A Complete Parametric Cycle Analysis for Ideal TurboFan ...



A Complete Parametric Cycle Analysis for Ideal TurboFan Engine with Interstage Turbine Burner

S.L. Yang, Y.K. Siow, K.H. Liew, and E. Urip

Mechanical Engineering – Engineering Mechanics Department

Michigan Technological University

1400 Townsend Drive

Houghton, MI 49931-1295

906/487-2624

906/487-2822 (Fax)

slyang@mtu.edu

C. J. Marek

Combustion Technology Branch, MS 5-10

NASA Glenn Research Center

21000 Brookpark Road

Cleveland, OH 44135

216/433-3584

216/433-3000 (Fax)

Cecil.J.Marek@grc.

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 engine’s 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.

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 user’s 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 analysis, he has given us many valuable suggestions on how the program could be enhanced for increased usefulness in the future.

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

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 thrust vs flight Mach number

(both Fortran77 and Excel) …………………………………….…………. 32

Figure 6.2 – Turbofan Engine with ITB: specific thrust vs flight Mach number

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

Figure 6.3 – Turbofan Engine with ITB: specific thrust vs flight Mach number

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

Figure 6.4 – Turbofan Engine ITB: specific thrust vs flight Mach number

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

Figure 7.1 – Turbofan Engine: specific thrust vs flight Mach number……………….… 36

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

number ……………………………………………………………………. 37

Figure 7.3 – Turbofan Engine: specific thrust vs 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 thrust vs fan pressure ratio …………….…….. 40

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

ratio ………………………………………………………..……….……. 40

Figure 7.8 – Turbofan Engine: specific thrust vs bypass ratio ……………………..….. 41

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

ratio …………………………………………………….………………... 42

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 7.3 – Input Data for Option 2 (SI unit) ……………………………………... 37

Table 7.4 – Input Data for Option 3 (SI unit) ……………………………………... 39

Table 7.5 – Input Data for Option 4 (SI unit) ……………………………………... 41

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

NOMENCLATURE

A cross-sectional area

a sound speed

CP specific heat at constant pressure

D drag force

e polytropic efficiency

F force uninstalled thrust

f fuel/air ratio

gc Newton’s constant

h enthalpy

hPR low heating value of fuel

M mach number

[pic] mass flow rate

P pressure

Pt total pressure

[pic] 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

[pic] power

α bypass ratio

γ ratio of specific heats, [pic]

[pic] mechanical Efficiency

ηO overall Efficiency

ηP propulsive Efficiency

ηT thermal Efficiency

π ratio of total pressure

πr (exception) ratio between total pressure and static pressure due to the ram effect, [pic]

τ ratio of total temperature

(r (exception) ratio between total temperature and static temperature due to the ram effect, [pic]

τλ ratio between total enthalpy and enthalpy at ambient condition

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)

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.

[pic]

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 to driving 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.

The main objective of this analysis is to determine the relationships between engine performance (primarily specific thrust [pic], 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 thrust F of a jet engine (single inlet and single exhaust) is given by

[pic] (2.1)

where [pic] are mass flow rates of air and fuel respectively

[pic] are velocities at inlet and exit respectively

[pic] are pressure at inlet and exit respectively

For the ideal case, the hot gas is expanded to the ambient pressure which gives Pe = Po. Equation (2.1) then becomes

[pic] (2.2)

The installed thrust T is given by

[pic] (2.3)

where Dinlet and Dnozzle 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

[pic] (2.4)

[pic] (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).

[pic] (2.6)

where,

[pic]

The propulsive efficiency defines the ratio between the engine power output and the power being used to run the aircraft.

[pic] (2.7)

where,

[pic]

An overall performance of a propulsion system is given by the combination between thermal and propulsive efficiencies.

[pic] (2.8)

where,

[pic]

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:

[pic] (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:

[pic] ( [pic] (2.10)

where,

[pic]

Stagnation pressure or total pressure Pt 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

[pic] (2.11)

The ratio of total temperatures τ and the ratio of total pressure π across a component is denoted by the subscript: d for diffuser, LPC for low pressure compressor, HPC for high pressure compressor, b for main burner, ITB for inter-stage turbine burner, LPT for low pressure turbine, HPT for high pressure turbine, n for nozzle, and f for fan.

For example:

[pic]

[pic]

Exceptions

For the free stream, ram, we define τr as a ratio of total temperature/static temperature and πr as a ratio of total pressure/static pressure.

[pic] (2.12)

[pic] (2.13)

A ratio between total enthalpy of the burner exit and ambient enthalpy, denoted by τλ, is defined such that it will be one of the input parameters.

[pic] (2.14)

[pic] (2.15)

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, γc), from ITB entrance to the main burner exit (Cpb, γb), and from ITB exit downstream (Cpt, γt).

Inlet and Diffuser

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

[pic] (2.16)

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

[pic] (2.17a,b,c)

Compressor and Turbine

The compressor is measured through two type of efficiencies namely, isentropic efficiency and poly-tropic efficiency. The Isentropic efficiency is defined by

[pic] (2.18)

The poly-tropic efficiency is defined as

[pic]

(2.19)

With the assumption of constant ec, we can obtain the relation between τc and πc:

[pic] (2.20)

Going through a similar procedure as the compressor, we obtain turbine isentropic efficiency, turbine poly-tropic efficiency and the relationship between τt and πt as follows:

[pic] (2.21)

[pic] (2.22)

3. TurboFan-Seperate Exhaust Streams with ITB Cycle

Analysis

[pic]

Figure 3.1 – TurboFan with Interstage Turbine Burner (ITB)

Assumptions:

1. Perfect gas upstream of main burner with constant properties γc, Rc, Cpc.

2. Perfect gas between station four and five with constant properties γb, Rb, Cpb.

3. Perfect gas downstream of inter-stage burner with constant properties γt, Rt, Cpt.

4. All components are adiabatic, no heat loss.

5. The efficiencies of the compressor-HPC, compressor-LPC, fan, turbine-HPT, and turbine-LPT are described through the use of polytropic efficiencies eHPC, eLPC, ef, eHPT, and eLPT, respectively.

Fan Stream

Step 1.

Uninstalled thrust of the fan stream Ff is given by

[pic] (3.1)

rearranging gives:

[pic] (3.2)

Step 2.

[pic] (3.3)

Step 3.

[pic] (3.4a)

where

[pic] (3.4b)

Step 4.

[pic] (3.5a)

where

[pic] (3.5b)

Engine Core Stream

Step 1.

Uninstalled thrust

[pic] (3.6)

rearranging gives:

[pic] (3.7)

Step 2.

[pic] (3.8a)

where

[pic] (3.8b)

[pic] (3.8c)

[pic] (3.8d)

[pic] (3.8e)

Step 3.

[pic]multiplied by [pic] (3.9)

rearranging gives:

[pic] (3.10)

Step 4.

Uninstalled thrust for the engine core becomes:

[pic]

(3.11)

Step 5.

[pic] (3.12)

From the total pressure and mach number relation

[pic] (3.13)

[pic] (3.14a)

where

[pic] (3.14b)

[pic] (3.14c)

[pic] (isentropic) (3.14d)

[pic] (isentropic) (3.14e)

[pic] (3.14f)

Step 6.

Applying the First Law of Thermodynamics and ideal gas relation to the main burner, neglecting kinetic and potential energy changes:

[pic] (3.15)

Multiplying the above equation with [pic], and re-arranging gives:

[pic] (3.16)

Solving for fb

[pic] (3.17a)

where

[pic]; [pic] for the case adiabatic (3.17b)

[pic] (3.17c)

Step 7.

Applying the First Law of Thermodynamics and the ideal gas relation to the ITB, neglecting kinetic and potential energy changes:

[pic] (3.18)

Multiplying the above equation with [pic] , and re-arranging gives:

[pic] (3.19)

Solving for fITB

[pic] (3.20a)

where

[pic] ; [pic] for the case adiabatic (3.20b)

[pic] (3.20c)

[pic] (3.20d)

[pic] (3.20e)

Step 8.

Applying the first law to each individual compressor and turbine, neglecting kinetic and potential energy changes:

Power balance for LPC: [pic] (3.21)

Power balance for HPC: [pic] (3.22)

Power balance for HPT: [pic](3.23)

Power balance for LPT: [pic] (3.24)

Power balance for Fan: [pic] (3.25)

It is chosen that the HPT and HPC are connected by a single shaft; therefore for an ideal turbofan the work relation is given by:

[pic] (3.26)

Multiplying both sides by [pic] gives:

[pic] (3.27)

Solving for τHPT:

[pic] (3.28a)

where

[pic] (3.28b)

LPT, LPC, and the fan are connected by a single shaft; therefore for an ideal turbofan, the work relation is given by:

[pic] (3.29)

multiplying both sides by [pic] gives:

[pic] (3.30)

Solving for τLPT:

[pic] (3.31a)

where

[pic] (3.31b)

[pic] (3.31c)

Step 9.

The total uninstalled thrust per unit mass flow rate intake is given by:

[pic] (3.32)

Step 10,

The thrust specific fuel consumption S is give by:

[pic] (3.33)

4. Summary of Equations:

INPUTS: M0, T0, γc, Cpc, γb, Cpb, γt, Cpt, hPR-b, hPR-ITB, πd max, πb, πITB, πn, πfn, eHPC, eLPC, ef, eHPT, eLPT, ηb, ηITB, ηm-HPT, ηm-LPT, P0/P10, P0/P19, Tt4, Tt6, πHPC, πLPC, πf, α

OUTPUTS: [pic]

EQUATIONS:

[pic] (4.1)

[pic] (4.2)

[pic] (4.3) [pic] (4.4)

[pic] (4.5)

[pic] (4.6)

[pic] (4.7)

[pic] (4.8)

[pic] (4.9)

[pic] (4.10)

[pic] (4.11)

[pic] (4.12)

[pic] (4.13)

[pic] (4.14)

[pic] (4.15)

[pic] (4.16)

[pic] (4.17)

[pic] (4.18)

[pic] (4.19)

[pic] (4.20)

[pic] (4.21)

[pic] (4.22)

[pic] (4.23)

[pic] (4.24)

[pic] (4.25)

[pic] (4.26)

[pic] (4.27)

[pic] (4.28)

[pic] (4.29)

[pic] (4.30)

[pic] (4.31)

[pic] (4.32)

[pic] (4.33)

[pic] (4.34)

[pic] (4.35)

[pic] (4.36)

[pic] (4.37)

[pic] (4.38)

[pic] (4.39)

[pic] (4.40)

[pic] (4.41)

[pic] (4.42)

[pic] (4.43)

[pic] (4.44)

5. User’s 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.

Figure 5.1 – Excel Input Sheet Screenshot

Input sheet

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 Input sheet (Combo Box is a list box that displays a list of values and lets the users select one of the values in the list) namely ITB, Units, and Choose a Plot as 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 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.

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 consumption versus 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 for compressor 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.

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

When you choose this option, the program closes the plot sheets and data sheets from the previous use and opens one plot sheet and one data sheet, ST_VS_Mo and DataSTMo or SF_VS_Mo and DataSFMo. You will then be directed from Input sheet to ST_VS_Mo or SF_VS_Mo. This sheet is used to plot specific thrust or thrust specific fuel consumption versus flight condition Mach number with 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 click Calculate to run the program and plot the results. Data computed associated with this sheet will be stored in the DataSTMo sheet.

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

Similar to Flight Condition Mach Number, this option opens ST_VS_PIf and DataSTPIf or SF_VS_PIf and DataSTPIf. It plots specific thrust or thrust 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 Plot combo 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 thrust or thrust specific fuel consumption vs bypass ratio with different fan total pressure ratio, πf. The steps to run the program in this sheet are the same from option two or three of the Choose a Plot combo box.

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

1. Go to the Input sheet

2. Specify the Unit system (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. Click Enter 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 Input sheet, you need to go to the Input sheet.

SF_VS_PIc:

a. Specify number of bypass 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 bypass ratio. If you want to change the input parameters in the Input sheet or in the ST_VS_PIc sheet, you need to go back to one of those sheets and change the input parameters.

ST_VS_Mo, SF_VS_Mo, ST_VS_PIf, and SF_VS_PIf:

a. Specify number of bypass 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 the Input sheet, you need to go to the Input sheet.

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 the Input sheet, you need to go to the Input sheet.

Discussions

The last sheet in the program is the Otape&Test; this is where the user can check a single quantity namely Specific Thrust or Thrust Specific Fuel Consumption. Most of the input parameters are from the Input sheet; 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 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 the plot sheet (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!

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.[pic], SI unit: [pic]) 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 shown below.

Figure 6.1 – Turbofan engine with ITB: Specific thrust vs flight Mach number

Figure 6.2 – Turbofan engine with ITB: Specific thrust vs compressor pressure ratio

Figure 6.3 – Turbofan engine with ITB: Specific thrust vs fan pressure ratio

Figure 6.4 – Turbofan engine with ITB: Specific thrust vs bypass ratio

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 7.1 –Input data for Engine parameters (SI unit) |

|Pressure drop ratio | | | | | |

|main burner total pressure ratio |πb = |0.96 | | |Specific heat at constant pressure |

|ITB - burner total pressure ratio |πIT|0.96 | | |

| |B =| | | |

| |eHPC =|0.9066 | | |region 0 --> 3|

| |ηm-|0.92 | | | | |

| |HPT| | | | | |

| |= | | | | | |

|main-burner |Tt|1785.594 |K |

| |4 | | |

| |= | | |

|Figure 7.2 - TSFC vs flight M0 | | | |

| | | | | | | |

|Mo = |0 |To |3 | |α1 = |0.5 |

|πHPC = |25 | | | | | |

|πLPC = |1.3 | | | | | |

|πf = |1.3 | | | | | |

Figure 7.1 – Turbofan engine: Specific thrust vs flight Mach number

Figure 7.2 – Turbofan engine: thrust specific fuel consumption vs flight Mach

number

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 ratio | |

| | |Scalec = |19.23 | | |

|πLPC = |1.01 |πc = |19.62 |to |50 |

|πHPC = |19.42 |Δ πc = |1 | | |

|πf = |1.3 |α1 = |0.5 | | |

|Μο ’ |0.9 |α2 = |2 | | |

Figure 7.3 – Turbofan engine: Specific thrust vs compressor pressure ratio

Figure 7.4 – Turbofan engine: thrust specific fuel consumption

vs compressor pressure ratio

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

Table 7.4 - The input data for Option 3:

|Figure 7.6 - Specific thrust vs fan pressure ratio |

|Figure 7.7 - TSFC vs fan pressure ratio | |

| | | | | |

|πf = |1.01 |To |10 | |

|Δ πf = |0.25 | | | |

| | | |α1 = |3 |

|πHPC = |25 | |α2 = |5 |

|πLPC = |1.3 | |α3 = |10 |

|Μο ’ |0.9 | | | |

| | | | | |

Figure 7.6 – Turbofan engine: Specific thrust vs fan pressure ratio

Figure 7.7 – Turbofan engine: thrust specific fuel consumption

vs fan pressure ratio

Table 7.5 - The input data for Option 4:

|Figure 7.8 - Specific thrust vs bypass ratio |

|Figure 7.9 - TSFC vs bypass ratio | |

| | | | |

|α = |0 |To |10 |

|Δ α = |0.1 | | |

| | | | |

|πHPC = |25 |πf1 = |1.5 |

|πLPC = |1.3 |πf2 = |3.5 |

|Μο ’ |0.9 | | |

Figure 7.8 – Turbofan engine: Specific thrust vs bypass ratio

Figure 7.9 – Turbofan engine: thrust specific fuel consumption

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 Propulsion’ by 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 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.

Appendix

A - MACRO VISUAL BASIC CODE in MS EXCEL

|VB code |variable | |VB code |variable | |VB code |variable |

|a0 |a0 | |gamab |γb | |T10_T0 |T10/T0 |

|alpha |α | |gamac |γc | |T19_T0 |T19/T0 |

|Cpb |Cpb | |gamat |γt | |tau_alp_itb |τλ-b |

|Cpc |Cpc | |hPRb |hPR-b | |tau_alp_itb |τλ-ITB |

|Cpt |Cpt | |hPRitb |hPR-ITB | |tau_b |τb |

|ef |ef | |M10 |M10 | |tau_c |τc |

|eff_hpc |ηHPC | |M19 |M19 | |tau_f |τf |

|eff_hpt |ηHPT | |pi_d |πd | |tau_hpc |τHPC |

|eff_lpc |ηLPC | |pi_f |πf | |tau_hpt |τHPT |

|eff_lpt |ηLPT | |pi_hpc |πHPC | |tau_itb |τITB |

|eff_r |ηr | |pi_hpt |πHPT | |tau_lpc |τLPC |

|effm_hpt |ηm-HPT | |pi_lpc |πLPC | |tau_lpt |τLPT |

|effm_lpt |ηm-LPT | |pi_lpt |πLPT | |tau_r |τr |

|ehpc |eHPC | |pi_r |πr | |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

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"

Msg5 = "Division by zero ==> Refer to equation 16"

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

Msg7 = "Division by zero ==> Refer to equation 20"

Msg8 = "Square root of a negative quantity ==> Refer to equation 34"

Msg9 = "Square root of a negative quantity ==> Refer to equation 37"

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

response = MsgBox(Msg2, Style, Title)

Msg2 = "Occurs at " & "PIc,PIf,Mo,ByPass = " & pi_hpc * pi_lpc & "," & pi_f & "," & M0 & "," & alpha

response = MsgBox(Msg2, Sytle, Title)

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

response = MsgBox(Msg3, Sytle, Title)

Msg3 = "Occurs at " & "PIc,PIf,Mo,ByPass = " & pi_hpc * pi_lpc & "," & pi_f & "," & M0 & "," & alpha

response = MsgBox(Msg3, Style, Title)

jump = MsgBox(Msg, Style1, Title)

GoTo 10

End If

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

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

If M0 >Error: iM0 >= fM0 !!'

go to 2

endif

c

write(*,*) 'Delta M0 (dM0):'

read (*,*) dM0

write(*,*) 'HPC Pressure Ratio (pihpc):'

read (*,*) pihpc

write(*,*) 'LPC Pressure Ratio (pilpc):'

read (*,*) pilpc

write(*,*) 'Fan Pressure Ratio (pif):'

read (*,*) pif

endif

c

c +++ Plot 2

c

if (plot.eq.2) then

write(*,*) 'LPC Pressure Ratio (pilpc):'

read (*,*) pilpc

write(*,*) 'Constant between LPC & HPC (scalec):'

write(*,*) ' i.e. HPC = scalec*LPC'

read (*,*) scalec

c

pihpc = scalec*pilpc

ipic = scalec*pilpc*pilpc

write(*,'(a6,f6.2)') ' HPC =',pihpc

write(*,'(a21,f6.2)') ' Initial pic (ipic) =',ipic

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

read (*,*) fpic

c

if (fpic.le.ipic) then

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

go to 3

endif

c

write(*,*) 'Delta pic (dpic):'

read (*,*) dpic

write(*,*) 'Fan Pressure Ratio (pif):'

read (*,*) pif

write(*,*) 'Mach Number (M0):'

read (*,*) M0

endif

c

c +++ Plot 3

c

if (plot.eq.3) then

4 write(*,*) 'Initial pif (ipif):'

read (*,*) ipif

c

if (ipif.le.1.0) then

write(*,*)'>>Error: "ipif" has to be greater than 1.0'

go to 4

endif

c

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

read (*,*) fpif

c

if (fpif.le.ipif) then

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

go to 5

endif

c

write(*,*) 'Delta pif (dpif):'

read (*,*) dpif

write(*,*) 'HPC Pressure Ratio (pihpc):'

read (*,*) pihpc

write(*,*) 'LPC Pressure Ratio (pilpc):'

read (*,*) pilpc

write(*,*) 'Mach number (M0):'

read (*,*) M0

endif

c

c +++ Plot 4

c

if (plot.eq.4) then

write(*,*) 'Initial alpha (ialp):'

read (*,*) ialp

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

read (*,*) falp

c

if (falp.le.ialp) then

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

go to 6

endif

c

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

read (*,*) dalp

write(*,*) 'HPC Pressure Ratio (pihpc):'

read (*,*) pihpc

write(*,*) 'LPC Pressure Ratio (pilpc):'

read (*,*) pilpc

write(*,*) 'Mach number (M0):'

read (*,*) M0

write(*,*)

write(*,*) 'Plot at different fan pres. ratio (pif)'

write(*,*) '---------------------------------------'

write(*,*) 'Number of pif (npif):'

read (*,*) npif

write(*,*) 'Please input',npif,' pif(s):'

do 7 i=1,npif

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

read (*,*) pi_f(i)

7 continue

endif

c

if (plot.le.3) then

write(*,*)

write(*,*) 'Plot at different bypass ratio (alpha)'

write(*,*) '--------------------------------------'

write(*,*) 'Number of alpha (nalpha):'

read (*,*) nalpha

write(*,*) 'Please input',nalpha,' alpha(s):'

do 8 i=1,nalpha

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

read (*,*) alp(i)

8 continue

endif

c

return

end

c

*deck start

subroutine start

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

c

c START performs initialization for 'itb' run.

c

c START is the first subroutine called by the driver.

c

c START is called by: itb

c

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

c

include 'comitb.i'

logical present

c

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

c

open(unit=3,file='check')

c +++

c +++ ensure that 'input' file exists

c +++

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

if(.not.present) then

write(*,300)

write(3,300)

call exit(0)

endif

c

open(unit=1,file='input')

read (1,301) name

write(3,301) name

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

301 format(a80)

return

end

Variable initialization: comitb.i

*deck comitb

c

c implicit double precision (a-h,o-z)

parameter (na=10,ncomp=1000)

c na = maximum number of different alpha values

c

REAL M0,iM0,M10,M19,num,ipic,ialp,ipif,itbsw

CHARACTER *80 name

c

common /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

c

common /outputs/ f,st,tsfc

c

common /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

c

common /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

c

common /chardat/ name

c

Input data file: input

/062302/ ITB

unitsys 0.0

itbsw 1.0

T0 390.0

gamac 1.39999

cpc 0.239

gamab 1.27284

cpb 0.277

gamat 1.27882

cpt 0.274

hprb 18400.0

hpritb 18400.0

pidmax 0.99

pib 0.96

piitb 0.96

pin 0.99

pifn 1.3

ehpc 0.9066

elpc 0.9036

ef 0.8961

ehpt 0.9029

elpt 0.9174

effb 0.999

effitb 0.999

effmhpt 0.92

effmlpt 0.93

p0op10 0.9

p0op19 0.9

Tt4 3214.07

Tt6 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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