Journal Name International Journal of Civil Aviation
ISSN 1943-3433
2009, Vol. 1, No. 1: E3
Compressor Effects on Specific Fuel Consumption of
Kerosene-fueled Civil Turbofans
Onder Turan (Corresponding author)
Aircraft Propulsion &Structure Maintenance Department, School of Civil Aviation,
Anadolu University, PO Box 26470, Eskisehir, Turkey
Tel: +90-222-323-2722
E-mail: onderturan@anadolu.edu.tr
T. Hikmet Karakoc
Aircraft Propulsion &Structure Maintenance Department, School of Civil Aviation,
Anadolu University
PO Box 26470, Eskisehir, Turkey
Tel: +90-222-323-2722
E-mail: hkarakoc@anadolu.edu.tr
Abstract
All gas turbine propulsion must have a compressor component that develops the pressure rise
specified by the cycle. The main objective of the present study is to perform axial compressor
pressure ratio effects on the specific fuel consumption of civil turbofans in both ideal and real
cycles. At the beginning of this study, ideal and real cycle curves were drawn individually to
explain the compressor pressure ratio behavior on the specific fuel consumption in excel and
visual programming languages, respectively. At the second step, three dimensional response
surfaces of the specific fuel consumption had been drawn according to the compressor
pressure ratio. At the end of the study, real engines compressor data were marked on these
curves and compared with results obtained in this paper.
Keywords: Turbofan, Compressor, Bypass ratio, Cycle analysis
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Journal Name International Journal of Civil Aviation
ISSN 1943-3433
2009, Vol. 1, No. 1: E3
1. Introduction
Cycle analysis studies the thermodynamic changes of the working fluid (air and products of
combustion in most cases) as it flows through the engine. The object of cycle analysis is to
obtain estimates of the performance parameters (primarily thrust and specific fuel
consumption) in terms of design limitations (such as maximum allowable turbine temperature
and attainable component efficiencies), the flight conditions (the ambient pressure,
temperature, and Mach number), and design choices (such as compressor pressure ratio, fan
pressure ratio, bypass ratio, as soon) (Mattingly, 2002).
The engine design starts with the on-design (or design point) analysis, which presumes that
all design choices are still under control, and that the size of the engine has yet to be chosen.
The value of parametric cycle analysis depends directly on the realism with the engine
components are characterized. For example, the compressor is described by a total pressure
ratio and the isentropic efficiency, and if the analysis purpose claims to select the best total
pressure ratio for a particular mission, then the choice may determined by the pressure ratio
on the variation of efficiency with total pressure ratio must be comprised in the analysis.
In off-design performance analysis no component performances are available so that the
component efficiencies as functions of operating conditions must be estimated. Final choice
of an engine is based on its off-design performance over the entire aircraft mission. In both
forms of analysis, the components of an engine are characterized by the change in properties
they produce On-design cycle analysis curves are very important for the cycle analysis of
objective engine research. Because it is easy to see effect of the independent design
parameters of the engine such as fan pressure ratio and bypass ratio on the dependent
parameters such as the specific thrust and specific fuel consumption instead of numerical
values (Mattingly, 2002; Oates, 1997).
In this paper, on design analysis of civil turbofan engines with separate flow and non
afterburning used in commercial aircraft were analyzed and then effects of compressor
pressure ratio on specific fuel consumption for ideal and real cycle analysis for different
bypass ratios. Then specific fuel consumption points were evaluated on compressor pressure
ratiobypass ratiospecific fuel consumption response surfaces. New software programs
had been developed for this purpose in visual and excel programming language for real and
ideal cycles, and MATLAB language for three dimensional cycle curves by Turan (2007).
Ideal and real cycle steady state performance prediction of high bypass turbofan was
investigated in Excel (Mert, 2008) and Visual Basic program languages (Turan, 2000)
respectively. Compressor pressure ratio effects on specific fuel consumption with different
bypass ratios can be easily analyzed in these programs.
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Journal Name International Journal of Civil Aviation
ISSN 1943-3433
2009, Vol. 1, No. 1: E3
2. Compressor Design Parameters for Parametric Study
Figure 1 shows both the ideal and actual compression processes for a given compressor
pressure ratio on a T-s diagram.
Pt3
Pt2
(a)
Pressure drop during
heat addition
3
3i
Pressure drop during
heat rejection
2
Compressor process
(b)
Figure 1. a) A modern axial flow compressor (Geae, 2008) b) actual (3) and ideal (3i)
compressor processes in T-s diagram (Çengel, 2008)
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Journal Name International Journal of Civil Aviation
ISSN 1943-3433
2009, Vol. 1, No. 1: E3
Compressors are, to a high degree of approximation, adiabatic. To overall efficiency used to
measure a compressor’s performance is the isentropic efficiency ηc, defined by
ideal work of compressio n for given pressure ratio
actual work of compressio n for given pressure ratio
ηc =
(1)
The actual work per unit mass wc is ht3- ht2 [=Cp(Tt3-Tt2)] and the ideal work per unit mass
wci=ht3i- ht2 [=Cp(Tt3i-Tt2)]. Here, ht3i is the isentropic compressor leaving total enthalpy.
Compressor isentropic efficiency can be written as follows:
ηc =
wci ht 3i − ht 2
=
wc
ht 3 − ht 2
(2)
For a calorifically perfect gas, it can be written as Equation (3);
ηc =
wci C p (Tt 3i − Tt 2 ) τ ci − 1
=
=
wc
Tt 3 − Tt 2
τc − 1
(3)
In Equation (3) τci is the ideal compressor temperature ratio which is related to the
compressor pressure ratio by the isentropic relationship
(γ −1) / γ = π (γ −1) / γ
c
τ ci = π ci
(4)
Thus we have
π (γ −1) / γ − 1
ηc = c
τc −1
(5)
2. Compressor Pressure Ratio Effects on the Specific Fuel Consumption for Ideal and
Real Cycles
The station numbering of a commercial turbofan can be shown engine in Figure 1. Station
numbering is most important for thermodynamic study and energy analysis of air breathing
engines. Ideal and real cycle equations were given in Appendix 1 and Appendix 2,
respectively. Compressor pressure ratio effects on the specific fuel consumption of
commercial turbofans for ideal and real cycles can be easily shown in Figure 2 and Figure 3.
Figure 1. Station numbering of commercial turbofan (Borguet, 2006)
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Journal Name International Journal of Civil Aviation
ISSN 1943-3433
2009, Vol. 1, No. 1: E3
α: bypass ratio
28
Specific fuel consum ption (g/kN.sn)
26
24
α=0,5
α=1
α=1,5
22
α=2
α=3
α=4
α=5
α=8
20
α=12
18
16
14
V2500
CFM56-7B
GE90-92B
12
1
5
10
15
20
25
30
Compressor pressure ratio
Figure 2. Specific fuel consumption variation with compressor pressure for ideal cycle
18
Specific fuel consumption [g/(kN.s)]
17
x: bypass ratio
16
x=0.5
x=1
x=2
x=5
15
V2500
CFM56-7B
14
GE90-92B
13
12
0
5
10
15
20
25
30
35
Compressor pressure ratio
Figure 3. Specific fuel consumption variation with compressor pressure for real cycle
It can be observed in Figure 2 and Figure 3 that while the compressor pressure ratio increases,
the specific fuel consumption decreases in ideal and real cycles. V2500, CFM56-7B and
GE90-92B engines value are also shown in Figure 2 and Figure 3.
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Journal Name International Journal of Civil Aviation
ISSN 1943-3433
2009, Vol. 1, No. 1: E3
3. Compressor Pressure RatioBypass RatioSpecific Fuel Consumption Response
Surfaces
Compressor pressure ratiobypass ratiospecific fuel consumption response surfaces were
developed by Turan (2008) in MATLAB programming environment. Parametric calculation
can be implemented for observing specific fuel consumption variation according to the
compressor pressure ratio and the bypass ratio as a three dimensional and color scaled plots.
Specific fuel consumption variation with bypass ratio and compressor pressure ratio can be
easily shown in Figure 4 coupled with input parameters in Table 1.
Table 1. On-design parameters for compressor pressure ratiobypass ratiospecific fuel
consumption plots
M0
T 0 (K)
hPR
(kJ/kg)
43100
πf
T 4(K)
0.8
220
1.5
1500
pt 4 / pt 3
p t19 / p t13
ec
ef
et
0.99
0.99
0.90
0.89
0.89
Cpc
kJ/(kg.K)
1.00488
Cpt
kJ/(kg.K)
1.147
γc
γt
1.4
1.33
ηb
0.99
ηm
0.99
p0 / p 9
0.90
p0 / p19
0.90
V2500
CFM56-7B
Specific fuel consumption (g7kN.s)
GE90-92B
Bypass ratio
Compressor pressure ratio
Figure 4. (a)
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Journal Name International Journal of Civil Aviation
ISSN 1943-3433
2009, Vol. 1, No. 1: E3
Specific fuel consumption surface
GE90-92B
V2500
CFM56-7B
Bypass ratio
Compressor pressure ratio
(b)
Figure 4. Specific fuel consumption color-scaled surface according to bypass ratio and
compressor pressure ratio a) sideview b) upper view
4. Conclusions
In this study, firstly new computer software were developed for ideal and real cycle analysis
of a turbofan engine and then compressor pressure ratiobypass ratiospecific fuel
consumption response surfaces of high bypass turbofan engine in the conceptual design phase
in MATLAB environment. In this regard, three different software programs were developed.
It can be seen that three color scaled surface performance plots of a high bypass turbofan
engine are easy to evaluate compressor effects on specific fuel consumption.
Then, additional effects, such as the weight, noise, exergy efficiency and thrust of the
commercial engine or its pollutant emissions should be introduced in the model to define new
figures of merit.
References
Mattingly J. (2002), Heiser H., Daley H., Aircraft Engine Design , AIAA Education Series,
USA.
Oates G. (1997), Aerothermodynamics of Gas Turbine and Rocket Propulsion, AIAA
Education Series, USA.
Geae (2008), [Online] Available http://www. geae.com (September 2, 2008)
Çengel Y., Boles M.A. (2006), Thermodynamics : an engineering approach (5th ed.),
McGraw-Hill Higher Education, USA.
45
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Journal Name International Journal of Civil Aviation
ISSN 1943-3433
2009, Vol. 1, No. 1: E3
Borguet S., Kelner V., L´eonard O. (2006), Cycle Optimization of a Turbine Engine: an
Approach
Based
on
Genetic
Algorithms,
[Online]
Available
http://
www.ulg.ac.be/turbo/research/paper/ NCTAM2006.pdf (September 13, 2008)
Mert M. (2008), Ideal cycle analysis of turbofan engines with excel program, Bachelor of
Science Thesis, Anadolu University, Eskisehir, Turkey.
Turan O. (2000), Performance analysis and evaluation program of gas turbine engines,
Master of Science Thesis, Anadolu University, Eskisehir, Turkey.
Turan O. (2008), Elitism-based genetic algorithm of turbofan engines, PhD thesis, Anadolu
University, Eskisehir, Turkey.
Nomenclature
a
Cp
Cv
e
f
F
FR
F/ m&
gc
hPR
m&
M
P
R
SFC
T
V
α
w
Speed of sound, m/s
Specific heat at constant pressure, kJ/(kg-K)
Specific heat at constant volume, kJ/(kg-K)
Politropic efficiency
Fuel –air ratio
Thrust, kN
Thrust ratio
0
Specific thrust, N.s/kg
Newton’s constant
Fuel heating value, kJ/kg
Mass flow rate, kg/s
Mach number
Pressure, Pa
Universal gas constant, m2/(s2-K)
Specific fuel consumption, g/(kN.s)
Temperature, K
Velocity, m/s
Bypass ratio
specific work
Greek Letters
η
γ
π
τ
τλ
Efficiency
Specific heat ratio
Pressure ratio
Temperature ratio
Enthalpy ratio of combustion chamber
Subcripts and supercripts
b
Burner
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Journal Name International Journal of Civil Aviation
ISSN 1943-3433
2009, Vol. 1, No. 1: E3
c
d
e
fn
i
DB
O
P
t
TH
Compressor
Diffuser
Exit
Fan nozzle
Isentropic
Duct bypass
Overall
Propulsive
Total
Thermal
Appendix
Appendix 1. Ideal cycle parametric equations for separate flow and no afterburning turbofan
Table E1. Input and output parameters for ideal parametric cycle
Input parameters
M0, T0,
γ , cp, hPR, Tt4, πc, πf, α
Output parameters
F / m& 0 ƒ, SFC, ηTH, ηP, ηO,FR
Table E2. Ideal parametric cycle equations
Equation
R =
γ −1
γ
No
(e.1)
Cp
a 0 = γ g R T0
τr = 1+
τλ =
γ -1
2
M 02
C p Tt 4
Equation
a0
F
=
m& 0 (1 + α )g c
f =
( γ -1) / γ
(e.5)
τc = πc
( γ -1) / γ
τf =πf
h PR
η P = 2M 0
(e.11)
f
(1 + α )(F / m& 0 )
1
τr τc
(e.12)
V9 / a 0 − M 0 + α (V19 / a 0 − M 0 )
(e.13)
ηTH = 1 −
C p T0
(e.10)
C p T 0 (τ λ − τ r τ c )
SFC =
(e.4)
(e.9)
V9
V

− M 0 + α  19 − M 0  

V
a
 0
 
 0
(e.2)
(e.3)
No
(
2
V92 / a 02 − M 02 + α V19
/ a 02 − M 02
)
η 0 = ηTH η P
(e.6)
47
(e.14)
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Journal Name International Journal of Civil Aviation
ISSN 1943-3433
2009, Vol. 1, No. 1: E3
V9
=
a0
(e.7)
τλ 
2 
τ λ − τ r τ c − 1 + α τ f − 1 −

γ -1 
τrτc 
[
V19
=
a0
)]
(
V9 / a 0 − M 0
V19 / a 0 − M 0
(e.15)
(e.8)
2
τ r τ f −1
γ -1
{
FR =
}
Appendix 2. Real cycle parametric equations for separate flow and no afterburning turbofan
Table E3. Input and output parameters for real parametric cycle
Input parameters
M0, T0,
γ
c,
Cpc,
γ t, cpt, hPR, πdmax, πb, πfn
πn, πfn, ec, ef, et, ηb, ηm, P0/P9, P0/P19, Tt4, πc, πf, α
Output parameters
F / m& 0 ƒ, SFC, ηTH, ηP, ηO
Table E4. Real parametric cycle equations
Equation
Rc =
Rt =
No
γc − 1
C pc
γc
(e.16)
γt − 1
C pt
γt
(e.17)
a 0 = γ c g c Rc T0
V0 = a 0 M 0
τr = 1+
γc - 1 2
M0
2
π r = τ rγc
/( γ c -1)
π d = π d max ηr
Equation
ηc =
No
(e.25)
π (c γc -1)/γc - 1
τ c -1
(e.26)
( γc -1) /( γc e f )
τf =πf
(e.18)
( γc -1)/γc
ηf =
(e.19)
f =
(e.20)
πf
(e.27)
-1
τ f -1
(e.28)
τ λ - τr τc
h PR ηb /( C pc T0 ) - τ λ
τ t = 1-
τ r [τ c - 1 + α(τ f − 1)]
(e.29)
ηm τ λ ( 1 + f )
pt 9 / p0 = ( p 0 / p9 )π r π d π c π b π t π n
(e.21)
(e.22)
M9 =
48
( γt -1) 

2  p t 9 γt
(
)
- 1
γt - 1  p0


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(e.30)
(e.31)
Journal Name International Journal of Civil Aviation
ISSN 1943-3433
2009, Vol. 1, No. 1: E3
τλ =
C pcTt 4
p t 9 / p19 = ( p 0 / p19 )π r π d π f π fn
γc -1 

2  p t19 γc
(
)
- 1
γc -1  p0


τλτ f
T19
=
T0 ( p t19 / p19 )( γc -1)/γc
V19
T
= M 19 19
V0
T0
(e.24)
(e.34)
(e.32)
τ λ τ t C pc
T9
=
T0 ( p t 9 / p 9 )( γt -1)/γt C pt
C pcT0
τ c = π c( γc -1) /( γcec )
M 19 =
(e.23)
(e.33)
V9
γ RT
= M9 t t 9
V0
γ c R c T0

a0
V9
R T / T 0 1 − P0 / P9 
F
=
− M 0 + (1 + f ) t 9
(1 + f )
+
&
m 0 (1 + α )g c 
V0
R c V9 / V0
γc

 V19
αa 0
T / T 0 1 − P0 / P19 
− M 0 + 19

V19 / V 0
γc
(1 + α )g c  V 0

(e.35)
SFC =
(e.36)
(1 + f )
FR =
(e.37)
ηP =
η TH
(e.39)
f
(1 + α )(F / m& 0 )
(e.40)
V9
R T / T 1 − P0 / P9
− M 0 + (1 + f ) t 9 0
V0
Rc V9 / V0
γc
V19
T19 / T0 1 − P0 / P19
−M0 +
V0
V19 / V0
γc
(e.41)
2 M 0 [(1 + f )V 9 / a 0 + α V19 / a 0 − (1 + α )M 0 ]
[(1 + f )(V
9
/ a 0 )2 + α (V19 / a 0 )2 − (1 + α )M 02
[
]
a 2 (1 + f )(V 9 / a 0 )2 + α (V 19 / a 0 )2 − (1 + α )M
= 0
2 h PR ( f + f AB + α f DB )
2
0
]
η0 = ηTH η P
49
(e.38)
(e.42)
(e.43)
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