19-10-2016, 11:52 AM
1459817771-Jetengine.pdf (Size: 715.52 KB / Downloads: 41)
The thrust for a turbojet engine can be derived from Newton’s second law which
implies that the force equals to the time rate of change of momentum:
F
d (mV )
dt
where mV is the momentum.
The net thrust of a jet engine is the difference between the outgoing exhaust gas
momentum flow and incoming air momentum flow. Outgoing exhaust gas
momentum is usually referred the gross thrust, and incoming air momentum flow
is called momentum drag or ram drag. Since m& dm / dt is the mass flow rate of
the air passing through the engine, then the gross thrust
Tg m& V j A j ( p j− p am )
where
V j exhaust gas velocity,
A j area of jet nozzle,
p j static pressure at the jet nozzle discharge, and
p am atmospheric pressure.
The incoming air momentum flow (momentum drag)
Ti m& Vi
© Prof. Dr. Mustafa Cavcar, 2004.
1
where Vi is the incoming air velocity. Therefore, the net thrust
Net thrust Gross thrust - Momentum drag
TmV j A j ( p j− p am )− mVi
m& (V j− Vi ) A j ( p j− p am )
Factors Affecting Jet Thrust
Air Velocity
Incoming air velocity affects
the thrust in two different and
opposite ways. When the
aircraft is static, as when an
engine is being run up prior to
take-off at the end of a
runway, momentum drag is
equal to zero, because Vi 0 .
However, as the aircraft
commences to move, the
velocity of the air entering the
engine also begins to increase
because of the speed of the
aircraft. Therefore, the
difference between V j and Vi
Figure 2 Jet engine thrust versus airspeed [1].
will become less as airspeed,
or Vi , increases. On the other hand, as the aircraft gains speed down a runway, the
movement of the aircraft relative to the outside air causes air to be rammed into
the engine inlet duct. This compression of air in an inlet duct arising from forward
motion is called ram pressure or ram effect. The ram effect both increases the air
mass flow to the engine and the intake pressure, and consequently, increases the
thrust. Figure 2 shows how the thrust varies with airspeed considering both
velocity difference variation and ram effects.
However, ram pressure rise is not significant at lower speeds, thus it cannot offset
the effect of (V j− Vi ) difference and the thrust decreases as the aircraft speeds up
during take-off. Thrust decrease due to airspeed increase during take-off is more
significant for the turbofan engines as shown in Figure 3. Because the pure jet and
the lower by-pass ratio engines have less airflow per unit of thrust, they suffer less
momentum drag as speed increases.
Air Temperature
The thrust generated by a jet
engine is inversely
proportional with the ambient
air temperature, thus the
thrust decreases as the air
temperature increases.
However, this also means an
increase of thrust when the
temperature decreases, so that
an engine may generate
higher thrust than its design
rating at lower ambient air
temperatures. Higher thrust
above the design rating can
harm the engine. For this
reason, engines are restricted Figure 4 Thrust versus air temperature for a flat
to a maximum thrust. This rated engine.
thrust restriction is called
“flat rating,” and engines with restricted maximum take-off thrust are called “flat
rated.” At a given pressure altitude, temperature has no influence on engine
takeoff thrust, below the so-called reference temperature ( Tref ) or flat rating