448
12 Thrust Gas Turbines
then much too high for reaching a good propulsive efficiency. The specific thrust
may be lowered by lowering the TIT. This lowers somewhat the thermodynamic
efficiency, but not very much. So, obviously, there is an optimum TIT for each bypass ratio and TIT = 1675 K, as used here, is certainly too high for b = 5. We do not
attempt here to determine the optimum TIT, but, of course, results may be recalculated for different values of TIT (see Exercise 12.7.5). Remark that specific thrust
may also be lowered by increasing the pressure ratio.
The pressure ratio attainable within a stage of an axial compressor is at maximum about 1.75, when flow velocity and blade speed are set to the maximally attainable values (see Chap. 13). This demonstrates that a single-stage fan becomes
optimal for bypass ratio 10 or above it. For bypass ratio 5, the pressure ratio of a
single-stage fan is too low for optimum (but the necessary value lowers with lower
TIT). With pressure ratio 1.75, the efficiency may be calculated with the above
formulae. The results are:
The value T T
2
1 1 514
/
.
=
is lower than the optimal value T T
2
1 1 632
/
.
=
in Table 12.2.
We further note that the cold flow requires several compressor stages for low bypass
ratio.
12.5.2 Mixed Flows (Bypass Engine)
Pressures and velocities of two flows to be mixed have to be equal for zero mixing
loss. This implies comparable total pressures before mixing. Therefore, for the purpose of the analysis, we take equal total pressures. The h-s diagram is as sketched
in Fig. 12.12, but now with the condition that the total pressure at the outlet of the
cold flow compressor p 05 is equal to the total pressure p 06 at the outlet of the turbine
that drives the cold flow compressor. This condition implies a relation between the
bypass ratio and the common pressure level p 05 = p 06 . The state point 07 is the mixed
flow entering the common nozzle.
2
2
2
1
5;
1.75;
1.587;
3.365;
1.514.
cold
cold
hot
T
b
r
s
s
T
=
=
=
=
=
Table 12.2 Performance of a double-jet engine (turbofan) for s 1 = 4.50 and η b = 0.85
b
s hot
2
s cold
2
r cold
T 2 /T 1
h d h p
5
2.231
1.896
2.483
1.632
0.594
10
1.836
1.560
1.700
1.840
0.669
20
1.560
1.326
1.330
2.021
0.735
50
1.348
1.146
1.119
2.185
0.795
100
1.266
1.076
1.050
2.257
0.821
12 Thrust Gas Turbines
then much too high for reaching a good propulsive efficiency. The specific thrust
may be lowered by lowering the TIT. This lowers somewhat the thermodynamic
efficiency, but not very much. So, obviously, there is an optimum TIT for each bypass ratio and TIT = 1675 K, as used here, is certainly too high for b = 5. We do not
attempt here to determine the optimum TIT, but, of course, results may be recalculated for different values of TIT (see Exercise 12.7.5). Remark that specific thrust
may also be lowered by increasing the pressure ratio.
The pressure ratio attainable within a stage of an axial compressor is at maximum about 1.75, when flow velocity and blade speed are set to the maximally attainable values (see Chap. 13). This demonstrates that a single-stage fan becomes
optimal for bypass ratio 10 or above it. For bypass ratio 5, the pressure ratio of a
single-stage fan is too low for optimum (but the necessary value lowers with lower
TIT). With pressure ratio 1.75, the efficiency may be calculated with the above
formulae. The results are:
The value T T
2
1 1 514
/
.
=
is lower than the optimal value T T
2
1 1 632
/
.
=
in Table 12.2.
We further note that the cold flow requires several compressor stages for low bypass
ratio.
12.5.2 Mixed Flows (Bypass Engine)
Pressures and velocities of two flows to be mixed have to be equal for zero mixing
loss. This implies comparable total pressures before mixing. Therefore, for the purpose of the analysis, we take equal total pressures. The h-s diagram is as sketched
in Fig. 12.12, but now with the condition that the total pressure at the outlet of the
cold flow compressor p 05 is equal to the total pressure p 06 at the outlet of the turbine
that drives the cold flow compressor. This condition implies a relation between the
bypass ratio and the common pressure level p 05 = p 06 . The state point 07 is the mixed
flow entering the common nozzle.
2
2
2
1
5;
1.75;
1.587;
3.365;
1.514.
cold
cold
hot
T
b
r
s
s
T
=
=
=
=
=
Table 12.2 Performance of a double-jet engine (turbofan) for s 1 = 4.50 and η b = 0.85
b
s hot
2
s cold
2
r cold
T 2 /T 1
h d h p
5
2.231
1.896
2.483
1.632
0.594
10
1.836
1.560
1.700
1.840
0.669
20
1.560
1.326
1.330
2.021
0.735
50
1.348
1.146
1.119
2.185
0.795
100
1.266
1.076
1.050
2.257
0.821