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1.5 Conceptual turbofan design
1.5.1 Flow annulus
A cycle design point calculation yields the mass flows, total temperatures, and total pressures.
However, the size of the engine is not directly visible from these numbers, except for the exhaust
area. That is the reason why performance calculation programs are sometimes called 0-D
programs. This characterization creates the impression that these programs are primitive and vastly
inferior to any 3-D CFD program. However, 0-D performance programs can – when the
component maps have been calibrated with measured data –predict thrust and fuel consumption
very accurately as well as temperatures, pressures, and spool speeds for any operating condition,
all without knowing the engine geometry in detail.
As mentioned above, thermodynamic cycle calculations deal only with total pressures and
temperatures. Static pressures and temperatures are not relevant, apart from the ambient pressure
downstream of the exhaust. When we want to know more about the flow annulus, then we need to
make assumptions about the Mach numbers in all thermodynamic stations.
Fig. 1.5-1: Typical hub-tip radius ratios and Mach numbers for a turbofan
1.5.1.1 Local Mach numbers
Station 2 defines the engine inlet diameter which should not be bigger than necessary – therefore
high Mach numbers are preferred. Just the opposite is true at the entry to the combustion chamber
(Station 3) where high velocity would endanger burner stability. The local Mach number is
moderate because the sonic velocity is high (due to the relatively high T3) and the absolute velocity
is low. The temperature at the inlet to the core compressor is higher than at the fan face, so is the
local sonic velocity. Therefore, the Mach number at this location is lower than at station 2. Mach
numbers at the exit of the turbines are moderate, again due to the high local sonic velocity.
1.5.1.2 Hub-tip radius ratio
Mach number, mass flow, total temperature and pressure determine the flow area. If we also
estimate the hub-tip radius ratio rh/rt, then we can calculate the hub and tip radii at each of the
2
thermodynamic stations around the turbomachines. Fig. 1.5-1 shows typical values for turbofans
together with local Mach numbers.
Low radius ratios are desirable at the engine inlet to minimize overall engine diameter and
hence nacelle drag, weight and increase ground clearance. The lower limit is often set by the
ability to accommodate the roots of the fan blades.
1.5.1.3 Relationships between components
High circumferential speed is advantageous for stage pressure ratio. However, non-dimensional
speed reduces along a multi-stage compressor as temperature rises. Therefore, the speed tends to
be too high at the front and too low at the rear. To compensate for this, the exit radius is raised by
selecting a high hub tip radius. This can be assisted by using a constant tip radius, which in turn
leads to short blade height rt - rh and tip clearance may become a problem: If the blade height gets
too small, then the relative tip clearance (expressed in percentage of the blade height) becomes
unacceptable due to losses in efficiency and stall margin.
The HP compressor exit radius does not limit the HP turbine radius. At the turbine inlet,
we need a much bigger annulus area since the density of the gas is considerably lower than at the
compressor exit. Thus, we can make the turbine diameter bigger than the compressor exit diameter
without getting blades which are too short. The benefit for the turbine is higher circumferential
speed which reduces the aerodynamic loading. The mean turbine diameter is typically 10% bigger
than the compressor exit diameter.
The fan dictates the rotational speed of the low pressure turbine (LPT). For acceptable
aerodynamic loading and for minimizing the stage count, we need the highest feasible
circumferential speed. Therefore, in high bypass ratio engines the LPT entry diameter is up to 60%
bigger than the HPT exit diameter.
The space available in the nacelle limits the exit diameter of the LP turbine. It usually
cannot be more than 20% bigger than the outer diameter of the core entry. Another way to set the
LPT exit diameter is to choose a hub tip radius ratio of 0.6.
1.5.1.4 Spool speed
Selecting spool speed is a complex compromise between aerodynamic and stress requirements.
Compressor stage count depends on circumferential speed since stage loading ΔH/U² must remain
within limits. The length of the engine depends on the number of stages and the magnitude of the
radius differences between the turbomachines.
Estimating the rotational spool speeds based on the conditions at the fan and the HP
compressor entry is a suitable starting point. Given corrected flow W√T/P, absolute Mach number,
hub tip radius ratio and blade tip circumferential speed yield revolutions per minute. The blade tip
relative Mach number is a byproduct of this calculation.
1.5.1.5 Core size
Local Mach numbers, hub-tip radius ratios and AN² at turbine exit (as a measure of blade root
stress) have always been used in conceptual design studies of gas turbines. In the recent years a
new term has become popular in this context: the so-called core size. It is defined as
(1.5-1)
In this formula W25 is the core compressor inlet mass flow, Θ3 is the corrected compressor
exit temperature T3/288.15K and δ3 is the corrected compressor exit pressure P3/101.325Pa.
From this definition, we can immediately see that only properties of the high pressure
compressor are considered. It is obvious that this definition of core size cannot describe burner
volume effects or whether there are one or two HP turbine stages.
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If core size does not stand for the size of the core in total, the question arises if it can be
used to describe at least the size of the core compressor. To check that, we expand the above
formula as follows:
(1.5-2)
The mass flow ratio W25/W3 reflects an inter-stage bleed off-take. If air is bled off, then
the compressor size upstream of the bleed off-take location increases and this is reflected in an
increase of cs.
For further examination of cs we assume that for a given application of the compressor,
W25/W3 is constant. In any case, the Mach number M3 will be selected such that it is as high as
possible within the limits of stable burner operation because high velocities are favorable for the
design of the last compressor stage. Therefore, we can consider the Mach number M3 also as
constant.
Thus, the term core size as defined here is proportional to the compressor exit area since
both W25/W3 and M3 are constant (except for minor variations) within any conceptual design study.
Since also the hub-tip radius ratio at the compressor exit is within narrow limits we can say:
Core size is proportional to the blade height of the last compressor stage.
The difficulties of manufacturing small high quality blades and maintaining tight tip
clearance during operation amplify with decreasing blade height. Introducing an efficiency penalty
and eventually an increased surge margin requirement for compressors with small core size can be
adequate in a sophisticated conceptual engine design study. However, there is no hard limit for
minimum blade height which could justify restricting the design space to engines with a certain
minimum core size.
The uncritical use of core size as engine quality criterion can be misleading if the term is
understood as a measure of the geometrical size, of the volume or of the weight of the gas
generator. Consider the following two cases:
1) The geometry of a gas generator changes despite constant core size if
• A two-stage turbine replaces a single stage high pressure turbine.
• In a cycle study with constant overall pressure ratio, the booster pressure ratio is decreased
and the HPC pressure ratio is increased in such a way that more HPC stages are needed.
• The gas generator spool speed is increased and the HPC stage count decreases as a
consequence.
• Inlet mass flow (and thus inlet area) is increased and simultaneously the pressure ratio (and
the required number of stages) is decreased in such a way that core size is constant.
2) The geometry of a gas generator does not change, but core size varies during off-design
operation if
• Bleed air is taken from the burner.
• Power is taken from the gas generator spool.
• The efficiencies of compressor and turbine decrease due to deterioration.
• HPT flow capacity is modified by re-staggering the nozzle guide vanes.
• LPT flow capacity is modified.
• The engine is operated transiently.
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As a summary: the term core size is only useful as a correlating parameter for size effects
on compressor efficiency and eventually for correlating surge margin requirements. If the
geometry of a compressor is given, then it makes no sense to use core size as a criterion for
anything.
1.5.2 Direct drive or with a gearbox?
Cruise specific fuel consumption of turbofan engines depends on core efficiency, transmission
efficiency and propulsive efficiency. Core efficiency depends on the core component efficiencies,
the overall pressure ratio and the burner exit temperature.
The aerodynamic quality of the turbomachines has already reached a very high level – there
is little room for further improvements. Increasing burner exit temperature did contribute to better
core cycle efficiency in the past but increasing it further yields less and less improvement in
thermodynamic efficiency because present day T4 values are already near to the theoretical
optimum. Increasing the cycle pressure ratio above 50 will also lead only to small improvements
in core efficiency.
So, we can significantly decrease turbofan specific fuel consumption only if we increase
propulsive efficiency and using higher bypass ratios (i.e. lower specific thrust) is the key to
success.
Flight condition
Altitude
35000ft
Mach 0.8
Fan outer efficiency
polytropic
0.91
Fan inner efficiency
polytropic
0.91
Booster efficiency
polytropic
0.91
HPC efficiency
polytropic
0.91
Burner efficiency
0.9995
HPT efficiency
polytropic
0.89
NGV cooling air
% of W25
8
1st Rotor cooling air
% of W25
5
LPT efficiency
polytropic
0.91
Compressor inter-duct pressure loss
%
2
Burner pressure loss
%
5
Turbine inter-duct pressure loss
%
2
Turbine exit duct pressure loss
%
1
Bypass pressure loss
%
1
Accessory parasitic power
% of PWHPT
1
T4
K
1700
Fan inner and booster pressure ratio P24/P2
2.551
HPC pressure ratio
-
18
Overall pressure ratio P3/P2
-
45
Jet velocity ratio V18/V8
-
0.8
Table 1.5-1: Main assumptions for the simple cycle study
Let us examine the theoretical SFC reduction potential with a simple cycle study. All cycle
input data are constant, except bypass ratio and fan pressure ratio. If we were to do the study as a
systematic variation of these two parameters, many of their combinations would not make sense.
Therefore, for each bypass ratio, we adjust fan pressure ratio in such a way that the ratio of fan jet
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velocity V18 to core jet velocity V8 is constant. Convince yourself with a parametric study that a
jet velocity ratio of V18/V8=Fan×LPT 0.8 yields the lowest SFC for any bypass ratio.
Table 1.5-1 summarizes the most important constant input data for this simple cycle study;
only some minor details of the secondary air system (which are difficult to describe) are missing.
Note that the table contains neither a thrust value nor one for mass flow - the size of the engine has
no effect on the thermodynamic cycle. Fig. 1.5-2 shows the result: Going from a bypass ratio of 6
to 12 yields 12% lower SFC, increasing the bypass ratio by another 6 to 18 leads to a further 4.1%
SFC reduction.
The question is: What do the engines look like that achieve this SFC level? In the following
we will show how the flow path changes with bypass ratio. All the engines have the same core,
the same overall pressure ratio and the same burner exit temperature T4. In other words: we
consider an engine family with a common core. The thermodynamic data of this core are listed in
Table 1.5-1, and for fixing its size we set the standard day corrected flow of the compressor
W25Θ25/δ25 to 25kg/s.
Any change in bypass ratio requires a new fan, a redesigned booster and a new low pressure
turbine. For conventional direct drive two spool turbofans we examine bypass ratios between 6
and 14 and for turbofans with gearbox we consider bypass ratios between 10 and 18. We compare
the fundamental differences between conventional turbofans and those with a gearbox for the
bypass ratio of 12 - the middle of the bypass ratio range.
The cycle design point is Max Climb rating at the flight condition Mach 0.8/35000ft, which
is typical for commercial airliners.
Fig. 1.5-2: Specific fuel consumption result from a simple thermodynamic cycle study
Different rules apply for optimizing turbofans of conventional designs and those with a
gearbox. Various criteria need to be considered for optimizing the respective engines and their
components. We begin with conventional direct drive turbofans.
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Fig. 1.5-3: Conventional turbofan, bypass ratio 6
1.5.3 Conventional turbofans with bypass ratios between 6 and 14
The corrected flow at the entry of the gas generator W25Θ25/δ25 is 25kg/s. The true air flow is
almost the same (W25≈20.9 kg/s) for all members of the engine family because the pressure ratio
P25/P2 is constant and the temperature ratio T25/T2 changes only slightly due to minor changes in
booster efficiency. The total airflow of the bypass ratio 6 engine, for example, is W2=146.4kg/s
and it delivers 29.8kN net thrust.
Now let us go to the details of engine design; we want to see how the various engines look.
The simple thermodynamic cycle calculation yields only total pressures and total temperatures - if
we want to know the geometry of the engine then we also need to know the static conditions. We
get these by setting appropriate local Mach numbers at the thermodynamic stations indicated in
Fig. 1.5-3. We can select all these local Mach numbers freely except for stations 8 and 18. The
Mach numbers the thermodynamic cycle directly determines them.
Mach number, mass flow, total temperature and total pressure determine the required flow
areas. The Mach number at the fan face (station 2) together with the hub-tip radius ratio determines
the fan tip diameter. We choose M2=0.6 for Max Climb – this leaves some room for higher mass
flow within the same nacelle. The selected hub-tip radius ratio of 0.28 is at the lower limit because
some room must remain for the blade attachment.
All the Mach numbers and hub-tip radius ratios from station 25 to station 44 remain
unchanged because we are considering an engine family with a given core. Reasonable Mach
numbers are chosen for the other stations, as in Table 1.5-2.
Station
Mach number
22
0.5
24
0.5
45
0.4
5
A result of the LPT design
6
Same as in station 5
13
0.45
16
0.478
Table 1.5-2: Mach numbers at selected thermodynamic stations of Fig. 1.5-3
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The lengths of the compressors and turbines depend on the stage count and the blade aspect
ratios. Low aspect ratios are favorable for compressor stability; high aspect ratios make both
compressor and turbine shorter. There is no strict rule saying how large the blade aspect ratios
must be. Our numbers are typical of modern turbofans.
As mentioned before, the gas generator of our turbofan engine family is the same for all
bypass ratios, for both direct drive and geared configurations. So, we can now limit our exploration
of engine geometry to the fan, the booster and the low pressure turbine.
1.5.3.1 Fan and booster
The core stream pressure increases in the hub region of the fan and in the booster from P2 to P24.
The specified values of P24/P2 (2.551) and pressure loss in the compressor inter-duct (2%) lead to
P25/P2=2.5. Combining this with the HPC pressure ratio of 18, gives us the overall pressure ratio
P3/P2=45. Combustor exit temperature (T4), LPT inlet temperature (T45) and LPT inlet pressure
(P45) are all the same in our engines.
We make use of the energy available at the LPT inlet for three processes. First, we extract
the power we need for compressing the core stream in the fan and the booster. Second, we generate
the shaft power necessary for compressing the bypass stream to P18. Third we generate thrust in
the core nozzle.
The power we extract in the first process is always the same. In the other two processes,
we have a choice;we generate thrust in either the core or the bypass nozzle. High shaft power
extraction from the core flow delivers much thrust in the bypass nozzle and little thrust in the core
nozzle, low power extraction doesthe opposite. Theoretically, the best thrust distribution between
core and bypass thrust happens when the jet velocity ratio V18/V8 is equal to the product of fan and
LPT efficiency.
We can use a constant value of V18/V8 =0.8 for all bypass ratios since the sum of core and
bypass thrust is only a weak function of the jet velocity ratio near to the optimum. Assuming
constant V18/V8 makes the fan pressure ratio a function of bypass ratio. Increasing bypass ratio
leads to decreasing fan pressure ratio, decreasing bypass jet velocity and decreasing core jet
velocity – propulsive efficiency gets better.
The lower the fan pressure ratio, the lower the required circumferential fan speed U
becomes. In a first parametric study we adjust the fan tip speed in such a way that the average pitch
line loading ∆H/U² is 0.4. This choice leads to a relatively high rotational speed, which is beneficial
for both the booster and LP turbine efficiencies and hence contributes to low specific fuel
consumption. We can achieve 91% polytropic efficiency with the selected aerodynamic loading
(Ref. 1). The disadvantage of our choice is the noise which accompanies the high fan tip speed.
Both the fan tip and hub diameters increase with bypass ratio because their radius ratio is
constant. The increase in core inlet radius with bypass ratio benefits the aerodynamic loading of
the booster stages. However, the effect of decreasing the fan tip speed dominates so much that the
booster stage pitch line loading would increase significantly if the number of stages were not
increased.
If we kept the aerodynamic loading of the booster stages exactly constant, then we would
need more booster stages than is practical. The bypass ratio 6 engine has two booster stages in our
example. Additional stages in higher bypass ratio engines prevent an excessive increase in the
aerodynamic stage loading. The limited increase of the loading results in only a modest drop in
booster efficiency (according to a correlation in Ref. 1) as shown in Fig. 1.5-4. This reduction
affects specific fuel consumption only very slightly: a 1% booster efficiency drop increases SFC
by only 0.12%.
8
Fig. 1.5-4: Booster pressure ratio and efficiency
In our study we assume that the fan root pressure ratio is lower than that in the bypass
stream because the circumferential speed in the hub region is much lower:
(1.5-3)
The booster pressure ratio P24/P22 must increase slightly with bypass ratio because P22/P2
decreases with fan pressure ratio P13/P2.
1.5.3.2 Bypass
The pressure loss in the bypass duct has a significant effect on the specific fuel consumption. 1%
reduction in P16/P13 increases SFC by 0.6% if BPR=6 and the penalty increases to 1.4% if the
bypass ratio is 12. The use of a constant pressure ratio P16/P13 is inadequate in an ambitious cycle
study. Therefore, we make the bypass pressure loss a function of the ratio of the bypass length to
the hydraulic diameter of the duct. The pressure loss in an engine with bypass ratio 6 is assumed
to be 1.8%. This value decreases to 0.9% in a bypass ratio 12 engine.
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Fig. 1.5-5 The 8 stage LPT design point of the bypass ratio 12 turbofan in the Smith diagram
1.5.3.3 Low pressure turbine
We determine the efficiency of the low pressure turbine with the help of a simple velocity diagram
analysis. The velocity triangles are assumed to be symmetrical and the loading H/U² - which is
the same for all stages - is optimally matched to the flow factor Vax/U as indicated by the dotted
line in the Smith diagram (Fig. 1.5-5)
Fig. 1.5-6: LPT efficiency result from the velocity diagram analysis
If we employed only four LPT stages in all engines, then as BPR increases we would get
excessive aerodynamic stage loading and consequently poor LPT efficiency because the rotational
speed of the low pressure spool decreases from 7603rpm (BPR=6) to 4110rpm (BPR=12).
Increasing the LPT diameter helps a little but we still must increase the number of LPT stages with
bypass ratio to achieve an acceptable LPT efficiency. Fig. 1.5-6 shows how the efficiency varies
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with bypass ratio and the number of LPT stages. The blue line indicates a reasonable assumption
for the number of stages versus bypass ratio.
Fig. 1.5-7: Effect of LPT stage count on SFC
We could always get better efficiency with an additional turbine stage. However, that
would mean more weight, length and manufacturing cost. Our stage count selection is a
compromise between performance and other requirements. Fig. 1.5-7 shows that the SFC of our
engines is nearly as good as our simple thermodynamic cycle has predicted (i.e. the black line with
the circle).
Fig. 1.5-8: Boundary conditions for the LPT
The next two figures show some details of the LPT design. Our model describes a sort of
“rubber engine” which changes its shape with design bypass ratio. Both the inner radius of the
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LPT at the turbine inlet and exit grow with bypass ratio. The slope of the hub at the turbine inlet
increases also because this gives a shorter transition duct from the HPT to the LPT.
We do the velocity diagram analysis with the geometric boundary conditions of Fig. 1.5-8.
Among many other details we get from the velocity diagram analysis are the hub-tip radius ratio
as well as the Mach number at the LP turbine exit (Fig. 1.5-9). These two quantities influence the
shape and dimensions of the exhaust system.
Fig. 1.5-9: Calculated hub-tip radius ratio and Mach number at the LPT exit
With all these assumptions, we get a reasonable idea of the behavior of our “rubber engine” model.
Fig. 1.5-10: Polytropic fan efficiency as function of the average pitch line loading ∆H/U² (Ref.1)
12
1.5.3.4 Effect of spool speed
In the next investigation we compare turbofans with and without a gearbox in a parametric study
where fan tip speed is the major driver. It varies between 400 and 650m/s and results in relative
tip Mach numbers at Max Climb from 1.53 (BPR=14) to 2.18 (BPR=6).
Polytropic fan efficiency drops as soon as we deviate from the optimal aerodynamic
loading of ∆H/U² =0.4, and this is seen in Fig. 1.5-10. Fig. 1.5-11 shows that the best isentropic
efficiency we can achieve increases slightly with bypass ratio because fan pressure ratio falls.
Isentropic LPT efficiency is also affected by low circumferential speed in a different manner. That
is illustrated in Fig. 1.5-12, where the range of efficiency difference over fan tip speed tends to be
maintained as bypass ratio increases.
Fig. 1.5-11: Calculated isentropic fan efficiency
Fig. 1.5-12: Isentropic LPT efficiency
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Fig. 1.5-13: Effect of fan tip speed on SFC
Fig. 1.5-13 shows how SFC changes with fan tip speed. Low fan tip speed is certainly
desirable for noise reasons; however, it increases specific fuel consumption, especially for the low
bypass ratio engines.
Fig. 1.5-14: Comparison of conventional turbofan models with BPR=6 and 12
SFC optimized engines with bypass ratios 6 and 12 have quite different cross sections.
Note that in Fig. 1.5-14, not only is the annulus different but so are the disk shapes in the booster
and the LPT. The stresses in each of the disks have been calculated - their shape is optimized for
weight. The disk bore diameter can be much bigger in the high bypass ratio engine because of the
low rotational speed. Therefore, the weight penalty for an 8 stage LPT, for example, is not as large
as might be expected.
1.5.4 Turbofan with gearbox
Conventional turbofans would need to have excessive numbers of low pressure turbine stages
when the bypass ratio increases above 12. Introducing a gearbox makes the rotational speed of the
fan independent of that of the booster and the low pressure turbine. We need fewer booster and
LPT stages and at the same can time maintain the low aerodynamic loading levels required for
good efficiency.
14
The bearing arrangement in a turbofan with gearbox differs from that of a direct drive
turbofan, in which the front bearing structure is inside the compressor inter-duct. Mounting the
gearbox and the fan spool requires an additional structure between fan and booster. Fig. 1.5-15
shows as an example of a turbofan with gearbox the cross section of the PW1000G PurePower®
Geared Turbofan™.
Fig. 1.5-15: PW1000G PurePower® Geared Turbofan™
Reproduced with permission from United Technologies Corporation, Pratt & Whitney.
The layout of our study engine with bypass ratio 12 in Fig. 1.5-16, is very like that of the
PW1000G. In the following analysis, we examine such turbofans with three booster and three LPT
stages over a range of bypass ratio from 12 to 18. The flow path of the core stream does not change
very much. The important characteristic which changes with bypass ratio is not visible in the
engine cross section: it is the gear ratio.
Fig. 1.5-16: Cross section of a turbofan with gearbox (bypass ratio 12)
For the conventional turbofan we established the LP spool speed from the average fan pitch
line loading of 0.4. The number of booster and LPT stages were increased with bypass ratio to
keep the respective stage loadings within reasonable limits. This approach not only gave us the
optimum fan efficiency but also the highest possible booster and high LP turbine efficiencies.
15
Fan and LPT spool speeds for turbofans with gearbox are consequences of optimizing the
gear ratio. Fan efficiency changes with average pitch line loading, as shown in Fig. 1.5-10, and LP
turbine efficiency is a result of the velocity triangle analysis.
Fig. 1.5-17 shows AN² (a measure of blade root stress) at the exit of the LPT for gear ratios
between 2 and 3. The coloured contour bands represent specific fuel consumption of engines with
bypass ratio 12. All the loss assumptions for the cycle calculation described above are the same as
those used for the direct drive turbofan. We assume that the gearbox losses are 0.8% of the
transferred shaft power.
The point with gear ratio 2.5 and AN²=40 is a compromise between blade root stress, SFC
and fan tip speed. Selecting a point with lower gear ratio and higher fan tip speed would yield only
a slightly better SFC, but the noise generated by the fan would be significantly higher.
Fig. 1.5-17: Optimizing the gear ratio for the bypass ratio 12 engine
Repeating the parametric study for bypass ratio 18 yields the data in Fig. 1.5-18. It is
reasonable to choose the gear ratio 3 as a practical design point because we get a lower fan tip
speed and less blade root stress in the last LPT stage. In the following parametric study, we make
the gear ratio a linear function of the design bypass ratio.
16
Fig. 1.5-18: Optimizing the gear ratio for the bypass ratio 18 engine
1.5.5 Comparison
Now we compare engines with and without gearbox more directly. Fig. 1.5-19 compares sections
of the most efficient direct drive turbofan and the optimized turbofan with gearbox each with a
bypass ratio of 12with gearbox. For thrust (see Fig. 1.5-20) and SFC (compare the numbers in Fig.
1.5-13 with those in Fig. 1.5-17), the engines are essentially equal, however, there are many other
significant differences worthy of discussion.
Fig. 1.5-19: Turbofans with and without gearbox, common core, bypass ratio 12
In the following figures, practical bypass ratio 12 engine designs are indicated by blue solid
circles. The white open circles mark the design points of a conventional bypass ratio 6 turbofan
and a bypass ratio 18 turbofan with gearbox.
1.5.5.1 Mechanics
From the engine cross sections, we can immediately see that the booster and LPT disks of the
turbofan with gearbox have a much smaller bore radius and a bigger bore width than those of its
conventional counterpart. On the other hand, fewer stages are sufficient to achieve the same SFC.
The fan will be lighter because of the lower rotational speed, but the weight penalty of the gearbox
17
and the additional oil cooler must also be considered. In summary, it is difficult to know which of
the two engines will be lighter.
Fig. 1.5-20: Low pressure turbine torque
The power to be transferred to the fan and the booster is the same for the two BPR 12
engines. However, remember that the torque in the LPT shaft is inversely proportional to the spool
speed. The upper limit for the bypass ratio of a conventional turbofan may be restricted by the disk
bore diameter of the core components and the resulting maximum permissible LPT shaft torque.
Fig. 1.5-21: LPT Torque and AN² at the LPT exit
The low LPT shaft torque advantage of the turbofan with gearbox is accompanied by a
very significant increase in the blade root stress in the last LPT stage, expressed as AN² in Fig.
1.5-21. The actual blade root stress can be reduced by using noticeably tapered hollow blades made
from a material with low density. It is a challenge to design tapered turbine blades for highly
18
efficient work extraction as the pitch to chord ratio at the blade root will be quite different to that
at the blade tip. Conventional LP turbines do not pose such a stress problem and their aerodynamic
design can be optimized without exceptional mechanical constraints.
Fig. 1.5-22: Stage pressure ratio and efficiency of the booster
1.5.5.2 Aerodynamics
The differences in the aerodynamics of the booster and the LPT originate from the dissimilar spool
speeds. As we see from Fig. 1.5-22, the booster stages of a direct drive turbofan produce only a
very modest pressure ratio because the circumferential speed is so low.
With a gearbox, however, we can achieve quite high stage pressure ratios and therefore the
booster stage count of such a turbofan can be lower than in a direct drive turbofan. Similarly, the
modest aerodynamic loading of the LPT allows a lower stage count for this component.
Fig. 1.5-23 shows the blade tip speed of the fan – which can be regarded as a crude measure
of fan noise - and the LPT efficiency. The two BPR 12 engines have similar fan tip speeds and
will therefore not differ noticeably in fan noise.
19
Fig. 1.5-23: LPC (Fan) tip speed and LPT efficiency
Fig. 1.5-24: The 3 stage LPT design point of the bypass ratio 12 turbofan with gearbox
The efficiency of the three stage LPT of the turbofan with gearbox is better than that of its
conventional eight stage LPT counterpart due to the lower aerodynamic loading, see Fig. 1.5-24.
Note that in this preliminary engine design study we did not apply any efficiency decrement for
the mechanically challenging blade design of the high speed LPT.
20
Fig. 1.5-25: Specific fuel consumption
Fig. 1.5-25 shows the specific fuel consumption over the full range of bypass ratios for the
uninstalled engine at Max Climb rating. No minimum exists as SFC gets continuously better when
bypass ratio increases. However, if we consider the engine together with the nacelle, then we reach
a minimum for the corresponding installed SFC because nacelle drag increases with bypass ratio.
This minimum is somewhere in the region between bypass ratios 13 and 16. The precise number
depends on the aircraft design and its mission.
Fig. 1.5-26: Turbofans with gearbox, bypass ratio 12 and 18
1.5.6 The fundamental differences
Four selected engine design points are marked in the preceding figures. Let’s compare their cross
sections in Fig. 1.5-3, Fig. 1.5-14, Fig. 1.5-19 and Fig. 1.5-26 to see the main differences in the
flow paths. Table 1.5-3 lists the design parameters that are most relevant for the comparison of
turbofans with and without a gearbox.
21
Engine Configuration
C6
C12
G12
G18
Bypass Ratio
6
12
12
18
Gear Ratio
n/a
n/a
2.5
3
Fan Tip Diameter [m]
1.60
2.19
2.19
2.64
Fan Pressure Ratio
2.136
1.543
1.548
1.358
Fan Tip Relative Mach Number
2.18
1.66
1.54
1.44
Booster Pressure Ratio
1.34
1.78
1.77
1.98
Booster Stage Count
2
5
3
3
LPT Pressure Ratio
7.23
8.96
8.96
9.75
LPT Torque [kN*m]
12.8
25.2
11.2
12.5
LPT AN² [m²RPM²*10-6]
24.8
10.8
40
35
LPT Stage Loading ∆H/U²
2.10
2.71
1.69
2.08
LPT Isentropic Efficiency
0.922
0.913
0.925
0.920
LPT Stage Count
4
8
3
3
SFC@Max Climb, 35000ft Mach
0.8
15.8
14.2
14.1
13.6
Table 1.5-3: Important design parameters
The fundamental differences between the two engine configurations are highlighted with
bold letters in the columns 2 and 3. Note that we see no significant SFC advantage for the turbofan
with gearbox if we compare it with a conventional turbofan at a bypass ratio of 12.
Noise is of course not relevant during flight at altitude. Nevertheless, we can use fan tip
relative Mach number at Max Climb as an indicator of Take Off noise. Due to our spool speed
selection, the direct drive turbofan emits more noise than the variant with gearbox.
The fan is not the only source of noise, because the low pressure turbine also contributes
to the total acoustic emission. Noise originating in the high speed LPT of the turbofan with gearbox
is generated at a very high frequency, much higher than the noise from the LPT of a direct drive
turbofan. This is an advantage because high frequency noise attenuates quickly with increasing
distance.
Engine Configuration
C6
C12
G12
G18
Bypass Ratio
6
12
12
18
Gear Ratio
n/a
n/a
2.5
3
Fan Mass [kg]
No of Rotor Blades
No of Bypass Exit Vanes
No of Core Exit Vanes
333
826
736
1370
30
30
30
30
19
19
25
25
74
111
52
69
Booster Mass [kg]
No of Blades & Vanes
45.4
128
100
109
568
2072
890
1106
LPT Mass [kg]
No of Blades &Vanes
252
500
244
221
1207
3599
733
736
Table 1.5-4: Component mass and parts count
Table 1.5-4 shows mass data and parts count for the low pressure components. These data
have been calculated with rather crude assumptions which are certainly debatable. Nevertheless,
the blade and vane counts of the direct drive turbofan will be much bigger in any case than those
of the turbofan with gearbox.
22
The booster of the engine variant with gearbox has about the same mass as the booster of
an engine with direct drive - despite the lower stage count and the smaller diameter. This is because
the disks are much heavier since they rotate so fast. The three stage LPT of the turbofan with
gearbox is lighter than the eight-stage turbine of the engine with direct drive, but it is heavier than
the stage count ratio of 3/8 would lead us to expect. This is again due to the high rotational speed,
which results in heavy disks.
If we consider the weight of the gearbox and the indispensable oil cooler, it’s hard to
conclude which of the engines is lighter overall. For making such a statement A reliable conclusion
would require much more detailed design studies.
1.5.7 References
[1] P.P. Walsh, P. Fletcher
Gas Turbine Performance, Second Edition
Blackwell Science Ltd, 2004
23
List of figure captions
Fig. 1.5-1: Typical hub-tip radius ratios and Mach numbers for a turbofan
Fig. 1.5-2: Specific fuel consumption result from a simple thermodynamic cycle study
Fig. 1.5-3: Conventional turbofan, bypass ratio 6
Fig. 1.5-4: Booster pressure ratio and efficiency
Fig. 1.5-5 The 8 stage LPT design point of the bypass ratio 12 turbofan in the Smith
diagram
Fig. 1.5-6: LPT efficiency result from the velocity diagram analysis
Fig. 1.5-7: Effect of LPT stage count on SFC
Fig. 1.5-8: Boundary conditions for the LPT
Fig. 1.5-9: Calculated hub-tip radius ratio and Mach number at the LPT exit
Fig. 1.5-10: Polytropic fan efficiency as function of the average pitch line loading ∆H/U²
(Ref.1)
Fig. 1.5-11: Calculated isentropic fan efficiency
Fig. 1.5-12: Isentropic LPT efficiency
Fig. 1.5-13: Effect of fan tip speed on SFC
Fig. 1.5-14: Comparison of conventional turbofan models with BPR=6 and 12
Fig. 1.5-15: PW1000G PurePower® Geared Turbofan™
Fig. 1.5-16: Cross section of a turbofan with gearbox (bypass ratio 12)
Fig. 1.5-17: Optimizing the gear ratio for the bypass ratio 12 engine
Fig. 1.5-18: Optimizing the gear ratio for the bypass ratio 18 engine
Fig. 1.5-19: Turbofans with and without gearbox, common core, bypass ratio 12
Fig. 1.5-20: Low pressure turbine torque
Fig. 1.5-21: LPT Torque and AN² at the LPT exit
Fig. 1.5-22: Stage pressure ratio and efficiency of the booster
Fig. 1.5-23: LPC (Fan) tip speed and LPT efficiency
Fig. 1.5-24: The 3 stage LPT design point of the bypass ratio 12 turbofan with gearbox
Fig. 1.5-25: Specific fuel consumption
Fig. 1.5-26: Turbofans with gearbox, bypass ratio 12 and 18
