International Conference on Recent Advances in Mechanical Engineering and Interdisciplinary Developments [ICRAMID - 2014]

Stability and Performance Analysis of a Two Spool

Gas Turbine Aero-Engine
N Sathyanarayanan

S Jayavel

Indian Institute of Information Technology, Indian Institute of Information Technology,

Design and Manufacturing Kancheepuram Design and Manufacturing Kancheepuram
Chennai-600127, India
Chennai-600127, India
sjv@iiitdm.ac.in
mdm10b012@iiitdm.ac.in
Abstract The effect of the flying conditions on the operation
of an aero-engine similar to one powering the Boeing 777 aircraft
has been investigated and critical performance parameters of a
gas-turbine aero-engine such as net thrust, specific fuel
consumption and specific thrust are analyzed. A computational
tool developed by School of Engineering, Cranfield University,
United Kingdom, has been used to investigate the performance
parameters and the operating stability of the engines by plotting
compressor running lines. The variations of these parameters
with the flying conditions are studied. The effect of ambient
temperature on the performance parameters of the aero-engine
has also been studied. The results are plotted in the form of
specific fuel consumption, net thrust and specific thrust versus
turbine entry temperature for a series of flying conditions, which
includes varying flight Mach number and flying altitudes. The
net thrust at takeoff when altitude and Mach number are zero
and TET=1705K was found to be 3.70 times the thrust generated
by the aero-engine at cruise condition. The specific fuel
consumption at cruise was found to be 1.98 times the value of
specific fuel consumption at takeoff. The specific thrust at cruise
was found to be 0.582 times the value of specific thrust at takeoff.
Keywords
Aero-engines,
Off-design
Compressor map, Running Lines, Turbo-match.

Theoklis Nikolaidis*

Cranfield University, Cranfield,

Bedfordshire, United Kingdom
t.nikolaidis@cranfield.ac.uk

atmosphere passes into the engine, and is followed by

compressor(s), combustor(s) and turbine(s) in the core. The
aero-engine has a propelling nozzle in the core following the
turbine(s), which converts the pressure energy of the gases to
kinetic energy, thus accelerating the fluid. In case of turbofan
engines there is bypass duct through which the air sucked by
the frontal fan is bypassed. It is followed by a propelling
nozzle. The thrust required by the aircraft is provided by the
propelling nozzle(s), according to Newtons third law.
II. GAS TURBINE PERFORMANCE SIMULATION
Turbo-match, an in-house code developed in the School of
Engineering, Cranfield University is a code that predicts the
performance of a gas turbine engine under a given condition.
For an aero-engine, the performance of an engine could be
talked about in terms of Specific thrust, thrust produced by the
engine and the specific fuel consumption, given a particular
operating condition. The engine is assumed to be running at the
steady state. The aircraft is assumed to be flying at a steady
state and the work and flow compatibility is assumed to be
satisfied.

performance,

III. COMPRESSOR, TURBINE AND COMBUSTOR MAPS

I. INTRODUCTION

Compressor and turbine maps are graphical representation

of behaviour of compressors and turbines, respectively under
different rotational speeds, mass flow rates, entry total
temperatures and entry total pressures. These maps are crucial
in predicting the off-design performance characteristics of a
gas turbine engine [2] - [5]. A typical compressor map has the
pressure ratios and the efficiencies plotted for a range of values
of non-dimensional speeds (CN) and non-dimensional mass
flow rates (TF). Non dimensional mass flow rate (TF) and
speed (CN) are respectively given by Eq. (1) and Eq. (2).

The aero-engine industry has been dominated by gas

turbines for a long time now. A gas turbine is a type of an
internal combustion engine, operating on Brayton cycle [1].
With its high power-weight ratio the gas turbine engines have
been dominating the area of aerospace propulsion. It is
becoming an increasingly popular prime mover in the power,
process and oil industries. Some components of a gas turbine
engine vary based on the application, even though there are
three basic components that are common to a gas turbine
engine i.e., compressor, combustor and a turbine. The
compressor does the function of increasing the pressure of the
incoming air thus facilitating combustion, and aiding power
extraction in the turbine. From a compressor, the high pressure
air enters the combustor, where fuel is injected to increase the
energy and temperature of the gas. The hot, high pressure, high
energy air then passes through the turbine where the enthalpy
of the gas is converted into the rotational energy of the turbine.
An aero-engine has an intake, through which the air from the

w T
TF =
P

(1)

PCN
CN =

(2)

A typical turbine has non-dimensional mass flow rate (TF)

plotted against the ratio of total pressure ratio at the entry to

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International Conference on Recent Advances in Mechanical Engineering and Interdisciplinary Developments [ICRAMID - 2014]

that at the exit for various non-dimensional speeds (CN). In this

paper, the compressor map has corrected mass flow in (kg/s)
on the X-axis and pressure ratio on the Y-axis. Corrected mass
flow (in Kg/s) is the mass flow that would pass through a
device (e.g. compressor, bypass duct, etc.) if the inlet pressure
and temperature corresponded to ambient conditions at sea
level, on a standard day. Corrected mass flow, m can be
calculated using Eq. 3.

w T
=
m
P

101.25

288.15

V. RESULTS AND DISCUSSION

The engine with the mentioned design data was simulated
for design point and off-design performance and the running
lines and the variation of performance parameters such as netthrust, specific-fuel-consumption and specific-thrust, for
different flying and takeoff conditions are analyzed. The scaled
compressor maps of the three compressors and running lines of
the fan, intermediate-booster-compressor and high-pressurecompressor, are studied and the running lines of the fan is
shown in Fig. 1.

(3)

A. Running Lines
All the compressors have a particular operating range for
altitudes between 0 and 8000m and Mach numbers between 0
and 0.85, without surging problems, even though the required
thrust at a particular operating condition might restrict the
compressor's working point.
Like the running lines of the fan suggest, in the areas where
CN is beyond 1.15, it is not advisable to run the engine in those
regions since the lines cross the surge line. The CN of the fan
needs to be kept below 1.10 to ensure a safe surge margin,
always. For a given Mach number, the running lines for fan
almost trace each other for varying altitudes. The running
speed of the fan is limited by the intermediate compressor.
The intermediate compressor restricts the operating speed
of the spool. Since the square roots of total temperature at the
entry of the fan and intermediate compressor are comparable,
we could say the same about their non dimensional speeds at a
particular running condition. For M < 0.4, the spool can be
operated at any CN > 0.5, to ensure smooth operation and
giving the compressor sufficient surge margin. For flight Mach
numbers greater than 0.4, care must be taken to ensure that the
non-dimensional speed of the intermediate compressor is above
0.85 to ensure that there is fairly sufficient surge margin. For a
given Mach number, the running lines for fan almost trace each
other for varying altitudes.
The running lines of the high pressure compressor lie in a
narrow region. The running lines imply good functional
stability for the flight Mach number range. The running lines
also imply that it is safe to operate the gas turbine within any
CN value less than 1.10. The running range of the high
pressure compressor reduces slightly and progressively with
increase in altitude for a given mach number.

A combustor map has values of fuel to air ratio plotted

against the combustion temperature rise, for different
combustor entry temperatures. Turbomatch is an iterative
FORTRAN code that runs a series of calculations based on offdesign matching process. Turbomatch has a set of inbuilt
compressor and turbine maps which are scaled accordingly to
fit the given design conditions of a particular gas turbine
engine. The scaled compressor map is then used as a tool to
predict the off-design performance characteristics of the
engine. The definitions of key parameters in gas turbine
performance are given in Eq. (4a) & (4b).
Net Thrust Generated
Specific Thrust =

Air Mass Flow Rate

(4a)

Specific Fuel Fuel air ratio in combustor

(4b)

=
Specific Thrust
Consumption

IV. ENGINE SPECIFICATIONS

The engine has a frontal fan and the low pressure
compressor coupled on a single spool and has the high pressure
compressor on the second spool. A gas turbine aero-engine
with design point engine parameters as presented in Table-I is
taken for analysis. The results are also presented in Table-I.
TABLE I. DESIGN POINT ENGINE PARAMETERS
Sl.No.
1

Parameter
Number of spools

Type of engine

3
4
5
6

Design point altitude

Design point Mach number
Turbine entry temperature at design point
Bypass ratio at design point
Overall pressure ratio of engine at design
point
Mass flow rate into the engine at design
point
Thrust of the engine as published in
Open source data
Thrust of the engine predicted by
Turbomatch
Error Percentage

7
8
9
10
11

Value
2
High
bypass
0m
0
1705K
6.41

B. Variation of Net-Thrust, Specific-Thrust and SFC

Variation of net-thrust specific-thrust and specific fuel
consumption (SFC) with Mach number are shown in Fig. 2 for
altitude of 2000m and the variations are further studied for
6000m. As expected, for a given turbine entry temperature, and
given altitude, thrust decreases with increasing Mach number
owing it to the increased mass flow into the engine, and thus a
reduction in the overall pressure ratio of the engine, failure of
ram pressure increase in intake to compensate for the decrease
in pressure ratio, and also to higher momentum drag. Further,
increase in turbine entry temperature increases the net thrust
produced, for a constant mach number. Moreover, the variation
is almost linear.

34.2
1157kg/s
373650N
368244N
1.4

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International Conference on Recent Advances in Mechanical Engineering and Interdisciplinary Developments [ICRAMID - 2014]

(a)

(b)

(c)
Fig. 2 Variation of net thrust, specific thrust and SFC
with turbine entry temperature and Mach number (Altitude=2000m)

For a constant turbine entry temperature and constant Mach

number, the net thrust produced reduces with increase in
altitude. Taking a Turbine entry temperature of around 1825K
and mach number of 0.8, net thrust produced at an altitude of
2000m is almost 50% more than that produced at 6000m. This
reduction in thrust could be attributed to reduction in the mass
flow rate with increasing altitudes and thus reducing air
density. As expected the specific thrust increased with an
increase in turbine inlet temperature for a particular mach
Fig. 1 Running lines of fan

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International Conference on Recent Advances in Mechanical Engineering and Interdisciplinary Developments [ICRAMID - 2014]

number. For a given turbine inlet temperature, increase in

Mach number reduces the specific thurst owing it to increase in
momentum drag. For a given TET and a given Mach number,
the specific thrust increases with increase in altitude.
With the increase in turbine inlet temperature there is an
increase in the rotational speed of the spool, thus increasing the
overall pressure ratio and the overall thrust. So a drop in SFC
with increase in TET is clearly noticeable. Though SFC falls
initially, the SFC starts increasing from a particular point on
the curve. This could be attributed to the choking of the nozzle
that occurs with an increase in mass flow rate due to increase in
rotational speed. After the point of choking, there is no increase
in thrust due to momentum thrust, although there is an increase
in pressure thrust. But the increase in overall thrust does not
compensate proportionally for the increase in pressure thrust,
thus increasing the SFC.
For a given TET and given Mach number, the SFC is
slightly lesser at higher altitudes. This could be owed to the
slightly higher gross thrust to momentum drag ratio at higher
altitudes, when compared to that at lower altitudes. For a TET
of around 1500K and M=0.4, the gross thrust to momentum
drag ratio equals 2.29 at 2000m and 2.63 at 6000m.
Variation of net-thrust, specific-thrust and SFC with
varying takeoff ambient temperature for a TET of 1705K is
shown in Fig. 3.

For a given TET, thrust increases almost linearly, with

decrease in ambient temperature. SFC and specific thrust
increase with decrease in ambient temperature. There is an
increase in fuel consumption, because lower ambient
temperature thermodynamically causes lesser temperature at
the entrance of combustor, thus requiring more fuel to be burnt
to reach the required TET. The graphs clearly imply that
achieving a certain amount of thrust consumes lesser fuel with
reduction in ambient temperature and requires a lesser TET,
since a lower rotational speed would balance out the reduction
in temperature and give the required value of CN, to generate
the required amount of thrust.
VI. CONCLUSIONS
The gas turbine aero-engine with the given specifications
was modeled and simulated on Turbomatch. Turbomatch
predicted the running lines for the three compressors of the
engine and the engine was found to be stable and running
below the surge line for all the cases considered. The variation
of the performance parameters- Net thrust, SFC and specific
thrust were studied by simulating various off-design cases. The
effects of off-design performance could be more appreciated by
the following comparision- The net thrust at takeoff when
altitude and Mach number are zero and TET=1705 K was
found to be 3.70 times the thrust generated by the aeroengine at
cruise condition, which was also the design point. The specific
fuel consumption at cruise was found to be 1.98 times the value
of specific fuel consumption at takeoff.
The specific thrust at cruise was found to be 0.582 times
the value of specific thrust at takeoff. The trend predicted by
turbomatch was found to be consistent with the theoretical
predictions. The time dependency of the performance has not
been discussed about in this paper. Future works of ours would
focus on the time dependence of performance. One can expect
rapid changes in the running lines when transient responseacceleration and deceleration of aircraft are considered. The
results obtained are still of significance, since there there is not
much acceleration and deceleration encountered by aircrafts
except during takeoff, landing and during turbulent conditions.

(a)

ACKNOWLEDGMENT
This research work was carried out at the Department of
Power and Propulsion, Cranfield University, Cranfield, UK.
REFERENCES

(b)
[1]
[2]
[3]
[4]
[5]

(c)
Fig. 3 Variation of net-thrust, specific thrust and SFC
with ambient temperature (TET=1705K)

ISBN 978-1-4799-3158-3
945

Cohen, H., Rogers, G.F.C., Saravanamuttoo, H.I.H., 1996. Gas Turbine

Theory, fourth ed., Longman Group Limited, 336-370.
Nikolaidis, Theoklis, Water ingestion effects on Gas Turbine Engine
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Pachidis, A. Vassilios, Gas turbine advanced performance simulation,
PhD thesis, Cranfield University, UK, 2006.
Yin, Junfei, San Li, Man, Hing Huang, Wen, Performance analysis and
diagnostics of a small gas turbine, IGTC2003Tokyo TS-006, 2003.
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