Conceptual Design of a 3-shaft Turbofan Engine

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M¨

alardalen University

School of Innovation, Design and Engineering

V¨

aster˚

as, Sweden

Thesis for the Degree of Bachelor of Science in Engineering

-Aeronautical Engineering 15.0 credits

CONCEPTUAL DESIGN OF A

3-SHAFT TURBOFAN ENGINE

Andreas Dik

adk12001@student.mdh.se

Niklas Bit´en

nbn12005@student.mdh.se

Examiner: Dr. H˚

akan Forsberg

M¨

alardalen University, V¨

aster˚

as, Sweden

Supervisor: Dr. Konstantinos G. Kyprianidis

M¨

alardalen University, V¨

aster˚

as, Sweden

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M¨alardalen University

Abstract

During the forthcoming years many new aircrafts such as A350 and B787 are being

designed and continually improved. With these new aircrafts and systems, new

en-gines needs to be designed as well, to meet certain requirements such as fuel burn

and weight improvement. In this thesis, a baseline engine with technical

specifi-cations consistent with a year 2010 EIS has been selected, and the goal was to

create a preliminary design of a new engine named AN15 with year entry into

ser-vice (EIS) 2025 specifications. While no mechanical or cost analyses were performed,

main emphasis was on thermodynamic and aerodynamic analysis. Literature studies

were performed by reading scientific articles combined with books and educational

papers. It was very useful and it also let the students know which direction the

development of jet engines are going. The thermodynamical analysis was performed

in NPSS (Numerical Propulsion System Simulation).

A code, written in C++,

was produced in order to fit the requirements of a 3-shafted turbofan engine and

with the acquired knowledge from the literature studies it was thermodynamically

analysed. The thermodynamical analysis included optimizing parameters such as

temperatures and pressure ratios to have an engine as efficient as possible. Once

the thermodynamical analysis was done, MATLAB was used to write a script which

covered the aerodynamical design such as plotting aspects as well as calculations

which were available from open literatures. Velocity triangles for compressor and

turbine components in the engine was also generated through the MATLAB script.

The result was a 3-shafted turbofan jet engine which had almost the same length as

the baseline engine, a 21% larger fan diameter and a fuel burn improvement of 11%

compared to the baseline engine. Some of the main conclusions were that propulsive

efficiency was increased, but also that the development is going towards jet engine

designs with lower fuel consumption.

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M¨alardalen University

Acknowledgements

We would like to thank our supervisor and mentor Dr. Konstantinos G. Kyprianidis

who guided us through the project and took his time to help us quickly when needed.

We would also like to thank Dr. H˚

akan Forsberg for giving feedback during the

project.

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M¨alardalen University Table of Contents

3.4.7 Temperature optimization . . . 16 3.5 Aerodynamic design . . . 16 3.5.1 Software description . . . 16 3.5.2 Turbomachinery Efficiencies . . . 16 3.5.3 Velocity triangles . . . 17 4 Results 18 4.1 Baseline Engine . . . 18 4.2 Engine Schematic . . . 19 4.3 AN15 . . . 20 4.3.1 Parametric studies . . . 21 4.3.1.1 V18/V8 optimization . . . 21 4.3.1.2 SF Ccr optimization . . . 22 4.3.2 Inlet . . . 23 4.3.3 Compressors . . . 24 4.3.3.1 Fan . . . 24 4.3.3.2 IPC . . . 25 4.3.3.3 HPC . . . 26 4.3.4 Combustion chamber . . . 27

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M¨alardalen University Table of Contents 4.3.5 Turbines . . . 28 4.3.5.1 HPT . . . 28 4.3.5.2 IPT . . . 29 4.3.5.3 LPT . . . 30 4.3.6 Nozzle . . . 31 4.3.7 Internal ducts . . . 32

4.4 Comparison to baseline engine . . . 32

4.5 Sensitivity analysis . . . 33

4.6 Off-design . . . 34

5 Conclusions 35 5.1 Future work . . . 35

5.1.1 Recommendations for future work . . . 35

References 36 Appendix A Formulas 37 Appendix B NPSS outputs 39 B.1 On Design . . . 39

B.2 Off Design, cruise . . . 40

B.3 Off Design, EoR T-O . . . 41

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Nomenclature

α Alfa angle [◦] β Beta angle [◦] ∆ Change in property η Efficiency

ηcore Core efficiency

ηoverall Overall efficiency

ηprop Propulsive efficiency

ηthermal Thermal efficiency

ηtrans Transfer efficiency

φ Flow Coefficient

ψ Stage Loading Coefficient

# Number of

AR Aspect Ratio

BPR Bypass Ratio

C Velocity, absolute [m

s]

EoR End of Runway

Fg Gross Thrust [N ]

Fn Net Thrust [N ]

HPC High Pressure Compressor

HPT High Pressure Turbine

IPC Intermediate Pressure Compressor

IPT Intermediate Pressure Turbine

LPC Low Pressure Compressor

LPT Low Pressure Turbine

N Mechanical speed [RPM]

NGV Nozzle Guide Vane

OGV Outlet Guide Vane

OPR Overall Pressure Ratio

P0 Total Pressure [Pa]

PR Pressure Ratio

RR Rolls Royce

SFC Specific Fuel Consumption [ g

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SFN Specific Net Thrust [N × s

kg ]

SL Sea Level

T-O Take Off

T0 Total Temperature [K]

T41 Turbine Inlet Temperature [K]

T44 LPT inlet temperature [K]

TIT Turbine Inlet Temperature [K]

ToC Top of Climb

UHBPR Ultra High Bypass Ratio

V Velocity, relative [m

s]

VT Velocity Triangles

WATE Weight Analysis of Turbine Engines

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M¨alardalen University List of Tables

List of Tables

1 Review of EIS change in BPR, OPR, fan. . . 15

2 Key data from baseline engine at design point. . . 18

3 Key data from AN15 engine at design point. . . 20

4 SF Ccr over V18/V8 ToC. . . 21

5 Summary of SFC study. . . 22

6 Fan key data. . . 23

7 Fan VT data at mean blade. . . 24

8 Fan key data. . . 24

9 IPC VT data at mean blade. . . 25

10 IPC key data. . . 25

11 HPC VT data at mean blade. . . 26

12 HPC key data. . . 26

13 Combustor chamber key data. . . 27

14 HPT VT data at mean blade. . . 28

15 HPT key data. . . 28

16 IPT VT data at mean blade. . . 29

17 IPT key data. . . 29

18 LPT VT data at mean blade. . . 30

19 LPT key data. . . 31

20 Nozzle key data. . . 31

21 Internal ducts key data. . . 32

22 Comparison. . . 32

23 Sensitivity analysis on component efficiencies. . . 33

24 Sensitivity analysis on engine ducts. . . 33

25 M0.85 at 40000 ft. . . 34

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M¨alardalen University List of Figures

List of Figures

1 The Recuperator. . . 10

2 The preliminary design process. . . 13

3 Velocity triangles. . . 17

4 Baseline engine view. . . 18

5 3-shaft turbofan engine schematic. . . 19

6 AN15 view. . . 20

7 SF Ccr over V18/V8 ToC. . . 21

8 SF Ccr over T41 and T44 at EoR T-O. . . 22

9 Inlet and fan view. . . 23

10 VT for fan at mean blade. . . 24

11 VT for IPC at mean blade. . . 25

12 IPC view. . . 25

13 VT for HPC at mean blade. . . 26

14 HPC view. . . 26

15 Combustor section view. . . 27

16 VT for HPT at mean blade. . . 28

17 HPT view. . . 28

18 VT for IPT at mean blade. . . 29

19 IPT view. . . 29

20 VT for LPT at mean blade. . . 30

21 LPT view. . . 31

22 Nozzle view. . . 31

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M¨alardalen University 1 Introduction

1 Introduction

In recent years, major engine manufacturers have been trying to develop replacement engines for the new generations of long haul aircrafts, Boeing 787, Airbus A380 and A350. The manufacturers are continually evaluating and revising their technical and business plans to make sure that they meet the objective of these aircrafts. Rolls Royce has been developing the new engines Trent 1000 and Trent XWB engines during the last few years and they have revealed their road map for the coming years. Rolls Royce wants to expand their engine programs further by creating engines that have higher bypass ratios, improved cruise propulsive as well as reduced fuel consumption and emissions for an entry into service around in 2025 or beyond.

1.1 Problem Formulation

The main problem was to retain the core of the baseline engine (an EIS 2010 baseline engine) and generate a new LP/IP system that fitted around it, using aerodynamic similarities. Another problem was also regarding the fuel consumption and emissions; the new engine was supposed to burn less fuel and produce less emissions through a lower SFC.

With new techniques and development come new requirements. For example, low cost carriers have taken a big part of the market in just a couple of years. This means that the carriers need engines that produce the same thrust and/or propulsive efficiency at the same time as they are lighter. They also need engines that reduce the maintenance costs and are as reliable as possible. With lower fuel consumption, reduced emissions and less maintenance costs, many airlines make it cheaper to fly than traveling by train or car.

If a number of parameters, for example OPR, BPR and TIT are increased, then a reduction of the fuel consumption will be achieved. Since the CO2 emissions are directly proportional to the fuel consumption, this also means that the emissions from the engine will be reduced.

1.2 Aims and objectives

The aim of this project was to design a new three-spool, high bypass ratio turbofan for entry into service around year 2025 for use on twin-engine, wide-body passenger and freight aircraft.

The objective of this project was to investigate whether a reduced fuel burn as a result of a change in fan diameter, EIS and hence propulsive efficiency (assuming a common core) could be achieved or not. To assess this, a generic three-shaft engine model was used as the project baseline and comparisons were made against a variant model for a reduced specific thrust engine design.

1.3 Limitations

The students that carried out this thesis were writing a 15 hp Bachelor thesis in ten weeks. In line with recommendation from the IDT committee a full detailed design was not feasible. Mechanical analyses as well as cost analyses were not performed, so the work focused on conceptual design aspects utilizing as much as possible the design work inherited from previous undergraduate student thesis.

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M¨alardalen University 2 Literature review

2 Literature review

During this project, a large number of articles and publications were studied. In this chapter, some of the most important topics will be reviewed and summarized. During the literature review, it was hard to find articles about the change in SFC over fan sizing, hence the objective of this project got even more interesting to investigate.

2.1 Fuel consumption

As written in section 1.1, fuel consumption is a big and very interesting part of the engine. As early as 1976, reducing fuel consumption has been discussed. Back then, conventional and heat-exchanged cores were analysed as well as looking into geared and open rotor arrangements. Roughly 15 years later, Peacock and Sadler started to bring up the subject again, but this time they focused on a rather advanced technology, namely UHBR configuration [1]. With engines serving aircrafts in the first decade of the 21th century, a BPR of 9:1 [2] is achieved (on a B777 with GE90 engines), but in the future (around year 2025), a BPR of 12-20:1 is expected.

Another design theory for reducing fuel consumption is with the help from a recuperator. A recuperator is located at the end of the LP-turbine and if the air in the LP-turbine is hotter than the air in HP-compressor, it will use the LPT air to pre-heat the HPC air. This means that the larger temperature difference between the LPT and HPC air, the better effectiveness from the recuperator will be achieved. This will increase the overall efficiency of the engine.

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2.2 Materials

Material is also a very important factor when it comes to the design of the engine. In the previous section, different kinds of BPR’s were discussed. An UHBR engine needs a bigger duct than a HBR engine in order to achieve the same efficiency. This means that if the UHBR engine doesn’t use different materials, it will burn more fuel since it will weigh more than the HBR engine. So to compensate this, another material must be used in order to have the same fuel consumption. However, the cost of the material must be considered. It can’t cost too much, but at the same time the material must be strong enough and fulfill some certain requirements.

Parts of the engine where materials are interesting to analyze are the hot sections such as the turbines. Hot sections are generally very interesting because of the high temperatures that occurs in these sections. Generally, HP and IP turbines use single crystal metal while LP turbines use Inconel 718.

2.3 Conceptual design tools

During the years of airplane engine evolution, computers have become a very essential and im-portant tool to make demanding calculations. Today several different calculation programs and languages are used for different purposes. In this section some of these will be quickly reviewed.

In [3] a computer language called FORTRAN is introduced. FORTRAN has been used since the 1950s and because of its age it has certain limitations when it comes to compatibility with current control design and analysis tools. FORTRAN can be used for many different purposes, but for jet engines it is widely used with the object-oriented code WATE.

WATE was originally developed by Boeing [4] in the late 1970s. It was supposed to be used by NASA but today other companies use it as well. It is used to calculate the weight and dimension of each major engine section like the compressor, combustor, turbine and frames. For example this code has been used to calculate weight and dimension of the engine belonging to the Boeing 777, GE90.

Today with the current technology, other more newly developed programs as MATLAB and Simulink are being more considered when it comes to engine design, mainly because of the current requirements in system development [3]. Such advanced programs in software modelling with more suitable graphical interfaces make it easier to control the whole conceptual design process of an engine. Engine parameters and engine health can easily be assessed with these tools.

Other means of performing specific calculations during the development of an engine design have been made through several EU financed projects in the 21st century and NEW Aeroengine Core concepts (NEWAC) is one of them. TERA2020 is a tool developed through those projects in cooperation with close university partners with a purpose of making a more automated concep-tual design of an engine. [5] It is used for performance modeling as well as sizing and emissions calculations just to mention a few capabilities.

Another software tool developed by the company MTU Aero Engines called ’MOdular Perfor-mance and Engine Design System’ (MOPEDS) [6] is a high quality program that precisely guides the designer through the essential steps of a conceptual engine design. With that in mind, the derivation of an engine’s general arrangement starts with a thermodynamic cycle, from which most engine requirements are set by the customer and may beyond that step continue to other design variables of the engine to complete the preliminary design process of an engine.

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2.4 State of the Art (SOTA) in engine design

There are research studies in the designing of jet engines in many different areas. Designing an engine does not only cover the thermodynamical aspects but also aspects such as aerodynamics, mechanical design and financial aspects. For engines with entry into service around year 2025-2030, many articles have been published with assumptions of different parameters through estimated calculations.

Two students at the same university have carried out a similar project in the previous year. They, however, were to create a conceptual design of a supersonic turbofan. Their literature studies were very helpful when choosing and optimizing parameters, which would result in a MATLAB script and a NPSS code. With help from these scripts and codes, a conceptual engine plot was made together with a summarization of all the basic engine data as well as velocity triangles for certain components of the engine.

Before this project was started, there was a MATLAB script and a NPSS code which was modified to fit this project’s outcome.

2.5 Specific thrust

Another part of the literature studies was to study the specific thrust. The project has an outcome to reduce fuel consumption and this can partially be done by changing the fan pressure as well as the fan sizing. Studies that have been made (both numerically and analytically) shows that fan pressure ratio is highly dependent on specific thrust, SFN. It also worth to mention that the determination of an optimum FPRopis very important as this value together with TIT, BPR and

OPR will ensure minimum SFC. [7] When designing a jet engine for civil aircraft, only one fan stage is generally used with large bypass ratios, and the maximum FPR is around 1.8.

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M¨alardalen University 3 Methodology

3 Methodology

This chapter will cover all the methods used and being relevant for the results. When designing an engine, analyses must cover all of the aspects hence the emphasis was on the thermodynamic analysis as well as the aerodynamic design.

3.1 The preliminary engine design process

The first step within the design process starts at the aircraft manufacturer (the customer). The customer negotiates with the engine manufacturer (the supplier) to produce an engine specifica-tion. The requirements can include parameters such as: Thrust, SFC, mass, size, cost etc.

After this step has been completed, the process continues with the creation of the thermody-namic cycle. In this step, different parameters are set up. For example, what pressure ratio the engine will have, the bypass ratio, the temperatures in the cycles etc.

The process continues with the geometry creation. Basic designs of the different components in the engine (such as blades, discs) are brought up with aerodynamic, mechanical and engine installed performance (engine weight and nacelle drag) aspects in mind. This is done to be able to start the calculations. After the calculations have begun, a program usually performs iterations. An example of the process can be taken from Rolls Royce, who has a software called Genesis, which calculates different parameters. After the parameters are set, the specification from the customer will be met.

The last step of the process is to make a cost analysis. The engine needs to be designed to not cost too much but still meet the requirements.

During the entire process, the different phases will need feedback from each other in order to make sure that the requirements are met perfectly. [8]

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3.2 Different types of analyses

To achieve the objective of this project, the conceptual design of the engine consists of several analytic steps that must be examined before the engine is finished. The focus lied on calculations of numerous key parameters in the engine.

These parameters were analyzed in a thermodynamic, aerodynamic. The way of performing these analyses were mainly in the programs MATLAB and NPSS.

MATLAB is an advanced computer language used by engineers worldwide and it is suitable for this project mainly due to the simplicity of doing graphical plotting with many parameters. [9] Numerical Propulsion System Simulation (NPSS) is a program developed by NASA to make the best simulations of complex systems. The program has the ability to interact with multiple and diverse parameters dependent of each other and therefore varying other inputs as well when the user input is changed. [10]

Both programs are designed for engineering purposes of complex systems and they are very suitable since they have a very good user flexibility due to open architecture.

3.3 Entry Into Service

The Entry Into Service (EIS) term was very helpful when estimating various parameters and values. For example when the component efficiencies were estimated, an EIS correlation, ηpoly,EIS,

was used to predict the changes between EIS year and present time. [11] Parameters such as BPR, FPR and TIT have a similar method for comparing changes from year to year. This term is not only good for knowing if the development is going in the right way, but also for doing calculations for the engines to be designed in the future.

3.4 Thermodynamic analysis

The thermodynamic analysis was carried as a second step in the preliminary design process. The analysis included doing on-design and off-design performance calculations as well as using the literature studies to select and set up initial parameters.

3.4.1 Software description

The software used to optimize a thermodynamic cycle was NPSS which was presented in section 3.2. A code has been created in the program to fetch data such as pressure, temperatures and efficiencies. The code has been written in C++ and has a very flexible way of working; for example it allows the user to set a parameter as a dependent on another parameter, which in this report will be mentioned as the ’NPSS solver’.

3.4.2 On-design and off-design performance

The thermodynamic cycle analysis was performed to ensure that the requirements of the engine (at different operating points) were met. [11] To be able to predict various parameters such as max fan flow and fan diameter a reference point has been set at Top of Climb, M0.82 at 35 000 ft. with a net thrust of 69 400 N. To proceed with the calculations of the performance, certain parameters are required from the baseline model. The TIT, OPR, FPR and BPR was used as primary parameters for optimizing the cycle of the engine.

The off-design performances was run as soon as the parameters mentioned above were set. The off-design performances were run to ensure that the engine works correctly throughout a normal flight cycle. The off-design were performed at the following points:

• End of Runway, Take-Off M0.25 • Cruise, M0.85 at 12190 m (40 000 ft.)

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3.4.3 Engine efficiencies

There are different kinds of efficiencies which are important to understand when it comes to defining the performance of an engine. These are:

• Thermal efficiency - the ratio between net work output divided by the heat supplied. The overall efficiency of an ideal simple cycle improves with rising pressure ratio [12]

• Propulsive efficiency - the ratio between useful propulsive power divided by the power at the nozzle. It is shown that if the flight velocity is equal to zero, none propulsive work will be produced and therefore propulsive efficiency will also be equal to zero [12]

• Core efficiency - this is the usable energy after the core stream power input divided by the energy of the fuel

• Transfer efficiency - the ratio between thermal efficiency and core efficiency

• Overall efficiency - the sum of propulsive efficiency, transfer efficiency and core efficiency multiplied with each other

The formulas can be found in Appendix A. 3.4.4 Fan area

An initial assumption of the hub-to-tip ratio has been set to 0.3. With a known hub-to-tip ratio, a fan area was calculated and the NPSS solver varied the mass fan flow through a determined fan area.

3.4.5 Velocity Ratio

From the literature studies, the optimum velocity ratio Vbypass Vcore

, also referred as V18/V8, of the

engine was set to 0.8. Through this fixed parameter, the NPSS solver selected the best possible BPR. [7]

3.4.6 Pressure Ratio

During the literature studies, a lot of different three-shafted engines have been studied to be able to determine the baseline models parameters. To be able to do an optimization of the different pressure ratios in the engine, an assumption has been made. Table 1 below summarizes the BPR, OPR, number of fan blades and the fan diameter for the engines that has been studied.

Engine type BPR OPR Fan blades/diameter

Trent 700 (A330) EIS 1995 [13] 5:0 36:1 26 / 97.4 Trent 800 (B777) EIS 1996 [14] 6:2 40:7 22 / 110” Trent 900 (A380) EIS 2007 [15] 7:7 - 8:5 39:1 24 / 116” Trent 1000 (B787) EIS 2011 [16] >10:1 50:1 20 / 112” Trent XWB (A350) EIS 2014 [17] 9.3:1 50:1 22 / 118” Table 1: Review of EIS change in BPR, OPR, fan.

As seen in the table, the newer the engines become, the greater value BPR and OPR is being pushed to. Another observation is that BPR and OPR are directly proportional to each other. The fan blades are generally decreased (exception: Trent XWB) as the fan diameter is increased. The baseline engine that will be used for this project is an EIS 2010 baseline engine hence an assumption of the OPR has been set to 45:1 at ToC.

3.4.6.1 Overall Pressure Ratio Based on the literature studies, with aspects of time period change and engine type, an OPR has been selected for the engine. It may be varied a bit because of temperature and material limitations.

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3.4.6.2 Fan Pressure Ratio Once the BPR and the OPR were set, the FPR was calculated by letting the NPSS solver select an optimum FPR for a fixed OPR.

3.4.7 Temperature optimization

From the literature review it is known that the limitation within the temperature starts at T3, also known as the HPC temperature. A predicted temperature of 940 K and 980 K for an EIS 2010 respectively EIS 2025 engine was set as reference for the T3 temperature at EoR T-O. [18] Should the temperature be lower than this, another optimization of OPR must be done since reduced OPR results in a reduced T3 temperature.

A turbine inlet temperature (TIT) was also optimized. The choice of this parameter was varied by the limitation of the material as well as the NGV and rotor cooling. The NGV cooling has initially been selected to 10% and the cooling for the rotor to 8% for the high pressure stages. [18]

3.5 Aerodynamic design

3.5.1 Software description

The software used to design the engine aerodynamically was MATLAB. It has been chosen because of its ability to implement and work with external sources (such as NPSS) and because of the ability to plot an actual engine together with its components.

3.5.2 Turbomachinery Efficiencies

There are two frequent terms of efficiencies that are related to the ideal compression and expansion process of a jet engine, which will be explained in this section.

Isentropic efficiency - The isentropic efficiency is normally expressed in terms of a ratio between the actual and ideal work transfer, i.e. for compressors this is the ratio of the change in enthalpy in an ideal process over the actual one. Similarly for turbines it is defined as the ratio of the change in enthalpy in the actual process over the ideal one. [19]

Polytropic efficiency - The polytropic efficiency is defined as ’the isentropic efficiency of an in-finitely small stage in the compression or expansion process, such that it can be assumed constant throughout the entire process’. [12] Even though the isentropic efficiency is valuable it can also be misleading when compressors and turbines operates at different inlet situations and at different pressure ratios. For example if it is assumed that each stage in the compressor or turbine is op-erated at the same isentropic efficiency, the result will be that the stage efficiency is higher than the component efficiency itself. [12] Since this is not a optimum result, the polytropic efficiency will be used for efficiency calculations. The method used for calculating and estimating polytropic efficiencies for different components throughout the thesis can be found in [11].

The polytropic efficiency formula is as following: ηpoly = ηpoly∗ + ∆ηpoly, EIS+ ∆ηpoly, M + ∆ηpoly, Re

Where the nominal polytropic efficiency, η∗_poly, needs correction through three terms which are: • Entry Into Service, ∆ηpoly, EIS

• Component size, ∆ηpoly, M

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3.5.3 Velocity triangles

When designing the blades, the power input could not be obtained from basic thermodynamics, thus velocity triangles are used. Velocity triangles were created to describe the power outputs and the gas flow through all compressor and turbine stages. With the outputs given from the velocity triangles it was possible to calculate reaction rates, diffusion rates and stage loadings for all stages. These values were later correlated with guideline values for these parameters found in [20]. The velocity triangles data in the chapter ’Results’ will show the data for each compressor and turbine component in the engine of the mean blade while the full output of the velocity triangles can be found in Appendix C. The velocity triangles for a typical compressor stage can be seen in figure 3. The air advances the rotor with a velocity called C1 at an angle α1 in the axial direction. C1

together with the blade speed U produces a velocity which is related to the blade, V1with an angle

β1. After the passage through the rotor, the fluid leaves the rotor in a relative velocity V2in angle

β2 which is set by the rotor blade out angle. If one assumes that the axial velocity Ca is constant

throughout the flow, the relative velocity V2can be acquired and the outlet velocity triangle α2will

then be designed by combining the V2 together with U to give C2 at α2. The difference between

the in and out speed of the stage is called ∆Cw. When leaving the rotor at angle α2, the air passes

through the stator where it is separated in to C3and a given angle α3. The regular design is that

C3 ≈ C1 and α3≈ α1 so that the same procedure can be repeated in the next similar stage.

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M¨alardalen University 4 Results

4 Results

4.1 Baseline Engine

The baseline engine has been set up to be consistent with year 2010 EIS. It is equipped with a one stage fan, eight stage IPC, six stage HPC, one stage HPT, two stage IPT and a six stage LPT. The table below shows the engine’s key parameters together with a view of the engine in figure 4.

Altitude 10 670 m ηpoly,fan 0.905

Mach 0.82 ηpoly,IPC 0.921

ISA +10 K ηpoly,HPC 0.943

Net Thrust 69 400 N ηpoly,HPT 0.899

Mass Flow 490 kg/s ηpoly,IPT 0.898

SFN 142 N*s/kg ηpoly,LPT 0.906 SFC 15.3 g/kN*s ηcore 0.577 OPR 45 ηprop 0.782 TIT 1440 K ηtran 0.828 BPR 6.7 ηthermal 0.478 FPR 1.63 ηoverall 0.373

Fan Diameter 2.93 m Pressure ratio split exp. 0.478

Table 2: Key data from baseline engine at design point.

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4.2 Engine Schematic

A 3-shaft turbofan engine schematic can be viewed in figure 5. The engine is equipped with three shafts as well as a power offtake from the intermediate pressure compressor. There are two cooling flow stages, one for the IP stage and one for the HP stage. The station numbering in the schematic corresponds to the station numbering in the formulas (Appendix A) and NPSS outputs (Appendix B).

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4.3 AN15

This is the result of previous chapters. A 3-shafted turbofan engine named AN15 has been designed based on EIS 2025 specifications. While the important data of the engine and its components are presented in this section, the full output of the engine can be seen in Appendix B and C. Key data at design point for AN15 can be found in table 3 and a view of the engine in figure 6.

Altitude 12 160 m ηpoly,fan 0.946

Mach 0.82 ηpoly,IPC 0.918

ISA +10 K ηpoly,HPC 0.945

Net Thrust 69 400 N ηpoly,HPT 0.910

Mass Flow 710 kg/s ηpoly,IPT 0.915

SFN 97.6 N*s/kg ηpoly,LPT 0.921 SFC 13.7 g/kN*s ηcore 0.610 OPR 57 ηprop 0.839 TIT 1650 K ηtran 0.813 BPR 14 ηthermal 0.496 FPR 1.43 ηoverall 0.416

Fan Diameter 3.54 m Pressure ratio split exp. 0.476

Table 3: Key data from AN15 engine at design point.

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4.3.1 Parametric studies

In this section, the parametric studies that was carried out on the AN15 will be presented. Two parametric studies were performed and through these parametric studies, the other parameters has been solved by using the NPSS solver, which was described in the chapter ’Methodology’. 4.3.1.1 V18/V8 optimization In order to optimize the V18/V8, a parametric study has been

performed. The parametric study involved studying the change of SFC over the ideal jet velocity ratio, V18/V8, at ToC. The result is presented in figure 7 and the measuring points can be seen in

table 4. It shows that in order to achieve the lowest SFC for cruise, the optimum V18/V8 at ToC

is 0.75 which will result in a V18/V8 value at cruise of 0.77. Note that this is not the actual SFC

of AN15, it only shows the optimum V18/V8for the engine.

(V18/V8)T oC SF CCr 0.67 13.6200 0.69 13.6178 0.71 13.6158 0.73 13.6147 0.75 13.6145 0.77 13.6147 0.79 13.6157 0.81 13.6174 0.83 13.6193

Table 4: SF Ccr over V18/V8ToC.

0.66 0.68 0.7 0.72 0.74 0.76 0.78 0.8 0.82 0.84 13.612 13.614 13.616 13.618 13.62 13.622 (V18/V8)T oC S F Ccr [g/kN*s] Optimum V18/V8

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4.3.1.2 SF Ccr optimization The next parametric study involved studying the change of SFC

at cruise over T41 (also known as TIT) at EoR T-O together with T44 (also known as the LPT

inlet temperature) at EOR T-O. The T44is the limiting temperature factor as the material in this

section cannot handle too high temperatures. Since a desired T44has been set, based on material

selection, the study will analyze whether a increasing T41and T44is increasing or decreasing SFC.

The material that has been chosen for the LPT is Inconel 718, which can handle temperatures up to 1200 K. During the study, the rotor and NGV metal temperatures for respectively stages were kept constant.

The result and the measuring points can be seen in figure 8 respectively table 5. It is proven that the higher T44become, the lower SFC is achieved. The lowest SFC will therefore be achieved

at the highest possible temperature for the T44 at EoR T-O.

As a result of this, a T41for EoR T-O temperature at 1883 K has been selected.

SF CCr T41T-O (K) T44 T-O (K) HP Cooling (%) IP Cooling (%)

13.98 1665 1035 6.6 3.6

13.86 1726 1089 8.2 4.6

13.77 1787 1133 9.6 5.5

13.67 1883 1200 11.7 6.7

Table 5: Summary of SFC study.

1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000 13.4 13.6 13.8 14 14.2 Temperaure [K] S F Ccr [g/kN*s] T44 T41

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4.3.2 Inlet

An inlet with smooth nacelle curvature was chosen to start at 0.125 m below the fan tip radius level. This, together with a total inlet length of 1.6 m, made it possible to achieve an inlet pressure recovery of 0.983. The design of the inlet nosecone was most favorable with a hade angle of 20 degrees. The design can be seen in figure 9 together with key data in table 6.

Pressure recovery 0.983

Length 1.6 m

Hade angle 20◦

Inlet diameter 3.29 m Inlet area 8.50 m2

Table 6: Fan key data.

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4.3.3 Compressors

The spacing between the rotor and stator blades in all compressor components was chosen to 30% of the axial chord. [19] To be able to see that allowable diffusion rates are used in the compressors, the de Haller number was used. The de Haller number has a lower limit of 0.69 according to [20] of which all compressor stages in AN15 exceeds.

4.3.3.1 Fan With an axial Mach number in and out of the fan of 0.603 respectively 0.380 and a FPR of 1.43, the AR of the fan blade was selected to 2.4 in order to receive satisfactory perfor-mance. Assumptions from [19] regarding the hub-to-tip ratios created a slightly higher tip out on AN15 compared to the baseline engine which is also why the baseline engine’s fan tip looks rather straight compared to the divergent tip on AN15. The fan is also equipped with an OGV which minimizes the swirl entering the IPC as well as functioning as the main structural component of the engine.

To achieve the required design point performance, a fan diameter of 3.54 m was the most satisfactory option. From this point an initial assumption of the LP-shaft speed was made and together with the correlated value of 1.45 for the relative tip Mach number found in [19] it was possible to set the LP-shaft speed to 2315 rpm.

Mean blade velocity triangles (VT) data can be found in table 7 together with a view of the velocity triangle in figure 10. The red triangle shows the in power and the black triangle shows the out power. The fan hub blade had a high deflection which was a result of low blade speed together with a high enthalpy increase which causes inlet swirl at the hub. This is known as a big challenge in real fan designs but given the time constraints for this project, it was decided that only mean blade VT would be presented. A view of the fan can be seen together with the inlet in figure 9 (on the previous page) together with the key data in table 8.

Stage 1 β1 56 β2 47 α1 0 α2 30 Deflection 9 Ca1 186 Ca2 186 U1 273 U2 307 V1 330 V2 273 C1 186 C2 215 Reaction 0.804 Diffusion 0.225 De Haller 0.827 φ 0.683 ψ 0.706 Temp Rise 26

Table 7: Fan VT data at mean blade.

Figure 10: VT for fan at mean blade.

# stages 1 ARin 2.4

Length 1.13 m ARout 2.4

ηpoly 0.946 Max,in 0.603

rhub/rtip in 0.273 Max,out 0.380

rhub/rtip out 0.361 Fan diameter 3.54 m

FPR 1.43 Fan area 9.84 m2

Avg. ψ 0.706 Avg. φ 0.683

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4.3.3.2 IPC It was decided that the rotational speed of the IP shaft would be such that a value of Mtip,rel 1.3 would be reached, which resulted in a rotational speed of 6000 rpm. The

IPC was chosen to have eight stages to keep the average stage loading at a lower level thus giving higher blade speeds. The most favorable aspect ratios together with hub to tip ratios in and out from the IPC were based on recommendations from [19] which essentially created a design of a dropping hub line for the IPC. The dropping hub line together with a gradually decreasing blade height made it possible to increase the diffusion factor towards 0.4 at the end of the IPC while lowering the reaction rate to near 0.5. The most efficient blade reaction occurs at a value of 0.5. The IPC VT data at the mean blade can be found in table 9 together with the triangles in figure 11. Key data and a IPC view is found in table 10 and figure 12.

Stage 1 2 3 4 5 6 7 8 β1 66 61 56 54 54 54 55 51 β2 58 54 44 38 38 37 37 31 α1 15 16 29 32 29 25 20 25 α2 33 38 47 50 49 48 46 47 Deflection 8 8 12 16 16 17 18 20 Ca1 177 178 178 178 177 177 176 174 Ca2 177 178 178 178 177 177 176 174 U1 394 378 366 354 342 327 311 294 U2 386 379 373 368 362 356 350 343 V1 432 372 320 301 302 303 304 275 V2 330 299 248 226 225 222 219 203 C1 183 185 204 210 202 195 187 192 C2 211 225 263 279 270 262 252 257 Reaction 0.79 0.75 0.60 0.54 0.56 0.58 0.61 0.54 Diffusion 0.28 0.27 0.36 0.41 0.41 0.42 0.43 0.43 De Haller 0.76 0.80 0.77 0.75 0.74 0.73 0.72 0.74 φ 0.45 0.47 0.49 0.50 0.52 0.54 0.57 0.60 ψ 0.34 0.43 0.45 0.48 0.53 0.58 0.64 0.62 Temp Rise 26 30 30 30 30 30 30 26

Table 9: IPC VT data at mean blade. Figure 11: VT for IPC at mean blade.

# stages 8 ARin 1.9

Avg. φ 0.516 Max,out 0.341

Avg. ψ 0.509

Table 10: IPC key data.

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4.3.3.3 HPC The high pressure compressor was placed at a lower height than the IPC. The HPC was designed as a six stage compressor to have a constant tip radius with a gradually de-creasing area towards the end of the component, which reduced the stage loading and gave higher blade speeds. Since the HPT is the limiting factor of the HP-shaft speed because of tendency for high blade root stresses together with big expansion of the turbine disk, the rotational speed of the HP-shaft was set to 12000 rpm which resulted in a Mtip,rel of 1.15 in the HPC. The velocity

triangles data output for mean blades can be seen in table 11 and figure 13. A view of the HPC can be seen in figure 14 while key data is presented in table 12.

Stage 1 2 3 4 5 6 β1 66 64 61 64 67 68 β2 56 55 48 53 56 58 α1 10 15 32 26 24 31 α2 36 42 53 51 52 54 Deflection 10 9 13 11 10 9 Ca1 214 209 200 189 176 161 Ca2 214 209 200 189 176 161 U1 471 482 486 488 489 489 U2 477 484 487 488 489 489 V1 517 475 412 437 446 426 V2 382 363 300 313 318 307 C1 217 216 237 211 193 187 C2 264 279 330 304 285 279 Reaction 0.80 0.75 0.60 0.66 0.69 0.67 Diffusion 0.32 0.32 0.41 0.41 0.41 0.41 De Haller 0.74 0.76 0.73 0.72 0.71 0.72 φ 0.45 0.43 0.41 0.39 0.36 0.33 ψ 0.50 0.52 0.52 0.53 0.53 0.50 Temp Rise 54 58 58 58 58 54

Table 11: HPC VT data at mean blade. Figure 13: VT for HPC at mean blade.

# stages 6 ARin 1.9

Avg. φ 0.396 Max,out 0.263

Avg. ψ 0.518

Table 12: HPC key data.

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4.3.4 Combustion chamber

Due to limited space available in the combustion area, an annular combustor has been chosen for the AN15. Of the three different combustor types (can, can-annular and annular), the annular combustor is the most efficient combustor. This kind of combustion chamber also require the least cooling air to prevent the turbine from being damaged as a result of the high temperatures that flows out of the combustion chamber. [21] The flow velocity was assumed to have the lowest recommended Mach number value of 0.04 to permit a permissible residence time in the combustion chamber. A beta angle of 12.8 degrees was necessary to make the HPT start at a higher level thus increasing the stage loading for that component. Key data are presented in table 13 and a section view can be seen in figure 15.

Vcc 0.036 m3 dP /dPin 2

Vliner 0.018 m3 Combustor residence time 3.3 ms

Total length 0.160 m Stochiometric temp 2300 K

Efficiency 0.999 β 12.8◦

Table 13: Combustor chamber key data.

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4.3.5 Turbines

The blade spacing in the turbines was set to 20% in HPT and IPT while LPT had a blade spacing of 40%. In order to get proper reaction rates and power output in the turbines, the swirl angle, α3, was set to 18◦ in HPT and 15◦ in IPT and LPT.

4.3.5.1 HPT With the HPT connected to the HPC through the HP-shaft rotating at the high-est speed in the core engine, an one stage HPT was chosen in order to keep the stage loadings at a reasonable value. The blade root stress level parameter AN2 _{was the main factor for the}

determination of the stator inlet area. Mach number estimations for the HPT were made through an iterative method to keep reaction rates of the component at acceptable values. The aspect ratio of the stator and rotor component was based on facts that can be expected for an EIS 2025 engine. Key data can be viewed in table 15 together with a view in figure 17. The velocity triangles and its data can be seen in table 14 and figure 16.

Stage 1 β2 41 β3 65 α2 70 α3 18 Deflection 107 Ca 287 U 534 V2 282 V3 689 C2 836 C3 301 Mrel 0.37 Reaction 0.35 φ 0.54 ψ 3.30 Temp drop 372

Table 14: HPT VT data at mean blade.

Figure 16: VT for HPT at mean blade.

# stages 1 ARin 1.16

Avg. φ 0.538 Max,out 0.42

Avg. ψ 3.30 Last stage AN2 3202

Table 15: HPT key data.

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4.3.5.2 IPT It was found that a two stage IPT was necessary to achieve proper reaction rates and stage loadings through both stages. With a high Mach number out, it was possible to reduce the blade root stress levels and give the component the most optimum aspect ratios. Key data can be viewed in table 17 together with a view in figure 19. The velocity triangles data for the IPT can be seen in table 16 and figure 18.

Stage 1 2 β2 24 17 β3 54 51 α2 57 52 α3 15 15 Deflection 78 69 Ca 266 308 U 297 301 V2 292 324 V3 454 505 C2 495 572 C3 275 318 Mrel 0.44 0.47 Reaction 0.42 0.47 φ 0.90 1.02 ψ 3.29 3.21 Temp drop 120 120

Table 16: IPT VT data at mean blade.

Figure 18: VT for IPT at mean blade.

# stages 2 ARin 2

Avg. ψ 3.25 Last stage AN2 1242

Table 17: IPT key data.

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4.3.5.3 LPT While the LPT has a very low mechanical speed due to its connection with the fan, it was most favorable to choose a ten stage option for the LPT to achieve the best efficiency and hence the best power outputs from it. High flow coefficient was the result of the low blade speed versus the axial flow into the LPT. A steep upward slope gradually decreasing towards the end of the LPT was necessary to guarantee proper reaction rates for all LPT stages because of the low speed in the LP shaft. If the LPT was put on a lower level, a less efficient LPT with increased stage loadings would have been obtained. LPT VT data can be seen in table 18 and figure 20 while key data for the LPT can be seen in table 19 together with a view in figure 21.

Stage 1 2 3 4 5 6 7 8 9 10 β2 17 11 6 1 -2 -5 -8 -10 -11 -14 β3 44 44 45 45 46 46 46 47 47 48 α2 45 42 40 37 36 34 33 32 31 30 α3 15 15 15 15 15 15 15 15 15 15 Deflection 61 56 51 47 44 41 39 37 35 34 Ca 221 226 231 235 238 241 244 245 246 247 U 153 161 169 176 182 187 192 195 199 204 V2 232 230 232 235 239 242 246 249 251 254 V3 307 317 327 335 342 349 354 358 362 366 C2 313 306 301 297 294 292 291 290 288 286 C3 229 234 239 243 247 249 252 254 255 255 Mrel 0.38 0.37 0.36 0.36 0.36 0.36 0.36 0.36 0.36 0.36 Reaction 0.47 0.55 0.61 0.66 0.70 0.73 0.76 0.77 0.79 0.81 φ 1.45 1.40 1.36 1.33 1.31 1.29 1.27 1.25 1.24 1.21 ψ 3.69 3.30 3.01 2.78 2.60 2.46 2.34 2.25 2.16 2.06 Temp drop 38 38 38 38 38 38 38 38 38 38 P2/Pchoke< 1 0.65 0.64 0.63 0.63 0.62 0.62 0.62 0.61 0.61 0.61

Table 18: LPT VT data at mean blade.

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# stages 10 ARin 2.10

Avg. ψ 2.66 Last stage AN2 ₁₀₂₀

Table 19: LPT key data.

Figure 21: LPT view.

4.3.6 Nozzle

The LPT ends with an OGV thus minimizing the swirl of the airflow entering the nozzle. A convergent nozzle was chosen in order to achieve a gradual acceleration of the flow towards the nozzle throat where it is expected that the flow will choke at M1. The nozzle, which can be seen in figure 22, has a length of 0.60 m, a cone angle from the centerline of 24◦ _{and the key data can}

be found in table 20.

Figure 22: Nozzle view.

Jetpipe angle 23◦

Cone angle 27◦

Nozzle length 0.60 m

Throat diameter 1.32 m

Throat area 0.52 m2

Core nozzle inlet diameter 1.86 m Core nozzle inlet area 0.80 m2

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4.3.7 Internal ducts

The internal ducts of the AN15 can be seen in figure 23. There are five different ducts in this engine and they are distinguished by the light-blue lines that covers them. Table 21 shows the length and pressure recovery of each duct. The data from the table shows that the biggest pressure losses are in the bypass duct and the fan duct. The reason for this is because of the big dimensions of these ducts.

Figure 23: Internal ducts view.

Duct 1. Fan 2. Intercompr. 3. HPT 4. Interturbine 5. Bypass

PR 0.970 0.980 0.980 0.980 0.970

Length [m] 0.667 0.100 0.120 0.209 2.90

Table 21: Internal ducts key data.

4.4 Comparison to baseline engine

In table 22, a comparison between AN15 and the baseline engine can be seen. The comparison shows that the overall efficiency on AN15 was increased by 12% while the fuel consumption was reduced by 11%. The core length (which is from the beginning of the fan until the end of the LPT) on AN15 was the same as on the baseline engine while the total engine length on AN15 was 2.2% longer due to bigger components such as the fan and the bypass duct. To achieve satisfying performance on AN15, the fan diameter had to be increased by 21%. As mentioned previously, an increase in OPR, BPR and TIT would result in a lower SFC but it would also result in a reduced SFN. In this case, the SFN was reduced by 31%, which also improved the propulsive-transfer efficiency difference, i.e. the change between these two efficiencies were increased.

Baseline AN15 Change (%)

ηcore 0.577 0.610 5.8 ηthermal 0.478 0.496 3.8 ηtran 0.828 0.813 -1.8 ηprop 0.782 0.839 7.3 ηoverall 0.373 0.416 12 SFC (g/kN*s) 15.3 13.7 -11 Fan Diameter (m) 2.93 3.54 21 OPR 45 57 27 BPR 7 14 100 TIT (K) 1440 1650 15 SFN (N*s/kg) 142 97.6 -31

Engine core length (m) 3.38 3.38 0

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4.5 Sensitivity analysis

Sensitivity analyses in NPSS were performed. A sensitivity analysis is useful when one must deter-mine the cost of development regarding for example component efficiencies. Important questions that could be considered in these contexts could be if it is beneficial to have a component with a higher efficiency or not in order to reduce the fuel consumption? Or if it is beneficial to construct a duct with minimal pressure losses?

The first analysis was performed by varying the component efficiencies at the expense of SFC. The result, which can be observed in table 23, shows that higher efficiency results in lower SFC. It is also proven that the efficiency of the fan has the greatest impact on fuel consumption and this is because of the big mass flow that flows through it.

∆Efficiency

∆SFC (%)

η

poly,f an

+ 1 %

-0.7

η

poly,IP C

+ 1 %

-0.4

η

poly,HP C

+ 1 %

-0.4

η

poly,HP T

+ 1 %

-0.3

η

poly,IP T

+ 1 %

-0.2

η

poly,LP T

+ 1 %

-0.5

Table 23: Sensitivity analysis on component efficiencies.

The second analysis was performed on the ducts in the engine, where pressure losses were varied on the expense of the fuel consumption. Table 24 shows that added pressure losses increases fuel consumption and that the bypass duct has the biggest impact on SFC with 1.9%. This is logical as the bypass duct controls the flow of air flowing into bypass duct which in its turn controls the BPR which has a rather big impact on SFC.

∆Pressure loss

∆SFC (%)

Splitter duct + 1 %

0.2 Bypass duct + 1 %

1.9 Intercompressor duct + 1 %

0.3 Combustor + 1 %

0.3 Interturbine duct + 1 %

0.3

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4.6 Off-design

Off-design mechanical speeds and ηpoly of the components can be seen in table 25 and 26. At EoR

take-off, the net thrust was set to 311.3 kN and at cruise it was set to 52.9 kN. Table 26 shows that the highest mechanical speed is obtained at EoR T-O. This is primarily due to that this phase of the flight cycle extracts the most power from the engine but also because the highest temperatures occurs at this phase of the cycle. The engine is designed to operate mostly at cruise and this is also why the average efficiencies of the components are highest at this phase. The full output for the two off-design performances can be found in Appendix B.

Component N ηpoly Fan 2255 0.9531 IPC 5829 0.9253 HPC 11762 0.9465 HPT 11762 0.9099 IPT 5829 0.9149 LPT 2255 0.9208 Table 25: M0.85 at 40000 ft. Component N ηpoly Fan 2429 0.9380 IPC 6439 0.9250 HPC 12926 0.9473 HPT 12926 0.9103 IPT 6439 0.9152 LPT 2429 0.9201 Table 26: M0.25 at SL.

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M¨alardalen University 5 Conclusions

5 Conclusions

The main purpose of this project was to reduce fuel burn, which was accomplished by optimizing the engine’s parameters through a thermodynamic and aerodynamical analysis. The result was a 11% reduced fuel burn which would make the engine more efficient in financial aspects. The fan diameter was also increased by 21% in order for the engine to have a satisfactory performance.

Conclusions that was drawn from this project were:

• Future turbofan engines will most likely be designed in such a manner that they will have reduced fuel consumption

• Future turbofan engines will require the latest technology in aspects of materials in the hot sections to achieve best possible performance

• Year 2025 engines offers an improved propulsive efficiency at the expense of a bigger fan diameter

The future for jet engine looks very promising. Engines are to be more efficient, generate more power but at the same time burn less fuel. Modern design tools such as MATLAB combined with old tools like NPSS makes it possible to ease the designer’s work. The simulations in these soft-wares taught the students where the constraints of the engines were, e.g. positive change in one primary parameter (such as OPR, BPR, TIT) could affect several parameters (such as SFC, T44)

in a negative way, which is why the right balance between all parameters must be found.

All in all, with supervising from a good supervisor, it was certainly a very interesting project to perform and great knowledge was achieved at the same time.

5.1 Future work

Due to time limitations, some parts of the design process have not been possible to fulfill and must be considered in order to get a full preliminary design. These parts include:

• Mechanical design

• Evaluating the nacelle drag

• Perform additional thermodynamic analysis at the off-design points • Weight calculations

5.1.1 Recommendations for future work

To carry on with this preliminary design a few steps are recommended to perform. Looking into mechanical design of the engine is useful to determine valuable disk information such as material selections, weight and stress calculations. Analyzing and evaluation of the nacelle drag on the engine would also be preferable to perform.

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M¨alardalen University References

References

[1] G. E. Aviation, The GE90 Fact Sheet, 1995, [Accessed: 10 April 2015]. [Online]. Available:

http://www.geaviation.com/press/ge90/ge90 19951109a.html

[2] ENOVAL, [Accessed: 10 April 2015]. [Online]. Available: http://www.enoval.eu

[3] K. I. Parker and T.-H. Guo, Development of a Turbofan Engine Simulation in a Graphical Simulation Environment. NASA/TM-2003-212543, 2003.

[4] M. Tong and B. A. Naylor, An object-oriented computer code for aircraft engine weight esti-mation. GT2008-50062, 2008.

[5] A. M. Rolt and K. G. Kyprianidis, Assessment of New Aeroengine Core Concepts and Tech-nologies in the EU Framework 6 NEWAC Programme, 2010.

[6] J. P.Jeschke and C. R.Schaber, Premlinary Gas Turbine Design Using the Multidisciplinary Design System MOPEDS. MTU Aero Engines GmbH, Munich 2004.

[7] A. Guha, Optimum Fan Pressure Ratio for Bypass Engines with Separate or Mixed Exhaust Streams, 2001.

[8] M. Jones, S. Bradbrook, and K. Nurney, A Preliminary Engine Design Process for an Afford-able Capability.

[9] MathWorks and MATLAB, [Accessed: 18 April 2015]. [Online]. Available: http: //se.mathworks.com/products/matlab/

[10] W. Ventures, About NPSS, [Accessed: 18 April 2015]. [Online]. Available: http://www. wolverine-ventures.com/index.php?option=com content&view=article&id=2&Itemid=2

[11] S. Samuelsson, K. G. Kyprianidis, and T. Gr¨onstedt, Consistent Conceptual Design and Per-formance Modeling of Aero Engines, 2015.

[12] K. G. Kyprianidis, Lecture Notes on Gas Turbine Performance, Chalmers University, 2014. [13] R. R. plc, Trent 700 Poster, 2014.

[14] ——, Trent 800 Poster, 2014. [15] ——, Trent 900 Poster, 2014. [16] ——, Trent 1000 Poster, 2014. [17] ——, Trent XWB Poster, 2014.

[18] K. G. Kyprianidis, Personal communications, 2015.

[19] T. Gr¨onstedt, Conceptual aero engine design modeling, Engine Sizing, 2011.

[20] H. Saravanamuttoo, G. Rogers, H. Cohen, and P. Straznicky, Gas Turbine Theory, 6th Edition, 2009, ISBN: 978-0-13-222437-6.

[21] D. Crane, Aviation Maintenance Technician Series, Powerplant third edition, 2011, ISBN: 978-1-56027-862-7.

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M¨alardalen University A Formulas

A

Formulas

Propulsive efficiency ηprop= V0× FN W8× V2 8 − V02 2 Thermal efficiency ηthermal= 1 2W8× V 2 8 − 1 2W0× V 2 0 W0× LHV Core efficiency ηcore= 1 2W44× V 2 44,is− 1 2Wcore× V 2 0 Wf× LHV Transfer efficiency ηtrans= ηthermal ηcore Overall efficiency

ηoverall= ηprop× ηtrans× ηcore

Polytropic efficiency

ηpoly = ηpoly∗ + ∆ηpoly, EIS + ∆ηpoly, M+ ∆ηpoly, Re

Specific Fuel Consumption SF C = Wf

FN

Overall Pressure Ratio OP R =P03

P01

Fan Pressure Ratio F P R =P23

P02

Bypass Ratio BP R =W13

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M¨alardalen University A Formulas

Turbine Inlet Temperature T IT = T41 Stage loading ψ = ∆h U2 Flow coefficient φ =Cx U Diffusion factor DF = 1 −V2 V1 +∆Cw 2V1 ×s c De Haller deHaller =V2 V1 Deflection = α1− α2

Combustor residence time τ = LL

CL

Degree of reaction R = h2− h1

h02− h01

Pressure ratio split exponent n = logOP R(

P25

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M¨alardalen University B NPSS outputs

B

NPSS outputs

B.1 On Design

All units are imperial

MN alt W Fg Fn SFC Wfuel WAR OPR BPR FPR SFn

0.820 35000.0 1565.5 54923.0 15600.0 0.4853 7571.05 0.0000 57.000 13.97 1.43 9.96 ETA,core ETA,prop ETA,tran ETA,th Vbp/Vcore %HP CoolFlow %IP CoolFlow

0.6103 0.839 0.813 0.496 0.75 11.7 6.7

INPUT FLOW

W Pt Tt ht FAR Wc Ps Ts Aphy MN gamt

FS0 Inlet.Fl_I 1565.48 5.379 458.34 109.50 0.0000 4020.56 3.458 403.85 12070.0 0.8200 1.40128 FS1 Fan.Fl_I 1565.48 5.290 458.34 109.50 0.0000 4088.34 4.146 427.46 14152.6 0.6000 1.40128 FS2 Splitter.> 1565.48 7.572 510.88 122.09 0.0000 3015.40 0.000 0.00 0.0 0.0000 1.40065 FS13 DuctBP.Fl> 1460.88 7.572 510.88 122.09 0.0000 2813.92 0.000 0.00 0.0 0.0000 1.40065 FS23 DuctSplit> 104.60 7.572 510.88 122.09 0.0000 201.48 0.000 0.00 0.0 0.0000 1.40065 FS24 IPC.Fl_I 104.60 7.421 510.88 122.09 0.0000 205.59 0.000 0.00 0.0 0.0000 1.40065 FS25 HPC.Fl_I 97.56 51.945 931.25 223.96 0.0000 36.98 0.000 0.00 0.0 0.0000 1.38495 FS3 Burner.Fl> 86.18 306.610 1542.65 380.47 0.0000 7.12 0.000 0.00 0.0 0.0000 1.34813 Blc HPT.Bl_I2 4.57 51.945 1483.50 364.82 0.0000 2.19 0.000 0.00 0.0 0.0000 1.35123 FS4 HPT.Fl_I 88.28 291.279 2974.92 809.83 0.0244 10.67 0.000 0.00 0.0 0.0000 1.28799 NGVc HPT.Bl_I1 6.81 51.945 1483.50 364.82 0.0000 3.26 0.000 0.00 0.0 0.0000 1.35123 FS42 DuctIT.Fl> 99.66 108.127 2305.53 606.06 0.0216 28.56 0.000 0.00 0.0 0.0000 1.30385 BlcIT IPT.Bl_I4 2.83 7.421 764.60 183.21 0.0000 6.81 0.000 0.00 0.0 0.0000 1.39364 FS43 IPT.Fl_I 99.66 105.965 2305.53 606.06 0.0216 29.14 0.000 0.00 0.0 0.0000 1.30385 NGVcIT IPT.Bl_I3 4.21 7.421 764.60 183.21 0.0000 10.12 0.000 0.00 0.0 0.0000 1.39364 FS44 LPT.Fl_I 106.70 48.823 1873.29 480.21 0.0201 61.04 0.000 0.00 0.0 0.0000 1.31887 FS5 JetPipe.F> 1567.59 7.269 559.73 133.88 0.0013 3292.34 5.815 525.20 11720.0 0.5737 1.39905 FS6 Nozzle.Fl> 1567.59 7.196 559.73 133.88 0.0013 3325.60 0.000 0.00 0.0 0.0000 1.39905 FS8 Fl_end.Fl> 1567.59 7.196 559.73 133.88 0.0013 3325.60 3.458 453.95 9739.7 1.0790 1.39905 CBlHP Fl_end_CB> 0.00 51.945 931.25 223.96 0.0000 0.00 0.000 0.00 0.0 0.0000 1.38495 CBlLP Fl_end_CB> 0.00 51.945 931.25 223.96 0.0000 0.00 0.000 0.00 0.0 0.0000 1.38495

INLETS COMPRESSORS & TURBINES

eRam Afs Fram Wc|Wp PR TR effPoly eff Nc|Np pwr

Inlet 0.9834 12070.00 39323.0 Fan 4088.34 1.431 1.1146 0.9460 0.9432 2462.6 -27870.4 IPC 205.59 7.000 1.8228 0.9180 0.8938 6045.5 -14671.1 DUCTS HPC 36.98 5.903 1.6565 0.9450 0.9310 8955.6 -21352.0 dPqP MNin Aphy HPT 16.53 2.694 1.2269 0.9100 0.9190 220.0 21567.4 DuctBP 0.03000 0.0000 0.00 IPT 45.16 2.170 1.1822 0.9150 0.9219 125.0 14786.2 DuctSplit 0.02000 0.0000 0.00 LPT 94.59 6.912 1.5654 0.9210 0.9378 53.5 27898.2 DuctIT 0.02000 0.0000 0.00

JetPipe 0.01000 0.5737 11720.02 MAP POINTS - COMPRESSORS & TURBINES Wc|WpMap PRmap effMap Nc|NpMap Rline

Fan 1441.71 1.677 0.8703 1.000 2.0000 SPLITTERS IPC 1441.71 1.677 0.8703 1.000 2.0000 BPR dP/P1 dP/P2 HPC 123.57 24.136 0.8216 1.000 2.0000 Splitter 13.96616 0.0000 0.0000 HPT 15.77 4.975 0.9220 100.000 IPT 15.77 4.975 0.9220 100.000 LPT 78.56 4.271 0.9171 100.000

ADDERS AND SCALARS

s_Wc|WpAud a_Wc|WpAud s_PRaud a_PRaud s_effAud a_effAud

BURNERS Fan 1.0000 0.0000 1.0000 0.0000 1.0000 0.0000

TtOut eff dPqP Wfuel FAR IPC 1.0000 0.0000 1.0000 0.0000 1.0000 0.0000 Burner 2975.00 0.9999 0.0500 2.10307 0.02440 HPC 1.0000 0.0000 1.0000 0.0000 1.0000 0.0000 HPT 1.0000 0.0000 1.0000 0.0000 1.0000 0.0000 NOZZLES IPT 1.0000 0.0000 1.0000 0.0000 1.0000 0.0000 PR Cfg CdTh Cv Ath Vactual Fg LPT 1.0000 0.0000 1.0000 0.0000 1.0000 0.0000 Nozzle 2.081 1.00 1.00 1.00 9691.10 1127.3 54923.0 BLEEDS SHAFTS Wb/Win dhb/dh dPb/dP Tt ht

Nmech trqIn trqNet pwrIn HPX dNqdt BlcIT IPC.Bl_cool4 0.0271 0.6000 0.0000 764.60 183.21 HP_SHAFT 12000.0 9439.5 -0.1019 21567.4 0.00 0.00 NGVcIT IPC.Bl_cool3 0.0402 0.6000 0.0000 764.60 183.21 IP_SHAFT 6000.0 12943.1 0.2642 14786.2 100.00 0.00 Blc HPC.Bl_cool2 0.0469 0.9000 0.0000 1483.50 364.82 LP_SHAFT 2315.0 63293.4 -0.2222 27898.2 0.00 0.00 CBlHP HPC.CBlHP 0.0000 0.0000 0.0000 931.25 223.96 CBlLP HPC.CBlLP 0.0000 0.0000 0.0000 931.25 223.96 NGVc HPC.Bl_cool1 0.0698 0.9000 0.0000 1483.50 364.82

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B.2 Off Design, cruise

All units are imperial

0.850 40000.0 1277.8 44594.3 11899.9 0.4836 5755.37 0.0000 55.447 14.14 1.42 9.31 ETA,core ETA,prop ETA,tran ETA,th Vbp/Vcore %HP CoolFlow %IP CoolFlow

0.6139 0.851 0.816 0.501 0.77 11.7 6.7

INPUT FLOW

ADDERS AND SCALARS

BURNERS Fan 1.0000 0.0000 1.0000 0.0000 1.0000 0.0000

Nmech trqIn trqNet pwrIn HPX dNqdt BlcIT IPC.Bl_cool4 0.0271 0.6000 0.0000 738.21 176.81 HP_SHAFT 11761.5 7442.4 0.0040 16666.3 0.00 0.00 NGVcIT IPC.Bl_cool3 0.0402 0.6000 0.0000 738.21 176.81 IP_SHAFT 5829.1 10283.8 -0.0129 11413.6 100.00 0.00 Blc HPC.Bl_cool2 0.0469 0.9000 0.0000 1429.45 350.61 LP_SHAFT 2255.0 49675.2 2.1161 21328.5 0.00 0.00 CBlHP HPC.CBlHP 0.0000 0.0000 0.0000 897.73 215.72 CBlLP HPC.CBlLP 0.0000 0.0000 0.0000 897.73 215.72 NGVc HPC.Bl_cool1 0.0698 0.9000 0.0000 1429.45 350.61

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B.3 Off Design, EoR T-O

All units are imperial

0.250 0.0 3830.5 103710.3 70000.8 0.3339 23371.29 0.0000 56.151 12.97 1.44 18.27

ETA,core ETA,prop ETA,tran ETA,th Vbp/Vcore %HP CoolFlow %IP CoolFlow

0.5565 0.492 0.774 0.431 0.70 11.7 6.7

INPUT FLOW

ADDERS AND SCALARS

BURNERS Fan 1.0000 0.0000 1.0000 0.0000 1.0000 0.0000

Nmech trqIn trqNet pwrIn HPX dNqdt BlcIT IPC.Bl_cool4 0.0271 0.6000 0.0000 896.76 215.48 HP_SHAFT 12926.1 26289.1 0.2698 64701.0 0.00 0.00 NGVcIT IPC.Bl_cool3 0.0402 0.6000 0.0000 896.76 215.48 IP_SHAFT 6438.6 36543.8 -1.4410 44799.4 100.00 0.00 Blc HPC.Bl_cool2 0.0469 0.9000 0.0000 1705.35 424.04 LP_SHAFT 2429.3 179875.6 1.0530 83198.7 0.00 0.00 CBlHP HPC.CBlHP 0.0000 0.0000 0.0000 1087.31 262.80 CBlLP HPC.CBlLP 0.0000 0.0000 0.0000 1087.31 262.80 NGVc HPC.Bl_cool1 0.0698 0.9000 0.0000 1705.35 424.04