Mach number) and so, upon condition the conduit is LONG ENOUGH, an initially subsonic flow will evolve accelerating to M=1 and an initially supersonic flow will evolve decelerating to M=1. This threshold (choked condition) could not be overcome and more generally a subsonic flow will never turn into supersonic flow and vice versa.

 

[Latexman]

I don't know about your scenario, but in a relief valve with a tailpipe there can be two areas where the flow chokes. The first is in the flow nozzle of the relief valve, and the other is at the end of the tailpipe where the gas exits to atmosphere. This is very common.

Good luck,
Latexman

 

[rjw57]

Here is my dilemma. I am familiar with following the plots of T (ordinate - static temp) vs. s (entropy). I enter my pipeline from some reservoir ~isentropically (humor me here). The flow follows the isentropic (vertical) line down to some FANNO line and continues to travel for some distance without reaching M=1. It next isentropically enters a reducer moving to ANOTHER FANNO line. Only in this case, it reaches maximum entropy and chokes at M=1. However, just on the other side of the reducer, it expands and fills a new larger pipe with a greatly reduced velocity and presumably some recovery in static pressure. Could it not then be on a brand new FANNO line with some capacity to reach M=1 again. Obviously, this is not an isentropic process so it would still continue to move to the right on the overall T-s plot. Does this all make sense? Latexman seems to indicate that in real life it can happen, but I'm not sure my scenario even comes close to real life.

 

[rjw57]

Slight correction to my previous post. The reducer has some finite length of piping between the inlet reduction and the outlet expansion. Should make more sense in this context.

 

[Latexman]

My real life example is more like 2">1">3">atmosphere. Mach 1 occurs in the 1" nozzle and at the end of the 3" exhaust.



Good luck,
Latexman

 

[ione]

rjw57,

Not to be too picky, but we are talking about adiabatic and not isentropic conditions, when referring to Fanno flows. Entropy is not constant , but it increases to its maximum (for M = 1) due to friction effects and if and only if the length of conduit allows this.

Coming back to your question (now the scenario is clearer), having segment of conduit with increased cross section is a mandatory condition to have multiple choke points. And so the answer to your dilemma is YES.
As already pointed out by Latexman, a configuration with a pressure relief valve, followed by segments of different cross section conduit, can experience multiple choking points. Be aware that the mass flux varies in each segment of conduit. An increased cross section leads to a decreasing mass flux (as pressure drops and specific volume increases).

 

[rjw57]

@ ione:

I don't recall saying that FANNO was isentropic, only that area changes (specifically reductions in area) involved ~isentropic changes in the flow state (see my 22Dec09 17:44 post). There is no "pickiness" involved in describing FANNO flows as adiabatic and not isentropic. I am aware that FANNO is by definition adiabatic (but NOT isentropic). Otherwise, the plot I posted previously would have had straight vertical lines for the T-s plot.

When I siad "obviously, this is not an isentropic process," I was referring to the expansion process from the outlet of the smaller conduit into the larger conduit. I am trying to understand if the expansion is increasing T and increasing s -OR- decreasing T and increasing s on the plot I attached. I think now that it must be the former: T and s simultaneously increase (T being T_static and NOT T_total, which is by definition constant).

I see that you have reiterated what Latexman has said previously, but I would be very interested in knowing if what I described in my 22Dec09 17:44 & 18:13 posts make sense from a thermodynamic POV. After hearing these anecdotal replies, I would have to conclude that the answer is YES.

Anyhow, thanks to everyone for your time.

 

[ione]

In an adiabatic expansion, shaft work is carried out at the expense of internal energy, and so the temperature decreases. Then (second conduit segment after the expander) the flow evolves on a new Fanno line over which the flow develops towards increasing entropy (M-->1).

 

[rjw57]

@ione

Not sure why you are mentioning shaft work since the expansion is a work-less process. If you look at the graph I attached to my earlier post, if the expansion from the smaller tube (where M=1 to start with) causes a decrease in T_static, then you would necessarily have to violate the principle of choked flow since a decrease in T_static would require that the flow be supersonic, something clearly not happening in an expansion that is not shaped properly. Can you visualize what I am describing?

 

[ione]

rjw57,
You were right. The correlation between temperature and Mach number is reported below (for ideal gas)

T1/T2 = [1 + 0.5*(k-1)*M2^2]/ [1 + 0.5*(k-1)*M1^2]
With:
T1 = temperature in state 1 (before expansion)
T2 = temperate in state 2 (after expansion)
M1 = Mach number in state 1
M2 = Mach number in state 2
k = ratio of specific heats (>1)

As the gas expands, its velocity decreases and so does Mach number (M2<M1). And from equation above this implies that temperature increases (T2>T1).