Modern Engineering Thermodynamics

522 CHAPTER 13: Vapor and Gas Power Cycles
CASE STUDIES IN APPLIED THERMODYNAMICS Continued
produces thrust by a combination of high-speed exhaust gas plus
low-speed “bypass” air produced by an external “fan” (or a lowpressure
ratio compressor stage) directly connected to the engine’s
turbine to increase the value of the air mass flow rate _m air
(see Figure 13.63b). Finally, a turboprop engine is a Brayton cycle
gas turbine engine that produces some thrust with a high-speed
exhaust gas, like the turbojet, with the remaining thrust coming
from a standard low-speed propeller driven by the engine’s turbine
through a speed-reducing gearbox (see Figure 13.63c).
Compressor
Burners
Turbine
Neglecting the momentum associated with the mass flow rate of
the fuel, the thrust of a turbojet engine is given by
T turbojet = _m a ðV exhaust − V aircraft Þ/g c
and the thrust of a turbofan or turboprop engine is given by
where
_m a = air mass flow rate,
T turbofan
= _m a ðV exhaust − V aircraft Þ/g c
or turboprop
V aircraft = V inlet air (the air inlet velocity is the same as the aircraft
velocity),
Compressor
Fuel
Fuel
Compressor
(a) Turbojet
Burners
Fuel
Fuel
(b) Turbofan
Burners
Fuel
Fuel
Turbine
Turbines
V exhaust = turbojet exhaust gas velocity,
V exhaust = turbofan or turboprop average exhaust gas velocity,
defined as
V exhaust = ð _m aH V eH + _m aC V eC Þ/ ð _m aH + _m aC Þ = ð _m aH V eH + _m aC V eC Þ/ _m a ,
where _m aH and V eH are the mass flow rate and exhaust gas velocity of
that portion of the exhaust passing through the hot combustion chamber,
and _m aC and V eC are the mass flow rate and exhaust velocity of
that portion of the exhaust gases that “bypass” the combustion chamber
to produce additional thrust by increasing the magnitude of _m a .
Then, the propulsion efficiencies can be written as
η propulsion
turbojet
_m a ðV exhaust − V aircraft
ÞðV aircraft /g c Þ
=
_m a ðV exhaust − V aircraft ÞðV aircraft /g c Þ+ ð _m a /2g c ÞðV exhaust − V aircraft Þ 2
2
=
1 + V exhaust /V aircraft
and
ðη propulsion Þ turbofan
or turboprop
(c) Turboprop
=
_m a ðV exhaust − V aircraft ÞðV aircraft /g c Þ
_m a ðV exhaust − V aircraft ÞðV aircraft /g c Þ + ð _m a /2g c ÞðV exhaust − V aircraft Þ 2
FIGURE 13.63
Brayton cycle gas turbine engines.
Each of these engine designs has its advantages and disadvantages.
A turbojet engine is ideal for very high-speed flight, but it does not
perform well at low speeds or low altitudes. A turbofan engine performs
well at moderate to high speeds, and a turboprop engine
performs well at low aircraft speeds but not at high speeds.
The propulsion efficiency of these three engine designs is given by
η propulsion =
Thrust power output
Thrust power output + Lost kinetic energy rate
2
=
1 + V exhaust /V aircraft
Note that η propulsion increases as aircraft speed approaches the engine’s
exhaust velocity (V aircraft → V exhaust ), but the engine’s thrust vanishes as
V aircraft → V exhaust . So, to maintain the thrust while we increase V aircraft ,
we must increase _m a . Therefore, an engine with a large _m a and a small
V exhaust is more efficient than an engine with the same thrust moving a
small _m a at a high V exhaust .
Another measure of aircraft performance is its thrust efficiency,
defined as
η thrust =
Thrust power
Fuel power
= T × V aircraft
_Q fuel