Intuitive explanation of Fanno Flow

In summary, the counter-intuitive fact that friction both accelerates and cools subsonic flow of a compressible gas can be explained by the formation of boundary layers, which result in a virtual narrowing of the duct. For subsonic flow, this leads to an increase in velocity and a decrease in pressure, temperature, and density. This phenomenon is reversed for supersonic flow due to the Mach-area relationship. This explanation may not be found in textbooks, but it provides an intuitive understanding of the concept.
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Earhart
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TL;DR Summary
Can anyone explain how is it that friction can both accelerate and cool an adiabatic subsonic gas flow, as it does in Fanno Flow?
OK, I have read all the Fanno flow equations, I understand mass and enthalpy conservation for adiabatic flows give the result that friction causes Mach number go to 1... But I cannot think of a physical explanation for the counter-intuitive fact that friction both accelerates and cools the subsonic flow of a compressible gas. Can someone give an INTUITIVE explanation of how this works? Taking also into account that, for an incompressible adiabatic pipe flow (which should be the limit case for very low Mach numbers), viscous friction work (viscous dissipation) is converted to heat, which raises the fluid temperature, according to the energy equation.
Thanks a lot to anyone who can help me understand this.
 
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  • #2
It's a surprisingly straightforward answer, but the key here is boundary layers. In a real flow, a boundary layer forms, leading to a displacement thickness that grows in the downstream direction. That results in a virtual narrowing of the duct. For a subsonic flow, that means an increase in velocity, which in turn means a decrease in pressure, temperature and density.

Since the Mach-area relationship is reversed for supersonic flow, the opposite happens as a result of the same virtual constriction.
 
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  • #3
This is the answer I was looking for, which I could not find in textbooks. As you say, it is surprisingly straightforward. Thank you very much!
 
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1. What is Fanno Flow?

Fanno Flow is a type of compressible flow that occurs in a channel with friction, such as a pipe or nozzle. It is named after Italian physicist Gino Fanno, who first described the phenomenon in 1948.

2. How is Fanno Flow different from other types of flow?

Fanno Flow is characterized by the presence of friction, which causes the flow to slow down and the temperature to increase. This is in contrast to other types of flow, such as isentropic flow, where there is no friction and the flow remains at a constant speed and temperature.

3. What is the intuitive explanation for Fanno Flow?

The intuitive explanation for Fanno Flow is that as the fluid flows through a channel with friction, it loses energy due to the work done against the frictional forces. This loss of energy causes the flow to slow down and the temperature to increase.

4. What are the practical applications of Fanno Flow?

Fanno Flow has several practical applications in engineering, such as in the design of gas turbine engines, supersonic nozzles, and high-speed wind tunnels. It is also important in the study of heat transfer and fluid mechanics.

5. How is Fanno Flow mathematically described?

Fanno Flow can be mathematically described using the Fanno Line, which is a plot of the Mach number and static temperature of the flow. It is governed by the Fanno Flow equations, which take into account factors such as friction, heat transfer, and changes in area along the channel.

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