jet report

8172019 Jet Report

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H O S T E D B Y

ORGINAL ARTICLE

Optimization of gas turbines for sustainable

turbojet propulsion

Yousef SH Najjarn Ibrahim AI Balawneh

Mechanical Engineering Department Jordan University of Science and Technology Irbid Jordan

Received 17 March 2014 accepted 14 January 2015

Available online 25 June 2015

KEYWORDS

Optimization

Green technology

Sustainable turbojet

engines

Performance carpets

Abstract Gas-turbines are widely used to power aero planes because they are light compact

with a high power-to-weight ratio In the turbo jet engine the main operating variables are

compressor pressure ratio r p and turbine inlet temperature (TIT ) These variables affect the

speci1047297c thrust and speci1047297c fuel consumption (SFC ) which represent the main performance

parameters In addition to the analytical work a computer program of the General Algebraic

Modeling System (GAMS) was used for analysis and optimization The analysis shows that the

speci1047297c thrust strongly depends on turbine inlet temperature (TIT ) where a 10 decrease in TIT

results in 67 decrease in speci1047297

c thrust and 68 decrease in SFC Furthermore the value of optimum pressure ratio r f for maximum speci1047297c thrust increases with TIT A 10 decrease from

design TIT results in 1143 decrease in r f The value of optimum pressure ratio for the turbojet

engine operating at Ma frac14 08 and altitude Alt frac14 13000 m and TIT frac14 1700 K was found to be 14

amp 2015 National Laboratory for Aeronautics and Astronautics Production and hosting by Elsevier BV

This is an open access article under the CC BY-NC-ND license

(httpcreativecommonsorglicensesby-nc-nd40 )

1 Introduction

Energy ef 1047297ciency could be obtained by different meth-

ods among which is waste-heat recovery [1] combinedcycles [2] using energy storage for peak shaving and load

leveling [3] and in the limit widening the range of fuel

speci1047297cations to improve thermo economics [4]

With turbojet engines air as the working 1047298uid is used to

produce thrust based on the variation of kinetic energy of

burnt gases after combustion [56] Performance typically

focuses on use of cycle ef 1047297

ciency speci1047297

c thrust and spe-ci1047297c fuel consumption [78]

Early studies handled the model of the turbojet to

evaluate performance parameters [9] Further investiga-

tions were carried out using variable cycles of turbojet

engine at supersonic speeds [10] In the last few years

many papers presented thermodynamic and aerodynamic

analyses of the behavior of a turbojet operating with and

without afterburners [11]

httppprbuaaeducn

wwwsciencedirectcom

Propulsion and Power Research

2212-540X amp 2015 National Laboratory for Aeronautics and Astronautics Production and hosting by Elsevier BV This is an open access article under the

CC BY-NC-ND license (httpcreativecommonsorglicensesby-nc-nd40 )

httpdxdoiorg101016jjppr201505004

nCorresponding author Tel thorn00962 785793463

E-mail address ysnajjarjustedujo (Yousef SH Najjar)

Peer review under responsibility of National Laboratory for Aeronautics

and Astronautics China

Propulsion and Power Research 20154(2)114ndash121

8172019 Jet Report


Theoretical and practical engineering developments were

necessary for the design building and testing of an engine

with an afterburner [12] Other research works studied the

effects compressor pressure ratio on thrust and other perfor-

mance parameters [13] In military applications there were

special studies on the factors which determine the proper choice

of engine cycle for a combat aircraft to suit the requirements of the designed mission [14] Some researchers used energy and

exergy analyses with a turbojet engine over 1047298ight altitudes

ranging from sea level to 15000 m to determine the relative

effects of operating variables [15]

The main objective of this work is carrying out energy

analysis for the different components of the turbo jet engine

[16] Consequently optimum performance including maximum

speci1047297c thrust and minimum speci1047297c fuel consumption are

obtained [17] This will be done through an analytical method

using Excel and a speci1047297ed software using the language of the

General Algebraic Modeling System (GAMS) for comparison

[1819]

2 Theoretical analysis

A schematic diagram of the turbojet engine and the

relevant T -s diagram are shown in Figures 1 and 2

21 Overall performance

The heating value of the fuel is H vfrac14 43100 kJkg The

thrust of turbojet engine is produced from summation of

momentum and pressure components

F frac14 m C 5 C aeth THORN thorn A5 P5 Paeth THORN eth1THORN

To get the speci1047297c thrust (F s) divide Eq (1) by mass 1047298ow

Figure 1 Turbojet engine Figure 2 T-s diagram

Nomenclature

A area (unit m 2)

a speed of sound (unit ms)

Alt altitude (unit m)

C a inlet air velocity (unit ms)

C 5 exit air velocity (unit ms)

C p constant pressure speci1047297c heat (unit kJ(kg∙K))

F thrust (unit N)

F s speci1047297c thrust (unit (N∙s)kg)

f ac actual fuel air ratio

f th theoretical fuel air ratio

H v heating value (unit kJkg)

h enthalpy (unit kJkg)

Ma Mach number

m mass 1047298ow rate (unit kgs)

ORL optimum running line

P pressure (unit bar)

P x pressure at some point x (unit bar)

R ideal gas constant (unit J(kg∙K))

r f optimum compressor pressure ratior p compressor pressure ratio

SFC speci1047297c fuel consumption (unit kg(N∙s))

T temperature (unit K)

T x temperature at some point x (unit K)

TIT turbine inlet temperature (unit K)

wc compressor work (unit kJkg)

wtc turbine work needed for driving the compressor

(unit kJkg)

Greek letters

γ ration of speci1047297c heats

η isentropic ef 1047297ciency

ρ 1047298uids density (unit kgm 3

)

Subscripts

a air

c compressor

cc combustion chamber

d diffuser

g gas

j nozzle

m mechanical

pr propulsive

t turbine

Optimization of gas turbines for sustainable turbojet propulsion 115

8172019 Jet Report


rate

F s frac14 C 5 C aeth THORN thorn A5=m

P5 Paeth THORN eth2THORN

Hence the speci1047297c fuel consumption related to the propul-

sive ef 1047297ciency of the turbojet engine is shown as

SFC frac14 f ac=F s eth3THORN

η pr frac14 2= 1 thorn C 5=C a

eth4THORN

Diffuser (a-1)

T 1 frac14 T a thorn C 2a=2C pa eth5THORN

P1=Pa

frac14 T 1s=T a

ethγ a=ethγ a 1THORNTHORNeth6THORN

ηd frac14 T 1s T aeth THORN= T 1 T aeth THORN eth7THORN

Hence

P1 frac14 Pa 1 thorn ηd C 2a=2C pT a ethγ a=ethγ a 1THORNTHORN

eth8THORN

Compressor (1 ndash 2)

P2=P1

frac14 T 2s=T 1


ηd frac14 T 2s T 1eth THORN= T 2 T 1eth THORN eth10THORN

Hence

T 2 frac14 T 1 thorn T 1=ηc

P2=P1

ethethγ a 1THORN=γ aTHORN 1

h i eth11THORN

Combustor (2 ndash 3)

From energy balance equation

eth1 thorn f THORNC pg T 3 298eth THORN thorn f H v thorn C pa 298ndashT 2eth THORN frac14 0 eth12THORN

f th frac14 C pg T 3 298eth THORN thorn C pa 298 T 2eth THORN

= H v thorn C pg 298 T 3eth THORN

eth13THORN

ηcc frac14 f th= f ac eth14THORN

P3 frac14 P2 1 ΔΡcc=P2 eth15THORN

Turbine (3 ndash

4)wtc frac14 wc=ηm eth16THORN

C pg T 3ndashT 4eth THORN frac14 C pa T 2ndashT 1eth THORN=ηm eth17THORN

T 4 frac14 T 3ndash C pa T 2ndashT 1eth THORN=ηmC pg

eth18THORN

From the isentropic relations

ηt frac14 T 3ndashT 4eth THORN= T 3 T 4seth THORN eth19THORN

Hence

T s4 frac14 T 3ndash T 3ndashT 4eth THORN=ηt eth20THORN

P4 frac14 P3 T s4=T 3 ethγ g=ethγ g 1THORNTHORN

eth21THORN

Nozzle (4 ndash

5)

T c frac14 T 4 2= γ g thorn 1

eth22THORN

Pc frac14 P4 1 1=η j

γ g 1

= γ g thorn 1 ethγ g=ethγ g 1THORNTHORN

eth23THORN

The nozzle is choking if (P4 Pa)4(P4 Pc)

Then

P5frac14Pc T 5frac14 T c

C 5 frac14 γ g RT 5 05

eth24THORN

ρ frac14 P5= RT 5eth THORN eth25THORN

Table 1 The range of operating conditions for the turbojet

engine

r p 9 11 13 DP 16

15

TIT K 1400 1500 1600 1700 1800

Ma 05 06 07 08 09

Alt m 6000 8000 1000 13000 15000

Yousef SH Najjar Ibrahim AI Balawneh116

8172019 Jet Report


A5=m

frac14 1= ρC 5eth THORN eth26THORN3 Discussion of results

The speci1047297c thrust (F s) and speci1047297c fuel consumption

(SFC ) are calculated at design point and other off-design

conditions and shown as in Table 1

Carrying out the variation of compressor pressure ratio

r p while keeping the other variables namely TIT Ma and

altitude the same at the design point results in Figure 3

The optimum r p for maximum speci1047297c thrust (F s) is 14 The

Figure 3 Relation of F s with SFC at design point but variable r p

Figure 4 Relation of F s with SFC at design point with variable TIT

Figure 6 Relation of F s with SFC at design point with variable

altitude

Figure 7 Performance carpet at Alt frac14 13000 m and Ma frac1408

Figure 8 Performance carpet at Alt frac14 8000 m and Ma frac1408Figure 5 Relation of F s with SFC at design point with variable Ma


8172019 Jet Report


in1047298ection at this point is expected to be due to the effect of

the relative increase of (compressorturbine) work ratio

Carrying out the variation of turbine inlet temperature

(TIT ) while keeping the other variables namely r p Ma and

altitude at the design point results in Figure 4 Increasing

TIT increases F s and SFC but this is limited of course by

the metallurgical limit of the turbine blades From sensitiv-

ity analysis reducing turbine inlet temperature TIT by 10from the design point the SFC decreases by 68 and F sby 67

Carrying out the variation of Ma while keeping the other

variables namely r p TIT and altitude the same as at the

design point results in Figure 5 Increasing of madecreases

the F s and increases SFC because the engine drag increases

with aircraft speed From sensitivity analysis reducing Ma

by 10 from the design point the SFC decreases by 146

and F s increases by 235

Carrying out the variation of altitude while keeping the

other variables namely r p TIT and Ma the same as at the

design point results in Figure 6 After 11500 m the F s and

SFC remain constant because ambient temperature

andspeed of sound remains constant

A carpet of performance is produced as shown inFigure 7 This depicts the relation between F s and SFC

over wide range of operating conditions including r p and

TIT while keeping Ma and altitude at design conditions

Figure 8 is drawn similarly but at Alt frac14 8000 m whereas

Figure 9 at Mafrac1406


Table 2 Relative effect of 10 reduction in operating variables

from design point on performance

Variable F s (N∙skg) SFC (kg(h∙N))

r p 00217 thorn134

TIT K 67 68

Ma thorn235 146

Alt m No effect No effect

Figure 10 Optimum values of (r f ) and (TIT ) that give maximum (F s)

and minimum (SFC ) at Alt frac1413000 m and Ma frac1408

Figure 11 The optimum running line (ORL ) superimposed on the

performance carpet

Table 3 Relative effect of 10 reduction in TIT on performance

along the ORL

Variable Effect

r f 1143

F s 121

SFC 46

Figure 12 Comparing points on the ORL using the analytical model

of this work with that from GAMS


8172019 Jet Report


Carrying out the sensitivity analysis it was possible to

calculate the relative effects of 10 drop of operating

variables from the design point on performance as depicted

in Table 2

4 Optimization

When considering the design of a turbojet the basic

thermodynamic variables at the disposal of the designer are

the TIT and r p which are used to get the optimum

performance of a turbojet Performance optimization is

intended to 1047297nd the maximum F s and minimum SFC of

the engine [20]

The method of optimization utilized here searches for the

optimum compressor pressure ratio r f at certain TIT for

which the turbojet engine has optimum performance that

gives maximum F s and minimum SFC

For each TIT there is r f that gives maximum F s hence

the optimum running line (ORL ) was formed over wide

range of operating conditions using the analytical model

with excel

A computer program called GAMS was used to solve the

optimization problem for comparison GAM was originally

developed to provide a high-level language for the compact

representation of large and complex models (Appendix A)

The optimum running points at different combinations of

operating conditions are plotted in Figure 10 The locus of

these points forms the optimum running line (ORL ) reco-

mmended for the engine to follow This line is super imp-

osed on the carpet of performance as shown in Figure 11

to show how the optimum performance is achieved over

wide range of operating conditionsCarrying out sensitivity analysis for the effect of TIT on

performance it was possible to obtain the corresponding

variation in r f F s and SFC as shown in Table 3

Its obvious from Figure 12 that there is difference in r f values between GAMS and the analytical model but in

some cases the values are very close The difference bet-

ween GAMS and the analytical method is due to the nesting

steps carried out by the GAMS leading to F s as function of

r p because the equation has one independent variable But

in the analytical method the problem is dealt with in

consecutive detailed steps using excel

5 Conclusions

a) Sensitivity analysis shows that reducing turbine inlet

temperature TIT of the turbojet engine by 10 results

in 68 increase in SFC and 67 in F s

b) On the other hand reducing the pressure ratio r p by

10 results in 134 increase in SFC and 0022

decrease in F s

c) After altitude of 11500 m there is no effect for

increasing altitude on F s and SFC This is due to the

ambient temperature and hence the speed of sound

which remaining constant after this altitude

d) Reducing Ma by 10 results in 146 decrease in SFC

and 235 increase in F s

e) The value of optimum pressure ratio r f for maximum

speci1047297c thrust increased as the turbine inlet tempera-

ture TIT increased A 10 decrease in TIT results in

1143 decrease in r f

f) After optimum r f the speci1047297c thrust decreases as r p

increases but the speci1047297c fuel consumption stilldecreases as r p increases

g) The optimum value of compressor pressure ratio r f at

1700 K is 14

Appendix A General Algebraic ModelingSystem (GAMS)

Systems approach

Planning management and design are a critical element of sustainable economic development and expansion In the

process of planning and design there is a need to critically

analyze the true economic costs bene1047297ts and environmental

consequences of projects A lack of this analysis can often

lead to a level of design quality which falls far short of

optimal with respect to the utilization of scarce economic

and natural resources and will not improve the ecological

balance of systems in general

Systems analysis can aid in identifying those likely

situations where a minimum investment of funds and

energies will produce maximum gains in terms of resource

allocations economic development and environmental wel-

fare Generally speaking systems analysis is the art andscience of disassembling complex phenomena into smaller

isolated more readily understood subsystems and analyz-

ing the interactions between the subsystems and between

the subsystems and the larger environment [21] The central

method used in water resource systems analysis is to couple

the descriptions of physical and socioeconomic systems

through the use of mathematical models

A system is a collection of components and their

interrelationships forming an entity (eg a riverbasin)

which is acted upon by external forces in1047298uences or inputs

(precipitation) and produces a speci1047297c effect or output

(stream 1047298ow) That is a system is a set of objects whichtransforms an input into an output the exact output

produced depending on certain system properties or para-

meters (eg soil types vegetation topography) This

transformation depends upon the parameters of the system

and the design policies imposed on it

Systems analysis involves the construction and linkage of

mathematical models of the physical and subsystems

associated with resource allocation systems The purpose

of constructing these models is to aid engineers planners

and decision makers in identifying and evaluating alter-

native designs and to determine which ones meet project

objectives in an ef 1047297cient manner


8172019 Jet Report


These mathematical models are able to predict a systems

response to different design alternatives and conditions The

models are a set of mathematical expressions (partial or

ordinary differential or algebraic equations) describing the

physical biological chemical and economic processes

which take place in the system Most systems models are

based on statements of basic conservation laws (mass

energy and momentum) but they can also be empiricalor statistical Systems analysis models are generally broken

down into two categories simulation models and optimiza-

tion models

Simulation and optimization models

Optimization models provide a means of reducing the

number of alternatives which need to be simulated in detail

ie screening them These models search the space of

possible design variable values and identify an optimal

design andor operating policy for a given system design

objective and set of constraints The sensitivity of the

optimal solution to changes in the model parameter scan

be readily determined and tradeoffs between several con-

1047298icting objectives can also be calculated with most optimi-

zation models These models are usually extensions of

simulation models and include as unknowns the design or

operating variables (decision variables) of each alternative

Model building process

In this procedure the model outputs are compared with

actual historical or measured outputs of the system and the

parameters are adjusted until the model predicted and the

measured values agree Then a model veri1047297cation exercise

is carried out in which an independent set of input data is

used in the model and the predicted results are compared

with measured outputs and if they are found to agree the

model is considered to be veri1047297ed and ready for use in

simulation or optimization

Book organization

Examples of optimization models from several technical

areas of interest are covered in Part 1 general equationssolving water resources management agricultural manage-

ment canal design power system design and management

heat transfer and 1047298uid 1047298ow

These models are presented for the purpose of introdu-

cing the reader to the possibilities of modeling these

systems using optimization techniques There are certainly

many additional application areas and techniques that could

be covered but the examples selected cover a wide enough

range to introduce the reader to the topic Part 2 of the book

covers many of the basics of the modeling language used in

this book That language is the General Algebraic Modeling

System (GAMS)

High-level modeling system for mathematical program-

ming problems [19] This section of the book is intended to

provide the reader with suf 1047297cient information to construct

simple models without having to read through the full

language documentation

By using GAMS it was found that the modeling

languages are more useful than the other types of modeling

packages such as LINGO [22] since these products do not allow the easy construction of general modeling structures

such as those needed for solving differential equations

References

[1] M Akyurt NJ Lamfon YSH Najjar MH Habeebullah

TY Alp Modeling of waste heat recovery by looped water-

in-steel heat pipes The International Journal of Heat and

Fluid Flow 16 (4) (1995) 263-27

[2] YSH Najjar M Akyurt Combined cycles with gas turbine

engines Journal of Heat Recovery Systems amp CHP 14 (2)

(1994) 93ndash103[3] YSH Najjar N Jubeh Comparison of performance of

compressed - air energy - storage plant (CAES) with

compressed - air storage with humidi1047297cation (CASH)

Proceedings of the Institution of Mechanical Engineers

(IMechE) 220 Part A Journal of Power and Energy 220

(2006) 581ndash588

[4] YSH Najjar Some performance characteristics of the gas

turbine combustor using heavy fuels Journal of the Institute

of Energy LV 425 (1982) 187ndash194

[5] YA Cengel MA Boles Thermodynamics an Engineering

Approach 7th ed Mc-Graw Hill 2007

[6] F Noori M Gorji A Kazemi H Nemati Thermodynamic

optimization of ideal turbojet with afterburner engines using

non-dominated sorting genetic algorithm II Aerospace Engi-

neering 224 (2010) 1285ndash1296

[7] NU Rahman JF Whidborne A numerical investigation

into the effect of engine bleed on performance of a single-

spool turbojet engine Aerospace Engineering 222 (2008)

939ndash949

[8] A Cavcar M Cavcar Impact of aircraft performance

differences on fuel consumption of aircraft in air traf 1047297c

management environment Aircraft Engineering and Aero-

space Technology 76 (2004) 502ndash515

[9] DP Bakalis AG Stamatis Data analysis and performance

model calibration of a small turbojet engine Aerospace

Engineering 1 (2011) 78ndash85

[10] A Wood P Pilidis A variable cycle jet engine for ASTOVLaircraft Aircraft Engineering and Aerospace Technology 69

(1997) 534ndash539

[11] UK Saha M Miltra SJ Menon NT Jhon SS Gajapathi

Preliminary design analysis of a lightweight combat aircraft

Aerospace Engineering 222 (2008) 507ndash513

[12] J Cooper L Dingle Engineeringan afterburner for a

miniature gas turbine engine Aircraft Engineering and

Aerospace Technology 77 (2005) 104ndash108

[13] J Yin P Pilidis KW Ramsden SD Probert Assessment

of variable-cycle propulsion systems for ASTOVL Aircraft

Engineering and Aerospace Technology 72 (2000) 537ndash544

[14] RM Denning NA Mitchell Trendsin military aircraft

propulsion Aerospace Engineering 203 (1989) 11ndash23


8172019 Jet Report


[15] SC Kaushika RV Siva SK Tyagib Energy and exergy

analyses of thermal power plants Review Renewable and

Sustainable Energy Reviews 15 (2011) 1857ndash1872

[16] YSH Najjar SF Al-Sharif Thermodynamic optimization

of turbofan cycle Aircraft Engineering and Aerospace

Technology 78 (2006) 467ndash480

[17] DS Pascovici S Sorato SO Ogaji P Pilidis Overview of

coupling noise prediction for turbofans engine and aircraft

performance Aerospace Engineering 222 (2008) 515ndash529

[18] A Zanj A Kalabkhani MA Abdous H Karimi Model-

ling simulation and optimization of a hot pressurization

system for a liquid propellant space engine and comparison

with experimental results Aerospace Engineering 224 (2010)

1141ndash1150

[19] A Brook D Kendrick A Meeraus R Raman GAMS a

User Guide GAMS Development Corporation Washington

DC 1998

[20] T Katra šnik F Trenc Innovative approach to air manage-

ment strategy for turbocharged diesel aircraft engines Aero-

space Engineering 1 (2011) 173ndash198

[21] CW Churchman The Systems Approach Dell Publishing

Co New York 1968

[22] L Schrage Optimization Modeling with LINGOrsquo Lindo

Systems 1999


8172019 Jet Report


Theoretical and practical engineering developments were

necessary for the design building and testing of an engine

with an afterburner [12] Other research works studied the

effects compressor pressure ratio on thrust and other perfor-

mance parameters [13] In military applications there were

special studies on the factors which determine the proper choice

of engine cycle for a combat aircraft to suit the requirements of the designed mission [14] Some researchers used energy and

exergy analyses with a turbojet engine over 1047298ight altitudes

ranging from sea level to 15000 m to determine the relative

effects of operating variables [15]

The main objective of this work is carrying out energy

analysis for the different components of the turbo jet engine

[16] Consequently optimum performance including maximum

speci1047297c thrust and minimum speci1047297c fuel consumption are

obtained [17] This will be done through an analytical method

using Excel and a speci1047297ed software using the language of the

General Algebraic Modeling System (GAMS) for comparison

[1819]

2 Theoretical analysis

A schematic diagram of the turbojet engine and the

relevant T -s diagram are shown in Figures 1 and 2

21 Overall performance

The heating value of the fuel is H vfrac14 43100 kJkg The

thrust of turbojet engine is produced from summation of

momentum and pressure components

F frac14 m C 5 C aeth THORN thorn A5 P5 Paeth THORN eth1THORN

To get the speci1047297c thrust (F s) divide Eq (1) by mass 1047298ow

Figure 1 Turbojet engine Figure 2 T-s diagram

Nomenclature

A area (unit m 2)

a speed of sound (unit ms)

Alt altitude (unit m)

C a inlet air velocity (unit ms)

C 5 exit air velocity (unit ms)

C p constant pressure speci1047297c heat (unit kJ(kg∙K))

F thrust (unit N)

F s speci1047297c thrust (unit (N∙s)kg)

f ac actual fuel air ratio

f th theoretical fuel air ratio

H v heating value (unit kJkg)

h enthalpy (unit kJkg)

Ma Mach number

m mass 1047298ow rate (unit kgs)

ORL optimum running line

P pressure (unit bar)

P x pressure at some point x (unit bar)

R ideal gas constant (unit J(kg∙K))

r f optimum compressor pressure ratior p compressor pressure ratio

SFC speci1047297c fuel consumption (unit kg(N∙s))

T temperature (unit K)

T x temperature at some point x (unit K)

TIT turbine inlet temperature (unit K)

wc compressor work (unit kJkg)

wtc turbine work needed for driving the compressor

(unit kJkg)

Greek letters

γ ration of speci1047297c heats

η isentropic ef 1047297ciency

ρ 1047298uids density (unit kgm 3

)

Subscripts

a air

c compressor

cc combustion chamber

d diffuser

g gas

j nozzle

m mechanical

pr propulsive

t turbine


8172019 Jet Report


rate







eth4THORN

Diffuser (a-1)


P1=Pa

frac14 T 1s=T a



Hence


eth8THORN


P2=P1

frac14 T 2s=T 1



Hence


P2=P1


h i eth11THORN






eth13THORN



Turbine (3 ndash




eth18THORN



Hence



eth21THORN

Nozzle (4 ndash

5)


eth22THORN


γ g 1


eth23THORN


Then



eth24THORN



engine

r p 9 11 13 DP 16

15

TIT K 1400 1500 1600 1700 1800

Ma 05 06 07 08 09

Alt m 6000 8000 1000 13000 15000


8172019 Jet Report


A5=m












altitude




8172019 Jet Report































r p 00217 thorn134

TIT K 67 68

Ma thorn235 146





performance carpet


along the ORL

Variable Effect

r f 1143

F s 121

SFC 46




8172019 Jet Report





in Table 2

4 Optimization






the engine [20]








with excel





















5 Conclusions






decrease in F s














1700 K is 14


Systems approach





































8172019 Jet Report











tion models
























Book organization













System (GAMS)










References




Fluid Flow 16 (4) (1995) 263-27








(2006) 581ndash588









neering 224 (2010) 1285ndash1296




939ndash949









(1997) 534ndash539













8172019 Jet Report















1141ndash1150



DC 1998





Co New York 1968


Systems 1999


8172019 Jet Report


rate







eth4THORN

Diffuser (a-1)


P1=Pa

frac14 T 1s=T a



Hence


eth8THORN


P2=P1

frac14 T 2s=T 1



Hence


P2=P1


h i eth11THORN






eth13THORN



Turbine (3 ndash




eth18THORN



Hence



eth21THORN

Nozzle (4 ndash

5)


eth22THORN


γ g 1


eth23THORN


Then



eth24THORN



engine

r p 9 11 13 DP 16

15

TIT K 1400 1500 1600 1700 1800

Ma 05 06 07 08 09

Alt m 6000 8000 1000 13000 15000


8172019 Jet Report


A5=m












altitude




8172019 Jet Report































r p 00217 thorn134

TIT K 67 68

Ma thorn235 146





performance carpet


along the ORL

Variable Effect

r f 1143

F s 121

SFC 46




8172019 Jet Report





in Table 2

4 Optimization






the engine [20]








with excel





















5 Conclusions






decrease in F s














1700 K is 14


Systems approach





































8172019 Jet Report











tion models
























Book organization













System (GAMS)










References




Fluid Flow 16 (4) (1995) 263-27








(2006) 581ndash588









neering 224 (2010) 1285ndash1296




939ndash949









(1997) 534ndash539













8172019 Jet Report















1141ndash1150



DC 1998





Co New York 1968


Systems 1999


8172019 Jet Report


A5=m












altitude




8172019 Jet Report































r p 00217 thorn134

TIT K 67 68

Ma thorn235 146





performance carpet


along the ORL

Variable Effect

r f 1143

F s 121

SFC 46




8172019 Jet Report





in Table 2

4 Optimization






the engine [20]








with excel





















5 Conclusions






decrease in F s














1700 K is 14


Systems approach





































8172019 Jet Report











tion models
























Book organization













System (GAMS)










References




Fluid Flow 16 (4) (1995) 263-27








(2006) 581ndash588









neering 224 (2010) 1285ndash1296




939ndash949









(1997) 534ndash539













8172019 Jet Report















1141ndash1150



DC 1998





Co New York 1968


Systems 1999


8172019 Jet Report































r p 00217 thorn134

TIT K 67 68

Ma thorn235 146





performance carpet


along the ORL

Variable Effect

r f 1143

F s 121

SFC 46




8172019 Jet Report





in Table 2

4 Optimization






the engine [20]








with excel





















5 Conclusions






decrease in F s














1700 K is 14


Systems approach





































8172019 Jet Report











tion models
























Book organization













System (GAMS)










References




Fluid Flow 16 (4) (1995) 263-27








(2006) 581ndash588









neering 224 (2010) 1285ndash1296




939ndash949









(1997) 534ndash539













8172019 Jet Report















1141ndash1150



DC 1998





Co New York 1968


Systems 1999


8172019 Jet Report





in Table 2

4 Optimization






the engine [20]








with excel





















5 Conclusions






decrease in F s














1700 K is 14


Systems approach





































8172019 Jet Report











tion models
























Book organization













System (GAMS)










References




Fluid Flow 16 (4) (1995) 263-27








(2006) 581ndash588









neering 224 (2010) 1285ndash1296




939ndash949









(1997) 534ndash539













8172019 Jet Report















1141ndash1150



DC 1998





Co New York 1968


Systems 1999


8172019 Jet Report











tion models
























Book organization













System (GAMS)










References




Fluid Flow 16 (4) (1995) 263-27








(2006) 581ndash588









neering 224 (2010) 1285ndash1296




939ndash949









(1997) 534ndash539













8172019 Jet Report















1141ndash1150



DC 1998





Co New York 1968


Systems 1999


8172019 Jet Report















1141ndash1150



DC 1998





Co New York 1968


Systems 1999


jet report

Documents