441
12.4 Performance of the Gas Generator and the Single-Jet Engine
The last result demonstrates that an efficient propulsion system is reached at a sufficiently high flight Mach number, without any compressor and turbine parts. This
is called a ramjet (see Exercise 12.7.7).
12.4.2 Analysis with Component Losses
The foregoing analysis with hand calculations may easily be adapted for adiabatic
compressor and turbine efficiencies and change of the heat capacity of the working
fluid in the combustion chamber (but with constant values for air and for combustion gas). Taking into account cooling of the turbine and variable gas properties
requires a numerical simulation technique. With the analysis of power gas turbines
(Chap. 11), we observed that the results of hand calculations are quite near to the
results of numerical simulations. The main difference is that the effect of the cooling brings the efficiency results for different turbine inlet temperatures near to each
other, while these are more distinct with an adiabatic hand analysis. But this is a
minor effect. Therefore, we consider here only analysis by hand calculations. We
set the polytropic efficiencies of the compressor and the turbine parts at 0.9. We
set the heat capacity ratios for air and combustion gas at 1.40 and 1.33, combined
with the gas constant 287 J/kgK (these are the typical values in the literature; air is
dry in cruise conditions). Further, we consider flight at Mach number 0.85, so that
r a = 1.60. We still treat the inlet and the nozzle with efficiency equal to 1.
In the design of an aircraft engine, optimum efficiency is aimed for cruise conditions, but the engine also has to function at take-off and during climb. With the
current (2014) typical specifications of cruise conditions: Mach 0.8–0.85 at altitude
10,500 m and lift/drag ratio of the airplane around 18–21, take-off thrust: 0.275–0.3
times the take-off weight and rate of climb at top of climb: 2.5 m/s, the three operating points of the fan, which provides the largest part of the thrust in a turbofan
engine (the thrust ratio of the two flows is about the bypass ratio), are close to each
other in the non-dimensional performance chart. For concise discussions on the
topic, we refer to Crichton et al. [2] and Cumpsty [3]. By the non-dimensional performance chart is meant pressure ratio as a function of the non-dimensional mass
flow function ( / )
/
m A RT p
0
0 at constant values of the non-dimensional rotational
speed Ω D RT
/
0 , where A and D are representative values of through-flow area
and diameter of the fan (see Chap. 15, Sect. 15.3). Mostly, such a chart is represented in corrected mass flow rate and corrected rotational speed, which means that
these quantities are recalculated to reference conditions for p 0 and T 0 according
to the non-dimensional expressions. The necessity for having the operating points
0
0
0.85 :
1.60
1.40 ,
64;
0.695
1.40 ;
0.644
1.33 ;
3 :
36.7 : with
1:
0.643
1.40 ,
0.591
1.3
(
)
(
)
(
)
(
)
(
3).
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
a
a c
td
td
a
c
td
td
M
r
r r r
M
r
r
g
g
g
h
h
h
g
h
g
12.4 Performance of the Gas Generator and the Single-Jet Engine
The last result demonstrates that an efficient propulsion system is reached at a sufficiently high flight Mach number, without any compressor and turbine parts. This
is called a ramjet (see Exercise 12.7.7).
12.4.2 Analysis with Component Losses
The foregoing analysis with hand calculations may easily be adapted for adiabatic
compressor and turbine efficiencies and change of the heat capacity of the working
fluid in the combustion chamber (but with constant values for air and for combustion gas). Taking into account cooling of the turbine and variable gas properties
requires a numerical simulation technique. With the analysis of power gas turbines
(Chap. 11), we observed that the results of hand calculations are quite near to the
results of numerical simulations. The main difference is that the effect of the cooling brings the efficiency results for different turbine inlet temperatures near to each
other, while these are more distinct with an adiabatic hand analysis. But this is a
minor effect. Therefore, we consider here only analysis by hand calculations. We
set the polytropic efficiencies of the compressor and the turbine parts at 0.9. We
set the heat capacity ratios for air and combustion gas at 1.40 and 1.33, combined
with the gas constant 287 J/kgK (these are the typical values in the literature; air is
dry in cruise conditions). Further, we consider flight at Mach number 0.85, so that
r a = 1.60. We still treat the inlet and the nozzle with efficiency equal to 1.
In the design of an aircraft engine, optimum efficiency is aimed for cruise conditions, but the engine also has to function at take-off and during climb. With the
current (2014) typical specifications of cruise conditions: Mach 0.8–0.85 at altitude
10,500 m and lift/drag ratio of the airplane around 18–21, take-off thrust: 0.275–0.3
times the take-off weight and rate of climb at top of climb: 2.5 m/s, the three operating points of the fan, which provides the largest part of the thrust in a turbofan
engine (the thrust ratio of the two flows is about the bypass ratio), are close to each
other in the non-dimensional performance chart. For concise discussions on the
topic, we refer to Crichton et al. [2] and Cumpsty [3]. By the non-dimensional performance chart is meant pressure ratio as a function of the non-dimensional mass
flow function ( / )
/
m A RT p
0
0 at constant values of the non-dimensional rotational
speed Ω D RT
/
0 , where A and D are representative values of through-flow area
and diameter of the fan (see Chap. 15, Sect. 15.3). Mostly, such a chart is represented in corrected mass flow rate and corrected rotational speed, which means that
these quantities are recalculated to reference conditions for p 0 and T 0 according
to the non-dimensional expressions. The necessity for having the operating points
0
0
0.85 :
1.60
1.40 ,
64;
0.695
1.40 ;
0.644
1.33 ;
3 :
36.7 : with
1:
0.643
1.40 ,
0.591
1.3
(
)
(
)
(
)
(
)
(
3).
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
a
a c
td
td
a
c
td
td
M
r
r r r
M
r
r
g
g
g
h
h
h
g
h
g