UserManual_ITB

7/29/2019 UserManual_ITB

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A Complete Parametric Cycle Analysis for Ideal

TurboFan Engine with Interstage Turbine Burner

S.L. Yang, Y.K. Siow, K.H. Liew, and E. UripMechanical Engineering Engineering Mechanics Department

Michigan Technological University

1400 Townsend Drive

Houghton, MI 49931-1295

906/487-2624

906/487-2822 (Fax)

[email protected]

C. J. Marek

Combustion Technology Branch, MS 5-10

NASA Glenn Research Center

21000 Brookpark RoadCleveland, OH 44135

216/433-3584

216/433-3000 (Fax)

[email protected]


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October 23, 2002

ABSTRACT

Today modern aircraft is based on air-breathing jet propulsion systems, which uses

moving fluids as substances to transform energy carried by the fluids into output power.

Throughout aero-vehicle evolution, improvements have been made on the engine

efficiency and pollutants reduction. This parametric study focuses on a complete

parametric cycle analysis of a turbofan engine with an Interstage Turbine Burner (ITB).

The major advantages associated with the addition of an ITB are the improvement of

thermal efficiency and reduction in NOx emission. Lower temperature peaks in the main

combustor results in lower thermal NOx emission and a lower amount of cooling air

required.

The objective of this study is to make use of the engine component parameters, namely

compressor or turbine polytropic efficiency, burner efficiency, pressure drop across the

engine components, design limitation (burner exit temperature), and flight environment

as inputs to calculate engine performance, specific thrust and thrust specific fuel

consumption. This relation can provide guidance in identifying the characteristics of the

engines components. The knowledge can subsequently be used to develop and optimize

the performance and integration of each component.

In this study, each component in the engine is treated individually. The first-law energy

equation, second-law, and conservation of momentum are then applied.

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Visual Basic program, Excel macrocode, and Excel neuron code are used to facilitate

Excel software to plot engine performance versus engine design parameters. This

program computes and plots the data sequentially without forcing users to open other

types of plotting programs. A users manual on how to use the program is also included

in this report.

ACKNOWLEDGEMENTS

This project on evaluating the improvement in performance of an aircraft gas turbine by

adding an Interstage turbine burner (ITB) is really challenging and would have not been

accomplished without the technical assistance and suggestion given from our graduate

advisor, Dr. S.L. (Jason) Yang.

Our sincere gratitude next goes to Dr. Cecil John Marek, for giving us this opportunity to

employ our limited knowledge in engineering mechanics in solving such an interesting

and practical problem related to gas turbine propulsion like this.

The authors would like to thank Dr. Paul Penko for being the grant monitor on this

project. Appreciation also goes to Dr. Scott John at NASA Glenn Research Center for

providing us the listing data for a two-spool high bypass turbofan engine with and

without ITB, and suggesting some valuable improvement that can be done to the code.

Special thank is due to Mr. Jeffrey R. Herbon from Williams International for carefully

reviewing and test-driving the code. Based on his experience and expertise in cycle

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analysis, he has given us many valuable suggestions on how the program could be

enhanced for increased usefulness in the future.

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TABLE OF CONTENTS

ABSTRACT .... ii

ACKNOWLEDGEMENT ... iii

LIST OF FIGURES ... v

LIST OF TABLES . vi

NOMENCLATURE ... vii

1. INTRODUCTION ............. 1

2. ENGINE PERFORMANCE PARAMETERS. 3

3. TURBOFAN with ITB CYCLE ANALYSIS.. 11

4. SUMMARY of EQUATIONS... 20

5. USER MANUAL ... 24

6. DATA VALIDATION... 32

7. RESULTS AND DISCUSSIONS.. 35

APPENDIX

A1 EXCEL MACRO VISUAL BASIC CODE .. 44

A2 FORTRAN 77 CODE ..... 52

REFERENCES.. 78

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LIST OF FIGURES

Figure 1.1 A Gas Generator propulsion system.. 1

Figure 1.2 A TurboJet Engine. 1

Figure 1.3 A TurboFan Engine... 2

Figure 3.1 Turbofan with Interstage Turbine Burner 11

Figure 5.1 Excel Input sheet screenshot.... 25

Figure 6.1 Turbofan Engine with ITB:specific thrustvs flight Mach number

(both Fortran77 and Excel) .. 32

Figure 6.2 Turbofan Engine with ITB:specific thrustvs flight Mach number(both Fortran77 and Excel) .. 33

Figure 6.3 Turbofan Engine with ITB:specific thrustvs flight Mach number

(both Fortran77 and Excel) ...... 33

Figure 6.4 Turbofan Engine ITB:specific thrustvs flight Mach number

(both Fortran77 and Excel) ...... 34

Figure 7.1 Turbofan Engine:specific thrustvs flight Mach number. 36

Figure 7.2 Turbofan Engine: thrust specific fuel consumption vs flight Mach

number . 37

Figure 7.3 Turbofan Engine:specific thrustvs compressor pressure ratio .. 38

Figure 7.4 Turbofan Engine: thrust specific fuel consumption vs compressor pressure

ratio ..... 38

Figure 7.5 Turbofan Engine:fuel/air ratio vs flight Mach number ..... 39

Figure 7.6 Turbofan Engine:specific thrustvs fan pressure ratio ... 40

Figure 7.7 Turbofan Engine: thrust specific fuel consumption vs fan pressure

ratio .... 40

Figure 7.8 Turbofan Engine:specific thrustvs bypass ratio .... 41

Figure 7.9 Turbofan Engine: thrust specific fuel consumption vs bypass pressure

ratio .... 42

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LIST OF TABLES

Table 7.1 Input Data for Engine Parameters (SI unit) ... 35

Table 7.2 Input Data for Option 1 (SI unit) ... 36




Table A.1 Description of variables in MS Excel Macro Visual Basic code ..44

Table B.1 Description of Input Variables in input file (English and SI unit).. 55

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NOMENCLATURE

A cross-sectional areaa sound speed

CP specific heat at constant pressure

D drag force

e polytropic efficiency

F force uninstalled thrust

f fuel/air ratio

gc Newtons constant

h enthalpy

hPR low heating value of fuel

M mach number

m

mass flow rate

P pressure

Pt total pressure

Q

rate of thermal energy released or absorbed

R universal gas constant

S uninstalled thrust specific fuel consumption

T temperature or installed thrust

TSFC installed specific fuel consumption

Tt total temperature

V absolute velocity

W

power

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bypass ratio

ratio of specific heats,v

p

c

c

m mechanical Efficiency

O overall Efficiency

P propulsive Efficiency

T thermal Efficiency

ratio of totalpressure

r (exception) ratio between total pressure and static pressure due to the

ram effect,P

Pt

ratio of total temperature

r (exception) ratio between total temperature and static temperature due

to the ram effect, T

Tt

ratio between total enthalpy and enthalpy at ambient condition

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SUBSCRIPTS

b main burner or properties between main burner exit and ITB

c properties between upstream and main burner or engine core

d diffuser

e exit

f fan

fn fan-nozzle

HPC high pressure compressor

HPT high pressure turbine

ITB interstage turbine combustors

LPC low pressure compressor

LPT low pressure turbine

O inlet

n nozzle

r ram

t properties between ITB exit and downstream or total/stagnation

values of properties (i.e. temperature, pressure or enthalpy)

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1. Introduction

This program is designed to give a complete parametric cycle analysis of an ideal Turbo

Fan air-breathing propulsion system. In most common air-breathing propulsion engines,

the heart of a gas turbine is the gas generator. It consists of three major components

namely, compressor, combustor, and turbine as shown schematically in Figure 1.1.

Figure 1.1 A Gas Generator Propulsion System

The idea behind a gas generator is to convert intake air mixed with fuel into high

temperature and high pressure gas. Depending on the applications of the gas turbine, the

energy provided is extracted and used for different applications (turbojet, turbofan, turbo-

shaft, turboprop, and ramjet) through different mechanisms. A turbojet engine can be

constructed by adding an inlet and a nozzle as shown in Figure 1.2.

Figure 1.2 A Turbo Jet Engine

The nozzle converts the internal energy of the hot gas into kinetic energy or thrust. The

work extracted by the turbine is used to drive the compressor. In the case of a turbofan,

turboprop, and turbo-shaft engine, the work from the turbine is required to drive a shaft

for the turbo-shaft, a fan for the turbofan, and a propeller for the turboprop in addition todriving the compressor. The ramjet engine consists of an inlet, a combustor, with a nozzle

at the exit. It does not require the compressor because the inlet already uses a ram air-

compressing mechanism such that intake air has sufficient kinetic energy to increase its

pressure.

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The main objective of this analysis is to determine the relationships between engine

performance (primarily specific thrust m

F, thrust specific fuel consumption) to design

parameters (compressor pressure ratio, fan pressure ratio, bypass ratio, etc), to design

constraints (burner exit temperature, compressor exit pressure, etc), and to flight

environment (Mach number, ambient temperature, ambient pressure, etc).

Figure 1.3 A Turbo Fan Engine

2. Aircraft Engine Performance Parameters

Thrust

Thrust is the force used to sustain the flight (thrust = drag), accelerated flight (thrust >

drag), deceleration (thrust < drag). Using Figure 1.3 for the control volume, we can apply

a momentum balance to the control volume. Uninstalled thrustFof a jet engine (single

inlet and single exhaust) is given by

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)( ) APP

g

VmVmmeoe

c

oe ofueloF +

+

=

(2.1)

where mm

fuelo

..

, are mass flow rates of air and fuel respectively

VV eo , are velocities at inlet and exit respectively

PP eo , are pressure at inlet and exit respectively

For the ideal case, the hot gas is expanded to the ambient pressure which gives P e = Po.

Equation (2.1) then becomes

)g

VmVmm

c

oe ofueloF

+

= (2.2)

The installed thrustTis given by

DDFT nozzleinlet = (2.3)

whereDinletandDnozzle are the drag force from the inlet and the nozzle.

Specific Fuel Consumptions

The specific fuel consumption is the rate of fuel use by the propulsion system per unit of

thrust produced. The installed specific fuel consumptions, TSFC, and the uninstalled

specific fuel consumptions, S, are given by

T

mTSFC fuel

= (2.4)

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F

mS fuel

= (2.5)

Efficiency of an Engine

Some of the following parameters will be used widely in this program namely, thermal

efficiency, propulsive efficiency, and overall efficiency

The thermal efficiency characterizes the net energy output extracted (shaft work) from

the engine divided by the available thermal energy (fuel).

Q

W

in

out

T

= (2.6)

where,

=

=

=

hmreleasedenergythermalofrateQ

engineofoutpowernetW

efficiencythermal

PR

out

T

fin

The propulsive efficiency defines the ratio between the engine power output and the

power being used to run the aircraft.

W

VT

out

P =0 (2.7)

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where,

engineofoutpowernetW

aircraftofvelocityV

systempropulsionofthrustT

engineofefficiencypropulsive

out

P

==

=

=

0

An overall performance of a propulsion system is given by the combination between

thermal and propulsive efficiencies.

TPO

= (2.8)

where,

efficiencyoverallO

=

Notations

Some useful quantity notations for compressible flow will be used in this report namely,

stagnation temperature, stagnation pressure, and Mach number.

Stagnation temperature or total temperature Tt is defined as the temperature obtained

when steadily flowing fluid is brought to rest adiabatically without extraction of work.

Applying the first law of thermodynamic to a calorically perfect gas gives:

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2

V+h=h

2

t

(2.9)

where,

h = static enthalpy

ht = enthalpy at stagnation condition

V = velocity

With the assumptions of constant specific heat coefficient, the above equation can be

written as:

C2V

TP

2

t+T=

2

1+1T= MT

2

t(2.10)

where,

heatsspecificofratio

numberMachMetemperaturstaticT

etemperaturstagnationTt

==

=

=

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Stagnation pressure ortotal pressurePt is defined as the pressure reached when a steady

flowing fluid is brought to rest adiabatically and reversibly. Using the isentropic relation,

the total pressure is given by

M2

1+1P 2P=

1

t

(2.11)

The ratio of total temperatures and the ratio of total pressure across a component is

denoted by the subscript: dfor diffuser,LPCfor low pressure compressor,HPCfor high

pressure compressor, b for main burner, ITB for inter-stage turbine burner, LPTfor low

pressure turbine,HPTfor high pressure turbine, n for nozzle, andffor fan.

For example:

diffuserenteringpressuretotal

diffuserleavingpressuretotald =

diffuserenteringetemperaturtotal

diffuserleavingetemperaturtotald =


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Exceptions

For the free stream, ram, we define ras aratio of total temperature/static temperature

and ras a ratio of total pressure/static pressure.

MTT

021

+1==2

0

0t

r

(2.12)

( )

M2

1+1

PP

02

==

1

0

0t

r

(2.13)

A ratio between total enthalpy of the burner exit and ambient enthalpy, denoted by ,

is defined such that it will be one of the input parameters.

( )TCTC

p

tp

=ambientfor,0

exitburner

b

(2.14)

( )TCTC

p

tp

ambientfor

exitburnerstageInter

ITB

,0

= (2.15)


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Component Performance

In this analysis it is acceptable to assume that the working fluid in the engine can be

idealized as a perfect gas. Properties of an ideal gas strongly depend on the temperature.

This cycle allows fluid properties variation across the engine which assumes constant

fluid properties from the main burner entrance upstream (Cpc, c), from ITB entrance to

the main burner exit (Cpb, b), and from ITB exit downstream (Cpt, t).

Inlet and Diffuser

Pressure losses occur due to the friction with the inlet wall. The total pressure ratio, d, is

always less than 1.

In supersonic flight, the pressure losses cause shock waves which produce greater

pressure losses. The inlet total pressure is defined as the product of the ram pressure ratio

and the diffuser pressure ratio. Therefore the portion of the pressure loss due to the shock

waves and wall friction is defined by:

rdd max= (2.16)

From the Military Specification 5008B (Ref. 2), the following relation is obtained:

( )

+


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T

T

C

C t

pc

pt

ITB

0

6= (4.11)

HPCeHPCcc

HPC

1= (4.12)

LPCeLPCcc

LPC

1= (4.13)

( ) ( )

f

efccf

1= (4.14)

LPCHPCc = (4.15)

cr

tb

T

T

0

4= (4.16)

1

1

=

HPCHPC

HPCeHPC

(4.17)

1

1

=

LPC

LPC

LPCeLPC

(4.18)

1

1

=

f

ffe

f (4.19)

TCh

f

pc

bPRbB

brc

b

0

=

(4.20)

( )

HPTmbHPC

pc

pb

b

HPCHPT

C

Cf +

+=1

11

(4.21)

[ ]f

TCh

CC

C

C

fb

pb

ITBPRITBITB

pb

pc

ITB

pb

pc

HPTbcr

ITB+

=

1

0

(4.22)

fffITBb

+= (4.23)

HPTbcr

tITB

T

T

0

6= (4.24)


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ITBHPTbHPCLPCt

t

T

T =2

6(4.25)

)

( )

LPTm

t

t

pc

pt

fLPC

LPT

TT

CCf +

++=

2

61

111

(4.26)

HPTeHPTtt

HPT

1= (4.27)

LPTeLPTtt

LPT

1= (4.28)

HPTeHPT

HPT

HPT 11

1

= (4.29)

LPTeLPT

LPT

LPT 11

1

= (4.30)

nLPTITBHPTbHPCLPCdrt

P

P

P

P

10

0

10

10 = (4.31)

LPTITBHPTbcr

t

T

T=

0

10(4.32)

( )

==

PP

TT

TT

TT

T

T

ttt

t

t

t

10

101

010

10

10

0

10

0

10

(4.33)

( )

=

11

21

10

10

10

tt

P

PM

t

t

(4.34)

TR

TRM

a

V

cc

tt

0

10

10

0

10

= (4.35)

fnfdrt

P

P

P

P

19

0

19

19 = (4.36)

( )

=

11

21

19

19

19

cc

P

PM

t

c

(4.37)


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frt

T

T =0

19(4.38)

( ) cc

PP

TT

TT

TT

T

T

t

t

t

t

1

19

19

019

19

19

0

19

0

19

== (4.39)

MT

T

a

Ma

a

V19

0

19

0

1919

0

19 == (4.40)

( ) ( )

+++=

cc

t

c

c

P

P

aV

TT

R

RfM

a

Vf

g

a

m

F

c

1111

10

0

0

10

0

10

0

0

100(4.41)

+=

cc

f

f PP

aVT

T

MaV

ga

m

F 190

0

19

0

19

0

0

190

1

(4.42)

)1(

+

+

=

f

f

c

c

m

F

m

F

m

F (4.43)

( )

+

+

=

0

1

m

FS

ffITBb

(4.44)


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5. Users Manual

The excel program is written in combination between spreadsheet neuron cells, Visual

Basic, and macro code. These three combinations provide user-friendly software such

that compilation and preprocessing are no longer necessary. The user obtains result plots

right a way just by clicking some simple buttons.

The program is mainly comprised of six sheets namely CoverPage, Instruction, Input,

plot sheet, data sheet, and Otape&Test.

CoverPage sheet

The CoverPage sheet contains the authors of this program. Any questions regarding the

program can be addressed to us through email or phone.

Instruction sheet

First time users are strongly recommended to read this sheet before running the program.

Since there are always possibilities of getting error computations such as division by

zero, square root of a negative quantity, or over floating under floating number, the

program is written such that it will not crash if those errors are encountered during the

computation. It will instead tell the user where the computation encounters those errors.

In this sheet, you will find details of how to run the program and how to fix a problem if

something goes wrong.

This sheet also explains several assumptions made in the equations so that the users are

aware of some cases in the equations that have been idealized to simplify the problems.


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Figure 5.1 Excel Input Sheet Screenshot

Inputsheet

This sheet is where most of the inputs are specified. The program will check input value

in this sheet to make sure that all of the inputs are specified. It will tell the user if there

are inputs that are not specified. There are three Combo Box in the Inputsheet (Combo

Box is a list box that displays a list of values and lets the users select one of the values in

the list) namelyITB, Units, and Choose a Plotas shown in Figure 5.1. You need first to

specify the value in combo box ITB and combo box Units before moving on to combo

box Choose a Plot. Combo Box Units lets you specify the input and output unit system.

Currently, the program can handle only two units systems, which are English or SI.

Combo Box ITB lets you turn ON or OFF the Interstage Burner (ITB) feature. This

feature provides a flexibility to choose two types of engine and they are engine with ITB

- ON and engine with ITB - OFF. With this feature, you will be able to see how much

additional engine performance you can get with ITB-ON or with ITB-OFF. Note that the

equations used for ITB-OFF are not the same as the equations from the reference book,

Elements of Gas Turbine Propulsion. This is because the cycle analysis in this program is


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based on two shafts engine, and the one in the reference book is based on one shaft

engine.

When ITB-OFF is chosen, the program will execute as if there is no ITB added to the

Turbofan engine. Accordingly, the following variables will be changed internally and

automatically:

1. Cpt = Cpc

2. t = c

3. fitb = 0

4. itb = 1.0

5. itb = 1.0

Once all the inputs values are specified and combo box values on both ITB and Units are

specified, you can specify a value in combo box Choose a Plot. This combo box provides

several option lists to choose from, and they are:

1. Specific Thrust and TSFC Vs Compressor Pressure Ratio

2. Specific Thrust Vs Flight Condition Mach Number

3. TSFC Vs Flight Condition Mach Number

4. Specific Thrust Vs Fan Pressure Ratio

5. TSFC Vs Fan Pressure Ratio

6. Specific Thrust Vs ByPass Ratio

7. TSFC Vs ByPass Ratio

Once you select one of them, you will be directed to a new sheet. Basically once the

value of the combo box changed, it will execute a certain macro code. The macro code

associated with this combo box will open hidden plot sheets and hidden data sheets

depending on the selection you made.


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The following discussion describes the instruction of how to run the program for each

different option.

Specific Thrust and TSFC Vs Compressor Pressure Ratio

When this option is chosen, the program opens four sheets namely ST_VS_PIc,

SF_VS_PIc, DataSTPIc, and DataSFPIc. You will be directed from Input sheet to

ST_VS_PIc sheet. ST_VS_PIc plots specific thrust and fuel-air mass fraction versus

compressor pressure ratio, and SF_VS_PIc plots thrust fuel specific consumptionversus

compressor pressure ratio.

ST_VS_PIc

You expect to see result profiles similar to Figure 7-13a1 and Figure 7-13b1. You need to

complete all the inputs parameters indicated in green cells of the Input sheet and

ST_VS_PIc sheet. Click the combo box to select number of plots for different s,

bypass ratio. New input parameters for different bypass ratio will be created indicated in

green cells. Once all the green cells are filled, you will need to specify the relation

between high total pressure compressor and low total pressure compressor ratios. To do

this you need to click on the Enter Relation. Once the relation between the two

compressors has been established, you need to click Generate to generate a table forcompressor pressure ratio. At this point you are ready to run the program and generate the

plots, simply by clicking Calculate button. Data computed will be stored in the

DataSTPIc sheet.

SF_VS_PIc

You expect to see results profiles similar to Figure 7-13c1. Most of the inputs are taken

from the Input sheet and ST_VS_PIc sheet except for the bypass ratio. You need to

specify number of bypass ratio you want to plot, then you can click Calculate to perform

computation and to plot the results. Data computed will be stored in the DataSFPIc sheet.


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Specific Thrust Vs Flight Condition Mach Number or TSFC Vs Flight Condition Mach

Number

When you choose this option, the program closes theplot sheets and data sheets from the

previous use and opens one plot sheet and one data sheet, ST_VS_Mo andDataSTMo or

SF_VS_Mo andDataSFMo. You will then be directed from Inputsheet to ST_VS_Mo or

SF_VS_Mo. This sheet is used to plot specific thrustorthrust specific fuel consumption

versus flight condition Mach numberwith different bypass ratio.

ST_VS_Mo or SF_VS_Mo

You expect to see result profiles similar to Figure 7-14a1 or Figure 7-14b1. You need to

complete all the input parameters indicate in the green cells of this sheet. Then you can

clickCalculate to run the program and plot the results. Data computed associated with

this sheet will be stored in theDataSTMo sheet.

Specific Thrust Vs Fan Pressure Ratio or TSFC Vs Fan Pressure Ratio

Similar to Flight Condition Mach Number, this option opens ST_VS_PIfand DataSTPIf

orSF_VS_PIfand DataSTPIf. It plots specific thrustorthrust specific fuel consumption

vs fan pressure ratio with different bypass ratio. The steps to run the program in this

sheet are the same from option two or three of the Choose a Plotcombo box.

Specific Thrust Vs ByPass Ratio or TSFC Vs ByPass Ratio

This option opens ST_VS_Alp and DataSTAlp or SF_VS_Alp and DataSFAlp. It plots

specific thrustorthrust specific fuel consumption vs bypass ratio with different fan total

pressure ratio, f. The steps to run the program in this sheet are the same from option two

or three of the Choose a Plotcombo box.


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In summary you need to do the followings to run the program:

1. Go to theInputsheet

2. Specify the Unitsystem (SI or English)

3. Specify the ITB switch. Is the computation for engine with ITB-ON or for

engine with ITB-OFF?

4. Enter all the input parameters indicated in green cells (do not modify or

change the value indicated in cyan).

5. Specify Choose a Plot. You will be directed to a new sheet depending on the

selection.

If you select to engine performance (Specific Thrust and TSFC) Vs Compressor Pressure

Ratio, do the followings:

ST_VS_PIc:

a. Specify number of bypass ratio (new green cells will be created).

b. ClickEnter Relation (Enter relation).

c. Specify all input parameters indicated in green.

d. Click Generate to generate compressor total pressure ratio.

e. Click Calculate to compute and plot the results.

f. Repeat the above steps for different input parameters. If you want to

change the input parameters in the Inputsheet, you need to go to the

Inputsheet.

SF_VS_PIc:


b. Specify all input parameters indicated in green.c. Click Calculate.

d. Repeat the above steps for different bypass ratio. If you want to

change the input parameters in theInputsheet or in the ST_VS_PIc

sheet, you need to go back to one of those sheets and change the input

parameters.


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ST_VS_Mo, SF_VS_Mo, ST_VS_PIf, and SF_VS_PIf:


b. Specify all input parameters indicated in green.

c. Click Calculate.

d. Repeat the above steps for different input parameters. If you want to

change the input parameters in theInputsheet, you need to go to the

Inputsheet.

ST_VS_Alp and SF_VS_Alp:

a. Specify number of fan total pressure ratio (new green cells will be

created).

b. Specify all input parameters indicated in green.

c. Click Calculate.

d. Repeat the above steps for different input parameters. If you want to

change the input parameters in theInputsheet, you need to go to the

Inputsheet.

Discussions

The last sheet in the program is the Otape&Test; this is where the user can check a single

quantity namely Specific ThrustorThrust Specific Fuel Consumption. Most of the input

parameters are from theInputsheet; additional inputs are inputs parameters that you see

in the plot sheets. By clicking the Test, you will obtain Specific Thrust and Thrust

Specific Fuel Consumption stored in cyan cells.

This program has been debugged several times. Therefore whenever you encounter

computation errors due to either zero division or square root of a negative quantity, you

will be notified by a pop up window indicating where the computation problem is. It will

indicate which equation that the computational error is encountered. If you have any


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comments or bug problems you encounter in the program, you can report them to us for

further improvement. Detail about the contact number can be found in the CoverPage

sheet of the program.

It is also predicted that the plotting macro can encounter some problems in the future if

the users are not fully understand the program. Therefore I have set up a way how to fix

the problem. In case the plot starts giving problem, you need to do the followings (apply

to all plot sheets: ST_VS_PIc, SF_VS_PIc, ST_VS_PIf, SF_VS_PIf, ST_VS_Mo,

SF_VS_Mo, ST_VS_Alp, and SF_VS_Alpp):

a. Go to theplotsheet (e. ST_VS_Mo)

b. Go to cell D5

c. Note that you will not be able to click on that cell because it is lying on the

back of the plot chart. You may want to use cursor button from your

keyboard.

d. In that cell it reads SUCCESS. Change the value to any other type of

character, FAIL for example.

e. Clear the series in the chart plot by clicking right mouse button on the chart

plot.

f. Choose Source Data

g. Select Series and remove all the series. For the case ST_VS_PIc, you need to

clear the series on both charts.

Users are not expected to understand macro code in the program. However the part that

takes care the computation can be found in Module1 Sub Itb( ). In order to open it, you

need to open Excel Visual Basic by pressing Alt + F11. Any modification can be made in

subroutine Itb ( ). Do not add new variables into the program!


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6. Data Validation

Since there is no experimental data for this application, a Fortran 77 code is written for

the comparison between results computed by Excel and Fortran 77. All the equations

used are the same in both codes and can be found in section 4 of Summary of equations.

Under the same turbofan engine operating conditions with ITB-ON, specific thrust (i.e.

m

F, SI unit:

skg

N

/) is computed using both codes and plotted versus various design

parameters, namely flight Mach number (M0), compressor pressure ratio (c), fan

pressure ratio (f), and bypass ratio (). All the plots are in Tecplot 9.0 format as shownbelow.

Figure 6.1 Turbofan engine with ITB: Specific thrustvs flight Mach number


43/87

Figure 6.2 Turbofan engine with ITB: Specific thrustvs compressor pressure

ratio

Figure 6.3 Turbofan engine with ITB: Specific thrustvs fan pressure ratio


44/87

Figure 6.4 Turbofan engine with ITB: Specific thrustvs bypass ratio


45/87

7. RESULTS AND DISCUSSIONS

Using data provided in eng_itb.dat(a sample listing data file for a two-spool high bypass

turbofan provided by Scott Jones, currently at Propulsion Systems Analysis Office,

NASA Glenn Research Center), results at different operating conditions are plotted using

Tecplot 9.0 and shown as below.

Table 7.2 - The input data for Option 1:

Table 7.1 Input data for Engine parameters (SI unit)

Pressure drop ratioengine-core P0/P10 = 0.9 T0 = 216.6667K

engine - fan P0/P19 = 0.9

Total pressure ratio

Maximum diffuser total pressure ratio d max = 0.99 Properties of air and fuel

main burner total pressure ratio b = 0.96 Specific heat at constant pressure

ITB - burner total pressure ratio ITB = 0.96 region 0 --> 3 Cpc = 1.000645KJ/Kg-K

engine nozzle total pressure ratio n = 1.333 region 4 --> 5 Cpb = 1.159743KJ/Kg-K

fan nozzle total pressure ratio fn = 1.274 region 6 -->10 Cpt= 1.147183KJ/Kg-K

Polytropic efficiency Ratio of specific heat

eHPC = 0.9066 region 0 --> 3 c = 1.39999

eLPC = 0.9036 region 4 --> 5 b = 1.27284

eHPT = 0.9029 region 6 -->10 t= 1.27882

eLPT = 0.9174 Low heating value of fuelef = 0.8961 Burner hPR-b = 7917.12KJ/Kg

Burner efficiency ITB hPR-ITB = 7917.12KJ/Kgb = 0.999

ITB = 0.999

Turbine mechanical efficiencym-HPT = 0.92

m-LPT = 0.93

Burner exit temperature

main-burner Tt4 = 1785.594KITB - burner Tt6 = 1563.844K


46/87

Figure 7.1 - Specific thrust vs flight M0

Figure 7.2 - TSFC vs flight M0

Mo = 0 To 3 1 = 0.5 Mo = 0.1 2 = 2

HPC = 25LPC = 1.3

f = 1.3

Figure 7.1 Turbofan engine: Specific thrustvsflight Mach number


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Figure 7.2 Turbofan engine: thrust specific fuel consumptionvsflight Machnumber

Table 7.3 - The input data for Option 2:Figure 7.3 - Specific thrust vs compressor pressure ratio

Figure 7.4 - TSFC vs compressor pressure ratio

Figure 7.5 - Fuel/air ratio vs compressor pressure ratioScalec = 19.23

LPC = 1.01 c = 19.62 to 50HPC = 19.42 c = 1

f= 1.3 1 = 0.5 = 0.9 2 = 2


48/87

Figure 7.3 Turbofan engine: Specific thrustvs compressor pressure ratio

Figure 7.4 Turbofan engine: thrust specific fuel consumption

vs compressor pressure ratio


49/87

Figure 7.5 Turbofan engine:fuel/air ratio vs compressor pressure ratio:


Figure 7.6 - Specific thrust vs fan pressure ratio

Figure 7.7 - TSFC vs fan pressure ratio

f = 1.01 To 10

f = 0.251 = 3

HPC = 25 2 = 5

LPC = 1.3 3 = 10 = 0.9


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Figure 7.6 Turbofan engine: Specific thrustvsfan pressure ratio


vsfan pressure ratio


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Figure 7.8 - Specific thrust vs bypass ratio

Figure 7.9 - TSFC vs bypass ratio

= 0 To 10 = 0.1

HPC = 25 f1 = 1.5LPC = 1.3 f2 = 3.5 = 0.9

Figure 7.8 Turbofan engine: Specific thrustvs bypass ratio


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vs bypass ratio

Discussions

The computations are successful in providing an estimation of how the turbofan

performance is improved by adding an Inter-Stage Turbine Burner. As expected, the

specific thrust is increased at four different engine design parameters, namely Mach

number, compressor pressure ratio, fan pressure ratio and bypass ratio with the addition

of ITB. Nevertheless, the specific fuel consumption is relatively increased.

Typical ranges for each engine design parameter is based on Chapter 7 of Elements of

Gas Turbine Propulsionby Dr. Jack Mattingly1.

In addition, more plots will be added in the future if necessary. For convenience purpose,

a Visual-Basic code may be developed to act as an interface between fortran77 data file


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and MS Excel plot function. Then, user can plot the result data computed using Fortran77

on MS Excel without knowing how to use Tecplot 9.0 or any other equivalent post-

processing software.


54/87

Appendix

A - MACRO VISUAL BASIC CODE in MS EXCEL

VB code variable VB code variable VB code variable

a0 a0 gamab b T10_T0 T10/T0

alpha gamac c T19_T0 T19/T0

Cpb Cpb gamat t tau_alp_itb -b

Cpc Cpc hPRb hPR-b tau_alp_itb -ITB

Cpt Cpt hPRitb hPR-ITB tau_b b

ef ef M10 M10 tau_c c

eff_hpc HPC M19 M19 tau_f f

eff_hpt

HPT pi_d

d tau_hpc

HPC

eff_lpc LPC pi_f f tau_hpt HPT

eff_lpt LPT pi_hpc HPC tau_itb ITB

eff_r r pi_hpt HPT tau_lpc LPC

effm_hpt m-HPT pi_lpc LPC tau_lpt LPT

effm_lpt m-LPT pi_lpt LPT tau_r r

ehpc eHPC pi_r r Tt10_T0 Tt10/T0

elpc eLPC Pt10_P10 Pt10/P10 Tt19_T0 Tt19/T0

fb fb Pt19_P19 Pt19/P19 Tt6_Tt2 Tt6/Tt2

fc_mc rb Rb v0 v0

ff_mf rc Rc v10_a0 v10/a0

fitb fITB rt Rt v19_a0 v19/a0

f_mo s S

Table A.1 Description of variables in MS Excel Macro Visual Basic code

c

c

m

F

f

f

m

F

0

m

F


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Sub itb()

Dim rc, rb, rt, a0, v0, tau_r, pi_r, eff_r, pi_d, tau_alp_b, tau_alp_itb, tau_hpc, tau_lpc,

tau_f

Dim tau_c, tau_b, eff_hpc, eff_lpc, eff_f, fb, tau_hpt, fitb, tau_itb, Tt6_Tt2, tau_lpt

Dim pi_hpt, pi_lpt, eff_hpt, eff_lpt, Pt10_P10, Tt10_T0, M10, v10_a0, Pt19_P19, M19,

Tt19_T0

Dim T19_T0, v19_a0, fc_mc, ff_mf, T10_T0

'zero-ing internal variables

rc = 0#: rb = 0#: rt = 0#: a0 = 0#: v0 = 0#: tau_r = 0#: pi_r = 0#: eff_r = 0#: pi_d = 0#

tau_alp_b = 0#: tau_alp_itb = 0#: tau_hpc = 0#: tau_lpc = 0#: tau_f = 0#tau_c = 0#: tau_b = 0#: eff_hpc = 0#: eff_lpc = 0#: eff_f = 0#: fb = 0#

tau_hpt = 0#: fitb = 0#: tau_itb = 0#: Tt6_Tt2 = 0#: tau_lpt = 0#

pi_hpt = 0#: pi_lpt = 0#: eff_hpt = 0#: eff_lpt = 0#: Pt10_P10 = 0#: Tt10_T0 = 0#

M10 = 0#: v10_a0 = 0#: Pt19_P19 = 0#: M19 = 0#: Tt19_T0 = 0#

T19_T0 = 0#: v19_a0 = 0#: fc_mc = 0#: ff_mf = 0#

'empty-ing output variables

F_mo = Empty: s = Empty: f = Empty

Style = vbYes

Title = "ITB Cycle Analysis"

Style1 = vbYesNo

Msg = "Do you want to jump to the next alpha?"

Msg1 = "Division by zero ==> Refer to equations 1, 2, 3"

Msg2 = "Square root of a negative quantity ==> Refer to equation 4"

Msg3 = "Division by zero ==> Refer to equation 7"

Msg4 = "Division by zero ==> Refer to equations 10, 11, 12, 13, 14"


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Msg6 = "Division by zero ==> Refer to equations 17, 18, 19"




If gamac = 0# Or gamab = 0# Or gamat = 0# Then

response = MsgBox(Msg1, Sytle, Title)

Msg1 = "Occurs at " & "PIc,PIf,Mo,ByPass = " & pi_hpc * pi_lpc & "," & pi_f & ","

& M0 & "," & alpha

response = MsgBox(Msg1, Style, Title)

jump = MsgBox(Msg1, Style1, Title)

GoTo 10

End If

rc = (gamac - 1#) * Cpc / gamac '(1)

rb = (gamab - 1#) * Cpb / gamab '(2)

rt = (gamat - 1#) * Cpt / gamat '(3)

If gamac < 0# Or rc < 0# Or T_o < 0# Or gc < 0# Then



& M0 & "," & alpha


jump = MsgBox(Msg, Style1, Title)

GoTo 10

End If

a0 = (gamac * rc * T_o * gc) ^ 0.5 '(4)

v0 = a0 * M0 '(5)

If gamac = 1# Then


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& M0 & "," & alpha



GoTo 10

End If

tau_r = (gamac - 1#) * (0.5 * M0 ^ 2) + 1# '(6)

pi_r = tau_r ^ (gamac / (gamac - 1)) '(7)

If M0


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tau_c = tau_hpc * tau_lpc '(15)

If T_o = 0# Or tau_r = 0# Or tau_c = 0# Then



& M0 & "," & alpha



GoTo 10

End If

tau_b = Tt4 / (T_o * tau_r * tau_c) '(16)

If tau_hpc = 1# Or tau_lpc = 1# Or tau_f = 1# Then



& M0 & "," & alpha



GoTo 10

End If

eff_hpc = ((tau_hpc ^ ehpc) - 1#) / (tau_hpc - 1#) '(17)

eff_lpc = ((tau_lpc ^ elpc) - 1#) / (tau_lpc - 1#) '(18)

eff_f = ((tau_f ^ ef) - 1#) / (tau_f - 1#) '(19)

If tau_alp_b = eff_b * hPRb / (Cpc * T_o) Then



& M0 & "," & alpha




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GoTo 10

End If

fb = (tau_c * tau_r - tau_alp_b) / (tau_alp_b - (eff_b * hPRb / (Cpc * T_o)))

'(20)

tau_hpt = 1# + (1# - tau_hpc) / ((1# + fb) * (Cpb / Cpc) * tau_hpc * tau_b * effm_hpt)

'(21)

If Sheets("Input").ComboBox2.Value = "ON" Then '(22)

fitb = (1# + fb) * (tau_r * tau_c * tau_b * tau_hpt - (Cpc / Cpb) * tau_alp_itb) / ((Cpc /

Cpb) * tau_alp_itb - eff_itb * hPRitb / (Cpb * T_o))

Else

fitb = 0#

End If

f = fb + fitb '(23)

If Sheets("Input").ComboBox2.Value = "ON" Then

'(24)

tau_itb = Tt6 / (T_o * tau_r * tau_c * tau_b * tau_hpt)

Else

tau_itb = 1#

End If

Tt6_Tt2 = tau_c * tau_b * tau_hpt * tau_itb '(25)

tau_lpt = 1# + (1# - tau_lpc + alpha * (1# - tau_f)) / ((1# + f) * (Cpt / Cpc) * Tt6_Tt2 *

effm_lpt) '(26)

pi_hpt = tau_hpt ^ (gamat / ((gamat - 1#) * ehpt)) '(27)

pi_lpt = tau_lpt ^ (gamat / ((gamat - 1#) * elpt)) '(28)


60/87

eff_hpt = (1# - tau_hpt) / (1# - tau_hpt ^ (1# / ehpt)) '(29)

eff_lpt = (1# - tau_lpt) / (1# - tau_lpt ^ (1# / elpt)) '(30)

Pt10_P10 = P0_P10 * pi_r * pi_d * pi_lpc * pi_hpc * pi_b * pi_hpt * pi_itb * pi_lpt *

pi_n '(31)

Tt10_T0 = tau_r * tau_c * tau_b * tau_hpt * tau_itb * tau_lpt

'(32)

T10_T0 = Tt10_T0 / Pt10_P10 ^ ((gamat - 1#) / gamat)

'(33)

If gamat < 1# Or Pt10_P10 ^ ((gamat - 1#) / gamat) < 1# Then



& M0 & "," & alpha



GoTo 10

End If

M10 = (((Pt10_P10 ^ ((gamat - 1#) / gamat)) - 1#) * 2# / (gamat - 1#)) ^ 0.5

'(34)

v10_a0 = M10 * (gamat * rt * T10_T0 / (gamac * rc)) ^ 0.5

'(35)

Pt19_P19 = P0_P19 * pi_r * pi_d * pi_f * pi_fn '(36)

If gamac < 1# Or Pt19_P19 ^ ((gamac - 1#) / gamac) < 1# Then



61/87


& M0 & "," & alpha



GoTo 10

End If

M19 = (((Pt19_P19 ^ ((gamac - 1#) / gamac)) - 1#) * 2# / (gamac - 1#)) ^ 0.5

'(37)

Tt19_T0 = tau_r * tau_f '(38)

T19_T0 = Tt19_T0 / Pt19_P19 ^ ((gamac - 1#) / gamac)

'(39)

v19_a0 = M19 * T19_T0 ^ 0.5 '(40)

fc_mc = (a0 / gc) * ((1# + f) * v10_a0 - M0 + (1# + f) * (rt / rc) * (T10_T0 / v10_a0) *

(1# - P0_P10) * (1# / gamac)) '(41)

ff_mf = (a0 / gc) * (v19_a0 - M0 + (T19_T0 / v19_a0) * (1# - P0_P19) / gamac)

'(42)

F_mo = (fc_mc + alpha * ff_mf) / (1# + alpha)

'(43)

s = f / ((1# + alpha) * F_mo)

'(44)

10

End Sub


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B - FORTRAN 77 code

Three separate files are needed to execute this code, namely itb.f, comitb.i, and

input. All the equations used in this code are summarized in the section 4 - Summary of

equations.

(A) Main program: itb.f

itb.fis the main program for this application. It comprises of a main driver and

nine subroutines. Each subroutine has its own specific function and is described in detail

below.

1) Subroutine START

STARTis the first subroutine called by main driveritb. It ensures that the input

file exists, and then the program will carry on. Or else, the program will terminate.

2) Subroutine RINPUT

Once the file inputis provided at the same directory as itb.f is located,RINPUTwill

then be called and read in the data file.

3) Subroutine CONSTANT

All the constants will be initialized in this subroutine.This subroutine is called only

once before performing necessary computation.


63/87

4) Subroutine SELECT

SELECT allows user to specify which plot they desire to get. Up to this point, there

are only four options to choose, which include:

Option 1:

(a). Specific Thrust vs Mach Number (ST_M0.dat)

(b). TSFC vs Mach Number (TSFC_M0.dat)

Option 2:

(a). Specific Thrust vs Compressor Pressure Ratio (ST_PIc.dat)

(b). TSFC vs Compressor Pressure Ratio (TSFC_PIc.dat)

(c). Fuel-air Ratio vs Compressor Pressure Ratio (f_PIc.dat)

Option 3:

(a). Specific Thrust vs Fan Pressure Ratio (ST_PIf.dat)

(b). TSFC vs Fan Pressure Ratio (TSFC_PIf.dat)

Option 4:

(a). Specific Thrust vs Bypass Ratio (ST_Alpha.dat)

(b). TSFC vs Bypass Ratio (TSFC_Alpha.dat)

The selected plots will be plotted and stored in the same directory where the program

is executed.

5) Subroutine MACH

MACH is called to plot engine performance parameters (for instance,specific thrust

orthrust specific fuel consumption) vsflight mach number.


64/87

6) Subroutine COMPR

COMPR is called to plot engine performance parameters vs compressor pressure

ratio.

7) Subroutine FANPR

FANPR is called to plot engine performance parameters vsfan pressure ratio.

8) Subroutine BYPASS

BYPASS is called to plot engine performance parameters vs bypass ratio.

9) Subroutine EQUATION

EQUATION is called to perform all necessary computations. It includes all

equations here.

(B) Variable initialization: comitb.i

All variables will be declared and initialized before running main program and all

subroutines. Variables are grouped into five common blocks, i.e. inputs, outputs,

equations, constants, and chardat.


65/87

(C) Data file: input

Since two types of unit system will be used for computation, namely SI and

English unit, user needs to specify the input parameter unitsys to be either 0.

(English unit) or 1.0 (SI unit).

Another important input parameter is itbsw. When itbsw is set to be 1.,

ITB will be turned on and vice versa (i.e. itbsw is set to be 0.0).

Table shown below is the brief descriptions of input variables in input file:

Input Variables Unit

program literature English SI

unitsys - - -

itbsw - - -

T0 T0 R Kgamac c - -

cpc cpc

Rlbm

Btu

KkgkJ

gamab b - -

cpb cpb

Rlbm

Btu

KkgkJ

gamat t - -

cpt cpt

Rlbm

Btu

KkgkJ

hprb hPR-b

lbm

Btu

kg

kJ

hpritb hPR-itb

lbm

Btu

kg

kJ

pidmax d max - -

pib b - -

piitb itb - -

pin n - -

pifn fn - -

ehpc eHPC - -

elpc eLPC - -


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ef ef - -

ehpt eHPT - -

elpt eLPT - -

effb b - -

effitb itb -

effmhpt hpt -effmlpt lpt -

p0op10

10

0

P

P -

p0op19

19

0

P

P -

Tt4 Tt4 R KTt6 Tt6 R K

Table B.1 Description of input variables in input file in Fortran77 code (both SI

and English units)

Main program: itb.f

*deck itbprogram itb

cc +++cc===========================================================cc ITB is the main driver.cc===========================================================c

include 'comitb.i'cc//////////////////////////////\\\\\\\\\\\\\\\\\\\\\\\\\\\\\c


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c +++call start

c +++call rinput

c +++call constant

ccall select

c +++if (plot.eq.1) call mach

cif (plot.eq.2) call compr

cif (plot.eq.3) call fanpr

cif (plot.eq.4) call bypass

c +++end

c*deck bypass

subroutine bypasscc===========================================================cc BYPASS determines the range for bypass ratio forc plotting.cc BYPASS is called by: itbcc===========================================================c


write(3,*) 'Subroutine BYPASS'c

open(unit=18,file='ST_Alpha.dat')open(unit=19,file='TSFC_Alpha.dat')

cWRITE(18,*) 'Title="','Specific Thrust VS Alpha"'if (unitsys.eq.0.0) thenWRITE(18,*) 'Variables = "à","Sp. thrust [lbf/(lbm/sec)]"'elseWRITE(18,*) 'Variables = "à","Specific thrust [N/(kg/s)]"'endif

c

WRITE(19,*) 'Title="','TSFC VS Alpha"'if (unitsys.eq.0.0) thenWRITE(19,*) 'Variables = "à","TSFC [(lbm/hr)/lbf]"'elseWRITE(19,*) 'Variables = "à","TSFC [mg/(N-sec)]"'endif

cif (npif.gt.0) thendo 90 i=1,npif

pif=pi_f(i)


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write(*,*) 'pif(',i,')=',pifc

if (itbsw.eq.0.) thenwrite(18,314)'Zone T="`p_f = ',pif,'(no itb)"'write(19,314)'Zone T="`p_f = ',pif,'(no itb)"'

elsewrite(18,314)'Zone T="`p_f = ',pif,'(itb)"'write(19,314)'Zone T="`p_f = ',pif,'(itb)"'

endifc

do 100 alpha = ialp,falp,dalpc

alpp1 = alpha+1.0ralpp1 = 1.0/alpp1

ccall equationif (error.eq.1.0) then

write(*,*) 'error'go to 90

endif

write(18,313) alpha,stwrite(19,313) alpha,tsfc

100 continue90 continue

endifc

close(18)close(19)return

313 format(f10.5,2x,f13.8)314 format(a15,f5.2,a9)

endc*deck compr

subroutine comprcc===========================================================cc COMPR determines the range for compressor pressurec ratio for plotting.cc COMPR is called by: itbcc===========================================================c

include 'comitb.i'c

c//////////////////////////////\\\\\\\\\\\\\\\\\\\\\\\\\\\\\c

write(3,*) 'Subroutine COMPR'c

open(unit=15,file='ST_PIc.dat')open(unit=16,file='TSFC_PIc.dat')open(unit=17,file='f_PIc.dat')

cWRITE(15,*) 'Title="','Specific Thrust VS Pi Comp"'if (unitsys.eq.0.0) then


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WRITE(15,*)'Variables ="`p_c","Sp.thrust [lbf/(lbm/sec)]"'elseWRITE(15,*)'Variables ="`p_c","Sp.thrust [N/(kg/s)]"'endif

cWRITE(16,*) 'Title="','TSFC VS Pi Comp"'if (unitsys.eq.0.0) thenWRITE(16,*)'Variables = "`p_c","TSFC [(lbm/hr)/lbf]"'elseWRITE(16,*)'Variables = "`p_c","TSFC [mg/(N-sec)]"'endif

cWRITE(17,*) 'Title="','f VS Pi Comp"'WRITE(17,*) 'Variables = "`p_c","f"'

cipic = scalec*pilpc*pilpck=1do 60 pic = ipic,fpic,dpic

term = pic/scalectpilpc(k) = sqrt(term)

tpihpc(k) = pic/tpilpc(k)k=k+1

60 continuewrite(3,*) pilpc,pihpc,picwrite(3,*) ipic,fpic,dpic

cif (nalpha.gt.0) thendo 70 i=1,nalpha

alpha=alp(i)write(*,*) 'alpha(',i,')=',alphaif (itbsw.eq.0.) then

write(15,12)'Zone T="à =',alpha,'(no itb)"'write(16,12)'Zone T="à =',alpha,'(no itb)"'write(17,12)'Zone T="à =',alpha,'(no itb)"'

elsewrite(15,12)'Zone T="à =',alpha,'(itb)"'write(16,12)'Zone T="à =',alpha,'(itb)"'write(17,12)'Zone T="à =',alpha,'(itb)"'

endifc

alpp1 = alpha+1.0ralpp1 = 1.0/alpp1

c write(3,*) 'alpp1=',alpp1c write(3,*) 'ralpp1=',ralpp1c

j=1write(3,*) pilpc,pihpc,pic

write(3,*) ipic,fpic,dpicdo 80 pic = ipic,fpic,dpic

pilpc = tpilpc(j)pihpc = tpihpc(j)write(3,*) pilpc,pihpc,pic

ccall equationif (error.eq.1.0) then

write(*,*) 'error'go to 70


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endifwrite(15,11) pic,stwrite(16,11) pic,tsfcwrite(17,11) pic,f

c count=count+1j=j+1


endifc

close (15)close (16)close (17)return


endc*deck constant

subroutine constant

cc===========================================================cc EQUATION performs all necessary computations.cc EQUATION is called by: mach,compr,fanpr,bypasscc===========================================================c


write(3,*)write(3,*) '*******Check constant begins!!******'

cgc=32.174if (unitsys.eq.1.0) gc = 1.0

cecvrn = 778.14if (unitsys.eq.1.0) ecvrn = 1000.0

crgc = 1.0/gcwrite(3,*) 'gc=',gcwrite(3,*) 'rgc=',rgc

crgamac = 1.0/gamac

rgamat = 1.0/gamatrgamab = 1.0/gamabwrite(3,*) 'rgamac=',rgamacwrite(3,*) 'rgamat=',rgamatwrite(3,*) 'rgamab=',rgamab

cgcm1ogc = (gamac-1.0)*rgamacgtm1ogt = (gamat-1.0)*rgamatgbm1ogb = (gamab-1.0)*rgamabwrite(3,*) 'gcm1ogc=',gcm1ogc


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write(3,*) 'gtm1ogt=',gtm1ogtwrite(3,*) 'gbm1ogb=',gbm1ogb

crgcm1ogc = 1.0/gcm1ogcrgtm1ogt = 1.0/gtm1ogtrgtm1 = 1.0/(gamat-1.0)rgcm1 = 1.0/(gamac-1.0)write(3,*) 'rgcm1ogc=',rgcm1ogcwrite(3,*) 'rgtm1ogt=',rgtm1ogtwrite(3,*) 'rgcm1=',rgcm1write(3,*) 'rgtm1=',rgtm1

cTt4oT0 = Tt4/T0Tt6oT0 = Tt6/T0write(3,*) 'Tt4oT0=',Tt4oT0write(3,*) 'Tt6oT0=',Tt6oT0

ccpbocpc = cpb/cpccptocpc = cpt/cpccpcocpb = 1.0/cpbocpc

write(3,*) 'cpbocpc=',cpbocpcwrite(3,*) 'cptocpc=',cptocpcwrite(3,*) 'cpcocpb=',cpcocpb

crehpc = 1.0/ehpcrelpc = 1.0/elpcwrite(3,*) 'rehpc=',rehpcwrite(3,*) 'relpc=',relpc

crehpt = 1.0/ehptrelpt = 1.0/elptwrite(3,*) 'rehpt=',rehptwrite(3,*) 'relpt=',relpt

ctaud = 1.0

cwrite(3,*) '******constant check ENDs!!******'write(3,*)

creturnend

c*deck equation

subroutine equationcc===========================================================c

c EQUATION performs all necessary computations.cc EQUATION is called by: itbcc===========================================================c

include 'comitb.i'INTEGER eqn

cc//////////////////////////////\\\\\\\\\\\\\\\\\\\\\\\\\\\\\


72/87

cerror=0.eqn = 0write(3,*) '-----------------------------'write(3,*) 'Subroutine EQUATION'write(3,*) '-----------------------------'

cc --- equation 1,2,3c

rc = gcm1ogc*cpc*ecvrnrb = gbm1ogb*cpb*ecvrnrt = gtm1ogt*cpt*ecvrnwrite(3,*) 'Rc=',rcwrite(3,*) 'Rt=',rtwrite(3,*) 'Rb=',rb

crtorc = rt/rcwrite(3,*) 'rtorc=',rtorc

cc --- equation 4 & 5

cterm = gamac*rc*gc*T0if (term.lt.0) then

eqn = 4write(3,201) eqn

endifc

a0 = sqrt(term)v0 = a0*M0write(3,*) 'a0=',a0write(3,*) 'v0=',v0


taur = 1.0+(gamac-1.0)/2*M0*M0pir = taur**rgcm1ogceffr = 1.if (M0.gt.5.0) then

effr = 800/(M0**4+935.0)else if (M0.gt.1.0) then

effr = 1.0-0.075*(M0-1)**1.35endif

cwrite(3,*) 'taur=',taurwrite(3,*) 'pir=',pirwrite(3,*) 'effr=',effr

c

c --- equation 9,10,11c

pid = pidmax*effrtaulb = cpbocpc*Tt4oT0taulitb = cptocpc*Tt6oT0write(3,*) 'pid=',pidwrite(3,*) 'taulb=',taulbwrite(3,*) 'taulitb=',taulitb

cc


73/87

c --- equation 12 & 13c

tauhpc = pihpc**(gcm1ogc*rehpc)taulpc = pilpc**(gcm1ogc*relpc)write(3,*) 'tauhpc=',tauhpcwrite(3,*) 'taulpc=',taulpc


if (ef.lt.0) theneqn = 14write(3,201) eqn

endifc

tauf = pif**(gcm1ogc/ef)tauc = tauhpc*taulpc

cterm = taur*tauc*taudif (term.lt.0) then

eqn = 16

write(3,201) eqnendif

ctaub = Tt4oT0/(term)

cwrite(3,*) 'tauf=',taufwrite(3,*) 'tauc=',taucwrite(3,*) 'taub=',taub


if (tauhpc.eq.1.0) theneqn = 17write(3,201) eqn

go to 299endif

ceffhpc = (tauhpc**ehpc-1.0)/(tauhpc-1.0)write(3,*) 'effhpc=',effhpc

cif (taulpc.eq.1.0) then


go to 299endif

cefflpc = (taulpc**elpc-1.0)/(taulpc-1.0)

write(3,*) 'efflpc=',efflpcc

if (tauf.eq.1.0) theneqn = 19write(3,201) eqn

go to 299endif

cefff = (tauf**ef-1.0)/(tauf-1.0)write(3,*) 'efff=',efff


74/87

cc --- equation 20c

num = tauc*taur-taulbdenom = taulb-(effb*hprb)/(cpc*T0)write(3,*) 'num=',numwrite(3,*) 'denom=',denom

cif (denom.eq.0) then


go to 299endif

cfb = num/denomwrite(3,*) 'fb=',fb

cc --- equation 21c

denom = (1.0+fb)*cpbocpc*tauhpc*taub*effmhpt

write(3,*) 'denom=',denomc

if (denom.eq.0) theneqn = 21write(3,201) eqn

go to 299endif

ctauhpt = 1.0+(1.0-tauhpc)/denomwrite(3,*) 'tauhpt=',tauhpt

cc --- equation 22 & 23c

if (itbsw.eq.1.0) thendenom1 = cpcocpb*taulitbdenom2 = (effitb*hpritb)/(cpb*T0)denom = denom1-denom2num = taur*taud*tauc*taub*tauhpt-cpcocpb*taulitbwrite(3,*) 'denom1=',denom1write(3,*) 'denom2=',denom2write(3,*) 'denom=',denomwrite(3,*) 'num=',num

cif (denom.eq.0) then


go to 299

endiffitb = num/denom*(1.0+fb)

elsefitb = 0.0

endifc

f = fb+fitbwrite(3,*) 'fitb=',fitbwrite(3,*) 'f=',f

c


75/87


if (itbsw.eq.1.0) thennum=taur*tauc*taub*tauhptwrite(3,*) 'num=',numif (num.eq.0) then

eqn = 24write(3,201) eqngo to 299

endiftauitb = Tt6oT0/num

elsetauitb = 1.0

endifc

Tt6oTt2 = tauitb*taulpc*tauhpc*taub*tauhptwrite(3,*) 'tauitb=',tauitbwrite(3,*) 'Tt6oTt2=',Tt6oTt2

cc --- equation 26,27,28,29,30

cfp1 = f+1.0num = 1.0-taulpc+alpha*(1.0-tauf)denom = fp1*cptocpc*Tt6oTt2*effmlptwrite(3,*) 'num=',numwrite(3,*) 'denom=',denom

cc

if (denom.eq.0) theneqn = 26write(3,201) eqn

go to 299endif

ctaulpt = 1.0+num/denomwrite(3,*) 'taulpt=',taulpt

cpihpt = tauhpt**(rgtm1ogt*rehpt)pilpt = taulpt**(rgtm1ogt*relpt)write(3,*) 'pihpt=',pihptwrite(3,*) 'pilpt=',pilpt

cdenom = 1.0-tauhpt**rehptwrite(3,*) 'denom=',denomif (denom.eq.0) then


go to 299endif

ceffhpt = (1.0-tauhpt)/denomwrite(3,*) 'effhpt=',effhpt

cdenom = 1.0-taulpt**relptwrite(3,*) 'denom=',denomif (denom.eq.0) then

eqn = 30


76/87

write(3,201) eqngo to 299endif

cefflpt = (1.0-taulpt)/denomwrite(3,*) 'efflpt=',efflpt

cc --- eqaution 31,32,33,34,35c

pt10op10 = p0op10*pir*pid*pilpc*pihpc*pibpt10op10 = pt10op10*pihpt*piitb*pilpt*pinwrite(3,*) 'pt10op10=',pt10op10

cTt10oT0 = taur*tauc*taub*tauhpt*taulpt*tauitbdenom = pt10op10**gtm1ogtwrite(3,*) 'Tt10oT0=',Tt10oT0write(3,*) 'denom=',denomif (denom.eq.0) then


go to 299endif

cT10oT0 = Tt10oT0/denomwrite(3,*) 'T10oT0=',T10oT0

cterm = denomif (term.lt.1.0) then


go to 299endif

cM10 = sqrt(2.0*(term-1.0)/(gamat-1.0))

cterm = rtorc*T10oT0*gamat/gamacwrite(3,*) 'term=',term

cif (term.lt.0.0) then


go to 299endif

cv10oa0 = M10*sqrt(term)write(3,*) 'M10=',M10write(3,*) 'v10oa0=',v10oa0

cc --- equation 36,37,38,39,40c

pt19op19 = p0op19*pir*pid*pif*pifnc

term = pt19op19**gcm1ogcwrite(3,*) 'pt19op19=',pt19op19write(3,*) 'term=',termif (term.lt.1.0) then

eqn = 37


77/87

write(3,200) eqngo to 299endif

cM19 = sqrt(2.0*(term-1.0)/(gamac-1.0))write(3,*) 'M19=',M19

cTt19oT0 = taur*tauf

cdenom = termT19oT0 = Tt19oT0/denomwrite(3,*) 'Tt19oT0=',Tt19oT0write(3,*) 'T19oT0=',T19oT0

cif (T19oT0.lt.0) then


go to 299endif

c

v19oa0 = sqrt(T19oT0)*M19write(3,*) 'v19oa0=',v19oa0

cc --- equation 41 & 42c

term = fp1*rtorc*T10oT0*(1.0-p0op10)*rgamac/v10oa0write(3,*) 'term=',termwrite(3,*) 'a0=',a0write(3,*) 'rgc=',rgcwrite(3,*) 'fp1=',fp1write(3,*) 'v10oa0=',v10oa0write(3,*) 'M0=',M0fcomc = a0*rgc*(fp1*v10oa0-M0+term)if (fcomc.lt.0) then


go to 299endif

cwrite(3,*) 'term=',termwrite(3,*) 'fcomc=',fcomc

cterm = T19oT0*(1.0-p0op19)*rgamac/v19oa0ffomf = a0*rgc*(v19oa0-M0+term)write(3,*) 'term=',termwrite(3,*) 'ffomf=',ffomf

c


st = (fcomc+ffomf*alpha)*ralpp1c

tsfc = ((1.0-unitsys)*3600+unitsys*1e6)*(f*ralpp1/st)write(3,*) 'st=',stwrite(3,*) 'tsfc=',tsfcwrite(3,*) '------------------------------'

c ---299 if (eqn.gt.0) error=1.0


78/87

returnc200 format(' Error: Square root of a negative number! Check

& equation',i3)201 format(' Error: Division by zero !! Check equation', i3)202 format(' Error: Negative Fc/mcdot !! Check equation',i3)

endc*deck fanpr

subroutine fanprcc===========================================================cc FANPR determine the range of Fan pressure ratio forc plotting.cc FANPR is called by: itbcc===========================================================c


write(3,*) 'Subroutine FANPR'c

open(unit=13,file='ST_PIf.dat')open(unit=14,file='TSFC_PIf.dat')

cWRITE(13,*) 'Title="','Specific Thrust VS Pi Fan"'if (unitsys.eq.0.0) thenWRITE(13,*)'Variables = "`p_f","Sp. thrust [lbf/(lbm/sec)]"'elseWRITE(13,*)'Variables = "`p_f","Sp. thrust [N/(kg/s)]"'endif

cWRITE(14,*) 'Title="','TSFC VS Pi Fan"'if (unitsys.eq.0.0) thenWRITE(14,*)'Variables = "`p_f","TSFC [(lbm/hr)/lbf]"'elseWRITE(14,*)'Variables = "`p_f","TSFC [(mg/(N-sec)]"'endif


alpha=alp(i)write(*,*) 'alpha(',i,')=',alpha

cif (itbsw.eq.0.) then

write(13,12)'Zone T="à = ',alpha,'(no itb)"'write(14,12)'Zone T="à = ',alpha,'(no itb)"'

elsewrite(13,12)'Zone T="à = ',alpha,'(itb)"'write(14,12)'Zone T="à = ',alpha,'(itb)"'

endifc

alpp1 = alpha+1.0


79/87

ralpp1 = 1.0/alpp1write(3,*) 'alpp1=',alpp1write(3,*) 'ralpp1=',ralpp1

cdo 50 pif = ipif,fpif,dpif

call equationif (error.eq.1.0) then

c write(*,*) 'error'go to 40

endifwrite(13,11) pif,stwrite(14,11) pif,tsfc

c count=count+150 continue40 continue

endifc

close (13)close (14)return


endc*deck mach

subroutine machcc===========================================================cc MACH determine the range of Mach number for plotting.cc MACH is called by: itbcc===========================================================c


write(3,*) 'Subroutine MACH'c

open(unit=11,file='ST_M0.dat')open(unit=12,file='TSFC_M0.dat')

cWRITE(11,*) 'Title="','Specific Thrust VS Mach #"'if (unitsys.eq.0.0) thenWRITE(11,*)'Variables = "M_0","Sp. thrust [lbf/(lbm/sec)]"'

elseWRITE(11,*)'Variables = "M_0","Sp. thrust [N/(kg/s)]"'endif

cWRITE(12,*) 'Title="','TSFC VS Mach #"'if (unitsys.eq.0.0) thenWRITE(12,*)'Variables = "M_0","TSFC [(lbm/hr)/lbf]"'elseWRITE(12,*)'Variables = "M_0","TSFC [mg/(N-sec)]"'endif


80/87


alpha=alp(i)write(*,*) 'alpha(',i,')=',alpha

c count=0if (itbsw.eq.0.) then

write(11,12)'Zone T="à = ',alpha,'(no itb)"'write(12,12)'Zone T="à = ',alpha,'(no itb)"'

elsewrite(11,12)'Zone T="à = ',alpha,'(itb)"'write(12,12)'Zone T="à = ',alpha,'(itb)"'

endifc

alpp1 = alpha+1.0ralpp1 = 1.0/alpp1write(3,*) 'alpp1=',alpp1write(3,*) 'ralpp1=',ralpp1

cdo 10 M0 = iM0,fM0,dM0

call equationif (error.eq.1.0) then

write(*,*) '!!error!!'go to 20

endifwrite(11,11) M0,stwrite(12,11) M0,tsfc


endifc

close(11)close(12)return


endc*deck rinput

subroutine rinputcc===========================================================cc RINPUT reads the 'input' data file.cc RINPUT is called by: itbc

c===========================================================c

include 'comitb.i'character *10 id(4)

cc//////////////////////////////\\\\\\\\\\\\\\\\\\\\\\\\\\\\\c

read (1,310) id(1),unitsyswrite(3,310) ' unitsys',unitsys

c


81/87

read (1,310) id(1),itbswwrite(3,310) ' itbsw ',itbsw

cread (1,310) id(1),T0write(3,310) ' T0 ',T0

cread (1,310) id(1),gamac,id(2),cpcwrite(3,310) ' gamac ',gamac,' cpc ',cpc

cread (1,310) id(1),gamab,id(2),cpbwrite(3,310) ' gamab ',gamab,' cpb ',cpb

cread (1,310) id(1),gamat,id(2),cptif (itbsw.eq.0.0) then

cpt = cpbgamat = gamab

endifwrite(3,310) ' gamat ',gamat,' cpt ',cpt

cread (1,310) id(1),hprb,id(2),hpritb

write(3,310) ' hprb ',hprb, ' hpritb ',hpritbc

read (1,310) id(1),pidmax,id(2),pib,id(3),piitbif (itbsw.eq.0.0) piitb = 1.0write(3,310) ' pidmax ',pidmax,' pib ',pib,& ' piitb ',piitb

cread (1,310) id(1),pin,id(2),pifnwrite(3,310) ' pin ',pin,' pifn ',pifn

cread (1,310) id(1),ehpc,id(2),elpc,id(3),efwrite(3,310) ' ehpc ',ehpc,' elpc ',elpc,& ' ef ',ef

cread (1,310) id(1),ehpt,id(2),elptwrite(3,310) ' ehpt ',ehpt,' elpt ',elpt

cread (1,310) id(1),effb,id(2),effitbwrite(3,310) ' effb ',effb,' effitb ',effitb

cread (1,310) id(1),effmhpt,id(2),effmlptwrite(3,310) ' effmhpt',effmhpt,' effmlpt',effmlpt

cread (1,310) id(1),p0op10,id(2),p0op19write(3,310) ' p0op10 ',p0op10,' p0op19 ',p0op19

cread (1,310) id(1),Tt4,id(2),Tt6

write(3,310) ' Tt4 ',Tt4,' Tt6 ',Tt6c

return310 format(a8,f14.8)311 format(a8,i5)

endc*deck select

subroutine selectc===========================================================


82/87

cc SELECT allows user to specify the desired plots.cc SELECT is called by: itbcc===========================================================c

include 'comitb.i'CHARACTER *2 try

cc///////////////////////////////\\\\\\\\\\\\\\\\\\\\\\\\\\\\c1 write(*,*)

write(*,*) 'Please choose a plot:'write(*,*) '--------------------'write(*,*) '(1)'write(*,*) ' a. Specific Thrust vs Mach Number'write(*,*) ' b. TSFC vs Mach Number'write(*,*) '(2)'write(*,*) ' a. Specific Thrust vs Compressor Pres.Ratio'

write(*,*) ' b. TSFC vs Compressor Pres.Ratio'write(*,*) ' c. Fuel-air Ratio vs Compressor Pres.Ratio'write(*,*) '(3)'write(*,*) ' a. Specific Thrust vs Fan Pres.Ratio'write(*,*) ' b. TSFC vs Fan Pres.Ratio'write(*,*) '(4)'write(*,*) ' a. Specific Thrust vs Bypass Ratio'write(*,*) ' b. TSFC vs Bypass Ratio'write(*,*) '--------------------'write(*,*) '(1~4)?'read (*,*) plot

cif (plot.lt.1.or.plot.gt.4) then

write(*,*) '!!Invalid selction number!!'write(*,*) ' Try again (y/n)?'read (*,*) try

if (try.eq.'y'.or.try.eq.'Y') go to 1endif

cc +++ Plot 1c

if (plot.eq.1) thenwrite(*,*) 'Initial M0 (iM0):'read (*,*) iM0

2 write(*,*) 'Final M0 (fM0):'read (*,*) fM0

c

if (fM0.le.iM0) thenwrite(*,*) ' >>Error: iM0 >= fM0 !!'go to 2

endifc

write(*,*) 'Delta M0 (dM0):'read (*,*) dM0write(*,*) 'HPC Pressure Ratio (pihpc):'read (*,*) pihpcwrite(*,*) 'LPC Pressure Ratio (pilpc):'


83/87

read (*,*) pilpcwrite(*,*) 'Fan Pressure Ratio (pif):'read (*,*) pif

endifcc +++ Plot 2c

if (plot.eq.2) thenwrite(*,*) 'LPC Pressure Ratio (pilpc):'read (*,*) pilpcwrite(*,*) 'Constant between LPC & HPC (scalec):'write(*,*) ' i.e. HPC = scalec*LPC'read (*,*) scalec

cpihpc = scalec*pilpcipic = scalec*pilpc*pilpcwrite(*,'(a6,f6.2)') ' HPC =',pihpcwrite(*,'(a21,f6.2)') ' Initial pic (ipic) =',ipic

3 write(*,*) 'Final pic (fpic):'read (*,*) fpic

cif (fpic.le.ipic) then

write(*,*) ' >>Error: ipic >= fpic'go to 3

endifc

write(*,*) 'Delta pic (dpic):'read (*,*) dpicwrite(*,*) 'Fan Pressure Ratio (pif):'read (*,*) pifwrite(*,*) 'Mach Number (M0):'read (*,*) M0

endifcc +++ Plot 3c

if (plot.eq.3) then4 write(*,*) 'Initial pif (ipif):'

read (*,*) ipifc

if (ipif.le.1.0) thenwrite(*,*)'>>Error: "ipif" has to be greater than 1.0'go to 4

endifc

5 write(*,*) 'Final pif (fpif):'read (*,*) fpif

cif (fpif.le.ipif) then

write(*,*) ' >>Error: ipif >= fpif'go to 5

endifc

write(*,*) 'Delta pif (dpif):'read (*,*) dpifwrite(*,*) 'HPC Pressure Ratio (pihpc):'read (*,*) pihpc


84/87

write(*,*) 'LPC Pressure Ratio (pilpc):'read (*,*) pilpcwrite(*,*) 'Mach number (M0):'read (*,*) M0

endifcc +++ Plot 4c

if (plot.eq.4) thenwrite(*,*) 'Initial alpha (ialp):'read (*,*) ialp

6 write(*,*) 'Final alpha (falp):'read (*,*) falp

cif (falp.le.ialp) then

write(*,*) ' >>Error: ialp >= falp'go to 6

endifc

write(*,*) 'Delta alpha (dalp):'

read (*,*) dalpwrite(*,*) 'HPC Pressure Ratio (pihpc):'read (*,*) pihpcwrite(*,*) 'LPC Pressure Ratio (pilpc):'read (*,*) pilpcwrite(*,*) 'Mach number (M0):'read (*,*) M0write(*,*)write(*,*) 'Plot at different fan pres. ratio (pif)'write(*,*) '---------------------------------------'write(*,*) 'Number of pif (npif):'read (*,*) npifwrite(*,*) 'Please input',npif,' pif(s):'do 7 i=1,npif

write(*,*) 'pif',i,' ->'read (*,*) pi_f(i)

7 continueendif

cif (plot.le.3) then

write(*,*)write(*,*) 'Plot at different bypass ratio (alpha)'write(*,*) '--------------------------------------'write(*,*) 'Number of alpha (nalpha):'read (*,*) nalphawrite(*,*) 'Please input',nalpha,' alpha(s):'do 8 i=1,nalpha

write(*,*) 'alpha',i,' ->'read (*,*) alp(i)

8 continueendif

creturnend

c*deck start

subroutine start


85/87

c===========================================================cc START performs initialization for 'itb' run.cc START is the first subroutine called by the driver.cc START is called by: itbcc===========================================================c

include 'comitb.i'logical present

cc///////////////////////////////\\\\\\\\\\\\\\\\\\\\\\\\\\\\c

open(unit=3,file='check')c +++c +++ ensure that 'input' file existsc +++

inquire(file='input',exist=present)

if(.not.present) thenwrite(*,300)write(3,300)call exit(0)

endifc

open(unit=1,file='input')read (1,301) namewrite(3,301) name

300 format(' data file input is missing: run aborted')301 format(a80)

returnend

Variable initialization: comitb.i

*deck comitbcc implicit double precision (a-h,o-z)

parameter (na=10,ncomp=1000)c na = maximum number of different alpha valuesc

REAL M0,iM0,M10,M19,num,ipic,ialp,ipif,itbswCHARACTER *80 name

ccommon /inputs/ unitsys,itbsw,T0,gamac,cpc,gamab,cpb,1 gamat,cpt,hprb,hpritb,pidmax,pib,piitb,pin,pifn,ehpc,2 elpc,ef,ehpt,elpt,effb,effitb,effmhpt,effmlpt,p0op10,3 p0op19,Tt4,Tt6,M0,iM0,dM0,fM0,pihpc,pilpc,pic,ipic,4 dpic,fpic,tpilpc(ncomp),tpihpc(ncomp),scalec,pif,ipif,5 dpif,fpif,npif,pi_f(na),ialp,dalp,falp,nalpha,alpha,6 alp(na),taud,plot


86/87

ccommon /outputs/ f,st,tsfc

ccommon /equations/ rc,rb,rt,a0,v0,taur,pir,effr,pid,taulb,1 taulitb,tauhpc,taulpc,tauf,tauc,taub,effhpc,efflpc,efff,2 fb,tauhpt,fitb,tauitb,Tt6oTt2,taulpt,pihpt,pilpt,effhpt,3 efflpt,pt10op10,Tt10oT0,t10oT0,M10,v10oa0,pt19op19,M19,4 Tt19oT0,T19oT10,v19oa0,fcomc,ffomf

ccommon /constants/ gc,rgc,ecvrn,gcm1ogc,gbm1ogb,gtm1ogt,1 rgcm1ogc,denom,fp1,rgtm1ogt,rehpt,relpt,num,pt10rgt,2 rgtm1,term,rgcm1,pt19rgc,rgamac,alpp1,ralpp1,rgamat,3 rgamab,Tt4oT0,Tt6oT0,cpbocpc,cptocpc,cpcocpb,rehpc,4 relpc,denom1,denom2,rtorc,error

ccommon /chardat/ name

c

Input data file: input

/062302/ ITBunitsys 0.0itbsw 1.0

T0 390.0gamac 1.39999cpc 0.239

gamab 1.27284cpb 0.277gamat 1.27882cpt 0.274hprb 18400.0hpritb 18400.0pidmax 0.99pib 0.96piitb 0.96


87/87

pin 0.99pifn 1.3ehpc 0.9066elpc 0.9036ef 0.8961ehpt 0.9029

elpt 0.9174effb 0.999effitb 0.999effmhpt 0.92effmlpt 0.93p0op10 0.9p0op19 0.9Tt4 3214.07Tt6 2814.92

References

1. Mattingly, J. D., Elements of Gas Turbine Propulsion, McGraw-Hill series in

mechanical engineering, McGraw Hill, Inc. Singapore 1996.

2. Model Specification for Engines, Aircraft, Turbojet, Military Specification MIL-E-

5008B, Department of Defense. January 1959

3. F. Liu, W.A. Sirignano, Turbojet and Turbofan Engine Performance Increases

Through Turbine Burners,Journal of Propulsion and Power, Vol. 17, No. 3, May-June

2001, pp 695-705.

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