Thermodynamic Analysis and Performance Characteristics of a Turbofan Jet Engine

AEROSPACE ENGINEERING

SCHOOL OF MECHANICAL ENGINEERING AND DESIGN

THE THERMODYNAMIC ANALYSIS AND PERFORMANCE CHARACTRISTICS OF A TURBOFAN JET ENGINE

By J. E, Ibok
2011
Supervisor: Dr Lionel Ganippa

ABSTRACT
This work focuses on the performance analysis of a twin spool mixed flow turbofan engine. The main objective was to investigate the effects of using hydrogen, kerosene and natural gas fuel on the performance characteristics such as net thrust, specific fuel consumption and propulsive efficiency of the turbofan. Another aim of this work was to introduce the concept of exergy and thermoeconomics analysis for twin spool mixed flow turbofan engine and show the components that contributes the most to the inefficiency of the engine. A generic simulation was carried out using Gas Turb 11 software to obtain reasonable analysis results that were verified with a real-time JT8D-15A turbofan engine. The parametric analysis was done for constant value of mass flow rate of fuel and constant turbine inlet temperature for all three fuels. The result were rightfully obtained for these analysis cases and discussed accordingly.

Brunel University
Mechanical Engineering Academic Session: 2010/2011 Name of Student: Johnson Essien Ibok Supervisor: Dr Lionel Ganippa
Title: The Performance Characteristics and Thermodynamics Exergy and Thermoeconomics analysis of a Twin Spool Mixed Flow Turbofan Engine Operating at 30,000ft at M0 0.8 using Kerosene, natural Gas and Hydrogen Fuel.
Abstract: This work focuses on the performance analysis of a twin spool mixed flow turbofan engine. A generic simulation was carried out using Gas Turb 11 software to obtain reasonable analysis results that were verified with a real-time JT8D-15A turbofan engine. The parametric analysis was done for constant value of mass flow rate of fuel and constant turbine inlet temperature for all three fuels. The result were rightfully obtained for these analysis cases and discussed accordingly.
Objectives: The main aim of this work is to conduct the parametric cycle simulation of a twin spool mixed flow turbofan engine and investigate the performance characteristics of it. Another aim of this work is to show the effects of using hydrogen, Kerosene and natural gas fuel on the overall performance of the twin spool mixed flow turbofan engine. Also, the purpose of this work is to introduce the use of the second law of thermodynamics analysis known as exergy and thermoeconomics in analysis the twin spool mixed flow turbofan engine
Background/Applications: This work is applicable in so many ways when it comes to the overall performance optimization and feasibility analysis of a jet engine. This work relates to the aerospace and aviation industries since the turbofan engine is amongst the vast number of jet engine used in propulsion of aircrafts. There is increasing pressure in the aviation industry to reduce pollution and depletion of energy resources while at the same time maintaining reasonable investment cost and high overall performance. Hence, this research was conducted in hopes of coming up with a new solution to this problem.
Conclusions: The main conclusion drawn from the performance analysis is that hydrogen fuel produced the highest thrust level and the lowest specific fuel consumption between the three fuels for a constant mass flow rate of fuel. Kerosene fuel generated thrust level can be increased if it is mixed with a small amount of hydrogen. The Exit jet velocity ratio remained constant despite the increasing bypass ratio for all three fuels at constant mass flow rate of fuel. Using the exergetic analysis showed that the combustion chamber and the mixer contributed the most to the inefficiency of the turbofan engine. The amount of exergy transferred into the turbofan engine by hydrogen was depleted in the smallest ratio compared to natural gas and kerosene for constant mass flow rate of fuel. The thermoeconomics analysis showed that it is preferable to use local based cost evaluation to quantity specific thermoeconomics cost of thrust than the global method since the value was lower.
Results: The results obtained from the simulation using Gas Turb 11 produced an error range of 0.25% - 8.5% when verified with the actual test data of the JT8D-15A turbofan engine. The results obtained for the analysis defined a reference design point at which the parametric analysis was conducted on. The analysis was done in three cases as shown clearly in the test matrix in table 1 below. Analysis | Parameters being varied | Parameters Kept Constant | Performance Characteristics | case 1 | * Bypass ratio * Turbine Inlet temperature | * HPC Pressure Ratio * LPC Pressure Ratio * Fan Pressure Ratio | * Velocity ratio * Fuel-Air-ratio * Turbine inlet temperature * Net thrust * Specific Fuel Consumption * Thermal efficiency * Propulsive efficiency | case 2 | * Bypass Ratio * Three different fuelsmH2mCH4mC12H23 | * Mass flow rate of fuel * HPC Pressure Ratio * LPC Pressure Ratio * Fan Pressure Ratio | | Case 3 | * Bypass Ratio * Three different fuelsmH2mCH4mC12H23 | * Turbine inlet temperature * HPC Pressure Ratio * LPC Pressure Ratio * Fan Pressure Ratio | |
Table 1 The Test matrix of the Parametric Analysis.
The exergy analysis was done for the parametric analysis of case 2 and case 3 where the exergy destruction rates, exergetic efficiency, exergy improvement potential rate and fuel depletion ratio were calculated. The distribution of these results throughout each component of the turbofan engine was represented with bar charts and Grassmann diagram. The thermoeconomics analysis was conducted for analysis case 2 using kerosene fuel. The specific thermoeconomics cost of thrust was calculated using global and local based cost evaluation methods.
ACKNOWLEDGEMENTS
First of all, I would like to thank my parents for their financial support and encouragement because without them I would not be here and be able to do this work. I am deeply thankful to my supervisor, Dr Lionel Ganippa for believing in me and giving me the opportunity to work with him in this field of study. I am also thankful to him for giving the necessary guidance and advice and his enthusiasm and innovative ideas inspired me. Finally, I would like to thank Mr Joachim Kurzke for providing me with the necessary software needed for my dissertation.

Table of Contents
Acknowledgements i
Contents ii
List of Notations and Subscripts iv
List of Tables vi
List of Figures vi
Chapter 1: Introduction1 1.1. Aims and Objectives2 1.2. Computational Modeling3
Chapter 2: Jet Engines4
2.1. Performance characteristics4 2.1.1. Thrust4 2.1.2. Thermal Efficiency5 2.1.3. Propulsive efficiency5 2.1.4. Overall efficiency6 2.1.5. Specific Fuel Consumption6 2.2. Fuel and Propellants For Jet Engines7
Chapter 3: Turbofan Jet Engines ……………………………………………………………...…8 3.1. Introduction 8 3.2. Classification of Turbofan Engines9 3.3. Major Components of a Turbofan Engine10 3.3.1. Diffuser10 3.3.2. Fan and Compressor11 3.3.3. Combustion Chamber12 3.3.4. Turbine13 3.3.5. Exhaust Nozzle14 3.4. Thermodynamic Process and Cycle of a Twin Spool Mixed Flow Turbofan Engine15
Chapter 4: Mathematical and Gas turb 11 Modeling of the turbofan Engine18 4.1. Station Numbering and Assumptions18 4.2. Design Point Cycle Simulation of the Turbofan Engine18 4.3. Off-design Point Cycle Simulation of the Turbofan Engine21 4.3.1. Module/Component Matching 22 4.3.2. Off-Design Point Component Modeling22
Chapter 5: Methodology, Results and Discussions26 5.1. General Relationship equations of the Major Parameters27 5.2. Results and Discussions of Parametric cycle Analysis of Case 129 5.3. Results and Discussions of Parametric Cycle Analysis of Case 235 5.4. Results and Discussions of Parametric Cycle Analysis of Case 343
Chapter 6: Exergy and Thermoeconomics Analysis of the Turbofan Engine49 6.1. Exergy Analysis49 6.1.1. Exergy Analysis Modeling 50 6.1.2. Exergy and Energy Balance Equations of the Components58 6.1.3. General Relationships in Exergetic Analysis of the Turbofan Engine60 6.1.4. Results and Discussions61 6.1.5. Grassmann Diagram72 6.2. Thermoeconomics Analysis74 6.2.1. Thermoeconomics Analysis Modelling74 6.2.2. Global Based Cost Evaluation76 6.2.3. Local Based Cost Evaluation77 6.2.4. Results and Discussion of the Thermoeconomics Analysis78
Chapter 7 Conclusions and Future Work80
Reference
Appendix A
Exergy Analysis Results
Appendix B
Thermoeconomics Analysis results

List of Notations and Units η | Isentropic efficiency | π | Total Pressure ratio | m | Mass Flow Rate (kg/s) | f | Fuel/Air Ratio | M | Mach Number | Pt | Total pressure (kPa) | Tt | Total Temperature (K) | NCV | Net Calorific Value (MJ/kg) | Ht | Total Enthalpy (kJ/kg) | V | Velocity (m/s) | α | Bypass Ratio | T | Static Temperature (K) | P | Static Pressure (kPa) | N | Actual Spool Speed (RPM) | Nc | Corrected Spool Speed (RPM) | mc | Corrected Mass Flow Rate (kg/s) | R | Universal Gas Constant (kJ/kmolK) | ε0 | Standard Chemical Exergy (kJ/kmol) | Ex | Exergy Rate (MW) | xi | Mole Fraction | cp | Specific Heat at Constant Pressure (kJ/kgK) | φ | Ratio of Chemical Exergy to NCV | ε | Exergetic Efficiency | δ | Fuel Depletion Ratio | W | Power Rate of Work done (MW) | List of Subscripts | | LPT | Low Pressure Turbine | HPT | High Pressure Turbine | CC | Combustion Chamber | HPC | High Pressure Compressor | LPC | Low Pressure Compressor | d | Diffuser | noz | Nozzle | mix | Mixer | dest | Destruction Rate | 0, ambFAR | Ambient conditionFuel-Air-Ratio | CH | Chemical | PH | Physical | KN | Kinetic | PN | Potential | IP | Exergy Improvement Potential Rate (MW) | CRF | Cost Recovery Factor | c | Specific Thermoeconomic Cost (MJ/kg) | STD | Standard Temperature and Pressure | TIT | Turbine Inlet Temperature | TSFC | Thrust Specific Fuel Consumption (g/kNs) | SFC | Specific Fuel Consumption | p | Propulsive | TH | Thermal | O | Overall | T | Thrust | equip | Equipment | PEC | Capital Cost of Equipment |

List of Tables
Table 1 input parameters for Design Point Cycle Simulation on Gas Turb 1119
Table 2 Comparison table for the Actual Test Data and Simulated Data using gas Turb 1121
Table 3 Comparison Table for Actual Test Data and Simulated Off-Design Point data Using gas Turb 11. 25
Table 4 Equivalence Ratio of the three Fuels Combustion Processes..............................62
Table 5 Assumed Capital costs of Each Component of the Turbofan Engine. 75
Table 6 Flow of Specific Thermoeconomics Cost in all the Components 79

List of Figures
Figure 1 Classification of Turbofan Engine9
Figure 2 Layout of Forward Fan Twin Spool Mixed Flow Turbofan16
Figure 3 T-S Diagram for the Forward Fan Twin Spool Mixed Flow Turbofan17
Figure 4 Design Point Cycle Simulation Algorithm Using Gas Turb 1120
Figure 5 Example of a Compressor Performance Map/Curve24
Figure 6 Effects of Varying Bypass Ratio at Constant Values of TIT on Fuel-Air-Ratio30
Figure 7 Effects of Varying Bypass Ratio at Constant Values of TIT on Exit Velocity Ratio30
Figure 8 Effects of Varying Bypass Ratio at Constant Values of TIT on LPT Exit Pressure Ratio31
Figure 9 Effects of Varying Bypass Ratio at Constant Values of TIT on Net Thrust32
Figure 10 Effects of Varying Bypass Ratio at Constant Values of TIT on Specific Fuel Consumption33
Figure 11 Effects of Varying Bypass Ratio at Constant Values of TIT on Propulsive Efficiency34
Figure 12 Effects of Varying Bypass Ratio at Constant Values of TIT on Thermal Efficiency35
Figure 13 T-S diagram of using Hydrogen Fuel when the bypass Ratio is increased36
Figure 14 Variation of Fuel-Air-Ratio with Bypass Ratio at Constant Fuel Flow Rate using three different Fuels37
Figure 15 Variation of TIT with Bypass Ratio at Constant Fuel Flow Rate using three different Fuels37
Figure 16 Variation of Exit Velocity Ratio with Bypass Ratio at Constant Fuel Flow Rate using three different Fuels38
Figure 17 Variation of LPT Exit Pressure Ratio with Bypass Ratio at Constant Fuel Flow Rate using three different Fuels39
Figure 18 Variation of Net Thrust with Bypass Ratio at Constant Fuel Flow Rate using three different Fuels40
Figure 19 Variation of Specific Fuel Consumption with Bypass Ratio at Constant Fuel Flow Rate using three different Fuels41
Figure 20 Variation of Thermal Efficiency with Bypass Ratio at Constant Fuel Flow Rate using three different Fuels42
Figure 21 Variation of Propulsive Efficiency with Bypass Ratio at Constant Fuel Flow Rate using three different Fuels43
Figure 22 Variation of Fuel-Air-Ratio with Bypass Ratio at Constant TIT using the three Different Fuels44
Figure 23 Variation of Exit Velocity Ratio with Bypass Ratio at Constant TIT using the three Different Fuels44
Figure 24 Variation of LPT Exit Pressure Ratio with Bypass Ratio at Constant TIT using the three Different Fuels45
Figure 25 Variation of Net Thrust with Bypass Ratio at Constant TIT using the three Different Fuels46
Figure 26 Variation of Specific Fuel Consumption with Bypass Ratio at Constant TIT using the three Different Fuels46
Figure 27 Variation of Propulsive Efficiency with Bypass Ratio at Constant TIT using the three Different Fuels47
Figure 28 Variation of Thermal Efficiency with Bypass Ratio at Constant TIT using the three Different Fuels48
Figure 29 Variation of Exergy Destruction Rate Using the three Fuels for Analysis Case 262
Figure 30 Variation of Exergy Destruction Rate Using the three Fuels for Analysis Case 364
Figure 31 Variation of Exergetic Efficiencies Using the three Fuels for Analysis Case 266
Figure 32 Variation of Exergetic Efficiencies Using the three Fuels for Analysis Case 367
Figure 33 Distribution of Exergy Improvement potential Rate Using the three Fuels for Analysis Case 268
Figure 34 Distribution of Exergy Improvement potential Rate Using the three Fuels for Analysis Case 369
Figure 35 variation of Fuel Depletion ratio using the Three Fuels for Analysis Case 270
Figure 36 variation of Fuel Depletion ratio using the Three Fuels for Analysis Case 371
Figure 37 Grassmann Diagram for the Exergetic analysis of Case 2 using kerosene Fuel for the Turbofan engine.72

Chapter 1

Introduction Jet engines are complex thermodynamic systems that use a series of non-linear equation to define their thermodynamic processes and they operate under the principle of Brayton cycle. Brayton cycle is a cycle that comprises of the compressor, combustor and turbine working as a unit. Additionally, the major parameters that dictate the operational conditions of the engine at any point during the process are the relative altitude and Mach number. Mach number is the ratio of the velocity of the jet engine to the speed of sound. Basically, the main purpose of this type of thermodynamic system in aerospace industry is to accelerate a jet of air and as a result, generate enough thrust needed for flight. In addition, the design of jet engines is dependent of what purpose it will be used for in order to derive its maximum performance. For instance, in military application, jet engines are required to generate maximum thrust in minimum response time which consumes a lot of fuel whereas commercial jet engines are required to less noise generative, less fuel consuming and at the same time have high overall efficiency (El-sayed, 2008). There are certain factors that jet engine manufacturers take into consideration when designing jet engines which are the operating cost, engine noise, environmental emissions, fuel burn and overall efficiency. Accordingly, this has caused a global market competition for engine manufacturers like Rolls Royce, Pratt and Whitney, General Electric and CFM on who can produce the most efficient jet engines. In fact, Pratt and Whitney Company is working on a geared turbofan jet engine that they believe will reduce fuel burn, produce lesser noise and emit less toxics while General Electric is coming up with simpler “ecore” jet engines that will be more fuel efficient than the current jet engines with as much as almost two fifths of current jet engines (Cassidy, 2008). Taking all that has been said into consideration, it can easily be asserted that by reducing the fuel consumption of the jet engine, the total temperature at the turbine blades will reduce thereby increasing the operating life and overall efficiency of the engine. Also, the total cost of the engine can be cut down. Indeed, Dr Pallan cited in (Ward, 2007) stated that reducing the fuel consumption by as little as 1% is highly longed after by engine manufacturers and this can result in very significant increase in the overall performance. In a general point of view, it can be said that the maximum point of achievement for jet engine manufacturers would be to design an engine that consumes the minimum amount of work in the compressor unit while generating the maximum amount of work in the turbine unit at minimum fuel supply. The main purpose of this work is to analyse the thermodynamic processes and performance of a jet engine using a simulation tool, exergy and thermoeconomics concept.

1.1. Aims and Objectives The main objective of this work is to carry out the thermodynamic analysis and show the performance characteristics of a turbofan jet engine. In this work, the vivid explanation of the thermodynamics processes and cycle of each component of the turbofan engine starting from the diffuser to the nozzle will be covered. Also, the first and second law of thermodynamics with other laws will be applied extensively throughout this work. However, in the aspect of performance characteristics of the turbofan engine, a generic simulation will be carried out on a twin spool mixed flow turbofan engine. To relate this work to real life application, a JT8D-15A turbofan engine manufactured by Pratt and Whitney Company will be used as the twin spool mixed flow turbofan for the simulation using the original design data. Indeed, the simulation tool that will be used is GasTurb 11 which was designed by Joachim Kurke and for more details on how it works can be found in (Kurke, 2007). This work will use the reference design point of the twin spool mixed flow turbofan at sea level with maximum take-off thrust to obtain the operating point of 30,000ft at M0 0.8 using the off-design performance simulation which will serve as the operating design point for the analysis in this work since the engine will spend most of its time in the cruise phase between 30000ft to 38000ft. The purpose of carrying this generic simulation of the turbofan engine is to investigate the effects of varying bypass ratio and turbine inlet temperature (thermal limit parameter) on the performance characteristics of the turbofan engine. In other words, the parametric cycle studies of the turbofan engine. This investigation will be done for three different cases which case 1 will be studying the effects of varying bypass ratio and turbine inlet temperature on the performance characteristics of the turbofan engine when some of the design choices are kept constant. The second case of study will be the comparison of the performance characteristics of the turbofan engine when three different fuels (kerosene, natural gas and Hydrogen) are used at the same mass flow rate using the same design point in case 1. Finally, the third case of study will be the comparison of the performance characteristics of the turbofan engine when the three fuels are undergoing the same combustion process that is constant turbine inlet temperature for the design point in case 1. This aspect of this analysis is very important owing to the growing problem of greenhouse effect and depletion of energy resources. In fact, statistics by the intergovernmental panel shows that aerospace industry is amongst one of the fast growing sources of greenhouse effect and that the emission of carbon dioxide will increase to five times what it is presently which is 3% (Symonds, 2005). Based on this, using alternative fuels like hydrogen and natural gas can tend to reduce pollution and consumption of energy resources risk and this work aims to show how that can be achieved while the overall efficiency of the engine is still high. Another approach of analysis in this work will be the use of the second law of thermodynamics analysis also known as exergy and thermoeconomics. This aspect of analysis of the turbofan engine will be done for the parametric analysis of case 2 and case 3 in efforts to also compare the three fuels that are being considered and show which fuel will cause the turbofan engine components to be most inefficient or have the most irreversibility. This analysis will be done by calculating the exergy relationships such as exergy transfer rates, exergy destruction rates, exergetic efficiencies, exergy improvement potential rates, and fuel depletion ratios. Furthermore, the exergy analysis will be represented in a Grassmann diagram for parametric analysis case 2 of study. However, as for the thermoeconomics analysis of the turbofan engine, only parametric analysis case 3 studies will be done for only kerosene fuel and this work will aim to show how to use concept of local and global evaluation of thermoeconomic cost.

1.2. Computational Modelling It will be very expensive and time wasting to design and develop new aircraft engine whenever an optimization or analysis wants to be done. In fact, Caoa Y, Jin, Meng and Fletcher (2005) stated that new ways should be developed to reduce aircraft engine design, maintenance and manufacturing cost in order to have effective worldwide market competition. Surprisingly, computer modelling is one approach of reducing manufacturing cost and time wasting. Computational modelling can simply be defined as the use of computer codes to replicate a typical system using some of its original data in order to analyse the system at varying conditions. The other side of the medallion shows simulation. There are many types of simulation tools normally used in simulating gas turbines such as Matlab/simulink, Modelica, Gas Turb 11, NPSS and many more. However, the simulation tool that will be adopted for the purpose of this dissertation is Gas Turb 11 designed by Joachim Kurzke. Gas Turb 11 is a language oriented program with a command prompt that calculates the output data without using block diagrams or graphical interface. It is user friendly in a sense that it is easy to find the tools library and to substitute data in for simulation. The Gas Turb 11 is specifically designed for simulation of all kinds of gas turbines starting from power generators to jet engines. Gas Turb 11 usually carries out two types of analysis which are the on design cycle point simulation and off-design cycle point simulation. Engine design point cycle simulation involves the study of comparing gas turbines of different geometry. This cycle design point must be defined before any other simulation can be done. On the other hand, off-design performance cycle point simulation involves the study of the behaviour of a gas turbine with known geometry. This cycle outlines the performance characteristics of each component such as performance maps, Overall efficiency. The type of simulation that will be done in this dissertation will involve the off-design and design point cycle.
Chapter 2

Jet Engines

2.1. Performance Parameter of Jet Engines 2.2.1. Thrust Thrust is the way of quantifying the ability of a jet engine to effectively utilise the energy added to it in order to propel or push itself forward in the opposite direction of the exiting jet in the exhaust nozzle. In other words, it is the reactive force to the force imparted by the exiting jet in the nozzle in accordance to Isaac Newton’s third law of motion. It is the most important parameter that has to be obtained for any jet engine and it depends heavily on the ingested mass of air, exiting velocity and pressure, the area of the nozzle, the flight velocity and ambient conditions. In fact, the mathematical expression for thrust which incorporates these factors is shown below as.
Thrust=meVe-m0V0+Pe-P0Ae
Where, e=the exit conditions at the exhaust nozzle, 0=ambient conditions at the inlet me=m0+mfuel Momentum Thrust=meVe; This is the thrust obtained from the reaction of the hot exhaust gases high velocity.
Momentum Drag= m0V0 ; This the friction or drag force caused by the high velocity ingestion of air mass at the inlet.
Pressure Thrust=Pe-P0Ae; This force is generated as a result of the higher exit static pressure compared to the ambient pressure which pushes back at the engine.
Gross Thrust=meVe+Pe-P0Ae; It is the maximum obtainable positive thrust a jet engine can have when the drag forces are ignored.
Special Cases of Thrust
Take-off Thrust It is the thrust a jet engine can generate with its own power at static or low power setting which means the momentum drag component of thrust is ignored and the power of the engine at this point is equivalent to zero. This can be used to explain why the thrust of an engine at take-off condition is usually higher than at cruise condition since there is no momentum drag and effects of varying ambient condition. This only applies to turbojet, turbofan, and turboprop jet engines but when it comes to ramjet and scramjet, the air flow has to be accelerated by a booster system before it can start producing a positive take-off thrust.
Pressure Thrust Component This is the thrust generated as a result of the static pressures of the exiting jet and ambient environment. In ideal cases where the nozzle has perfectly expanded the jet exit pressure to that of the ambient condition, the pressure thrust component will disappear which this case is not possible in reality. However, if the nozzle is choked which indicates that the ambient pressure is lower than the exit pressure of the jet, the pressure thrust component will have a positive effect on the net thrust. Also, if the nozzle tends to over expand the jet because of low energy addition to the jet and the exit pressure is lower than the ambient pressure, the pressure thrust component will have a negative effect on net thrust. 2.2.2. Thermal efficiency It is simply the measure at which energy in the engine system is converted. In other words, it is the measure at which total energy supplied to the engine system as heat transfer is converted to kinetic energy. In another way, it can easily be said to be the ratio of the power generated in the engine airflow to the rate at which energy is supplied in the fuel. ηTH=Power Generated in the Engine AirflowRate of Energy Supplied in the Fuel
=12×meVe2-12×m0V02mfuel×NCV
2.2.3. Propulsive efficiency It is a measure at which kinetic energy possessed by air as it passes through the engine is converted into power of the propulsion of the engine. In mathematical terms, it is simply known as the ratio of thrust power to the power generated in the engine airflow. ηp=Thrust PowerPower Generated in the Engine Airflow
= T×V012×meVe2-12×m0V02

2.2.4. Overall Efficiency As the name overall depicts, it is the resultant efficiency of a jet engine can have which is simply the product of the thermal and propulsive efficiencies. In mathematical terms, it is represented as shown below. ηO=ηTH×ηp =12×meVe2-12×m0V02mfuel×NCV×T×V012×meVe2-12×m0V02
=T×V0mfuel×NCV

2.2.5. Specific Fuel Consumption Specific fuel consumption as any other performance characteristics is a ratio and surprisingly it has a major effect on the economics of the aircraft as it is used to determine the aircrafts flight ticket costs. Specific fuel consumption has different expressions depending on what type of jet engine it is. For instance, in ramjet, turbojet and turbofan jet engines, it is the measure of the fuel mass flow rate to the thrust force generated. Also, it is sometimes called the thrust specific fuel consumption (TSFC).
TSFC=mfT
However, in turbopropeller jet engines, it is the ratio of the fuel mass flow rate to the power generated in the engine shaft by the turbomachinery. It is sometimes referred to as the brake-specific fuel consumption (BSFC).
TFSC=mfSP

2.2. Fuel and Propellants for Jet Engines Fuels can implicitly be defined as substances used to add heat energy to a system through combustion or other processes. Fuels are mostly hydrocarbons like kerosene, diesel, petrol, alcohol, paraffin and butane and can also be in the form of individually free reactive molecular substances like hydrogen or chemical composites like natural gas, coal, wood. The gaseous state substances used as fuels such as hydrogen, and natural gas (94% methane and 6% ethane) are usually made into a cryogenic state as in liquefied at very low temperature because of their low boiling point. It can easily be asserted by anyone that the only purpose that fuels have in jet engines is to add energy but little do they know that the purposes grows as the speed of the aircraft increases. For instance, Kerrebrock (2002) stated that supersonic aircrafts which attains very high stagnation temperature that can create destabilization to the airframe structure, engine component and organic substances like lubricants, uses its fuel as a coolant to this parts or components. The energy added by the fuel burned per unit mass of air flow is called the heating value of the fuel and it is a very crucial parameter to be defined before any combustion process analysis is done on a jet engine since it shows how complete the combustion process is through efficiency. The heating value can either be said to be higher or lower depending on if the water product of combustion is a vapour or a liquid. Since the combustion process in jet engine produces vaporised water, the lower heating value of the fuel is used. The most frequently used fuels for jet engines are kerosene jet A1, A2, JP10 and many more but diesel can also be used. The disadvantages of these fuels are their inevitable emission of toxic substances that contribute to greenhouse effect and their risk of depletion. Accordingly, this has been the driving force for the use of alternative fuels such as cryogenic hydrogen and natural gas which is believed will reduce toxic emissions. Besides, hydrogen is a carbon-free energy carrier and possesses almost no risk of toxic emission since most of its combustion product will be water Chiesa and Laozza (2005).

Chapter 3 Turbofan Jet Engine 3.1. Introduction Between 1936 and the next decade when turbofan engines were invented, people showed little or no interest in them as they described them to be a complicated version of a turbojet engine. However, in 1956, the benefits of turbofan engines started to be noticed as major companies like Rolls-Royce and General Electric began manufacturing them. Since then, it is been one of the most used jet engine for commercial purposes because of its low fuel consumption and less noise production. In fact, it has been concluded to be the most reliable jet engine ever manufactured El –Sayed (2008). The turbofan jet engine gas generator unit comprises of a fan unit, compressor section, combustion chamber and turbine unit. Fundamentally, a turbofan jet engine operates as a result of the compressors pressuring air and supplying it afterwards for further processing. The majority of the pressurised air is bypassed around the core of the engine through a duct to be mixed or exhausted whereas the rest of it flows into the main engine core where it combusts with the fuel in the combustion chamber. The hot expanded gas products from the combustion process passes through the turbine thereby rotating the turbine as it leaves the engine. Consequently, the rotating turbine spins the engine spool which in turn rotates the other turbo machinery in the engine. This causes the front fan to pressurise more and more air into the engine for the process to start all over again in continuous state. The turbofan engine is believed to be the perfect combination of the turboprop and turbojet engine and as a result, its advantages are usually compared to that of the turboprop and turbojet. In fact, Kerrebrock (1992) said that turbofan engine provides a better way of improving the propulsive efficiency of a basic turbojet. It is asserted that at low power setting, low altitude condition and low speed, the turbofan engine is more fuel efficient and has better performance than a turbojet engine. Unlike turboprop engine where vibration occurs in the propeller blades at relative low velocities, the fan in the turbofan engine can attain high relative velocities of Mach 0.9 before vibration occurs. Also, since the fan in turbofan engines has many blades, it is more stable than the single propeller so even if the vibration velocity is reached, the vibration will not destabilize the airflow because the vibrations are almost negligible. Since the flow into the diffuser of the turbofan is usually subsonic, there very slim chances of shock waves being developed at the entrance.

3.2. Classification of Turbofan Engines There are various types of turbofan engine ranging from high and low bypass ratio, afterburning and non-afterburning, mixed and unmixed flow with multi-spool, after fan and geared or ungeared. The classification of the various types of turbofan engines is shown below in figure 1. Nonetheless, the type of turbofan engine that would be used for the purpose of this dissertation is a forward fan two spool mixed flow turbofan engine. This type of turbofan engine was chosen because it is the compromise of a simple and complex turbofan engine. This is said because it comprises of almost all the classes of a turbofan which are low bypass ratio, forward fan with mixed flow, twin spool with ungeared fan. Moreover, because of the mixed flow introduced, it produces additional thrust in the hot nozzle compared to the high bypass and it can also permit the addition of afterburner which produces a lot of thrust while consuming a lot of fuel which makes it suitable for military application which shows little worry on fuel consumption. In essence, carrying out a study on this type of turbofan engine will be of great relevance to the military air force sector especially if new research is discovered.
TURBOFAN ENGINES
Low Bypass Ratio
Aft Fan
Forward Fan
Nonafterburning
Afterburning
High Bypass Ratio
Geared Fan
Single Spool
Short Duct
Ungeared Fan
Two Spool
Mixed Fan and Core Flow
Unmixed Flow
Long Duct
Three Spool
Figure 1 Classification of Turbofan Jet Engines (El-sayed, 2008) 3.3. Major Components of Turbofan Engine 3.4.1. Diffuser or Inlet Diffuser is the first component that air encounters as it flows into the engine. Basically, the purpose of a diffuser is to suck in air smoothly into the engine, reduce the velocity of the air, increase the static pressure of the air and finally, supply the air in a uniform flow to the compressor. Given the fact that overall performance of an engine is highly dependent on the pressure supplied to the burner, it is necessary to design a diffuser that incurs the minimum amount of pressure loss. To demonstrate this, Flack (2005) stated that if the diffuser incurs a large total pressure loss, the total pressure in the burner will be reduced by the compressor total pressure ratio time this loss. In other words, a small pressure drop in the diffuser can translate into a significant drop in the total pressure supplied to the burner. Another point taken into consideration when designing a diffuser is the angle because if the angle is too big, there will be tendency of eddy flow generation due to early separation. The major causes of pressure losses in the diffuser are as follows. First, losses due to generation of shock waves outside the diffuser and it majorly occur in supersonic diffusers. Secondly, the loss due to the unfavourable or adverse pressure gradient of the diffuser geometry which makes the flow separate a lot earlier and generates eddies. This separation causes a convergent area which makes the velocity not to be reduced by much. Due to the separation, the wall shear deteriorates the static pressure even further. Further analysis done by El-Sayed (2008), describes ways of accounting for this losses like using Fanno line flow and combined area and friction.
Thermodynamic Process Equation In this analysis, the loss due to heat transfer is negligible so the process can be adiabatic. The initial kinetic energy is used to raise the static pressure p0 to the total pressure πd=pt2pt0 (inlet pressure recovery) efficiency ηd=IdealReal=ht2s-h0ht2-h0 assuming the gas is ideal and the specific heat at constant pressure is constant efficiency ηd=Tt2s-T0Tt2-T0 simplifying the equation given that ht0=ht2=ht2s and Tt2=Tt0and pt2s=pt2
TtT0=1+γ-12M02 and TtT0=ptp0γ-1γ pt2p0=1+ ηdγ-12M02γγ-1

3.4.2. Fan And Compressors Compressor is a very crucial component for the operation of an engine in the sense that it prepares the air for the combustion process in the burner. The main purpose of a compressor as the first rotating component is to use its rotating blades to add kinetic energy to the air and later translate it into total pressure increase. There are basically two types of compressors which are the centrifugal and the axial compressor. Firstly, centrifugal compressor as the name implies changes the direction of an axial airflow to a radial outflow of the air. It was the early compressors adapted in jet engines. It comprises of three main parts which are the impellers, the diffusers and the compressor manifold. The purpose of the impeller is to change the direction of the flow from axial to radial and at the same time increases its static pressure. The diffuser slows down the airflow and further increase the static pressure as it is supplied axially by the compressor manifold to the combustion chamber. The centrifugal compressor is advantageous because the cost of manufacturing it is low compared to axial compressor and as a result is suitable for small engines like turboshafts and turboprops. It is also advantageous because the pressure ratios at single stage are higher than that of the axial compressor. The centrifugal compressor has the tendency of attaining low flow rates and as a result is ideally suitable for helicopters and small aircrafts which require low flow rates. On the other hand, the centrifugal compressor cannot attain high pressure ratio and so it is not suitable when high peak efficiency is required. It incurs a lot of losses due to the change in direction. Secondly, an axial compressor is the most reliable type of compressor and is usually applied when higher pressure ratios of up to 40:1 are required. An axial compressor does not change the axial flow direction of the air but increases the total pressure. Indeed, an axial compressor comprises of three major components which are the rotor with blades, stator can and the inlet guide vane. A stage is a combination of a stator and a rotor. The assembly of the full rotor blade and stator can form the number of stages in a compressor and the greater the number of stages, the higher the total pressure ratio. In this arrangement, the air flows into the inlet guide vane and then into the rotor and stator assembly where compression starts. Also, the length of the rotor and stator reduces along the whole unit which signifies a reduction in volume which induces the increase in pressure. A fan or low pressure compressor is a type of axial compressor but the only differences are that the blades are longer, the total pressure ratio is lower than the typical compressor and the number of stages is usually 1 or 2. The main purpose of creating a fan is to compress more air and to create a bypass air which can be used to generate addition thrust or used for mixing process.
Fan Equation Process
Given that, isentropic efficiency ηfan= Ideal CycleActual cycle=ht3s-ht2ht3-ht2
Since the specific heat is constant, the equation deduces to ηfan=Tt3s-Tt2Tt3-Tt2 Simplifying the equation whenpt3s=pt3, Tt3sTt2=pt3pt2γ-1γ, πfan=pt3pt2 and τfan=Tt3Tt2 ηfan=πfanγ-1γ-1τfan-1 Bypass Ratio=msma where ms is the bypass flow rate and ma is the engine core flow rate.
For the high pressure compressor, the equations remain the same as that of the fan except the changes in station numbering and the bypass ratio.

3.4.3. Combustion Chamber/ Burner The combustion chamber as the Brayton cycle implies is the only source of heat energy addition to the system. Accordingly, the combustion chamber causes very significant increase in the temperature of the air which results in the air gaining enormous internal energy. This energy gained is extracted to be used to power the turbine while the rest is used to create highly accelerated gases from the nozzle. There are three types of combustor namely; the can combustor, the annular combustor and the cannular combustor. The main considerations when designing a combustion chamber is to ensure that the combustion process is complete with no fuel waste, the combustor should have long life materials because any failure can lead to engine explosion. The other consideration is that the air must be heated enough above the ignition fuel temperature in order to ensure stoichiometric combustion.
Equations of the Combustion Chamber In the real process of the combustor, total and static pressure drops and the temperature also drop. The major causes of pressure losses are the high level of irreversibility or non-isentropic process and viscous effects in the burner. The burner pressure ratio πb=pt5pt4Burner temperature ratio τb=Tt5Tt4
Since no work is done only heat transfer, the efficiency of the burner is analysed using the heating value NCV of the fuel used. Thus, efficiency ηb=heat addedHeating value of fuel=ma+mfht5-maht4NCVmf
Given that f=mfma, ηb= 1+fht5- ht4NCVf
Equivalence Ratio of combustion It is the ratio of the actual fuel to air ratio of the combustion process to the stoichiometric fuel to air ratio. This ratio produces a means of classifying the combustion process to show whether it is a lean, rich or stoichiometric combustion. The mathematical expression for this is as shown below
Φ=Actual FARStiochiometric FAR
Φ<1 Lean combustion process
Φ=1 Stiochiometric combustion process
Φ>1 Rich combustion process

3.4.4. Turbine Turbine can simply be said to be the antonym of a compressor. In response, a turbine extracts molecular kinetic energy from the air and uses it to drive the turbo machineries which results in the pressure and temperature of the air to drop. If truth be told, Flack (2005) asserted that the turbine uses 70% to 80% of the total energy gained by the air in the combustion chamber to drive the turbo machineries while the remaining 20% to 30% is used to generate thrust in the nozzle. Since the geometry of a turbine have favourable pressure gradient unlike the compressor which is adverse, the efficiency of the turbine is usually very high. Since the turbine is the opposite of the compressor, it has exactly the same configuration of rotor and stator but the volume increase across it which induces the pressure drop. One major problem faced when design a turbine is the deterioration of the blades due to high inlet temperature from the combustion chamber. Based on this, (Song et al. 2002) demonstrated that General Electric uses about 16.8% of the compressor air to cool the turbine blades of GE 7f engine.
Turbine Equation Analysis
Given that,
Turbine efficiency ηT=ActualIdeal=ht6-ht5ht6s-ht5 ηT=Tt6-Tt5Tt6s-Tt5
Simplifying the equation given that pt6s=pt6 Tt6sTt5=pt6pt5γ-1γ πT=pt6pt5 τT=Tt6Tt5 ηT=τT-1πTγ-1γ-1 3.4.5. Exhaust Nozzle The nozzle is the final component of the jet engine that the air passes through. The main purposes of the nozzle is to add extra acceleration to the high velocity exiting air, reduces its total pressure to that of ambient condition and finally generate sufficient thrust. There are two conditions that occur in the exit of the nozzle depending on the ambient pressure. The first condition is termed under-expansion which occurs when the ambient pressure is less than the exit pressure of the gases. The result of this is that the exit velocity will be lower than it normally is and this makes the momentum component of thrust to be lower than ideal. On the other hand, it will create a positive thrust component for the pressure terms. The second case termed as overexpansion which occurs when the ambient pressure is greater than the exit pressure of the gases. Consequentially, the opposite of what happens in the under-expansion condition occurs where the pressure term is lower and the momentum is higher.
Nozzle efficiency ηn=ActualIdeal=ht8-h9ht8-h9s=Tt8-T9Tt8-T9s for constant specific heat
Using the steady state energy equation and balancing it out, U9=2ht8-h9 . When specific heat is constant U9=2cpTt8-T9 p9pt8=T9sTt8γ-1γT9Tt8=11+γ-12M92 p9pt8=11+γ-12M92-1+ ηn ηn

3.4. Thermodynamic Process and Cycle of Twin Spool Mixed Flow Turbofan Engine Before any explanation is done from Figure 2, the blue arrows represent the incoming air into the diffuser and the red represent the air flow into the core of the engine while the black arrow represent the bypass air flow through the fan. Finally, the brown arrow represents the air flow after the bypass air and the core air flow have mixed. Based on the arrangement of the turbofan engine in figure 2, it can be seen that air at ambient condition is sucked into the diffuser where the air velocity is reduced and some of its kinetic energy is used to increase the static pressure to the total pressure. The air exiting the diffuser enters the fan or low pressure compressor where it is compressed. Indeed, the molecules of the air gains kinetic and internal energy by colliding rapidly with one another and as a result increase the enthalpy and static pressure. Also, in the fan, some of the compressed air is bypassed through a duct to be used for the mixing process later while the rest of the air enters into the high pressure compressor of the engine core. In the high pressure compressor, the air is further compressed where the enthalpy and pressure increases as it is released into the combustion chamber. Also, in the high pressure compressor, some of the air mass flow rate is bled out to be used to cool the turbine blades and for air conditioning in the aircraft. In the combustion chamber, the incoming fuel reacts with the air in an oxidation process at constant pressure where the by-product gases gain molecular kinetic energy thereby increasing the enthalpy. This high temperature gases escapes into the high pressure turbine where it is expanded and the gases lose some of their kinetic molecular energy as it enthalpy and static pressure reduces. In other words, it can be said that the molecular kinetic energy of the gases is being converted to mechanical work which is used to power the high pressure spool. Consequently, the gases enters into the low pressure turbine where it is further expanded to a lower pressure and enthalpy as their molecular kinetic energy is converted to mechanical work to power the low pressure spool. These gases escaping from the low pressure turbine enters the mixing zone or mixer after it has lost most of its total enthalpy and mixes with the bypassed cold air from the duct to further reduce its enthalpy as that of the cold air increases. In other words, the cold air absorbs some of the heat energy from the hot gases until they both attain equilibrium enthalpy. The mixture of the cold air and hot gases both escape at the same equilibrium enthalpy and pressure through the nozzle where their velocity is increased and the pressure is reduced considerably to that of the ambient condition. Furthermore, the exhausted high velocity gases is used to produced thrust for propulsion according to Newton’s third law of motion (In every action, there is equal and opposite reaction).
2
4.5
6
4
13
0
HPC
DIFFUSER
FAN/LPC
HPT
LPT
NOZZLE
COMBUSTION CHAMBER
2.5
3
5
8
16
BYPASS DUCT
HP Spool
LP Spool
MIXING ZONE

Figure 2 Layout of a Forward Fan Twin Spool Mixed Flow Turbofan Engine

P0
P3
P4.5
P5
P8
P6
P2.5
P2
P13
P4
ENTROPY (S)(kJ/kg)
TEMPERATURE (K)

Figure 3 T-S Diagrams for the Forward Fan Twin Spool Mixed Flow Turbofan Engine

Chapter 4
Mathematical and Gas Turb 11 Modelling of the Engine
4.1. Station Numbering and Assumptions Station numbering is a very crucial step that has to be taken when analysis of any thermodynamic system involving many processes is to be done. Moreover, station numbering contributes immensely to showing how the properties of one process relate to another and how the interaction between these processes derives the functional relationship of the thermodynamic system. Returning to the work in hand, the station numbering system that has been adopted for this work on a JT8D-15A turbofan engine is in accordance with the Aerospace Recommended Practice (ARP) and it is shown in figure 2. Assumptions The following assumption were made based on Mattingly (2002) and Kurzke (2007) in order to perform the modelling as listed below * The air flow through the engine is assumed to be steady and one dimensional * The fan and the low pressure Compressor are driven by the low pressure turbine * The overall engine is assumed to have no bleeds in mass flow or power off-take in turbine. * The nozzle of the engine is choked which means the exit pressure will be greater than the ambient pressure. * The air is assumed to act as a half ideal gas where the specific heat and ratio is dependent on temperature only. * The areas of each station of the engine is assumed to be constant

4.2. Design Point Cycle Analysis of the Turbofan Engine The off-design or performance cycle analysis cannot be done without the design point cycle being defined. The design point cycle in this analysis is obtained using exactly the same data used in the actual test analysis for a JT8D-15A turbofan engine operating at sea level with maximum take-off thrust as shown in (“JT8D Typical Temperature and Pressure”) and (“ICAO”). Some of the input parameters such as the isentropic efficiencies and pressure ratios from the actual test data had to be calculated. Since not all the input parameters were given from the actual test data, some of the parameters like inlet corrected mass flow rate, diffuser pressure ratio and efficiency; mechanical spool efficiency had to be guessed in order to complete the analysis and the data are represented below in Table 1. With all the Input Parameter being specified as shown in table 1, the design point cycle simulation of the JT8D-15A turbofan Engine using the Gas Turb 11 software can then be performed. All the steps taken to model the mixed flow turbofan engine on Gas Turb 11 is clearly represented in the algorithm shown in figure 3 below. COMPONENT | INPUT PARAMETER | | DIFFUSER | Pressure Ratio (πd) | 1 | | Inlet Corrected Mass Flow Rate (mc2) | 138.618 kg/s | FAN | Pressure Ratio (πfan) | 2.054 | | Isentropic Efficiency (ηfan) | 0.78 | | Bypass Ratio (α) | 1.08 | Low Pressure Compressor (LPC) | Pressure Ratio (πLPC) | 4.37 | | Isentropic Efficiency (ηLPC) | 0.88 | | Nominal Low Pressure Shaft Speed (NLP) | 8160RPM | High Pressure Compressor (HPC) | Pressure Ratio (πHPC) | 3.77 | | Isentropic Efficiency (ηHPC) | 0.864 | | Nominal Low Pressure Shaft Speed (NHP) | 11420RPM | Combustion Chamber (cc) | Pressure Ratio (πCC) | 0.934 | | Isentropic Efficiency (ηCC) | 0.99 | | Burner Exit Temperature (TIT) | 1277.15K | High Pressure Turbine (HPT) | Isentropic Efficiency (ηHPT) | 0.9 | | HP Spool Mechanical efficiency (ηm) | 1 | Low Pressure Turbine (LPT) | Isentropic Efficiency (ηLPT) | 0.91 | | LP Spool Mechanical efficiency (ηm) | 1 |
Table 1 Input Parameters for the Design Point Cycle Simulation
START
Specify all the input data gotten from the actual test data as shown in Table 1
Run the Gasturb 11 software and select mixed flow turbofan from the drag down Tab list. Set the scope to ‘More’, set the Calculation Mode as Design and click ‘Run’
Choose the Units to either Imperial or SI and Select the type of fuel from to drop down list to Kerosene, Natural Gas or Hydrogen
Estimate the inlet Corrected mc2 Mass Flow rate to the FAN/LPC
Choose ‘Single Cycle’ for ‘Select a Task ‘Option and click ‘Run’
Check if the Thrust, SFC, πHPT, πLPT and EPR are within (0-10) % of the actual test Experiment
END
YES
NO

Figure 4 Design Point Cycle Simulation Algorithm Using Gas Turb 11
Verification of the Design Point simulation Results Since not all the input parameters were specified in the actual test data and some of them had to be guessed, it is without any doubt that errors are bound to generate in the simulation results using the Gas Turb 11 software. In order to ensure that the errors accumulated in the simulation were within range, the major output parameters obtained such as net thrust, fuel flow rate, Engine exit pressure ratio, etc were compared to the actual test data as shown in Table 2 and the error range was calculated to be between 0.25% to 8.5% which is within an acceptable range. PARAMETERS | ACTUAL TEST DATA | SIMULATED DATA USING GASTURB 11 | Net Thrust | 69307.74 | 69320 | Engine Exit Pressure Ratio P8P0 | 2.09 | 2.167 | Burner Fuel Flow | 1.100843 | 1.09781 | HPT pressure Ratio (πHPT) | 0.415 | 0.449 | LPT Pressure Ratio (πLPT) | 0.3294 | 0.3514 | HPT temperature Ratio (τHPT) | 0.8097 | 0.8435 | LPT temperature Ratio (τLPT) | 0.7718 | 0.793 |
Table 2 Comparison Table for the Actual Test Data and Simulated Data Using GasTurb 11 4.3. Off-Design Point Cycle Simulation of the Turbofan Engine The off-design or performance cycle simulation takes into account the concept of module matching of each component through performance maps. This cycle analysis enables the determination of different operating point of the engine at a given design point of the engine. Considering the work in hand, the design point have been defined and verified for the JT8D-15A turbofan engine operating at sea level with maximum take-off thrust which means that different operating points of the engine can be defined with the concept of off-design module matching of the engine. Indeed, the off-design operating point that was considered for the parametric analysis in this work was 30,000ft at M0 0.8 for the turbofan engine. The off-design modelling of the JT8D-15A engine for the operating point of 30,000ft at M0 0.8 based on the reference design point defined earlier is clearly demonstrated as follows. The off-design performance cycle simulation may contain some errors because of the component performance maps that were used for the simulation.

4.3.1. Module/Component Matching This process only applies to the off-design performance cycle point of the engine. It can simply be defined as the act of synchronising each component of a jet engine to coexist as a unit in order to derive the overall performance characteristics of the jet engine. Component matching involves the process closely studying the ramifications of the actual jet engine overall performance behaviour on the components major characteristics such as pressure ratio, temperature ratio, efficiency and spool speed. This process introduces the concept of empirically determined component performance maps that establishes the relationship between the thermodynamic properties and the geometry of the jet engine itself.
4.3.2. Off-Design Component Modelling
Diffuser
The diffuser was assumed to be adiabatic and the pressure ratio πd=1
The Isentropic Efficiency was assumed to be 1
For Sea Level,
Pamb=101325pa , Tamb=288.15K
For 30,000ft and M0 0.8,
Tamb=288.15-0.0065×9144
=288.15-59.436
=228.71K
Pamb=101325×Tamb288.155.2561
=30.09kpa
Tt1=228.71×1+γ-12M02
=228.71×1+1.4-12×0.82
=258K pt1p0=1+ ηdγ-12M02γγ-1 pt1=30.09×1+ 1×1.4-120.821.41.4-1 pt1=45.8674kPa pt1=pt2
Tt1=Tt2
Fan and Low Pressure Compressor The inlet corrected mass flow rate is estimated as 138.618kg/s , As for the off design simulation using the component performance maps for the altitude of 30000ft and Mach no. 0.8, the actual spool speeds and inlet mass flow rate are calculated based on the estimated inlet corrected mass flow rate as shown below.
Low and High pressure spool mechanical efficiency is assumed to be=1
HP spool Speed=11420RPM, LP spool Speed=8160RPM m2=Pt2PSTD×mc2Tt2TSTD =45.878101.325×138.618258288.15
Actual Mass flow rate m2=66.3323kg/s
N=Tt2TSTD×NcLP=228.71288.15×8160=7722 RPM
The calculated actual mass flow rate and spool speed were used to evaluation the isentropic efficiency and the pressure ratio of the LPC for that operating condition from the compressor performance map.

Figure 5 Example of a Compressor Performance Map/Curve
The diagram above in figure 4 depicts a typical compressor performance map that was used for the off-design point analysis in this work. It can be seen that the x-axis represents the inlet corrected mass flow rate mc2 into the compressor, the y-axis represents the compressor pressure, the red contour lines represents the isentropic efficiencies and the black curved lines represent the relative corrected spool speed. To add to that, the red dash line that ends the speed lines and efficiency lines represent the surge margin which is also known as the stall line that must be avoided since the flow will become unstable in that region. In this work, the inlet corrected mass flow rate and spool speed were calculated which were interpolated on the performance map to obtain the pressure ratio and the isentropic efficiency. For instance, the yellow dot on the map represents a design point traced for a given pressure ratio,
High Pressure Compressor
The inlet corrected mass flow rate into the HPC mc2.5=mc21+α mc2.5=138.6182.08=66.64kgs m2.5=Pt2.5PSTD×mc2.5Tt2.5TSTD N=Tt2.5TSTD×NcHP
The same equation used for the LPC is used to calculate the actual mass flow rate and spool speed which is used to evaluate the isentropic efficiency and pressure ratio when it is operating at an altitude of 30000ft at M0 =0.8.
Verification of the off-design modelling for 30000ft at Mo 0.8
In order to verify the simulation result gotten for the operational design point of 30000ft at M0 0.8, the actual test data results gotten from Mattingly, Heiser and Pratt (2002) for the same operating condition was compared. Due to the difficulties in obtaining a lot of output parameters for this operating point, the result will be verified with only the net thrust generated and the specific fuel consumption. Indeed, the error accumulated was 1.71% for the net thrust and 0.83% for the specific fuel consumption. PARAMETERS | ACTUAL TEST DATA | SIMULATED DATA USING GASTURB 11 | Net Thrust (lb) | 4920 | 4836 | Specific Fuel Consumption(lb/lbh) | 0.779 | 0.7855 |
Table 3 Comparison Table for the Actual Test Data and Simulated Off-design Data Using GasTurb 11

Chapter 5 Methodology, Results and Discussions Given that the design point of the JT8D-15A turbofan engine at sea level has been obtained and verified with the actual test data, the operating point of 30000ft at M0 0.8 was simulated and obtained which now served as the design point for the analysis in this work. Moreover, the procedure taken to define this design point of 30000ft at M0 0.8 of the JT8D-15A turbofan engine has been clearly stated earlier which gives the permission to conduct the parametric cycle study of the turbofan engine. The parametric cycle studies were done for three different cases for the operational design point of 30000ft at M0 0.8 of the JT8D-15A turbofan engine as explained as follows. 1. The first parametric analysis case 1 aim to create an understanding of the effects of varying major design parameters on the performance parameters of the turbofan engine when some of the design choices are kept constant. In other words, the bypass ratio and thermal limit parameter (turbine inlet temperature) were varied when the design choices such as the compressor pressure ratio, fan pressure ratio and isentropic efficiencies were kept constant in order to investigate their effects on the performance parameters such as the net thrust, specific fuel consumption, propulsive efficiency, thermal efficiency, and fuel-air-ratio. Much interest is shown nowadays in using alternative fuels like hydrogen and Natural gas in efforts to reduce the cancer known as pollution and the risk of depletion of energy resources. Based on this, conducting a research that focuses of comparing different fuels consumption rate, their risk of pollution and their contribution to the performance of the engine will be really valuable. Based on this, a parametric analysis had to be done on the JT8D-15A turbofan engine using three different fuels which are the design point fuel kerosene, hydrogen and natural gas. Since the original design point of the JT8D-15A turbofan was obtained using kerosene fuel, the design points of using hydrogen and natural gas was obtained using the same design choices as that of kerosene. Now that the design points of the JT8D-15A turbofan engine had been defined when using the three different fuels, it had given a go ahead to perform whatever parametric cycle studies of the turbofan engine using the three fuels. In order to compare the performance characteristics of the turbofan engine when it is using the three different fuels, different approaches had to be devised to compare them effectively on a rational basis which defines the last two parametric analysis cases as follows. 2. The second case of parametric analysis was that the fuel flow rate would be kept constant for the three fuels that would be used as the bypass ratio is varied with design choices remaining the same. 3. The third case of study was to make the energy supply into the combustion chamber of the turbofan engine the same for all three fuels which means the turbine inlet temperature was kept constant as the bypass ratio was varied.
Having taken all that has been said into consideration, the vivid description of all three cases for the parametric cycle analysis of the turbofan engine is explained later on.

5.1. General Relationship Equations of Major Parameters
Fan
The relationship of core mass flow rate and fan mass flow rate is shown below
Bypass Ratio α=mfanmcore, mfan+mcore=m0 mcore=m01+α ……………………………………………. 1
From the relationship derived in equation (1), it can be seen that for a constant value of the inlet air mass flow rate, reducing the bypass ratio will increase the core air mass flow rate and vice versa.
Combustion Chamber
Considering the energy balance equation in the combustion chamber, ηccmfuelNCV=mcoreht4-mcoreht3+mfuelht4 Tt4=ηcc×f×NCV+ht3cp,41+f ………………………………2 f=mfuelmcore……………………………….(3) For the turbine inlet temperature to remain constant, the fuel-air-ratio at all-time must be equal but that does not necessarily mean that the mass flow rate of fuel and the core mass flow rate is constant.
High Pressure Turbine
Considering the high pressure spool energy balance given that the mechanical efficiency is assumed to be 1 is shown below mcoreht3-ht2.5=mcore1+fht4-ht4.5 Tt4.5=1+fcp,4Tt4-ht3-ht2.5cp,4.51+f ………………………….………….4
Pt4.5=1-1-Tt4.5Tt4ηLPTγγ-1Pt4………………………………….(5)

Low Pressure Turbine
The low Pressure Spool Energy Balance given that the mechanical efficiency is assumed to be 1 is shown below mcoreht2.5-ht2+mfanht13-ht2=mcore1+fht4.5-ht5 ht2.5-ht2+αht13-ht2=1+fht4.5-ht5
Tt5=1+fht4.5-ht2.5-ht2-αht13-ht2cp,51+f …………………..(6)
LPT Exit Pressure Pt5=1-1-Tt5Tt4.5ηLPTγγ-1Pt4.5…………………….(7)

Mixer
Given that the mixer assumed to be adiabatic, the sum the total enthalpy of the cold air stream and the total enthalpy of the hot stream is equal to the mixed air flow as shown in
Ht13+Ht5=Ht64
αcp,fanTt13+1+fcp,LPTTt5= αcp,fan+1+fcp,LPTTt64
Tt64= αcp,fanTt13+1+fcp,LPTTt5 αcp,fan+1+fcp,LPT……………..8
Pressure ratio of bypass duct exit pressure to turbine exit pressure =Pt13Pt5…………(9)

Nozzle
Since the Nozzle in this analysis is choked which means M8=1,
The exit static temperature can be calculated as
T8=2×Tt641+γnoz……………………………………………………………(10)
The exit static temperature is related to the exit velocity as shown below
V8=γnoz×R×T8 …………………………………………….11
The continuity equation for the exit nozzle is given as mcore1+α+f=ρ8V8A8 A8=mcore1+α+fρ8V8……………………………(12)
Performance Parameters
Net thrust
T=mcore1+α+fV8-mcore1+αV0+A8P8-P0
=mcore1+α+fV8-1+αV0+A8mcoreP8-P0………………..(13)
Specific Fuel Consumption
SFC=mfuelThrust
SFC=f1+α+fV8-1+αV0+A8mcoreP8-P0………………..(14)
Thermal Efficiency ηth=mcore+mfan+mfuelV82-mcore+mfanV02mfuel×NCV ηth=1+α+fV82-1+αV022×f×NCV…………15

Propulsive Efficiency ηp=Thrust×V0mcore+mfan+mfuelV82-mcore+mfanV02 ηp=2×1+α+fV8-1+αV0+A8P8-P0mcore×V01+α+fV82-1+αV02……………………..(16) 5.2. Results and Discussion of Parametric Analysis Case 1 The layout of case 1 parametric studies for the operational design point of 30000ft at M0 0.8 of the turbofan engine, the following parameters were kept constant in order to perform the analysis. * Isentropic efficiencies, ηfan, ηLPC, ηHPC, ηCC, ηHPT, ηLPT * Compressor Pressure ratio =πLPC×πHPC * Fan pressure Ratio ηfan * Inlet mass Flow rate m0 * Compressor and Fan total temperature ratio also remains constant because of the constant isentropic efficiency and pressure ratio. From all that has been stated, the bypass ratio was varied from 0.1-2.8 for a constant thermal limit parameters (turbine inlet temperatures) of 1000K, 1050K, 1100K, 1155.2K, 1200K and 1250K. This parametric cycle analysis was used to plot the graph of net thrust, specific fuel consumption, thermal efficiency, propulsive efficiency, exit velocity ratio, LPT exit pressure ratio and fuel-air-ratio for the varying bypass ratio and constant values of thermal limit parameter (turbine inlet temperature) as shown in figure 6-12 below.

Figure 6 the Effects of Varying Bypass Ratio at Constant Values of TIT on the Fuel-Air-Ratio Looking at figure 6, it can be seen that for a given turbine inlet temperature as the bypass ratio increases, the fuel-air-ratio remained constant. This can be explained by saying that for the constant value of the turbine inlet temperature to be maintained, the fuel air ratio must be constant but the mass fuel rate of fuel and core mass flow rate of air will change due to increasing bypass ratio. Also, it can be seen that the fuel-air-ratio increases as the turbine inlet temperature increases for a given bypass ratio. Considering equation (2), it can be asserted that the only way the turbine inlet temperature will increase is if the fuel-air-ratio increases since the other parameters are kept constant.

Figure 7 the Effects of Varying Bypass Ratio at Constant Values of TIT on the Velocity Ratio It was observed that the exit velocity ratio of the jet decreased as the bypass ratio increased for a given turbine inlet temperature but the exit velocity ratio increased with increasing turbine inlet temperature for a given bypass ratio as shown in figure 7. From equation (4) and (6), it can be deducted that for a given TIT with increasing bypass ratio, the LPT exit temperature will decrease since the other parameters are kept constant and this LPT exit temperature will further be decreased when mixed with the bypass cold air as shown in equation (8). Since the mixed flow air temperature is related to the exit velocity as shown in equation (10) and (11), any reduction in the temperature will directly translate into a drop in the exit velocity. On the other hand, for a given bypass ratio with increasing TIT, the exit jet velocity will increase since the increase in TIT will result in an increase in LPT exit temperature as can be deducted from equations (4) and (6). This increase in the temperature will result in the increase of the mixed air flow which increases the exit velocity according to equation (8) (10) and (11).

Figure 8 the Effects of Varying Bypass Ratio at Constant Values of TIT on the LPT Exit Pressure ratio Pt5P0
The LPT exit pressure decreased for a given TIT with increasing bypass ratio but increased for a given bypass ratio with increasing TIT as described in figure 8. It has been explained earlier the effects of increasing parameters on the LPT exit temperature and since the isentropic efficiencies are kept constant for the HPT and LPT, the pressure across the LPT exit will have the same effects which means with increasing TIT, the exit pressure will increase and vice versa. This relationship can be seen according to the thermodynamic state equation (5) and (7).

Figure 9 The Effects of Varying Bypass Ratio at constant values of TIT on Net Thrust From figure 9, it can be seen that increasing the bypass ratio for a given TIT has a negative effect on net thrust. From equation (13) given earlier, net thrust is related to the exit pressure, exit velocity, bypass ratio and fuel-air-ratio. Since the fuel-air-ratio is constant for a given TIT, the increase in the bypass ratio in the momentum thrust component will compliment for the increase in bypass ratio for the momentum drag component. In spite of the increase in nozzle exit area due to the decreasing exit velocity as shown in equation (12), the effect of decrease in exit jet velocity and pressure will be dominant and this result in a net decrease in thrust. Also, for a given bypass ratio as the TIT increased, the net thrust increased accordingly. In this case, the momentum drag remains constant but the increasing exit jet velocity, pressure and fuel-air-ratio will result in a direct increase in the momentum and pressure component of thrust and the effects of decreasing exit area due to increasing exit velocity will be almost negligible which the net effect is an increase in thrust.

Figure 10 The Effects of Varying Bypass Ratio at constant values of TIT on the SFC It was observed that increasing the bypass ratio for a constant value of TIT resulted in a decrease in the specific fuel consumption up to a point before the specific fuel consumption started to increase as demonstrated in figure 10. Given the relationship of SFC as shown in equation (14), this can be attributed to the fact that with increasing bypass ratio, the core mass flow rate will decrease and in order to maintain the fuel-air-ratio for constant TIT, the fuel flow rate will decrease correspondingly and it has been explained that thrust decreases as well. However, the reason for the increasing and decreasing trend of the specific fuel consumption can be said to be that in the decreasing trend, the decrease in the mass flow rate of fuel is much more than the decrease in the net thrust while in the increasing trend, the decrease in thrust is much more than the decrease in mass flow rate of fuel. Furthermore, it was also noticed that for a given bypass ratio as the TIT was being increased, the specific fuel consumption decreased and this can be directly attributed to the increase in fuel-air-ratio and mass flow rate of fuel with simultaneous increase in thrust. Nonetheless, the increase in mass flow rate of fuel is more dominant than that of thrust which results in the increase in specific fuel consumption. From all that has been said, it can be asserted that increasing the bypass ratio does not necessarily mean that the specific fuel consumption will keep decreasing and also increasing the TIT does not mean the specific fuel consumption will keep increasing. This can be explained in an economic viewpoint that decreasing thrust of the engine at some point would not decrease specific fuel consumption but will increase it, meaning that the prices of flight tickets since it is evaluated from specific fuel consumption could still be high even though the demanded thrust for the aircraft is low.

Figure 11 Effects of Varying Bypass Ratio at Constant Values of TIT on the Propulsive Efficiency The propulsive efficiency of the turbofan engine increased as the bypass ratio increased for a given TIT whereas it decreased as the TIT increased for a given bypass ratio as shown in figure 11. It has been shown in equation (16) that the propulsive efficiency is dependent on thrust and change in kinetic energy in the engine air stream. Given that it has already been justified that the thrust decreases with increasing bypass ratio, the change in kinetic energy will decrease by a greater rate since the decrease in exit velocity is being multiplied compared to the constant value of incoming air velocity. The net effect of all this will result in a decrease in thrust power and decrease in change in kinetic energy but the decrease in change in kinetic energy is much more dominant. This can be used to explain why high bypass turbofan engine have higher propulsive efficiency than low bypass because of the increasing bypass ratio and low hot nozzle exit velocity. In the aspect of increasing the TIT for a given bypass ratio, the propulsive efficiency decreased and this can directly be attributed to the increase in exit velocity which will result in an increase thrust power and change in kinetic energy. However, the increase in change in kinetic energy will be higher than the increase in thrust power which results in the decrease in propulsive efficiency.

Figure 12 Effects of Varying Bypass Ratio at Constant Values of TIT on the Thermal Efficiency The thermal efficiency of the turbofan engine increased with increasing bypass ratio for a given TIT but decreased with increasing TIT for a given bypass ratio as displayed in figure 12. From the equation (15), it was deducted that the increase in bypass ratio in the exit jet kinetic energy would tend to compliment for the increase in bypass ratio of the inlet jet kinetic energy which leaves the effect of decreasing exit velocity to be dominant. With the fuel-air-ratio, inlet velocity remaining constant, the decreasing exit velocity with increasing bypass ratio will cause the change in kinetic energy to reduce since the exit jet kinetic energy will be reducing. The net effect of all this is a increasing thermal efficiency since the heat energy supply is constant for constant fuel-air-ratio. 5.2. Results and Discussion of Parametric Analysis Case 2 mfuel,H2=mfuel,CH4=mfuel,C12h23 As stated earlier that three fuels will be considered which are kerosene, natural gas and hydrogen, a means had to be devised in order to compare them effectively on a rational basis. On way of doing that was to investigate the effects of using the three fuels when the mass flow rate of fuel into the combustion chamber was kept constant and the constant value of the fuel flow rate was chosen arbitrarily as 0.26kg/s. The design choices such as compressor pressure ratio, fan pressure ratio and isentropic efficiencies were also kept constant. With the design limitations imposed, the bypass ratio of the turbofan engine was varied as 0.1, 0.3, 0.6, 0.8 and 1.09 in order to compare the turbine inlet temperature, exit velocity ratio, the net thrust generated, specific fuel consumption, thermal efficiency, propulsive efficiency, and LPT exit pressure ratio Pt5P0 for the operating design point of 30000ft at M0 0.8. The graphs of the fuel-air-ratio, turbine inlet temperature, Exit velocity ratio, LPT exit pressure ratio, net thrust, specific fuel consumption, thermal efficiency and propulsive efficiency was plotted against the bypass ratio as shown in figure 7-12 below respectively. This chronology of the graphs is done to build a step by step discussion of the performance parameters.

TIT1

TIT2
Increases
Mixer α=1.09 α=0.1
FAR increases tyrtytrytincreasincreases,Type equation here.
Pt5-Pt13
Tt64 Figure 13 T-S diagram of using Hydrogen Fuel when the bypass Ratio is increased. The temperature entropy diagram above in figure 13 represents the analysis cycle of using hydrogen fuel when the bypass ratio is being increased. The dark black cycle lines with yellow dots represent the cycle when the bypass ratio is set at 0.1 for constant fuel flow rate whereas the slight light dark lines with white dots represents the cycle for when the bypass ratio is set to 1.09 for constant fuel flow rate. The thick dash red and purple lines represent the isobars for the LPT exit pressure and bypass exit pressure respectively for the bypass ratio of 1.09. Generally, it can be seen that the cycle for increasing bypass ratio will look the same for the compression unit due to the constraints imposed and will be different for is the expanding units.

Figure 14 The Variation of Fuel-Air-Ratio with Bypass Ratio at constant fuel flow rate using the Three Different Fuels From the condition that the fuel mass flow rate into the combustion chamber is constant for all three fuels, increasing the bypass ratio will decrease the core mass flow rate which will result in an increase in the fuels-air-ratio from the relationship shown in equation (3). This effect was observed for all three fuels since the fuel mass flow rate was kept constant and the bypass varied according as seen in figure 14.

Figure 15 The Variation of Turbine Inlet Temperature with Bypass Ratio at constant fuel flow rate using the Three Different Fuels The turbine inlet temperature of the three fuels increased as the bypass ratio increased and this is due to the increasing fuel-air-ratio as shown in figure 15. This is so because the increase in fuel-air-ratio is multiplied in the numerator while it is added in the denominator which makes the increase in the numerator more dominant than that of the denominator and results in a net increase in TIT as shown in equation (2). Also in figure 15, it was noticed that for a given bypass ratio, hydrogen fuel had the highest turbine inlet temperature followed by natural gas and then kerosene. This can be attributed to the fact that the net calorific value of hydrogen is way higher than that of kerosene and natural gas by more than 2.5 times. Another observation made was that the increase in TIT with increasing bypass ratio for all three fuels diverged instead of increasing in parallel. The divergence in the trend can be said to represent the magnification of the amount by which the net calorific value of hydrogen and natural gas are higher than that of kerosene. Additionally, it can be seen that the divergence of natural gas is small because its net calorific value is slightly higher than that of kerosene but the divergence of hydrogen fuel is way bigger because of its high net calorific value compared to kerosene.

Figure 16 The Variation of Exit Velocity Ratio with Bypass Ratio at constant fuel flow rate using the Three Different Fuels As explained earlier, the nozzle exit velocity will increase as the turbine inlet temperature increases and in this case hydrogen fuel had the highest turbine inlet temperature for the constant fuel flow rate which explains why its velocity ratio is high at a given bypass ratio. This whole effect can be seen clearly in figure 16. An interesting point noted was that when the bypass ratio was increased for the constant fuel flow rate of the fuels, their velocity ratios remained fairly constant which signifies that the increasing bypass ratio does not really have an effect on the exit velocity. This effect can be explained by referring to the temperature-entropy diagram shown in figure 13 above. It can be seen that with increasing bypass ratio which propagates an increase in fuel-air-ratio, the mixed air flow temperature tends to remain the same. Since mixed air temperature is proportional to the exit static temperature, the exit velocity will remain the same according to equation (10) and (11). It is known that for an ideal mixing process, the bypass exit air pressure must be equal to the LPT exit pressure but for real cases, the difference must be reasonably low to avoid increasing loss in mixer pressure. However in this case, the pressure difference kept increasing which signifies a lot of drop in pressure across the mixer. When the bypass ratio is increased, the reduced mass hot gases exiting the LPT will have a very high mach no while the increased mass of bypass air for constant temperature and pressure will become slower with decreasing Mach no. Due to this, the high turbine inlet temperature gained by increasing fuel-air-ratio will be used to heat up the lager mass of slow cold air which returns the mixed air temperature to approximately what it was before. In short, the increase in TIT due to increasing bypass ratio is used to maintain the equilibrium of the less mass high velocity hot air and the more mass slow cold air.

Figure 17 The Variation of LPT Exit Pressure Ratio with Bypass Ratio at constant fuel flow rate using the Three Different Fuels The LPT exit temperature has been shown already to be increasing due to the increasing turbine inlet temperature and when these three different fuels were used the turbine inlet temperature increased due to increasing fuel-air-ratio with bypass ratio. According to the expression given in equation (7) above, the LPT exit pressure will increase simultaneously with increasing temperature since the isentropic efficiency is constant. Accordingly, hydrogen with the highest turbine inlet temperature has the highest pressure followed by natural gas and then kerosene as shown in figure 17 above.

Figure 18 The Variation of Net Thrust with Bypass Ratio at fuel flow rate Using Three Different Fuels. Hydrogen fuel was noticed to have the highest amount of net thrust followed by natural gas and then kerosene when the fuel flow rate was kept constant and this is attributed to the high exit jet velocity when hydrogen is used as explained earlier. This effect can be seen in figure 18 above. Also, the net thrust was noticed to be increasing slightly with increasing bypass ratio for natural gas and kerosene fuel but decreasing slightly for hydrogen fuel. The reason for this is that when hydrogen fuel is used, the LPT exit pressure is way higher than the bypass duct exit pressure which with increasing bypass ratio will cause the mixed air pressure to keep decreasing due to the loss of pressure in mixing. As for kerosene and natural gas fuel, their LPT exit pressure were lower than the bypass duct exit pressure which with increasing bypass ratio the pressure losses will decrease since the LPT exit pressure is approaching that of the bypass duct. With this all said, the pressure difference of the mixed air flow will be the only contributory factor to the increase or decrease in thrust since the exit velocity is fairly constant if equation (13) is considered.

Figure 19 The Variation of Specific Fuel Consumption with Bypass Ratio at fuel flow rate using the Three Different Fuels Because of the different thrust levels of the turbofan engine when it is using the three fuels, the specific fuel consumption will differ with the type of fuel used. It was noticed in figure 19 that hydrogen fuel had the least specific fuel consumption followed by natural gas and then kerosene. This can be said to be as a result of the higher thrust of hydrogen compared to natural gas and kerosene when the fuel flow rate is kept constant. The specific fuel consumption exhibited an increasing trend with increasing bypass ratio for hydrogen fuel but decreasing trend for natural gas and kerosene. Since thrust is inversely proportional to specific fuel consumption form equation (14), the increasing trend of thrust for kerosene and natural gas will translate to a decreasing trend of SFC and vice versa for hydrogen with decreasing thrust.

Figure 20 The variation of thermal Efficiency with Bypass ratio at constant fuel flow rate using the three different fuels It can be seen from figure 20 that kerosene fuel had the highest thermal efficiency of the followed by natural gas and then hydrogen for a given bypass ratio at const fuel flow rate and this as a result of the low exit velocity of kerosene. When the bypass ratio was varied, the thermal efficiency remained approximately the same for all three fuels and this is said to be as a result of the constant exit velocity and increasing fuel-air-ratio. In essence, the increasing fuel-air-ratio in the numerator will keep complimenting for the increasing fuel-air-ratio in the denominator as shown in equation (15)

Figure 21 The Variation of Propulsive Efficiency with Bypass ratio at constant fuel flow rate using the three different fuels The propulsive efficiency is highly dependent on the thrust generated and change in kinetic energy. Increasing thrust will dampen the propulsive efficiency while decreasing thrust will enrich the propulsive efficiency. Looking at figure 21, it can be seen that the propulsive efficiency decreased with increasing bypass ratio for kerosene and natural gas due to the increasing thrust and decreased for hydrogen fuel due to the decreasing thrust.

5.3. Results and Discussion of Parametric Analysis Case 3 Third case of study as stated earlier was to consider the parametric cycle study of the JT8D-15A turbofan engine when the turbine inlet temperature (thermal limit parameter) was kept constant when using the three fuels kerosene, hydrogen and natural gas. The turbine inlet temperature obtained for the operational design point of the engine when using kerosene fuel was taken as the constant value of the turbine inlet temperature for all remaining two fuels. In fact, it can be expressed mathematical as shown below.
TITH2=TITCH4=TITC12H23=1155.2K
The analysis was done by varying the bypass ratio as 0.1, 0.4, 0.7, 1.0 and 1.091 when the design choices were kept constant. The graphs of the fuel-air-ratio, Exit velocity ratio, LPT exit pressure ratio, net thrust, specific fuel consumption, thermal efficiency and propulsive efficiency was plotted against the bypass ratio as shown respectively in figure 22-28 below. This chronology of the graphs was done in efforts to build a step by step discussion of the effects of the performance parameters of the turbofan engine.
TIT = 1155.2k

Figure 22 The Variation of Fuel-Air-Ratio with Bypass ratio at Constant TIT using the three different fuels This analysis case assumed a constant TIT for all three fuels and it was observed that the fuel-air-ratio remained constant with increasing bypass ratio but differed as different fuels where used as shown in figure 24. As explained earlier that in order to maintain the same TIT, the fuel-air-ratio must be the same but the difference in the fuel-air-ratio when it comes to the three fuels is up to their net calorific value or energy content. In other words, according to equation (2) with increasing net calorific value, the fuel-air-ratio will decrease which explains why hydrogen fuel has the least fuel-air-ratio because of its high calorific value of 118.429MJ/kg followed by natural gas with a calorific value of 49.7365MJ/kg and then kerosene with a calorific value of 43.3MJ/kg. Thus, this means the mass flow rate of the three fuels will be different at each given value of bypass ratio.

Figure 23 The Variation of Exit Velocity Ratio with Bypass ratio at Constant TIT using the three different fuels Since the turbine inlet temperature is assumed to be the same for all the fuels, the only cause of difference increase in the LPT exit temperature for the three fuels would be the fuel-air-ratio. This means that the lower the fuel-air-ratio, the higher the LPT exit temperature for a given bypass ratio from the expression shown in equation (5) above. This slight difference in the LPT exit temperatures for the three fuels would ultimately convert to a slight difference in the exit velocities of the three fuels as shown in figure 23.

Figure 24 The Variation of LPT Exit Pressure Ratio with Bypass ratio at Constant TIT using the three different fuels From the relationship explained earlier that LPT exit temperature is related to the LPT exit pressure by its isentropic efficiency as shown in equation (7), the LPT exit pressure will have the same slight differences in value for the three fuels as shown in figure 24.

Figure 25 The Variation of Net Thrust with Bypass ratio at Constant TIT using the three different fuels Net thrust has been shown to decrease with decreasing exit and increasing bypass ratio. Being known that the exit jet velocity and pressure differed slightly with the type of fuels used, this effect will spontaneously transfer to the net thrust generated. This explains why there is a slight difference in the net thrust of the turbofan engine when it is using the three different fuels as seen in figure 25.

Figure 26 The Variation of Specific Fuel Consumption with Bypass ratio at Constant TIT using the three different fuels Looking at figure 26, it was noticed that the specific fuel consumption decreased as the bypass ratio increased for the three fuels and this effect has already been explained in analysis case 1 which is due to the decreasing effect of thrust being more dominant than the decreasing effect of fuel flow rate. However, the specific fuel consumption of kerosene fuel was seen to be the highest followed by that of natural gas fuel and that of hydrogen being the least. This can be chalked up to be as a result of the different mass flow rates of fuel imposed by the different net calorific values of the fuels and since thrust is fairly constant for all three fuels, the specific fuel consumption will be dependent only on the mass flow rate of fuel. In other words, hydrogen with high calorific value will have a small fuel flow rate which means the specific fuel consumption will be small and natural gas with a slightly higher calorific value than kerosene will have smaller specific fuel consumption than kerosene. If a conventional way is devised to produce and store renewable hydrogen on low cost, the amount of fuel being wasted and pollution risk will be reduced remarkably since the consumption will be low to produce the same net effect as natural gas and kerosene. From the results, if hydrogen is mixed slightly with kerosene fuel, it could be possible to reduce the specific fuel consumption of the turbofan engine since some of the high calorific value of hydrogen is added to that of kerosene and still be able to obtain same overall performance.

Figure 27 The Variation of Propulsive Efficiency with Bypass ratio at Constant TIT using the three different fuels The propulsive efficiency at this point increased with increasing bypass ratio but remained approximately the same for all three fuels as shown in figure 27. However, the interesting point picked up is that the propulsive efficiency of the turbofan engine was slightly lower for hydrogen fuel because of hydrogen fuel has a slightly higher thrust and exit velocity than the other two fuels.

Figure 28 The Variation of Thermal Efficiency with Bypass ratio at Constant TIT using the three different fuels The thermal efficiency of the turbofan engine increased despite the bypass ratio being decrease when the three fuels were used as shown in figure 28. It was noted that the variation thermal efficiency of the turbofan engine when it was using hydrogen fuel increased slightly than that of kerosene and natural gas which were the same. This effect is caused by the high calorific value of hydrogen that completely outweighs the low fuel-air-ratio in the expression for thermal efficiency in equation (15)
.

Chapter 6
Exergy and Thermoeconomics Analysis

Taking into consideration the recent plunge in the economy, there is increasing pressure on jet engine manufacturers to reduce operating cost if they want to break even since the prices of oil have increased. In fact, recent statistics show that the average cost of oil now is twice what it was in 2006. To demonstrate the extent of this, even the military which consumes a lot of fuel is starting to cut down on cost. Another cry for help is pollution or global warming which has left jet engine manufacturers on their toes trying to reduce carbon dioxide and toxic emissions. Given the fact that the number of aircrafts that is being used is predicted to be three times more in the next three decades, reducing carbon dioxide and toxic emission is essential. Based on this, many methods have been devised to tackle this problem such as improving air traffic control and modifying aircraft winglet to reduce drag (Symonds, 2005). Surprisingly, another method that can be used to reduce cost and carbon dioxide emissions is the use of exergetic and thermoeconomics analysis concept which shows the potential for improvement in a system. Applying exergy and thermoeconomics will show areas where improvements can be made and where cost can be cut down.

6.1. Exergy Analysis Exergy in a layman terms can simply be known as available energy or better still, the potential for more work to be done by a system. Exergy is also known as the second law of thermodynamics analysis which takes into consideration the generation of entropy in a system as it interacts with its environment. In fact, (Moran, Shapiro, 2006) defines exergy of a closed system in a thermodynamics sense as the maximum theoretical work that can be done by a combined system of the closed system and the environment as the closed system state properties approaches that of the environment or dead state. However, Kotas (1985) considers the concept of exergy to be associated with an ordered form of energy due to (potential and kinetic energy) and a disordered form of energy due to (entropy and enthalpy). Accordingly, the ordered form of energy creates a potential and kinetic exergy while the disordered form of energy creates the physical and chemical exergy. It concluded that the total exergy possessed by a moving stream of matter in any form in the absence of nuclear effects, magnetism, electricity and surface tension is the sum of the potential, kinetic, physical and chemical exergy. The analysis that will be done in this work involves a turbofan engine which is a steady flow system of air with constant interaction with its environment. As a result, the Kotas (1985) approach will be adopted for its exergtic anaylsis.
Previous Investigations An investigation done by Roth, Mcdonald and Mavris (n.d) proposed a method of using the exergy or thermodynamic work potential analysis on an aero engines. In addition, it showed the derivations of the major relationship of exergetic parameters with the state process equations of the entire aero engine. To add to that, Fagbenle (n.d) looked at the implications of considering the environmental conditions and exergy transfer on typical gas turbines by clearly taking into account the first and second law of thermodynamics with the common fuels being used and their toxic emissions. Also, the work done by Roth B. and Mavris D (n.d) shaded more light on the concept of availability or exergy analysis in a turbofan engine by strategically explaining the contributions that each single component performance has on exergy transfer and loss or destruction of exergy. Another research done using exergy analysis was by Turgut, Karakoc and Hepbasil (n.d) on a CF6-80 high bypass turbofan engine which demonstrated that the combustion chamber destroyed the most exergy in the system followed by the fan unit and it also showed that by increasing the isentropic efficiency of the components decreased the rate of exergy destruction. Previous studies carried out by Turgut, Karakoc and Hepbasil (2007) on a twin spool mixed flow turbofan with an afterburner with kerosene as the fuel using exergy analysis showed that more exergy is destroyed in the engine at take-off condition than during cruise condition while the potential for improvement of the component was higher at take-off condition than at cruise condition and this was said to be caused by the variation of temperature and pressure with altitude. However, Gogus, Camdali and Kavsaoglu (2002) investigated the implication of varying environmental conditions on exergy balance of thermodynamic systems exposed to changing ambient conditions and concluded that the reference environment should be taken respective to the ambient condition that the system is exposed to at that time but not to a particular fixed environment in order to avoid inaccuracies in the analysis. Given the perception that using alternatives fuels will resolve the problem of toxic emissions, 6.2.1. Exergy Analysis Modelling As stated earlier, the exergetic analysis would be done for two analysis cases which are analysis case 2 of constant fuel mass flow rate and analysis case 3 of constant turbine inlet temperature of the three fuels for the operational point of 30,000ft and M0 0.8.
Assumptions
1. The air and gases are ideal 2. The reference environment that will be used in the analysis is chosen respective to the ambient conditions at altitude 30,000ft. 3. The components of the engine are in average adiabatic. 4. The pressure of the fuel is taken to be 6126.6Kpa in order to have a healthy vaporisation for the combustion process. The data obtained from the generic simulation of the turbofan were used here in order to conduct the exergetic analysis of the engine. The total Exergy transfer into or out of each component was obtained by calculating the physical, chemical, potential and kinetic energy according to Kotas (1985). However, since the reference environment was chosen to be the outside ambient condition at any altitude of the engine and there are no different in altitude of any component in the engine, the potential effects of exergy is ignored. The following equations were used to calculate the components of exergy.
Physical Exergy
It is calculated as
ExPH=cpT-T0-T0lnTT0+RT0lnPP0
Kinetic Exergy It is calculated as
ExKN=mV22
Chemical Exergy
It is given as
ExCH=ixiε0i+RT0ixilnxi
where, ε0=Standard Chemical Exergy, R=Universal Gas Constant , and xi=Mole fraction in the mixture. The chemical exergy of the reference substances are calculated respective to the reference environment chosen using the equation as shown below. ε0=RT0lnP0P00 Where P00=partial pressure of the substance and P0=101.325kPa T0=288.15K R=8.3144kJkmolK | O2 | CO2 | H2O | N2 | xi | 0.2059 | 0.0003 | 0.019 | 0.7748 | P00 | 20.863 | 0.0304 | 1.9252 | 78.51 | ε0 | 3786.23 | 19433.84 | 9495.28 | 611.29 |

When the Reference environment is at 30000ft whereP0=30.09kPa T0=228.71K, | O2 | CO2 | H2O | N2 | xi | 0.2059 | 0.0003 | 0.019 | 0.7748 | P00(kPa) | 6.362 | 0.00927 | 0.587 | 23.941 | ε0 | 3005.2 | 15425.2 | 7536.6 | 485.19 |

Now that the standard chemical exergies have been found for the reference gases, the combustion process balance equations of the three fuels can then be done.
Kerosene Fuel Combustion Process
For a stoichiometric combustion process of kerosene, the reaction of one kmol of kerosene with air is shown below
C12H23+86.210.7748N2+0.2059O2+0.0003CO2+0.019H20
→61.796N2+12.026CO2+13.14H20
From that,
Stoichiometric Fuel-Air-Ratio=12×12+23×186.21×28.6384
Stoichiometric Fuel-Air-Ratio=114.784
Analysis of Case 2:
The mass flow rate of fuel is taken as constant which is 0.26kg/s and the core mass flow rate is taken as 31.7213kg/s.
Actual Fuel-Air-Ratio=0.2631.7213=1122.01
% of Excess Air=122.01-14.78414.784=7.25
The combustion equation of one kmol of kerosene with excess air of 725%
C12H23+711.490.7748N2+0.2059O2+0.0003CO2+0.019H20
→551.27N2+128.75O2+12.2135CO2+25.02H20
Equivalence Ratio Φ=Actual FARStoichiometric FAR=0.1212
The chemical Exergy of the combustion products is calculated as shown below | O2 | CO2 | H2O | N2 | | m | 32 | 44 | 18 | 28 | | xim | 5.744 | 0.748 | 0.63 | 21.518 | M=28.64 | n | 128.75 | 12.214 | 25.02 | 551.27 | | ε0 | 3005.2 | 15425.2 | 7536.6 | 485.19 | | xi=n∑n | 0.1795 | 0.017 | 0.035 | 0.7685 | | xilnxi | -0.3083 | -0.0693 | -0.1173 | -0.2024 | ixilnxi= -0.697 | xiε0i | 539.43 | 262.23 | 263.781 | 372.91 | ixiε0i= 1438.35 |

From the values of the table above, the chemical exergy of the combustion products can be calculated for analysis case 2 at 30,000ft at M0 0.8 operating condition using the equation given earlier as
ExCH=1438.35+8.3144×228.71×-0697
=1438.35-1325.98
=112.38kJkmol
From the simulation results, the combustor mass flow rate = 31.7213kg/s and Molar mass of mixture = 28.64
ExCH=112.38×31.721328.64
=124.47kW
ExCH=0.1245MW
Analysis of Case 3:
The Turbine Inlet Temperature (thermal limit parameter) of the three fuels are taken as constant which makes the mass flow rate of kerosene to be is 0.4785kg/s and the core mass flow rate is taken as 31.7213kg/s.
Actual Fuel-Air-Ratio=0.478531.7213=166.29
% of Excess Air=66.29-14.78414.784=3.48
The combustion equation of one kmol of kerosene with excess air of 348%
C12H23+386.560.7748N2+0.2059O2+0.0003CO2+0.019H20
→299.5N2+61.84O2+12.12CO2+18.85H20
Equivalence Ratio Φ=Actual FARStoichiometric FAR=0.223
This same procedure in calculating the chemical exergy for the combustion products in analysis case 2 was repeated for analysis case 3 and the chemical exergy of the combustion products was 0.284MW. The chemical exergy of the kerosene fuel was taken to be 45.8MJ/kg from (Turgut, Karakoc and Hepbasli).

Natural Gas Fuel Combustion process For a stoichiometric combustion process of natural gas, the reaction of one kmol of natural gas with air is shown below
0.96CH4+0.04C2H6+100.7748N2+0.2059O2+0.0003CO2+0.019H20
→7.748N2+1.043CO2+2.23H20
From that,
Stoichiometric Fuel-Air-Ratio=0.96×16+0.04×3010×28.6384
Stoichiometric Fuel-Air-Ratio=167.53
Analysis of Case 2:
The mass flow rate of fuel is taken as constant which is 0.26kg/s and the core mass flow rate is taken as 31.7213kg/s.
Actual Fuel-Air-Ratio=0.2631.7213=1122.01
% of Excess Air=122.01-67.5367.53=0.807
The combustion equation of one kmol of Natural gas with excess air of 80.7%
0.96CH4+0.04C2H6+18.070.7748N2+0.2059O2+0.0003CO2+0.019H20
→14N2+1.661O2+1.0454CO2+2.383H20
Equivalence Ratio Φ=Actual FARStoichiometric FAR=0.553
This same procedure in calculating the chemical exergy for the combustion products using kerosene fuel was repeated here and the chemical exergy for the combustion products using natural gas fuel for analysis case 2 was 1.7296MW.
Analysis of Case 3:
The Turbine Inlet Temperature (thermal limit parameter) of the three fuels are taken as constant which makes the mass flow rate of Natural gas to be is 0.42234kg/s and the core mass flow rate is taken as 31.7213kg/s.
Actual Fuel-Air-Ratio=0.4223431.7213=175.11
% of Excess Air=75.11-67.5367.53=0.1122
The combustion equation of one kmol of natural gas with excess air of 11.22%
0.96CH4+0.04C2H6+11.220.7748N2+0.2059O2+0.0003CO2+0.019H20
→8.693N2+0.25O2+1.04112CO2+2.257H20
Equivalence Ratio Φ=Actual FARStoichiometric FAR=0.8991
This same procedure in calculating the chemical exergy for the combustion products using kerosene fuel was repeated here and the chemical exergy for the combustion products using natural gas fuel in analysis case 3 was 0.964MW. According to Kotas (1985), the chemical exergy of a gaseous fuel is dependent on the ratio of chemical exergy to the net calorific value given as φ and for a natural gas is taken as 1.04. Thus, the chemical exergy of the natural gas is φ×NCV which is equal to 1.04×49.74MJkg=51.73MJkg
Hydrogen Combustion Process
For a stoichiometric combustion process of hydrogen, the reaction of one kmol of hydrogen fuel with air is shown below
H2+2.4250.7748N2+0.2059O2+0.0003CO2+0.019H20
→1.879N2+0.00073CO2+1.046H20
From that,
Stoichiometric Fuel-Air-Ratio=2×12.425×28.6384
Stoichiometric Fuel-Air-Ratio=134.724
Analysis of Case 2:
The mass flow rate of fuel is taken as constant which is 0.26kg/s and the core mass flow rate is taken as 31.7213kg/s.
Actual Fuel-Air-Ratio=0.2631.7213=1122.01
% of Excess Air=122.01-34.72434.724=2.514
The combustion equation of one kmol of Hydrogen with excess air of 251.4%
H2+8.5210.7748N2+0.2059O2+0.0003CO2+0.019H20
→6.6N2+1.254O2+0.00256CO2+1.162H20
Equivalence Ratio Φ=Actual FARStoichiometric FAR=0.285
This same procedure in calculating the chemical exergy for the combustion products using kerosene fuel was repeated here and the chemical exergy for the combustion products using hydrogen fuel in analysis case 2 was 0.331MW.
Analysis of Case 3:
The Turbine Inlet Temperature (thermal limit parameter) of the three fuels are taken as constant which makes the mass flow rate of Hydrogen to be is 0.17781kg/s and the core mass flow rate is taken as 31.7213kg/s.
Actual Fuel-Air-Ratio=0.1778131.7213=1178.4
% of Excess Air=178.4-34.72434.724=4.14
The combustion equation of one kmol of hydrogen with excess air of 414%
H2+12.4650.7748N2+0.2059O2+0.0003CO2+0.019H20
→9.66N2+2.066O2+0.00374CO2+1.237H20
Equivalence Ratio Φ=Actual FARStoichiometric FAR=0.195
This same procedure in calculating the chemical exergy for the combustion products using kerosene fuel was repeated here and the chemical exergy for the combustion products using hydrogen fuel in analysis case 3 was 0.0241MW.
The chemical exergy of hydrogen follows the same procedure as that of the natural gas andφ=0.985. As a result, the chemical exergy is 0.985×118.43MJkg=116.654MJkg
Mixer
The mixer used for this simulation is assumed to have an efficiency of 0.5. Since in the mixing chamber the cold air coming with low enthalpy molecules mixes with the hot gases from the LPT with very high enthalpy molecules and this reduces the enthalpy of the mixture which in turn reduces the chemical exergy of the hot gases since the molecular composition will change. The chemical exergy of the hot gases is assumed to be reduced by almost half according to (Turgut, Karakoc, Hepbasli, 2007). Thus, in this case, the chemical exergy in the mixer is approximated to be reduced by half.

6.2.2. Exergy and Energy Balance Equations of the components After the chemical, kinetic and physical exergies had been calculated based on the simulation results as explained above, the balance exergy equations for each component was written down in order to calculate the exergy transfer in or out, exergetic efficiency, fuel depletion ratio, improvement potential rate and exergy destruction rate. The potential energy effects are completely ignored.

Fan
The power transferred from the LPT to the fan is calculated as
Wfan=mfanCp,fanTt13-Tt2 ……………………………………………..…..(1) Exergy balance
Ex13+Exdest,fan=Ex2+Wfan ………………………………………………...(2)
Exergetic efficiency εfan=Exergy outExergy in=Ex13Ex2+Wfan ……………………(3)
Low Pressure Compressor
The power transmitted to the LPC form the LPT is calculated as
WLPC=mLPCCp,LPCTt2.5-Tt2 …………………………………………………(5)
Exergy Balance
Ex2.5+Exdest,LPC=Ex2+WLPC ……………………………………………(6)
Exergetic Efficiency εLPC=Exergy outExergy in=Ex2.5Ex2+WLPC ……………….(7)
High Pressure Compressor
The power transmitted to the HPC from the LPT is calculated as
WHPC=mHPCCp,HPCTt3-Tt2.5 …………………………………………..(9) Exergy Balance
Ex3+Exdest,HPC=Ex2.5+WHPC …………………………….…………….(10)
Exergetic Efficiency εHPC=Exergy outExergy in=Ex3Ex2.3+WHPC………………(11)
Combustion Chamber
There is no power transmission in the combustion chamber but there is transfer of exergy into it through the fuel energy
WCC=0
Exergy Balance
Ex4+Exdest,CC=Ex3+Exfuel …………………………………………(13)
Exergetic Efficiency εcc=Exergy outExergy in=Ex4Ex3+Exfuel ………..…..(14)
High pressure Turbine
The energy extracted from the hot gases by the HPT is equivalent to the work done by the HPC since the mechanical efficiency is assumed to be 1.
WHPT=WHPC
Exergy Balance
Ex4.5+Exdest,HPT+WHPT=Ex4
εHPT=Exergy outExergy in=Ex4.5+WHPTEx4

Low Pressure Turbine
The energy extracted from the hot gases by the LPT is equivalent to the work done by the fan and LPC since the mechanical efficiency of the low pressure spool is assumed to be 1
WHPT=Wfan+WLPT
Exergy Balance
Ex5+Exdest,LPT+Wfan+WLPT=Ex4.5
εLPT=Exergy outExergy in=Ex5+WLPT+WfEx4
Mixer
There is no heat transfer or work done but only the mixture of the cold bypassed air and hot gases. Given that the pressure ratio in the bypass duct is assumed to be i.e πbypass=1, the exergy transferred out of the fan will be the exergy transferred into the mixer.
Exergy Balance
Ex6+Exdest,mix=Ex5+Ex16
εmix=Exergy outExergy in=Ex6Ex5+Ex16

Exhaust Nozzle
Exergy Balance
Ex8+Exdest,noz=Ex6
εnoz=Exergy outExergy in=Ex8Ex6

6.2.3. General Relationships in Exergy Analysis of the Components
Exergy destruction Rate/irreversibility Rate Exergy destruction rate is the measure of entropy generation with reference to the ambient environment. Exergy destruction provides information on where the real inefficiencies in a system lie. Mathematical, it can be defined as the difference between the total exergy transferred into and out of a system as shown below. Exdest=Exergy in-Exergy out

Exergetic Efficiency Exergetic efficiency is the ratio of exergy rate transferred out of a system to the exergy rate transferred into the system which is a measure of how exergy is properly utilised by the system. It can be expressed mathematically as shown below. εLPT=Exergy outExergy in
Fuel Depletion Ratio This measures the rate at which the exergy rate transferred in by the fuel is consumed by each component due to irreversibility within the component. In other words, it is simply the ratio of exergy destroyed in the component to the exergy possessed by the fuel. δ=ExdestExfuel Exergetic Improvement Potential Rate (IP) The improvement potential rate of a given component is highly dependent on its exergetic efficiency and exergy destruction rate. When a component is restrained by physical, technological and economic constraints, its improvement potential can be calculated by its irreversibility rate under a given set of conditions in relation to the minimum irreversibility rate possible. The mathematical expression is shown below
IP=1-εExdest

6.2.4. Results and Discussions of Exergetic Analysis The equations above were used to evaluated the exergy rate transfer in and out of the components, the exergetic efficiency, fuel depletion ratio, exergy improvement potential rate, relative irreversibility, exergy destruction rate for the parametric analysis case 2 (constant fuel flow rate) and case 3(constant TIT) for the fuels kerosene, hydrogen and natural gas. The Tables 7-18 in the appendix represents the exergetic resource data of all three fuels for the two parametric cases. Based on the result, bar charts were constructed for each parametric case to shown the distribution of exergy destruction rates in each components, the exergetic efficiency, the exergy improvement potential and the fuel depletion ratio as shown in figure 29-36.

Type of Fuel | Analysis Case 2 (Constant mf )Equivalence Ratio | Analysis Case 3 (Constant TIT)Equivalence Ratio | Kerosene | 0.1212 | 0.223 | Natural Gas | 0.553 | 0.8991 | Hydrogen | 0.285 | 0.195 |
Table 4 Equivalence Ratio of the Combustion Process of the three Fuels.
Exergy destruction Rate/irreversibility Rate The exergy destruction rates of the fan, LPC and HPC units remained constant when the three fuels were used for both analysis cases as can be seen in figure 29 and 30. The reason for this is that the isentropic efficiency, pressure and temperature ratios were kept constant throughout the analysis which means the interaction of exergy rates will be the same. It was general observed that the combustion chamber and the mixer had the most exergy destruction rate followed by the fan and LPC. The reason for this higher exergy destruction rate is due to the chemical reaction and rapid mixing process which generates a lot of entropy and entropy generation destroys exergy.

Figure 29 Variation of Exergy Destruction Rate Using the three Fuels for Analysis Case 2 From figure 29 above, it was observed that when hydrogen fuel was used, the combustion chamber destroyed the highest amount of exergy rate followed by when kerosene fuel was used and then natural gas. The reason for this is that the total exery rate transferred into the combustion chamber by hydrogen fuel is considerably high with a value of 30.33MW due to its high net calorific value compared to natural gas fuel that transferred in just 13.5MW and kerosene with 11.93MW. Consequentially, this means that hydrogen fuel exergy rates stand more chance of being depleted than the others. Also, it is known that the leaner a combustion process is, the lower the efficiency of combustion and the equivalence ratio quantifies how lean a combustion process is. Returning to the case in hand, the equivalence ratio was obtained as 0.285 for hydrogen process, 0.553 for natural gas process and 0.1212 for kerosene. With equivalence ratio of hydrogen fuel as 0.285 for case 2, the effective conversion of exergy transferred into combustion process to the exergy transferred out will be limited since the process is extremely lean and the chemical exergy possessed by the gas products will be low.
The exergy destruction rate in the HPT and LPT decreased as the fuel was changed from kerosene to natural gas to hydrogen and this can be attributed to the difference in chemical composition of product gases from the combustion processes of the three fuels. This means the density of the gas products when the three fuels are used will be different and the lower then density the more effective the turbine will be able to extract the entire exergy rate transferred in. The mixer was observed to destroy the most exergy rate when hydrogen fuel was used compared to the other two fuels for analysis case 2 of constant fuel flow rate. The high LPT turbine exit temperature into the mixer as explained earlier is the major cause of the high exergy destruction rate for hydrogen fuel and with natural gas and kerosene fuel it can be seen that the exergy destruction rate is reasonably low due to the low LPT exit temperatures.

Figure 30 Variation of Exergy Destruction Rate Using the three Fuels for Analysis Case 3 For analysis case 3 where the turbine inlet temperature was maintained for the three fuels, kerosene fuel caused the most exergy rate destruction in the combustion chamber follow by hydrogen and then natural gas. Natural gas fuel still caused the least exergy rate destruction in the combustion chamber even when the turbine inlet temperature was kept constant because of its high equivalence ratio of 0.8991 compared to 0.223 for kerosene and 0.195 for hydrogen. In other words, natural gas has an inherent ability to effectively utilise all it fuel for a particular combustion process which causes the chemical exergy possessed by the product gases to be high by 1.73MW compared to just 0.024MW for hydrogen and 0.284MW for kerosene. In essence, it can be said that using natural gas can reduce the amount of optimization needed in a combustion process since the efficiency will be high due to lower exergy destruction. The same effects were observed in the HPT and LPT for analysis case 3 that hydrogen still had the better side of the other two fuels with the amount of exergy rate destroyed. The high chemical exergy rate of the product gases from natural gas as shown earlier will translate into a negative factor in the mixer since more exergy will be transferred in and stands more chance of being destroyed compared to the product gases of hydrogen fuel and kerosene. Based on this, the benefits of reduced exergy destruction in the combustion chamber using natural gas is conteracted with the increase in exergy destruction rate in the mixer. Thus, it can be said that fuels that provided a better efficiency for the combustion chamber will make the mixer to be deficient when the turbine inlet temperature is kept constant for all the fuels.

Exergetic Efficiency
It can be said that the closer the exergetic efficiency of a component is to 1, the more efficiently the component will operate which contributes to the overall performance of the engine The exergetic efficiencies of the exhaust nozzle and turbomachineries except for the fan and LPC were very close to 1 signifying that a small amount of exergy rate was destroyed in them as shown in figure 31 and 32. The incoming kinetic exergy rate transferred into the fan and LPC by the moving jet approaching the inlet at Mo 0.8 causes the total exergy rate input to increase while the exergy rate output still remains almost constant making the exergetic efficiency of the fan and LPC to reduce. This can be explained in the maintenance point of view to mean that the fan and LPC stands more chance of becoming unstable and faulty when ingesting high velocity air during cruise phase of the aircraft than the turbines. It was also noticed that the mixer and the combustion chamber had low exergetic efficiency but not as low as that of the fan and LPC. The interesting point noted is that components can have high exergy destruction rate while its exergetic efficiency is reasonably high.

Figure 31 Variation of Exergetic Efficiencies Using the three Fuels for Analysis Case 2
When hydrogen was being used the exergetic efficiency of the components especially the HPT, LPT and Exhaust nozzle increases as shown in figure 31 which justifies the decrease in exergy destruction rates explained earlier. When natural gas fuel was used, the combustion chamber had the highest exergetic efficiency which corresponds to the low exergy destruction rate from the process as stated earlier.

Figure 32 Variation of Exergetic Efficiencies Using the three Fuels for Analysis Case 3
Exergy Improvement Potential Rate: As stated earlier, the exergy improvement potential rate is highly dependent on the exergetic efficiency and exergy destruction rate. It is a very important parameter in exergetic analysis because it shows the maximum limit the component efficiency can be improved before it starts being at a disadvantage like heaping huge operating cost. Looking at figure 33 and 34, it can be seen that the HPC, HPT, LPT and the exhaust nozzle had the least exergy improvement potential Rate and this is because of their high exergetic efficiency with low exergy destruction rate. However, it was also noticed that the fan, mixer, low pressure compressor and combustion chamber had the highest exergy improvement potential rate and this is due to the low exergetic efficiency and high destruction rate. Thus, it can be said that components with high exergy improvement potential rate are in a better position to be improved which can have a very positive effect on the overall performance of the engine than the other components with low improvement potential rate.

Figure 33 Distribution of Exergy Improvement potential Rate Using the three Fuels for Analysis Case 2
With the mass flow rate of the three fuels being kept the same, the exergy improvement potential rate in the combustion chamber was smallest for natural gas fuel followed by kerosene and then hydrogen as shown in figure 33 above. The reason for this dates back to the high exergetic efficiency and low exergy destruction rate when using natural gas as explained earlier. In the mixer, hydrogen fuel showed the highest potential for improvement of the mixer. Despite the mixer having the highest exergetic efficiency compared to the other fuels as shown in figure 31, the exergy destruction rate is still too high that it outweighs the positive effect of high exergetic efficiency.

Figure 34 Distribution of Exergy Improvement potential Rate Using the three Fuels for Analysis Case 3 From figure 34 above, it can be seen that when natural gas is used, the combustion chamber had the smallest exergy improvement potential rate with hydrogen coming next and kerosene with the highest. For a constant turbine inlet temperature of the three fuels, when natural gas was used the exergy destruction rate reduced and the exergetic efficiency increased which results in the net decrease in exergy improvement potential rate. However, the opposite happened in the mixer with kerosene fuel reducing the exergy improvement potential rate and natural gas having the highest. It was noticed that the low pressure turbine seemed to have a greater potential for improvement when kerosene fuel is used.

Fuel Depletion Ratio
This is the ratio of exergy destruction rate in a component to the exergy rate transferred into the system by the fuel. Considering figure 35 and 36, it can be seen that majority of the fuel energy or exergy rate is destroyed in the combustion chamber and mixer. This happens because combustion and mixing process result in a very significant growth in entropy and entropy is known to destroy exergy.

Figure 35 variation of Fuel Depletion ratio using the Three Fuels for Analysis Case 2 Despite the isentropic properties of the compression unit being kept constant, the fuel depletion ratio will differ depending on the amount of exergy transferred in by the reacting fuels. In analysis case 2 shown in figure 35 of constant fuel flow rate, it can be seen that the fuel depletion ratio of the compression unit was smallest when hydrogen fuel was used with natural gas following up and kerosene having the highest. This variation in fuel depletion ratio is due to the high exergy rate transferred into the turbofan engine by hydrogen fuel which the value is 30.33MW compared to 13.5MW of kerosene fuel and 11.93MW of natural gas. In the mixer, the amount of exergy rate destroyed when hydrogen fuel was used was higher than that in the combustion chamber. Furthermore, it can be seen that almost all the components had the smallest fuel depletion ratio when hydrogen fuel was used. The majority of the high exergy rate transferred in by hydrogen fuel is being lost in the exhaust while some is converted to a remarkable high thrust. This justifies the result obtained earlier of increasing thrust with hydrogen fuel.

Figure 36 variation of Fuel Depletion ratio using the Three Fuels for Analysis Case 3 The fuel depletion ratio in the compression unit was observed to remain the same when natural gas and kerosene fuel were used but increased slightly when hydrogen fuel was used as shown in figure 36 above. The reason for this is that for the three fuels to produce the same turbine inlet temperature, the total exergy rate possessed by all the fuels would approximately be the same. In this case, the exergy rate transferred in by hydrogen, natural gas and kerosene fuel were obtained to be 20.742MW, 21.846MW and 21.984MW respectively as shown in table 7-18 in the appendix.

6.2.5. Grassmann Diagram Grassmann diagram is the pictorial or graphical representation of the exergy rate transfers in and out of a system components and their exergy destruction rate. Grassmann provides a way of visualising how the exergy transfers of each component are interacting with one another. The importance of Grassmann diagram grows as the complexity of the thermal system grows according to Kotas (1985) because it clearly shows not only the exergy losses but also the recirculation and splitting of exergy. Looking at the Grassmann diagram shown in figure 37 below, it can clearly be seen how the exergy rates are being transferred in and out of each components in the system. In the diagram, the arrow at the inlet to the fan and low pressure compressor represents the exergy rate transferred into the system by the kinetic exergy possessed by the incoming jet. The black shaded triangles at each component block represent the exergy destruction rate in the component. In the diagram, the wider arrow that point inwards to the combustion chamber represents the exergy rate transferred into the system by the fuel through combustion process. Also in the diagram, the direction of the flow of exergy rate through each component as either power or bypassed can be seen. Finally, the red font numerical values represent the exergy destruction rates at each component. The numerical values would change for the different fuels being used for parametric analysis case 2 but the overview of the Grassmann diagram will remain fairly the same for all three fuels. Figure 37 Grassmann Diagram for the Exergetic Analysis of Case 2 using Kerosene Fuel.

6.2. Thermoeconomics Analysis Thermoeconomics as the name implies is the relationship between thermodynamics and economics. In other words, it is the aspect of cost consideration in thermodynamics. It is logical that for any system to be designed, the total cost and maintenance cost must be considered. Accordingly, the effective way of managing this cost and design process of thermodynamic system is described as thermoeconomics. Thermoeconomics basically uses the concept of exergy to calculate total cost of thermodynamic system in order to show where cost can be cut down. The sole purpose of manufacturing jet engines is to make profit and one way of achieving this is by reducing the total cost. Based on that, it makes thermoeconomics a very important tool for strategizing the cost to ensure that maximum profit is obtained. Moreover, Kotas (1985) said that ‘thermoeconomics analysis could decide whether using more advanced and more expensive turbomachineries is offset by decreasing exergy’. Thermoeconomics analysis is a very interesting method of radically assessing the economic justification of cost in order to favour and be fair to the consumers. In fact, (Tona, Raviolo, Pellegrini, Junior, 2009) conducted a study on the exergoeconomics analysis of a turbofan engine during a typical commercial flight using ground reference and engine reference and arrived that if increasing the overall efficiency of an engine means increasing the total cost then such improvement should not be done. However, using the concept of thermoeconomics can create a balance to this in a sense that efficiency can be increased while cost still remains the fairly the same 6.3.1. Thermoeconomics Analysis Modelling This can simply be referred to as the cost accounting of exergy of thermal systems. The following listed below are the thermoeconomics parameters that must be defined in order the conduct the cost analysis of exergy of the turbofan engine.
Interest Ratio (i): Interest ratio is the percentage at which the total cost being invested in a particular system is being charged profitably over a period of time which could be either monthly or annually.
Economic System Operating Years and hours (n): This is the total number of years that the jet engine or any thermal system is estimated to be operated for a constructive period of hours each year.
Capital recovery Factor (CRP): It is the ratio of a constant annuity to the present value of receiving that annuity for a given length of time. Using interest rate,
CRF=ii+1ni+1n-1
Levelised Capital Cost Rate (C): This measures the rate at which the capital cost of investment of a system or its component is being recovered over a period of one year.
C=CRF×(Capital cost)operating hours
Specific Thermoeconomics Cost (c): This is the total cost of exergy transfer rate that a system or its component will possess due to the levelised capital cost rates of the equipment. This parameter is very important because it provides a way of properly costing energy output through the concept of exergy. It can simply be expressed as the levelised captital cost divided by the exergy transfer rate. As shown below c=CEx £MJ
Assumptions
The capital cost of the components or equipment were taken to be as shown in the table 5 below. The interest ratio based on the capital cost is taken to be 10%, the economic system operating years is taken to be 20 years while the operating hours per year is 5110 hours. The fuel specific cost of kerosene was taken as 5.5533£/GJ as seen in (Tona, Raviolo, Pellegrini, Junior, 2009) COMPONENTS | CAPITAL/INVESTMENT EQUIPMENT COST(£) | Whole Engine | 1,230,580 | Diffuser | 61,529 | Fan/Low Pressure compressor | 209,198.6 | High Pressure Compressor | 270,727.6 | Combustor | 172,281.2 | High Pressure Turbine | 221,504.4 | Low pressure Turbine | 147,669.6 | Mixer | 49,223.2 | Exhaust Nozzle | 98,446.4 |
Table 5 Assumed Capital Costs of Each Component of the Turbofan Engine The thermoeconomics analysis is conducted using Global and local power plant production cost evaluation for the exergy analysis of the turbofan engine when it was operating at 30,000ft using kerosene fuel for parametric analysis case 2. Global based cost Evaluation takes the system to be one unit without considering the sub components while the local based cost evaluation takes into account the flow of exergy stream cost in and out of each sub components. The main aim of this is to show whether using the global balance and local balance cost evaluation will produce the same specific thermoeconomics cost for the output thrust. Given that the exergetic analysis had already been done for the turbofan engine at the operating condition of 30000ft whilst using kerosene at constant mass flow of 0.26kg/s, a table was constructed in order to conduct the thermoeconomic analysis as shown in table 20 in the appendix. This table shows the flow of exergy in each components, the thrust power or exergetic thrust, fan and HPC power. With all these parameters obtained and tabulated, the global and local exergy based cost analysis was then able to be done as follows. 6.3.2. Global Based Cost Evaluation This is the type of economics cost evaluation that calculates the cost of an exergy output by considering the thermal system as a unit without considering the subcomponents. This type of cost evaluation usually lacks the understanding of how the subcomponents efficiencies contribute to the cost of the output exergy stream. Since in this concept the system is considered to be one, the cost evaluation would take into account the exergetic cost flow rate in and out of the system. Additionally, the fuel used is the only source of cost in exergy rate transferred in and the exhaust thrust power is the only source of useful cost of exergy rates transferred out. Based on that, the thermoeconomic cost useful thrust exergy output was calculated as shown below for the exergetic analysis results.
The cost Balance;
Levelised cost rate of Fuel + Levelised cost rate of the whole engine = Levelised cost rate of thrust Cfuel+Cequip=CT cTExT=cfuelExfuel+Cequip cT=cfuelExfuel+CequipExT
From the table below, the specific thermoeconomic cost of thrust cT using the global exergy cost evaluation was calculated as shown below cT=0.0055333×11.938+0.007862.643 =0.028 £/MJ 6.3.3. Local Based Cost Evaluation:
This cost evaluation cost takes into account the flow of specific thermoeconomic cost of each stream of exergy in each component. In other words, it helps in attributing the appropriate cost to each stream of exergy into each component.
Component Modelling
Diffuser:
c1Ex1+Cdiff=c2Ex2, where c1=costless specific thermoeconomic cost flowing out of the diffuser c2= CdiffEx2
FAN and LPC: c2Ex2+Cfan+Wfan/LPCcfan/LPC=c13Ex13+c2.5Ex2.5, where cfan=c2.5=c13=c specific thermoeconomic cost flowing out of the Fan c2.5= c2Ex2+CfanEx13+Ex2.5-Wfan
High Pressure Compressor: c2.5Ex2.5+CHPC+WHPCcHPC=c3Ex3, where c3=cHPC specific thermoeconomic cost flowing out of the HPC c3= c2.5Ex2.5+CHPCEx3-WHPC
Combustion Chamber: c3Ex3+Ccc+Exfuelcfuel=c4Ex4 specific thermoeconomic cost flowing out of the CC c4=c3Ex3+Ccc+ExfuelcfuelEx4
High Pressure Turbine:
WHPC=WHPT
c4Ex4+CHPT=c4.5Ex4.5+WHPCcHPT, where c4.5=cHPT c4.5=c4Ex4+CHPTEx4.5+WHPC Low Pressure Turbine:
Wfan/LPCcfan/LPC=WLPT
c4.5Ex4.5+CLPT=c5Ex5+WfancLPT, where c5=cLPT c5=c4.5Ex4.5+CLPTEx5+Wfan Mixer: c5Ex5+Cmix+Ex13c13=c64Ex64 c64=c5Ex5+Cmix+Ex13c13Ex64
Exhaust Nozzle:
Cnoz+Ex64c64=cTExT
cT=Cnoz+Ex64c64ExT
Where, ExT is the thrust power of Exergy rates obtained from the exhaust exergy rate

6.3.4. Results and Discussion of the ThermoeconomicAnalysis From the analysis done, the global based exergy cost evalution method used showed a value of specific thermoeconomics cost as 0.028£/MJ for the output thrust generated. However, the local exergy based cost evaluation presented the specific thermoeconomics flow of cost progressively in each components up to the output thrust of 0.0103£/MJ as shown in table below. From the two values of specific thermoeconomics cost obtained for thrust, it can be seen that when the local cost evaluation was used, the specific thermoeconomics cost of thrust reduced by more than half compared to when the global exergy based method was used. The local method can be said to provide a favourable costing of thrust for consumers using the turbofan engine compared to the global method. Moreover, using the global cost evaluation method will not show which components contribute the most to the specific thermoeconomics cost of thrust. FLOW | Thermoeconomics Specific Cost (£/MJ) | Specific Thermoeconomics Cost (E/MWh) | Fan/Low pressure compressor inlet c2 | 0.00014 | 0.51043 | High pressure compressor inlet c2.5 | 0.00079 | 2.84646 | Combustor inlet c3 | 0.00123 | 4.41189 | High pressure turbine inlet c4 | 0.00394 | 14.19145 | Low Pressure turbine inlet c4.5 | 0.00409 | 14.72461 | Mixer inlet from fan c13 | 0.00079 | 2.84646 | Mixer inlet from Turbine c5 | 0.00434 | 15.62374 | Exhaust nozzle inlet c64 | 0.00380 | 13.69054 | Thrust cT | 0.01032 | 37.16953 |
Table 6 Flow of Specific Thermoeconomics Cost in all the Components

Chapter 6 Conclusions and Future Work
6.1. Conclusion The work presented a way of analysing the performance characteristics of a twin spool mixed flow turbofan engine using kerosene, natural gas and hydrogen fuel. The concept of exergy and thermoeconomics analysis of the mixed flow turbofan engine has also been presented. The main conclusions drawn from the results obtained are as follows. The performance characteristics such as net thrust, specific fuel consumption decreased with increasing bypass ratio for a given turbine inlet temperature which resulted in an increase in the propulsive and thermal efficiency. However, the performance parameters had a contradicting effect as the turbine inlet temperature increased for a given bypass ratio. For the parametric analysis case two of constant fuel flow rate, hydrogen fuel produced the most thrust with very high turbine inlet temperature with natural gas fuel and kerosene fuel following up respectively. Also, the specific fuel consumption of hydrogen was seen to be the lowest followed by natural gas and kerosene fuel. This was said to be caused by the higher net calorific value of hydrogen compared to the rest of the fuels. For this condition of constant fuel flow rate, the high turbine inlet temperature caused by hydrogen fuel would provide a way to reduce the compressor pressure ratio which will increase the overall efficiency of the compressor due to reduced number of stages. The high thrust levels of using hydrogen fuel can be taken advantage of at the expense of its unavailability by mixing a small percentage of it with either kerosene fuel or natural gas. The net thrust will not only be higher than using just kerosene fuel in this case, but the pollution risk will be reduced as well. When the bypass ratio was varied for the constant fuel flow rate, it showed that the increasing turbine inlet temperature did not have any effect on the nozzle exit velocity as in the change in kinetic energy of the exit jet was not seen. This effect was attributed to mixing process of the bypass air and hot air which shows the importance of the mixer in this type of turbofan engine if the bypass ratio is to be increased. The effect of increasing the bypass ratio when the turbine inlet temperature was kept constant showed that all the performance parameter such as net thrust, propulsive efficiency, and thermal efficiency of all the three fuels were almost the same with a decreasing trend. On the contrary, the specific fuel consumptions of the three fuels were different with hydrogen consumption rate being the least but had a decreasing trend with increasing bypass ratio. Based on this, it can be concluded that the effects of using the three different fuels on the turbofan engine performance characteristics was really noticed when hydrogen fuel was used. The overall exergetic analysis showed that the combustion chamber and the mixer contributed the most to the inefficiencies in the turbofan engine for both analysis cases irrespective of the fuel being used because of the high exergy destruction rates obtained. It can be concluded that unless an unconventional or unorthodox way is devised to reduce the irreversibilities in the combustion process, it will probably be impossible to achieved reasonable improvement in the efficiency of the combustion chamber. The exergetic analysis also showed that using natural gas fuel provided a better efficiency for the combustion chamber because of the low exergy destruction rates in both analysis cases. Hydrogen fuel was shown to contribute the most to the inefficiency of the mixer when the fuel flow rate was kept constant. Additionally, the ratio of depletion of hydrogen fuel in this case was the lowest for all the components due to the higher exergy rate transferred in by hydrogen. The thermoeconomic analysis showed that the specific thermoeconomics cost of output thrust from the mixed flow turbofan engine differed as the global and local based cost evaluation methods were applied by more than 50%. Hence, it can be concluded that in real life situations, the cost evaluation method of any jet engine should be chosen meticulously in order to be fair and rational when assigning cost to avoid over charging or under charging.

6.2. Future Work The work here considered the analysis of a twin spool mixed flow turbofan engine with low bypass ratio however, the analysis can prove to be more interesting if a reheat or afterburner is added into the picture because of the military purposes of maximum thrust in minimum response time. Three fuels were compared here in this work through the performance characteristics they imposed on the turbofan engine but a future work can be done that will show more emphasis on the pollution aspect of the three fuels by taking into account the NOx formation, Soot, CO and Hydrocarbon. Also in this work, the compression units (i.e fan, LPC and HPC) were assumed to have a constant isentropic properties (pressure ratio and temperature ratio) which caused a bit of discrepancy in the mixer efficiency due to the extreme difference of the bypass duct exit pressure and LPT exit pressure as the bypass ratio and turbine inlet temperature were increased. The next step forward would be to vary the fan pressure ratio accordingly with increasing bypass and temperature ratio in order to maintain almost the same bypass duct exit pressure as the LPT exit pressure to ensure efficient mixing. The thermoeconomics analysis aspect was covered in an introductory manner without much emphasis on the optimising characteristics of thermoeconomics analysis of the turbofan engine. The future work will focus more intense on the optimisation process of the turbofan engine using thermoeconomics.
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Appendix A
EXERGY ANALYSIS

Appendix B
THERMOECONOMICS ANALYSIS
Table 29 Levelised capital Cost Rates of all the Components Components initial costs | Capital cost (£) | Levelized Capital Rate (£/s) | Whole Engine | 1230580 | 0.007857331 | Diffuser | 61529 | 0.000392867 | Fan/Low Pressure compressor | 209198.6 | 0.001335746 | High Pressure Compressor | 270727.6 | 0.001728613 | Combustor | 172281.2 | 0.001100026 | High Pressure Turbine | 221504.4 | 0.00141432 | Low pressure Turbine | 147669.6 | 0.00094288 | Mixer | 49223.2 | 0.000314293 | Exhaust Nozzle | 98446.4 | 0.000628586 |

Table 20 Exergy Transfer Rates for the Thermoeconomics Analysis Description | Exergy Transfer Rates (MW) | Fan/LPC Inlet (2) | 2.7708 | Fan Outlet (13) | 3.5881 | LPC Outlet (2.5) | 6.1106 | HPC Outlet (3) | 12.4024 | HPT Inlet (4) | 20.9512 | HPT Outlet (4.5) | 13.4889 | LPT Outlet (5) | 5.4174 | Mixer Outlet (64) | 7.0111 | Nozzle Outlet (8) | 6.6602 | Kerosene Fuel | 11.9380 | Thrust | 2.6432 | Fan/LPC Power | 7.5125 | HPC Power | 7.0495 |