Chapter: Mechanical - Gas Dynamics and Jet Propulsion - Flow Through Ducts

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Fanno Flow

A steady one-dimensional flow in a constant area duct with friction in the absence of Work and heat transfer is known as “fanno flow”.

Fanno Flow

 

A steady one-dimensional flow in a constant area duct with friction in the absence of Work and heat transfer is known as “fanno flow”.

 

1Applications

 

Fanno flow occurs in many practical engineering applications of such flow includes

 

Ø Flow problems in aerospace propulsion system.

 

Ø Transport of fluids in a chemical process plants.

 

Ø Thermal and nuclear power plants.

 

Ø Petrochemical and gas industries.

 

Ø Various type of flow machineries.

 

Ø Air conditioning systems.

 

Ø High vacuum technology.

 

Ø Transport of natural gas in long pipe lines.

 

Ø Emptying of pressured container through a relatively short tube

 

Ø Exhaust system of an internal combustion engine

 

Ø Compressed air systems

 

When gases are transported through pipe over a long distances. It is also a practical importance when equipment handling gases are connected to high pressure reservoirs which may be located some distance away. Knowledge of this flow will allow us to determine the mass flow rate that can be candled, pressure drop etc…

 

In real flow, friction at the wall arises due to the viscosity of the fluid and this appears in the form of shear stress at the walls far in our discussion, we have assumed the fluid to be calorically perfect in viscid as well. Thus, strictly speaking, viscous effects cannot be accounted for in this formulation.However,in reality, viscous effects are confined to very thin region (boundary layer)near the walls. Effects such as viscous dissipation are also usually negligible.Hence, we can still assume the fluid to be inviscid and take the friction force exerted by the wall as an externally imposed force. The origin of this force is of significance to the analysis.

 

The following are the main assumptions employed for analyzing the frictional flow problem. in fanno flow

 

Ø  One dimensional steady flow.

 

Ø  Flow takes place in constant sectional area.

 

Ø  There is no heat transfer or work exchange with the surroundings.

 

Ø  The gas is perfect with constant specific heats.

 

Ø  Body forces are negligible.

 

Ø  Wall friction is a sole driving potential in the flow.

 

Ø  There is no obstruction in the flow.

 

Ø  There is no mass addition or rejection to or from the flow.

 

In thermodynamics coordinates, the fanno flow process can be described by a curve know as Fanno line and it’s defined as the locus of the state which satisfies the continuity and energy and entropy equation for a frictional flow is known as “fanno line”.

 


Chocking in Fanno flow

 

In a fanno flow, subsonic flow region, the effect of friction will increase the velocity and Mach number and to decrease the enthalpy and pressure of the gas. In supersonic flow region, the effect of friction will decrease the velocity and Mach number and to increase the enthalpy and pressure of the gas. In both cases entropy increases up to limiting state where the Mach number is one (M=1) and it is constant afterwards. At this point flow is said to be chocked flow.

 


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