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being exceeded, thus resulting in reduced thrust and,
overall, similar curve characteristics to those shown
in fig. 21-8. In the instance of a triple-spool engine
the pressure ratio is expressed as P4/P1. i.e. H.P.
compressor delivery pressure/engine inlet pressure.
PROPULSIVE EFFICIENCY
37. Performance of the jet engine is not only
concerned with the thrust produced, but also with the
efficient conversion of the heat energy of the fuel into
kinetic energy, as represented by the jet velocity, and
the best use of this velocity to propel the aircraft
forward, i.e. the efficiency of the propulsive system.
38. The efficiency of conversion of fuel energy to
kinetic energy is termed thermal or internal efficiency
and, like all heat engines, is controlled by the cycle
pressure ratio and combustion temperature.
Unfortunately, this temperature is limited by the
thermal and mechanical stresses that can be
tolerated by the turbine. The development of new
materials and techniques to minimize these
limitations is continually being pursued.
39. The efficiency of conversion of kinetic energy to
propulsive work is termed the propulsive or external
efficiency and this is affected by the amount of kinetic
energy wasted by the propelling mechanism. Waste
energy dissipated in the jet wake, which represents a
loss, can be expressed as where (vJ-V)
is the waste velocity. It is therefore apparent that at
the aircraft lower speed range the pure jet stream
wastes considerably more energy than a propeller
system and consequently is less efficient over this
range. However, this factor changes as aircraft
speed increases, because although the jet stream
continues to issue at a high velocity from the engine
its velocity relative to the surrounding atmosphere is
reduced and, in consequence, the waste energy loss
is reduced.
40. Briefly, propulsive efficiency may be expressed
as:
or simply
Work done is the net thrust multiplied by the aircraft
speed. Therefore, progressing from the net thrust
equation given in para. 18, the following equation is
arrived at:
Propulsive efficiency =
Performance
223
Fig. 21-8 The effect of air temperature on a typical twin-spool engine.
2g
W(v V)2
J −
Energy imparted to engine airflow
Work done on the aircraft
Work done + work wasted in exhaust
Work done
2g
W(v V)
g
V (P - P )A W(v V)
g
V (P - P )A W(v V)
2
J J
0
J
0
− +
+ −
+ −
In the instance of an engine operating with a nonchoked
nozzle (Part 20), the equation becomes:
41. This latter equation can also be used for the
choked nozzle condition by using vj to represent the
jet velocity when fully expanded to atmospheric
pressure, thereby dispensing with the nozzle
pressure term (P-P0)A.
42. Assuming an aircraft speed (V) of 375 m.p.h.
and a jet velocity (vj) of 1,230 rn.p.h., the efficiency
of a turbo-jet is:
On the other hand, at an aircraft speed of 600 m.p.h.
the efficiency is:
Propeller efficiency at these values of V is approximately
82 and 55’per cent, respectively, and from
Performance
224
Fig. 21-9 Propulsive efficiencies and aircraft speed.
J
2
2 J
1
J
J
V v
Simplified to : 2V
WV(v V) W(v V)
WV(v V)
+
− + −
−
approx. 47 per cent
375 1,230
2 375 =
+
×
approx. 66 per cent
600 1,230
2 600 =
+
×
reference to fig. 21-9 it can be seen that for aircraft
designed to operate at sea level speeds below
approximately 400 m.p.h. it is more effective to
absorb the power developed in the jet engine by
gearing it to a propeller instead of using it directly in
the form of a pure jet stream. The disadvantage of
the propeller at the higher aircraft speeds is its rapid
fall off in efficiency, due to shock waves created
around the propeller as the blade tip speed
approaches Mach 1.0. Advanced propeller
technology, however, has produced a multi-bladed,
swept back design capable of turning with tip speeds
in excess of Mach 1.0 without loss of propeller
efficiency. By using this design of propeller in a
contra-rotating configuration, thereby reducing swirl
losses, a ’prop-fan’ engine, with very good propulsive
efficiency capable of operating efficiently at aircraft
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