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)
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)
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
Across-sectional area
asound speed
CPspecific heat at constant pressure
Ddrag force
epolytropic efficiency
Fforce uninstalled thrust
ffuel/air ratio
gcNewton’s constant
henthalpy
hPRlow heating value of fuel
Mmach number
mass flow rate
Ppressure
Pttotal pressure
rate of thermal energy released or absorbed
Runiversal gas constant
Suninstalled thrust specific fuel consumption
Ttemperature or installed thrust
TSFCinstalled specific fuel consumption
Tttotal temperature
Vabsolute velocity
power
αbypass ratio
γratio of specific heats,
mechanical Efficiency
ηOoverall Efficiency
ηPpropulsive Efficiency
ηTthermal Efficiency
πratio of totalpressure
πr(exception) ratio between total pressure and static pressure due to the ram effect,
τratio of total temperature
r(exception) ratio between total temperature and static temperature due to the ram effect,
τλratio between total enthalpy and enthalpy at ambient condition
SUBSCRIPTS
bmain burner or properties between main burner exit and ITB
cproperties between upstream and main burner or engine core
ddiffuser
eexit
ffan
fnfan-nozzle
HPChigh pressure compressor
HPThigh pressure turbine
ITBinterstage turbine combustors
LPClow pressure compressor
LPTlow pressure turbine
Oinlet
nnozzle
rram
tproperties between ITB exit and downstream or total/stagnation values of properties (i.e. temperature, pressure or enthalpy)
1
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 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 , 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 thrustF of a jet engine (single inlet and single exhaust) is given by
(2.1)
where are mass flow rates of air and fuel respectively
are velocities at inlet and exit respectively
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
(2.2)
The installed thrustT is given by
(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
(2.4)
(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).
(2.6)
where,
The propulsive efficiency defines the ratio between the engine power output and the power being used to run the aircraft.
(2.7)
where,
An overall performance of a propulsion system is given by the combination between thermal and propulsive efficiencies.
(2.8)
where,
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 temperatureTtis 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:
(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:
(2.10)
where,
1
Stagnation pressure or total 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
(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, HPTfor high pressure turbine, n for nozzle, and f for fan.
For example:
Exceptions
For the free stream, ram, we define τras aratio oftotal temperature/static temperature and πr as a ratio of total pressure/static pressure.
(2.12)
(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.
(2.14)
(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:
(2.16)
From the Military Specification 5008B (Ref. 2), the following relation is obtained:
(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
(2.18)
The poly-tropic efficiency is defined as
(2.19)
With the assumption of constant ec,we can obtain the relation between τc and πc:
(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:
(2.21)
(2.22)
3. TurboFan-Seperate Exhaust Streams with ITB Cycle
Analysis
Figure 3.1 – TurboFan with Interstage Turbine Burner (ITB)
Assumptions:
- Perfect gas upstream of main burner with constant properties γc, Rc, Cpc.
- Perfect gas between station four and five with constant properties γb, Rb, Cpb.
- Perfect gas downstream of inter-stage burner with constant properties γt, Rt, Cpt.
- All components are adiabatic, no heat loss.
- 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
(3.1)
rearranging gives:
(3.2)
Step 2.
(3.3)
Step 3.
(3.4a)
where
(3.4b)
Step 4.
(3.5a)
where
(3.5b)
Engine Core Stream
Step 1.
Uninstalled thrust
(3.6)
rearranging gives:
(3.7)
Step 2.
(3.8a)
where
(3.8b)
(3.8c)
(3.8d)
(3.8e)
Step 3.
multiplied by (3.9)
rearranging gives:
(3.10)
Step 4.
Uninstalled thrust for the engine core becomes:
(3.11)
Step 5.
(3.12)
From the total pressure and mach number relation
(3.13)
(3.14a)
where
(3.14b)
(3.14c)
(isentropic) (3.14d)
(isentropic)(3.14e)
(3.14f)
Step 6.
Applying the First Law of Thermodynamics and ideal gas relation to the main burner, neglecting kinetic and potential energy changes:
(3.15)
Multiplying the above equation with , and re-arranging gives:
(3.16)
Solving for fb
(3.17a)
where
; for the case adiabatic (3.17b)
(3.17c)
Step 7.
Applying the First Law of Thermodynamics and the ideal gas relation to the ITB, neglecting kinetic and potential energy changes:
(3.18)
Multiplying the above equation with , and re-arranging gives:
(3.19)
Solving for fITB
(3.20a)
where
; for the case adiabatic (3.20b)
(3.20c)
(3.20d)
(3.20e)
Step 8.
Applying the first law to each individual compressor and turbine, neglecting kinetic and potential energy changes:
Power balance for LPC:(3.21)
Power balance for HPC:(3.22)
Power balance for HPT:(3.23)
Power balance for LPT:(3.24)
Power balance for Fan:(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:
(3.26)
Multiplying both sides by gives:
(3.27)
Solving for τHPT:
(3.28a)
where
(3.28b)
LPT, LPC, and the fan are connected by a single shaft; therefore for an ideal turbofan, the work relation is given by:
(3.29)
multiplying both sides by gives:
(3.30)
Solving for τLPT:
(3.31a)
where
(3.31b)
(3.31c)
Step 9.
The total uninstalled thrust per unit mass flow rate intake is given by:
(3.32)
Step 10,
The thrust specific fuel consumption S is give by:
(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:
EQUATIONS:
(4.1)
(4.2)
(4.3) (4.4)
(4.5)
(4.6)
(4.7)
(4.8)
(4.9)
(4.10)
(4.11)
(4.12)
(4.13)
(4.14)
(4.15)
(4.16)
(4.17)
(4.18)
(4.19)
(4.20)
(4.21)
(4.22)
(4.23)
(4.24)
(4.25)
(4.26)
(4.27)
(4.28)
(4.29)
(4.30)
(4.31)
(4.32)
(4.33)
(4.34)
(4.35)
(4.36)
(4.37)
(4.38)
(4.39)
(4.40)
(4.41)
(4.42)
(4.43)
(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.