442
12 Thrust Gas Turbines
at take-off and during climb near to the operating point for cruising comes from
the requirement of stable operation of the fan in the other conditions than cruise
(sufficient margin to choking and stall; see Chap. 13). In reality, there are more
conditions, as all compressor and turbine components should be able to function
in all flight conditions of the aircraft. But compressors parts typically have first
stages with adjustable stator vane angles, so that their performance parameters may
be adjusted. The fan of a turbofan engine has no adjustable parts. The analysis of
the equilibrium between the components of an aero gas turbine for different flight
conditions and the determination of optimal characteristics of these components is
very complicated. We refer to specialist books on aircraft gas turbines [4]. For basic
understanding, as intended here, such detailed analyses are not necessary, as will
become clear hereafter. Current values of maximum turbine inlet temperature (TIT)
and maximum pressure ratio (PR) at take-off are around 1650 °C for TIT and 40 for
PR [1, 3]. The limitations come from maintaining sufficient strength of the turbine
blades in the HP section and sufficient strength of the outer confinement of the combustion chamber at take-off. At sea level ( T 0 = 288 K), the temperature ratio is about
6.67. The ratio at cruise cannot be much higher, which means that the TIT at cruise
must be much lower than the TIT at take-off. Manufacturers do not reveal values
of TIT in cruise conditions and only specify values of maximum TIT. Cumpsty [3]
estimates the turbine entry temperature (TET) of the most recent turbofan engines
at about 1475 K in cruise conditions. But with TET is meant the temperature at the
entrance of the first rotor of the HP turbine. The choking pressure ratio with the
combustion gas properties is around 1.82 (see Chap. 4). Typically, stator parts of the
HP turbine are just choked (see Chap. 15). The corresponding temperature ratio is
about 1.137. With this ratio, the TIT becomes about 1675 K, so about 1400 °C. This
TIT is then determined without taking into account the supplementary temperature
drop due to cooling and mixing of the combustion gas and the cooling air. So, the
temperature drop in the first stage stator vanes, estimated here at 200 K, might even
be somewhat higher in reality. With TIT equal to 1675 K and T 0 = 225 K, the temperature ratio is about 7.44. So, it seems unlikely that it can be higher. We will use
this value of TIT in the following analysis. It will become clear during the analysis
that the turbine inlet temperature is a parameter that can be optimised, so that we
may obtain it from the analysis itself. It is difficult however to start an analysis
without an initial guess of TIT. The analysis will reveal that TIT = 1675 K goes with
a very large value of the bypass ratio, of the order of 10–12, as with the most recent
turbofan engines. So, in principle, a full analysis should encompass a study of the
influence of the TIT on the global performance. But we will not do this, as the only
aim here is basic understanding (see however Exercise 12.7.5).
The relations of the previous section are adapted.
a. Compressor
01
02
02
01
0
0
0
01
(
)
(
1)
(
1).
pa
c pa
R
R
C
C
c
pa
pa
pa
a
c
T T
W C T
T
C T
C T r
r
T T
h ∞
=
−
=
− =
−
12 Thrust Gas Turbines
at take-off and during climb near to the operating point for cruising comes from
the requirement of stable operation of the fan in the other conditions than cruise
(sufficient margin to choking and stall; see Chap. 13). In reality, there are more
conditions, as all compressor and turbine components should be able to function
in all flight conditions of the aircraft. But compressors parts typically have first
stages with adjustable stator vane angles, so that their performance parameters may
be adjusted. The fan of a turbofan engine has no adjustable parts. The analysis of
the equilibrium between the components of an aero gas turbine for different flight
conditions and the determination of optimal characteristics of these components is
very complicated. We refer to specialist books on aircraft gas turbines [4]. For basic
understanding, as intended here, such detailed analyses are not necessary, as will
become clear hereafter. Current values of maximum turbine inlet temperature (TIT)
and maximum pressure ratio (PR) at take-off are around 1650 °C for TIT and 40 for
PR [1, 3]. The limitations come from maintaining sufficient strength of the turbine
blades in the HP section and sufficient strength of the outer confinement of the combustion chamber at take-off. At sea level ( T 0 = 288 K), the temperature ratio is about
6.67. The ratio at cruise cannot be much higher, which means that the TIT at cruise
must be much lower than the TIT at take-off. Manufacturers do not reveal values
of TIT in cruise conditions and only specify values of maximum TIT. Cumpsty [3]
estimates the turbine entry temperature (TET) of the most recent turbofan engines
at about 1475 K in cruise conditions. But with TET is meant the temperature at the
entrance of the first rotor of the HP turbine. The choking pressure ratio with the
combustion gas properties is around 1.82 (see Chap. 4). Typically, stator parts of the
HP turbine are just choked (see Chap. 15). The corresponding temperature ratio is
about 1.137. With this ratio, the TIT becomes about 1675 K, so about 1400 °C. This
TIT is then determined without taking into account the supplementary temperature
drop due to cooling and mixing of the combustion gas and the cooling air. So, the
temperature drop in the first stage stator vanes, estimated here at 200 K, might even
be somewhat higher in reality. With TIT equal to 1675 K and T 0 = 225 K, the temperature ratio is about 7.44. So, it seems unlikely that it can be higher. We will use
this value of TIT in the following analysis. It will become clear during the analysis
that the turbine inlet temperature is a parameter that can be optimised, so that we
may obtain it from the analysis itself. It is difficult however to start an analysis
without an initial guess of TIT. The analysis will reveal that TIT = 1675 K goes with
a very large value of the bypass ratio, of the order of 10–12, as with the most recent
turbofan engines. So, in principle, a full analysis should encompass a study of the
influence of the TIT on the global performance. But we will not do this, as the only
aim here is basic understanding (see however Exercise 12.7.5).
The relations of the previous section are adapted.
a. Compressor
01
02
02
01
0
0
0
01
(
)
(
1)
(
1).
pa
c pa
R
R
C
C
c
pa
pa
pa
a
c
T T
W C T
T
C T
C T r
r
T T
h ∞
=
−
=
− =
−