PAKISTAN NAVY ENGINEERING COLLEGE NATIONAL UNIVERSITY OF SCIENCES & TECHNOLOGY DESIGN AND DESIGN AND FABRICATION OF OF A A STIRLING CYCLE ENGINE
PROJECT ADJUDICATION PROJECT ADJUDICATION REPORT
Project Advisor: Group Members:
Dr. Waqar A Khan
Rehan Azhar (ME‐722‐06) Shahzad Ahmad (ME‐723‐06) M.Sajjad Ashraf (ME Ashraf (ME‐710‐06))
Project Examiners: Mr. Aijaz Ahmad Dr. Noman Danish
FINAL YEAR PROJECT REPORT
DESIGN AND FABRICATION OF A STIRLING CYCLE ENGINE
Table of Contents of Contents PREFACE……………… ................................................................................................................................ 8 ACKNOWLEDGEMENTS .......................................................................................................................... 9 PROJECT APPROVAL............................................................................................................................. 10 NOMENCLATURE…………………………………………… NOMENCLATURE………………… …………………………………………………… ………………………………………………… ……………………………..…………………… ……..…………………………..1 ……..1 1 CHAPTER 1
LITERATURE REVIEW ............................................................................................... 13
CHAPTER 2
INTRODUCTION....................................................................................................... INTRODUCTION....................................................................................................... 16
2.1
AIM OF PROJECT ......................... ...................................... .......................... ........................... ........................... .......................... .......................... .......................... ....................... .......... 16
2.2
SCOPE ........................... ........................................ .......................... .......................... .......................... .......................... .......................... .......................... .................................. ....................... 16
2.3
PROJECT DESCRIPTION .......................... ........................................ ........................... .......................... .......................... .......................... .......................... .......................... ............... 16
2.3.1
Stirling Engine............ Engine ......................... .......................... .......................... .......................... .......................... .......................... .......................... ........................... ................... ..... 16
2.3.2
History ............. History ........................... ........................... .......................... .......................... .......................... .......................... .......................... .......................... ............................ ............... 16
2.4
TERMS ASSOCIATED WITH THE STIRLING ENGINE .......................... ....................................... .......................... .......................... .......................... ..................... ........ 17
2.4.1
Heat engine Heat engine .......................... ....................................... .......................... .......................... .......................... .......................... .......................... .......................... ..................... ........ 17
2.4.2
Sink ............ Sink ......................... .......................... .......................... .......................... .......................... .......................... .......................... .......................... .................................. ....................... 17
2.4.3
Source ......................... ...................................... .......................... ........................... ........................... .......................... .......................... .......................... .............................. ................. 17
2.4.4
Internal Combustion Internal Combustion Engine .......................... ....................................... .......................... .......................... .......................... ........................... ...................... ........ 17
2.5
MAJOR COMPONENTS OF THE STIRLING ENGINE .......................... ........................................ ........................... .......................... .......................... .................. ..... 17
2.5.1
Displacer .......................... ....................................... .......................... .......................... .......................... .......................... .......................... .......................... .......................... ............. 17
2.5.2
Power piston............ piston ......................... .......................... .......................... .......................... .......................... .......................... .......................... .......................... ..................... ........ 18
2.5.3
Crank shaft Crank shaft ............. .......................... ........................... ........................... .......................... .......................... .......................... .......................... .......................... ..................... ........ 18
2.5.4
Connecting rod ............ rod ......................... .......................... .......................... .......................... ........................... ........................... .......................... .......................... ................ ... 18
2.5.5
Regenerator (optional) Regenerator (optional) ......................... ...................................... .......................... .......................... .......................... .......................... .......................... .................. ..... 18
2.6
STIRLING ENGINE‐EXTERNAL COMBUSTION ENGINE .......................... ....................................... .......................... .......................... .......................... ................ ... 18
2.7
BASICS OF STIRLING ENGINE .......................... ....................................... .......................... .......................... .......................... .......................... .......................... .................... ....... 19
2.8
THE STIRLING ENGINE CYCLE .......................... ....................................... .......................... .......................... .......................... .......................... .......................... .................... ....... 19
2.8.1
2‐3 Isothermal Expansion Isothermal Expansion .......................... ....................................... .......................... .......................... .......................... .......................... .......................... ............. 20
2.8.2
3‐4 Constant Volume Constant Volume Heat Rejection Heat Rejection............ ......................... .......................... .......................... .......................... .......................... ....................... .......... 20
2.8.3
4‐1 Isothermal Compression Isothermal Compression............. .......................... .......................... .......................... .......................... .......................... ........................... ...................... ........ 20
2.8.4
1‐2 Constant Volume Constant Volume Heat Addition............. Addition .......................... .......................... .......................... .......................... .......................... ....................... .......... 20
2.9
OPERATION OF STIRLING CYCLE ENGINE ......................... ...................................... .......................... .......................... .......................... .......................... ................... ...... 20
2.10
HOW TO INCREASE THE POWER OUTPUT OF A STIRLING ENGINE ......................... ....................................... ........................... ....................... .......... 21
2.10.1 Pressurization ......................... ...................................... .......................... .......................... .......................... .......................... .......................... ........................... ................... ..... 24 2.10.2 Lubricants and friction............. friction .......................... .......................... .......................... .......................... .......................... .......................... .......................... .................. ..... 24 2.11
COMPARISON OF STIRLING ENGINE WITH AN INTERNAL COMBUSTION ENGINE .......................... ....................................... .................. ..... 24
2.11.1 Advantages............. Advantages........................... ........................... .......................... .......................... .......................... .......................... .......................... .......................... ..................... ........ 24 2.11.2 Disadvantages............. Disadvantages .......................... .......................... .......................... .......................... ........................... ........................... .......................... .......................... ................ ... 25 2.12
APPLICATIONS OF STIRLING ENGINE ......................... ...................................... .......................... .......................... .......................... .......................... ........................ ........... 25
CHAPTER 3
DESIGN SELECTION.................................................................................................. SELECTION .................................................................................................. 28
3.1
CONFIGURATIONS OF STIRLING ENGINE .......................... ....................................... .......................... .......................... .......................... .......................... ................... ...... 28
3.2
ALPHA STIRLING ENGINE......................... ...................................... .......................... .......................... .......................... .......................... .......................... .......................... ............... 28
3.2.1
Advantages............. Advantages........................... ........................... .......................... .......................... .......................... .......................... .......................... .......................... ..................... ........ 28
3.2.2
Disadvantages............. Disadvantages .......................... .......................... .......................... .......................... ........................... ........................... .......................... .......................... ................ ... 29
3.2.3
Action of an of an alpha type Stirling engine............. engine.......................... ........................... ........................... .......................... .......................... .................. ..... 29
Page 2
FINAL YEAR PROJECT REPORT
DESIGN AND FABRICATION OF A STIRLING CYCLE ENGINE
Table of Contents of Contents PREFACE……………… ................................................................................................................................ 8 ACKNOWLEDGEMENTS .......................................................................................................................... 9 PROJECT APPROVAL............................................................................................................................. 10 NOMENCLATURE…………………………………………… NOMENCLATURE………………… …………………………………………………… ………………………………………………… ……………………………..…………………… ……..…………………………..1 ……..1 1 CHAPTER 1
LITERATURE REVIEW ............................................................................................... 13
CHAPTER 2
INTRODUCTION....................................................................................................... INTRODUCTION....................................................................................................... 16
2.1
AIM OF PROJECT ......................... ...................................... .......................... ........................... ........................... .......................... .......................... .......................... ....................... .......... 16
2.2
SCOPE ........................... ........................................ .......................... .......................... .......................... .......................... .......................... .......................... .................................. ....................... 16
2.3
PROJECT DESCRIPTION .......................... ........................................ ........................... .......................... .......................... .......................... .......................... .......................... ............... 16
2.3.1
Stirling Engine............ Engine ......................... .......................... .......................... .......................... .......................... .......................... .......................... ........................... ................... ..... 16
2.3.2
History ............. History ........................... ........................... .......................... .......................... .......................... .......................... .......................... .......................... ............................ ............... 16
2.4
TERMS ASSOCIATED WITH THE STIRLING ENGINE .......................... ....................................... .......................... .......................... .......................... ..................... ........ 17
2.4.1
Heat engine Heat engine .......................... ....................................... .......................... .......................... .......................... .......................... .......................... .......................... ..................... ........ 17
2.4.2
Sink ............ Sink ......................... .......................... .......................... .......................... .......................... .......................... .......................... .......................... .................................. ....................... 17
2.4.3
Source ......................... ...................................... .......................... ........................... ........................... .......................... .......................... .......................... .............................. ................. 17
2.4.4
Internal Combustion Internal Combustion Engine .......................... ....................................... .......................... .......................... .......................... ........................... ...................... ........ 17
2.5
MAJOR COMPONENTS OF THE STIRLING ENGINE .......................... ........................................ ........................... .......................... .......................... .................. ..... 17
2.5.1
Displacer .......................... ....................................... .......................... .......................... .......................... .......................... .......................... .......................... .......................... ............. 17
2.5.2
Power piston............ piston ......................... .......................... .......................... .......................... .......................... .......................... .......................... .......................... ..................... ........ 18
2.5.3
Crank shaft Crank shaft ............. .......................... ........................... ........................... .......................... .......................... .......................... .......................... .......................... ..................... ........ 18
2.5.4
Connecting rod ............ rod ......................... .......................... .......................... .......................... ........................... ........................... .......................... .......................... ................ ... 18
2.5.5
Regenerator (optional) Regenerator (optional) ......................... ...................................... .......................... .......................... .......................... .......................... .......................... .................. ..... 18
2.6
STIRLING ENGINE‐EXTERNAL COMBUSTION ENGINE .......................... ....................................... .......................... .......................... .......................... ................ ... 18
2.7
BASICS OF STIRLING ENGINE .......................... ....................................... .......................... .......................... .......................... .......................... .......................... .................... ....... 19
2.8
THE STIRLING ENGINE CYCLE .......................... ....................................... .......................... .......................... .......................... .......................... .......................... .................... ....... 19
2.8.1
2‐3 Isothermal Expansion Isothermal Expansion .......................... ....................................... .......................... .......................... .......................... .......................... .......................... ............. 20
2.8.2
3‐4 Constant Volume Constant Volume Heat Rejection Heat Rejection............ ......................... .......................... .......................... .......................... .......................... ....................... .......... 20
2.8.3
4‐1 Isothermal Compression Isothermal Compression............. .......................... .......................... .......................... .......................... .......................... ........................... ...................... ........ 20
2.8.4
1‐2 Constant Volume Constant Volume Heat Addition............. Addition .......................... .......................... .......................... .......................... .......................... ....................... .......... 20
2.9
OPERATION OF STIRLING CYCLE ENGINE ......................... ...................................... .......................... .......................... .......................... .......................... ................... ...... 20
2.10
HOW TO INCREASE THE POWER OUTPUT OF A STIRLING ENGINE ......................... ....................................... ........................... ....................... .......... 21
2.10.1 Pressurization ......................... ...................................... .......................... .......................... .......................... .......................... .......................... ........................... ................... ..... 24 2.10.2 Lubricants and friction............. friction .......................... .......................... .......................... .......................... .......................... .......................... .......................... .................. ..... 24 2.11
COMPARISON OF STIRLING ENGINE WITH AN INTERNAL COMBUSTION ENGINE .......................... ....................................... .................. ..... 24
2.11.1 Advantages............. Advantages........................... ........................... .......................... .......................... .......................... .......................... .......................... .......................... ..................... ........ 24 2.11.2 Disadvantages............. Disadvantages .......................... .......................... .......................... .......................... ........................... ........................... .......................... .......................... ................ ... 25 2.12
APPLICATIONS OF STIRLING ENGINE ......................... ...................................... .......................... .......................... .......................... .......................... ........................ ........... 25
CHAPTER 3
DESIGN SELECTION.................................................................................................. SELECTION .................................................................................................. 28
3.1
CONFIGURATIONS OF STIRLING ENGINE .......................... ....................................... .......................... .......................... .......................... .......................... ................... ...... 28
3.2
ALPHA STIRLING ENGINE......................... ...................................... .......................... .......................... .......................... .......................... .......................... .......................... ............... 28
3.2.1
Advantages............. Advantages........................... ........................... .......................... .......................... .......................... .......................... .......................... .......................... ..................... ........ 28
3.2.2
Disadvantages............. Disadvantages .......................... .......................... .......................... .......................... ........................... ........................... .......................... .......................... ................ ... 29
3.2.3
Action of an of an alpha type Stirling engine............. engine.......................... ........................... ........................... .......................... .......................... .................. ..... 29
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FINAL YEAR PROJECT REPORT 3.3
DESIGN AND FABRICATION OF A STIRLING CYCLE ENGINE
BETA STIRLING ENGINE.......................... ........................................ ........................... .......................... .......................... .......................... .......................... .......................... ............... 29
3.3.1
Advantages............. Advantages........................... ........................... .......................... .......................... .......................... .......................... .......................... .......................... ..................... ........ 30
3.3.2
Disadvantages............. Disadvantages .......................... .......................... .......................... .......................... ........................... ........................... .......................... .......................... ................ ... 30
3.3.3
Action of a of a Beta Type Stirling Engine............ Engine......................... .......................... .......................... .......................... .......................... ....................... .......... 30
3.4
GAMMA STIRLING ENGINE .......................... ....................................... .......................... .......................... .......................... ........................... ........................... ...................... ......... 30
3.4.1
Advantages............. Advantages........................... ........................... .......................... .......................... .......................... .......................... .......................... .......................... ..................... ........ 30
3.4.2
Disadvantages............. Disadvantages .......................... .......................... .......................... .......................... ........................... ........................... .......................... .......................... ................ ... 31
3.5
WEIGHTING MATRIX FOR STIRLING ENGINE TYPES......................... ....................................... ........................... .......................... .......................... .................. ..... 31
3.6
RATING MATRIX FOR STIRLING ENGINE TYPES .......................... ....................................... .......................... .......................... .......................... ....................... .......... 31
3.6.1
Pie Charts (Based on the data from data from the rating matrix) ......................... ...................................... .......................... ..................... ........ 32
3.6.2
Final analysis Final analysis for for the the choice of configuration of configuration of Stirling of Stirling Engine............. Engine .......................... .......................... .................... ....... 33
3.7
CHOICE OF GAS (WORKING FLUID) .......................... ....................................... .......................... .......................... .......................... .......................... ........................ ........... 33
3.7.1
Hydrogen ......................... ...................................... .......................... .......................... .......................... .......................... .......................... ........................... .......................... ............ 33
3.7.2
Helium ........................... ........................................ .......................... .......................... .......................... .......................... .......................... .......................... ............................ ............... 34
3.7.3
Air (primarily Air (primarily nitrogen) nitrogen)............ ......................... .......................... .......................... .......................... .......................... .......................... .......................... .................. ..... 34
3.8
WEIGHTING MATRIX FOR WORKING FLUID......................... ...................................... .......................... .......................... ........................... ........................... ............... 36
3.9
RATING MATRIX FOR WORKING FLUID.......................... ........................................ ........................... .......................... .......................... .......................... ................... ...... 36
3.9.1
Pie Charts (Based on the data from data from the rating matrix of matrix of working working fluid) fluid) .................................37 .................................37
3.9.2
Final analysis Final analysis for for the the choice of gas of gas .......................... ....................................... .......................... .......................... .......................... ......................... ............ 38
CHAPTER 4
4.1
THERMAL ANALYSIS ................................................................................................ 39
CALCULATION OF THE ADIABATIC FLAME TEMPERATURE| ......................... ...................................... .......................... .......................... ...................... ......... 39
4.1.1
Introduction............ Introduction .......................... ........................... .......................... .......................... .......................... .......................... .......................... .......................... ..................... ........ 39
4.1.2
Assumptions ......................... ...................................... .......................... .......................... .......................... .......................... .......................... .......................... ..................... ........ 39
4.1.3
Calculations for Calculations for liquid liquid kerosene kerosene (C 12 )......................... ........................... .......................... .......................... .......................... .................. ..... 39 12H26 )...........
4.1.4
Conclusion............. Conclusion.......................... .......................... .......................... .......................... ........................... ........................... .......................... .......................... ....................... .......... 41
4.2
CALCULATIONS FOR METHANE (CH4) .......................... ....................................... .......................... .......................... .......................... ........................... ...................... ........ 41
4.2.1
Conclusion............. Conclusion.......................... .......................... .......................... .......................... ........................... ........................... .......................... .......................... ....................... .......... 42
4.2.2
Final conclusion Final conclusion with respect to respect to the choice of fuel ............ fuel ......................... .......................... .......................... .......................... ............... .. 42
4.3
HEAT TRANSFER CALCULATION ......................... ...................................... .......................... .......................... .......................... .......................... .......................... .................. ..... 42
4.3.1
Formulas to be used ............. used .......................... ........................... ........................... .......................... .......................... .......................... .......................... .................... ....... 42
4.3.2
Data............. Data .......................... .......................... .......................... .......................... .......................... .......................... .......................... .......................... ................................. .................... 43
4.3.3
Calculations for Calculations for thermal thermal resistance resistance network ......................... ...................................... .......................... .......................... ........................ ........... 46
4.3.4
Calculations for Calculations for the the flame flame temperature ......................... ...................................... .......................... .......................... .......................... .................. ..... 47
4.3.5
Calculations for Calculations for thermal thermal efficiency: efficiency: ......................... ...................................... .......................... .......................... .......................... ......................... ............ 49
CHAPTER 5
5.1
SELECTION OF SWEPT VOLUME ............................................................................... 50
ANALYSIS OF STIRLING ENGINE ......................... ...................................... .......................... .......................... .......................... .......................... .......................... .................. ..... 50
5.1.1
1st ‐order method order method ......................... ...................................... .......................... .......................... .......................... .......................... .......................... .......................... ............... 50
5.1.2
2nd ‐order method order method ............ ......................... .......................... .......................... .......................... .......................... .......................... .......................... ......................... ............ 50
5.1.3
3rd ‐order methods order methods............ ......................... .......................... .......................... .......................... .......................... .......................... .......................... ......................... ............ 50
5.2
THE SCHMIDT ANALYSIS ......................... ...................................... .......................... .......................... .......................... .......................... .......................... .......................... ............... 50
5.2.1
Assumptions of Schmidt of Schmidt Model Model for Gamma for Gamma Stirling Analysis Stirling Analysis............ ......................... .......................... ......................... ............51 51
5.2.2
Indicated Work Indicated Work ............ ......................... .......................... .......................... .......................... ........................... ........................... .......................... .......................... ................ ... 51
5.2.3
Root Mean Root Mean Cycle Pressure ......................... ...................................... .......................... .......................... .......................... .......................... .......................... ............. 52
5.2.4
Forced Work Forced Work ............ ......................... .......................... .......................... .......................... .......................... .......................... .......................... .......................... ..................... ........ 52
5.2.5
Shaft Work Shaft Work ............ ......................... .......................... .......................... ........................... ........................... .......................... .......................... .......................... ....................... .......... 53
5.3
1ST‐ORDER ANALYSIS METHOD .......................... ....................................... .......................... .......................... .......................... ........................... ........................... ............... .. 54
5.3.1
Effectiveness & Mechanical Efficiency Mechanical Efficiency ......................... ...................................... .......................... .......................... ........................... ..................... ....... 54
5.3.2
Compression Ratio............ Ratio ......................... .......................... .......................... .......................... .......................... .......................... .......................... ......................... ............ 54
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DESIGN AND FABRICATION OF A STIRLING CYCLE ENGINE
5.3.3
Workspace Charging Effect ..................................................................................................... 55
5.3.4
Dead Space Effects .................................................................................................................. 57
5.3.5
Conclusion................................................................................................................................ 58
5.4
DESIGN APPROACH ........................................................................................................................... 58
5.5
ACTUAL TREND OF GRAPH .................................................................................................................. 64
5.6
SELECTION OF COMPRESSION RATIO ..................................................................................................... 65
5.7
CALCULATIONS (AT OPTIMUM VALUES) ................................................................................................. 67
5.7.1
Values of Designed Parameters ............................................................................................... 67
5.7.2
Total Volume
.................................................................................................................. 67 Mass of Working Fluid (m) ...................................................................................................... 67 Root Mean Cycle Pressure ( ) ................................................................................................. 68
5.7.3 5.7.4 5.7.5
Indicated Work (W) ................................................................................................................. 68
5.7.6
Forced Work ............................................................................................................................ 68
5.7.7
Shaft Work ............................................................................................................................... 68
5.7.8
Mechanical Efficiency .............................................................................................................. 68
CHAPTER 6
6.1
KINETICS & TURNING MOMENT .............................................................................. 69
KINETICS AND TURNING MOMENT ....................................................................................................... 69
6.1.1
Assumptions ............................................................................................................................ 70
6.1.2
Calculations ............................................................................................................................. 70
CHAPTER 7
SIMULATION OF STATIC TEMPERATURE................................................................... 76
7.1
MODELING ...................................................................................................................................... 76
7.2
MESHING ........................................................................................................................................ 77
7.3
GRAPHICAL DISTRIBUTION .................................................................................................................. 77
7.4
TEMPERATURE PROFILE ...................................................................................................................... 78
CHAPTER 8
CAD DRAFTS............................................................................................................ 79
CHAPTER 9
INSTRUMENTATION ................................................................................................ 90
9.1
PROXIMITY SENSOR ........................................................................................................................... 90
9.2
MODEL EXPLANATION OF PROXIMITY SWITCH ......................................................................................... 91
9.3
MAIN FEATURES: .............................................................................................................................. 91
9.4
THERMOCOUPLE ............................................................................................................................... 92
9.5
TYPES OF THERMOCOUPLES: ............................................................................................................... 93
9.6
K‐TYPE ........................................................................................................................................... 93
9.7
TABLE FOR TYPE K THERMOCOUPLE (REF JUNCTION 0 C) ........................................................................ 94 ◦
CHAPTER 10
EXPERIMENTAL RESULTS ......................................................................................... 95
10.1
FLAME CHARACTERISTICS .................................................................................................................... 95
10.2
EXPERIMENTAL FINDINGS.................................................................................................................... 95
CHAPTER 11
POST DESIGNING..................................................................................................... 98
11.1
COST ESTIMATES .............................................................................................................................. 98
11.2
RISK ASSESSMENT ............................................................................................................................. 99
11.3
SAFETY ASSESSMENT: ...................................................................................................................... 102
11.3.1 Introduction:.......................................................................................................................... 102 11.3.2 System Operation: ................................................................................................................. 102 11.3.3 Safety Engineering:................................................................................................................ 103 11.3.4 Objectives Assessment:.......................................................................................................... 105
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DESIGN AND FABRICATION OF A STIRLING CYCLE ENGINE
GALLERY………………………….................................................................................................................. 110 APPENDIX A “GANTT CHART”............................................................................................................. 114 APPENDIX B “SOR” ............................................................................................................................ 116 APPENDIX C “TERMS & DEFINITIONS” ................................................................................................ 127 APPENDIX D “REFERENCES” ............................................................................................................... 133
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FINAL YEAR PROJECT REPORT
DESIGN AND FABRICATION OF A STIRLING CYCLE ENGINE
List of Figures Figure 2‐1 Ideal Stirling Cycle ........................................................................................................................ 19 Figure 2‐2 Operation of Ideal Stirling Cycle Engine (Displacer at the Lower‐Dead Center) ..........................21 Figure 2‐3 Operation of Ideal Stirling Cycle Engine (Displacer at the Upper‐Dead Center)..........................21 Figure 2‐4 Expansion (Driving the Power Piston Upward) ............................................................................22 Figure 2‐5 Transfer of Warm Gas to the Upper Cool end.............................................................................. 22 Figure 2‐6 Contraction (Driving the Power Piston Downward)..................................................................... 23 Figure 2‐7 Transfer of Cooled Gas to the Lower Hot End.............................................................................. 23 Figure 3‐1 Alpha Engine Configuration.......................................................................................................... 28 Figure 3‐2 Beta Engine Configuration ........................................................................................................... 29 Figure 3‐3 Gamma Engine Configuration ...................................................................................................... 30 Figure 3‐4 Ease of Sealing.............................................................................................................................. 32 Figure 3‐5 Design Simplicity .......................................................................................................................... 32 Figure 3‐6 Problem of Hot Moving Seals....................................................................................................... 32 Figure 3‐7 Compression Ratio ...................................................................................................................... 32 Figure 3‐8 Availability.................................................................................................................................... 37 Figure 3‐9 Cost (cheap) ................................................................................................................................. 37 Figure 3‐10 Non‐Flammable .......................................................................................................................... 37 Figure 3‐11 Low Diffusivity............................................................................................................................ 37 Figure 3‐12 Low Viscosity.............................................................................................................................. 37 Figure 3‐13 High Thermal Conductivity......................................................................................................... 37 Figure 4‐1 1D Heat Transfer Across the Displacer Cylinder...........................................................................46 Figure 4‐2 Thermal Resistive Network Schematic......................................................................................... 46 Figure 4‐3 Thermal Resistances..................................................................................................................... 48 Figure 5‐1 Effect of Increasing Swept Volume Ratio ..................................................................................... 52 Figure 5‐2 Effect of Increasing Size on Forced Work..................................................................................... 53 Figure 5‐3 Graph of Maximum Mechanical Efficiency versus Compression Ratio ........................................55 Figure 5‐4 PV Diagram of Charged Stirling Engine ........................................................................................ 56 Figure 5‐5 Variation of maximum specific shaft work Ws versus dead space ratio χ ...................................57 Figure 5‐6 Work and Mechanical Efficiency as a Function of Swept Volume Ratio at τ=0.2.........................61 Figure 5‐7 Work and Mechanical Efficiency as a Function of Swept Volume Ratio at τ=0.3.........................62 Figure 5‐8 Work and Mechanical Efficiency as a Function of Swept Volume Ratio at τ=0.4.........................63 Figure 5‐9 Actual Graphical Representation from Experimental Data ..........................................................64 Figure 5‐10 Mechanical Efficiency as a Function of Compression Ratio at T=0.3 .........................................66 Figure 6‐1 Crank‐angle Mechanism............................................................................................................... 69 Figure 6‐2 Kinetics of Flywheel...................................................................................................................... 70 Figure 6‐3 Turning Moment Diagram............................................................................................................ 75 Figure 7‐1 Modeling of 2D Cylinder in ANSYS ............................................................................................... 76 Figure 7‐2 Meshing of 2D Cylinder in ANSYS................................................................................................. 77 Figure 7‐3 Contours of Temperature Distribution......................................................................................... 77 Figure 7‐4 Graph of Temperature Variation Along Cylinder Height..............................................................78 Figure 9‐1 Proximity Sensor (RPM Measuring Device).................................................................................. 91 Figure 9‐2 Dimensions of Proximity Sensor................................................................................................... 92 Figure 9‐3 Construction of Thermocouple .................................................................................................... 92 Figure 9‐4 K Type Thermocouple .................................................................................................................. 93 Figure 10‐1 Temperature vs. Height.............................................................................................................. 96 Figure 10‐2 RPM vs. Flame Temperature...................................................................................................... 97
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List of Tables Table 3‐1 Weighting Matrix for Stirling Engine Types ................................................................................... 31 Table 3‐2 Rating Matrix for Stirling Engine Types ......................................................................................... 31 Table 3‐3 Weighting Matrix for Working Fluid.............................................................................................. 36 Table 3‐4 Rating Matrix for Working Fluid .................................................................................................... 36 Table 4‐1 Data Input...................................................................................................................................... 43 Table 4‐2 For Horizontal Plate with Hot Side Facing Down...........................................................................43 Table 4‐3 Assumed Ts.................................................................................................................................... 44 Table 4‐4 Film Temperature at Ts ................................................................................................................. 44 Table 4‐5 Air Properties at Various Tf ........................................................................................................... 44 Table 4‐6 Air Properties at Film Temperatures for Various Ts Values...........................................................46 Table 4‐7 Thermal Resistances...................................................................................................................... 47 Table 4‐8 Various Temperatures Calculated via Thermal Resistance Network.............................................48 Table 5‐1 Engine Operating Parameter as a Function of Volume Ratio........................................................ 60 Table 5‐2 Engine Operating Parameters as a Function of Compression Ratio..............................................65 Table 6‐1 Parameters at Different Crank Positions....................................................................................... 74 Table 9‐1 Types of Thermocouple................................................................................................................. 93
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Preface The final year project plays a significant role in BE degree classes in order to furbish the students with practical skills along with the theoretical knowledge. It also provides the opportunity to the members to work as a team which is the basic requirement of any reputable organization. It also creates managerial skills in an individual’s personality as no project can be accomplished without proper management. In order to manage and plan the project, it is necessary that the progress of the project should be documented as it serves as a good tool for having a good and unanimous consensus amongst the project members. We being final year students are going through the same phase of our degree. The purpose of writing this report is to present our progress and work on this initial phase of our project titled “Design and Fabrication of a Stirling Cycle Engine” in a presentable form as it is the requirement of the Design Evaluation Board and in addition it will also be helpful for future reference as it would be needed for our final report. The report is divided into four sections. The first section mainly consists of the introduction and how a stirling engine works. The second section comprises of the design criteria and our proposed selection. The third section is on risk assessment and the fourth section is on cost evaluation. Readers are requested to kindly compromise with any deficiency that they might find in this report as this was our first attempt in its compilation and thus might be subjected to some un‐intentional oversight. In light of the above mentioned we would like to request you to kindly consider this as our first step and we assure you that the future editions of this report will be comprehensibly better and complete.
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Acknowledgements This report is the product of sheer hard work and pure dedication. We would like to take this opportunity to first of all thank Allah the Almighty for giving us the mental and physical strength to manage our project work simultaneously with our academic routine, deal with the various problems involved, overcome the various obstacles encountered and accomplish it on time. Furthermore we would also like to thank our families for their continued support and bearing with our hectic schedule. This project would not have culminated without their cooperation. Last but by no means the least, we would like to acknowledge with gratitude the following individuals whose valued suggestions, guidance and constructive criticism helped in shaping our project and above all our professional lives and personalities, which will be very beneficial for our future career:
Project Advisor • Dr. Waqar A. Khan (Professor)
Project Examiner • Mr. Aijaz Ahmed (Lecturer) Project Co Examiner • Dr. Nouman Danish (Associate Professor)
Though the following were not actively involved in the project, nonetheless they do deserve special mention for their continued support and advice:
•
Gp. Capt. Shoaib Ahmed (Associate Professor)
•
Mr. Khurram Jammal Hashmi (Assistant Professor)
•
Mr. Mirza Ahmed Ali (Lecturer)
•
Mr. Atif (Lab Supervisor)
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Project Approval It is certified that the contents and form of the thesis entitled “The Design and Fabrication of a Stirling Cycle Engine” submitted by Mr. Rehan Azhar, Mr. Shahzad Ahmad and Mr. M. Sajjad Ashraf have been found to be satisfactory for the requirement of B.E degree.
Project Advisor: _____________________________ Name: Dr. Waqar Ahmed Khan (Professor)
Project Examiner 1: __________________________ Name: Mr. Aijaz Ahmad (Lecturer) Project Examiner 2: __________________________ Name: Dr. Noman Danish (Associate Professor)
Project Coordinator: _________________________ Name: Cdr. (R) Muhammad Shakeel (Associate Professor)
HOD (Mechanical): __________________________ Name: Gp. Capt. (R) Shoib Ahmed (Associate Professor)
Dean ES: __________________________________ Name: Cdr Dr. Nadeem Ahmed
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Nomenclature = displacer swept volume = dead volume = cold space temperature = external buffer pressure = root mean cycle pressure or mean
= piston swept volume = hot space temperature = dead space temperature = ⁄2
pressure
piston crank
τ
=
= ratio of temperatures of cold to hot
ω
= angular velocity of crankshaft
= angle by which displacer crank leads κ =
= ratio of piston swept volume to
space
displacer swept volume
r
χ
=
ωt
= instantaneous angular position of piston
= uncompressed volume / compressed
volume
= dead volume ratio
crank
= instantaneous total engine volume
= instantaneous pressure throughout engine spaces
l= Length of the connecting rod
c= Crank radius
A1= Cross‐sectional area on the back end side
A2= Cross‐sectional area on the crank end side
of the piston a= Cross‐sectional area of the connecting rod
of the piston p1= Pressure on the back end side of the piston
p2= Pressure on the crank end side of the
d= Outer diameter of power piston
piston=Buffer pressure=pb B= Bore of the power cylinder
L= Stroke of the piston
mR= Mass of the reciprocating parts
Vd= Displaced Volume of the power cylinder
T= Torque or Turning moment of the crank
N = Crankshaft speed in revolutions per minute (rpm)
P= Desired power in Watts
Fp= Piston Effort
FL= Net load on piston
FI= Inertia Force
W R= Weight of reciprocating parts
T = Torque or Turning moment on the crankshaft at any instant
Tmean = Mean Resisting Torque
P = Desired power in Watts
N = Crankshaft speed in revolutions per
CE = Co‐efficient of fluctuation of Energy
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minute (rpm) CS = Co‐efficient of fluctuation of Speed
mf = Mass of the flywheel
k = Radius of Gyration of the flywheel
I = Mass moment of Inertia of flywheel
h = convective heat transfer coefficient
k = thermal conductivity
ε = emissivity
σ = Stefan Boltzmann constant
Ts = External surface temperature at the top of
Tli = Internal surface temperature at the top of
the displacer
the displacer
To = Ambient temperature
Tflame = Temperature of the applied flame
Th = External surface temperature at the base
Tu = Internal surface temperature at the base
of the displacer
of the displacer
Tf = Film temperature
Pr = Prandtl number
Ra = Rayleigh number
Nu = Nusselt number
β = Volume expansion coefficient
υ = Kinematic viscosity
τ = Temperature ratio of sink to source
D = Diameter
A = Area
R = Thermal resistances
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CHAPTER 1 LITERATURE REVIEW [1]
Iskander Tlili, Youssef Timoumi and Sassi Ben Nasrallah presented the study and
design of a mean temperature differential Stirling engine for solar application. The system uses hydrogen as working fluid and is designed for a temperature difference of 300 C, with the source at 320 C and the sink at 20 C. They also discuss design ◦
◦
◦
considerations which may be taken to develop a solar Stirling engine with average concentration operating on mean temperature difference of 300 C. Detailed design ◦
considerations pertaining to the output power, energy losses as well as the effectiveness of the regenerator used are presented. Then the relationship between different operating parameters is discussed.
[2]
Bancha Kongtragool and Somchai Wongwises gave different approaches to determine
the designed power output, discussing their relative significance. In the preliminary design phase, some design parameters are unknown. The Schmidt formula and West formula are more difficult to use when compared with the Beale formula and the mean pressure formula. In principle, the Beale formula is simpler, however, an accurate value of the Beale number is critical and the existing data on the Beale number are not available for Low Temperature Differential (LTD) Stirling engines.
For design purposes, the mean pressure power formula can be used to calculate the engine rated output, or inversely, to evaluate the approximate operating parameters of the Stirling engine for a required or given power output. The mean pressure power formula allows us to initiate an initial design process rapidly. For LTD Stirling engines operated by a low temperature source, results from this study indicate that the rated power output of a LTD Stirling engine can be directly calculated from the mean pressure power formula.
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Can Cinar and Halit Karabulut presented study of a gamma type Stirling engine with
276 cc swept volume that was designed and manufactured. The engine was tested with air and helium by using an electrical furnace as heat source. Working characteristics of ₀
the engine were obtained within the range of heat source temperature 700–1000 C and range of charge pressure 1–4.5 bar. Maximum power output was obtained with helium ₀
at 1000 C heat source temperature and 4 bar charge pressure as 128.3 W. The ₀
maximum torque was obtained as 2 Nm at 1000 C heat source temperature and 4 bar helium charge pressure. Results were found to be encouraging to initiate a Stirling engine project for 1 kW power output.
[4]
Bancha Kongtragool, Somchai Wongwises presented results from their study which
indicated that stirling engines working with relatively low temperature air are potentially attractive engines of the future, especially solar‐powered low temperature differential stirling engines with vertical, double ‐acting, gamma‐configuration. New materials and good heat transfer to working fluid are the keys to the success of a stirling engine. Good heat transfer needs high mass flows, then a lower viscosity working fluid is used to reduce pumping losses, or higher pressure is used to reduce the required flow or the combination of both. Simplicity and reliability is the key to a cost effective Stirling solar generator. Since, during two‐thirds of the day, solar energy is not available, solar/fuel hybrids are needed. For solar operation, the cover plate acts as the solar absorber and also the displacer cylinder head, it must therefore be able to tolerate the effects of high maximum internal pressures and temperatures.
[5]
D.G. Thombarea and S.K. Vermab stated that the performance of stirling engines
meets the demands of the efficient use of energy and environmental security; hence the development and investigation of stirling engine have come to the attention of many scientific institutes. The stirling engine is simple, reliable and safe. Today stirling cycle‐ based systems are in commercial use as a heat pump, cryogenic refrigeration and air liquefaction. It is seen that for successful operation of engine system with good efficiency a careful design of heat exchangers, proper selection of drive mechanism and engine configuration is essential. The reliable and efficient operation of the engine depends upon the dynamic behavior of engine mechanism and performance of all heat
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exchangers, which are interdependent. This difficult task to design a system where thermal, fluid and mechanical design considerations are required to be taken into account jointly with system optimization. An additional development is needed to produce a practical engine by selection of suitable configuration; adoption of good working fluid and development of better seal may make stirling engine a real practical alternative for power generation.
[6]
Leonardo Scollo, Pablo Valdez and Jorge Baro´n focused on the local design,
construction and testing of Stirling engine. They presented the research work carried on an external combustion engine which makes it a versatile machine along with the advantage of using any external heat source like concentrated solar energy, hydrogen, biomass and fossil fuels. Moreover, it explains the working of cycles quite elaborately on a PV diagram which serves a good source of understanding the ideal stirling cycle scheme. The formulated power for this project is in the range of 0.5‐1kW. The engine is designed from a previously designed prototype engine of known parameters and characteristics through scaling. The results of this research were marked encouraging and it was foreseen to redesign each part of the engine.
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CHAPTER 2
INTRODUCTION 2.1
Aim of Project
To obtain useful mechanical work output from a given heat input by employing a stirling cycle engine mechanism.
2.2
Scope
The design, analysis and fabrication of a stirling engine by systematic study of basic operating principles, design parameters and the study of a home‐made scaled down version of the engine (as per the PCSIR project competition requirement) in order to identify the engineering complications associated with it.
2.3
Project Description
2.3.1
Stirling Engine
It is a heat engine that operates by cyclic compression and expansion of air or another gas, the working fluid, at different temperature levels such that there is a net conversion of heat energy to mechanical work.
2.3.2
History
The Stirling was invented and patented by Robert Stirling in 1816. Subsequent development by Robert Stirling and his brother James, an engineer, resulted in patents for various improved configurations of the original engine including pressurization which had by 1843 sufficiently increased power output to drive all the machinery at a Dundee iron foundry.
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Though it has been disputed it is widely supposed that as well as saving fuel, the inventors were motivated to create a safer alternative to the steam engines of the time, whose boilers frequently exploded, causing many injuries and fatalities. The need for Stirling engines to run at very high temperatures to maximize power and efficiency exposed limitations in the materials of the day and the few engines that were built in those early years suffered unacceptably frequent failures.
2.4
Terms associated with the Stirling engine
2.4.1
Heat engine
A heat engine is a device that converts thermal energy into mechanical work output.
2.4.2
Sink
The heat sink is typically the environment at ambient temperature to where heat is lost and the temperature is lowered.
2.4.3
Source
Source is the venue from where heat energy is obtained.
2.4.4
Internal Combustion Engine
An engine, where combustion takes place inside the power cylinder.
2.5
Major Components Of The Stirling Engine
2.5.1
Displacer
The displacer resembles a large piston, except that it has a smaller diameter than the cylinder, thus its motion does not change the volume of gas in the cylinder—it merely transfers the gas around within the cylinder.
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DESIGN AND FABRICATION OF A STIRLING CYCLE ENGINE
Power piston
Power piston is the piston located in the expansion chamber. The expanding gases in the cylinder exert a pressure on the power piston which in turn rotates the crank and provides the system with the power stroke.
2.5.3
Crank shaft
The crankshaft, sometimes casually abbreviated to crank, is the part of an engine which translates reciprocating linear piston motion into rotation.
2.5.4
Connecting rod
Transfers power from the power piston to the crankshaft.
2.5.5
Regenerator (optional)
The regenerator is an internal heat exchanger and temporary heat storage element placed between the hot and cold spaces such that the working fluid passes through it first in one direction then the other. Its function is to retain within the system that heat which would otherwise be exchanged with the environment at temperatures intermediate to the maximum and minimum cycle temperatures, thus enabling the thermal efficiency of the cycle to approach the limiting Carnot efficiency.
2.6
Stirling Engine-External Combustion Engine
Stirling engine uses an external heat source that could be concentrated solar energy through the use of parabolic troughs, flame, combustion of fuel etc, this heat energy flows in and out through the walls and creates a temperature difference which is the key in the operation of the Stirling engine. Due to the external heat source it is known as external combustion engine in contrast to internal combustion engine where the heat source is the combustion of fuel inside the working fluid. Stirling engine uses a permanently sealed gaseous working fluid (air, helium or hydrogen) much like a refrigerant or air‐conditioner.
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DESIGN AND FABRICATION OF A STIRLING CYCLE ENGINE
Basics Of Stirling Engine
In a Stirling engine, a fixed amount of a gas is sealed inside the engine. The Stirling cycle involves a series of events that change the pressure of the gas inside the engine, causing it to do work. There are several properties of gases that are critical to the operation of Stirling engines: If you have a fixed amount of gas in a fixed volume of space and you raise the temperature of that gas, the pressure will increase. If you have a fixed amount of gas and you compress it (decrease the volume of its space), the temperature of that gas will increase.
2.8
The Stirling Engine Cycle
The Stirling cycle engine consists of four thermodynamic process cycles as show in Figure 2‐1. 1‐2
Constant Volume Heat Addition
2‐3
Isothermal Expansion
3‐4
Constant Volume Heat Rejection
4‐1
Isothermal Compression
Figure 2‐1 Ideal Stirling Cycle
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DESIGN AND FABRICATION OF A STIRLING CYCLE ENGINE
2-3 Isothermal Expansion
The expansion‐space and associated heat exchanger are maintained at a constant high temperature, and the gas undergoes isothermal expansion absorbing heat from the hot source.
2.8.2
3-4 Constant Volume Heat Rejection
Constant ‐volume (known as iso‐volumetric or isochoric) heat‐removal. The gas is passed through the regenerator, where it cools transferring heat to the regenerator for use in the next cycle.
2.8.3
4-1 Isothermal Compression
The compression space and associated heat exchanger are maintained at a constant low temperature so the gas undergoes isothermal compression rejecting heat to the cold sink.
2.8.4
1-2 Constant Volume Heat Addition
Constant ‐Volume (known as iso‐volumetric or isochoric) heat‐addition. The gas passes back through the regenerator where it recovers much of the heat transferred in 2 to 3, heating up on its way to the expansion space.
2.9
Operation of Stirling Cycle Engine
A simple stirling engine uses two cylinders and two pistons: power piston and displacer piston. The vertical cylinder (see Figure 2‐2) is constantly heated up on the top while it is cooled at the lower part. The displacer piston does not seal with the walls of cylinder, and lets air pass through. If the displacer piston is now in the lower dead‐center, air is strongly heated up and the pressure pushes on the working piston on the right, which slides to the right now. The left piston (see Figure 2‐3) now gets pulled upward by the coupling of the two pistons. Air is strongly cooled, and together with compression work from the flywheel the working piston is brought again to the left, the displacer piston slides down and the air is heated up again.
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Figure 2‐2 Operation of Ideal Stirling Cycle Engine
Figure 2‐3 Operation of Ideal Stirling Cycle Engine
(Displacer at the Lower‐Dead Center)
(Displacer at the Upper‐Dead Center)
2.10
How To Increase The Power Output Of A Stirling Engine
The stirling engine only makes power during the first part of the cycle. There are two main ways to increase the power output of a stirling cycle: Increase power output in stage one ‐ In part one of the cycle, the pressure of the heated gas pushing against the piston performs work. Increasing the pressure during this part of the cycle will increase the power output of the engine. One way of increasing the pressure is by increasing the temperature of the gas. A look at a two‐ piston Stirling engine later in this article, shows how a device called a regenerator can improve the power output of the engine by temporarily storing heat. Decrease power usage in stage three ‐ In part three of the cycle, the pistons perform work on the gas, using some of the power produced in part one. Lowering the pressure during this part of the cycle can decrease the power used during this stage of the cycle (effectively increasing the power output of the engine). One way to decrease the pressure is to cool the gas to a lower temperature. The four phases of the cycle are explained in a clear manner as follows:
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Figure 2‐4 Expansion (Driving the Power Piston Upward)
Expansion The majority of the gas is in contact with the warmer plate. The gas heats and expands, driving the power piston upward (see Figure 2‐4)
Figure 2‐5 Transfer of Warm Gas to the Upper Cool end
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Transfer Flywheel momentum carries the displacer downward, transferring the warm gas to the upper, cool end of the cylinder (see Figure 2‐5).
Figure 2‐6 Contraction (Driving the Power Piston Downward)
Contraction Now the majority of the gas is in contact with the cool plate. The gas cools and contracts, drawing the power piston downward (see Figure 2‐6)
Figure 2‐7 Transfer of Cooled Gas to the Lower Hot End
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Transfer Flywheel momentum carries the displacer up, transferring the cooled gas back to the lower, hot end of the cylinder(see Figure 2‐7).
2.10.1 Pressurization In most high power Stirling engines, both the minimum pressure and mean pressure of the working fluid are above atmospheric pressure. This initial engine pressurization can be realized by a pump, or by filling the engine from a compressed gas tank, or even just by sealing the engine when the mean temperature is lower than the mean operating temperature. All of these methods increase the mass of working fluid in the thermodynamic cycle.
2.10.2 Lubricants and friction At high temperatures and pressures, the oxygen in air‐pressurized crankcases, or in the working gas of hot air engines, can combine with the engine’s lubricating oil and explode. Thus, non‐lubricated, low‐coefficient of friction materials (such as graphite), with low normal forces on the moving parts, are preferred, especially for sliding seals. At times sliding surfaces are avoided altogether by using diaphragms for sealed pistons. These are some of the factors that allow Stirling engines to have lower maintenance requirements and a longer life than internal‐combustion engines.
2.11
Comparison Of Stirling Engine With An Internal Combustion Engine
2.11.1 Advantages
•
In contrast to internal combustion engines, they can use renewable heat sources more easily.
•
Are quieter than internal combustion engines.
•
More reliable with lower maintenance dues to lesser moving components.
•
More efficient and cleaner (creation of pollutants such as NOx can be avoided).
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Since the fuel is burned slowly and constantly outside the engine, there are no explosions to muffle. Thus there are no violent vibrations.
•
A Stirling cycle is truly reversible (this means that if you heat and cool the heat exchangers of the engine you get power out or if you power the engine you get heating or cooling out).
•
Most Stirling engines have the bearing and seals on the cool side of the engine, and they require less lubricant and last longer than other reciprocating engine types.
•
No valves are needed.
•
A Stirling engine uses a single‐phase working fluid which maintains an internal pressure close to the design pressure, and thus for a properly designed system the risk of explosion is low. In comparison, a steam engine uses a two‐phase gas/liquid working fluid, so a faulty relief valve can cause an explosion.
•
Since they run without an air supply, they can be used for air‐independent propulsion in submarines.
•
Easy to start, though slowly after warming up.
2.11.2 Disadvantages
•
Lower power output as compared to an internal combustion engine of the same size.
•
Gas leakage may pose design problems.
•
The Stirling engine must successfully contain the pressure of the working fluid, where the pressure is proportional to the engine power output/temperature. In addition, the expansion‐side heat exchanger is often at very high temperature, so the materials must resist the corrosive effects of the heat source, and have low creep.
2.12
Applications Of Stirling Engine
Since stirling engines employ external combustion and are quieter, cleaner and more efficient than internal combustion engines, thus they are used where use of internal
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combustion engines is either impractical or unfeasible. From cooling microchips to powering submarines, there uses are various. The following are a few practical applications of stirling of stirling engines: As a heat pump Since the stirling cycle is reversible, therefore if the crankshaft of the stirling engine is supplied with mechanical power, then it can act as a heat pump with the result that the sink of the of the engine will experience a drop in temperature and the source will experience an increase in temperature. This process may be employed for domestic air‐conditioning and heating. Power generation via utilization of waste of waste heat in domestic water heaters It is possible to generate electricity by employing a stirling engine that utilizes waste heat from a domestic water heater. However, this is not practical since stirling engines run on very high temperatures whereas the waste generated by such heaters is mostly warm and not hot. Generation of electricity of electricity via solar energy A stirling engine, with its source end placed at the focal point of a of a parabolic trough, can use the focused rays of the sun to drive the engine mechanism and generate electrical power. Care must be taken to ensure that the material used at the source can withstand the extreme temperatures generated. Power generation in submarines Stirling engines are a better alternative to diesel engines for submarines since they are quieter and do not experience heavy vibrations. They carry compressed oxygen to allow fuel combustion. Nuclear power generation The steam turbines of nuclear power plants may be replaced with stirling engines since they are more efficient and require less maintenance. It is also theorized that spacecraft
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on lengthy space missions may generate electricity for themselves by using a stirling engine with a nuclear fuel rod as the heat source and space itself as itself as the sink. Aircraft and automobile engines Due to their low power‐to‐weight ratios and long start‐up time, stirling engines are not yet feasible for automobiles. However they do hold some promise for aircraft propulsion if high power density and low cost can be achieved. They are quieter, less polluting, gain efficiency with altitude due to lower ambient temperatures, are more reliable due to fewer parts and the absence of an ignition system, produces much less vibration (meaning airframes last longer). Microchip cooling Miniature Stirling engine cooling systems for personal computer chips have been developed that use the waste heat from the chip to drive a fan in order to cool it.
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CHAPTER 3
DESIGN SELECTION 3.1
Configurations of Stirling of Stirling Engine
Stirling engines are distinguished according to the motion of air between the hot and cold sides of the of the cylinder. Two types of configurations of configurations are used:
•
Alpha‐type stirling engines
•
Displacer‐type stirling engines (Beta and Gamma).
3.2
Alpha Stirling engine
An alpha Stirling engine contains two power pistons in separate cylinders, one hot and one cold. The hot cylinder is situated inside the high temperature heat exchanger and the cold cylinder is situated inside the low temperature heat exchanger as shown in Figure 3‐1. This type of engine has a high power‐to‐volume ratio but has technical problems due to the usually high temperature of the of the hot piston and the durability of its of its seals.
Figure 3‐1 Alpha Engine Configuration
3.2.1
Advantages
•
High power‐to‐volume ratio
•
Relatively simple design as compared to the beta type stirling engine.
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FINAL YEAR PROJECT REPORT 3.2.2
DESIGN AND FABRICATION OF A STIRLING CYCLE ENGINE
Disadvantages
•
Causes technical problems due to the high temperature of the hot piston
•
Sealing of the hot and cold pistons is a primary problem due to dual pistons
3.2.3 Action of an alpha type Stirling engine The following diagrams do not show internal heat exchangers in the compression and expansion spaces, which are needed to produce power. A regenerator would be placed in the pipe connecting the two cylinders. The crankshaft has also been omitted.
3.3
Beta Stirling engine
A beta Stirling engine has a single power piston arranged within the same cylinder on the same shaft as a displacer piston as shown in Figure 3‐2. The displacer piston is a loose fit and does not extract any power from the expanding gas but only serves to shuttle the working gas from the hot heat exchanger to the cold heat exchanger. When the working gas is pushed to the hot end of the cylinder it expands and pushes the power piston. When it is pushed to the cold end of the cylinder it contracts and the momentum of the machine, usually enhanced by a flywheel, pushes the power piston the other way to compress the gas.
Figure 3‐2 Beta Engine Configuration
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3.3.1 Advantages
•
Just one cylinder needs to be sealed.
•
Beta type avoids the technical problems of hot moving seals.
3.3.2
•
Disadvantages Containing the moving power and displacer pistons in one cylinder poses design problems.
3.3.3 Action of a Beta Type Stirling Engine Again, the following diagrams do not show internal heat exchangers or a regenerator, which would be placed in the gas path around the displacer.
3.4
Gamma Stirling Engine
A gamma stirling engine is simply a beta Stirling in which the power piston is mounted in a separate cylinder alongside the displacer piston cylinder, but is still connected to the same flywheel as shown in Figure 3‐3. The gas in the two cylinders can flow freely between them and remains a single body.
Figure 3‐3 Gamma Engine Configuration
3.4.1 Advantages
•
Mechanically simpler in design when compared with a beta type engine due to the power piston and displacer being in separate cylinders.
•
Sealing is relatively easier.
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• 3.5 I
DESIGN AND FABRICATION OF A STIRLING CYCLE ENGINE
Avoids the technical problems of hot moving seals.
Disadvantages Produces a lower compression ratio.
Weighting Matrix for Stirling Engine Types
CRITERIA
A
B
C
D
E
TOTAL
WEIGHTAG
D A B C D E
E EASE OF SEALING DESIGN SIMPLICITY HOT MOVING SEALS COMPRESSION RATIO POWER TO VOLUME RATIO
1 0 0 0 0
0 0 0
1 1 0 0
1 1 1
1 1 1 1
4 3 2 1 0 10
0
0.4 0.3 0.2 0.1 0 1
Table 3‐1 Weighting Matrix for Stirling Engine Types
3.6
Rating Matrix for Stirling Engine Types
CRITERIA
EASE OF SEALING DESIGN SIMPLICITY PROBLEM OF HOT MOVING COMPRESSION RATIO POWER TO VOLUME RATIO
WEIGHTA
CONCEP
RATING
0.4 0.3 0.2 0.1 0
a 1 2 3 3 3
b 1. 0. 0. 0. 0 1.
b 3 1 1 2 2
c 3 3 1 1 1
a 0.4 0.6 0.6 0.3 0 ∑ 1.9
c 1.2 0.9 0.2 0.1 0 2.4
Table 3‐2 Rating Matrix for Stirling Engine Types
LEGEND a Alpha
1 Low
b Beta
2 Medium
c Gamma
3 High
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3.6.1
DESIGN AND FABRICATION OF A STIRLING CYCLE ENGINE
Pie Charts (Based on the data from the rating matrix)
EASE OF SEALING
DESIGN SIMPLICITY Alpha 14%
Gamma 43% Beta 43%
Figure 3‐4 Ease of Sealing
PROBLEM OF HOT MOVING SEALS Gamma 20%
Beta 20%
Alpha 60%
Figure 3‐6 Problem of Hot Moving Seals
Alpha 33% Gamma 50% Beta 17%
Figure 3‐5 Design Simplicity
COMPRESSION RATIO Gamma 17%
Beta 33%
Alpha 50%
Figure 3‐7 Compression Ratio
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FINAL YEAR PROJECT REPORT 3.6.2
DESIGN AND FABRICATION OF A STIRLING CYCLE ENGINE
Final analysis for the choice of configuration of Stirling Engine
After going through the analysis of the rating matrix (refer to Table 3‐1 and Table 3‐2) and pie charts shown in (Figure 3‐4 to Figure 3‐7) it can be seen that the rating of gamma stirling engine is quite higher (i.e. 2.4) as compared to the other configuration namely alpha and beta which have a rating of 1.9 each. So depending on these rating, the final choice for configuration of stirling engine is Gamma stirling engine. It is noteworthy to mention here that while creating these matrices priorities were given to the ease of sealing and design simplicity.
3.7
Choice Of Gas (Working Fluid)
Though just about any gas can be used as the working fluid in a stirling engine, however the most popular choices are hydrogen, helium or air (primarily nitrogen). The choice of the working fluid is very essential to the overall efficiency, power output, safety and performance of the stirling engine. The used gas should have the following characteristics:
•
A low heat capacity, so that a given amount of transferred heat leads to a large increase in pressure.
•
Low viscosity and high thermal conductivity.
•
Low rate of diffusivity diffusion rate.
•
Should not be a flammable gas, which is a major safety concern.
•
Should be cheap.
•
Should be easy available.
•
Should not condense at the sink temperature like CFCs.
Let us analyze the three gases that are available to us for selection:
3.7.1
Hydrogen
Advantages
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DESIGN AND FABRICATION OF A STIRLING CYCLE ENGINE
Its low viscosity and high thermal conductivity make it the most powerful working gas, primarily because the engine can run faster than with other gases.
•
Relatively cheaper than helium.
•
Can be generated by electrolysis of water, the action of steam on red hot carbon ‐based fuel or by the reaction of acid on metal.
•
Has a low heat capacity, meaning a given amount of transferred heat leads to a large increase in pressure.
Disadvantages
•
Hydrogen’s high diffusion rate associated with its low molecular weight causes it to diffuse through the walls of the cylinder particularly at high temperatures, thus reducing its pressure and mass.
•
Hydrogen also causes metals to become brittle.
•
Hydrogen is a flammable gas, which is a safety concern, although the quantity used is very small, and it is arguably safer than other commonly used flammable gases.
3.7.2
Helium
Advantages
•
Best gas because of its very low heat capacity.
•
Non‐flammable as it’s an inert gas.
•
Low viscosity and high thermal conductivity.
Disadvantages
•
High diffusivity but not as high as hydrogen’s.
•
Not available easily.
•
Very expensive.
3.7.3 Air (primarily nitrogen) Advantages
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•
Low diffusivity.
•
Easily available.
•
Very cheap.
•
Is not a flammable gas (though the oxygen in the air supports combustion).
Disadvantages
•
The oxygen in a highly pressurized air engine can cause fatal accidents caused by lubricating oil explosions.
•
Relatively higher viscosity and lower thermal conductivity.
•
Highest heat capacity of the three available gases.
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3.8 I D A B C D E F G
DESIGN AND FABRICATION OF A STIRLING CYCLE ENGINE
Weighting Matrix For Working Fluid
CRITERIA
A B C D E F G
AVAILABILITY COST (CHEAP) NON‐FLAMMABLE LOW DIFFUSIVITY LOW VISCOSITY HIGH THERMAL CONDUCTIVITY LOW HEAT CAPACITY
0 0 0 0 0 0
1 1 1 0 0 0 0 0 0 0 0 0
1 1 1 1 1 1 1 1 1 1 1 0 1 0 0 0 0 0
1 1 1 1 1 1 ∑
TOTA L 6 5 4 3 2 1 0 21
WEIGHTAGE
0.2857143 0.2380952 0.1904762 0.1428571 0.0952381 0.047619 0 1
Table 3‐3 Weighting Matrix for Working Fluid
3.9
Rating Matrix For Working Fluid
CRITERIA
AVAILABILITY COST (CHEAP) NON‐ LOW LOW VISCOSITY HIGH THERMAL LOW HEAT
WEIGHTAG E
0.28571428 0.23809523 0.19047619 0.14285714 0.09523809 0.04761904 0
CONCEPT
a 3 3 3 3 1 1 1
b 2 2 1 1 3 3 3
c 1 1 3 2 3 3 3 ∑
RATING
a 0.85714285 0.71428571 0.57142857 0.42857142 0.09523809 0.04761904 0 2.71428571
b 0.571428571 0.476190476 0.19047619 0.142857143 0.285714286 0.142857143 0 1.80952381
c 0.28571428 0.23809523 0.57142857 0.28571428 0.28571428 0.14285714 0 1.80952381
Table 3‐4 Rating Matrix for Working Fluid
LEGEND a Air
1 Low
b Hydrogen
2 Medium
c Helium
3 High
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3.9.1
DESIGN AND FABRICATION OF A STIRLING CYCLE ENGINE
Pie Charts (Based on the data from the rating matrix of working fluid)
AVAILABILITY
COST(CHEAP)
Helium 17%
Helium 17% Air 50%
Hydrogen 33%
Air 50% Hydrogen 33%
Figure 3‐9 Cost (cheap)
Figure 3‐8 Availability
NON‐FLAMMABLE
Helium 43%
LOW DIFFUSIVITY
Helium 33%
Air 43%
Hydrogen 14%
Air 50%
Hydrogen 17%
Figure 3‐10 Non‐Flammable
LOW VISCOSITY
Figure 3‐11 Low Diffusivity
Helium 43% Hydrogen 43%
Figure 3‐12 Low Viscosity
HIGH THERMAL CONDUCTIVITY
Air 14%
Air 14%
Helium 43% Hydrogen 43%
Figure 3‐13 High Thermal Conductivity
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FINAL YEAR PROJECT REPORT 3.9.2
DESIGN AND FABRICATION OF A STIRLING CYCLE ENGINE
Final analysis for the choice of gas
The utmost priority in the selection of the working fluid after going through the rating matrix (refer to Table 3‐3 and Table 3‐4 and also the pie charts as shown in Figure 3‐8 to Figure 3‐13) is to ensure that it is not flammable and has a low rate of diffusivity since safety and containment of the gas are to two vital aspects of this project. Also it must be cheap (due to financial constraints) and be easily available. Since it is not desired to achieve a high power output thus low heat‐capacity, low viscosity and high thermal conductivity do not fall within the primary criteria. Keeping all these factors in mind, the working fluid that suits is Air.
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CHAPTER 4
THERMAL ANALYSIS 4.1
Calculation of the Adiabatic Flame Temperature|
4.1.1
Introduction
The determination of the adiabatic flame temperature is important because it indicates the maximum temperature that can be used at the source. Also, it is useful in determining what the choice of fuel should be. For example, if the required temperature o
o
of the source is to be 1000 C and the adiabatic flame temperature of Fuel A is 900 C o
and that of Fuel B is 1200 C, then Fuel B is to be used as the maximum temperature as compared to Fuel A that is less than the required temperature at the source. If Fuel B is employed, then after convective heat transfer losses, the temperature of the flame will o
drop down to the required source of temperature of 1000 C.
4.1.2 Assumptions 1. Steady flow combustion process 2. Combustion chamber is adiabatic (Q=0) 3. There are no work interactions 4. Air and the combustion gases are ideal gases 5. Changes in kinetic and potential energies are negligible 6. Combustion reaction is stoichiometric (i.e. 100% theoretical air) o
7. Standard conditions of 1 atm and 25 C apply
4.1.3
Calculations for liquid kerosene (C12H26)
Combustion equation: C12H26(l) + 18.5(O2+3.76N2) 12CO2 + 13H2O + 69.56N2 Enthalpy of products = Enthalpy of reactants (Hprod = Hreact)
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Note: o
All values of hf and h have been taken from enthalpy tables. The values of hf for elements are taken to be zero.
∑ Np (hf + h ‐ ho) = ∑ Nr (hf + h ‐ ho) 12(‐393,520 + hCO2 – 9364) + 13(‐241,820 + hH20 – 9904) + 69.56(0 + hN2 – 8669) 0
= 1(‐24,149 + h298 – h
298)
0
+ 18.5(0 + h298 – h
298)
0
+ 69.56(0 + h298 – h
298)
12hCO2 + 13hH2O + 69.56hN2 = 8685886.64 kJ Divide by total number of moles to get 91855.82 kJ/kmol For N2 this value corresponds to T = 2741.4K For H2O this value corresponds to T = 2179.23K For CO2 this value corresponds to T = 1851K Since majority of the moles are of N2, the temperature should be close to 2741.4K but somewhat under it. After trying different values of temperature under 2741.4K it is determined between which two temperatures the value of sum of the enthalpies of the products fluctuates about the value of the sum of the enthalpies of the reactants. For T = 2700K
∑Hprod = 9562976.68 kJ which is greater than ∑Hreact = 8685886.64 kJ For T = 2650K
∑Hprod = 9362504.28 kJ which is greater than ∑Hreact = 8685886.64 kJ For T = 2450K
∑Hprod = 8563731.44 kJ which is less than ∑Hreact = 8685886.64 kJ For T = 2500K
∑Hprod = 8762922.36 kJ which is greater than ∑Hreact = 8685886.64 kJ
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FINAL YEAR PROJECT REPORT 4.1.4
DESIGN AND FABRICATION OF A STIRLING CYCLE ENGINE
Conclusion
It is clear that the value of the adiabatic flame temperature lies between 2450K and 2500K. After interpolation, it is found to be 2480.66K
4.2
Calculations for methane (CH4)
Combustion equation: CH4 (g) + 2(O2+3.76N2) CO2 + 2H2O + 7.52N2 Enthalpy of products = Enthalpy of reactants (Hprod = Hreact) o
Note: All values of hf and h have been taken from enthalpy tables. The values of hf for elements are taken to be zero.
∑ Np (hf + h ‐ ho) = ∑ Nr (hf + h ‐ ho) (‐393,520 + hCO2 – 9364) + 2(‐241,820 + hH20 – 9904) + 7.52(0 + hN2 – 8669) 0
= 1(‐74,850 + h298 – h
298)
+ 2(0 + h298 – h
0 298)
+ 7.52(0 + h298 – h
0 298)
hCO2 + 2hH2O + 7.52hN2 = 896672.88 kJ Divide by total number of moles to get 85235 kJ/kmol For N2 this value corresponds to T = 2561.5K For H2O this value corresponds to T = 2051.5K For CO2 this value corresponds to T = 1741K Since majority of the moles are of N2, the temperature should be close to 2561.5K but somewhat under it. After trying different values of temperature under 2561.5K it is determined between which two temperatures the value of sum of the enthalpies of the products fluctuates about the value of the sum of the enthalpies of the reactants. For T = 2500K
∑Hprod = 973043.12 kJ which is greater than ∑Hreact = 896672.88 kJ For T = 2450K
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DESIGN AND FABRICATION OF A STIRLING CYCLE ENGINE
∑Hprod = 950825.48 kJ which is greater than ∑Hreact = 896672.88 kJ For T = 2300K
∑Hprod = 884516.52 kJ which is less than ∑Hreact = 896672.88 kJ For T = 2350K
∑Hprod = 906552.92 kJ which is greater than ∑Hreact = 896672.88 kJ 4.2.1
Conclusion
It is clear that the value of the adiabatic flame temperature lies between 2300K and 2350K. After interpolation, it is found to be 2327.6K
4.2.2
Final conclusion with respect to the choice of fuel
Since there is very little difference in the values of the adiabatic flame temperatures of the two fuels and since both temperatures are sufficiently higher than the required o
source temperature of 720 C, methane is employed as the fuel for the following reasons: 1. It is easily available 2. Its flow can be regulated easily using a valve 3. It burns more cleanly than kerosene
4.3
Heat Transfer Calculation
4.3.1
Formulas to be used
( C/W) ( C/W) Thermal convective resistance, Thermal conductive resistance,
o
o
(W/m . C) Convective heat transfer coefficient, Rayleigh number,
β
υ
2 o
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DESIGN AND FABRICATION OF A STIRLING CYCLE ENGINE
For horizontal plate with hot side facing down: Nusselt number,
0.27.
For horizontal plate with hot side facing up: Nusselt number,
0.54. (For Ra 10
4
7
‐ 10 )
For internal side of the cylinder at the base: Nusselt number,
0.4.
Volume expansion coefficient, β
(K ) ‐1
(W) Indicated power, 4.3.2
Data External Diameter (m) Internal Diameter (m) Height (m) Thickness (m) o Tc (K) and ( C) Temp Ratio (Tc/Th) o Th (K) and ( C) o Tf (K) and ( C)
0.05506 0.05056 0.0872 0.00225 298 25 0.3 993.3333333 720.3333333 645.6666667 372.6666667
Table 4‐1 Data Input
For horizontal plate with hot side facing down: Properties of air at Tf = 372.5 oC and 1 atm (Table A‐15) 2o k (W/m . C) 0.048533 Pr k of steel @ 993K 25 ‐1 v (m2/s) 0.0000580980 B (K ) Ra 362678.18090 1/4 Nu = 0.27Ra 6.62588847 h=(k/Dext)(Nu) 5.840433075
0.694195 0.001548787
Table 4‐2 For Horizontal Plate with Hot Side Facing Down
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DESIGN AND FABRICATION OF A STIRLING CYCLE ENGINE
For horizontal plate with hot side facing up: o
Assume external surface temperatures at the top of the displacer ( C) and (K) Ts o
Ts ( C) 600 500 300 250 200 150 100 75 55 30
Ts (K) 873 773 573 523 473 423 373 348 328 303
Table 4‐3 Assumed Ts o
The corresponding film temperatures in K and C are: K 585.5 535.5 435.5 410.5 385.5 360.5 335.5 323 313 300.5
o
C 312.5 262.5 162.5 137.5 112.5 87.5 62.5 50 40 27.5
Table 4‐4 Film Temperature at Ts
Corresponding air properties at the respective film temperatures: o
k air @ 27.5 C o Pr air at 27.5 C o V air @ 27.5 C o B air @ 27.5 C k steel @ 303 K Ra Nu h
0.025695 0.7289 0.00001585 0.003327787 14.86 79051.94752 9.054654911 4.225560442
o
k air @ 40 C o Pr air at 40 C o V air @ 40 C o B air @ 40 C k steel @ 328 K Ra Nu h
0.02662 0.7255 0.00001702 0.003194888 15.34 393072.67204 13.52109837 6.537080253
Table 4‐5 Air Properties at Various Tf
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FINAL YEAR PROJECT REPORT o
k air @ 50 C o Pr air at 50 C V air @ 50 oC o B air @ 50 C k steel @ 348 K Ra Nu h o k air @ 87.5 C o Pr air at 87.5 C V air @ 87.5 oC o B air @ 87.5 C k steel @ 423 K Ra Nu h
o
DESIGN AND FABRICATION OF A STIRLING CYCLE ENGINE 0.02735 0.7228 0.00001798 0.003095975 15.705 566740.01803 14.81629886 7.359712567 0.0300625 0.71375 0.00002175 0.002773925 13.09 856662.92389 16.42843723 8.969849148
o
k air @ 62.5 C o Pr air at 62.5 C V air @ 62.5 oC o B air @ 62.5 C k steel @ 373 K Ra Nu h o k air @ 112.5 C Pr air at 112.5 V air @ 112.5 oC o B air @ 112.5 C k steel @473 K Ra Nu h
o
0.0282625 0.7195375 0.0000192075 0.002980626 16.145 713934.08478 15.69669751 8.057172417 0.031825 0.708725 0.00002441 0.002594034 17.745 884165.34491 16.55873409 9.571044539
k air @ 137.5 C Pr air at 137.5 V air @ 137.5 o B air @ 137.5 C k steel @ 523 K Ra Nu h
0.03356625 0.7048 0.0000273 0.002436054 18.65 848765.24234 16.39044167 9.992111561
k air @ 162.5 C Pr air at 162.5 V air @ 162.5 B air @ 162.5 k steel @573 K Ra Nu h
0.03528125 0.701075 0.0000300375 0.002296211 19.4 803450.40882 16.16715227 10.35955941
k air @ 262.5 oC Pr air at 262.5 o V air @ 262.5 C o B air @ 262.5 C k steel @ 773 K Ra Nu h
0.0420475 0.6939 0.0000425 0.001867414 22.25 557995.62058 14.75881393 11.27081781
k air @ 312.5 oC Pr air at 312.5 V air @ 312.5 B air @ 312.5 k steel @ 873 K Ra Nu h
0.0449375 0.69355 0.000049425 0.001707942 23.53 456565.39765 14.03684513 11.45624279
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DESIGN AND FABRICATION OF A STIRLING CYCLE ENGINE
For internal side of the cylinder at the base: o
Assumed base temperature Tu of 718 C (991K):
Table 4‐6 Air Properties at Film Temperatures for Various Ts Values
4.3.3
Calculations for thermal resistance network
Figure 4‐1 1D Heat Transfer Across the Displacer Cylinder
Tflame
Rconv1
Th
Rcond1
Tu
Rpar
Tli
Rcond2
Ts
Rconv2
Figure 4‐2 Thermal Resistive Network Schematic
Page 46
To
FINAL YEAR PROJECT REPORT
DESIGN AND FABRICATION OF A STIRLING CYCLE ENGINE 2
0.002381014
2
0.002007722
Area External m Area Internal m
4.3.4
Calculations for the flame temperature Power = h1(Tflame‐Tu)‐h2(Tli‐ Power (W) =
11.248
Table 4‐7 Thermal Resistances
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DESIGN AND FABRICATION OF A STIRLING CYCLE ENGINE
Intersection of Ts assumed with Ts resistance
Figure 4‐3 Thermal Resistances
Conclusion: From the graph it can be clearly observed that Ts assumed and Ts calculated via the o
thermal resistance network, have a common value at approximately 600 C. Thus the operating point and its associated values are as follows:
Table 4‐8 Various Temperatures Calculated via Thermal Resistance Network
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DESIGN AND FABRICATION OF A STIRLING CYCLE ENGINE
For internal side of the cylinder at the base: o
Base temp C and K
718
991
For cold side of the cylinder with hot side facing up: o
k air @ 312.5 C o Pr air at 312.5 C o V air @ 312.5 C o B air @ 312.5 C k steel @ 873 K Ra Nu h
4.3.5
0.0449375 0.69355 0.000049425 0.001707942 23.53 456565.39765 14.03684513 11.45624279
Calculations for thermal efficiency:
Carnot Efficiency (Maximum theoretical thermal efficiency):
1 ; (where T and T are in Kelvin) 1 298 993 0.7 70% o
h
Thermal Efficiency (Actual Efficiency)
8.43375 0.547993854.79% 15.39022973
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DESIGN AND FABRICATION OF A STIRLING CYCLE ENGINE
CHAPTER 5
SELECTION OF SWEPT VOLUME 5.1
Analysis of Stirling Engine
The analysis of Stirling engines are parted on three methods.
5.1.1
1st -order method
The analysis is based on the use of experimental value and engine size, or the ideal analysis models. For example Schmidt model.
5.1.2
2nd-order method
The analysis takes into consideration losses of various kind. It uses the results of ideal analysis and the losses of various kind.
5.1.3
3rd-order methods
This type of analysis solves homogeneous equations of flow and equations of various kinds of losses.
5.2
The Schmidt Analysis
It is an idealized model which captures the basic and essential features of a stirling engine basically the interconnection between the mechanically constraint motion of the parts and the interconnected or resulting thermodynamically cycle. The work here is basically focused to on finding the maximum indicated cycle work relative to the cycle pressure, relative to the mass to the working fluid or to the total swept volume.
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DESIGN AND FABRICATION OF A STIRLING CYCLE ENGINE
The fore coming calculations and analysis is to select that what should be the ratio of the swept volume of the piston to that of the displacer.
5.2.1
Assumptions of Schmidt Model for Gamma Stirling Analysis
•
The motion of piston and displacer is pure sinusoidal motion.
•
Working fluid in work space is an ideal gas
•
Isothermal hot, cold and dead spaces
•
Uniform instantaneous pressure throughout all the engine spaces
•
No leaking of working gas into or out of the engine.
•
All dead space is treated as being at the arithmetic average of the extreme cycle temperatures.
•
Temperature ratio represents the temperature extremes of the working gas.
•
The mechanism effectiveness is assumed constant throughout the cycle.
•
Limitations in the heat transfer are ignored.
5.2.2
Indicated Work
The closed form of indicated work of Schmidt’s gamma Stirling can be written as follows:
√ 1 κ κ 2κ 1cos 1 W=
Where:
6
κ
It can be seen that the only factors having dimensions is the total swept volume
and
root mean cycle pressure.
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Figure 5‐1 Effect of Increasing Swept Volume Ratio
The Figure 5‐1 shows that increasing the swept volume ratio correspondingly increases indicated work. It can be seen that the indicated work of the largest cycle is relatively higher than the smallest one.
5.2.3
Root Mean Cycle Pressure
can be written as: 2 √
The root mean cycle pressure =
5.2.4
Forced Work
The definition of the forced work of a cycle requires integrating the product of p− pb and dV over those portions of the cycle where they differ in sign. It can be written as follows:
After employing necessary numerical integration techniques and simplification, the following is obtained,
1 ln1 ln 1 Page 52
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Figure 5‐2 Effect of Increasing Size on Forced Work
Forced work depends upon the shape of the cycle and upon the buffer pressure level. It is the work that the mechanism must deliver to the piston to make it move in opposition to the pressure difference across it. Because of losses in transmission through the mechanism, more work, namely Wi (work input) , must be taken from the flywheel to supply W −. As can be seen from Figure 5‐2 that as the indicated work increases with increasing swept volume ratio, so does the forced work, represented as the shaded area. Therefore a careful compromise has to be made regarding the selection of the optimum swept volume ratio.
5.2.5
Shaft Work
The shaft work of Schmidt’s gamma stirling engine is given by:
1 It is worth mentioning here that the maximum indicated output does not ensure getting the maximum shaft or brake output. Since shaft work is not a simple multiple of indicated work but depends upon the shape of the engine cycle and the relative buffer pressure, as well as on the effectiveness of the engine mechanism.
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5.3
1st -Order Analysis Method
5.3.1
Effectiveness & Mechanical Efficiency
Mechanism effectiveness in principle depends in a complex way upon a number of variables. It obviously depends upon the instantaneous position of the parts of the mechanism, which determines the loading on the various joints and hence the acting Coulomb friction forces. Inertial effects due to the velocity and acceleration of parts with appreciable mass also affect the joint loads and friction. Mechanism effectiveness may also depend significantly upon the magnitude of the force applied to the piston as when a friction type other than Coulomb is present in some joints. Clearly, mechanism effectiveness is a non‐negative quantity and cannot exceed unity. There may in fact be portions of an engine cycle where the effectiveness is actually zero. This is the case in the situation where both piston and flywheel put work into the mechanism in certain parts of the cycle. During work input by the piston to the mechanism for transmittal to the flywheel shaft, some work is lost to friction and the reduced amount is actually delivered. This loss is due to the mechanism’s mechanical efficiency. The presence of any forced work always reduces mechanical efficiency to a value below that of the effectiveness of the mechanism.
5.3.2
Compression Ratio
Maximal mechanical efficiency ηms is simply equal to the Effectiveness as long as r ≤ 1 / τ. As no engine can have a better mechanical efficiency than
ηms,
so no engine can run
with a compression ratio beyond the r value where ηms becomes zero. Figure 5‐3 shows graphs of maximal mechanical efficiency
ηms
with respect to r for
2
specific values of E and τ .The smaller E is relative to τ , the faster ηms becomes zero. This means that for engines operating from relatively low temperature heat sources, the range of usable compression ratio is definitely limited. The closer
τ is
to 1, the more
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limited the compression ratio range becomes. This is precisely why low temperature differential engines require low compression ratios.
Figure 5‐3 Graph of Maximum Mechanical Efficiency versus Compression Ratio
On the other hand, if an engine is to operate from a very high temperature source, then τ =
2
T C /T H will be small enough so that E > τ for all practical values of E. In this case, there
is no intrinsic restriction on compression ratio, and it can be chosen to suit any other requirements or desires.
5.3.3
Workspace Charging Effect
In any monomorphic engine with constant mechanism effectiveness, if the charge of its workspace and its buffer pressure are increased by the same factor, then its shaft work also will increase by the same factor, and mechanical efficiency is preserved. An engine in which the buffer pressure never exceeds the workspace pressure will be referred to as being charged above buffer pressure or as buffered from below. There are a number of practical advantages to buffering from below. These advantages include preventing lubricant migration into the workspace, preventing or minimizing bearing load reversals, and perhaps most important, increasing output, albeit at the expense of mechanical efficiency. It often is the case in practice that buffer pressure
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cannot be modified. Charging the workspace alone is the only option to increase the output of such engines. Even when a crankcase is totally enclosed and pressure‐worthy, the other advantages may make charging above buffer pressure desirable. For engines buffered from below, there is no forced work arising during expansion. The forced work occurs over the whole compression process and is simply the absolute compression work minus the area below the buffer pressure line.
Figure 5‐4 PV Diagram of Charged Stirling Engine
The mechanical efficiency (ηm) is a decreasing function of the mass (m) inside the workspace. Therefore the output of the stirling engine can be increased by charging, but it can be done only at the expense of diminished mechanical efficiency.
For an Ideal Stirling engine, the absolute work ratio equals the temperature ratio: W c /W e = T C /T H = τ . Thus, if E2 > τ , cyclic shaft work output will increase indefinitely as the workspace is charged higher and higher above a fixed buffer pressure. Of course, mechanical efficiency will certainly decrease after the engine becomes buffered entirely from below. If, on the other hand, E2 < τ , then shaft output decreases as the workspace is charged above buffer pressure, and eventually the engine will even be unable to run itself.
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FINAL YEAR PROJECT REPORT 5.3.4
DESIGN AND FABRICATION OF A STIRLING CYCLE ENGINE
Dead Space Effects
The amount of dead space reduces the output potential of the stirling engine. The dead volume effect is greater for engines operating at a smaller temperature difference. Figure 5‐5 shows the variation of specific shaft work with increasing dead space over the range from χ = 0 to 10 for a particular engine with
τ =
0.5 and E = 0.7. Note that
performance drops off at a high rate over the entire usual range of relative dead volume, becoming what one might call gradual only for dead volume ratios much higher than ever necessary in practice.
Figure 5‐5 Variation of maximum specific shaft work Ws versus dead space ratio χ
Dead volume effects on brake output are not neutralized by increasing compression ratio, as one might have guessed prior to the analysis.
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FINAL YEAR PROJECT REPORT 5.3.5
DESIGN AND FABRICATION OF A STIRLING CYCLE ENGINE
Conclusion st
Some of the findings important for 1 order stirling engine design are summarized as follows:
•
Maximum shaft output occurs at smaller swept volume ratios than does maximum indicated work.
5.4
•
Less effective mechanisms favor smaller swept volume ratios.
•
Smaller swept volume ratios yield better mechanical efficiency.
•
Low temperature differential engines require small swept volume ratios.
•
Dead volume incurs a high penalty in brake output.
•
Higher engine speeds favor lower swept volume ratios.
•
Dead volume effects cannot be offset by increasing compression ratio.
Design Approach
Before going in to the details of the design, there are few things that must be kept in mind in order to clearly understand the design method presented here. The conventional approach of design, which is referred to as the “bottom‐up” method in which the design is focused towards obtaining the desired output from the device and thus setting other parameters accordingly, is not generally recommended for low‐ power, low temperature differential stirling engines. Therefore the design of Stirling Engine involves a significant question, that is what should be the ratio of swept volume of the power piston to that of the displacer, and what should be the phase angle between them. Thus a need arises for choosing optimum design parameters that would give a handful of power at suitable temperature ratio and good mechanical efficiency. The optimum phase angle is usually easy to adjust or reset and so the best phase angle can be experimentally determined to the engine operator’s satisfaction, and also the engine’s performance is not extremely sensitive to phase angle. But the swept volume ratio cannot be easily changed without affecting other engine features that might themselves affect output such as overall size and dead volume.
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Therefore an optimum swept volume ratio must be chosen to maximize the work per cycle. st
Design of the Stirling Engine is based on 1 order analysis method. Using this method different designing parameters which are stated above are being analyzed through the aid of experimental data and then plotted to study their behavior. The following data and graph shows the effect of swept volume ratio on the indicated power, shaft work, forced work and then connectively to the mechanical efficiency. Since the required temperature ratio was determined through the heat transfer analysis. Also setting the other parameters which are quite independent of each other as,
τ= 0.3 α= 90 E= 0.75
χ=0.2
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Table 5‐1 Engine Operating Parameter as a Function of Volume Ratio
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Figure 5‐6 Work and Mechanical Efficiency as a Function of Swept Volume Ratio at τ=0.2
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Figure 5‐7 Work and Mechanical Efficiency as a Function of Swept Volume Ratio at τ=0.3
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Figure 5‐8 Work and Mechanical Efficiency as a Function of Swept Volume Ratio at τ=0.4
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Actual Trend of Graph
Figure 5‐9 Actual Graphical Representation from Experimental Data
The graphs presented in (Figure 5‐6 to Figure 5‐8) above exhibit a similar trend as indicated by the actual curves of Figure 5‐9. Since the heat transfer analysis yielded the temperature ratio to be τ= 0.3, so looking in the graph for the stated temperature ratio, two swept volume ratios namely κ= 0.7 and κ= 2.1 yield good mechanical efficiency and allow lesser forced work. But κ= 0.7 is selected to be the optimum swept volume since limited heat transfer rates strongly favor choosing a small κ and also a smaller κ would allow the engine to start at a lower hot end temperature. Moreover, the ease of availability of the cylinder sleeves with swept volumes of 70 and 100cc.
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DESIGN AND FABRICATION OF A STIRLING CYCLE ENGINE
Selection of Compression Ratio
Table 5‐2 Engine Operating Parameters as a Function of Compression Ratio
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Figure 5‐10 Mechanical Efficiency as a Function of Compression of Compression Ratio at T=0.3
Now an optimum compression ratio is to be set, that would give the best mechanical efficiency. Keeping the already determined parameters fixed, and varying the compression ratio, gives the optimum value to be 3.3, as indicated in the table.
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DESIGN AND FABRICATION OF A STIRLING CYCLE ENGINE
Calculations (At optimum (At optimum values)
After getting the swept volume ratio and compression selected, calculations of root of root mean cycle pressure, indicated work, shaft work, forced work and mechanical efficiency can be shown.
5.7.1
Values of Designed of Designed Parameters
Displacer Volume
=100cc=0.0001
Temperature ratio τ=0.3 Swept Volume Ratio 6=0.7 Compression ratio r=3.3
Phase Angle α=90° Dead Volume Ratio χ = 0.2 Effectiveness E=0.75 Cold side Temperature = 300K Hot side Temperature =
= 1000 .
5.7.2
Total Volume
1 6 10.70.0001 1.7e 4
Since
‐
5.7.3
Mass of Working of Working Fluid (m)
= x 1.205(1.7e 4) 0.00020485 kg ‐
ρ=1.205
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FINAL YEAR PROJECT REPORT 5.7.4
DESIGN AND FABRICATION OF A STIRLING CYCLE ENGINE
Root Mean Root Mean Cycle Pressure ( )
1 κ & κ κ 2κ 1 cos cos 1 1 0.3 0.7 ... 10.3 cos90° 0.7 20.710.3 cos90° 10.3 10.3 2.184615385 0.989949 4937 = . .. =181.1355857 Now: √ .√ √ .. . Where:
5.7.5
Indicated Work (W) Work (W)
W √ .° . . .. . . . √ .. .. . 6
6
5.7.6
Forced Work
1 ln1 ln1 0.00020485)( 0.28710000.3ln0.3 10.3ln10.3 ln13.3ln0.3 5.7.7
Shaft Work Shaft Work
0.7556.748123e 3) . 0.756.864507e 7 . . e 3 kilo joule ‐
‐
5.7.8
‐
‐
Mechanical Efficiency
..
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CHAPTER 6
KINETICS & TURNING MOMENT 6.1
Kinetics and Turning Moment
Reciprocating engines employ a very popular mechanism known as slider crank mechanism. Kinematic analysis of the slider‐crank mechanism helps to answer many questions pertaining to the motion of various links of the mechanism viz. displacement, velocity and accelerations of driven members like connecting rod and piston, while kinetics involves the study of various forces acting on the mechanism. Figure 6‐1 shows arrangement of crank‐angle mechanism.
Figure 6‐1 Crank‐angle Mechanism
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The Figure 6‐2 indicates various forces acting on the slider‐crank mechanism:
Figure 6‐2 Kinetics of Flywheel
6.1.1 Assumptions Following are some assumptions used in the analysis of the forces in the slider‐crank mechanism:
•
The weight of the connecting rod is neglected in the analysis.
•
The unbalance of rotating masses is balanced using counterweight.
•
Frictional effects of link joints and gravitational effects are ignored.
6.1.2
Calculations
Earlier the following parameters had been developed, related to the operation of the stirling engine: Tc=300K
τ=0.3 κ=0.7 X=0.989926563 Y=2.184615385
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χ=0.2 E=0.75 r=3.3 Pb=100 Kpa m=0.00020485 kg
Now the design of the stirling engine focuses on obtaining a shaft power output of at a crankshaft speed of, having following parameters. l= 93mm 3
Vd= 0.00007 m 3
V1= 0.0001 m = Displacer swept volume B= 47.5mm
α=90° The displaced volume Vd is given by,
π 4 Thus,
0.0007 π 4 0.0475 or,
39.50217 It is known that in a reciprocating engine the stroke “L” and crank radius “c” are related as,
2 or,
19.75108 Similarly,
π 4 π 4 0.0469 Page 71
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0.00172757 And,
0.00172757 0.00000675 0.00172082 m Also,
1.20247 4.7086 The instantaneous pressure “p” inside the cylinder at any crank position is given by,
2 θ φ where,
φ
√
κ 1 τ α 0.7 10.390° 0.7 1 τ α 10.390° 0.7 Using values of A and B the following is obtained,
φ
7 45° 0.785398 √ 0.70.0.7
Now putting all the values of the required constants determined above, into the equation for the instantaneous pressure for various crank angle position. Net load on the piston is given by,
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p1 is taken to be the instantaneous pressure at a certain crank angle, while p2 is taken to be equal to the buffer pressure, which is atmospheric in the design. Inertia force is given by,
900 2 Weight of reciprocating parts is given by,
Then piston effort is determined as,
Finally Turning moment or Torque can be obtained as,
2√ 2 These parameters can now be obtained at different crank positions as shown in Table 6‐1 and then the turning moment diagram for the stirling engine is obtained. The mean resisting torque (Tmean) can be found as:
5.20π 61 0.805 .
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Table 6‐1 Parameters at Different Crank Positions
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Figure 6‐3 Turning Moment Diagram
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CHAPTER 7
SIMULATION OF STATIC TEMPERATURE
7.1
Modeling
In order to verify the static temperature distribution within the displacer cylinder, a simplified 2D‐model of the cylinder was analyzed using Finite Element software ANSYS. It should be kept in mind that the displacer is assumed to be absent in the analytical solution, in order to make the laborious task easy. Accompanying Figure 7‐1 shows modeling of 2D Cylinder in Ansys where the green region depicts the modeling of air whereas the thin purple region depicts the modeling of Cylinder.
Figure 7‐1 Modeling of 2D Cylinder in ANSYS
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DESIGN AND FABRICATION OF A STIRLING CYCLE ENGINE
Meshing
The two areas highlighted in separate colors in the figure 6‐2 are uniformly meshed in order to achieve accuracy of results.
Figure 7‐2 Meshing of 2D Cylinder in ANSYS
7.3
Graphical Distribution
Temperature distribution profile can finally be obtained and the results can be readily compared against those obtained from calculations. Figure 7‐3 shows contours of Temperature variation along the cylinder height.
Figure 7‐3 Contours of Temperature Distribution
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DESIGN AND FABRICATION OF A STIRLING CYCLE ENGINE
Temperature Profile
The solver enables a graph to be plotted between the temperature and the distance along the center line from the base of the cylinder. Figure 7‐4 shows the graph of temperature variation along cylinder height.
Figure 7‐4 Graph of Temperature Variation Along Cylinder Height
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CHAPTER 8
CAD DRAFTS
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CHAPTER 9
INSTRUMENTATION 9.1
Proximity Sensor
A proximity sensor is a sensor able to detect the presence of nearby objects without any physical contact. A proximity sensor often emits an electromagnetic field or a beam of electromagnetic radiation (infrared, for instance), and looks for changes in the field or the return signal. The maximum distance that this sensor can detect is defined "nominal range". Proximity switches open or close an electrical circuit when they make contact with or come within a certain distance of an object. Proximity switches are most commonly used in manufacturing equipment, robotics, and security systems. There are four basic types of proximity switches: 1. Infrared: Emits infra‐red radiation. 2. Acoustic: Emits inaudible sound waves 3. Capacitive: Measures changes in capacitance around it 4. Inductive: Emits magnetic field Inductive proximity switches sense distance to objects by generating magnetic fields. They are similar in principle to metal detectors. A coil of wire is charged with electrical current, and an electronic circuit measures this current. If a metallic part gets close enough to the coil, the current will increase and the proximity switch will open or close accordingly. The chief disadvantage of inductive proximity switches is that they can only detect metallic objects.
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Figure 9‐1 Proximity Sensor (RPM Measuring Device)
9.2
Model explanation of proximity switch
LM 18 – 30 08 N A 1. LM signifies the switch category (LM: inductance type; CM: capacitance type etc.) 2.
30 signifies the operating voltage (30: 6‐36VDC; 310: 5‐24VDC; 320: 12‐ 60VDC; 20:90‐250VAC; 210: 24‐250VAC;220: 380VAC; 40: 12‐240VDC/24‐ 240AC; 50: Special voltage)
3.
9.3
08 signifies the detection distance (01: 1mm; 05: 5mm; 10: 10mm)
Main features:
•
Compact volume
•
Wide voltage range
•
Dust proof, vibration proof, water proof and oil proof.
•
Long service life
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Figure 9‐2 Dimensions of Proximity Sensor
9.4
Thermocouple
A thermocouple is a junction between two different metals that produces a voltage related to a temperature difference. Thermocouples are a widely used type of temperature sensor for measurement and control and can also be used to convert heat into electric power. They are inexpensive and interchangeable, are supplied fitted with standard connectors and can measure a wide range of temperatures.
Figure 9‐3 Construction of Thermocouple
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DESIGN AND FABRICATION OF A STIRLING CYCLE ENGINE
Types of Thermocouples:
Certain combinations of alloys have become popular as industry standards. Selection of the combination is driven by cost, availability, convenience, melting point, chemical properties, stability, and output. Different types are best suited for different applications. They are usually selected based on the temperature range and sensitivity needed. Thermocouples with low sensitivities (B, R, and S types) have correspondingly lower resolutions. Other selection criteria include the inertness of the thermocouple material and whether it is magnetic or not.
Thermocouple Type
Overall Range (°C)
0.1°C Resolution
0.025°C Resolution
B
100..1800
1030..1800
-
E
-270..790
-240..790
-140..790
J
-210..1050
-210..1050
-120..1050
K
-270..1370
-220..1370
-20..1150
N
-260..1300
-210..1300
R
-50..1760
330..1760
-
S
-50..1760
250..1760
-
T
-270..400
-230..400
-20..400
340..1260
Table 9‐1 Types of Thermocouple
9.6
K -Type
Type K (chromel–alumel) is the most common general purpose thermocouple with a sensitivity of approximately 41 µV/°C chromel positive relative to alumel. It is inexpensive and a wide variety of probes are available in its −200 °C to +1350 °C range.
Figure 9‐4 K Type Thermocouple
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DESIGN AND FABRICATION OF A STIRLING CYCLE ENGINE
Table for Type K Thermocouple (Ref Junction 0 C) ◦
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CHAPTER 10
EXPERIMENTAL RESULTS 10.1
Flame characteristics Natural gas consumption ‐6
Type of Consumer
10
3
ft /hr Bunsen burner small Bunsen burner large
10.2
Heat dissipated
3
m /s
liters/s
Btu/hr
kW
3
20
0.02
3500
1
10
80
0.08
10000
3
Experimental findings
For Tamb= 33 C ◦
Flame
Displacer Base
Displacer Top
800
225
75
423
73
52
Maximum Temperature o
( C) Minimum Temperature (oC) Maximum Temperature o
( C) Minimum Temperature o
( C)
800
423
Maximum RPM
Minimum RPM
440
260
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FINAL YEAR PROJECT REPORT Flame
DESIGN AND FABRICATION OF A STIRLING CYCLE ENGINE Flame
RPM
Height
423
260
0
225
450
277
1
205
500
303
2
197
550
325
3
170
600
339
4
150
650
370
5
133
700
388
6
118
750
420
7
107
800
440
8
90
8.72
75
Temperature
Temperature
Figure 10‐1 Temperature vs. Height
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Figure 10‐2 RPM vs. Flame Temperature
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CHAPTER 11
POST DESIGNING 11.1
Cost Estimates
S No.
Component
Cost (in Rupees)
1.
Crankshaft
700
2.
Flywheel
750
3.
Power piston
900
4.
Displacer cylinder
1000
5.
Expansion cylinder
1000
6.
Two Connecting rods
800
7.
Displacer
500
8.
Bearings
500
9.
Nuts, bolts and brackets
500
11.
Transportation
5000
12.
Miscellaneous
2,100
13.
Proximity Sensor
400
14.
Thermocouple
300
15.
RPM Display Meter
1200
16.
Temperature Display Meter
950
TOTAL
Rs 16,600
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DESIGN AND FABRICATION OF A STIRLING CYCLE ENGINE
Risk Assessment
Risk Event
Description
Probability
Estimated
of
Project
Occurrence
Impact
Mitigation
Contingency
Strategy
Plan
Leakage of
Sealing
working
70%‐80%
fluid due to
(Very
improper
likely)
High (Catastrophic)
Control (Minimize the effect)
seals
Use of secure sealings/pist on rings
Dimensional non‐ compliance
Retention
Re‐designing
Dimensional
between
30%‐40%
Low
(Accept the
of the
inaccuracy
the stroke
(Unlikely)
(Marginal)
consequen
concerned
ces)
parts
and the cylinder length Resistance Mechanical friction
to smooth
70%‐90%
movement
(Very
of dynamic
likely)
High (Catastrophic)
Control (Minimize the effect)
components Leakage of
lubricants such as oil or grease
Coating of
working Diffusivity
Use of
Control
fluid
20%‐30%
Low
through the
(Unlikely)
(Marginal)
(Minimize the effect)
cylinder walls with thick heat‐
walls of the
resistant
cylinder due
paint to
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to low
reduce
molecular
diffusion
weight of
through
the fluid
them
with respect to the molecular spacing of the wall material Rise in
Use of
temperatur
effective
e of the material Overheating
due to non‐ uniform heating and ineffective cooling
50%‐60%
Medium
(Probable)
(Critical)
Control (Minimize the effect)
cooling mechanism by reducing the temperature at the sink
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DESIGN AND FABRICATION OF A STIRLING CYCLE ENGINE Impact Guidelines for Scope,
Probability Guidelines
Cost, Schedule, or
Mitigation Strategy
Quality
Very Likely
Probable
Unlikely
70‐100%
High (Catastrophic)
Deflection
40‐70%
Medium (Critical)
Control
0‐40%
Low (Marginal)
Transfer the risk to another party.
Retention
Avoidance
Minimize the effect. Accept the consequences. Reject the risk; do nothing.
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DESIGN AND FABRICATION OF A STIRLING CYCLE ENGINE
Safety Assessment:
11.3.1 Introduction: There is always considerable amount of risk and danger while working with power producing or energy conversion devices. Stirling Engine is one such device, and as compared to conventional internal combustion engine, it has increased amount of danger due to its external source of heat or combustion. This chapter aims to provide a complete in‐depth analysis of the safety concerns associated with the project, and the necessary remedial measures taken in this regard. It identifies all safety features of the system, design, and procedural hazards that may be present and specific procedural controls and precautions that should be followed. This study is based on the factors which were highlighted earlier during the risk assessment in the concept design phase.
11.3.2 System Operation: Stirling engine is a heat engine that operates by cyclic compression and expansion of air or another gas, the working fluid, at different temperature levels such that there is a net conversion of heat energy to mechanical work. The key components within the system are the power piston, displacer, the connecting rod, crankshaft and the heat source (flame). The synchronous operation of each of these components is necessary for the smooth operation of the engine. Otherwise, these components might induce unwanted vibrations, resulting in the complete malfunction of the engine or break‐up of these components, causing both material and human damage. The engine is operated after being provided a sufficient amount of heat with any of the available heat source such as flame, steam etc. It is important to contain the flame within a specified area so as to ensure uniform or continuous heating and therefore it must be prevented from gust of winds. Also the uncontrolled flame may go on to damage the instrumentation devices such as the thermocouple wire or the proximity sensor. The output shaft is coupled with a fan, so as to indicate the engine output and also to provide the engine with the initial push to get it started. This fan remains bare on the
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output shaft and a little carelessness from the operator may cause the hands of the operator to stick into the sharp blades of the fan, causing serious injuries. The reciprocating parts must be lubricated from time to time to ensure their smooth operation. Also the seals must be checked regularly to make sure that they are in order and functioning properly. The engine must be inspected periodically to assess the wearing of moving parts and to replace them if necessary. The gas pipe leading to the burner must be checked for any sort of blockage.
11.3.3 Safety Engineering:
Event
Description/Issue
Probability of Occurrence
Estimated Project Impact
Safety Feature Use of secure
Leakage of working
Sealing
fluid due to improper seals
70%‐80% (Very likely)
High
sealings and
(Catastrophi
strong
c)
gasketting fixtures Use of flame
Due to sudden
enclosures
increase in the mass
around the
Dispersed/ flow of gas the flame Uncontroll
may come up in
ed flame
contact with sensors
30%‐40%
Medium
base of the
(Unlikely)
(Critical)
burner and upto the
or measuring
base of
instruments
cylinders
Resistance to
Mechanica l friction
smooth movement
70%‐90% (Very
of dynamic
likely)
components
High (Catastrophi c)
Use of lubricants such as oil or grease
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DESIGN AND FABRICATION OF A STIRLING CYCLE ENGINE Coating of
Leakage of working
cylinder walls
fluid through the
with thick
walls of the cylinder due to low
Diffusivity
molecular weight of the fluid with
heat‐ 20%‐30%
Low
resistant
(Unlikely)
(Marginal)
paint to reduce
respect to the
diffusion
molecular spacing of
through
the wall material
them
Rise in temperature
Overheati
of the material due to non‐uniform
ng
heating and
50%‐60%
Medium
Heat sink or
(Probable)
(Critical)
fins are used
ineffective cooling The rotating fan
Blade
blades may get damaged or may
Damage
hurt someone during operation
Protective 30%‐40%
Low
cage is used
(Unlikely)
(Marginal)
to enclose the fan
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11.3.4 Objectives Assessment: This is to assess the percentage of success the project had as when compared with the SOR originally given.
Ref 1.5
Task
Proposed status
Description
Fabrication of a
Manufactured a can‐type
scaled down home‐
stirling engine with a
made stirling engine
W(L)
for PCSIR project
1.5
Result
A
manufacturing duration of four weeks, in order to study
competition
and analyze the design
requirement.
problems associated.
Design, analysis and
Successfully manufactured a
fabrication of stirling
gamma type stirling engine.
engine.
D
A
Initial problems associated with the manufactured engine were duly resolved.
1.5
3D geometrical modeling on Solid
D
A
Edge. 1.5
Completed a 3D geometric animated model on Solid Edge.
Optimization of components of stirling engine using
Did not manage to optimize W(L)
commercially
NA
the design due to time constraints.
available FEA package software. 1.5
Final presentation, project report and
Successfully achieved all three D
A
targets associated with the final year project.
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DESIGN AND FABRICATION OF A STIRLING CYCLE ENGINE
fabrication of model.
1.5
Submission of project in the form of a Did not manage to compile a
research paper to be submitted in a
W(L)
NA
reputable
research paper due to time constraints.
international journal/conference. Final design calculations of our Conducted one dimensional
fabricated engine 2.1.6
model based on the
steady state heat transfer, D
studies conducted on
A
geometric and mechanical calculations for a gamma type
the hand‐made (tin‐
stirling engine.
can) stirling engine model. Simulation of our design on FEA
Successfully managed to
software package.
simulate the thermal and
This will include
dynamic performance of the
optimization of the 2.1.7
design and
W(L)
A
design on ANSYS simulation software. The results were
performance
almost in agreement with the
parameters, the
analytical calculations
structural, dynamic,
performed.
thermal and flow analysis.
2.1.8
Final fabrication of the engine based on
D
A
Fabricated engine with minor changes in original design that
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DESIGN AND FABRICATION OF A STIRLING CYCLE ENGINE
our analysis.
were essential to overcome the problems encountered in the fabrication phase.
Comparison of our Did not manage to draw
design with an 2.1.9
equivalent power
W(L)
NA
internal combustion
combustion engine due to time and financial constraints.
engine. 2.2
comparisons with an internal
Should be capable of producing useful electrical output for
Did not manage to couple the W(H)
charging an electronic
NA
engine with a generator due to time and financial constraints.
device such as laptop or cell phone. 2.2.1
Combustion by‐
Engine did produce some
products produced by
noise initially due to
ICE such as NOx are
manufacturing faults. However
eliminated and must
D
A
these were duly rectified and it
generate less noise as
was found to be virtually
compared to an ICE.
noiseless and burned with a clean flame.
2.2.2
The temperature of the heat source shall not exceed the
The maximum temperature D
melting point
A
temperature of the
measured was found to be within the metallurgical limit of the chosen material.
expansion cylinder. 2.2.2
Pressure attained inside the expansion chamber should be
The maximum pressure inside D
A
the cylinder was found to be within the permissible design
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DESIGN AND FABRICATION OF A STIRLING CYCLE ENGINE
within permissible
limits.
design limits. 2.2.2
The stirling engine should produce a smooth and
This objective was achieved W(H)
A
continuous power
after an initial round of trouble shooting.
output. 2.3.1
Heat source must be properly concealed to
The heat source in shielded D
prevent direct human
A
an aluminum sheet.
contact. 2.3.1
The engine placement The engine rig is stably
rig must be stable to prevent any mishap
D
A
supported on three legs with soft rubber pegs for a firm
due to engine
grip.
dynamics. 2.3.3
from direct human contact by
Expansion chamber and displacer chamber must be air
W(H)
A
The working fluid is sealed shut inside the two cylinders.
tight to prevent leakage. 2.4
It shall be ensured All engine components are
that the components of the engine are
D
A
or can be easily manufactured
easily available in the
at minimal cost and time.
local market. 2.4
The engine shall be in compliance with the
easily available in the market
D
A
All moving and hot engine parts are shielded from direct
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DESIGN AND FABRICATION OF A STIRLING CYCLE ENGINE
environmental safety
human contact. No toxic
standards.
pollutants are emitted and the engine also does not create a lot of noise.
2.4
The engine shall not
The design is completely
be plagiarized from
indigenous though it may bear
an existing design.
D
A
some similarities to other designs due to its conventional nature.
2.5
The engine shall
Engine operates at standard
operate at STP.
conditions of 25 C ambient
o
D
A
temperature and 1 atm pressure. 2.6
Engine components shall be replaceable in
All engine components are D
case of
A
cost.
damage/malfunction. 2.7
Safe handling of parts during fabrication.
easily replaceable at a very low
None of the exposed parts D
A
contain sharp edges or anything that may pose an injury risk.
2.7
Project details shall
All project details from initial
be documented.
concept design to design D
A
calculations and final fabrication have been documented.
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GALLERY This gallery is dedicated to the pictures of the final and successfully fabricated Stirling engine prototype. The various engine components such as the displacer cylinder, power cylinder, connecting rod, displacer rod, crankshaft etc can be seen clearly. Also in the pictures can be seen the inductive proximity sensor and its associated wiring which was used to measure the RPM of the engine.
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APPENDIX A “GANTT CHART”
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APPENDIX B “SOR”
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Statement Of Requirement Title: Design and fabrication of
th
Issue: 01
Date: 7 November,
a Stirling Cycle Engine CHANGES
D/W
2009 REF
REQUIREMENTS
1
Introduction
1.1
Preamble Stirling engine is an external source heat engine that meets the demand for efficient energy utilization and that is why the study and investigation of stirling engine is a topic of great interest for many institutes including universities. In contrast to internal combustion engine, they are more reliable, simple in design, highly efficient, cheap, can utilize any heat source and above
all
they
are
environment
friendly
depending upon the source of heat. Especially due to the technological advances in material sciences and manufacturing techniques in the twentieth century, the interest in stirling engine has re‐kindled. 1.2
Objective To obtain useful mechanical work output from a given heat input by employing a stirling cycle engine mechanism.
1.3
Scope The design, analysis and fabrication of a stirling engine by systematic study of basic operating
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FINAL YEAR PROJECT REPORT
DESIGN AND FABRICATION OF A STIRLING CYCLE ENGINE principles, design parameters and the study of a home‐made scaled down version of the engine (as per the PCSIR project competition requirement) in order to identify the engineering complications associated with it. 1.4
Related Documents Bancha
Kongtragool,
Somchai
Wongwises,
Investigation on power output of the gamma‐ configuration low temperature differential Stirling engines, Renewable energy,30,pg. 465‐476,2005 Can Cinar, Halit Karabulut, Manufacturing and testing
of a
gamma
type
Stirling
engine,
Renewable Energy,30, pg. 57‐66,2005 Leonardo Scollo, Pablo Valdez, Jorge Baron ,Design and construction of a Stirling engine prototype, International journal of hydrogen energy, 33, pg.3506‐3510, 2008 1.4.1
Books Yunus
A.
Cengel
Thermodynamics:
and An
Michael
engineering
A
Boles,
approach,
McGraw Hill International Yunus A. Cengel, Heat Transfer, Tata‐McGraw Hill, New‐Delhi F.P. Beer, E.R. Johnston Jr., John T. Dewolf Mechanics of Materials, McGraw Hill International William D. Callister Jr, Material Science and Engineering: An Introduction, John Wiley & Sons,
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FINAL YEAR PROJECT REPORT
DESIGN AND FABRICATION OF A STIRLING CYCLE ENGINE 2003 R. S. Khurmi and J. K. Gupta, Theory of Machines and Mechanisms, Eurasia Publishing House, New Delhi, 1998 R.C. Hibbler, Engineering Mechanics –Statics and Dynamics, Prentice Hall International, New Jersey 1.4.2
Software
D
Solid Edge V20 or Solid Edge ST
W(L)
Ansys V11 FEA package software 1.5
Deliverables Fabrication of a scaled down home‐made stirling
W(L)
engine for PCSIR project competition requirement.
D
Design, analysis and fabrication of stirling engine.
D
3D geometrical modeling on Solid Edge. Optimization of components of stirling engine
W(L)
using commercially available FEA package software. Final presentation, project report and fabrication
D
of model. Submission of project in the form of research
W(L)
paper to be submitted in a reputable international journal/conference. 1.6
Definitions, Abbreviations and Symbols
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DESIGN AND FABRICATION OF A STIRLING CYCLE ENGINE 1.6.1
Definitions Displacer: The displacer resembles a large piston, except that it has a smaller diameter than the cylinder, thus its motion does not change the volume of gas in the cylinder—it merely transfers the gas around within the cylinder. Power piston: Power piston is the piston located in the expansion chamber. The expanding gases in the cylinder exert a pressure on the power piston which in turn rotates the crank and provides the system with the power stroke. Crank shaft: The crankshaft, sometimes casually abbreviated to crank, is the part of an engine which translates reciprocating linear piston motion into rotation. Connecting rods: The connecting rod connects the piston to the crank or crankshaft. Piston rings: A piston ring is an open‐ended ring that fits into a groove on the outer diameter of a piston with the primary aim to seal the expansion chamber. Flywheel:
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DESIGN AND FABRICATION OF A STIRLING CYCLE ENGINE A flywheel is a mechanical device with a significant moment of inertia used as a storage device for rotational energy. Heat engine: A heat engine is a device that converts thermal energy to mechanical work output.
Sink: The heat sink is typically the environment at ambient temperature to where heat is lost and the temperature is lowered. Source: Source is the venue from where heat energy is obtained, in this design via combustion. Internal Combustion Engine: An engine where combustion takes place inside the power cylinder. Heat Transfer Coefficient: A coefficient used in calculating the convective heat transfer between a fluid and a solid body. Fins: They are used to enhance convective heat transfer by increasing the area exposed to convection.
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DESIGN AND FABRICATION OF A STIRLING CYCLE ENGINE 1.6.2
Abbreviations ICE: Internal Combustion Engine NASA: National Aeronautics and Space Administration PCSIR: Pakistan Council of Scientific and Industrial Research FEA: Finite Element Analysis STP: 0
Standard Temperature & Pressure (25 C, 1atm) NOX: Nitrous Oxide 1.6.3
Symbols D Demand: A mandatory requirement. W(H) Wish high: A highly desirable attribute. W(L) Wish low: A less desirable attribute.
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DESIGN AND FABRICATION OF A STIRLING CYCLE ENGINE 2
Technical Requirements Conceptual knowledge of thermodynamics, heat transfer, mechanics of machines, engineering
D
dynamics, mechanics of solids and material sciences along with modeling and FEA software packages. 2.1
D
2.1.1
W(H)
2.1.2
Description and Purpose Study of the basic concept and three categories of stirling engine namely alpha, beta and gamma. Collecting the latest research literature and general subject matter on stirling engines. Narrowing down the selection to the right type
D
2.1.3
(alpha, beta and gamma) of stirling engine on which to base the design. Solid modeling of the selected stirling engine
W(H)
2.1.4
category on modeling software, for the home‐ made (tin‐can) stirling engine. Construction of the hand‐made (tin‐can) stirling engine in order to gain a better understanding of
W(L)
2.1.5
its working principles and identification of the associated mechanical problems coupled with their solutions (as per the PCSIR competition requirement). Final design calculations of the fabricated engine
D
2.1.6
model based on the studies conducted on the hand‐made (tin‐can) stirling engine model.
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DESIGN AND FABRICATION OF A STIRLING CYCLE ENGINE Simulation of the design on FEA software
W(L)
2.1.7
package. This will include optimization of the design and performance parameters, the structural, dynamic, thermal and flow analysis.
D
2.1.8
Final fabrication of the engine based on the analysis.
W(L)
2.1.9
Comparison of the design with an equivalent power internal combustion engine.
2.2
Functional Characteristics Should be capable of producing useful electrical
W(H)
output for charging an electronic device such as laptop or cell phone. 2.2.1
Qualitative issues Combustion by‐products produced by ICE such as NOx are eliminated.
D
Should generate less noise as compared to an ICE. 2.2.2
Quantitative issues The temperature of the heat source shall not
D
exceed the melting point temperature of the expansion cylinder. Pressure attained inside the expansion chamber
D
should be within permissible design limits. The stirling engine should produce a smooth and
W(H)
continuous power output. 2.3
Physical and other characteristics
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DESIGN AND FABRICATION OF A STIRLING CYCLE ENGINE 2.3.1
Health and safety criteria Heat source must be properly concealed to prevent direct human contact.
D The engine placement rig must be stable to prevent any mishap due to engine dynamics. 2.3.2
Protective finish and coatings Use of lubricants where desired.
2.3.3
Equipment sealing requirements Expansion chamber and displacer chamber must
W(H)
be air tight to prevent leakage. 2.4
Design & Construction It shall be ensured that the components of the engine are easily available in the local market. The engine shall be in compliance with the
D
environmental safety standards. The engine shall not be plagiarized from an existing design. 2.5 D
Environmental conditions The engine shall operate at STP.
2.6
Interchangeability Engine components shall be replaceable in case of
D
damage/malfunction. 2.7 D
Production Engine is to be developed by the students under
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DESIGN AND FABRICATION OF A STIRLING CYCLE ENGINE the guidance of project advisor and with the aid of reference books and online subject matter. Students may employ the use of modeling and FEA software to aid in the engine design. 2.8
Miscellaneous Safe handling of parts during fabrication. Project details shall be documented. Project content shall be monitored by project
D
advisor Dr. Waqar Ahmed Khan and overlooked by project examiner and co‐examiner, Mr. Aijaz Ahmed and Dr. Noman Danish respectively. 3
Cost The estimated cost of the project is Rs. 60,000 (10% contingencies). However the actual cost of the project may vary according to the circumstances and will be ascertained by the group members.
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APPENDIX C “TERMS & DEFINITIONS”
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Adiabatic Flame Temperature: In the absence of any work interactions or changes in the kinetic or potential energies, the chemical energy released during combustion is either lost as heat to the surroundings or is used to raise the temperature of the products. The smaller the heat loss, larger the temperature rise. When there is no heat loss, the temperature of the products will reach a maximum. This maximum is called the ‘adiabatic flame temperature’ of the of the reaction. Buffer Pressure: Pressure acting on the non‐workspace side of the piston is known as buffer pressure. The buffer gas like the fly wheel absorbs stores and returns energy during the cycle. Coefficient of Fluctuation of Fluctuation of Energy: of Energy: It is defined as the ratio of the maximum fluctuation of energy to the work done per cycle. Coefficient of Fluctuation of Fluctuation of Speed: of Speed: The difference between the maximum and minimum speeds during a cycle is called the maximum fluctuation of speed. The ratio of the maximum fluctuation of speed to the mean speed is called the coefficient of fluctuation of fluctuation of speed. of speed. Compression Ratio: It is the ratio of uncompressed of uncompressed volume upon compressed volume. It is denoted by r. Convection heat transfer coefficient (h): Defined as the rate of heat transfer per unit area, per unit temperature difference of fluid flow. The convective heat transfer coefficient is not a property of the fluid. It is an experimentally determined parameter whose value depends on the surface geometry, the nature of fluid of fluid motion, the properties of the of the fluid and the bulk fluid velocity.
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Dead Volume: Dead volume is a function of volume of heaters, coolers, piston clearances, ducts, etc and any other volumes in the gas circuit that is not swept by either piston, denoted by VD. Effectiveness: The ratio of actual of actual torque to ideal torque is called the effectiveness denoted by E. Efficacious Cycle: If τ r r ≤ 1, the Stirling cycle has the property that the minimum expansion process pressure is greater than or equal to the maximum compression process pressure. Efficacious engines are the most efficient mechanically, but they are not always the most practical. Enthalpy of Reaction of Reaction (hr): This is the difference between the enthalpy of the products at a specified state and the enthalpy of the of the reactants at the same state for a complete reaction. Enthalpy of Formation of Formation (hf ): This is the enthalpy of a of a substance at a specified state due to its chemical composition. Forced Work: The forced work is the work that the mechanism must deliver to make the piston move in opposition to the pressure difference across it. It is denoted by
.
Film Temperature (Tf ): To account for the temperature variation of the of the fluid in the thermal boundary layer (i.e. from the surface to the outer edge of the boundary layer), the fluid properties are usually evaluated at the ‘film temperature’ which is the arithmetic average of the surface and the free‐stream temperature.
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Grashof number Grashof number (Gr): It is a dimensionless number which represents the ratio of the buoyancy force to the viscous force acting on the fluid. The role played by Reynolds number in forced convection is played by the Grashof number Grashof number in natural convection. Inertia Force: (FI) It is an imaginary force, which when acts upon a rigid body, brings it in an equilibrium position. It is numerically equal to the accelerating force in magnitude, but opposite in direction. Indicated Work: It is the difference between the work done by the fluid during expansion and the work done during compression. It is denoted by Wi. It is also defined as the area enclosed by the P‐v diagram of the of the cycle. Maximum Fluctuation of Energy: of Energy: The variation of energy above and below the mean resisting torque line is called the fluctuation of energy, while the difference between the maximum and minimum energies is known as the maximum fluctuation of energy. of energy. Mean Resisting Torque: (Tmean) The product of the of the crank‐pin effort and the crank‐pin radius is known as crank effort or turning moment or torque on the crankshaft Mechanical Efficiency: It is the measure of how much the work produced by the thermodynamic cycle can actually be taken out to the shaft, outside the engine. Monomorphic Engine: A monomorphic engine is one in which its pressure–volume function is proportional to the gas mass content of its of its workspace.
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Net Load on Piston: (FL) It is the force acting on the piston due to the difference of pressures in the cylinder on the two sides of the piston. Non‐ Efficacious Cycle: Non‐Efficacious Stirling Cycle is the one, for which τ r > 1. Non‐efficacious engines potentially have a higher power density.
Nusselt number (Nu): It represents the enhancement of the heat transfer through a fluid layer as a result of convection relative to conduction across the same fluid layer. Piston Effort: (Fp) It is the net force acting on the piston or crosshead pin, along the line of stroke. Prandtl number (Pr): It is a dimensionless number that describes the relative thickness of the velocity and the thermal boundary layers. Radius of Gyration: A body when it rotates behaves as if all of its mass were concentrated in a ring at some distance from the axis of rotation. This distance is known as the Radius of Gyration of the body. Rayleigh number (Ra): It is simply the product of the Grashof number and the Prandtl number. Shaft Work: It is the difference between the cyclic work W o received by the flywheel/output shaft and indicated work Wi.
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DESIGN AND FABRICATION OF A STIRLING CYCLE ENGINE W s
= W o − W i
Stoichiometric Air: The minimum amount of air needed for the complete combustion of a fuel is called stoichiometric or theoretical air. Swept Volume: The volume displaced during the reciprocating motion of the piston is called the swept volume. Temperature Ratio: Ratio of cold space temperature to hot space temperature is known as temperature ratio. It is denoted by τ . Thermal conductivity (k): The rate of heat transfer through a unit thickness of the material per unit area, per unit temperature difference. Turning Moment or Torque on Crankshaft: (T) The product of the crank‐pin effort and the crank‐pin radius is known as crank effort or turning moment or torque on the crankshaft. Workspace: The working substance, typically a gas confined in an expansion chamber is known as working space.
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APPENDIX D “REFERENCES”
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[1] Iskander Tlili, Youssef Timoumi and Sassi Ben Nasrallah (2007), “Analysis and design consideration of mean temperature differential Stirling engine for solar application”, Renewable Energy, Vol. 33 (2008), pg 1911–1921. [2] Bancha Kongtragool and Somchai Wongwises (2004), “Investigation on power output of the gamma‐configuration low temperature differential Stirling engines”, Renewable Energy, Vol. 30 (2005), pg 465–476. [3] type
Can Cinar and Halit Karabulut (2004), “Manufacturing and testing of a gamma Stirling engine”, Renewable Energy, Vol. 30 (2005), pg 57–66.
[4] Bancha Kongtragool, Somchai Wongwises (2002), “A review of solar powered stirling engines and low temperature differential stirling engines”, Renewable and Sustainable Energy Reviews, Vol. 7 (2003), pg 131–154.
[5] D.G. Thombarea and S.K. Vermab (2006), “Technological development in the stirling cycle engines”, Renewable and Sustainable Energy Reviews, Vol. 12 (2008), pg 1‐ 38.
[6]
Leonardo Scollo, Pablo Valdez and Jorge Baro´n (2007), “Design and construction
of a
Stirling engine prototype”, International Association for Hydrogen Energy (2008).
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