Page 412 - Advanced thermodynamics for engineers

402 CHAPTER 17 GAS TURBINES

The total thrust is the sum of these two terms and is

F ¼ _ m V j V a þ A j p j p a
Now, in many engines the expansion in the nozzle is complete, and down to atmospheric pressure,
p a . This means that the pressure thrust is zero and the thrust then becomes

F ¼ _ m V j V a (17.60)
This thrust, at constant speed in level flight, must equal the drag on the aircraft. Hence it is possible
to evaluate the propulsive efficiency (h p ) of the engine.
useful propulsive energy
h ¼
p
useful propulsive energy þ K:E: of jet

mV a V j V a
¼ h . i
2 (17.61)
_ m V a V j V a þ V j V a 2
2
¼
1 þ V j V a
This is sometimes referred to as the Froude efficiency.
Note:
(1) The thrust (F) is maximum when V a ¼ 0 (i.e. static conditions) but h p ¼ 0.
(2) h p is maximum when V j /V a ¼ 1, but F ¼ 0.

Hence it is necessary for V j > V a but the difference should be as small as possible to achieve the
desired purpose.
The propulsive efficiency, h p , is just a relationship between ‘jet’ and aircraft velocities and does not
contain any information on the production of thrust as a function of the fuel flow. The efficiency of
energy conversion, h e , can be defined as

2
_ m V V a 2 =2
j
h ¼ (17.62)
e
_ m f Q 0 p
which gives an overall efficiency, h o ,of

_ m V j V a V a FV a
h ¼ ¼ (17.63)
o
_ m f Q 0 p _ m f Q 0 p
and
h ¼ h h : (17.64)
e p
o
This shows that the efficiency of the engine in propelling the aircraft is the product of the engine
and propulsion efficiencies.