CONCEPTUAL DESIGN OF A 3-SHAFT TURBOFAN ENGINE820082/FULLTEXT01.pdf · SLSea Level T-OTake O T 0...

Malardalen UniversitySchool of Innovation, Design and Engineering

Vasteras, Sweden

Thesis for the Degree of Bachelor of Science in Engineering -Aeronautical Engineering 15.0 credits

CONCEPTUAL DESIGN OF A3-SHAFT TURBOFAN ENGINE

Andreas [email protected]

Niklas [email protected]

Examiner: Dr. Hakan ForsbergMalardalen University, Vasteras, Sweden

Supervisor: Dr. Konstantinos G. KyprianidisMalardalen University, Vasteras, Sweden

May 27, 2015

Malardalen University

Abstract

During the forthcoming years many new aircrafts such as A350 and B787 are beingdesigned 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 burnand 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 tocreate 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 studieswere performed by reading scientific articles combined with books and educationalpapers. It was very useful and it also let the students know which direction thedevelopment of jet engines are going. The thermodynamical analysis was performedin NPSS (Numerical Propulsion System Simulation). A code, written in C++,was produced in order to fit the requirements of a 3-shafted turbofan engine andwith the acquired knowledge from the literature studies it was thermodynamicallyanalysed. The thermodynamical analysis included optimizing parameters such astemperatures and pressure ratios to have an engine as efficient as possible. Oncethe thermodynamical analysis was done, MATLAB was used to write a script whichcovered the aerodynamical design such as plotting aspects as well as calculationswhich were available from open literatures. Velocity triangles for compressor andturbine 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 asthe 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 propulsiveefficiency was increased, but also that the development is going towards jet enginedesigns with lower fuel consumption.

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Malardalen University

Acknowledgements

We would like to thank our supervisor and mentor Dr. Konstantinos G. Kyprianidiswho guided us through the project and took his time to help us quickly when needed.

We would also like to thank Dr. Hakan Forsberg for giving feedback during theproject.

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Malardalen University Table of Contents

Table of Contents

Abstract i

Acknowledgements ii

Nomenclature v

List of Tables vii

List of Figures viii

1 Introduction 91.1 Problem Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91.2 Aims and objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91.3 Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2 Literature review 102.1 Fuel consumption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102.2 Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112.3 Conceptual design tools . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112.4 State of the Art (SOTA) in engine design . . . . . . . . . . . . . . . . . . . . . . . 122.5 Specific thrust . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

3 Methodology 133.1 The preliminary engine design process . . . . . . . . . . . . . . . . . . . . . . . . . 133.2 Different types of analyses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143.3 Entry Into Service . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143.4 Thermodynamic analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

3.4.1 Software description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143.4.2 On-design and off-design performance . . . . . . . . . . . . . . . . . . . . . 143.4.3 Engine efficiencies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153.4.4 Fan area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153.4.5 Velocity Ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153.4.6 Pressure Ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

3.4.6.1 Overall Pressure Ratio . . . . . . . . . . . . . . . . . . . . . . . . 153.4.6.2 Fan Pressure Ratio . . . . . . . . . . . . . . . . . . . . . . . . . . 16

3.4.7 Temperature optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163.5 Aerodynamic design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

3.5.1 Software description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163.5.2 Turbomachinery Efficiencies . . . . . . . . . . . . . . . . . . . . . . . . . . . 163.5.3 Velocity triangles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

4 Results 184.1 Baseline Engine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184.2 Engine Schematic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194.3 AN15 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

4.3.1 Parametric studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214.3.1.1 V18/V8 optimization . . . . . . . . . . . . . . . . . . . . . . . . . . 214.3.1.2 SFCcr optimization . . . . . . . . . . . . . . . . . . . . . . . . . . 22

4.3.2 Inlet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234.3.3 Compressors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

4.3.3.1 Fan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244.3.3.2 IPC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 254.3.3.3 HPC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

4.3.4 Combustion chamber . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

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4.3.5 Turbines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 284.3.5.1 HPT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 284.3.5.2 IPT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 294.3.5.3 LPT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

4.3.6 Nozzle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 314.3.7 Internal ducts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

4.4 Comparison to baseline engine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 324.5 Sensitivity analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 334.6 Off-design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

5 Conclusions 355.1 Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

5.1.1 Recommendations for future work . . . . . . . . . . . . . . . . . . . . . . . 35

References 36

Appendix A Formulas 37

Appendix B NPSS outputs 39B.1 On Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39B.2 Off Design, cruise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40B.3 Off Design, EoR T-O . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

Appendix C MATLAB outputs 42

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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

kN × s]

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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

XWB Extra Wide Body

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Malardalen 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 SFCcr 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

26 M0.25 at SL. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

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Malardalen 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 SFCcr over V18/V8 ToC. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

8 SFCcr 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

23 Internal ducts view. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

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Malardalen University 1 Introduction

1 Introduction

In recent years, major engine manufacturers have been trying to develop replacement engines forthe new generations of long haul aircrafts, Boeing 787, Airbus A380 and A350. The manufacturersare continually evaluating and revising their technical and business plans to make sure that theymeet the objective of these aircrafts. Rolls Royce has been developing the new engines Trent 1000and Trent XWB engines during the last few years and they have revealed their road map for thecoming years. Rolls Royce wants to expand their engine programs further by creating engines thathave higher bypass ratios, improved cruise propulsive as well as reduced fuel consumption andemissions 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. Anotherproblem was also regarding the fuel consumption and emissions; the new engine was supposed toburn less fuel and produce less emissions through a lower SFC.

With new techniques and development come new requirements. For example, low cost carriershave taken a big part of the market in just a couple of years. This means that the carriers needengines that produce the same thrust and/or propulsive efficiency at the same time as they arelighter. 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 makeit 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 ofthe fuel consumption will be achieved. Since the CO2 emissions are directly proportional to thefuel 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 intoservice 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 achange in fan diameter, EIS and hence propulsive efficiency (assuming a common core) could beachieved or not. To assess this, a generic three-shaft engine model was used as the project baselineand 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 linewith recommendation from the IDT committee a full detailed design was not feasible. Mechanicalanalyses as well as cost analyses were not performed, so the work focused on conceptual designaspects utilizing as much as possible the design work inherited from previous undergraduate studentthesis.

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Malardalen 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 thisproject 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. Asearly 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. Roughly15 years later, Peacock and Sadler started to bring up the subject again, but this time they focusedon a rather advanced technology, namely UHBR configuration [1]. With engines serving aircraftsin 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. Arecuperator is located at the end of the LP-turbine and if the air in the LP-turbine is hotter thanthe air in HP-compressor, it will use the LPT air to pre-heat the HPC air. This means that thelarger temperature difference between the LPT and HPC air, the better effectiveness from therecuperator will be achieved. This will increase the overall efficiency of the engine.

Figure 1: The Recuperator.

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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 previoussection, different kinds of BPR’s were discussed. An UHBR engine needs a bigger duct than aHBR engine in order to achieve the same efficiency. This means that if the UHBR engine doesn’tuse different materials, it will burn more fuel since it will weigh more than the HBR engine. Soto 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 sametime 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 theturbines. Hot sections are generally very interesting because of the high temperatures that occursin these sections. Generally, HP and IP turbines use single crystal metal while LP turbines useInconel 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 andlanguages 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 sincethe 1950s and because of its age it has certain limitations when it comes to compatibility withcurrent 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 byNASA but today other companies use it as well. It is used to calculate the weight and dimensionof each major engine section like the compressor, combustor, turbine and frames. For example thiscode 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 andSimulink are being more considered when it comes to engine design, mainly because of the currentrequirements in system development [3]. Such advanced programs in software modelling with moresuitable graphical interfaces make it easier to control the whole conceptual design process of anengine. Engine parameters and engine health can easily be assessed with these tools.

Other means of performing specific calculations during the development of an engine designhave been made through several EU financed projects in the 21st century and NEW AeroengineCore concepts (NEWAC) is one of them. TERA2020 is a tool developed through those projectsin 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 emissionscalculations 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 guidesthe designer through the essential steps of a conceptual engine design. With that in mind, thederivation of an engine’s general arrangement starts with a thermodynamic cycle, from which mostengine requirements are set by the customer and may beyond that step continue to other designvariables 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 anengine 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 estimatedcalculations.

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 studieswere very helpful when choosing and optimizing parameters, which would result in a MATLABscript and a NPSS code. With help from these scripts and codes, a conceptual engine plot wasmade together with a summarization of all the basic engine data as well as velocity triangles forcertain components of the engine.

Before this project was started, there was a MATLAB script and a NPSS code which wasmodified 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 outcometo reduce fuel consumption and this can partially be done by changing the fan pressure as wellas the fan sizing. Studies that have been made (both numerically and analytically) shows thatfan pressure ratio is highly dependent on specific thrust, SFN. It also worth to mention that thedetermination of an optimum FPRop is very important as this value together with TIT, BPR andOPR will ensure minimum SFC. [7] When designing a jet engine for civil aircraft, only one fanstage is generally used with large bypass ratios, and the maximum FPR is around 1.8.

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Malardalen University 3 Methodology

3 Methodology

This chapter will cover all the methods used and being relevant for the results. When designingan engine, analyses must cover all of the aspects hence the emphasis was on the thermodynamicanalysis 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). Thecustomer 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 theengine will have, the bypass ratio, the temperatures in the cycles etc.

The process continues with the geometry creation. Basic designs of the different componentsin the engine (such as blades, discs) are brought up with aerodynamic, mechanical and engineinstalled performance (engine weight and nacelle drag) aspects in mind. This is done to be able tostart 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, whichcalculates different parameters. After the parameters are set, the specification from the customerwill be met.

The last step of the process is to make a cost analysis. The engine needs to be designed to notcost too much but still meet the requirements.

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

Figure 2: The preliminary design process.

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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 severalanalytic steps that must be examined before the engine is finished. The focus lied on calculationsof numerous key parameters in the engine.These parameters were analyzed in a thermodynamic, aerodynamic. The way of performing theseanalyses were mainly in the programs MATLAB and NPSS.MATLAB is an advanced computer language used by engineers worldwide and it is suitable forthis 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 thebest simulations of complex systems. The program has the ability to interact with multiple anddiverse parameters dependent of each other and therefore varying other inputs as well when theuser input is changed. [10]Both programs are designed for engineering purposes of complex systems and they are very suitablesince 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 andvalues. 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 notonly good for knowing if the development is going in the right way, but also for doing calculationsfor 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. Theanalysis included doing on-design and off-design performance calculations as well as using theliterature 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 section3.2. A code has been created in the program to fetch data such as pressure, temperatures andefficiencies. The code has been written in C++ and has a very flexible way of working; for exampleit allows the user to set a parameter as a dependent on another parameter, which in this reportwill 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 asmax fan flow and fan diameter a reference point has been set at Top of Climb, M0.82 at 35 000ft. with a net thrust of 69 400 N. To proceed with the calculations of the performance, certainparameters are required from the baseline model. The TIT, OPR, FPR and BPR was used asprimary parameters for optimizing the cycle of the engine.

The off-design performances was run as soon as the parameters mentioned above were set. Theoff-design performances were run to ensure that the engine works correctly throughout a normalflight 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.)

14


3.4.3 Engine efficiencies

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

• Thermal efficiency - the ratio between net work output divided by the heat supplied. Theoverall 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 thenozzle. It is shown that if the flight velocity is equal to zero, none propulsive work will beproduced 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 theenergy of the fuel

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

• Overall efficiency - the sum of propulsive efficiency, transfer efficiency and core efficiencymultiplied 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 fanarea.

3.4.5 Velocity Ratio

From the literature studies, the optimum velocity ratioV bypass

V core, also referred as V18/V8, of the

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

3.4.6 Pressure Ratio

During the literature studies, a lot of different three-shafted engines have been studied to be ableto determine the baseline models parameters. To be able to do an optimization of the differentpressure 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/diameterTrent 700 (A330) EIS 1995 [13] 5:0 36:1 26 / 97.4Trent 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 beingpushed 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 anassumption 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 periodchange and engine type, an OPR has been selected for the engine. It may be varied a bit becauseof temperature and material limitations.

15


3.4.6.2 Fan Pressure Ratio Once the BPR and the OPR were set, the FPR was calculatedby 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, alsoknown as the HPC temperature. A predicted temperature of 940 K and 980 K for an EIS 2010respectively EIS 2025 engine was set as reference for the T3 temperature at EoR T-O. [18] Shouldthe temperature be lower than this, another optimization of OPR must be done since reducedOPR results in a reduced T3 temperature.

A turbine inlet temperature (TIT) was also optimized. The choice of this parameter was variedby the limitation of the material as well as the NGV and rotor cooling. The NGV cooling hasinitially 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 becauseof its ability to implement and work with external sources (such as NPSS) and because of the abilityto 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 expansionprocess of a jet engine, which will be explained in this section.

Isentropic efficiency - The isentropic efficiency is normally expressed in terms of a ratio betweenthe actual and ideal work transfer, i.e. for compressors this is the ratio of the change in enthalpy inan ideal process over the actual one. Similarly for turbines it is defined as the ratio of the changein 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 constantthroughout the entire process’. [12] Even though the isentropic efficiency is valuable it can alsobe misleading when compressors and turbines operates at different inlet situations and at differentpressure 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 thanthe component efficiency itself. [12] Since this is not a optimum result, the polytropic efficiencywill be used for efficiency calculations. The method used for calculating and estimating polytropicefficiencies for different components throughout the thesis can be found in [11].

The polytropic efficiency formula is as following:

ηpoly = η∗poly + ∆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

• Reynolds Number, ∆ηpoly, Re

16


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 andthe gas flow through all compressor and turbine stages. With the outputs given from the velocitytriangles 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]. Thevelocity triangles data in the chapter ’Results’ will show the data for each compressor and turbinecomponent in the engine of the mean blade while the full output of the velocity triangles can befound 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, V1 with an angleβ1. After the passage through the rotor, the fluid leaves the rotor in a relative velocity V2 in angleβ2 which is set by the rotor blade out angle. If one assumes that the axial velocity Ca is constantthroughout the flow, the relative velocity V2 can be acquired and the outlet velocity triangle α2 willthen be designed by combining the V2 together with U to give C2 at α2. The difference betweenthe in and out speed of the stage is called ∆Cw. When leaving the rotor at angle α2, the air passesthrough the stator where it is separated in to C3 and a given angle α3. The regular design is thatC3 ≈ C1 and α3 ≈ α1 so that the same procedure can be repeated in the next similar stage.

Figure 3: Velocity triangles.

17

Malardalen 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 onestage 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 0.905Mach 0.82 ηpoly,IPC 0.921ISA +10 K ηpoly,HPC 0.943Net Thrust 69 400 N ηpoly,HPT 0.899Mass Flow 490 kg/s ηpoly,IPT 0.898SFN 142 N*s/kg ηpoly,LPT 0.906SFC 15.3 g/kN*s ηcore 0.577OPR 45 ηprop 0.782TIT 1440 K ηtran 0.828BPR 6.7 ηthermal 0.478FPR 1.63 ηoverall 0.373Fan Diameter 2.93 m Pressure ratio split exp. 0.478

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

Figure 4: Baseline engine view.

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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 threeshafts as well as a power offtake from the intermediate pressure compressor. There are two coolingflow stages, one for the IP stage and one for the HP stage. The station numbering in the schematiccorresponds to the station numbering in the formulas (Appendix A) and NPSS outputs (AppendixB).

Figure 5: 3-shaft turbofan engine schematic.

19


4.3 AN15

This is the result of previous chapters. A 3-shafted turbofan engine named AN15 has been designedbased on EIS 2025 specifications. While the important data of the engine and its components arepresented in this section, the full output of the engine can be seen in Appendix B and C. Key dataat 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 0.946Mach 0.82 ηpoly,IPC 0.918ISA +10 K ηpoly,HPC 0.945Net Thrust 69 400 N ηpoly,HPT 0.910Mass Flow 710 kg/s ηpoly,IPT 0.915SFN 97.6 N*s/kg ηpoly,LPT 0.921SFC 13.7 g/kN*s ηcore 0.610OPR 57 ηprop 0.839TIT 1650 K ηtran 0.813BPR 14 ηthermal 0.496FPR 1.43 ηoverall 0.416Fan Diameter 3.54 m Pressure ratio split exp. 0.476

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

Figure 6: AN15 view.

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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. Twoparametric studies were performed and through these parametric studies, the other parametershas 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 beenperformed. The parametric study involved studying the change of SFC over the ideal jet velocityratio, V18/V8, at ToC. The result is presented in figure 7 and the measuring points can be seen intable 4. It shows that in order to achieve the lowest SFC for cruise, the optimum V18/V8 at ToCis 0.75 which will result in a V18/V8 value at cruise of 0.77. Note that this is not the actual SFCof AN15, it only shows the optimum V18/V8 for the engine.

(V18/V8)ToC SFCCr

0.67 13.62000.69 13.61780.71 13.61580.73 13.61470.75 13.61450.77 13.61470.79 13.61570.81 13.61740.83 13.6193

Table 4: SFCcr over V18/V8 ToC.

0.66 0.68 0.7 0.72 0.74 0.76 0.78 0.8 0.82 0.8413.612

13.614

13.616

13.618

13.62

13.622

(V18/V8)ToC

SFC

cr

[g/k

N*s

]

Optimum V18/V8

Figure 7: SFCcr over V18/V8 ToC.

21


4.3.1.2 SFCcr optimization The next parametric study involved studying the change of SFCat cruise over T41 (also known as TIT) at EoR T-O together with T44 (also known as the LPTinlet temperature) at EOR T-O. The T44 is the limiting temperature factor as the material in thissection cannot handle too high temperatures. Since a desired T44 has been set, based on materialselection, the study will analyze whether a increasing T41 and T44 is increasing or decreasing SFC.The material that has been chosen for the LPT is Inconel 718, which can handle temperatures upto 1200 K. During the study, the rotor and NGV metal temperatures for respectively stages werekept constant.

The result and the measuring points can be seen in figure 8 respectively table 5. It is proventhat the higher T44 become, the lower SFC is achieved. The lowest SFC will therefore be achievedat the highest possible temperature for the T44 at EoR T-O.

As a result of this, a T41 for EoR T-O temperature at 1883 K has been selected.

SFCCr T41 T-O (K) T44 T-O (K) HP Cooling (%) IP Cooling (%)13.98 1665 1035 6.6 3.613.86 1726 1089 8.2 4.613.77 1787 1133 9.6 5.513.67 1883 1200 11.7 6.7

Table 5: Summary of SFC study.

1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 200013.4

13.6

13.8

14

14.2

Temperaure [K]

SFC

cr

[g/k

N*s

]

T44

T41

Figure 8: SFCcr over T41 and T44 at EoR T-O.

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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 radiuslevel. This, together with a total inlet length of 1.6 m, made it possible to achieve an inlet pressurerecovery of 0.983. The design of the inlet nosecone was most favorable with a hade angle of 20degrees. The design can be seen in figure 9 together with key data in table 6.

Pressure recovery 0.983Length 1.6 m

Hade angle 20◦

Inlet diameter 3.29 mInlet area 8.50 m2

Table 6: Fan key data.

Figure 9: Inlet and fan view.

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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 anda 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 onAN15 compared to the baseline engine which is also why the baseline engine’s fan tip looks ratherstraight compared to the divergent tip on AN15. The fan is also equipped with an OGV whichminimizes the swirl entering the IPC as well as functioning as the main structural component ofthe engine.

To achieve the required design point performance, a fan diameter of 3.54 m was the mostsatisfactory option. From this point an initial assumption of the LP-shaft speed was made andtogether with the correlated value of 1.45 for the relative tip Mach number found in [19] it waspossible 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 thevelocity triangle in figure 10. The red triangle shows the in power and the black triangle shows theout power. The fan hub blade had a high deflection which was a result of low blade speed togetherwith a high enthalpy increase which causes inlet swirl at the hub. This is known as a big challengein real fan designs but given the time constraints for this project, it was decided that only meanblade VT would be presented. A view of the fan can be seen together with the inlet in figure 9 (onthe previous page) together with the key data in table 8.

Stage 1β1 56β2 47α1 0α2 30

Deflection 9Ca1 186Ca2 186U1 273U2 307V1 330V2 273C1 186C2 215

Reaction 0.804Diffusion 0.225De Haller 0.827

φ 0.683ψ 0.706

Temp Rise 26

Table 7: Fan VT data at mean blade.

Figure 10: VT for fan at mean blade.

# stages 1 ARin 2.4Length 1.13 m ARout 2.4ηpoly 0.946 Max,in 0.603rhub/rtip in 0.273 Max,out 0.380rhub/rtip out 0.361 Fan diameter 3.54 mFPR 1.43 Fan area 9.84 m2

Avg. ψ 0.706 Avg. φ 0.683Mtip,rel 1.45

Table 8: Fan key data.

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4.3.3.2 IPC It was decided that the rotational speed of the IP shaft would be such that avalue of Mtip,rel 1.3 would be reached, which resulted in a rotational speed of 6000 rpm. TheIPC was chosen to have eight stages to keep the average stage loading at a lower level thus givinghigher blade speeds. The most favorable aspect ratios together with hub to tip ratios in and outfrom the IPC were based on recommendations from [19] which essentially created a design of adropping hub line for the IPC. The dropping hub line together with a gradually decreasing bladeheight made it possible to increase the diffusion factor towards 0.4 at the end of the IPC whilelowering 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 figure11. Key data and a IPC view is found in table 10 and figure 12.

Stage 1 2 3 4 5 6 7 8β1 66 61 56 54 54 54 55 51β2 58 54 44 38 38 37 37 31α1 15 16 29 32 29 25 20 25α2 33 38 47 50 49 48 46 47

Deflection 8 8 12 16 16 17 18 20Ca1 177 178 178 178 177 177 176 174Ca2 177 178 178 178 177 177 176 174U1 394 378 366 354 342 327 311 294U2 386 379 373 368 362 356 350 343V1 432 372 320 301 302 303 304 275V2 330 299 248 226 225 222 219 203C1 183 185 204 210 202 195 187 192C2 211 225 263 279 270 262 252 257

Reaction 0.79 0.75 0.60 0.54 0.56 0.58 0.61 0.54Diffusion 0.28 0.27 0.36 0.41 0.41 0.42 0.43 0.43De 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 0.60ψ 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 1.9Length 0.754 m ARout 1.3ηpoly 0.918 Max,in 0.539Avg. φ 0.516 Max,out 0.341Avg. ψ 0.509

Table 10: IPC key data.

Figure 12: IPC view.

25


4.3.3.3 HPC The high pressure compressor was placed at a lower height than the IPC. TheHPC 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 higherblade speeds. Since the HPT is the limiting factor of the HP-shaft speed because of tendency forhigh blade root stresses together with big expansion of the turbine disk, the rotational speed ofthe HP-shaft was set to 12000 rpm which resulted in a Mtip,rel of 1.15 in the HPC. The velocitytriangles data output for mean blades can be seen in table 11 and figure 13. A view of the HPCcan be seen in figure 14 while key data is presented in table 12.

Stage 1 2 3 4 5 6β1 66 64 61 64 67 68β2 56 55 48 53 56 58α1 10 15 32 26 24 31α2 36 42 53 51 52 54

Deflection 10 9 13 11 10 9Ca1 214 209 200 189 176 161Ca2 214 209 200 189 176 161U1 471 482 486 488 489 489U2 477 484 487 488 489 489V1 517 475 412 437 446 426V2 382 363 300 313 318 307C1 217 216 237 211 193 187C2 264 279 330 304 285 279

Reaction 0.80 0.75 0.60 0.66 0.69 0.67Diffusion 0.32 0.32 0.41 0.41 0.41 0.41De Haller 0.74 0.76 0.73 0.72 0.71 0.72

φ 0.45 0.43 0.41 0.39 0.36 0.33ψ 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 1.9Length 0.252 m ARout 1.3ηpoly 0.945 Max,in 0.482Avg. φ 0.396 Max,out 0.263Avg. ψ 0.518

Table 12: HPC key data.

Figure 14: HPC view.

26


4.3.4 Combustion chamber

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

Vcc 0.036 m3 dP/dPin 2Vliner 0.018 m3 Combustor residence time 3.3 msTotal length 0.160 m Stochiometric temp 2300 KEfficiency 0.999 β 12.8◦

Table 13: Combustor chamber key data.

Figure 15: Combustor section view.

27


4.3.5 Turbines

The blade spacing in the turbines was set to 20% in HPT and IPT while LPT had a blade spacingof 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 loadingsat a reasonable value. The blade root stress level parameter AN2 was the main factor for thedetermination of the stator inlet area. Mach number estimations for the HPT were made throughan iterative method to keep reaction rates of the component at acceptable values. The aspect ratioof 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 andits data can be seen in table 14 and figure 16.

Stage 1β2 41β3 65α2 70α3 18

Deflection 107Ca 287U 534V2 282V3 689C2 836C3 301Mrel 0.37

Reaction 0.35φ 0.54ψ 3.30

Temp drop 372

Table 14: HPT VT data at mean blade.

Figure 16: VT for HPT at mean blade.

# stages 1 ARin 1.16Length 0.060 m ARout 1.16ηpoly 0.910 Max,in 0.15Avg. φ 0.538 Max,out 0.42Avg. ψ 3.30 Last stage AN2 3202

Table 15: HPT key data.

Figure 17: HPT view.

28


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

Stage 1 2β2 24 17β3 54 51α2 57 52α3 15 15

Deflection 78 69Ca 266 308U 297 301V2 292 324V3 454 505C2 495 572C3 275 318Mrel 0.44 0.47

Reaction 0.42 0.47φ 0.90 1.02ψ 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 2Length 0.057 m ARout 2.5ηpoly 0.914 Max,in 0.35Avg. φ 0.96 Max,out 0.50Avg. ψ 3.25 Last stage AN2 1242

Table 17: IPT key data.

Figure 19: IPT view.

29


4.3.5.3 LPT While the LPT has a very low mechanical speed due to its connection with thefan, it was most favorable to choose a ten stage option for the LPT to achieve the best efficiencyand hence the best power outputs from it. High flow coefficient was the result of the low bladespeed versus the axial flow into the LPT. A steep upward slope gradually decreasing towards theend of the LPT was necessary to guarantee proper reaction rates for all LPT stages because of thelow speed in the LP shaft. If the LPT was put on a lower level, a less efficient LPT with increasedstage loadings would have been obtained. LPT VT data can be seen in table 18 and figure 20while 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 10β2 17 11 6 1 -2 -5 -8 -10 -11 -14β3 44 44 45 45 46 46 46 47 47 48α2 45 42 40 37 36 34 33 32 31 30α3 15 15 15 15 15 15 15 15 15 15

Deflection 61 56 51 47 44 41 39 37 35 34Ca 221 226 231 235 238 241 244 245 246 247U 153 161 169 176 182 187 192 195 199 204V2 232 230 232 235 239 242 246 249 251 254V3 307 317 327 335 342 349 354 358 362 366C2 313 306 301 297 294 292 291 290 288 286C3 229 234 239 243 247 249 252 254 255 255Mrel 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 0.81φ 1.45 1.40 1.36 1.33 1.31 1.29 1.27 1.25 1.24 1.21ψ 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 38P2/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.

Figure 20: VT for LPT at mean blade.

30


# stages 10 ARin 2.10Length 0.436 m ARout 6.4ηpoly 0.921 Max,in 0.35Avg. φ 1.31 Max,out 0.50Avg. 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. Aconvergent nozzle was chosen in order to achieve a gradual acceleration of the flow towards thenozzle throat where it is expected that the flow will choke at M1. The nozzle, which can be seenin figure 22, has a length of 0.60 m, a cone angle from the centerline of 24◦ and the key data canbe found in table 20.

Figure 22: Nozzle view.

Jetpipe angle 23◦

Cone angle 27◦

Nozzle length 0.60 mThroat diameter 1.32 mThroat area 0.52 m2

Core nozzle inlet diameter 1.86 mCore nozzle inlet area 0.80 m2

Table 20: Nozzle key data.

31


4.3.7 Internal ducts

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

Figure 23: Internal ducts view.

Duct 1. Fan 2. Intercompr. 3. HPT 4. Interturbine 5. BypassPR 0.970 0.980 0.980 0.980 0.970Length [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 comparisonshows that the overall efficiency on AN15 was increased by 12% while the fuel consumption wasreduced by 11%. The core length (which is from the beginning of the fan until the end of theLPT) on AN15 was the same as on the baseline engine while the total engine length on AN15 was2.2% longer due to bigger components such as the fan and the bypass duct. To achieve satisfyingperformance on AN15, the fan diameter had to be increased by 21%. As mentioned previously, anincrease in OPR, BPR and TIT would result in a lower SFC but it would also result in a reducedSFN. In this case, the SFN was reduced by 31%, which also improved the propulsive-transferefficiency difference, i.e. the change between these two efficiencies were increased.

Baseline AN15 Change (%)ηcore 0.577 0.610 5.8ηthermal 0.478 0.496 3.8ηtran 0.828 0.813 -1.8ηprop 0.782 0.839 7.3ηoverall 0.373 0.416 12SFC (g/kN*s) 15.3 13.7 -11Fan Diameter (m) 2.93 3.54 21OPR 45 57 27BPR 7 14 100TIT (K) 1440 1650 15SFN (N*s/kg) 142 97.6 -31Engine core length (m) 3.38 3.38 0Total engine length (m) 6.85 7.00 2.2

Table 22: Comparison.

32


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 questionsthat could be considered in these contexts could be if it is beneficial to have a component with ahigher efficiency or not in order to reduce the fuel consumption? Or if it is beneficial to constructa 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. Itis also proven that the efficiency of the fan has the greatest impact on fuel consumption and thisis because of the big mass flow that flows through it.

∆Efficiency ∆SFC (%)ηpoly,fan + 1 % -0.7ηpoly,IPC + 1 % -0.4ηpoly,HPC + 1 % -0.4ηpoly,HPT + 1 % -0.3ηpoly,IPT + 1 % -0.2ηpoly,LPT + 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 variedon the expense of the fuel consumption. Table 24 shows that added pressure losses increases fuelconsumption and that the bypass duct has the biggest impact on SFC with 1.9%. This is logicalas the bypass duct controls the flow of air flowing into bypass duct which in its turn controls theBPR which has a rather big impact on SFC.

∆Pressure loss ∆SFC (%)Splitter duct + 1 % 0.2Bypass duct + 1 % 1.9Intercompressor duct + 1 % 0.3Combustor + 1 % 0.3Interturbine duct + 1 % 0.3

Table 24: Sensitivity analysis on engine ducts.

33


4.6 Off-design

Off-design mechanical speeds and ηpoly of the components can be seen in table 25 and 26. At EoRtake-off, the net thrust was set to 311.3 kN and at cruise it was set to 52.9 kN. Table 26 shows thatthe highest mechanical speed is obtained at EoR T-O. This is primarily due to that this phase ofthe flight cycle extracts the most power from the engine but also because the highest temperaturesoccurs at this phase of the cycle. The engine is designed to operate mostly at cruise and this isalso why the average efficiencies of the components are highest at this phase. The full output forthe two off-design performances can be found in Appendix B.

Component N ηpolyFan 2255 0.9531IPC 5829 0.9253HPC 11762 0.9465HPT 11762 0.9099IPT 5829 0.9149LPT 2255 0.9208

Table 25: M0.85 at 40000 ft.

Component N ηpolyFan 2429 0.9380IPC 6439 0.9250HPC 12926 0.9473HPT 12926 0.9103IPT 6439 0.9152LPT 2429 0.9201

Table 26: M0.25 at SL.

34

Malardalen University 5 Conclusions

5 Conclusions

The main purpose of this project was to reduce fuel burn, which was accomplished by optimizingthe engine’s parameters through a thermodynamic and aerodynamical analysis. The result was a11% reduced fuel burn which would make the engine more efficient in financial aspects. The fandiameter 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 havereduced fuel consumption

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

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

The future for jet engine looks very promising. Engines are to be more efficient, generate morepower but at the same time burn less fuel. Modern design tools such as MATLAB combined withold 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 oneprimary 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 projectto 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 mustbe 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 intomechanical design of the engine is useful to determine valuable disk information such as materialselections, weight and stress calculations. Analyzing and evaluation of the nacelle drag on theengine would also be preferable to perform.

35

Malardalen 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 GraphicalSimulation 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 MultidisciplinaryDesign System MOPEDS. MTU Aero Engines GmbH, Munich 2004.

[7] A. Guha, Optimum Fan Pressure Ratio for Bypass Engines with Separate or Mixed ExhaustStreams, 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. Gronstedt, 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. Gronstedt, 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.

36

http://www.geaviation.com/press/ge90/ge90_19951109a.html

http://www.enoval.eu

http://se.mathworks.com/products/matlab/

http://se.mathworks.com/products/matlab/

http://www.wolverine-ventures.com/index.php?option=com_content&view=article&id=2&Itemid=2

http://www.wolverine-ventures.com/index.php?option=com_content&view=article&id=2&Itemid=2

Malardalen University A Formulas

A Formulas

Propulsive efficiency

ηprop =V0 × FN

W8 ×V 28 − V 2

0

2

Thermal efficiency

ηthermal =12W8 × V 2

8 − 12W0 × V 2

0

W0 × LHV

Core efficiency

ηcore =12W44 × V 2

44,is − 12Wcore × V 2

0

Wf × LHV

Transfer efficiency

ηtrans =ηthermal

ηcore

Overall efficiency

ηoverall = ηprop × ηtrans × ηcore

Polytropic efficiency

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

Specific Fuel Consumption

SFC =Wf

FN

Overall Pressure Ratio

OPR =P03

P01

Fan Pressure Ratio

FPR =P23

P02

Bypass Ratio

BPR =W13

W23

37

Malardalen University A Formulas

Turbine Inlet Temperature

TIT = T41

Stage loading

ψ =∆h

U2

Flow coefficient

φ =Cx

U

Diffusion factor

DF = 1 − V2V1

+∆Cw

2V1× s

c

De Haller

deHaller =V2V1

Deflection

ε = α1 − α2

Combustor residence time

τ =LL

CL

Degree of reaction

R =h2 − h1h02 − h01

Pressure ratio split exponent

n = logOPR(P25

P2)

38

Malardalen University B NPSS outputs

B NPSS outputs

B.1 On Design

All units are imperialMN 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

39


B.2 Off Design, cruise


0.850 40000.0 1277.8 44594.3 11899.9 0.4836 5755.37 0.0000 55.447 14.14 1.42 9.31


0.6139 0.851 0.816 0.501 0.77 11.7 6.7

INPUT FLOW


FS0 Inlet.Fl_I 1277.81 4.363 446.51 106.67 0.0000 3993.14 2.720 389.97 11873.0 0.8500 1.40133

FS1 Fan.Fl_I 1277.81 4.291 446.51 106.67 0.0000 4060.46 3.381 417.05 14152.6 0.5932 1.40133

FS2 Splitter.> 1277.81 6.078 495.73 118.45 0.0000 3020.57 0.000 0.00 0.0 0.0000 1.40088

FS13 DuctBP.Fl> 1193.41 6.078 495.73 118.45 0.0000 2821.05 0.000 0.00 0.0 0.0000 1.40088

FS23 DuctSplit> 84.40 6.078 495.73 118.45 0.0000 199.52 0.000 0.00 0.0 0.0000 1.40088

FS24 IPC.Fl_I 84.40 5.956 495.73 118.45 0.0000 203.59 0.000 0.00 0.0 0.0000 1.40088

FS25 HPC.Fl_I 78.72 41.317 897.73 215.72 0.0000 36.84 0.000 0.00 0.0 0.0000 1.38698

FS3 Burner.Fl> 69.54 241.933 1486.45 365.60 0.0000 7.15 0.000 0.00 0.0 0.0000 1.35107

Blc HPT.Bl_I2 3.69 41.317 1429.45 350.61 0.0000 2.18 0.000 0.00 0.0 0.0000 1.35421

FS4 HPT.Fl_I 71.14 229.836 2852.41 770.98 0.0230 10.67 0.000 0.00 0.0 0.0000 1.29106

NGVc HPT.Bl_I1 5.50 41.317 1429.45 350.61 0.0000 3.24 0.000 0.00 0.0 0.0000 1.35421

FS42 DuctIT.Fl> 80.32 85.217 2206.71 576.26 0.0203 28.57 0.000 0.00 0.0 0.0000 1.30735

BlcIT IPT.Bl_I4 2.29 5.956 738.21 176.81 0.0000 6.73 0.000 0.00 0.0 0.0000 1.39472

FS43 IPT.Fl_I 80.32 83.513 2206.71 576.26 0.0203 29.15 0.000 0.00 0.0 0.0000 1.30735

NGVcIT IPT.Bl_I3 3.40 5.956 738.21 176.81 0.0000 10.00 0.000 0.00 0.0 0.0000 1.39472

FS44 LPT.Fl_I 86.00 38.444 1789.73 456.07 0.0189 61.07 0.000 0.00 0.0 0.0000 1.32316

FS5 JetPipe.F> 1279.41 5.832 540.95 129.37 0.0013 3292.39 4.666 507.55 11720.0 0.5736 1.39949

FS6 Nozzle.Fl> 1279.41 5.774 540.95 129.37 0.0013 3325.65 0.000 0.00 0.0 0.0000 1.39949

FS8 Fl_end.Fl> 1279.41 5.774 540.95 129.37 0.0013 3325.65 2.720 436.20 9760.9 1.0950 1.39949

CBlHP Fl_end_CB> 0.00 41.317 897.73 215.72 0.0000 0.00 0.000 0.00 0.0 0.0000 1.38698

CBlLP Fl_end_CB> 0.00 41.317 897.73 215.72 0.0000 0.00 0.000 0.00 0.0 0.0000 1.38698



Inlet 0.9834 11873.00 32694.4 Fan 4060.46 1.416 1.1102 0.9531 0.9507 2430.5 -21306.3

IPC 203.59 6.937 1.8110 0.9253 0.9032 5962.5 -11302.2

DUCTS HPC 36.84 5.855 1.6558 0.9465 0.9330 8939.9 -16499.6


DuctBP 0.03000 0.0000 0.00 IPT 45.18 2.172 1.1844 0.9149 0.9219 124.1 11413.6

DuctSplit 0.02000 0.0000 0.00 LPT 94.64 6.832 1.5678 0.9208 0.9375 53.3 21328.5

DuctIT 0.02000 0.0000 0.00



Fan 1431.88 1.653 0.8773 0.987 2.0267

SPLITTERS IPC 1427.65 1.670 0.8795 0.986 1.9496

BPR dP/P1 dP/P2 HPC 123.08 23.913 0.8233 0.998 2.0146

Splitter 14.13914 0.0000 0.0000 HPT 15.76 4.983 0.9220 100.095

IPT 15.77 4.982 0.9220 99.304

LPT 78.60 4.226 0.9168 99.658

ADDERS AND SCALARS


BURNERS Fan 1.0000 0.0000 1.0000 0.0000 1.0000 0.0000


Burner 2852.44 0.9999 0.0500 1.59871 0.02299 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


Nozzle 2.123 1.00 1.00 1.00 9691.10 1121.5 44594.3

BLEEDS



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

40


B.3 Off Design, EoR T-O


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


0.5565 0.492 0.774 0.431 0.70 11.7 6.7

INPUT FLOW


FS0 Inlet.Fl_I 3830.53 15.349 540.34 129.15 0.0000 3743.44 14.696 533.67 26210.5 0.2500 1.40010

FS1 Fan.Fl_I 3830.53 15.094 540.34 129.15 0.0000 3806.55 12.408 510.90 14152.6 0.5365 1.40010

FS2 Splitter.> 3830.53 21.786 604.21 144.49 0.0000 2788.88 0.000 0.00 0.0 0.0000 1.39898

FS13 DuctBP.Fl> 3556.39 21.786 604.21 144.49 0.0000 2589.29 0.000 0.00 0.0 0.0000 1.39898

FS23 DuctSplit> 274.14 21.786 604.21 144.49 0.0000 199.59 0.000 0.00 0.0 0.0000 1.39898

FS24 IPC.Fl_I 274.14 21.350 604.21 144.49 0.0000 203.67 0.000 0.00 0.0 0.0000 1.39898

FS25 HPC.Fl_I 255.69 148.169 1087.31 262.80 0.0000 36.72 0.000 0.00 0.0 0.0000 1.37524

FS3 Burner.Fl> 225.85 861.854 1771.48 441.96 0.0000 7.12 0.000 0.00 0.0 0.0000 1.33728

Blc HPT.Bl_I2 11.98 148.169 1705.35 424.04 0.0000 2.15 0.000 0.00 0.0 0.0000 1.34025

FS4 HPT.Fl_I 232.35 818.761 3390.49 943.83 0.0287 10.66 0.000 0.00 0.0 0.0000 1.27942

NGVc HPT.Bl_I1 17.85 148.169 1705.35 424.04 0.0000 3.21 0.000 0.00 0.0 0.0000 1.34025

FS42 DuctIT.Fl> 262.18 304.679 2644.72 710.26 0.0254 28.56 0.000 0.00 0.0 0.0000 1.29331

BlcIT IPT.Bl_I4 7.43 21.350 896.76 215.48 0.0000 6.72 0.000 0.00 0.0 0.0000 1.38704

FS43 IPT.Fl_I 262.18 298.585 2644.72 710.26 0.0254 29.14 0.000 0.00 0.0 0.0000 1.29331

NGVcIT IPT.Bl_I3 11.03 21.350 896.76 215.48 0.0000 9.98 0.000 0.00 0.0 0.0000 1.38704

FS44 LPT.Fl_I 280.63 137.406 2160.24 564.89 0.0237 61.25 0.000 0.00 0.0 0.0000 1.30644

FS5 JetPipe.F> 3837.02 20.992 667.66 159.91 0.0017 3047.76 17.564 634.70 11720.0 0.5115 1.39619

FS6 Nozzle.Fl> 3837.02 20.782 667.66 159.91 0.0017 3078.55 0.000 0.00 0.0 0.0000 1.39619

FS8 Fl_end.Fl> 3837.02 20.782 667.66 159.91 0.0017 3078.55 14.696 605.03 9691.0 0.7217 1.39619

CBlHP Fl_end_CB> 0.00 148.169 1087.31 262.80 0.0000 0.00 0.000 0.00 0.0 0.0000 1.37524

CBlLP Fl_end_CB> 0.00 148.169 1087.31 262.80 0.0000 0.00 0.000 0.00 0.0 0.0000 1.37524



Inlet 0.9834 26210.46 33709.5 Fan 3806.55 1.443 1.1182 0.9380 0.9347 2380.1 -83115.1

IPC 203.67 6.940 1.7996 0.9250 0.9029 5965.5 -44656.3

DUCTS HPC 36.72 5.817 1.6292 0.9473 0.9345 8927.7 -64053.4


DuctBP 0.03000 0.0000 0.00 IPT 45.16 2.173 1.1770 0.9152 0.9219 125.2 44799.4

DuctSplit 0.02000 0.0000 0.00 LPT 94.93 6.551 1.5235 0.9201 0.9361 52.3 83198.7

DuctIT 0.02000 0.0000 0.00



Fan 1342.34 1.696 0.8625 0.966 1.4016

SPLITTERS IPC 1428.20 1.670 0.8792 0.987 1.9512

BPR dP/P1 dP/P2 HPC 122.68 23.730 0.8246 0.997 2.0276

Splitter 12.97288 0.0000 0.0000 HPT 15.76 4.960 0.9219 100.901

IPT 15.76 4.984 0.9220 100.193

LPT 78.84 4.071 0.9154 97.719

ADDERS AND SCALARS


BURNERS Fan 1.0000 0.0000 1.0000 0.0000 1.0000 0.0000


Burner 3390.53 0.9999 0.0500 6.49203 0.02874 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


Nozzle 1.414 1.00 1.00 1.00 9691.10 869.6 103710.3

BLEEDS



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

41

Malardalen University C MATLAB outputs

C MATLAB outputs

-----------------------------FAN-----------------------------

Entry Into Service: 2025

Stages: 1

1st stage Utip,in: 428.9678

1st stage Utip,in,corr: 456.3272

1st stage Umid,in: 272.9305

1st stage Cax,in: 186.3136

1st stage Hade angle: 20

(rhub/rtip)in: 0.2725

(rhub/rtip)out: 0.36108

AR,in 2.4

AR,out 2.4

M,ax,in 0.603

M,ax,out 0.38

Total length [m]: 1.1254

RNI: 0.42088

Mcorr: 1854.4027

dETAEIS: 0.028842

dETARe: -0.012236

dETAM: 0

ETA*: 0.92891

ETApol: 0.94552

-----------------------------IPC-----------------------------

Stages: 8

1:st stage(hub/tip)-ratio: 0.82254

Last stage(hub/tip)-ratio: 0.89986

1:st stage Mtiprel no IGV: 1.3

AR,in 1.8965

AR,out 1.3

M,ax,in 0.539

M,ax,out 0.341


RNI: 0.52527

Mcorr: 91.39

dETAEIS: 0.016354

dETARe: -0.0076307

dETAM: 0

ETA*: 0.90968

ETApol: 0.9184

-----------------------------HPC-----------------------------

Stages: 6

1:st stg(hub/tip)-ratio: 0.88965

last stg(hub/tip)-ratio: 0.96084

1:st stg Mtip,rel no IGV: 1.2224

AR,in 1.5

AR,out 1.1383

M,ax,in 0.482

M,ax,out 0.263


RNI: 1.7239

Mcorr: 17.9862

dETAEIS: 0.018391

dETARe: 0.0050351

dETAM: -0.0084912

ETA*: 0.92968

ETApol: 0.94462

-----------------------------Combuster-----------------------

At Cruise conditions

Pattern Factor: 0.35259

Dp: 1.913

Burning time: 0.0032786

Vcc [m^3]: 0.035849

Vliner [m^3]: 0.017925


At windmilling conditions

Loading: 439.2637

-----------------------------HPT-----------------------------

Stages: 1

Blade root stress - AN2: 3201.5112

AR,in 1.16

AR,out 1.16

M,ax,in 0.14997

M,ax,out 0.42


RNI: 2.4591

Mcorr: 4.8385

dETAEIS: 0.0060975

dETARe: 0.0082241

dETAM: -0.048327

ETA*: 0.95639

ETApol: 0.90967

-----------------------------IPT-----------------------------

Stages: 2

Last stg AN2: 1242.2053

AR,in 2

AR,out 2.5

M,ax,in 0.35

M,ax,out 0.5


RNI: 1.2054

Mcorr: 13.2179

dETAEIS: 0.0098318

dETARe: 0.0018184

dETAM: -0.02651

ETA*: 0.92973

ETApol: 0.91487

-----------------------------LPT-----------------------------

Stages: 10

Last stg AN2: 1019.7782

AR,in 2.054

AR,out 6.409

M,ax,in 0.35

M,ax,out 0.5


RNI: 0.70771

Mcorr: 25.8593

dETAEIS: 0.0098318

dETARe: -0.0035314

42


dETAM: -0.014571

ETA*: 0.92921

ETApol: 0.92094

-----------------------------Engine--------------------------

OPR: 57

BPR: 13.97

FPR: 1.4314

IPC pressure ratio: 6.8601

HPC pressure ratio: 5.9026

Fan diameter [m]: 3.539

Fan area [m^2]: 9.8365

Total engine length [m]: 7.0373

Engine length baseline engine [m]: 6.731

Fan diameter baseline engine [m]: 2.961

Core length [m]: 3.3873

Baseline core length [m]: 3.3808

LP-shaft speed [rpm]: 2315

IP-shaft speed [rpm]: 6000

HP-shaft speed [rpm]: 12000

-----------------------------Inlet---------------------------

Total pressure recovery [m]: 0.98345


Inlet diameter [m]: 3.289

Inlet area [m^2]: 8.4958

-----------------------------Ducts---------------------------

Fan-IPC duct length [m]: 0.6672

IPC-HPC duct length [m]: 0.1

Combustor length [m]: 0.16417

HPT-IPT duct length [m]: 0.12

IPT-LPT duct length [m]: 0.20868

LPT-exhaust length [m]: 0.25

BP-duct length [m]: 2.8978

Jet-pipe length [m]: 0.6

-----------------------------Nozzle--------------------------

Nozzle length [m] 0.6

Cone angle []: 23.3929

Jetpipe angle []: 27.2218

Bypass nozzle diameter [m]: 3.4934

Bypass nozzle area [m^2]: 6.5791

Throat diameter [m]: 1.239

Throat area [m^2]: 0.35903

Core nozzle inlet diameter [m]: 1.8563

Core nozzle inlet area [m^2]: 0.80143

----------------------------Velocity Diagram FAN------------

Mtip,rel: 1.45

Average Stage Load: 0.70584

Average Flow coefficient: 0.68264

Average Temp rise: 29.1889

Table =

Stage Hubradii Midradii Tipradii

_____ ________ ________ ________

beta1 1 43.868 55.681 65.562

beta2 1 6.0639 47.011 64.213

alpha1 1 -17.525 0 7.2337

alpha2 1 34.538 29.903 26.055

Deflection 1 37.804 8.6698 1.3494

C-axial in 1 181.1 186.31 184.3

C-axial out 1 206.7 186.31 175.8

Uin m/s 1 116.89 272.93 428.97

Uout m/s 1 164.22 307.02 449.83

V1 m/s 1 251.2 330.46 445.49

V2 m/s 1 207.86 273.24 404.12

C1 m/s 1 189.91 186.31 185.78

C2 m/s 1 250.92 214.93 195.69

Reaction 1 0.63609 0.80371 0.87255

Diffusion 1 0.31825 0.22509 0.10621

de Haller 1 0.72499 0.82686 0.95098

Flow coefficient 1 1.5492 0.68264 0.42963

Stage load 1 3.848 0.70584 0.28573

Stage Temp-rise K 1 26.189 26.189 26.189

----------------------------Velocity Diagram IPC-----

IGV angle: 15

First stage Mtip,rel: 1.2865




Table =


_____ ________ ________ ________

beta1 1 60.634 65.824 65.653

beta2 1 51.798 57.584 60.133

alpha1 1 11.99 15 14.63

alpha2 1 34.357 33.136 34.304

Deflection 1 8.8354 8.2396 5.5198

C-axial in 1 178.89 177.01 175.12

C-axial out 1 181.75 177.01 172.64

Uin m/s 1 355.91 394.3 432.7

Uout m/s 1 355.2 386.81 418.42

V1 m/s 1 364.79 432.21 424.76

V2 m/s 1 293.89 330.21 346.68

C1 m/s 1 182.88 183.25 180.98

C2 m/s 1 220.16 211.39 209

Reaction 1 0.77208 0.79333 0.81107

Diffusion 1 0.2659 0.28157 0.22999

de Haller 1 0.79296 0.76399 0.82786


Stage load 1 0.41553 0.33854 0.28113

Stage Temp-rise K 1 26.192 26.192 26.192

43


Table =


_____ ________ ________ ________

beta1 2 59.672 61.441 63.984

beta2 2 49.338 53.494 57.38

alpha1 2 14.841 16.085 17.189

alpha2 2 37.594 37.755 37.959

Deflection 2 10.334 7.9463 6.6048

C-axial in 2 179.8 177.7 175.61

C-axial out 2 182.82 177.7 172.89

Uin m/s 2 353.18 377.72 402.27

Uout m/s 2 353.59 379.3 405.01

V1 m/s 2 356.07 371.71 400.38

V2 m/s 2 280.57 298.71 320.72

C1 m/s 2 186 184.94 183.82

C2 m/s 2 230.73 224.76 219.28

Reaction 2 0.73463 0.75 0.77157

Diffusion 2 0.29996 0.27137 0.26095

de Haller 2 0.77494 0.80361 0.81365


Stage load 2 0.48223 0.42591 0.35431

Stage Temp-rise K 2 30.192 30.192 30.192

Table =


_____ ________ ________ ________

beta1 3 54.497 56.292 60.069

beta2 3 39.5 44.131 50.465

alpha1 3 27.678 29.188 30.643

alpha2 3 46.341 47.399 48.545

Deflection 3 14.997 12.161 9.6031

C-axial in 3 183.34 178.01 172.7

C-axial out 3 187.55 178.01 168.67

Uin m/s 3 347.1 366.27 385.44

Uout m/s 3 351.14 373.23 395.31

V1 m/s 3 315.7 320.76 346.13

V2 m/s 3 243.06 248.01 264.98

C1 m/s 3 207.03 203.9 200.73

C2 m/s 3 271.66 262.98 254.78

Reaction 3 0.58561 0.6 0.63549

Diffusion 3 0.37342 0.35573 0.34374

de Haller 3 0.75263 0.7732 0.78386


Stage load 3 0.48859 0.45427 0.37661

Stage Temp-rise K 3 30.192 30.192 30.192

Table =


_____ ________ ________ ________

beta1 4 52.795 53.787 58.324

beta2 4 34.654 38.177 46.296

alpha1 4 30.532 32.082 33.605

alpha2 4 49.09 50.341 51.702

Deflection 4 18.141 15.61 12.028

C-axial in 4 183.82 177.95 172.08

C-axial out 4 188.53 177.95 167.45

Uin m/s 4 338.05 354.58 371.1

Uout m/s 4 347.89 367.56 387.24

V1 m/s 4 303.99 301.21 327.69

V2 m/s 4 229.19 226.37 242.35

C1 m/s 4 213.4 210.03 206.61

C2 m/s 4 287.89 278.83 270.18

Reaction 4 0.53502 0.54 0.58498

Diffusion 4 0.41758 0.40835 0.39624

de Haller 4 0.73508 0.75154 0.76001


Stage load 4 0.49673 0.48547 0.39473

Stage Temp-rise K 4 30.192 30.192 30.192

Table =


_____ ________ ________ ________

beta1 5 54.328 54.046 58.795

beta2 5 36.405 37.804 46.578

alpha1 5 27.287 28.588 29.847

alpha2 5 47.974 48.938 49.975

Deflection 5 17.923 16.242 12.217

C-axial in 5 181.83 177.54 173.26

C-axial out 5 186.19 177.54 169.03

Uin m/s 5 326.38 341.53 356.69

Uout m/s 5 343.89 361.88 379.86

V1 m/s 5 311.81 302.39 334.41

V2 m/s 5 231.34 224.71 245.9

C1 m/s 5 204.6 202.2 199.75

C2 m/s 5 278.11 270.29 262.82

Reaction 5 0.56729 0.56 0.60996

Diffusion 5 0.42313 0.41451 0.39668

de Haller 5 0.72454 0.74311 0.75375


Stage load 5 0.50967 0.52643 0.41332

Stage Temp-rise K 5 30.192 30.192 30.192

Table =


_____ ________ ________ ________

44


beta1 6 55.768 54.244 59.437

beta2 6 37.895 37.104 46.99

alpha1 6 23.587 24.726 25.814

alpha2 6 46.815 47.542 48.32

Deflection 6 17.873 17.141 12.447

C-axial in 6 179.89 176.8 173.71

C-axial out 6 183.96 176.8 169.8

Uin m/s 6 312.44 326.96 341.49

Uout m/s 6 339.18 355.96 372.74

V1 m/s 6 319.78 302.58 341.63

V2 m/s 6 233.11 221.69 248.92

C1 m/s 6 196.29 194.65 192.96

C2 m/s 6 268.8 261.91 255.35

Reaction 6 0.59971 0.58 0.63677

Diffusion 6 0.42975 0.42295 0.39918

de Haller 6 0.71286 0.73266 0.74543


Stage load 6 0.52366 0.57604 0.43056

Stage Temp-rise K 6 30.192 30.192 30.192

Table =


_____ ________ ________ ________

beta1 7 57.444 54.729 60.412

beta2 7 39.749 36.686 47.866

alpha1 7 18.548 19.58 20.551

alpha2 7 45.217 45.695 46.209

Deflection 7 17.696 18.043 12.546

C-axial in 7 177.75 175.75 173.73

C-axial out 7 181.48 175.75 170.17

Uin m/s 7 296.58 311 325.41

Uout m/s 7 333.8 349.7 365.61

V1 m/s 7 330.31 304.35 351.85

V2 m/s 7 236.04 219.16 253.66

C1 m/s 7 187.49 186.53 185.54

C2 m/s 7 257.64 251.62 245.9

Reaction 7 0.64132 0.61 0.67308

Diffusion 7 0.43406 0.42961 0.39917

de Haller 7 0.69989 0.72008 0.736


Stage load 7 0.54159 0.63992 0.44942

Stage Temp-rise K 7 30.192 30.192 30.192

Table =


_____ ________ ________ ________

beta1 8 55.078 50.647 58.543

beta2 8 36.95 30.99 45.609

alpha1 8 23.938 24.976 25.971

alpha2 8 46.641 47.325 48.054

Deflection 8 18.128 19.657 12.934

C-axial in 8 177.23 174.39 171.54

C-axial out 8 180.99 174.39 167.91

Uin m/s 8 279.17 293.88 308.6

Uout m/s 8 327.8 343.08 358.37

V1 m/s 8 309.59 275.01 328.72

V2 m/s 8 226.47 203.42 240.03

C1 m/s 8 193.91 192.38 190.81

C2 m/s 8 263.61 257.27 251.21

Reaction 8 0.5935 0.54 0.62853

Diffusion 8 0.42608 0.42549 0.39841

de Haller 8 0.71632 0.73968 0.74598


Stage load 8 0.48861 0.62552 0.40782

Stage Temp-rise K 8 26.192 26.192 26.192

----------------------------Velocity Diagram HPC-----

IGV angle: 10

First stage Mtip,rel: 1.147




Table =


_____ ________ ________ ________

beta1 1 62.62 65.576 65.257

beta2 1 53.383 55.953 58.361

alpha1 1 7.6635 10 9.6729

alpha2 1 36.775 35.832 36.617

Deflection 1 9.2374 9.6225 6.8962

C-axial in 1 214.72 213.89 213.01

C-axial out 1 217.26 213.89 210.68

Uin m/s 1 443.49 471 498.5

Uout m/s 1 454.74 476.62 498.5

V1 m/s 1 466.9 517.29 508.92

V2 m/s 1 364.24 382.04 401.63

C1 m/s 1 216.66 217.19 216.08

C2 m/s 1 271.24 263.82 262.49

Reaction 1 0.78435 0.79601 0.80655

Diffusion 1 0.29001 0.31554 0.26553

de Haller 1 0.77102 0.73855 0.7979


Stage load 1 0.56628 0.50208 0.4482

Stage Temp-rise K 1 53.611 53.611 53.611

Table =


45


_____ ________ ________ ________

beta1 2 63.1 63.969 64.804

beta2 2 53.106 54.907 56.873

alpha1 2 14.265 14.912 15.525

alpha2 2 41.554 41.688 41.833

Deflection 2 9.9947 9.0626 7.9306

C-axial in 2 209.57 208.5 207.43

C-axial out 2 211.73 208.5 205.35

Uin m/s 2 466.37 482.43 498.5

Uout m/s 2 469.75 484.12 498.5

V1 m/s 2 463.2 475.11 487.24

V2 m/s 2 352.69 362.67 375.76

C1 m/s 2 216.23 215.77 215.28

C2 m/s 2 282.94 279.2 275.6

Reaction 2 0.74166 0.75 0.75784

Diffusion 2 0.325 0.31677 0.30308

de Haller 2 0.75362 0.76334 0.779


Stage load 2 0.56166 0.52488 0.49159

Stage Temp-rise K 2 58.111 58.111 58.111

Table =


_____ ________ ________ ________

beta1 3 59.799 60.909 61.985

beta2 3 45.633 48.131 50.709

alpha1 3 31.463 32.221 32.973

alpha2 3 52.029 52.681 53.362

Deflection 3 14.166 12.778 11.276

C-axial in 3 203.38 200.28 197.17

C-axial out 3 206.35 200.28 194.21

Uin m/s 3 473.87 486.19 498.5

Uout m/s 3 475.35 486.92 498.5

V1 m/s 3 404.3 411.93 419.78

V2 m/s 3 295.1 300.08 306.69

C1 m/s 3 238.43 236.74 235.02

C2 m/s 3 335.38 330.36 325.44

Reaction 3 0.58972 0.6 0.60978

Diffusion 3 0.41398 0.4079 0.39864

de Haller 3 0.7194 0.72847 0.74172


Stage load 3 0.55097 0.52342 0.49788

Stage Temp-rise K 3 58.111 58.111 58.111

Table =


_____ ________ ________ ________

beta1 4 63.585 64.321 65.037

beta2 4 50.875 52.825 54.758

alpha1 4 25.724 26.326 26.918

alpha2 4 51.012 51.472 51.95

Deflection 4 12.71 11.496 10.279

C-axial in 4 191.28 189.49 187.7

C-axial out 4 193.89 189.49 185.11

Uin m/s 4 477.23 487.86 498.5

Uout m/s 4 477.91 488.21 498.5

V1 m/s 4 429.96 437.29 444.75

V2 m/s 4 307.27 313.6 320.79

C1 m/s 4 212.32 211.42 210.51

C2 m/s 4 308.18 304.21 300.33

Reaction 4 0.65248 0.66 0.6672

Diffusion 4 0.41913 0.41018 0.39988

de Haller 4 0.705 0.71714 0.73139


Stage load 4 0.55026 0.52653 0.5043

Stage Temp-rise K 4 58.111 58.111 58.111

Table =


_____ ________ ________ ________

beta1 5 66.084 66.683 67.267

beta2 5 54.65 56.371 58.031

alpha1 5 23.691 24.258 24.813

alpha2 5 51.302 51.722 52.155

Deflection 5 11.433 10.311 9.236

C-axial in 5 177.73 176.35 174.97

C-axial out 5 180.2 176.35 172.53

Uin m/s 5 478.74 488.62 498.5

Uout m/s 5 478.97 488.74 498.5

V1 m/s 5 438.4 445.54 452.78

V2 m/s 5 311.45 318.44 325.86

C1 m/s 5 194.09 193.43 192.77

C2 m/s 5 288.22 284.68 281.21

Reaction 5 0.68362 0.69 0.69613

Diffusion 5 0.4184 0.40815 0.39752

de Haller 5 0.7007 0.71473 0.72987


Stage load 5 0.55404 0.53187 0.51099

Stage Temp-rise K 5 58.111 58.111 58.111

Table =


_____ ________ ________ ________

beta1 6 67.094 67.764 68.416

beta2 6 56.478 58.335 60.095

alpha1 6 29.869 30.513 31.151

alpha2 6 54.138 54.731 55.349

Deflection 6 10.616 9.4286 8.3209

46


C-axial in 6 162.92 161.04 159.15

C-axial out 6 165.58 161.04 156.49

Uin m/s 6 479.13 488.81 498.5

Uout m/s 6 479.02 488.76 498.5

V1 m/s 6 418.57 425.55 432.64

V2 m/s 6 299.83 306.77 313.88

C1 m/s 6 187.88 186.93 185.97

C2 m/s 6 282.64 278.9 275.23

Reaction 6 0.66332 0.67 0.67642

Diffusion 6 0.41953 0.40879 0.39829

de Haller 6 0.70479 0.72088 0.73785


Stage load 6 0.51652 0.49626 0.47716

Stage Temp-rise K 6 53.611 53.611 53.611

-----------------------------Velocity Diagram HPT------------

Average Stage load: 3.2956


Table =


_____ ________ ________ ________

beta2 1 46.259 41.316 35.751

beta3 1 64.848 65.393 65.876

alpha2 1 70.588 69.933 69.284

alpha3 1 18.615 18 17.475

Deflection 1 111.11 106.71 101.63

C-axial in 1 287.07 287.07 287.07

U m/s 1 514.69 533.54 552.39

V2 m/s 1 415.21 382.21 353.73

V3 m/s 1 675.42 689.43 702.37

C2 m/s 1 863.76 836.67 811.53

C3 m/s 1 301.84 300.91 300.13

Relative Mach # 1 0.40696 0.3733 0.34438

Reaction 1 0.32201 0.35094 0.37757


Stage load 1 3.2956 3.2956 3.2956

Stage Temp-drop K 1 371.88 371.88 371.88

P2/Pchoke < 1 1 0.88582 0.88582 0.88582

-----------------------------Velocity Diagram IPT------------



Table =


_____ ________ ________ ________

beta2 1 28.703 24.226 19.613

beta3 1 53.543 54.138 54.73

alpha2 1 58.365 57.429 56.512

alpha3 1 15.528 15 14.506

Deflection 1 82.245 78.364 74.343

C-axial in 1 266.38 266.38 266.38

U m/s 1 286.54 297.13 307.71

V2 m/s 1 303.7 292.1 282.79

V3 m/s 1 448.28 454.7 461.31

C2 m/s 1 507.86 494.81 482.78

C3 m/s 1 275.99 275.36 274.78

Relative Mach # 1 0.45908 0.44048 0.4255

Reaction 1 0.39166 0.41841 0.44578


Stage load 1 3.2872 3.2872 3.2872

Stage Temp-drop K 1 120.07 120.07 120.07

P2/Pchoke < 1 1 0.80588 0.80588 0.80588

Table =


_____ ________ ________ ________

beta2 2 21.969 17.834 13.672

beta3 2 51.49 51.251 52.6

alpha2 2 53.412 52.427 51.467

alpha3 2 14.788 15 13.875

Deflection 2 73.459 69.085 66.272

C-axial in 2 307.62 307.62 307.62

U m/s 2 290.31 300.88 311.44

V2 m/s 2 331.71 323.15 316.59

V3 m/s 2 494.05 491.48 506.48

C2 m/s 2 516.1 504.49 493.8

C3 m/s 2 317.71 317.99 316.52

Relative Mach # 2 0.47818 0.46491 0.45465

Reaction 2 0.48346 0.47251 0.53584


Stage load 2 3.2058 3.2058 3.2058

Stage Temp-drop K 2 120.07 120.07 120.07

P2/Pchoke < 1 2 0.78971 0.78971 0.78971

-----------------------------Velocity Diagram LPT------------



Table =


_____ ________ ________ ________

beta2 1 20.92 17.434 13.977

beta3 1 43.515 43.756 44.513

alpha2 1 46.252 45.102 43.997

47


alpha3 1 15.281 15 14.202

Deflection 1 64.435 61.19 58.49

C-axial in 1 221.4 221.4 221.4

U m/s 1 146.66 152.67 158.68

V2 m/s 1 237.03 232.06 228.16

V3 m/s 1 305.3 306.53 310.48

C2 m/s 1 320.18 313.67 307.77

C3 m/s 1 229.14 228.87 228.1

Relative Mach # 1 0.38599 0.37756 0.37091

Reaction 1 0.45494 0.46659 0.50377


Stage load 1 3.688 3.688 3.688

Stage Temp-drop K 1 37.59 37.59 37.59

P2/Pchoke < 1 1 0.65101 0.65101 0.65101

Table =


_____ ________ ________ ________

beta2 2 14.397 11.096 7.8559

beta3 2 44.179 44.433 45.137

alpha2 2 43.322 42.257 41.234

alpha3 2 15.288 15 14.273

Deflection 2 58.575 55.528 52.993

C-axial in 2 226.45 226.45 226.45

U m/s 2 155.42 161.33 167.23

V2 m/s 2 233.79 230.76 228.59

V3 m/s 2 315.75 317.12 321.01

C2 m/s 2 311.26 305.95 301.11

C3 m/s 2 234.37 234.08 233.37

Relative Mach # 2 0.37328 0.36819 0.36451

Reaction 2 0.53826 0.55041 0.58469


Stage load 2 3.3028 3.3028 3.3028

Stage Temp-drop K 2 37.59 37.59 37.59

P2/Pchoke < 1 2 0.64115 0.64115 0.64115

Table =


_____ ________ ________ ________

beta2 3 8.8858 5.7407 2.6773

beta3 3 44.723 44.999 45.666

alpha2 3 40.786 39.779 38.813

alpha3 3 15.305 15 14.323

Deflection 3 53.609 50.74 48.343

C-axial in 3 230.98 230.98 230.98

U m/s 3 163.17 169.08 175

V2 m/s 3 233.79 232.15 231.23

V3 m/s 3 325.09 326.65 330.52

C2 m/s 3 305.06 300.56 296.44

C3 m/s 3 239.08 238.77 238.09

Relative Mach # 3 0.36641 0.36363 0.36202

Reaction 3 0.60126 0.61435 0.64653


Stage load 3 3.0068 3.0068 3.0068

Stage Temp-drop K 3 37.59 37.59 37.59

P2/Pchoke < 1 3 0.63381 0.63381 0.63381

Table =


_____ ________ ________ ________

beta2 4 4.3552 1.3104 -1.637

beta3 4 45.166 45.473 46.116

alpha2 4 38.628 37.653 36.719

alpha3 4 15.334 15 14.357

Deflection 4 49.522 46.784 44.479

C-axial in 4 235 235 235

U m/s 4 169.89 175.94 182

V2 m/s 4 235.68 235.06 235.09

V3 m/s 4 333.3 335.11 339

C2 m/s 4 300.81 296.81 293.17

C3 m/s 4 243.27 242.91 242.26

Relative Mach # 4 0.36289 0.36177 0.36167

Reaction 4 0.6492 0.66367 0.69451


Stage load 4 2.7769 2.7769 2.7769

Stage Temp-drop K 4 37.59 37.59 37.59

P2/Pchoke < 1 4 0.62815 0.62815 0.62815

Table =


_____ ________ ________ ________

beta2 5 0.71913 -2.3011 -5.2086

beta3 5 45.523 45.871 46.507

alpha2 5 36.829 35.858 34.93

alpha3 5 15.375 15 14.373

Deflection 5 46.242 43.57 41.298

C-axial in 5 238.46 238.46 238.46

U m/s 5 175.58 181.93 188.28

V2 m/s 5 238.48 238.65 239.45

V3 m/s 5 340.36 342.48 346.46

C2 m/s 5 297.92 294.22 290.86

C3 m/s 5 246.9 246.5 245.85

Relative Mach # 5 0.36105 0.36116 0.36223

Reaction 5 0.68561 0.70194 0.73227


Stage load 5 2.5971 2.5971 2.5971

Stage Temp-drop K 5 37.59 37.59 37.59

P2/Pchoke < 1 5 0.62362 0.62362 0.62362

48


Table =


_____ ________ ________ ________

beta2 6 -2.1251 -5.219 -8.1802

beta3 6 45.806 46.209 46.858

alpha2 6 35.366 34.366 33.415

alpha3 6 15.431 15 14.368

Deflection 6 43.681 40.99 38.677

C-axial in 6 241.36 241.36 241.36

U m/s 6 180.26 187.1 193.93

V2 m/s 6 241.52 242.36 243.84

V3 m/s 6 346.23 348.77 352.96

C2 m/s 6 295.97 292.39 289.15

C3 m/s 6 249.96 249.49 248.83

Relative Mach # 6 0.35976 0.36087 0.36294

Reaction 6 0.71291 0.73174 0.76258


Stage load 6 2.4557 2.4557 2.4557

Stage Temp-drop K 6 37.59 37.59 37.59

P2/Pchoke < 1 6 0.61986 0.61986 0.61986

Table =


_____ ________ ________ ________

beta2 7 -4.2769 -7.5792 -10.717

beta3 7 46.028 46.507 47.198

alpha2 7 34.218 33.146 32.132

alpha3 7 15.509 15 14.334

Deflection 7 41.751 38.928 36.481

C-axial in 7 243.65 243.65 243.65

U m/s 7 183.92 191.53 199.15

V2 m/s 7 244.33 245.8 247.98

V3 m/s 7 350.93 354.01 358.59

C2 m/s 7 294.66 291 287.72

C3 m/s 7 252.42 251.86 251.16

Relative Mach # 7 0.35828 0.3603 0.36337

Reaction 7 0.7328 0.75507 0.78787


Stage load 7 2.3432 2.3432 2.3432

Stage Temp-drop K 7 37.59 37.59 37.59

P2/Pchoke < 1 7 0.6166 0.6166 0.6166

Table =


_____ ________ ________ ________

beta2 8 -5.8269 -9.5458 -13.044

beta3 8 46.204 46.792 47.578

alpha2 8 33.361 32.149 31.013

alpha3 8 15.625 15 14.255

Deflection 8 40.377 37.247 34.534

C-axial in 8 245.32 245.32 245.32

U m/s 8 186.56 195.44 204.32

V2 m/s 8 246.6 248.77 251.82

V3 m/s 8 354.46 358.32 363.66

C2 m/s 8 293.72 289.75 286.24

C3 m/s 8 254.28 253.59 252.8

Relative Mach # 8 0.35616 0.35915 0.36343

Reaction 8 0.74649 0.77371 0.81096


Stage load 8 2.2505 2.2505 2.2505

Stage Temp-drop K 8 37.59 37.59 37.59

P2/Pchoke < 1 8 0.61362 0.61362 0.61362

Table =


_____ ________ ________ ________

beta2 9 -6.8666 -11.382 -15.558

beta3 9 46.357 47.121 48.108

alpha2 9 32.761 31.285 29.925

alpha3 9 15.814 15 14.085

Deflection 9 39.491 35.739 32.549

C-axial in 9 246.33 246.33 246.33

U m/s 9 188.17 199.27 210.37

V2 m/s 9 248.11 251.27 255.7

V3 m/s 9 356.91 362 368.9

C2 m/s 9 292.92 288.24 284.22

C3 m/s 9 255.54 254.63 253.66

Relative Mach # 9 0.35311 0.35745 0.3636

Reaction 9 0.75495 0.79004 0.83688


Stage load 9 2.1647 2.1647 2.1647

Stage Temp-drop K 9 37.59 37.59 37.59

P2/Pchoke < 1 9 0.61069 0.61069 0.61069

Table =


_____ ________ ________ ________

beta2 10 -7.5421 -13.737 -19.27

beta3 10 46.549 47.645 49.133

alpha2 10 32.334 30.305 28.496

alpha3 10 16.182 15 13.683

Deflection 10 39.007 33.908 29.863

C-axial in 10 246.63 246.63 246.63

U m/s 10 188.77 204.44 220.11

V2 m/s 10 248.78 253.89 261.27

V3 m/s 10 358.61 366.07 376.93

49


C2 m/s 10 291.89 285.67 280.63

C3 m/s 10 256.28 254.94 253.57

Relative Mach # 10 0.34904 0.356 0.36617

Reaction 10 0.75926 0.80908 0.88012


Stage load 10 2.0567 2.0567 2.0567

Stage Temp-drop K 10 37.59 37.59 37.59

P2/Pchoke < 1 10 0.60742 0.60742 0.60742

50

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