Page 424 - Advanced thermodynamics for engineers

414 CHAPTER 17 GAS TURBINES

h i 1=2 1=2
ðT 06 T 7 Þ ¼½2 1:147 1000 98:5Š ¼ 476 m=s
V 7 ¼ 2c p g
_ m t 115
_ m c ¼ ¼ ¼ 28:75 kg=s
b þ 1 4:0
F c ¼ 28:75 475 ¼ 13700 N:
Thus the total thrust is

F t ¼ F b þ F c ¼ 25300 þ 13700 ¼ 39000 N ¼ 39:0kN:
This example illustrates the method followed when a propelling nozzle is unchoked, while the
example for the turbojet showed how to analyse a choked nozzle.
Note that at static conditions the bypass stream contributes approximately 65% of the total thrust.
At a forward speed of 60 m/s which is approaching a normal takeoff speed, the momentum drag _ mV a
will be 115 60 or 6900 N; the ram pressure ratio and temperature rise will be negligible and thus the
net thrust is reduced to 32,100 N. The drop in thrust during takeoff is even more marked for engines of
higher bypass ratio and for this reason it is preferable to quote turbofan thrusts at a typical takeoff
speed rather than at static conditions.
This engine would require a high pressure compressor with a pressure ratio of 11.5, which is rather
higher than desirable and may lead to the problems of stability.

17.3.4 OPTIMIZATION OF TURBOFAN ENGINES
The equations developed above were programmed to allow investigation of a number of features of
turbofan engine design and these will be discussed. When designing a turbojet engine the number of
variable parameters is quite limited. The designer can vary the pressure ratio and the maximum cycle
temperature to achieve a given efficiency. After that basic cycle design the mass flow rate can be
chosen to give a particular thrust. In the case of the turbofan engine there are two additional vari-
ables: fan pressure ratio (r f ) and bypass ratio (b). Thus the problem of design becomes significantly
more complex than for the turbojet because the operating envelope is defined by four independent
variables:
• overall pressure ratio
• maximum cycle temperature
• fan pressure ratio
• bypass ratio
The effect of varying fan pressure ratio on the engine defined above will now be considered.
Figure 17.24 shows the way in which the thrust varies with fan pressure ratio for a number of
maximum temperatures. It can be seen that the thrust reaches a maximum at a particular fan pressure
ratio for any temperature being considered. Also the fan pressure ratio for maximum thrust increases
with increasing temperature. The reason for this maximisation of thrust is because the bypass thrust
increases as the fan pressure ratio increases whereas the jet thrust decreases. Initially, when the fan
pressure ratio is low the jet operates with its nozzle choked. In the middle of the range both the fan and
jet are unchoked but when the fan pressure ratio gets high then the fan chokes. The change in thrust
distribution also indicates the significant change in work balance that occurs in the engine. At low fan