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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