STRUCTURAL DESIGN AND ANALYSIS OF A MICROTURBINE

COMPRESSOR

INDRA WENING MAHARSI

A Project report submitted in partial fulfillment of the

requirements for the award of the degree of

Master of Engineering in Mechanical Engineering

Faculty of Mechanical Engineering

Universiti Teknologi Malaysia

DECEMBER 2006

iii

Especially dedicated to:

my parents, Sugiharti and Bambang Soegeng;

my sister, Linda Cita Mahars;i

my little niece, Nafesa Shafira Azzahranisa;

my brother in law, Bambang Soedjajono; and my love Ratih Dewi Ayu Ningrum.

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ACKNOWLEDGEMENT

First and foremost, I thank Almighty God for giving me an opportunity to

complete this thesis. I would like to express my sincere appreciation to my supervisor

Ainullotfi Abdul Latif, for the guidance, assistance, criticism, and suggestions he

provided for this research.

I would also like to thank to my colleague Nandakumar for all the discussion,

help and provides of necessary information to the research I conducted here.

Deepest thanks to my family; my parents, my sister and my little niece, my

brother in law, and my love one; for their support and prayers throughout the process

of producing this project report and the whole years of my study.

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ABSTRACT

A structural design was conducted on a compressor for a microturbine

generating 100 kW output power. The scope concerned the conceptual design of gas

turbine system, the sizing of the compressor, the computation of loads acting on

compressor and the stress analysis for its structural integrity. The dimensions and the

physical properties of the compressor impeller were calculated based on the given

microturbine output power, using thermodynamic equations on turbomachinery

aspects. Thereafter a simplified one-tenth model of the ten-bladed impeller was

created in Fluent, a Computational Fluid Dynamic (CFD) program, taking into

consideration the axisymmetric boundary conditions. The analysis was run at the

standard sea level atmospheric conditions (ISA) to obtain the fluid forces acting on

the blade surfaces. These forces, together with the rotational inertial loads, were then

used as the loading input parameters for the structural integrity analysis done using

the Finite Element program MSC.Nastran. The resulting stresses and deformations

were obtained and contours plotted. Comparisons were done between the curved

blade and the straight blade designs. The results showed that the curved blade gave

better stress distribution, thus this shape was then tested for various rotational

speeds. Analyses were also conducted on different materials for the compressor

impeller structure, and steel was subsequently demonstrated to be the one which was

to be suitable and safe.

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ABSTRAK

Suatu rekabentuk struktur dijalankan ke atas pemampat bagi sebuah

mikroturbin yang menghasilkan kuasa keluaran sebesar 100 kW. Skop kerja

merangkumi rekabentuk konsep bagi sistem turbin gas, pensaizan pemampat,

pengiraan beban yang bertindak ke atas pemempat, dan analisis tegasan bagi

memastikan integriti struktur. Dimensi dan ciri fizikal pendesak pemampat dikira

berdasarkan kuasa keluaran yang diberikan oleh mikroturbin, menggunakan

persamaan-persamaan termodinamik untuk turbomesin. Seterusnya suatu model

sepersepuluh yang dipermudahkan dibina dalam perisian dinamik bendalir

komputasi (CFD) Fluent, mengambil kira keadaan sempadan simetri sepaksi.

Analisis dilaksanakan pada keadaan atmosfera aras laut piawai untuk mendapatkan

beban-beban bendalir yang bertindak ke atas permukaan bilah. Beban-beban ini,

bersama dengan beban inersia putaran, seterusnya digunakan sebagai parameter

pembebanan masukan bagi analisis integriti struktur menggunakan perisian unsur

terhingga MSC.Nastran. Tegasan-tegasan dan perubahan bentuk yang terhasil

diperolehi dan konturnya diplotkan. Perbandingan dijalankan ke atas rekabentuk

bilah melengkung dan bilah lurus. Keputusan menunjukkan bilah melengkung

mempunyai taburan tegasan yang lebih baik, lalu rekabentuk ini diuji pada beberapa

kelajuan putaran. Analisis juga dilakukan ke atas bahan struktur pemampat pendesak

yang berbeza, dan keluli menunjukkan bahan yang paling sesuai dan selamat.

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TABLE OF CONTENTS

CHAPTER CONTENTS PAGE

TITLE i

DECLARATION ii

DEDICATION iii

ACKNOWLEDGMENT iv

ABSTRACT v

ABSTRAK vi

TABLE OF CONTENTS vii

LIST OF FIGURES xi

LIST OF TABLES xiv

LIST OF SYMBOLS xv

CHAPTER 1 INTRODUCTION 1

1.1 Background 1

1.2 Objective of Study 2

1.3 Scope of Study 2

1.4 Outline of Projects 3

CHAPTER 2 LITERATURE REVIEW 5

2.1 Introduction 5

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2.1.1 Gas Turbine Cycles 6

2.2 Microturbine 7

2.2.1 Single-Shaft Microturbine 9

2.2.2 Twin-Shaft Microturbine 11

2.3 Microturbine Applications 13

2.4 Turbomachinery Performance 14

2.4.1 Compressor 15

2.4.1.1 Curved Blades 16

2.4.2 Turbine 17

2.4.3 Heat Recovery 18

2.5 The Microturbine Constraints 19

2.5.1 The Compressor Constraints 20

2.6 Finite Element Historical Background 22

CHAPTER 3 PROJECT METHODOLOGY 23

3.1 Engineering Design 23

3.2 Major Design Consideration 24

3.3 Shaft Material Design Consideration 26

3.4 Impeller Material Design Consideration 27

3.5 Compressor Properties 28

3.6 Compressor Blade Design Properties 29

CHAPTER 4 COMPRESSOR DIMENSIONING 28

4.1 Shaft Consideration 30

4.1.1 Shaft Power 30

4.1.2 Shaft Designation 31

4.1.3 Safety Check for Shaft Torsion 32

4.2 Impeller consideration 33

4.2.1 Impeller Condition 34

4.3 Atmospheric Condition 35

4.4 Compressor Properties 36

4.4.1 Compressor Blade 38

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CHAPTER 5 COMPUTATIONAL FLUID DYNAMIC (CFD) 40

5.1 Introduction 40

5.2 Steps in CFD Analysis 41

5.3 Fluid Flow in CFD Program 41

5.3.1 Introduction 41

5.3.2 Continuity and Momentum Equation 42

5.3.3 Flows in Rotating Reference Frame 43

5.3.4 Turbulence Modelling in Swirling Flows 44

5.4 Forces in the Body 46

5.5 Program 48

5.2.1 Model 48

5.2.2 CFD Pre-Solver Program (Gambit) 50

5.6 Properties 52

5.7 CFD Program (Fluent) 53

5.7.1 Total Pressure Contour 54

CHAPTER 6 FINITE ELEMENT METHOD (FEM) 58

6.1 Introduction 58

6.2 Fundamental Concepts 59

6.2.1 Stress Definition 59

6.2.2 The Stress Tensor (Stress Matrix) 60

6.2.3 Equations of Equilibrium 61

6.2.4 Failure Criteria 61

6.2.5 Saint Venant’s Principle 62

6.3 Three Dimensional Problems 63

6.3.1 Model 63

6.4 Finite Element Generation 64

6.5 Treatment of Boundary Condition 65

6.5.1 Loads (Forces) and Constraints 65

6.6 Compressor Material 67

6.7 Bending Stress in Finite Element Program 68

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6.7.1 Bending Stress Due to Centrifugal Forces 69

6.7.2 Bending Stress Due to Differential Growth 70

CHAPTER 7 RESULT ANALYSIS 72

7.1 Result Steps 72

7.2 Compressor Shape Comparison Analysis 73

7.2.1 Straight Blade 73

7.2.2 Curved Blade 75

7.2.3 Comparison Result 77

7.3 Analysis under Various Rotational Speed 78

7.3.1 Rotational Speed of 60000 rpm 78

7.3.2 Rotational Speed of 50000 rpm 80

7.3.3 Rotational Speed of 40000 rpm 83

7.3.4 Rotational Speed of 30000 rpm 86

7.3.5 Various Rotational Speed Results 89

7.3.6 Compressor Parametric Characteristic 90

7.4 Material Selection 93

7.4.1 Alternative Material 93

CHAPTER 8 CONCLUSIONS AND RECOMMENDATIONS 94

8.1 Conclusions 95

8.2 Recommendations for Future Development 96

REFERENCES 98

APPENDICES 102

xi

LIST OF FIGURES

FIGURE DESCRIPTION PAGE

2.1 Simple gas turbine diagram 5

2.2 Brayton Cycle, P-V Diagram 6

2.3 Microturbine 7

2.4 Single Shaft Microturbine 10

2.5 Twin Shaft Microturbine 11

2.6 Various Application for Microturbine 14

2.7 Compressor Efficiency Improvement 15

2.8 Radial-curved Blades 16

2.9 Forward-curved Blades 16

2.10 Backward-curved Blades 17

2.11 Pressure Ratio and TIT Effect for Nonrecuperated 17

2.12 Recuperator Performance Improvement 19

2.13 Achievable stage pressure ratio and required blade speed 21

3.1 Machine Design Flow 24

3.2 Major Flow Design 25

3.3 Shaft Material Design Flow 26

3.4 Impeller Material Design Flow 27

3.5 Compressor Design Properties Flow 28

3.6 Compressor Blade Design Flow 29

4.1 Shaft Rough Design 32

4.2 Compressor-Shaft Assembly Rough Design 37

4.3 Compressor Vane Angle 38

5.1 Application that can be modelled in a rotating reference frame 43

5.2 Control volume for steady flow with control surface cutting

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velocities angle 47

5.3 Particular forces acting on the control volume (surface) 47

5.4 Fully Compressor Design and Partial Design Focused 48

5.5 Compressor Boundary Analysis 49

5.6 Face Boundary Building 50

5.7 Face Meshed 51

5.8 Volume Meshed 51

5.9 Contours on Inner Blade Surfaces 54

5.10 Contours on Splitter Surface 55

5.11 Contours on Hub Surface 56

5.12 Contours on All Analyzed Surfaces 57

6.1 Free Body Diagram 59

6.2 Equilibrium of Elemental Volume 60

6.3 Three dimensional model of compressor blades 63

6.4 Simplification of the model 64

6.5 Tetrahedral Element 64

6.6 Loads from Fluids Pressure for Blade and Splitter 66

6.7 Inertial Load Constraints 66

6.8 Axisymmetric Constraints 67

6.9 Fixed Constraints 67

6.10 Rotating Blade Element 69

6.11 Blade Element in Bending 70

7.1 Straight Blade Geometry 73

7.2 Straight Blade Fluid Loads Contour 73

7.3 Straight Blade Stress Tensor, Von Mises 74

7.4 Straight Blade Deformation Magnitude 74

7.5 Curved Blade Geometry 75

7.6 Curved Blade Fluid Loads Contour 75

7.7 Curved Blade Von Mises Stress 76

7.8 Curved Blade Deformation Magnitude 76

7.9 60000 rpm Fluent Contour 78

7.10 60000 rpm Stress Tensor Contour 79

7.11 60000 rpm Deformation Contour 79

7.12 50000 rpm Fluent Contour 80

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7.13 50000 rpm Stress Tensor Analysis 81

7.14 50000 rpm Deformation Analysis 82

7.15 40000 rpm Fluent Contour 83

7.16 40000 rpm Stress Tensor Analysis 84

7.17 40000 rpm Deformation Analysis 85

7.18 30000 rpm Fluent Contour 86

7.19 30000 rpm Stress Tensor Analysis 87

7.20 30000 rpm Deformation Analysis 88

7.21 Compressor Characteristic on Titanium Alloy 90

7.22 Compressor Characteristic on Aluminium Alloy 91

7.23 Compressor Characteristic Regression on Titanium Alloy 91

7.24 Compressor Characteristic Regression on Aluminium Alloy 92

7.25 Thickening on Blade Root Attachment 92

7.26 60000 rpm Stress Tensor Contour on Stainless Steel 94

7.27 60000 rpm Deformation Contour on Stainless Steel 94

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LIST OF TABLES

TABLE DESCRIPTION PAGE

5.1 Compressor Geometry Parameter 49

5.2 CFD Parameter Analysis (Pre-solver) 52

5.3 CFD Parameter Analysis (Fluent) 53

6.1 Materials for compressor 68

7.1 Compressor Shape Result Comparison 77

7.2 60000 rpm Analysis 80

7.3 50000 rpm Analysis 83

7.4 40000 rpm Analysis 86

7.5 30000 rpm Analysis 89

7.6 Titanium Alloy Material Analysis 89

7.7 Aluminium Alloy 7075 Material Analysis 90

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LIST OF SYMBOLS

SYMBOL SUBJECT

2D Two Dimensional

3D Three Dimensional

Al 7075 Aluminium Alloy

b Impeller Outlet Depth

C1 Compressor Inlet Sound Velocity

C2 Compressor Outlet Sound Velocity

CFD Computational Fluid Dynamic

Cp Gas Constant Pressure

d Shaft Diameter

d.shaft Shaft Diameter

d1 Compressor Inducer Inner Diameter

d2 Compressor Outer Diameter

DOF Degree of Freedom

dP/P Change in Pressure

E Elastic Modulus

EGT Exhaust Gas Temperature

ETATH Gas Turbine System Efficiency

F, G, H Flux Vector

FEA Finite Element Analysis

FEM Finite Element Method

g Gravitational Acceleration

h Impeller-to-shaft Attachment Depth

H Air Enthalpy

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Hp Polytrophic Head

I Invariant of Stress Tensor

J Inertial Moment

Kt/Kb Shock and Fatigue Factor Applied to Torsional Bending Moment

LHV Lower Heat Value

Mb Bending Moment due to Centrifugal Force

MD.G Bending Moment due to Differential Growth

MIT Massachusetts Institute of Technology

Mrot Impellers Tip Mach number

Mt Shaft Torsional Moment

MTU Maschinen Triebwerken Unsere (German Aero Engine Company)

N Shaft Rotational Speed

n Polytrophic Constant

p1 Compressor Inlet Pressure

p2 Compressor Outlet Pressure

Q Heat

r Radial Coordinate

R Hydraulic Radius

RNG Renormalization Group

ROM Reduced Ordered Model

rp Gas Constant

S GasConstant Pressure

S.F. Safety Factor

Sb Bending Stress

SD.G Bending Test due to Differential Growth

Sm Mass Added to The Continuous Phase

t Impeller Hub Depth

T Traction

T1 Compressor Inlet Temperature

T2 Compressor Outlet Temperature

TC Thermal Expansion Coefficient

Tet Tetrahedral Topology

Ti-6Al-4V Titanium Alloy

TIT Turbine Inlet Temperature

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ŧ Shaft Torsional Stress

U Internal Energy

U.T.S Ultimate Tensile Strength

u1 Compressor Inner Diameter Speed

u2 Compressor Outer Diameter Speed

V Volume

v Specific Volume of Air

vr1 Inlet Tangential Air Velocity

vr2 Outlet Tangential Air Velocity

wp Polytrophic Shaft Power

x Axial Coordinate

z Compressibility Factor

β = α Degree of Curvature

ηp Compressor Polytrophic Efficiency

π Phi

σ Stress Tensor

VMσ Von Mises Stress

Ψ Characteristic of Pressure Number

m& Mass Flow

τ Impeller-to-shaft Applied Torsional Stress

γ Air Constant

ρ Specific Mass

grρ Gravitational Body Force

Fr

External Body Force

μ Air Molecular Viscosity

vr Absolute Velocity

Ωr

Angular Velocity Vector

ε−k Turbulence Transport Model

δ Deflection to Differential Growth

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LIST OF APPENDICES

APPENDIX DESCRIPTION PAGE

A Computer Fluid Dynamic Input File Fluent 6.2 102

B Finite Element Analysis input File 117

1

CHAPTER 1

INTRODUCTION

1.1 Background

Nowadays, the need of energy production to be used for either industrial or

several transportations is in great demand. The type of power generation has become

the major concern because of its widespread need. For the concern of recent time

needs, the suitable power generation type is one which achieves a relatively better

efficiency, low in cost, and satisfied the demanding criteria.

For those needs the gas turbine system is the answer. Gas turbines are

internal combustion engines that they use a rotating shaft or rotor instead of

"reciprocating" in cylinders. It has the advantages of small dimensions, light weight,

easy to be serviced (resulting to low maintenance cost), and most of all it can

produce more power (relative to the power produced-to-weight ratio) and faster

speed spin. They became practical sixty years ago; today gas turbines are one of the

keystone technologies of the civilization [1].

Because of its critical role, it is understandable that innovation to a step

further is needed. In a field where the major role needed and development costs both

2

are the major concerns, it was thought to build the smallest possible gas turbine, and

to explore whether the device could be made into smaller size. The microturbine is

actually the scale-down of the large ordinary gas turbine system.

This is what gave birth to this project – since the advantages of gas turbines

are already known compare to the others, this project deal with designing of

microturbine compressor and the corresponding overall integrity analysis of the

designated compressor.

1.2 Objective of Study

The objective of this study is to design a compressor shape for 100 kW

microturbine output, and conduct stress analysis based on static loading condition to

ascertain its structural integrity of shape under the loads experienced in its normal

operation.

1.3 Scope of Study

The project also includes the dimensional design of the compressor (impeller

and its shaft). The design, then, investigated by obtaining the load under various

operation conditions, and then the analysis of the structure’s integrity using finite

element method is conducted. It is expected that the project will provide the

recommendation that can help to improve the performance of compressor design

base on the previous analysis.

3

The scope of study consists of two major parts. The first is to design the

dimension of the compressor based on the given output power. The design is

expected to be the most optimal dimension to that proposed output.

The second part is the analysis of the designated dimension of the

compressor. This part is investigating the load acting on the compressor using

computational fluid dynamic program and conducting analysis of the structural

integrity using the finite element analysis program.

1.4 Outline of Report

This project is divided into six chapters. Chapter 1 presents the background

of the study, which gave birth to this project. It also covers the objective of study, the

scope of study and this project’s outline.

Chapter 2 describes the literature review of the project. It explains the general

review of the gas turbine concept. Several reference and cites’ are quotes in this

chapter to be the base knowledge of the design. The specific microturbine part

review is described to support the specific need of the assumptions on the project.

Chapter 3 describes the step methodology to determine the properties of the

design compressor to be used to the analysis. Here the flow diagrams are provided

into every part design such as the shaft material design, impeller material design,

compressor properties and compressor blade design, all to describe the step to obtain

the data needed.

Chapter 4 discussed the dimensioning of the compressor that can be

optimally suited to the designated output power. The calculations are conducted in

this chapter. Assumptions on various conditions are given here together with the

important base reference quotes. Then both of them will be calculated with the

4

appropriate equations to obtain the compressor dimension and initial data’s needed

for further analysis.

Chapter 5 examines the data provided by previous chapter to be used on the

Computational Fluid Dynamic (CFD) program, which is here will be the Fluent

program chosen. The result data will be regarded as the loads of certain operational

condition acting on the designated compressor dimension.

On chapter 6 will be introduced the using of Finite Element Analysis (FEA)

program, continue by modeled design approaches provided to be examined. The data

produced by the CFD program then applied to the structure analysis by using the

FEA program, which uses the Nastran program.

On chapter 7 will asses the analysis results both by fluid dynamic aspect and

finite element aspect. The safety criteria will also be provided in concern of safety

for the material used. Comparison result may also be provided in order to get the

optimum result of analysis. At the end the determination of material used is expected

to be established.

At the end of the project, which is will be on chapter 8, will provide the

highlighted conclusions and expected to have recommendation, could be provided to

help to improve the performance of compressor design base on the previous analysis.

This is by combining analysis from the initial design, loads acting on compressor

until the structure integrity. So by this way, it is expected to have a sufficient

conclusion on overall performance of the design that could be realized by making the

microturbine compressor into real.