Development of a Propulsion Model for a MDO Framework: Mission-Based Optimization

Development of a Propulsion Model for a MDO Framework: Mission-based Optimization

José Ricardo Teixeira Fernandes

Thesis to obtain the Master of Science Degree in Aerospace Engineering

Supervisors: Prof. Fernando José Parracho Lau Dr. José Lobo do Vale Prof. Michele Ferlauto

Examination Committee Chairperson: Prof. João Manuel Lage de Miranda Lemos Supervisor: Prof. Fernando José Parracho Lau Member of the Committee: Prof. Filipe Szonolky Ramos Pinto Cunha

November 2015 ii In thrust we trust.

iii iv Acknowledgments

I would like to start by expressing my gratitude to my supervisor Professor Fernando Lau, for all his support and careful attention on reading and correcting the drafts of my thesis. Also to him and to Professor Afzal Suleman for the possibility of working in this project. To my co-supervisor Dr. Jose´ Vale and to Dr. Frederico Afonso I am grateful for constant attention and availability for helping on every single difficulty as well as contributing to the good working environment that they created right from the first moment. My gratitude to my supervisor Professor Michele Ferlauto from the Politecnico di Torino for his review on the work developed and for its support on dealing with all the paperwork and bureaucracy needed for finalizing the thesis at PoliTO. Then a special thanks to Jose´ Oliveira, with whom I could share closely this thesis work development and who was always the first helping source for any difficulty. Also to David Brandao˜ which in a later phase helped me by reading and correcting my drafts. Lastly, I would like to express my gratitude to my family for their unconditional support and care along this complete journey and to my friends for all the good moments.

v vi Resumo

As regulamentaçoes˜ ambientais impostas a` industria´ do transporte aereo´ cada vez mais restritivas, aliadas as` previsoes˜ de crescimento deste sector, temˆ imposto uma grande pressao˜ sobre o desen- volvimento de aeronaves com um consumo de combust´ıvel cada vez menor. Para dar resposta a estes requisitos contraditorios,´ o projeto de novas aeronaves tem estado a desenvolver-se para que, desde os primeiros estudos preliminares, sejam tidas em consideraçao˜ todas as disciplinas envolvidas e incorporadas tecnicas´ de otimizaçao.˜ Com o objetivo de aplicar estes con- ceitos de otimizaçao˜ multidisciplinar, esta´ a ser criada pela Area´ Cient´ıfica de Engenharia Aeroespacial um ferramenta para ser usada na fase de projeto preliminar, o MDOGUI, a qual esta´ a ser desen- volvida no ambitoˆ do enquadramento do projeto NOVEMOR inserido no 7o Programa Quadro da UE. Um modulo´ capaz de modelar com media´ fidelidade um turborreator de duplo fluxo e um turboelice´ foi implementado que, contrariamente ao realizado noutros processos de otimizaçao˜ multidisciplinar, foi desenvolvido desde o in´ıcio para ser totalmente integrado juntamente com os restantes modulos.´ Os modelos do turborreator de duplo fluxo e do turboelice´ implementados inclu´ıram uma analise´ em Condiçoes˜ de Projeto, onde o desempenho do motor e´ estudado para um unico´ Ponto de Projeto, seguida por uma analise´ fora das Condiçoes˜ de Projeto e onde a performance do motor e´ testada para todas as condiçoes˜ de operaçao.˜ Adicionalmente, foi tambem´ implementado um modelo com base em dados historicos´ para o calculo´ do peso e dimensoes˜ do turborreator de duplo fluxo. Para validaçao˜ dos resultados dos modelos, estes foram comparados com resultados dispon´ıveis em literatura e num exemplo de motor e missao˜ fornecido pela Embraer, um dos parceiros do projeto NOVEMOR. Com o objetivo de reduzir o consumo de combust´ıvel de um motor, for executado um processo de otimizaçao˜ com o objetivo de determinar o Ponto de Projeto que define o motor com menor consumo de combust´ıvel ao longo de um dado perfil de missao.Com˜ este processo foram encontrados resultados promissores, uma vez que foi obtida uma reduçao˜ no consumo de combust´ıvel de ate´ 19%, quando comparado o motor otimizado com o motor standard.

Palavras-chave: Performance de motor, Turborreator de duplo fluxo, Turbo-helice,´ Otimizaçao˜ multidisciplinar, Minimizaçao˜ do consumo de combust´ıvel, Projeto preliminar de aeronaves.

vii viii Abstract

The more stringent environmental regulations imposed to air transportation together with the predicted growth of air travelling, demand a great effort in the development of more fuel efficient aircraft. In order to answer to these requirements, the design process for new aircraft is evolving. Nowadays, right from the preliminary studies, all aircraft disciplines are evaluated and are being incorporated in optimization environments. With the objective of applying Multidisciplinary Design Optimization (MDO) techniques, a preliminary design tool, MDOGUI, included in the scope of the EU 7th Framework project NOVEMOR, is being developed by the IST Aerospace Group. To be added to this tool a medium-fidelity propulsion module capable of modelling turbofan and turboprop engines was developed. Unlike to other already developed MDO frameworks, the propulsion module in this case was built from the scratch to be fully integrated with the other modules. The turbofan and turboprop models included an On-Design analysis, where the initial performance of the engine is studied for a single Design Point, followed by an Off-Design analysis where the engine performance is studied along its operating range. In addition, a weight and size models for the turbofan were defined based on historical data. A comparison of results with information found in literature and other engine and mission data provided by a NOVEMOR project partner, EmbraerTM, was done for the model verification. With the ultimate objective of reducing the fuel consumption of the engine, an optimization process was executed in order to determine the engine Design Point that delivers the most fuel efficient engine design across a given flight mission profile. From this process, promising results were obtained, given that reductions of up to 19% on the total fuel burned for a typical regional jet mission were achieved when comparing a standard engine design to a mission optimized engine design.

Keywords: Engine performance, Turbofan, Turboprop, Multidisciplinary Design Optimization, Fuel Consumption Minimization, Preliminary Aircraft Design.

ix x Contents

Acknowledgments...... v Resumo...... vii Abstract...... ix List of Tables...... xiii List of Figures...... xvi Nomenclature...... xix Glossary...... 1

1 Introduction 1 1.1 Context and Motivation...... 1 1.2 Multidisciplinary Design Optimization...... 2 1.3 Propulsion module...... 5 1.3.1 Aircraft engines...... 5 1.3.2 Propulsion models’ state-of-the-art...... 7 1.3.3 Objectives and Approach...... 11

2 Turbofan engine modelling 13 2.1 Parametric model (On-Design)...... 17 2.2 Performance model (Off-Design)...... 28 2.3 Weight and size model...... 35

3 Model Results and Veriﬁcation 41 3.1 On-design and Off-design analysis results...... 41 3.2 Model application for GE CF34-10E and results comparison...... 45 3.3 Application of a modelled engine to a ﬂight mission...... 48 3.4 On-design and Off-design analysis results for the Turboprop model...... 51

4 Optimization of a turbofan mission’s fuel consumption 55 4.1 Optimization of engine design variables for a Design Point...... 55 4.2 Optimization of fuel consumption on a given ﬂight mission...... 58

5 Conclusion 61 5.1 Future Work...... 62

xi Bibliography 66

A Engine database 67

xii List of Tables

2.1 Reference stations for High Bypass Ratio Turbofan model...... 18 2.2 Components of the engine and corresponding stations and subscripts...... 19 2.3 Mass ﬂow rates description, location and identifying subscript...... 21 2.4 Component polytropic efﬁciencies and total pressure losses [26]...... 22 2.5 Off-Design analysis variables...... 29

3.1 Input values for the on-design analyses...... 42 3.2 Input values for the off-design analysis...... 43 3.3 Input values for the GE CF34-10E analysis...... 46 3.4 Weight and Length comparison between modelled and real engine...... 48 3.5 Fuel consumption on Taxi, Take-off and Landing ﬂight phases...... 51 3.6 Input values for the on-design analyses of the turboprop engine...... 51

4.1 5-point mission ﬂight inputs...... 56 4.2 Results for design variables resulting from an optimization process using Interior Point algorithm...... 57 4.3 Results obtained for various optimization algorithm settings...... 58 4.4 Results of engine Weight and Block Fuel calculated for each DP engine...... 59

A.1 Turbofan engine Database...... 67 A.2 Turbofan engine Database cont...... 68

xiii xiv List of Figures

1.1 Diagram of a turbojet engine [16]...... 5 1.2 Diagram comparing turbojet, turbofan, turboprop and turboshaft [17]...... 6 1.3 Example of a typical compressor map [28]...... 9

2.1 Gas Turbine design system [26]...... 14 2.2 Preliminary propulsion design sequence [26]...... 15 2.3 Comparison between configurations...... 16 2.4 Comparison between internal mixing or un-mixing turbofan nozzle of the hot and cold flows. [43]...... 17 2.5 Gas Turbine design system [26]...... 18 2.6 Flow-chart with Inputs and Outputs of the On-design analysis...... 27 2.7 Flow-chart with Inputs and Outputs of the On-design analysis.(cont.) ...... 28 2.8 Flow-chart with Inputs and Outputs of the Off-design analysis (First part)...... 33 2.9 Flow-chart with Inputs and Outputs of the Off-design analysis (Second part)...... 34 2.10 Flow-chart with Inputs and Outputs of the Off-design analysis (Third part)...... 35 2.11 Turbofan weight as function of maximum take-off thrust with trend line...... 36 2.12 Turbofan weight as function of bypass ratio with trend line...... 37 2.13 Turbofan weight as function of bypass ratio with trend line for newer designed engines.. 37 2.14 Turbofan weight as function of the overall pressure ratio with trend line...... 38 2.15 Turbofan weight as function of the overall pressure ratio with trend line for newer designed engines...... 38 2.16 Turbofan length as function of the maximum take-off thrust ratio with trend line...... 40 2.17 Turbofan fan diameter as function of the maximum take-off thrust ratio with trend line... 40 2.18 Turbofan air mass flow as function of the maximum take-off thrust ratio with trend line.. 40

3.1 Speciﬁc Thrust (F/(m0)) as function of πc and α for the on-design model and for the on-design model calculated on [45]...... 42

3.2 Speciﬁc Fuel Consumption, SFC, as a function of α and πc for the on-design model and for the on-design model calculated on [45]...... 43

3.3 Off-design Fan pressure ratio (πc0 ) as function of Mach number and altitude...... 44

3.4 Off-design Overall Pressure Ratio (πc) as function of Mach number and altitude...... 44

xv 3.5 Off-design bypass ratio (α) as function of Mach number and altitude...... 45 3.6 Off-design partial throttle Speciﬁc Fuel Consumption (SFC) at different altitudes calculated with implemented model and with the model in [45]...... 45 3.7 Comparison of Thrust as function of Mach number and altitude calculated by the model and the Embraer engine deck...... 46 3.8 Error between the Embraer engine deck and the model calculated Thrust...... 47 3.9 Comparison of the Fuel Flow as function of Mach number and altitude calculated by the model and the Embraer engine deck...... 47 3.10 Error between the Embraer engine deck and the model calculated Fuel Flow...... 48 3.11 Mach number variation along mission travelled distance...... 49 3.12 Altitude variation along mission travelled distance...... 49 3.13 Thrust variation along mission travelled distance...... 49

3.14 Turbine inlet temperature (Tt4) variation along mission travelled distance...... 49 3.15 BPR (α) variation along mission travelled distance...... 50

3.16 OPR (πc) variation along mission travelled distance...... 50 3.17 SFC variation along mission travelled distance...... 50 3.18 Fuel ﬂow variation along mission travelled distance...... 50

3.19 Speciﬁc Thrust (F/(m0)) as function of τt and πc for the on-design model of the turboprop and for the on-design model calculated on [45]...... 52

3.20 Speciﬁc Fuel Consumption, SFC, as function of τt and πc for the on-design model of the turboprop and for the on-design model calculated on [45]...... 52 3.21 Off-design partial throttle Speciﬁc Fuel Consumption (S) at different altitudes for a turboprop engine model and for the same results calculated in [45]...... 52

4.1 Optimization process ﬂow-chart...... 56

4.2 Comparison of Turbine inlet temperature (Tt4) variation along mission travelled distance for the optimized and the original engine...... 59 4.3 Comparison of fuel ﬂow variation along mission travelled distance for the optimized and the original engine...... 60

xvi Nomenclature

Acronyms

BPR Bypass Ratio

DP Design Point

ECS Environmental Control System

EPDS Engine Performance Dataset

HPC High Pressure Compressor

HPT High Pressure Turbine

ISA International Standard Atmosphere

IST Instituto Superior Tecnico´

LPC Low Pressure Compressor

LPT Low Pressure Turbine

MDO Multidisciplinary Design Optimization

MFP Mass Flow Parameter

MRO Maintenance, Repair and Overhaul

MTOW Maximum Take-Off Weight

NOx Nitrogen Oxides

OPR Overall Pressure Ratio

RFP Request for Proposal

SFC Thrust Speciﬁc Fuel Consumption

TIT Turbine Inlet Temperature

TSL Sea Level static thrust

xvii Greek symbols

α Engine bypass ratio

β Bleed air fraction

η Efﬁciency

γ Ratio of speciﬁc heats

π Total Pressure Pressure Ratio

πr Isentropic freestream recovery pressure ratio

τ Total Temperature Pressure Ratio

τr Adiabatic freestream recovery temperature ratio

τλ Enthalpy ratio of burner

Roman symbols alt Altitude

Cp Speciﬁc heat at constant pressure

Cpc Speciﬁc heat at constant pressure upstream of main burner

Cpt Speciﬁc heat at constant pressure downstream of main burner

CP Power Coefﬁcient

CTO Power out-take coefﬁcient

D Fan diameter

F Uninstalled Thrust f Fuel-to-air ratio h Static enthalpy

L Length m Mass ﬂow rate

M Mach number

P Pressure

R Gas constant

T Temperature

TH Thermal

xviii V Velocity

W Weight

Subscripts

0 → 10 Station Location b Burner; bleed air

C Core air ﬂow c Compressor c0 Fan c1 cooling air 1 c2 cooling air 2 cH High pressure compressor d Diffuser e Polytropic efﬁciency

F Bypass ﬂow f Fuel g Gross m Mechanical m1 Coolant mixer 1 m1 Coolant mixer 2 n nozzle

O Overall

P Propulsive prop propeller

R Reference t Turbine; Total tH High Pressure Turbine tL Low Pressure Turbine

TO Power Out-take

xix xx Chapter 1

Introduction

1.1 Context and Motivation

With a continuous growth over the last decades, air transport industry is expected to maintain this rising trajectory with an expected 5% growth a year over the next 15 years [1]. Since the progressive developments in the aircraft energetic efficiency are below the rate at which the industry is growing, the environmental footprint has been increasing. To fight this problem, Vision 2020 targets objectives of 80% reduction in emissions and 50% reduction in noise levels [2][3]. During the past decades aircraft has maintained its basic configuration, with technological developments being made by the use of new materials, systems and new design tools. With technologies reach- ing a more mature phase, the rate at which the overall efficiency of the aircraft (engine efficiency and aerodynamic efficiency, for example) increases is slowing down. But as the environment requirements are becoming more stringent, a new design approach is mandatory to take new aircraft performance a step further. To accomplish those requirements a more complete integration of each design discipline has to be done to better optimize the performance of the resulting aircraft, having in consideration from the starting point the objectives for the aircraft’s operation and the constraints it has to exceed. Following this new approach, all systems of the aircraft are taken into consideration right from the first moment, but being modelled at each phase with a level of detail that corresponds to the degree of refinement required by the needed outputs at any given step [2]. The usual procedure is that the models start by being of low fidelity and broad coverage in the first steps of the design process and as the designing process evolves, models fidelity is incrementally increased. By using low fidelity models in the first stages of the development, it is easier and faster to test different concepts and to do the necessary trade-offs. Furthermore, this approach has the benefit of speeding up the process of designing an aircraft. The fidelity of a model is related to the level of accuracy needed in the results in comparison to the physical component that is being modelled. Low fidelity models are generally based in simple equations and table data. High fidelity models, on the other hand, represent fine details and frequently present non-linear behaviours. Due to the high level of time resources needed for high fidelity modelling it is primarily used for highly detailed studies in advanced phases of the development.

1 Given the fact that this approach generates a large amount of data, it relies heavily on computer calculations, and that explains the reason why only in the recent years these methods are becoming more and more used in the industry, given the great growth in computers processing capabilities. In this context it is being developed at Instituto Superior Tecnico´ (IST) a Multidisciplinary Design Optimization (MDO) Framework specially built for the preliminary design phase. It is being developed under the EU 7th Framework Program NOVEMOR (NOvel Air Vehicle Configurations: From Fluttering Wings to MORphing Flight) and will include aerodynamic, structural, propulsion, weights and balance, stability, control and cost modules. Moreover, with the intention of building a totally modular solution, new modules or higher fidelity ones will be possible to add in the future [4]. Besides the IST this project counts with the partnership of POLIMI (Italy), UBRIS (UK), KTH (Sweden), DLR (Germany), CSIR (South Africa) and EMBRAERTM(Brazil). The main objective of this tool is to develop a performance oriented analysis capable of studying new aircraft configurations and innovative morphing solutions. To allow this capabilities, a two level optimization architecture was designed. In the first level the optimization of the controls (including morphing devices) for a given aircraft configuration is done. In the second level the optimization of the aircraft configuration for a given performance based objective function and constraints is tried. One of the main advantages of this MDO framework is the strong development for a well-defined Graphical User Interface (MDOGUI). In the MDOGUI the user is able to select the desired modules to include in his analysis and in an organized way insert all the necessary inputs. Connecting the Graphical User Interface with the various individual modules is the Program Core. The Core is also responsible for managing the communication between the various modules. Considering the objectives of having a framework capable of handling with a large variety of aircraft configurations and operation characteristics, it is necessary to have a propulsion module capable of modelling a wide variety of aircraft engine configurations, with special attention to the more commonly used by commercial aircraft, as well as future configurations under development. Given the importance of the propulsive system for the performance of the aircraft, The ability to take this into consideration at an early stage is of high importance.

1.2 Multidisciplinary Design Optimization

The process of designing an aircraft starts by identifying the market needs for a new product and the capabilities that it needs to accomplish. [5] In this phase the sales that can be achieved with such an aircraft is forecasted. With that in mind, the mission requirements have to be defined. Those requirements are essential to the development of a conceptual design given that they are the base for establishing the main design drivers for which the aircraft will be optimized. A conceptual design phase follows next. In this phase the engineers have to evaluate the best solution of basic concept characteristics to address the requirements for the aircraft, thus generating the first general sizing and the configuration definition to sustain the requirements. If it is proven that it is not possible to achieve what the mission requirements ask, then a relaxation of those requirements must

2 be done. Only when the requirements are satisfied, the basic concept defined and the design space sufficiently constrained, a more detailed analysis of all the aircraft’s systems can start to be done with the aim of detailing the essential data for each discipline. This step is named the preliminary design phase. More detailed studies of aerodynamics, structure and all the systems are carried out, leading to the need of having to build scale models of the aircraft and of its components. It is also essential that in this phase, every decision for each system is analysed taking into consideration the constrains, objective performance and life-cycle performance of the aircraft in order to obtain a trade-off solution. At the end of this phase comes the final decision on whether to build or not to build the aircraft. If the decision is positive, a detailed design has to be done, with every aspect of the aircraft being analysed and carefully developed. Aircraft’s development are every time more complex, with the pursuit of more efficiency, better performance and lower costs to manufacture and operate. Therefore, the MDO is showing to be a good solution to tackle these rising challenges. MDO is defined as a design methodology where a high level of interdisciplinary analysis has to be done, with a constant exchange of data between the various disciplines to achieve an optimum solution for the aircraft as a whole and not only for structurally optimized wing or an optimized engine. This is especially significant in order to obtain an aircraft that is perfectly suited for the mission that it is intended [6]. The high level of interdisciplinarity associated with MDO leads to a great computational workload that is much more than a simple linear sum of the computational times of each subsystem. Moreover, it is frequent that a non-linear analysis has to be done, even though the subsystems are itself linear models. Adding to that, the complexity of the MDO analysis is getting increasingly higher with the addition of economy studies within the development project, to take into consideration the manufacture costs, the aircraft operation, support and maintenance [6]. There are already some studies involving the use of MDO approach to an aircraft as a whole, but it is still more common to find this approach of optimization to single or small number of systems. Given the objective of current work the examples presented next are orientated to the study of propulsive system solutions. In [7] a MDO approach was applied to study the applicability of distributed propulsion on a blended- wing-body aircraft. The objective of the research was to evaluate the aircraft performance and weight, considering the concept of distributed propulsion. This means that a small number of large engines was replaced by a larger number of small engines. It was also included in the analysis the hypothesis of ducting part of the exhaust flux to exit alongside the leading edge of the wing. For the development of the study two conceptual configurations were analysed, one with four pylon mounted engines and another configuration with eight boundary layer ingestion inlet engines. In the end, the MDO analysis allowed to conclude that for the distributed propulsion concept to achieve a similar SFC (Specific Fuel Consumption) to the standard blended-wing-body configuration a great development had to be made in engine technology to reduce its weight and SFC. In [8] a review of the state-of-the-art in performance codes for fixed-wing aircraft is done. Moreover,

3 a developed program that uses a multidisciplinary approach for aircraft performance calculations is presented, highlighting the importance of each module (aerodynamic, propulsion, flight mechanics, flight operation and numerical optimization) for the final results. In the development of the software, for the propulsion module a commercial software developed by NLR was used (GSP V.10) and integrated with the other modules. The complete research led to the main conclusion that performance has evolved slower than the other aerospace disciplines, potentially due to the necessity of large amount of information regarding the aircraft, its geometry and flight data. This explains that part of the codes used for performance analysis are developed by the main aircraft manufacturers and therefore they are not in the public domain. Furthermore, it was concluded that for a good performance analysis it is necessary to have both accurate aerodynamic and propulsive systems, being the engine the most critical aspect for the aircraft performance.

In some cases, the studies of optimization are focused in just some disciplines of the aircraft design. An example where an optimization analysis was carried out, with a special focus on level of NOx with a high engine performance, in [9]. In this study the optimization process was made using a genetic algorithm, using two modules, one modelling the engine performance (design point and off-design analysis) and the other modelling the level of emissions of the engine. This approach led to the conclusion that for achieving the minimum value of emissions a signiﬁcant increase in fuel consumption was necessary. Thanks to the optimization process by indicating the desired design parameters, a compromise for engine consumption and level of NOx could be found.

Another case where a genetic algorithm was used as an optimization tool can be seen in [10]. In this study the optimization method was applied to a turbofan engine, with a multi-objective of optimizing the thrust per unit air mass ﬂow rate and overall efﬁciency as a function of four parameters: Mach number at the engine entrance, compressor pressure ratio, fan pressure ratio and bypass ratio. In the end, the algorithm showed a good ability to deal with the problem presented.

During the last decades some software programs have been developed in order to model a specific discipline of the aircraft design. Following the actual trend of coupling all the aircraft systems into a single tool capable of connecting every design specification some works are being developed to interconnect those individual tools and to speed up the data analysis. Within this context, the work developed in [11] studies the connection of an aircraft engine design tool (PROOSIS) and an aircraft preliminary design tool (Pacelab APD) at the same time that optimizes the method of generating fast and accurate engine decks or EPDS (Engine Performance Dataset) and updating them to the aircraft design tool in order to run the optimization process. These EPDS’s are matrices containing all the relevant engine performance parameters at several flight conditions (thrust, SFC, fuel flow, altitude, Mach and ISA deviation). Where ISA stands for International Standard Atmosphere, with the deviation referring to the corrections to be made to the standard model to account for different atmospheric conditions verified on a certain day or location.

Given the already spoken high computational requirements associated with a MDO analysis of a complete aircraft, some older works tend to do an optimization study based only in a single discipline, for example, the propulsive system. In [12] and [13], two examples show the development of gas turbine

4 modelling tools (GasTurb and NEPP) which coupled with an optimization tool allows for various studies of the engine performance optimization for various design variables and operating conditions. As seen previously, a full MDO tool including all main aircraft disciplines is still not extensively used. That is why, the MDO tool under development at IST will represent a step forward, given it’s true multidisciplinary study.

1.3 Propulsion module

1.3.1 Aircraft engines

From the first flight by the Wright brothers till the Second World War, aircraft propulsion has been sus- tained by reciprocation engines. This engine, also known as piston engine, had been in use across every aircraft type and every purpose mission. Only during the WW II did the jet engine technology start to be developed, simultaneously in England and Germany. In 1939 a Heinkel experimental aircraft [14] took-off powered by a von Ohain developed turbojet. Two years later, the british Whittle engine took off. During the first years, the jet engine was only used for military and experimental applications, and revelled poor reliability and fuel consumption. Only after a longer development work was done, did the jet engine finally arrive to civil aviation in the beginning of the 1950s with the de Havilland Comet. With the introduction of this new engine, the reciprocating engine was systematically replaced and its use limited to light aircraft, due to the lower operating costs that the jet engine achieved with a better thrust to weight relation and lower maintenance costs [15]. This new engine has a layout such that the air is sucked in and compressed by the compressor. Then the air temperature is raised in the combustion chamber by burning the injected fuel. The hot air passes through the turbine and just the necessary mechanical force to rotate the compressor is extracted. The exhaust gas at high temperature and pressure is then expanded to the atmospheric conditions on a nozzle producing a high velocity jet responsible for generating the thrust necessary for the aircraft to speed-up, as can be seen in Figure 1.1.

Figure 1.1: Diagram of a turbojet engine [16].

According to the necessities of various aircraft types, several variants of the initial concept were developed, as shown in Figure 1.2. For higher power needs, such as supersonic aircraft, the notion of reheating the ﬂuid, or after-burner, in the exhaust nozzle by injecting more fuel was introduced. For lower

5 speed aircraft it was developed a combination of exhaust jet and a propeller, known as turboprop engine, delivering the best propulsive efﬁciency. In the turboprop there was also the need of coupling a gearbox connecting the gas turbine to the propeller. This enables the reduction of the propeller’s tip speed at the same time the turbine works at optimum rotation. For other applications, such as helicopters, it was developed the turboshaft engine, where a power turbine is added to extract power to the helicopter’s rotors.

Figure 1.2: Diagram comparing turbojet, turbofan, turboprop and turboshaft [17]

For high subsonic speed aircraft it was developed the turbofan, where part of the air bypasses the hot section of the engine (high pressure compressor, combustion chamber and turbine), being only compressed by a fan or a low pressure compressor. This approach generates a lower speed jet which at the same time provides better efficiency and reduces noise. The development trend in terms of turbofan engines has been the incremental increase of the bypass ratio (BPR), and the consequent increase of the fan dimensions. One of the initial problems limiting the efficiency of jet engines was the capacity of turbine blades to withstand the temperatures of the air mixture leaving the combustion chamber. With a continuous work in development of hollow blades cooled with air taken from the compressor and the breakthroughs in material sciences allowing to build blades of ceramic composites led to an increase on engines efficiency [18][19]. Meanwhile the further improvements of the popular turbofan engine are becoming every time more difficult given that the aerodynamics of the turbo machinery is already very efficient; an increase in the turbine inlet temperature doesn’t bring much benefit beyond the current 1900oK to 2000oK used; total pressure ratio doesn’t have also much to improve [20]. The only way to evolve is by increasing the bypass ratio [21]. Which is why gearboxes are now being applied to turbofan engines, increasing the bypass ratio, while better matching the fan and core aerodynamics. In [22] an optimization on a geared turbofan engine was developed. With this configuration a 3% lower fuel consumption when comparing with the conventional solution was achieved, given its lower weight and higher component efficiencies

6 obtained. Another evolutionary step on the process of increasing the bypass ratio of the turbofan engine is the open-rotor. This concept takes the air bypass to a higher value (50+) by eliminating the casing and exposing the fan or propeller. It can be configured in pusher or a puller configuration, having the propeller in the back or in the front of the turbo-machinery, respectively [19]. The big advantages of this concept are related with its good propulsive efficiency and lower weight and drag than the conventional solutions. Furthermore, it allows for efficient cruise speeds of up to Mach 0.8. The main drawback holding the commercial use of this technology is the level of noise generated, although it is believed that this problem can be minimized with a right optimization of the propeller. For special missions where high Mach number speed is required, the ramjet was developed. It has no turbo-machinery and tolerates operation at higher temperatures. However, this engine is unable of operating at subsonic speeds and can only work at speeds of up to about Mach 6. For even higher speeds, the supersonic combustion ramjet (scramjet) was developed where the combustion occurs in the supersonic air-stream, allowing for operations at higher speeds than Mach 4. Bearing in mind the requirements in terms of fuel consumption and emissions for future aircraft, new technology solutions are being studied. One of the possibilities being evaluated is the use of hydrogen to power aircraft engines [23][24]. An analysis was conducted in [24] using an MDO tool and GasTurb software to model the engine performance. This analysis draws a comparison between a hydrogen powered aircraft with a kerosene powered one for a long range transport aircraft. One of the main issues associated with hydrogen is the need to have large pressured tanks. In the concept studied fuel tanks in the interior of the fuselage were considered, giving an advantage for the wing design that would no longer be constrained by the necessity of storing fuel. The hydrogen has also the advantage of being less dense which has the advantage of reducing the take-off gross weight, even taking into consideration the large and bulky tanks. However, with the reduction in wing size and increased fuselage the aerodynamic efficiency of the hybrid aircraft is lower than the kerosene powered one. An economic analysis was also carried out which led to concluding that, at the time, an increase of 0.5 dollar per gallon of kerosene would make the hydrogen powered aircraft a valid solution.

1.3.2 Propulsion models’ state-of-the-art

By model it is understood the development of an abstract image of a given system so that it represents its behaviour, but in a simpler way. The creator of the model has the responsibility to define the depth and degree of detail desired for it. A balance between the level of accuracy and complexity of the model has to be done, given that not every detail has a beneficial effect on the results to be achieved. To begin with, for now a generic model for Gas Turbine will be assumed, given that with only some differences it can be obtained the equivalent models for turbojet, turbofan and turboprop engines. For a first analysis level, empirical relations for various engine parameters can be determined as function of a given parameter. This approach was followed in [25]. By using available data of 67 different turbofan engine models with bypass ratio of at least 2, relations were obtained for dry weight, length, fan

7 diameter, cruise thrust, air mass flow, bypass ratio, total pressure ratio, take-off specific fuel consumption, and cruise SFC as function of take-off thrust. This can be useful in a very early development phase to calculate some basic information about a possible engine to be fitted on a given aircraft. However, it has the drawback of not taking into account new technologies that can arise and changes on the trend lines and consequently invalidating the results and the models. Another issue with this approach is the difficulty associated with obtaining the engines data, given the fact that some of the necessary information is kept secret by manufacturers and operators. Moreover, a large data bank would have to be used for determining the properties of a broader range of aircraft engine types. Similarly, in [7] empirical relations were used with the objective of determining weight, thrust and SFC of the engines as a function of Mach number, altitude, maximum sea level static thrust, and sea level static SFC. Based on empirical data obtained from historical engine information, the dimensions and weight of the nacelles and pylons were also calculated. The weight of the engine was calculated in a similar way, as a function of the maximum sea-level static thrust. When referring to the level of detail of a gas turbine model it can be assumed some different steps of refinement. The simpler approach is defined as a 0-D model where components are seen as “black boxes” where average flow conditions are only computed for the components inlet and outlet. One of the advantages of using a 0-D model is that details of the engine geometry are not needed, and it still present thermodynamically good results without a heavy computational effort. Rising the level of refinement, a 1-D model adds continuity in one direction inside the engine. For some studies requiring a better level of detail in one engine component, it can be individually modelled as 1-D while the other components remain modelled as 0-D. In 2-D and 3-D models the engine is described with higher fidelity as an axisymmetric and as whole respectively. These levels of refinement require a higher computational cost given that CFD (Computational Fluid Dynamics) analysis has to be carried out eventually. Within the first phase of aircraft design process, the work of development of the engines start by knowing the static sea level thrust (TSL), as well as the assumed behaviour of thrust with altitude and Mach number [26]. In the first part of the development work a parametric cycle analysis has to be done to obtain a preliminary estimation of performance parameters (thrust and SFC) as a function of design limitations (such as maximum allowable turbine temperature and component efficiencies), the flight conditions (ambient temperature, pressure and Mach number), and design choices (such as compressor pressure ratio, fan pressure ratio and bypass ratio). In this parametric cycle analysis or on-design (or design point) analysis it is assumed that all engine choices can still be done. This stage of development is like having a “rubber” engine, and with the completion of design choices it will be obtained a piece of hardware with its operation characteristics. However, the final configuration of the engine will largely depend on the off-design performance analysis, or simply performance analysis, across all phases of the flight envelop. In other words, the best engine to choose is the one capable of better satisfying all the flying conditions. Even though the final engine performance can only be obtained with the off-design analysis, the on-design study has still great importance. Firstly because only after its completion and its outputs are generated the off-design analysis can be done. Secondly, immediately after obtaining the data output of

8 the on-design analysis, some conclusions can be taken, without the need of the more time-consuming off-design analysis. Lastly, the on-design analysis is also a good tool for obtaining parameters sensibility to help understand what are the performance effects of the design choices on each flight condition. In the GasTurb software [27], off-design calculations are done using real component maps. These maps are graphical databases of compressors and turbines performance, relating the corrected mass flow across the component with its pressure ratio. Furthermore, these maps show information about the corrected rotational axle speed and efficiency and surge margin. To fill the maps with information either compressor/turbine rig tests are performed or sophisticated calculation procedures are used. An example of a typical compressor map can be seen in Figure 1.3.

Figure 1.3: Example of a typical compressor map [28]

GasTurb software is a commonly used tool and several studies have been done with it. It is a software capable of modelling off-design performance, engine behaviour, and even transient operation. The software is capable of successfully modelling all the most frequently used aero-gas turbines, for example single and twin-spool turbofan, turboprops and turboshafts. Even though only performing a 0-D study of the engines, it generates good quality results. In [29] GasTurb was applied to 5 different engines of different size, type and age in order to validate the model used. The results proven a deviation on SFC results of approximately 2% between the model results and the manufacturer information. The capabilities of this software were also tested in [30] to help generating compressor and turbine characteristic maps to help a commercial aircraft engine Maintenance, Repair and Overhaul (MRO) facility to more easily detect anomalies in the engine performance. This was necessary given that the engine manufacturers keep the component maps in secrecy. In [27] a variety of studies have been conducted, with the aim of showing the GasTurb’s capabilities. Firstly, a cycle optimization has been done for a selected operation in order to evaluate the turbine blade life as a function of the variations of turbine efﬁciency and temperature; at the same time a confrontation between a two stage turbine architecture and a single stage turbine architecture was done. Secondly,

9 some considerations have been made to model a situation where an aircraft is flying with a high angle of attack and/or side-slip that generates significant variations in the speed of the air flow on the annulus area of the compressor. The solution found was to use a parallel compressor model. This model uses a compressor for the slower part of the flow and another for the faster part of flow. Moreover, this study presented a thorough description of the followed method for the off-design performance calculation. For a turbojet engine, by having a prescribed rotational speed and knowing the inlet conditions it can be obtained the compressor entry conditions. With that conditions and by reading the compressor maps it is possible to estimate the correct rotational speed. Consequently the burner inlet conditions are achieved. With an estimated burner exit temperature the fuel-to-air ratio is calculated, and with it the corrected flow at turbine inlet. By reading the turbine map the turbine exit conditions and shaft power are calculated. Lastly, the nozzle has only to be considered. During this process three estimations have been made, and consequently three iterative loops had also to be done. For a turbofan the necessary number of iterative loops can be of up to seven. For an easier and more advanced handling of compressor and turbine maps, the GasTurb can use its embedded software tools SMOOTH C and SMOOTH T responsible by scaling the component maps. [31] These features have special interest in an early aircraft engine development phase. Furthermore, these software features generate tabulated data that can then be used directly by GasTurb on the compressor and turbine calculations. In the study stated earlier in [8] for propulsive module it was used the GSP V.10 software (Gas Turbine Simulation Program). This software exchange his results with the main aircraft design software, by exporting a matrix with the parametric analysis including Mach number and altitude effects at fixed throttle that is interpolated for the aircraft designated operating points. The propulsion software is based in a 1-D compressible axial flow model capable of evaluating a large variety of parameters, such as thrust, mass flow, fuel flow, exhaust gas temperature and SFC. Furthermore, it can also be included options like compressor bleed, deterioration of one or more components and calculate emission indices. With the objective of building a standardized tool for gas turbine simulation, in the context of the Eu- ropean project VIVACE-ECP the PROOSIS software (Propulsion Object Oriented Simulation Software) was developed. The structure of this tool is described in detail in [32] as well as some of its functionali- ties that allow it to be used by professional users or as educational tool. It has tools for single operating point engine, but also has the tools for multi-point design procedures. PROOSIS was used in [11] for engine modelling . NASA has also developed a software for engine performance modelling [13]. The NEPP (NASA Engine Performance Program) evaluates the engine performance over its flight envelope for various mission points and it has the capability of optimizing some parameters at specific mission points. It does a 0-D, steady-state thermodynamic analysis of turbine engine cycles and with the use of component performance maps it also models off-design performance. The level of detail in some studies is focused on the modelling of one individual component, compressor or turbine, for example. This way, more detailed information is described, and higher fidelity models are analysed in order to more accurately represent the operating conditions of a Gas Turbine

10 [33][34][35]. Concerning the compressor performance in [33], step by step analysis of its modelling process and methods is done. This study has a special focus in the analysis of the compressor maps and its meaningful data. It also makes some considerations on second order effects on the compressor performance, namely, inlet distortion effects, unintended geometry changes, Reynolds number effects, working fluid effects, variable geometry, and transient effects. Additionally it does a thorough analysis of the performance effects of controlled geometry variations, specifically bleed off-take and variable stator vanes, which are responsible for preserving the best operation conditions on the compressor for off-design conditions or when it approaches a stall condition. The models’ fidelity is also analysed and developers try to correctly attribute the proper level of model detail to the level of precision needed for the results. Some considerations in this respect are analysed in [36][37]. These researches have a special focus on the analysis of the fluid modelling. Also in the researches, the usage of propulsive models to obtain information regarding the emissions of the engine is studied in greater detail. Some techniques of modelling aircraft engines were studied in order to obtain higher fidelity modelling while maintaining the necessary computational resources as low as possible. One possibility analysed is the zooming or multi-fidelity analysis [38]. This technique uses a higher order analysis code to a specific component and then integrates its results back to the 0-D model, increasing the accuracy of the results obtained.

1.3.3 Objectives and Approach

The main objective of this work is the development of models representing the performance and geometry of a turbofan and turboprop engine to be integrated on a the MDO framework being developed in the context of the NOVEMOR project. These models have to be able to estimate the size and weight of the engines, but specially have to be capable of computing the fuel consumption of the aircraft for a desired flight mission (knowing altitude, Mach speed, atmospheric conditions and aircraft payload). Then, their results will be integrated on a multidisciplinary optimization process with all the remaining aircraft discipline modules. This work has also the objective of testing and comparing the results obtained with available data of real engine performance. Furthermore, an optimization process will be carried out to obtain the values of total pressure ratio, BPR and total weight to obtain an optimum SFC. The thesis is divided in 5 chapters. Firstly, it is presented the development of the Turbofan model, with the parametric or on-design analysis followed by the performance or off-design analysis and weight and dimensions modelling. In the Chapter 3 are presented a series of results of the model developed and it is done a comparison with the literature and with available data on the NOVEMOR project as well as running the engine model for a flight mission profile. In the fourth chapter it is done a cycle of optimizations on the engine design parameters in order to minimize the fuel consumption on that same mission profile. Chapter five is destined for presenting the main conclusions of the work developed as well as presenting some future work that can be implemented.

11 12 Chapter 2

Turbofan engine modelling

Typically, the design process of a new aircraft engine starts as the airframe manufacturer defines the list of requirements needed to accomplish with the flight mission and the aircraft physical characteristics. The airframe manufacturer presents to the engine manufacturer a Request for Proposal (RFP), a docu- ment describing the mission profile for which the aircraft is being designed for, desired performance for the aircraft and some other restrictions that might influence the engine design. Along the development process some adjustments in the requests and constraints will eventually have to be made, in constant iterative process between the airframe and the engine designing teams. In the case of the project for which this propulsive system model is being developed, the objective is to bring all the aircraft development disciplines closer, and have the contribution of each one of them right from the first design studies. That said, the requirements for the development of the engines are sourced by the calculations of weight, drag and lift, generated in the other modules, and articulated with the user-defined mission and performance requirements. A common design process for a gas turbine engine is presented in the Figure 2.1, a largely iterative process, with several steps of refinement as the level of detail increases. It can also be seen in the figure the level of multidisciplinarity involved in the development of the engine alone, with thermodynamical, aerodynamic and mechanical studies. In the context of the current work, the objective is centred in the preliminary study, with thermodynamic design points so that the performance of the engine can be estimated. Further designing re- finements require heavier studies including CFD simulations, rig tests, mechanical studies of materials, becoming impossible to be carried out in this project phase. In Figure 2.2 the sequence of design steps of the current work is presented. The propulsive system model is integrated in the complete aircraft designing framework, with the initial design specifications regarding the type and mission for the aircraft and the performance requirements it needs to fulfil being supplied to the software as project constraints. With the information from the aerodynamic and structural modules, the aircraft Drag Polar as well as the initial definition of take-off weight (WTO) and sea-level static thrust (TSL) are generated. This information supports the development of the objectives for the propulsive system to achieve, and to a

13 Market Costumer Speciﬁcation Research Requirements

Preliminary studies, choice of cycle, type of turbomachinery layout

Thermodynamic Oﬀ-design design point studies performance

Mods Aerodynamics of aerody- compressor, turbine, namics inlet, nozzle, etc.

Components Mechanical de- test rigs: sign:stress of compressor, discs, blades, cas- turbine, com- ings, vibration, bustor, etc. whirling, bearings Control system studies Detail design and manufacture Design mods Test and development

Uprated and modiﬁed Production Field Service versions

Figure 2.1: Gas Turbine design system [26] selection of the correct engine cycle to choose. In other words, what type of engine better suites that given mission requirements. In this work two engine types are being modelled, the turbofan and the turboprop, given the fact of being the two most common types used in commercial aircraft.

The next step of the designing process is the Engine Design Point Analysis or On-Design analysis. In this phase of the project the engine performance can be parametrically studied at the same time that it is chosen a Design Point for the engine to be sized for. This process estimates the performance parameters, such as thrust and specific fuel consumption, as function of the design limitations (maximum turbine inlet temperature and maximum component efficiencies), flight conditions and design choices, compressor pressure ratio, fan pressure ratio and bypass ratio, to name some. This initial sizing for a design point will then have to be tested in the Engine Performance Analysis, or Off-Design Analysis, to check whether the engine can correctly perform across all the needed operating conditions of altitude, speed and thrust. This is a iterative process to find the design point conditions that originates an engine

14 Design speciﬁ- cation (RFP)

Constraint anal- Aircraft ysis TSL/WTO Drag Polar

Mission analysis, determine WTO vs TSL

Engine Cycle analysis

Engine Engine Design Performance Point analysis Analysis

Engine performance

Optimization Size Engine

Revised Predict air- aircraft craft performace Drag Polar

Final Results

Figure 2.2: Preliminary propulsion design sequence [26] with the desired performance. After the results converge the engine performance can be calculated and the sizing, including weight and external dimensions, can be estimated. With this values the total weight of the aircraft and its new Drag Polar are now known and the final performance of the aircraft can be calculated. At this phase, an optimization process can be run with the objective of trying to find a solution that better suits the needs. In the case that the size of the engines or their predicted performance still doesn’t match the requirements, one or more design constraints might have to be relaxed for a final result to be achieved. This designing methodology can be applied to a wide variety of aircraft engines. Lets focus now the attention in the particular case of the turbofan engine. 1 The Turbofan was created with the intention of achieving better propulsive efficiency by reducing the speed of the jet of flow exiting the engine. To obtain that speed reduction a new compressor stage of large dimensions coupled to a new stage of turbine compress the cold fluid up to a point where the air flow is separated, part of which continues to another series of compressor stages and then to the hot section of the engine. The other part of the flow is guided along the exterior section of the engine, bypassing the combustion chamber and the turbines. In the design process of a turbofan further choices may have to be done regarding the architecture

15 (a) Two-spool [41] (b) Three-spool [42]

Figure 2.3: Comparison between configurations. of the engine. The engineers team may have to do trade-off studies in order to define if the engine will have a two or three-spool system configuration, or whether to have or not to have a nozzle casing that mixes the hot with the cold air flux. In Figure 2.3 a comparison between a two and three-spool architecture can be seen. In the first case, Figure 2.3a, connected to one shaft, also called low pressure spool, are the fan, the low pressure compressor (LPC) and the low pressure turbine (LPT). Connected to the other shaft, named high pressure spool, are the high pressure compressor (HPC) and the hight pressure turbine (HPT). For the three- spool architecture, Figure 2.3b, mostly used in large civil turbofans, a third shaft is added, connecting a intermediate pressure compressor with a intermediate pressure turbine. With the three-spool configuration it is easier to obtain better transient response of the engine. However, this solution increases the weight and the mechanical complexity of the system. [39][40] The choice between an internal mixing of the cold and hot air fluxes on the nozzle or a non mixing solution, that can be seen in Figure 2.4, is usually related with the higher weight of former in comparison with the higher fuel consumption of the latter solution. Typically the mixing solution is more frequently used in turbofan engines with low bypass ratio to be used at supersonic speeds, given that for the same thrust it can have a smaller frontal area. The development of the engines is also interconnected with the project of aircraft avionic and non- avionic systems and its architecture. After defining what electric, hydraulic and pneumatic systems will be used in the aircraft and their sizing has been made, it is possible to define the required engines power out-take to supply them [44]. In addition, the Environmental Control System (ECS), responsible for the air supply to the cabin, its pressurization and temperature control, on its more common configurations uses bleed air from the engines for its supply. Alternatively, in some aircraft, a bleed-less architecture is used. With this solution, the air is pressurized by using electrically powered compressors. The place in the aircraft where the engine will be mounted influences the performance of the engine and the design of air intake. Whether the engine is mounted in nacelles or directly applied in the airframe influences the efficiencies of the diffuser. With all these restrictions in mind, the turbofan model presented next will be oriented for an engine to be applied on a 113-passenger regional jet. This way, a common two-spool architecture will be used, paired with a non mixing nozzle and capable of dealing with power and air out-takes to supply the aircraft

16 Figure 2.4: Comparison between internal mixing or un-mixing turbofan nozzle of the hot and cold flows. [43] systems. In case of necessity, the model can suffer updates to deal with a three-spool configuration and with mixed flow nozzles. Firstly, in this chapter the engine Design Point analysis or On-Design analysis, followed by the Per- formance or Off-Design analysis will be presented. The models behind both analyses were developed and described in detail in [45].

2.1 Parametric model (On-Design)

To start the development of the 0-D turbofan model, a definition of the internal stations has to be made. In Figure 2.5 and Table 2.1 all the intermediate stations and their location are presented. This information will take part in the nomenclature to be used across the variables of the model. These stations are used to limit the entrance and exit of each component of the engine, as can be seen in Table 2.2. In addition, the subscripts that will be used in the model to describe each component are defined there. Given the speeds at which a subsonic commercial aircraft usually travels, aerodynamic phenomena are dominated by compressible flows, which is why during the development of this model the relations for compressible flows will be considered. When dealing with temperature and pressure the concepts of Total or Stagnation temperature and pressure will be primarily used. The total temperature, Tt, is defined as the temperature that a moving flow at a given Mach number would reach if it was brought to a rest in a stagnation point assuming an

17 Figure 2.5: Gas Turbine design system [26].

Table 2.1: Reference stations for High Bypass Ratio Turbofan model Station Location Station Location

0 Far upstream 4b High pressure turbine exit Coolant mixer 2 entry

1 Inlet or diffuser entry 4c Coolant mixer 2 exit Low pressure turbine entry

2 Inlet or diffuser exit 5 Low pressure turbine exit Fan entry Core stream mixer entry

3’ Fan exit 7 Core exhaust nozzle entry High pressure compressor entry 3 9 High pressure compressor exit Core exhaust nozzle exit 3a 7’ Burner entry Bypass exhaust nozzle entry

Burner exit 4 Nozzle vanes exit 9’ Bypass exhaust nozzle exit Coolant mixer 1 entry High pressure turbine entry for πtH deﬁnition

Nozzle vanes exit 4a Coolant mixer 1 exit High pressure turbine entry for τtH deﬁnition

adiabatic process. In a similar way, the total pressure, Pt, is considered the pressure that a moving flow would reach when brought, in an isentropic way, to a rest in a stagnation point. Both total temperature and pressure are function of flow’s Mach number, M, and ratio of specific heats, γ, as shown in

18 Table 2.2: Components of the engine and corresponding stations and subscripts Station Component Subscript 0 → 2 Diffuser or inlet d 2 → 3 Compressor c 2 → 3’ Fan c’ 3’ → 3 High pressure compressor cH 3a → 4 Burner b 4 → 4a Coolant mixer 1 m1 4 → 4c High pressure turbine tH 4 → 5 Turbine t 4b → 4c Coolant mixer 2 m2 5 → 7 Core ﬂow mixer M 7 → 9 Core exhaust nozzle n 3’ → 7’ Fan duct - 7’ → 9’ Bypass exhaust nozzle n’

Equations 2.1 and 2.2, respectively.

γ − 1 T = T 1 + M 2 (2.1) t 2

γ γ − 1 γ−1 P = P 1 + M 2 (2.2) t 2

For a matter of simpliﬁcation of the nomenclature used, the ratio of total pressures and the ratio of total temperatures will be represented by π and τ respectively.

Total Pressure leaving component i πi = Total Pressure entering component i Total Temperature leaving component i τi = Total Temperature entering component i

This way, the following relations can be deﬁned:

Diffuser: Pt2 Tt2 πd = ; τd = = 1; (2.3) Pt0 Tt0 Fan: Pt30 Tt30 πc0 = ; τc0 = ; (2.4) Pt2 Tt2 High pressure compressor: Pt3 Tt3 πcH = ; τcH = ; (2.5) Pt30 Tt30 Compressor: Pt3 Tt3 πc = = πc0 πcH ; τc = = τc0 τcH ; (2.6) Pt2 Tt2 Burner: Pt4 Tt4 πb = ; τb = ; (2.7) Pt3a Tt3a

19 Coolant mixer 1: P4a T4a πm1 = ; τm1 = ; (2.8) P4 T4 High pressure turbine: Pt4b Pt4b Tt4b πtH = = πm1 ; τtH = ; (2.9) Pt4 Pt4a Tt4a Coolant mixer 2: Pt4c Tt4c πm2 = = 1; τm2 = ; (2.10) Pt4b Tt4b Low pressure turbine: Pt5 Tt5 πtL = ; τtL = ; (2.11) Pt4c Tt4c Core exhaust nozzle: Pt9 Tt9 πn = ; τn = ; (2.12) Pt7 Tt7 Bypass exhaust nozzle: Pt90 Tt90 πn0 = ; τn0 = . (2.13) Pt70 Tt70 For the relations above, by considering the bypass duct as adiabatic and with constant area, it was assumed Pt30 = Pt50 and Tt30 = Tt50 . By making similar considerations in the duct connecting the compressor exit and the burner entry, it was assumed Pt3 = Pt3a and Tt3 = Tt3a. Adding to the physical components of the engine there is also an compression effect to take into consideration: the effects of the adiabatic and isentropic freestream recovery. In the simpliﬁed case of a calorically perfect gas it can be deﬁned:

. Tt0 γ − 1 2 τr = = 1 + M0 ; (2.14) T0 2

γ γ γ−1 . Pt0 γ−1 γ − 1 2 πr = = τr = 1 + M0 . (2.15) P0 2

In the burner, an incremental step in enthalpy is given, so τλ is deﬁned as enthalpy ratio with the

Equation 2.16. This allows to easily stablish the ratio as function of Tt4, the maximum allowable turbine inlet temperature, which is a project design limitation,

. CptTt4 τλ = . (2.16) CpcT0

Next in the model development it is necessary to define a set of mass flow rates. The mass flow parameter, generically defined as m, necessary to obtain the rates will have the corresponding subscripts presented in the Table 2.3. Further information available in the Table shows the corresponding description of the mass flow parameters and the engine location where they can be calculated. Mass flow rates used in the model are presented next with their defining equations:

20 Table 2.3: Mass flow rates description, location and identifying subscript Subscript Description Location b Bleed air 3 - 3a C Core air flow 3’, 3 c1 Cooling air for high pressure turbine nozzle vanes 3-3a, 4-4a c2 Cooling air for remaining of high pressure turbine 3-3a, 4b-4c F Fan air flow through bypass duct 3’, 7’ f Fuel flow to burner 3a-4

Bypass ratio (α): . Bypass flow mF α = = ; (2.17) Core flow mC Bleed air ratio (β): . Bleed flow mb β = = ; (2.18) Core flow mC

Cooling air fraction (1 and 2): . mc1 1 = ; (2.19) mC

. mc2 2 = ; (2.20) mC Burner fuel to air ratio (f): . Burner fuel ﬂow mf f = = ; (2.21) Burner inlet air ﬂow m3a

Overall fuel to air ratio (f0):

. Total fuel ﬂow mf f0 = = . (2.22) Engine inlet air ﬂow mC + mF

As seen in Equations 2.19 and 2.20 and in Table 2.1 the model takes into consideration the necessary high pressure turbine cooling system. For that, an air flow fraction 1 and another 2 are extracted between stations 3 and 3a and used to cool down the high pressure turbine nozzle guide vanes and remaining high pressure turbine, respectively. With respect to the rotating machinery of the engine (fan, compressors and turbines), it is of vital importance to relate its pressure, π, and temperature, τ ratios with individual component’s efficiency. Two separate efficiencies will be defined, η and e. The first one, isentropic efficiency, expresses the ratio of actual and ideal work transfer absorbed or produced by the component, in other words, the component’s overall efficiency. [14] Its name results from the fact that the turbomachinery is essentially adiabatic and the ideal process is isentropic. For its calculation the stagnation enthalpy or stagnation temperature is used, this way taking into consideration the variations of the fluid kinetic energy inside the component. The second efficiency is defined as polytropic efficiency. It represents the efficiency of an hypothetical process where π and τ are close to one; this allows it to represent the state-of-the-art efficiency of a given component. Contrarily, the isentropic efficiency varies as pressure and temperature ratios changes, this way representing the component’s behaviour. Below, it can be seen the relationships between π, τ, η and e for the various rotating components of

21 Table 2.4: Component polytropic efﬁciencies and total pressure losses [26] Level of technology Component Figure of merit Type 1 2 3 4 Engine in Diffuser π 0.90 0.95 0.98 0.995 dmax nacelles Compressor ec 0.80 0.84 0.88 0.90 Fan ef 0.78 0.82 0.86 0.89 π 0.90 0.92 0.94 0.96 Burner b ηb 0.88 0.94 0.99 0.995 Uncooled 0.80 0.85 0.89 0.91 Turbine e t Cooled 0.83 0.87 0.89 Fixed-area Nozzle π 0.95 0.97 0.98 0.995 n convergent Maximum Tt4 (K) 1110 1390 1780 2000 the engine:

Fan: (γc−1)/γc 0 − (γc−1)/(γcec0 ) πc 1 τc0 = πc0 ; ηc0 = ; (2.23) τc0 − 1 High pressure compressor:

(γc−1)/γc (γc−1)/(γcecH ) πcH − 1 τcH = πcH ; ηcH = ; (2.24) τcH − 1

High pressure turbine:

γt/{(γt−1)etH } 1 − τtH τtH = π ; ηtH = ; (2.25) tH (γt−1)/γt 1 − πtH

Low pressure turbine:

γt/{(γt−1)etL} 1 − τtL τtL = π ; ηtL = . (2.26) tL (γt−1)/γt 1 − πtL

In the particular case of the combustion chamber, its efﬁciency characterizes the degree of completion of the chemical reactions. Equation 2.27 represents the actual thermal increase to the maximum possible thermal energy rise, represented by the lower heating value of the fuel (hPR).

m4CptTt4 − m3aCpcTt3a ηb = ≤ 1 (2.27) mf hPR

For calculation purposes in this model, the values of polytropic efﬁciencies, total pressure losses and maximum Tt4 presented in Table 2.4 will be used as inputs. The values presented correspond to subsonic aircraft with engines mounted in nacelles and a ﬁxed-area convergent nozzle. The technology levels presented correspond to the technical capabilities in steps of 20-year starting in 1945. Level 4 corresponds to the state-of-the-art for the period between 2005-2025.

22 Regarding the efﬁciency of the components used to transmit mechanical power, such as shafts and gears, the relation used is presented below:

Mechanical power output η = . (2.28) m Mechanical power input

In the model, this efﬁciency will be applied to the low pressure shaft, ηmL, the high pressure shaft,

ηmH , and power out-take shaft, ηmP . Having so far the essential parameters to be used in the model deﬁned and before proceeding with the analysis of performance parameters of the engine, it is necessary to specify the assumptions that will be made. The considerations are the ones that follow:

• The ﬂow is, on average, steady;

• The ﬂow is one-dimensional at the entry and exit of each component and at each axial station;

• The ﬂuid is considered to behave as a calorically perfect gas, meaning constant values of Cp, Cv and γ in the diffuser, fan, compressor, turbine, nozzle and all ducts connecting them;

• Across the burner the values of Cp, Cv, γ and R vary;

• The low pressure shaft connects the fan with the low pressure turbine and also provides mechani-

cal power to supply the aircraft, PTO;

• The high pressure compressor is connected to the high pressure turbine by the high pressure shaft;

• High pressure bleed air and cooling air is extracted between stations 3 and 3a;

• Flow in the bypass duct is considered isentropic;

• A reduction on etH by the inclusion of turbine cooling has to be accounted, due to mc1 and mc2;

• Engine is modelled as having both core and bypass air nozzles ﬁxed and convergent.

Focusing the attention on the performance parameters, the first parameter to be analysed is the Thrust. The thrust of an engine can be measured in various different ways but, for this study, will be considered the Uninstalled Thrust (F ). It is defined as the net axial force that would be produced by an engine immersed on an inviscid external flow. It has positive value when acting in the direction of the flight and has equal and opposite value to the force it exerted on the fluid around the engine. This unit of measure is only governed by the flow quantities dictated by the cycle parameters and is independent of the engine installation effects. Therefore it can be used as a standard when evaluating the engine performance. The generic form of the uninstalled thrust of an engine is presented in Equation 2.29, where a conservation of the moment entering and exiting a control volume is done.

F = m9V9 − m0V0 + A9(P9 − P0) (2.29)

23 In the particular case of a turbofan engine, and to account for the separated exhaust streams, 2.29 assumes the following form:

F = m9V9 + m90 V90 − m0V0 + A9(P9 − P0) + A90 (P90 − P0). (2.30)

In the development of the current model, the calculation of the Equation 2.30 will be rearranged to assume a nondimensional form of the Speciﬁc Thrust (F/m0):

F 1 V9 Rt T9/T0 (1 − P0/P9) = [1 + f0(1 + α) − β] − 1 + [1 + f0(1 + α) − β] 2 m0V0 1 + α V0 Rc V9/V0 γcM0 (2.31) α V90 T90 /T0 (1 − P0/P90 ) + − 1 + 2 , 1 + α V0 V90 /V0 γcM0 where

f0 = f(1 − β − 1 − 2)/(1 + α), (2.32) and f0 is the overall fuel-to-air ratio. f is the fuel to air ratio and is calculated with Equation 2.33:

τ − τ τ 0 τ f = λ r c cH . (2.33) hPRηb/(CcpT0) − τλ

Furthermore, pressure and temperature ratios in Equation 2.31 are calculated using:

( ) V 2 τ τ τ τ τ P −(γt−1)/γt 9 = λ m1 tH m2 tL 1 − t9 , (2.34) V0 τr − 1 P9

2 ( −(γc−1)/γc ) V 0 τ τ 0 P 0 9 = r c 1 − t9 , (2.35) V0 τr − 1 P90

T C τ τ τ τ τ 9 pc λ m1 tH m2 tL , (2.36) = (γ −1)/γ T0 Cpt (Pt9/P9) t t

T 0 τ τ 0 9 r c , (2.37) = (γ −1)/γ T0 (Pt90 /P90 ) c c and where:

Pt9 P0 = πrπdπc0 πcH πbπtH πtLπn, (2.38) P9 P9 Pt90 P0 = πrπdπc0 πn. (2.39) P90 P90

For the particular case of the turbofan engine, its independent design variables are the fan pressure ratio, πc0 , the overall pressure ratio (OPR), πc and the bypass ratio, α. The high pressure compressor pressure ratio is given by πcH = πc/πc0 . The other pressure and temperature ratios necessary for calculating the Equations 2.34 to 2.39 can be calculated as follows:

24 Cooling temperature ratios (τm1 and τm2):

(1 − β − 1 − 2)(1 + f) + 1τrτc0 τcH /τλ τm1 = ; (2.40) (1 − β − 1 − 2)(1 + f) + 1

(1 − β − 1 − 2)(1 + f) + 1 + 2{τrτc0 tancH /(τλτm1τtH )} τm2 = ; (2.41) (1 − β − 1 − 2)(1 + f) + 1 + 2

High pressure turbine total temperature ratio (τtH ):

A power balance on the high pressure spool is done, having

m4aCpt(Tt4a − Tt4b)ηmH = m0Cpc(Tt3 − Tt30 ), leading to τrτc0 (τcH − 1) τtH = 1 − . (2.42) ηmH τλ {(1 − β − 1 − 2)(1 + f) + 1τrτc0 τcH /τλ}

Low pressure turbine total temperature ratio (τtL):

A power balance on the low pressure spool is done, having

m4cCpt(Tt4c − Tt5)ηmL = m0Cpc(Tt30 − Tt2) + PTO/ηmP , and leading to

(1 + α){τr(τc0 − 1) + CTO/ηmP } τtL = 1 − , (2.43) ηmLτλτtH {(1 − β − 1 − 2)(1 + f) + (1 + 2/τtH )τrτc0 τcH /τλ} with

CTO = PTO/(m0CcpT0). (2.44)

To obtain the ratios P0/P9 and P0/P90 , presented in Equations 2.38 and 2.39, two flow regimes can be verified. A convergent nozzle can be choked or unchoked. By choked flow is understood the limiting velocity condition where the mass flow will not increase with a further decrease in the downstream pressure environment while upstream pressure is fixed. When the flow is choked:

P γ + 1γ/(γ−1) te ≥ , (2.45) P0 2 then γ/(γ−1) Pte γ + 1 P0 Pte/Pe Me = 1, = , = . (2.46) Pe 2 Pe Pte/P0

For the unchoked ﬂow, we have P γ + 1γ/(γ−1) te < , (2.47) P0 2

25 and then v u " (γ−1)/γ # u 2 Pte Pte Pte P0 Me = t − 1 , = , = 1. (2.48) γ − 1 P0 Pe P0 Pe

Continuing the performance analysis of the turbofan engine the next important parameter to study is the Uninstalled Thrust Speciﬁc Fuel Consumption, (S), which can be calculated by

m m /m f S = f = f 0 = 0 . (2.49) F F/m0 F/m0

Two other cycle performance parameters that can be studied are the Propulsive Efﬁciency, ηP , and

Thermal Efficiency, ηTH . The first one represents the ratio of thrust power to the rate of kinetic energy generation of gas turbine and can be seen in Equation 2.50. The second efficiency, shown in Equation 2.51, represents the ratio of the rate of kinetic energy generation of the gas flow plus the shaft power to the rate at which fuel is generating thermal energy.

F 2(1 + α) m V η = 0 0 (2.50) P 2 2 V9 V90 [1 + f0(1 + α) − β] − 1 + α − 1 V0 V0

2 2 2 V0 V9 V90 [1 + f0(1 + α) − β] − 1 + α − 1 + C h0 2(1+α) V0 V0 TO ηTH = (2.51) f0hPR Regarding the atmospheric conditions of the air entering the engine the following relations were considered:

alt T0 = T − 6.5 , (2.52) ISA 1000

alt 5.2561 P0 = PISA 1 − 0.0065 , (2.53) TISA with alt in meters and for ISA conditions PISA = 1013.25(hPa) and TISA = 288.15(K). Finally, the implemented model for the On-design or Design Point cycle analysis presents the following structure with the needed inputs and resulting outputs:

26 INPUTS: Flight parameters: alt(m), M0, T0 (K),P0 (Pa) Aircraft systems needs: β, CTO Design limitations: Perfect gas constants: γc,γt, Cpc, Cpt (J/(Kg.K)) Fuel Heating value: hPR (J/Kg) Component ﬁgures of merit: 1,2, πb, πdmax,πn, πn0 ec0 , ecH ,etH ,etL ηmH ,ηmL,ηmP ,ηb Design choices: πc0 ,πc,α,Tt4(K)

Preliminary Computations: τr (Eq. 2.14); πr (Eq. 2.15) πd = πdmax for M0 ≤ 1 1.35 πd = πdmax 1 − 0.075(M0 − 1) for M0 > 1 τλ (Eq. 2.16); πcH = πc/πc0 R = γc−1 C ; R = γt−1 C c γc pc t γt pt h0 = CpcT0

Fan and high pressure compressor: τc0 and ηc0 (Eq. 2.23) τcH and ηcH (Eq. 2.24)

Main burner: f (Eq. 2.33)

High and low pressure turbine: τm1 (Eq.2.40) and τtH (Eq. 2.42) πtH and ηtH (Eq. 2.25) τm2 (Eq.2.41) and τtL (Eq. 2.43) πtL and ηtL (Eq. 2.26)

(...)

Figure 2.6: Flow-chart with Inputs and Outputs of the On-design analysis.

27 (...)

Core stream exhaust nozzle: Fan stream exhaust nozzle: Pt9/P0 (Eq. 2.38) Pt90 /P0 (Eq. 2.39)

γ /(γ −1) γ +1 γt/(γt−1) γc+1 c c t If P 90 /P0 > , If Pt9/P0 > 2 , t 2 then M9 = 1, then M90 = 1, γ /(γ −1) P 0 +1 γc/(γc−1) Pt9 γt+1 t t t9 γc = , 0 = , P9 2 P9 2 0 and P0 = Pt9/P9 and P0 = Pt90 /P9 P9 Pt9/P0 P90 Pt90 /P0 P9 Pt9 Pt9 P90 Pt90 Pt90 else P = 1, P = P , else = 1, = , s0 9 0 P0 P90 P0 (γ −1)/γ s t t (γc−1)/γc 2 Pt9 2 Pt90 and M9 = − 1 and M90 = − 1 γt−1 P0 γc−1 P0

Overall engine performance: f0 (Eq. 2.32) T9 (Eq. 2.36), T90 (Eq. 2.37) T0 T0 V9 (Eq. 2.34), V90 (Eq. 2.35) V0 V√0 V0 = M0 γcRcT0 F (Eq. 2.31), S (Eq. 2.49) m0 ηP (Eq. 2.50), ηTH (Eq. 2.51)

OUTPUTS: Overall performance: F/m0(N/(Kg/s), S ((Kg/h)/N), f0, ηP , ηTH , V9/V0, V90 /V0 Component behavior: πtH , πtL, τc0 , τcH , τtH , τtL, τλ, f, ηc0 , ηcH , ηtH , ηtL, M9, M90 , Pt9/P9, T9/T0, P0/P9, Pt90 /P90 , T90 /T0, P0/P90

Figure 2.7: Flow-chart with Inputs and Outputs of the On-design analysis.(cont.)

2.2 Performance model (Off-Design)

After completing the on-design analysis the study evolves for the Performance Cycle analysis or Off- Design analysis. In this second part of the study, the objective is to use the outputs of the engine sized for a certain design point on the on-design analysis and test the engine’s performance across its complete operating envelope. By iterating the on-design and the off-design analysis, a choice of the engine with the most balanced performance to execute a certain ﬂight mission can be made.

28 Table 2.5: Off-Design analysis variables Variable Component Independent Known Dependent Engine M0, T0,P0 m0, α Diffuser πd, τd Fan πc0 , τc0 High pressure compressor πcH , τcH Burner Tt4 πb Coolant mixer 1 πm1 High pressure turbine πtH , τtH Coolant mixer 2 πm2, τm2 Low pressure turbine πtL, τtL Core Nozzle πn, τn P9/P0 Bypass Nozzle πn0 , τn0 P90 /P0

In off-design analysis, the design choices have already been made (πc, πc0 , α and Tt4max) and the engine performance per unit mass flow have been calculated. Now, variations on flight conditions, throttle settings and nozzle settings are implemented to obtain the performance of the engine for the chosen circumstances. This study can be compared to an engine with a fixed configuration that is taken to a test rig where it will be powered across its operating range to study its performance. The difference, in this study, is how easily the engine configuration can be changed in the case it doesn’t fulfil its requirements. The off-design performance of an engine can be calculated in two different ways, by modelling individual component performance as function of operating conditions or using component maps. However, given that this is a preliminary study and there are no component maps available, the off-design model to be developed will have to follow the first hypothesis and a series of relations will be used to obtain an estimation of the engine performance behaviour. When starting the model development, the internal stations configuration will be the same used for the on-design model and presented in Figure 2.5 and 2.1. Additionally, when referring to output values of the on-design that will be used in the off-design model, a R will be added as subscript to identify them as reference values. To develop this analysis on a turbofan a 10 dependent and 4 independent variables problem is faced, as can be seen in Table 2.5. Given that the off-design analysis is not a direct problem as the on-design analysis, a iterative process will have to be carried out to obtain values for the 10 independent variables. For this part of the engine model development the following assumptions were made, in addition to the ones presented in on-design model:

• The areas are considered to be constant in every engine station;

• The ﬂow is considered to be chocked at the high pressure turbine entrance nozzle (station 4), at the low pressure turbine entrance nozzle (station 4c);

• Component efﬁciencies and total pressure ratios ηc0 , ηcH , ηb, ηtH , ηtL, ηmL, ηmH , ηmP , πb and πn are considered to remain constant;

29 • Bleed air, cooling air fractions and power out-take are considered constant;

• Upstream and downstream of the burner gases are assumed as calorically perfect and no varia-

tions in γt and Cpt are considered when varying throttle settings.

Two techniques are crucial in the development of the off-design model. The ﬁrst is Referencing, given that the engine cycle analyses are based in relations of mass, energy, momentum and entropy (for a perfect one-dimensional steady ﬂow) on a engine on-design or off-design at a steady state operating point. If, at a certain off-design point, g(τ, π) = constant representing a relation between the two performance variables τ and π for a given steady state operating point, it can also be evaluated at the on-design conditions, so

g(τR, πR) = g(τ, π) = constant meaning that this technique allows to replace constants with reference conditions. The second technique is Mass Flow Parameter (MFP). Given that engine components performance is calculated as function of total temperature, total pressure or Mach number,

√ r m T r γ P T MFP = t = M t , (2.54) PtA R Pt T with Tt/T deﬁned in Equation 2.1 and P/Pt in Equation 2.2 it is obtained

√ γ+1 r 2(1−γ) m Tt γ γ − 1 2 MFP = = M 1 + M = MFP (M,Tt,R). (2.55) PtA R 2

Focusing now the attention on individual component performance relationships, regarding the high pressure turbine it is considered that for a cooled and an uncooled turbine parameters πtH and τtH are considered constant [26]. In what respects to the low pressure turbine, its performance parameters are calculated knowing, for starter, that the mass ﬂows in station 4c’ (nozzle throat downstream of station 4c) and in station 9 are equal. Then, writing them in terms of MFP:

m4c0 = m9,

Pt4c0 A4c0 Pt9A9 √ MFP (M4c0 ) = √ MFP (M9), Tt4c0 Tt9 r Pt9 Tt4c0 A4c0 MFP (M9) = MFP (M4c0 ). Pt4c0 Tt9 A9

As previously assumed, at station 4c’ the ﬂow is chocked, so M4c0 = 1 and MFP (M4c0 ) is constant. Rewriting the equations in terms of reference conditions, we have

πtLπn πtLR πnR √ MFP (M9) = √ MFP (M9R ), τtL τtLR

30 leading to r τtL MFP (M9R ) πtL = πtLR . (2.56) τtLR MFP (M9) From equation 2.26 it can be obtained:

γt−1 γt τtL = 1 − ηtL 1 − πtL . (2.57)

Following a similar path to πtL, a relation for bypass ratio (α) can be obtained by ﬁnding an expression for mC in terms of station 4 conditions, and an expression for mF in terms of station 9’ conditions.

Pt4A4 m4 = mC (1 − β − 1 − 2)(1 + f) = √ MFP (M4), (2.58) Tt4

Pt90 A90 mF = √ MFP (M90 ), Tt9 leading to s 0 0 πcHR τλ/(τrτc ) MFP (M9 ) a = aR . (2.59) π τ /(τ τ 0 ) MFP (M 0 ) cH λR rR cR 9R

In order to obtain the performance parameters of the fan the low pressure spool power balance is used. After some rearrangement of Equation 2.43:

(1 + α){τr(τc0 − 1) + (CTO/ηmP )} τλ(1 − τtL) = n o. (−1+2/τtH )τr τc0 τcH /τλ η τ (1 − β − 1 − 2)(1 + f) 1 + mL tH (1−β−1−2)(1+f)

By order of magnitude the braced term in the denominator can be considered equal to one, resulting that the whole denominator can be assumed as constant. Replacing the constant by reference condition values it is obtained:

1 − τtL τλ/τr 1 + αR τc0 = 1 + (τc0 − 1) 1 − τ τ /τ 1 + α R tLR λR rR (2.60) C 1 − τ τ /τ 1 + α τ m T + TOR tL λ r R − rR 0R 0R . τrR ηmPR 1 − τtLR τλR /τrR 1 + α τrm0T0 From equation 2.23 it results

γc/(γc−1) πc0 = {1 + (τc0 )ηc0 } . (2.61)

Regarding the HPC, using the power balance on the high pressure spool, Equation 2.42, and rear- ranging it,

τrτc0 {τcH [1 − 1ηmH (1 − τtH )] − 1} = ηmH (1 − β − 1 − 2)(1 + f)(1 − τtH ), τλ and replacing the constant in the right side of the equation by the reference conditions,

τ 0 1 τλ/τr cR 1 τcH = + τcHR − , (2.62) 0 1 − 1ηmH (1 − τmH ) τλR /τrR τc 1 − 1ηmH (1 − τtH ) the HPC pressure ratio can be calculated using Equation 2.24, leading to:

31 γc/(γc−1) πcH = {1 + (τcH )ηcH } . (2.63)

Lastly, using the conservation of mass and deﬁnition of α, there is a relation for the overall mass ﬂow

(m0):

m 1 + α m 0 = C . m0R 1 + αR mCR From the Equation 2.58 we have

m m P rT C = 4 = t4 t4R . m m 0 P T CR 4R t4R t4

With the assumptions of choked ﬂow at station 4’ and Pt4 = Pt40 , a combination of the two previous equations gives:

0 1 + α P0πrπdπc πcH m0 = m0R 0 . (2.64) 1 + αR P0R πrR πdR πcRπcHR

In order to solve the problem, the parameters chosen as variables for the iterative process were τc0 and m0. This choice was made after tests where other variables were tested for iteration and also after trying to use MATLAB’s own solver. With this pair of iteration variables the model generated realistic results for a wider range of input conditions than with the other options. The ﬁnal model for the Off-design or Performance Cycle analysis with its inputs, outputs and structure can be seen in the following ﬂow-chart:

32 INPUTS: Off-design conditions: Flight parameters: alt(m), M0, T0 (K),P0 (Pa) Throttle setings: Tt4 Design constants: Perfect gas constants: γc,γt, Cpc, Cpt (J/(Kg.K)) Fuel Heating value: hPR (J/Kg) Aircraft systems parameters: β,CTO π’s: πdmax,πb,πtH ,πn,πn0 τ’s: τm1,τtH ,τm2 η’s: ηc0 ,ηcH ,ηb,ηtL,ηmP ,ηmH Reference conditions:

Flight parameters: altR(m),M0R , T0R (K),P0R (Pa) Componente behaviour: π ,π ,π 0 ,π ,π ,π rR dR cR cHR cHR tLR τ ,τ 0 ,τ ,τ rR cR cHR tLR Other: M ,M 0 ,α ,m ,C 9R 9R R 0 TOR

Initial values of τtL, τc0 , πtL and m0: τ = τ τ 0 = τ 0 tL tLR c cR

πtL = πtLR m0 = m0R

High pressure compressor: τcH (Eq. 2.62) and πcH (Eq. 2.63)

Fan pressure ratio: πc0 (Eq. 2.61)

(...)

Figure 2.8: Flow-chart with Inputs and Outputs of the Off-design analysis (First part).

33 (...)

Core stream exhaust nozzle: Fan stream exhaust nozzle: Pt9/P0 (Eq. 2.38) Pt90 /P0 (Eq. 2.39)

Engine bypass ratio and fan temperature ratio: α (Eq. 2.59)

Low pressure turbine: τ − tL (Eq: 2.57) and πtL (Eq. 2.56) τc0 (Eq. 2.60)

No: |τc0 − τc0 | ≤ 0.0001? τ 0 = τ 0 R cR c

Engine mass ﬂow (m0): m0 (Eq. 2.64)

No: |m − m 0 | ≤ 0.0001? 0 cR m0R = m0

(...)

Figure 2.9: Flow-chart with Inputs and Outputs of the Off-design analysis (Second part).

34 (...)

Main burner: f (Eq. 2.33)

Overall engine performance: f0 (Eq. 2.32) T9 (Eq. 2.36), T90 (Eq. 2.37) T0 T0 V9 (Eq. 2.34), V90 (Eq. 2.35) V0 V√0 V0 = M0 γcRcT0 F (Eq. 2.31), S (Eq. 2.49) m0 ηP (Eq. 2.50), ηTH (Eq. 2.51)

OUTPUTS: Overall performance: F/m0(N/(Kg/s), S ((Kg/h)/N), f0, α m0(Kg/s), ηP , ηTH Component behavior: πc0 , πcH , πtL, τc0 , τcH , τtL, τλ, f ηc0 , ηcH , ηtL, M9, M90 Pt9/P9, T9/T0, P0/P9, V9/V0 Pt90 /P90 , T90 /T0, P0/P90 , V90 /V0

Figure 2.10: Flow-chart with Inputs and Outputs of the Off-design analysis (Third part).

2.3 Weight and size model

After the completion of the performance study of the engine, it is now possible to do its sizing. Depending on the level of detail of the design phase various approaches can be followed to estimate dimensions and weight. Given that the performance model of this engine is set for a preliminary phase, the weight and size model has to ﬁt into this same phase. That is why the approach chosen was to deﬁne a set of equations relating some engine design choices with dimensions, based on historic data for turbofan engines. This approach was followed in [25], where it was used to stablish relations for a wide variety of parameters, including the evaluation of the engine performance. For the current model development, the same engine’s database presented in [25] was used. his database dates from 1996 and since then new turbofan have been introduce to the market. Therefore to the 67 already included, 15 new turbofan engines were added in the database.

35 All the turbofan engines taken into account in the database have a minimum bypass ratio of 2 and have a value of maximum take-off thrust ranging from 1500 lb to 115300 lb. The complete database can be seen in the AppendixA.

In addition to maximum take-off thrust (FTO), the database includes information as maximum cruise thrust, (FCr), overall mass ﬂow (mO), bypass ratio (α), fan pressure ratio (πc0 ), overall pressure ratio

(πc), fan diameter (D), engine length (L) and engine weight (W ). With this information the first relation defined was a correlation between the maximum take-off thrust and engine weight, as shown in Figure 2.11. In the figure a good relation between the two parameters can be observed, showing that the increase in take-off thrust leads to a linear increase in weight.

25000

y = 0,1626x + 546,46 R² = 0,972 20000

15000

Weight(lb) 10000

5000

0 0 20000 40000 60000 80000 100000 120000 140000 Take-Off Thrust (lb)

Figure 2.11: Turbofan weight as function of maximum take-off thrust with trend line

Although a good relation was established with maximum take-off thrust, it is important to further analyse how engine weight varies with other design variables, specially the ones the engine designer can independently choose. With this in mind how weight changes with bypass ratio was studied. In Figure 2.12 the result is presented. From this analysis it is possible to conclude that there is not a good correlation between them, given the fact that there are turbofan engines with a high BPR, small thrust output and consequently low weight, at the same time that there are low BPR engines with high thrust output and high weight. A further reason contributing to this unreasonable relation is the recent trend of bypass ratio increase across all turbofan segments, from lower to higher thrust engines. Bearing in mind this idea, a new relation between BPR and weight was drawn but this time using data from the 16 newer engines. The graphic obtained is shown in Figure 2.13, and a better relation between the two variables can now be deﬁned. Next, a correlation between the weight and the OPR was tested in order to study the effect of this design choice in the engine’s total weight. The relation established is presented in Figure 2.14. Although better than the BPR relation but still worse than the maximum take-off thrust one, the OPR-weight relation does not have a perfectly deﬁned trend line.

36 20000

18000

16000

14000

12000

10000 y = 337,37x1,5633 R² = 0,2775

8000 Weight (lb) 6000

4000

2000

0 0 2 4 6 8 10 12 14 Bypass

Figure 2.12: Turbofan weight as function of bypass ratio with trend line

20000 18000 16000 14000 12000 10000 y = 13922ln(x) - 16981

8000 R² = 0,6055 Weight (lb) Weight 6000 4000 2000 0 0 2 4 6 8 10 12 14 Bypass

Figure 2.13: Turbofan weight as function of bypass ratio with trend line for newer designed engines

To study in further detail the relation between OPR and weight, a similar approach to the BPR on was followed. In Figure 2.15, the OPR-weight relation is presented for the 16 most recently developed engines. The resulting trend line shows a better approximation of the results.

The relations presented before can be summarized in the following equations:

W (FTO)(lbm) = 0.1626FTO(lbf) + 546.46, (2.65)

W (α)(lbm) = 13922ln(α) − 16981, (2.66)

37 25000

20000

15000

2,0574 Weight (lb) Weight 10000 y = 5,6303x R² = 0,7287

5000

0 0 10 20 30 40 50 60 Total Pressure ratio

Figure 2.14: Turbofan weight as function of the overall pressure ratio with trend line

20000

15000

10000

y = -23,165x2 + 2135x - 34806 R² = 0,86

Weight (lb) Weight 5000

0 0 10 20 30 40 50 60

-5000 Total pressure ratio

Figure 2.15: Turbofan weight as function of the overall pressure ratio with trend line for newer designed engines

2 W (πc)(lbm) = −23.165πc + 2135πc − 34806. (2.67)

Having these three relations, the desired objective is to create a single equation capable of taking in to consideration all three contributions to the engine’s total weight. Creating such equation will then enable to perform an optimization analysis and understand how an increase in BPR and/or OPR can inﬂuence the weight of the engine for a certain maximum take-off thrust.

The approach followed to stablish this complete equation was to select a set of 9 different turbofan

38 engines of diverse sizes and characteristics, but having in common the fact of powering currently under production aircraft (GE Genx 1B-70, GE90-115B, GE CF34-10E, Engine Alliance GP7000, PW6000, RR Trent 1000, RR Trent 771, PowerJet SaM146, CFM56-5B3). Then, 5 possible equation conﬁgurations were analysed:

W = x1W (FTO) + x2W (α) + x3W (πc), (2.68)

W = W (FTO) + x2(α − αR) + x3(πc − πcR ), (2.69)

W = W (FTO) + x2((α − αR)/αR) + x3((πc − πcR )/πcR ), (2.70)

W = x1W (FTO) + x2W (α) + x3W (πc) + x4WcompleteDB(α) + x5WcompleteDB(πc), (2.71)

y1 y2 y3 W = x1(W (FTO)) + x2(W (α)) + x3(W (πc)) , (2.72)

where αR and πcR are respectively the medium value bypass ratio and medium value overall pressure ratio of the complete database information. WcompleteDB is the relation of BPR-weight and OPR-weight generated with all the engines in the database. For each of the relations described on Equations 2.68 to 2.72 and the 9 engines, the MS Ofﬁce TM Excel GRG non linear solver was used to optimize the values of x1, x2, x3, x4, x5, y1, y2 and y3 P that originated a minimum for the ∆W = |Wreal − Wmodel|, where Wreal is the real weight of the engine and Wmodel is the weight calculated by the equations of the model. Then the results of ∆W were compared for each of the 5 possible equation conﬁgurations, resulting that with Equation 2.72 this value was minimized. After running this procedure, as best solution the following equation to model the total engine weight was chosen:

0,99631 1,00884 W (lbm) = 0, 90494[0.1626FTO(lbf) + 546.46] + 0, 18671[13922ln(α) − 16981] (2.73) 2 1,00445 −0, 09166[−23.165πc + 2135πc − 34806] .

With the database information further relations were established for engine Lenght L, engine Fan

Diameter D and overall air mass ﬂow mO as function of maximum take-off thrust, in Figures 2.16, 2.17 and 2.18 respectively. In all three Figures a generically good relation was established. Finally, three equations to be used in engine dimensioning can be deﬁned for the relations above:

0.3199 L(in) = 4.963(FTO) , (2.74)

0.4496 D(in) = 0.674(FTO) , (2.75)

mO(lb/s) = 0.0314(FTO) + 2.8625. (2.76)

39 350

300

250

200

150 Lenght(in)

0,3199 100 y = 4,963x R² = 0,7197

0 0 20000 40000 60000 80000 100000 120000 140000 Take-Off Thrust (lb)

Figure 2.16: Turbofan length as function of the maximum take-off thrust ratio with trend line

140

120

100

80 y = 0,674x0,4496 R² = 0,9666

60 Fan Diameter (in) Fan Diameter 40

0 0 20000 40000 60000 80000 100000 120000 140000 Take-Off Thrust (lb)

Figure 2.17: Turbofan fan diameter as function of the maximum take-off thrust ratio with trend line

4000

3500

3000

2500

2000

y = 0,0314x + 2,8625 1500

R² = 0,9617 Air Mass Mass Air Flow (lb/s) 1000

500

0 0 20000 40000 60000 80000 100000 120000 140000 Take-Off Thrust (lb)

Figure 2.18: Turbofan air mass ﬂow as function of the maximum take-off thrust ratio with trend line

40 Chapter 3

Model Results and Veriﬁcation

After being described in Chapter2 and implemented in MATLABTM, a presentation of the results extracted from the model and its verification need to be done. This way, the first thing to do will be the presentation of a series of graphics for the on-design and the off-design analysis showing the variation of the design parameters with the flight conditions and the variation of performance parameters with flight conditions and design choices. With these results the objective is to show the capabilities of the model at the same time that they are compared with theoretical behaviour of those parameters. Following the presentation of these first results, a validation of the model will be done. This process will be done by introducing in the model the data inputs to correctly recreate a General ElectricTMCF34- 10E engine, used in EmbraerTME-190 aircraft. The choice of this engine in particular for the results comparison was made due to the fact that the same engine was temporarily used in the MDOGUI’s routines under the form of a database of three performance variables (maximum engine thrust, SFC and fuel flow) as function of altitude and Mach number provided by EmbraerTM. This way, the model will receive the inputs for this engine and then the results will be compared with the mentioned database. To finalise the results presentation and validation, the modelled engine will be applied to a flight mission in order to calculate the total fuel burned during a complete flight (Block Fuel). A comparison of this value with the block fuel calculated for the same mission using the Embraer’s engine database will then be done. Additionally, a turboprop model has also been implemented even though has not been presented in detail. The model used was also presented in [45], as the turbofan one, and follow very similar assumptions and approaches, with both on-design and off-design analyses being done. Its results for the on and off-design analyses will also be presented and validated literature data.

3.1 On-design and Off-design analysis results

The ﬁrst results to present are outputs from the on-design analysis. Validating them helps assuring that the starting point of the model’s performance calculation is correct.

41 For the on-design analyses results that will be present next, the values contained in Table 3.1 were used as inputs.

Table 3.1: Input values for the on-design analyses. M0 = 0, 8 1 = 0, 05 ηmH = 0, 98 alt = 30000ft 2 = 0, 05 ηmP = 0, 98 2 ≤ α ≤ 16 πd = 0, 97 Tt4 = 1780(K) 5 ≤ πc ≤ 40 πb = 0, 97 hPR = 42800000(J/kg) πc0 = 1.3 πn = 0, 98 Cpc = 996, 458(J/(kgK) TISA = 288, 15(K) CTO = 0, 005 Cpt = 1235.1(J/(kgK) PISA = 1013, 25(P a) ηb = 0, 98 λc = 1, 4 β = 0, 03 ηmL = 0, 99 λt = 1, 3

After running the on-design analysis, the graphs contained in Figures 3.1 and 3.2 were obtained. As a way of verifying the on-design model, the results shown in Figures 3.1 and 3.2 do a comparison between the results obtained in the implemented model with results presented in [45], which were calculated in both cases for the same input values. Given that the values presented in [45] were originally presented in imperial units and in paper format, they were digitalized and the values contained on them were converted300,00 to SI units so that they could be more easily compared.

BPR=2 Model BPR=4 Model 250,00 BPR=6 Model BPR=8 Model

200,00 BPR=10 Model BPR=12 Model BPR=14 Model 150,00 BPR=2

Specific (N/kg/s) Thrust Specific BPR=4 BPR=6 100,00 BPR=8 BPR=10 BPR=12 50,00 10,00 15,00 20,00 25,00 30,00 35,00 40,00 BPR=14 Overall Pressure Ratio

Figure 3.1: Speciﬁc Thrust (F/(m0)) as function of πc and α for the on-design model and for the on- design model calculated on [45].

Doing a comparative analysis of the result on both graphs the same tendencies as OPR or BPR vary can be observed between the two sources of results which allows for verifying the on-design implemented model. In Figure 3.1 not only the trends match but also the values obtained are very similar. In the second ﬁgure a shift of around 5% can be seen between the two sources, probably resulting from small numerical errors in the implemented model adding to possible errors in the process of point by point digitalization and the later conversion of the results imported from the literature. With the implemented on-design analyses a series of other variables can also be calculated so that preliminary parametric studies can be made. Additionally, the single components behaviour and the overall engine performance variables can be parametrically studied. After the on-design analysis the presentation of the results and their validation can similarly be done

42 0,12 OPR=10 Model 0,11 OPR=15 Model OPR=20 Model 0,1 OPR=25 Model OPR=30 Model 0,09 OPR=35 Model

OPR=40 Model SFC SFC (Kg/s/N) 0,08 OPR=10 OPR=15 0,07 OPR=20 OPR=25

0,06 OPR=30 4 6 8 10 12 14 16 OPR=35 Bypass Ratio

Figure 3.2: Speciﬁc Fuel Consumption, SFC, as a function of α and πc for the on-design model and for the on-design model calculated on [45]. for the Off-design model.

Contrary to the on-design analysis, where by varying the α and πc a new Design Point (DP) was being defined, in the off-design analysis the design point has already been defined. This way, the results will be calculated as function of flight parameters, altitude and Mach number. For the results presented in the next series of graphs the inputs introduced to the model are the ones presented in Table 3.2. Executing the code for the defined inputs, the model will in the first place run the on-design analyses, as previously referred, so that it can then execute the off-design study. To show the capabilities of the code, Figures 3.3 through 3.5 show a series of engine component and overall performance information (πc0 , πc, and α) as function of the flight conditions (Mach number and altitude) at full throttle setting, in other words, with Tt4 constant. In addition, in Figure 3.6 the SFC is also calculated as function of the thrust generated at various Mach speeds, constant altitude of 30000 ft and varying the value of Tt4 to change the throttle setting.

Table 3.2: Input values for the off-design analysis.

M0DP = 0, 8 1 = 0, 05 ηmH = 0, 98 altDP = 30000ft 2 = 0, 05 ηmP = 0, 98 αDP = 8 πd = 0, 97 Tt4 = 1780(K)

πcDP = 30 πb = 0, 97 hPR = 42800000(J/kg) π 0 = 1.5 π = 0, 98 C = 996, 458(J/(kgK) cDP n pc TISA = 288, 15(K) CTO = 0, 005 Cpt = 1235.1(J/(kgK) PISA = 1013, 25(P a) ηb = 0, 98 λc = 1, 4 β = 0, 03 ηmL = 0, 99 λt = 1, 3

In Figures 3.3 and 3.4 a similar behaviour can be seen for the pressure ratios, showing a decrease as the Mach number increases and opposite tendency as altitude increases. Figure 3.5 shows, for a full throttle setting, the evolution of the BPR. Contrarily to the OPR, this value deceases as ﬂying altitude increases. This way, the highest values of BPR can be achieved at sea-level conditions, while the highest values of OPR are achieved when the aircraft gets to the top of its climb.

43 1,8

1,7

1,6 0 ft 1,5 10000 ft 20000 ft

FanPressure Ratio 1,4 30000 ft 40000 ft 1,3

1,2 0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 Mach Number

Figure 3.3: Off-design Fan pressure ratio (πc0 ) as function of Mach number and altitude.

35 0 ft

30 10000 ft OPR 20000 ft 25 30000 ft 20 40000 ft

10 0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 Mach Number

Figure 3.4: Off-design Overall Pressure Ratio (πc) as function of Mach number and altitude.

More than just calculating flight conditions at full throttle, the off-design analysis allows to study the effect of varying thrust settings on the engine fuel consumption, for example. In the Figure 3.6 this study is done maintaining a fixed altitude and Mach number while varying the Tt4, which implies an increase on the fuel mass flow injected into the combustion chamber. As done in the case of the on-design analysis, as a way of verifying the obtained results, a comparison with the results from a similar off-design analyses done in [45] with the same input values was conducted. Also in Figure 3.6 the results from both sources is presented. Generically, they present the same parameters behaviour but with a difference on the SFC results of around 10%. This difference may be influenced, once again, by the fact that the data obtained from [45] had to be digitalized and its results converted from imperial units leading to possible deviation of the results. Furthermore, this deviation may occur due to differences on the iterative process used for the off-design calculation. In conclusion, based in the comparison with results presented for the on and off-design analyses in

44 13

10 0 ft

10000 ft BPR 9 20000 ft 30000 ft 8 40000 ft

6 0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 Mach Number

Figure 3.5: Off-design bypass ratio (α) as function of Mach number and altitude.

0,1

M=0,4 Model 0,09 M=0,5 Model M=0,6 Model 0,08 M=0,7 Model M=0,8 Model

SFC (Kg/s/N) SFC 0,07 M=0.4 M=0.5

0,06 M=0.6 M=0.7

0,05 M=0.8 4000 9000 14000 19000 24000 29000 34000 Thrust (N)

Figure 3.6: Off-design partial throttle Speciﬁc Fuel Consumption (SFC) at different altitudes calculated with implemented model and with the model in [45].

[45], the model developed obtained results that generically reveal the same trends and approximated absolute values.

3.2 Model application for GE CF34-10E and results comparison

To further demonstrate the capabilities of the model and validate its results the case of the General Electric CF34-10E engine designed for a DP at sea-level and static thrust (alt = 0ft and M = 0.01) will be studied. The inputs for this case are presented in Table 3.3. The information contained in [46] was

45 used for deﬁning the inputs. Further considerations contained in Table 2.4 were added, according to a technological level III engine classiﬁcation.

Table 3.3: Input values for the GE CF34-10E analysis.

M0DP = 0, 01 1 = 0, 05 ηmH = 0, 98 altDP = 0ft 2 = 0, 05 ηmP = 0, 98 αDP = 5 πd = 0, 98 Tt4 = 1780(K)

πcDP = 20 πb = 0, 94 hPR = 42800000(J/kg) π 0 = 1.2 π = 0, 98 C = 996, 458(J/(kgK) cDP n pc TISA = 288, 15(K) CTO = 0, 00 Cpt = 1235.1(J/(kgK) PISA = 1235, 1(P a) ηb = 0, 99 λc = 1, 4 β = 0, 03 ηmL = 0, 99 λt = 1, 3

After running the on and off-design analyses, the graphs contained in Figures 3.7 and 3.9 were obtained. In the first one a variation of the full throttle thrust generated by changing the aircraft flying conditions (Mach number and altitude) can be seen, whereas in the second one the variation of the engine fuel flow as function of the same flight conditions is presented. At the same time the graphs also present a comparison with data sourced from an Embraer engine deck. Even though the engine in question is not identified it presents the same maximum thrust, size and weight as the GE CF34-10E.

90000

80000

70000 Deck 0 ft

60000 Deck 10000 ft Deck 20000 ft 50000 Deck 30000 ft

40000 Deck 40000 ft Thrust Thrust (N) Model 0 ft 30000 Model 10000 ft Model 20000 ft 20000 Model 30000 ft 10000 Model 40000 ft

0 0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 Machnumber

Figure 3.7: Comparison of Thrust as function of Mach number an altitude calculated by the model and the Embraer engine deck.

Comparing the results on Figure 3.7 it is possible to see the correspondence between them, with differences specially at higher values of Mach number. Those differences can be clearly seen in the results in Figure 3.8, where the error between the results from the two sources is presented. More than just showing the error variation along Mach number increase, the variation for various altitudes can also be observed. In this case it is seen that for medium altitudes lower errors are obtained. These differences may occur due to the fact that Embraer’s sourced engine DP is unknown and therefore possibly different from the DP chosen for the model-calculated results. Moreover, the differences can be motivated by some of the assumptions made in the model that allowed it be computationally efﬁcient. In the case of the graph in Figures 3.9 a better agreement between both sources can be observed,

46 60

Error 0 ft 30 Error 10000 ft

Error (%) Error 20000 ft

20 Error 30000 ft Error 40000 ft

0 0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 Machnumber

Figure 3.8: Error between the Embraer engine deck and the model calculated Thrust.

2500

Deck 0 ft 2000 Deck 10000 ft Deck 20000 ft 1500 Deck 30000 ft Deck 40000 ft Model 0 ft Fuel Flow (kg/h) 1000 Model 10000 ft Model 20000 ft 500 Model 30000 ft Model 40000 ft

0 0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 Mach number

Figure 3.9: Comparison of the Fuel Flow as function of Mach number and altitude calculated by the model and the Embraer engine deck.

as confirmed by the values of error shown in Figure 3.10. This is important given that the fuel flow parameter is highly significant for the calculation of the engine’s fuel consumption on a certain mission. Contrary to the error results obtained in the thrust results, here the discrepancy of the results is bigger for medium altitudes.

In parallel to the on and off-design analyses the calculations of the engine weight and length was also done using the model developed, with the results being presented in the Table 3.4. Comparing the calculated results with the weight and length of the real engine it is possible to see that the weights differ less than 10%, while the value of the calculated length has a bigger difference to the real one. These differences are motivated by the low ﬁdelity of the model behind the calculation of the weight and speciﬁcally the length.

47 30

Error 0 ft 15 Error 10000 ft

Error (%) Error Error 20000 ft

10 Error 30000 ft Error 40000 ft

0 0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 Machnumber

Figure 3.10: Error between the Embraer engine deck and the model calculated Fuel Flow.

Table 3.4: Weight and Length comparison between modelled and real engine Weight (kg) Length (m) Modelled engine 1 843,22 2,91 Real engine 1678 3,68 Error (%) 9,85 21,00

3.3 Application of a modelled engine to a ﬂight mission

To further test the developed model another study was made. This time a flight mission was defined and, using the model, the turbofan performance needed to accomplish the required thrust, velocity and altitude was calculated. The flight profile chosen to test the engines was based in previously studied missions with the MDOGUI software. From these previous studies it was possible to obtain information from the altitude, the Mach number, the lift coefficient, the variation of the weight of the aircraft along the flight, the Drag Polar, the angle of climb, the angle of attack and instantaneous axial acceleration. After compiling these inputs the informations contained in figures 3.11, 3.12 and 3.13 were obtained. The mission is defined to a total of 600 nm, with 500 nm being calculated with the engine model. The remaining 100 nm correspond to the descend phase but, due to the lack of input data, it was not possible to fully define the variation of the altitude, Mach number and thrust for this phase. Given that in this flight phase the fuel consumption can be neglected when compared with the rest of the flight [5], this fact does not have a significant influence on the block fuel calculation. Presented in Figures 3.14 through 3.18 are, respectively, the graphs with Turbine Inlet Temperature

(TIT) or Tt4, BPR (α), OPR (πc), SFC and Fuel Flow along the mission travelled distance. With the values of fuel ﬂow calculated along the ﬂight mission for discrete time intervals it was possible to calculate the total fuel burned in the mission. Given that there wasn’t information to be computed on the model about the taxi-out, take-off and initial climbing, approach and landing and taxi-in, guideline values already considered in the NOVEMOR project were used. They are presented in the Table 3.5.

48 0,8 0,75 0,7 0,65 0,6 0,55 0,5

Machnnumber 0,45 0,4 0,35 0 50 100 150 200 250 300 350 400 450 500 Distance travelled (nm)

Figure 3.11: Mach number variation along mission travelled distance.

40000 35000 30000 25000 20000 15000 Altitude (ft) 10000 5000 0 0 50 100 150 200 250 300 350 400 450 500 Distance travelled (nm)

Figure 3.12: Altitude variation along mission travelled distance.

100000

80000

60000

40000 Thrust (N)

20000

0 0 50 100 150 200 250 300 350 400 450 500 Distance travelled (nm)

Figure 3.13: Thrust variation along mission travelled distance.

1800

1700

1600

1500

TIT TIT (ºK) 1400

1300

1200 0 50 100 150 200 250 300 350 400 450 500 Distance travelled (nm)

Figure 3.14: Turbine inlet temperature (Tt4) variation along mission travelled distance.

49 15

BPR 9

5 0 50 100 150 200 250 300 350 400 450 500 Distance travelled (nm)

Figure 3.15: BPR (α) variation along mission travelled distance.

11 OPR 9

5 0 50 100 150 200 250 300 350 400 450 500 Distance travelled (nm)

Figure 3.16: OPR (πc) variation along mission travelled distance.

0,08

0,07

0,06

0,05 SFC SFC (kg/h/N) 0,04

0,03 0 50 100 150 200 250 300 350 400 450 500 Distance travelled (nm)

Figure 3.17: SFC variation along mission travelled distance.

2 100,00 1 900,00 1 700,00 1 500,00 1 300,00 1 100,00

Fuel Flow (kg/h) 900,00 700,00 500,00 0 50 100 150 200 250 300 350 400 450 500 Distance travelled (nm)

Figure 3.18: Fuel ﬂow variation along mission travelled distance.

50 Table 3.5: Fuel consumption on Taxi, Take-off and Landing ﬂight phases Flight phase Fuel Burned (kg) Taxi-out 50 Take-off & Initial Climb 150 Approach & Landing 100 Taxi-in 50

Finally, for this ﬂight mission using the developed model a block fuel of 2981kg was calculated. This calculated value was assumed for the 600 nm mission and considering an aircraft take-off weight of 47700 kg. For a similar 600 nm mission, but using the EmbraerTM’s sourced engine performance data the aircraft burned 2991kg of fuel, although for a take-off weight of approximately 51500 kg. The different values of take-off weight does not allow for a rigorous comparison of both results, still it can be concluded that they show that the model is able to predict with a good approximation the total fuel burned across a certain ﬂight mission. A mission with equal take-off weight to the EmbraerTM’s mission could not be developed due to the absence of data available for that same weight in anterior mission studies in the NOVEMOR project.

3.4 On-design and Off-design analysis results for the Turboprop model

As it was done for the turbofan in Section 3.1 the ﬁrst results to presented are outputs from the on-design analysis. They were achieved as inputs the values contained in Table 3.6.

Table 3.6: Input values for the on-design analyses of the turboprop engine. M0 = 0, 8 1 = 0, 05 ηmH = 0, 98 alt = 25000ft 2 = 0, 05 ηprop = 0, 82 0, 4 ≤ τt ≤ 0., 5 πd = 0, 97 Tt4 = 1780(K) 5 ≤ πc ≤ 35 πb = 0, 97 hPR = 42800000(J/kg) TISA = 288, 15(K) πn = 0, 98 Cpc = 996, 458(J/(kgK) PISA = 1013, 25(P a) ηg = 0.99 Cpt = 1235.1(J/(kgK) β = 0, 00 ηb = 0, 98 λc = 1, 4 CTO = 0, 00 ηmL = 0, 99 λt = 1, 3

After running the on-design analysis, the graphics contained in Figures 3.19 and 3.20 were obtained. These graphics include the variation of the Speciﬁc Thrust and the SFC as function of the design variables τt and πc. In Figures 3.19 and 3.20, in addition to the implemented model results, the values available in [45] for the same inputs are also presented. Comparing the two different source results is possible to be observed their strong similarities, with the same trends and approximated values shown. This way, is possible to validate the on-design model of the turboprop engine. Moving to the off-design analysis the same list of inputs shown in Table 3.6 was used. The only differences of inputs are the πc = 30, τt = 0, 6 and the maximum uninstalled thrust that for this engine is required to be 61000 N at static sea-level conditions.

51 2100,00 OPR=5 Model 1900,00 OPR=10 Model OPR=15 Model 1700,00 OPR=20 Model 1500,00 OPR=25 Model 1300,00 OPR=30 Model

1100,00 OPR=35 Model

Specific (N/kg/s) Thrust Specific OPR=5 900,00 OPR=10 700,00 OPR=15 500,00 OPR=20 0,4 0,45 0,5 0,55 0,6 0,65 0,7 0,75 OPR=25 Turbine Total Temperature Ratio

Figure 3.19: Speciﬁc Thrust (F/(m0)) as function of τt and πc for the on-design model of the turboprop for the on-design model calculated on [45]. 0,1

0,095 OPR=5 Model OPR=10 Model 0,09 OPR=15 Model 0,085 OPR=20 Model

0,08 OPR=25 Model OPR=30 Model 0,075 OPR=35 Model

SFC SFC (Kg/s/N) 0,07 OPR=5 OPR=10 0,065 OPR=15 0,06 OPR=20

0,055 OPR=25 OPR=30 0,05 0,4 0,45 0,5 0,55 0,6 0,65 0,7 OPR=35 Turbine Total Temperature Ratio

Figure 3.20: Speciﬁc Fuel Consumption, SFC, as function of τt and πc for the on-design model of the turboprop and for the on-design model calculated on [45].

0,09

0,08 M=0,9 Model M=0,8 Model M=0,7 Model 0,07 M=0,6 Model M=0,5 Model

SFC SFC (Kg/s/N) 0,06 M=0.9 M=0.8

0,05 M=0.7 M=0.6 M=0.5 0,04 4000 6000 8000 10000 12000 14000 16000 18000 Thrust (N)

Figure 3.21: Off-design partial throttle Speciﬁc Fuel Consumption (S) at different altitudes for a turboprop engine model and for the same results calculated in [45].

To verify the turboprop off-design analysis, in Figure 3.21 is presented the effect of varying thrust settings on the engine fuel consumption. This was done by maintaining a ﬁxed altitude (15000 ft) and

Mach number while varying the Tt4. As done in the case of the on-design analysis, the results presented

52 in [45] are also shown in the Figure 3.21. Generically, they present the same parameters behaviour, with similar trends and absolute values. As in the turbofan, the data available in the [45] used for the Figure 3.21, as well as the Figures 3.19 and 3.20 had to be digitalized and its data converted to SI units. In conclusion it can be seen that also the turboprop engine model shows results that are aligned with what is presented in the literature, generating conﬁdence for extensively using it.

53 54 Chapter 4

Optimization of a turbofan mission’s fuel consumption

The main objective of the propulsion model being developed is the integration on an MDO framework as already discussed. This model has also the potential to independently be used for optimization studies of an engine performance as function of its design choices. With this idea in mind, an optimization of a mission’s fuel consumption as function of the design point chosen will be done. The implemented process has a functional structure as presented in the Figure 4.1. For a simplified analysis of the process, the optimization routine can be divided in two separate segments: the first segment corresponds to steps 1 through 3 and is where the optimization process takes place; the second segment corresponds to the steps 4 through 6, and is where the mission profile is calculated for each DP inputs and the final choice of optimum DP is made. Next, the first segment, optimization of design variables for a DP, and the second segment, optimization of fuel consumption on a given flight mission, will be discussed in further detail.

4.1 Optimization of engine design variables for a Design Point

The ﬁrst segment of this complete optimization process has as objective optimizing the design variables

(α, πc, πc0 and m0) that generate the lowest values of fuel consumption and weight for a certain DP. With the objective of doing a comparison between different DPs in Section 4.2, 17 DPs covering a wide range of the engine operating envelop were chosen, being presented in Table 4.2. Additionally, for all the next optimization computations, the engine data inputs used were the ones already employed for representing the GE CF34-10E and are shown in Table 3.3 (except for the DP data inputs). To help with the calculations, a simple 5-point mission flight has also to be included in the inputs. For those 5 points, information corresponding to the altitude, the Mach number and the minimum thrust required for the engine have to be included. These chosen values can be seen in Table 4.1. They were selected to try to define 5 generic phases of the flight, with thrust ratings obtained from the graph in Figure 3.7 as a way of limiting the minimum performance of the optimized engine to the performance of the GE

55 1.INPUTS: - 17 DP’s (altitude and M0) - All inputs used for On and Off-design analyses - Simplified mission profile (5 points) - Full mission profile

2.1.On and Off de- 2.Optimization pro- sign analyses cess for each 17 DPs - Fuel burned in - Design var. = α, π , π 0 , m c c 0 the 5-point mission - Objective func. = g(SFC,W ) - Engine Weight

2.2.Contraints check 3.Optimization Outputs: - Verify if thrust required in the - α, π , π 0 , m , for each DP c c 0 5-point mission is achivable

4.Aplication to the 4.1.On and Off de- Flight Mission: sign analyses - Calculate for each - Calculate fuel ﬂow along the DP: W, L,Block Fuel, all mission points and engine weight performance variables

5.Choice of best DP for the mission: - Choose DP that minimizes f(Block Fuel, W )

6.FINAL OUTPUT: -Best DP for designing the engine for the mission

Figure 4.1: Optimization process ﬂow-chart

CF34-10E. A more detailed mission with more points was not used given that, as will be seen in further detail, these ﬁve points will have to be evaluated consecutively in the optimization algorithm leading to a very time-consuming computer simulation. In spite of that, the model can easily be updated to support a more detailed ﬂight mission.

Table 4.1: 5-point mission ﬂight inputs Mach number 0,01 0,4 0,5 0,6 0,8 Altitude (ft) 0 10000 20000 30000 40000 Minimum thrust requided (N) 80000 44000 36000 26500 18000

For each DP the MATLAB function fmincon will be applied and it will try to ﬁnd a set of α, πc, πc0 and m0 which minimizes the objective function:

56 FF W Objective function = 0.91 cumulative + 0.09 , (4.1) 2500 8500 where FF cumulative is a weighted sum of fuel ﬂows on each of the ﬁve points of the mission (FFcumulative =

0.1FF 1 + 0.1FF 2 + 0.1FF 3 + 0.2FF 4 + 0.5FF 5) to give special relevance for the point corresponding to the cruise phase. The definition of the objective function shown above was the result of a process of various simulations to try to determine the coefficients 2500 and 8500, so that the variables FF cumulative and W could be compared in the same order of size. The coefficients 0.91 and 0.09 were defined this way to give superiority to an engine lower fuel consumption over its weight. These coefficients were defined using information contained in the NOVEMOR studies stating the relative weight of the engines and fuel on the aircraft total weight and so understand how significant an increase in engine weight is for the total fuel consumption. To prevent the optimization algorithm of proposing unrealistic design variables figures, upper and lower boundaries were defined. The upper boundaries were defined as per the technology state-of-the- art for an engine of this size.

Table 4.2: Results for design variables resulting from an optimization process using Interior Point algorithm. o DP# Alt (ft) M0 Tt4( K) α πc πc0 m0(kg/s) 1 0 0,01 1780,00 4,32 41,14 1,54 386,81 2 5000 0,01 1780,00 4,00 22,07 1,80 184,70 3 10000 0,01 1780,00 3,91 44,76 1,74 287,08 4 0 0,20 1780,00 3,34 38,78 1,74 280,55 5 5000 0,20 1780,00 4,52 46,95 1,70 265,34 6 10000 0,20 1780,00 3,70 26,47 1,39 243,12 7 10000 0,50 1780,00 4,06 44,46 1,74 333,83 8 20000 0,50 1780,00 6,21 30,56 1,66 250,38 9 30000 0,50 1780,00 9,02 42,16 1,54 219,53 10 15000 0,60 1780,00 4,31 40,14 1,73 258,12 11 25000 0,60 1780,00 7,26 33,21 1,64 245,77 12 35000 0,60 1780,00 6,96 37,17 1,62 212,24 13 20000 0,80 1780,00 5,33 25,85 1,57 342,07 14 30000 0,80 1780,00 6,07 36,19 1,72 222,70 15 40000 0,80 1780,00 7,34 38,18 1,64 202,67 16 35000 0,85 1780,00 7,13 38,08 1,59 232,82 17 45000 0,85 1780,00 7,61 38,47 1,63 204,30

At the same time that the optimization is being run on the previously presented On and Off-design analyses codes, a parallel set of Off-design analysis is also being executed to check if the inputs set by the optimization function correctly generate an engine capable of accomplishing with the minimum thrust required at each of the five points of the mission. Only if this five constraints are satisfied the inputs can lead to an objective function evaluation. Using the fmincon function, several choices of optimization algorithms and its parameters can be made. This led to trying to run the same inputs for three different algorithms: Interior Point, Sequential Quadratic Point and Active-Set. From these, only the first two were able to converge to a result. For each of those two which obtained results, further studies were made varying the number of maximum iterations and equation evaluations. With the aim of further studying the optimization results, the initial

57 supplied design variables were varied. These changes had large inﬂuence on the optimization results, generating different outputs as shown in Table 4.3. With this differences in mind it is necessary to pay special attention to an appropriate choice of the starting parameters and the number of iterations and function evaluations, given that for some of the simulations with lower number of iterations and function evaluations the optimization have stopped before converging on a local minimum.

Table 4.3: Results obtained for various optimization algorithm settings. o Optimization algorithm DP# Tt4 ( K) Alt (ft) M0 α πc πc0 m0(kg/s) Interior Point 1 1780 0 0,01 10,89 33,11 1,37 433,48 Max Iterations: 500 5 1780 5000 0,20 4,01 37,22 1,72 386,94 Max function evaluations: 1000 8 1780 20000 0,50 7,04 31,90 1,65 271,92 Start inputs: [4;40;1,6;150] 16 1780 35000 0,85 9,14 41,71 1,50 215,66 Interior Point 1 1780 0 0,01 4,32 41,14 1,54 386,81 Max Iterations: 250 5 1780 5000 0,20 4,52 46,95 1,70 265,34 Max function evaluations: 400 8 1780 20000 0,50 6,21 30,56 1,66 250,38 Start inputs: [4;40;1,6;150] 16 1780 35000 0,85 7,13 38,08 1,59 232,82 Interior Point 1 1780 0 0,01 9,82 46,42 1,32 572,75 Max Iterations: 500 5 1780 5000 0,2 6,38 43,45 1,55 433,56 Max function evaluations: 1000 8 1780 20000 0,5 7,87 36,40 1,53 325,29 Start inputs: [4;25;1.3;100] 16 1780 35000 0,85 8,78 44,51 1,52 213,87 SQP 1 1780 0 0,01 11,10 32,36 1,38 433,88 Max Iterations: 400 5 1780 5000 0,2 10,68 33,42 1,40 387,61 Max function evaluations: 1000 8 1780 20000 0,5 9,28 40,27 1,48 281,92 Start inputs: [7;35;1,4;350] 16 1780 35000 0,85 8,50 44,64 1,54 208,10

4.2 Optimization of fuel consumption on a given ﬂight mission

After having determined the design variables α, πc, πc0 and m0 calculated for each DP, the computation of the flight mission is now possible. Once again the same 600 nm mission described in Section 3.3 will be used. In the flight mission results calculation, the first step to be done is, once again, the computation of the on-design analysis with all the DP inputs completely defined. Then, the off-design analysis will be responsible for the calculation of the performance of the engines. At the same time, the weight and length of the engine is once again calculated using the maximum values of BPR and OPR calculated in the off-design analysis. Once these calculations are completely executed, a set of data similar to the one presented in Table 4.4 is obtained. This Table includes a comparison of the block fuel and weight for the engine design for each DP as well as the αmax and πcmax that have been used for calculating the engine weight. Further data outputs can also be extracted from this off-design study, namely obtain for each DP a similar performance analysis as the one presented in Figures 3.14 through 3.18. From the Table 4.4 a selection can be made of the best DP to be selected for the engine development. This step is made by selecting the DP that minimizes the following equation:

Block Fuel W Best DP = 0.91 DP + 0.09 DP , (4.2) Block FuelMAX WMAX

58 where Block FuelDP and WDP are the fuel ﬂow and weight for the DP being analysed and Block FuelMAX and WMAX is the maximum value of each variable calculated for any of the 17 DPs.

Table 4.4: Results of engine Weight and Block Fuel calculated for each DP engine. o DP# Tt4( K) Alt (ft) M0 W (kg) L(m) αmax πcmax Block fuel (kg) 1 1780 0 0,01 1838 2,9 5,6 66,8 2785 2 1780 5000 0,01 1129 2,9 4,4 40,0 2425 3 1780 10000 0,01 1560 2,9 5,3 60,5 2952 4 1780 0 0,20 1441 2,9 4,0 67,8 2564 5 1780 5000 0,20 2086 2,9 5,9 70,7 2630 6 1780 10000 0,20 1313 2,9 5,0 38,6 2897 7 1780 10000 0,50 1834 2,9 5,1 69,2 3200 8 1780 20000 0,50 1908 2,9 8,1 41,4 3118 9 1780 30000 0,50 2648 2,9 14,3 41,2 3328 10 1780 15000 0,60 1597 2,9 5,4 60,8 2820 11 1780 25000 0,60 2167 2,9 9,9 41,6 3554 12 1780 35000 0,60 2384 2,9 10,9 35,6 3450 13 1780 20000 0,80 1542 2,9 6,2 43,7 3188 14 1780 30000 0,80 1911 2,9 8,2 46,0 3471 15 1780 40000 0,80 2421 2,9 11,4 36,9 3813 16 1780 35000 0,85 2215 2,9 10,3 43,1 3502 17 1780 45000 0,85 2597 2,9 12,4 33,8 4190

In the particular case of the optimization results presented in Table 4.4, which have been computed using an Internal Point algorithm (with 200 iterations, 500 function evaluations and [α = 4,πc = 40,πc0 =

1.6,m0 = 150] as starting values), the best DP to be chosen is the number 2. This engine, designed for an altitude of 5000 ft and a static operation, was able to calculate a total block fuel of 2425 kg. Comparing this result with the one achieved in Section 3.3 of 2991 kg, there is a decrease of 19% on the fuel burned to conduct the mission. The choice of Internal Point algorithm (with the presented options selected) was made given that this particular optimization process was able to source design variables that, when applied to the mission, were able to correctly achieve the desired thrust in all the mission points, contrarily to what occurred with other simulated optimizations.

1800

1700

1600

1500 GE CF34-10E TIT TIT (ºK) 1400 Optimized engine 1300

1200 0 50 100 150 200 250 300 350 400 450 500 Distance travelled (nm)

Figure 4.2: Comparison of Turbine inlet temperature (Tt4) variation along mission travelled distance for the optimized and the original engine.

As matter of comparison it can be seen in Figures 4.2 and 4.3 two graphics comparing the TIT (to show variation of the throttle settings) and the fuel ﬂow of the optimized engine with the standard GE CF34-10E. From the information presented in them, it is possible to see that the optimized engine

59 2 000,00

1 500,00

1 000,00 GE CF34-10E Optimized engine

Fuel Flow (kg/h) 500,00

0,00 0 50 100 150 200 250 300 350 400 450 500 Distance travelled (nm)

Figure 4.3: Comparison of fuel flow variation along mission travelled distance for the optimized and the original engine. can accomplish the mission with a lower throttle setting than the original engine, although the bigger difference between them being seen in fuel flow variation between the two. This may occur due to the different design choices which were specially optimized for this mission, while the original engine might have its design choices optimized for different mission. Looking at the results presented, it is possible to see that this optimization can present very promising results. In spite of that, this process has still the limitation of having only taken into consideration one mission profile, while the real aircraft will end up facing a series of different flight missions on its daily service. With this idea in mind the optimization code can in the future be updated to accomplish this objective. In such situation, the objective functions would have to be changed to correctly take into consideration how frequently each single mission will be executed.

60 Chapter 5

Conclusion

In an ever more complex design process of a new aircraft, a MSO approach is essential to study new solutions capable of generating a signiﬁcant reduction in fuel consumptions and emissions. In the spe- ciﬁc case of the MDOGUI tool, a module responsible for the calculation of the propulsive system needs to be implemented.

Contrarily to what is the standard in other MDO frameworks where the propulsive system is studied by using a commercial software together with the main aircraft optimization tool in this particular case the objective was to have the module fully integrated in the framework.

Additionally, to be able to support the MDOGUI’s capabilities of optimizing the aircraft for a given ﬂight mission it was important to implement a model capable of correctly calculating the engine performance across the complete operation range of the aircraft. This is why a model comprising the engine Design Point or On-Design analysis as well as its Off-Design analysis was chosen to be implemented.

The model developed has proved to have the ability of calculating the performance of a two-spool Turbofan engine across a flight mission and to further allow more detailed studies of individual variables as a function of the design choices and flight conditions. At the same time a similarly model was also developed for the Turboprop engine. Bearing in mind that for the NOVEMOR project a commercial 113-seat regional aircraft was defined, it is important to have those two (Turbofan and Turboprop) more frequently used engine types in the commercial aviation. In the particular case of the turbofan engine the model was complemented with the addition of relationships for the estimation of the engine weight, fan diameter and length. Those relationships, although being based on table-data, allowed to build relations depending not only on the static sea-level thrust but also on the BPR and the OPR which enabled them to be integrated in an optimization process.

To test and validate the implemented turbofan model a ﬁrst comparison with data found in the literature was made. Here, a good agreement in trends and total values was obtained, which was able to validate the on-design model implemented. A similar comparison was done for the off-design analysis, from which a similar behaviour between the two sources was also observed. A second comparison was made using an EmbraerTMsupplied engine data bank. In this case the results showed once again similar trends between them, although with errors in the absolute values. Those errors were motivated by the

61 absence of some of the necessary design parameters of the EmbraerTM’s engine. The engine dimensions were also compared, and less than 10 % approximation was obtained for the modelled weight. A third group of results using the turbofan model were calculated. This time, the model was used to simulate the behaviour of the engine along a 600 nm flight mission. A set of results comprising throttle settings, BPR, OPR, SFC and Fuel Flow were presented. From the flight mission test, the Block Fuel was obtained and compared to a similar mission which had been previously studied by EmbraerTMusing its engine data bank. Close results were obtained. With the aim at optimizing the fuel consumption for a given mission, the model was tested in a optimization process that, in the first place, optimized, for 17 possible DP’s for which an engine could be developed, the values of BPR, OPR, fan pressure ratio and overall mass flow for reducing the fuel consumption and engine weight. Then, each DP and its design variables defined were applied to the same 600 nm mission. This process allowed to determine that, for that same mission, an optimum DP existed when the engine was sized for 5000 ft at static-thrust condition. This way a 19% decrease on the Block Fuel comparing to the standard engine was achieved. In the also implemented Turboprop engine model, the same good results were obtained when the comparison of its on and off-design analyses results with the literature was done, generating a good level of confidence to support the extensively use of this model. With the results from the optimization process and all previous steps, the importance and the capabilities of this model were proved, with the most significant achievement being the ability to reach a double-digit efficiency increase. Furthermore, this model allows to do a thorough study of a great variety of engine performance variables and components behaviour.

5.1 Future Work

To further complement the developed model and better study new trends in aeronautical propulsion, this work can later be improved not only to model new technologies being applied in new engine designs but also to take into consideration more design constraints. The first improvements can be focused on the turboprop, whose model can be complemented with a detailed propeller behaviour simulation and with a series of relationships for weight and dimensions definition. Referring to new technologies, some work can be done to enable the model to take into account the new geared turbofan engines. Another addition that can be made to the module is the inclusion of a model for the open-rotor engine. In parallel adding emissions and noise estimation features would be of high interest. The optimization process can also suffer improvements to allow for the inclusion of more than one flight mission, given that the aircraft will end up executing more than one mission type in its operation. Lastly, by having both turbofan and turboprop engine models already developed, using the MDOGUI potentialities and its multiple disciplines an optimization in terms of operating costs could be run to determine whether using a turboprop instead of a turbofan could be an advantageous solution for the NOVEMOR reference regional jet.

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66 Appendix A

Engine database

Table A.1: Turbofan engine Database Designation FTO(lb) FCr(lb) m˙ (lb/s) α πc0 πc Df an(in) L (in) W (lb) 1 FJ44-1C 1500 600 63 3,28 12,8 19,7 41,9 445 2 FJ44-1A 1900 506 63 3,28 12,8 19,7 40,3 447 3 JT15D-5D 3045 75 3,3 1,5 10 61 632 4 AI-25 3307 976 100 2,1 1,7 9,6 78,5 705 5 TFE731-3 3700 817 118 2,8 14,6 28,2 59,8 754 6 PW545 3876 915 4 27,3 68 765 7 TFE731-5 4500 986 140 3,34 14,4 8 TFE731-5B 4750 1052 143 3,48 14,6 29,7 91,1 899 9 PW300 4750 1113 180 4,5 23 10 TFE731-60 5000 1120 4,4 14,6 30,7 82,3 929 11 ATF3-6A 5440 1055 162 2,8 21,3 102,3 1125 12 PW306A 5700 1320 4,5 12,7 31,7 75,6 1043 13 CFE738 5725 1464 210 5,3 1,7 23 99 1325 14 ALF502R-5 6790 2250 5,7 12,2 15 ALF502R-3A 6970 5,71 11,6 56,8 1336 16 AE 3007 7200 5 23 38,5 106,5 1581 17 ALF 502L-2 7500 5 13,6 58,6 1311 18 DV-22 8532 309 5 1543 19 TF34-GE-100 9065 333 6,42 1,5 20 100 1440 20 TF34-GE-400 9275 338 6,2 1,5 21 100 1478 21 FJR710 11243 2976 6,5 93 2160 22 Tay 611 13850 410 3,04 15,8 44 94,7 3135 23 D-36 14330 3527 562 5,6 20 136,6 2445 24 BR 710 14800 2300 435 26 48 134 3600 25 Tay 651 15400 426 3,07 16,6 44,8 94,7 3380 26 D-436K 18078 3439 6,2 21 136,6 3197 27 PS-90A10 20283 4343 582 3,76 23,1 55,1 168,5 4180 28 BR 715 22000 3600 636 32 58 142 4660 29 CFM56-2B1 22000 4969 784 6 30,5 68,3 95,7 4671 30 CFM56-3B2 22000 5040 683 4,9 28,8 60 93 4301 31 D-30KU 24250 6063 593 2,42 20 57,3 224 5110 32 CFM56-7B26 26400 5480 783 5,1 32,6 61 98,7 5216 33 PS-90A12 26455 5071 816 5,05 25,3 65,8 188,8 5071 34 D-30KU-90 26455 6063 540 2,44 35,02 57,3 224,4 5291

67 Table A.2: Turbofan engine Database cont. Designation FTO(lb) FCr(lb) m˙ (lb/s) α πc0 πc Df an(in) L (in) W (lb) 35 V2528-D5 28000 5752 4,7 30 126 5400 36 V2500-A5 30000 5752 848 4,6 1,7 29,4 126 5200 37 CFM56-5C4 34000 7100 1065 6,4 38,3 72,3 103 4995 38 PS-90A-76 35275 7716 1036 4,5 36,4 74,8 195,4 6503 39 535-C 37400 8453 1142 4,4 21,1 73,9 118,5 7294 40 PW2037 38350 6500 1210 6 31,8 78,5 146,8 7196 41 CF-6D 40000 9120 1307 4,4 30,4 86,4 188 10155 42 PW2040 40900 1340 6 1,7 27,6 78,5 146,8 7300 43 D-100 41887 8377 1581 8,1 1,42 40,75 95,9 44 TF39 43000 1541 8 22 96,2 100 7900 45 535-E4 43100 8700 1150 4,3 25,8 74,1 117,9 7189 46 JT9D3A 43600 10200 1495 5,17 21,5 128,2 8608 47 CFMXX 45000 84 48 CF6-80A3 50000 10477 1460 4,6 28,4 157,4 8420 49 RB211-524B 50000 11000 1513 4,5 28,4 84,8 119,4 9195 50 D-18T 51660 10716 1687 5,6 27,5 212,6 9039 51 F103-GE-101 51711 1476 4,31 30,2 173 8768 52 PW4052 52500 9400 1700 5 27,5 93,6 153,6 53 CF6-50C1 52500 10800 1484 4,4 30,4 86,4 183 10842 54 JT9D-59A 53000 11950 1640 4,9 24,5 132,2 9140 55 JT9D-7R4H1 56000 12250 1695 4,8 26,7 132,7 8885 56 CF6-80C2BIF 57160 11330 1769 5,06 29,9 168 9499 57 CF6-80C2DIF 60090 11330 1769 5,05 31,8 168 58 RB211-524H 60600 11813 1604 4,3 33 86,3 125 9874 59 Trent 768 67500 11500 1932 97,4 154 10550 60 CF6-80E1A4 70000 1926 5,3 34,6 96 173,5 11189 61 Trent 775 75150 11500 97,4 154 10550 62 GE90-76B 76400 17500 3000 8,4 39,3 123 193 63 Trent 875 77900 13000 2482 110 172 13333 64 PW4084 84600 13965 2558 4,85 1,7 30 93,6 191,7 13965 65 PW4090 90000 2550 6,41 34,4 93,6 191,7 66 GE90-92B 90200 18400 3221 9 45,5 123 193 16664 67 Trent 890 91300 13000 2720 5,75 1,7 42,8 110 172 13333 68 Trent 900 80000 2745 8,7 39 116 179 13770 69 Trent 1000 78000 2840 11 52 112 186,5 12710 70 Trent XWB 97000 3170 9,3 52 118 71 LEAP 1-A 32900 11 40 78 72 PW1135G 35000 12,5 81 150 73 Genx-1B70 69800 2559 9 53,3 111 184,7 12882 74 Genx-1B74 74100 2624 8,8 55,4 111 184,7 12882 75 Genx-2B67B 66500 2297 8 52,4 104,7 169,7 12374 76 GP7000 81500 2600 8,7 43,9 116 187 14797 77 GE90-115B 115300 3000 9 2 42 128 287 18260 78 CF34-10E 20000 5 29 57 145,5 3700 79 CF-34-3 9200 438 6,2 21 49 103 1670 80 PW6000 23800 5 28,2 56,5 108 5400 81 SaM146 17200 4,43 23,8 48 87 3765 82 LEAP 1-B 28000 9 40 78