Pelton Turbines (eBook)

Zhengji Zhang (Autor)

eBook Download: PDF

2016 | 1st ed. 2016
XIII, 311 Seiten
Springer International Publishing (Verlag)
978-3-319-31909-4 (ISBN)

Infos

This book concerns the theoretical foundations of hydro mechanics of Pelton turbines from a viewpoint of engineering. For reference purposes all relevant flow processes and hydraulic aspects in a Pelton turbine have been analyzed completely and systematically. The analyses especially include the quantification of all possible losses existing in the Pelton turbine and the indication of most available potential for further enhancing the system efficiency. As a guideline the book therefore supports further developments of Pelton turbines with regard to their hydraulic designs and optimizations. It is thus suitable for the development and design engineers as well as those working in the field of turbo machinery. Many laws described in the book can also be directly used to simplify aspects of computational fluid dynamics (CFD) or to develop new computational methods. The well-executed examples help better understanding the related flow mechanics.

Dr.-Ing. Zh. Zhang graduated from the School of Energy & Power Engineering of Xi'an Jiaotong University (PR China) in 1981. He received his PhD at the Institute of Thermo and Fluid Dynamics of Ruhr-University Bochum (Germany). Afterwards he joined Sulzer Markets & Technology Ltd in Winterthur, Switzerland, for experimental research of engineering flows. During this time he was awarded the company innovation prize. He changed later to the Oberhasli Hydroelectric Power Company (KWO) and later to Rütschi Fluids AG. Currently he is a visit engineer for supporting the research projects at the Laboratory of Hydraulics, Hydrology and Glaciology (VAW) of the Swiss Federal Institute of Technology in Zurich (ETHZ). He is the author of the monographs «Freistrahlturbinen» 2008 and «LDA Application Methods» 2010. In 2014, he was elected to ASME Fellow.

Inhalt

Foreword 6
Preface 8
Contents 10
Chapter 1: Introduction 15
1.1 Hydromechanics of the Pelton Turbine 16
1.1.1 General Developments 16
1.1.2 Development of Experimental Methods 17
1.1.3 Development by Numerical CFD Methods 19
1.1.4 Developments of the Analysis Methods 20
1.1.5 Further Hydraulic Aspects 21
1.2 Structural Mechanics of Pelton Turbines 21
1.3 Objectives of This Reference Book 22
References 23
Chapter 2: Working Principle of Pelton Turbines 26
2.1 Conversion of Hydraulic Energy into Mechanical Energy 26
2.2 Pelton Turbines and Specifications 30
2.2.1 Geometric Specification of the Pelton Wheel 30
2.2.2 Characteristic Hydromechanical Parameters 33
2.2.2.1 Peripheral Speed Coefficient km 33
2.2.2.2 Bucket Volumetric Load phivB 33
2.2.2.3 Specific Speed nq 34
2.2.2.4 Characteristic Bucket Position Angle ?o 36
2.2.2.5 Peripheral Speed of the Bucket Cutout Edge 37
2.2.3 Hydromechanical Specification of the Pelton Turbine 37
2.2.4 Installation Form of Pelton Turbines 40
2.2.5 Parameter Notations 41
References 41
Chapter 3: Injector Characteristics 42
3.1 Flow Acceleration in the Injector Nozzle 43
3.2 Discharge Coefficient phivD0 and the Injector Characteristics 45
3.3 Discharge Coefficient phivD Referred to the Effective Nozzle Opening Area 48
3.4 Reynolds Number Effect 50
3.5 Flow Dynamic Forces and the Force Balance in the Injector 50
3.5.1 Injectors with External Servomotor 51
3.5.1.1 Needle Force 51
Needle Force from the Internal Pressure 52
Recoil Force Outside of the Injector 53
Total Needle Force 56
3.5.1.2 Force at the Relief Piston 57
3.5.1.3 Spring Force 58
3.5.1.4 Regulation Force of the Servomotor 58
3.5.2 Injectors with an Internal Servomotor 59
3.6 Closing Law of the Injector Nozzle 60
References 64
Chapter 4: Jet Characteristics and Measurements 65
4.1 Laser Doppler Anemometry 66
4.2 Axially Symmetric Jet Flow 66
4.3 Jet Expansion 70
4.4 Secondary Flows in the Jet and the Jet Stability 72
References 74
Chapter 5: Interaction Between the Jet and Pelton Wheel 75
5.1 Jet Impingement on a Flat Plate 75
5.2 Minimum Number of Pelton Buckets 76
5.3 Water-Jet-Bucket Interaction and Its Specification 78
5.4 Coincidence and Symmetry Conditions 82
5.5 Number of Buckets of a Pelton Wheel 84
5.6 Relative Track of the Jet 87
5.7 Flow Detachment at the Cutting Edge of Bucket Cutout 89
5.8 Shockless Condition on the Bucket Rear Side 89
5.9 Shock Load Force and Related Power at Bucket Entries 93
5.9.1 Deflection of the Flow at the Bucket Main Splitter 93
5.9.2 Deflection of the Flow at the Bucket Cutout Edge 97
5.10 Effect of Eroded Main Splitters on Turbine Efficiency 99
5.10.1 Basic Model and Mechanism of Losses 100
5.10.2 Critical Width Ratio for Flow Detachment 102
5.10.3 Water Loss Related to Flow Deflection at Bucket Splitters 104
5.10.4 Comparison with Measurements 105
5.10.5 Negligible Impact Force on the Eroded Splitter Plane 106
References 107
Chapter 6: Fluid Mechanics in the Rotating Bucket 109
6.1 Basic Equations 109
6.1.1 Equation of Motion 109
6.1.2 Water Film Rotation and Pressure Distribution Through the Sheet Height 111
6.2 Relative Fluid Flow and Invariance Equation 112
6.2.1 Influence of the Pressure Gradient Due to the Surface Curvature 114
6.2.2 Jet Layer Method 115
6.2.3 Invariance Equation and Euler Equation 118
6.2.4 Example: Relative Flow in a Semicircular Bucket 120
6.3 Effective Driving Forces and Related Powers 122
6.3.1 Centrifugal Force 123
6.3.1.1 Special Case 1: Semicircular Bucket 125
6.3.1.2 Special Case 2: Semicircular Bucket for 127
6.3.2 Coriolis Force 129
6.3.2.1 Special Case 1: Semicircular Bucket 130
6.3.2.2 Special Case 2: Semicircular Bucket for 130
6.3.3 Impulsive Force Inferred from Streamline Curvature 131
6.3.3.1 Special Case 1: Bucket of Circular Form 132
6.3.3.2 Special Case 2: Semicircular Bucket for 133
6.3.4 Total Effect of Impulsive, Centrifugal, and Coriolis Forces 133
6.3.5 Examples 135
Reference 138
Chapter 7: Water Spreading in the Rotating Bucket 139
7.1 Relative Flow Rate 139
7.2 Width and Height of the Water Sheet in the Bucket 142
7.3 Overpressure in the Water Sheet 144
References 145
Chapter 8: Exit Flow Conditions 146
8.1 Velocity Distribution at the Bucket Exit 146
8.2 General Exit Flow Condition 147
8.3 Exit Flow Condition for Vertical Turbines 151
8.3.1 Exit Flow Condition at the Bucket Root Zone 151
8.3.2 Exit Flow Condition at the Bucket Cutout 156
8.3.3 Impact of Spray Water When kmkm,max 157
Reference 158
Chapter 9: Exit Flows and Hydraulic Losses 159
9.1 Swirling Losses 159
9.1.1 Influence of Exit Positions of Water Particles 161
9.1.2 Influence of the Exit Flow Angle 162
9.1.3 Influence of Jet Layer Positions 163
9.1.4 Swirling Loss of the Entire Jet 164
9.2 Friction Effect on the Bucket Rear Side 164
9.3 Deflection Effect on the Bucket Rear Side 167
Chapter 10: Friction Effects and FFT Theorem 169
10.1 Friction Number 170
10.2 Direct Friction Effects 173
10.3 Friction Effects via Changing the Pressure Distribution 175
10.4 Total Friction Effects 178
10.5 Flow Friction Theorem 180
References 180
Chapter 11: Viscous Cross-Flow Through the Bucket 181
11.1 Combined Hydraulic Losses 181
11.2 Real Swirling Losses 182
11.3 Hydraulic Dissipation and Energy Balance 185
11.4 Example of Friction Effects on the Hydraulic Efficiency 186
Chapter 12: Viscous Longitudinal Flow Through the Bucket 189
12.1 Kinematic Equation of Flow in a Rotating Bucket 189
12.2 Dynamic Equations and Calculations of Hydraulic Powers 193
12.3 Contributions of Flow Forces and Hydraulic Dissipation 195
12.3.1 Shock Load at the Bucket Entry 195
12.3.2 Impulsive Force in the Bucket 196
12.3.3 Centrifugal Force 196
12.3.4 Coriolis Force 197
12.3.5 Direct Friction Force 198
12.3.6 Hydraulic Dissipation 199
12.3.7 Overall Efficiency 200
12.4 Computations for a Concrete Realistic Example 201
Chapter 13: Friction and Windage Losses in Pelton Wheels 205
13.1 Pelton Turbines with Horizontal Axes 206
13.2 Pelton Turbines with Vertical Axes 209
13.3 Retardation Test Method 210
References 212
Chapter 14: Power Loss Due to Bearing Frictions 213
References 215
Chapter 15: Hydraulic and Mechanical Efficiency 216
15.1 Hydraulic Efficiency 216
15.2 Mechanical Efficiency 217
Reference 218
Chapter 16: Real Hydraulic Efficiency Characteristics 219
16.1 Critical Peripheral Speed Coefficient 219
16.2 Reaction Degree of the Jet 222
16.2.1 Reaction Degree in the Transition Speed Range 223
16.2.2 Reaction Degree in the Upper Range 225
16.2.3 Example for Reaction Degree of the Jet 225
16.3 Real Hydraulic Efficiency Characteristics 226
Reference 228
Chapter 17: Runaway Speed and Acceleration Profile 229
17.1 Theoretical Runaway Speed 229
17.2 Real Runaway Speed 232
17.2.1 Mechanical Power Loss 232
17.2.2 Effective Hydraulic Power 233
17.2.3 Realistic Runaway Speed 233
17.3 Acceleration Process to the Runaway Speed 235
17.3.1 Lower Speed Range: 236
17.3.2 Upper Speed Range: 237
17.3.3 Entire Acceleration Curve 238
Reference 238
Chapter 18: Hydraulic Design of Pelton Turbines 239
18.1 Dimensioning of the Pelton Wheel 239
18.2 Elliptical Bucket Form 242
Chapter 19: Multi-jet Pelton Turbines 250
19.1 Minimum Offset Angle Between Injectors 250
19.2 Injector Protection Shelter 252
Chapter 20: Geometric and Hydraulic Similarities 254
20.1 Geometric Similarity 255
20.2 Hydraulic Similarity 255
Chapter 21: Model Turbine Tests and Efficiency Scale-Up 259
21.1 Efficiency Scale-Up 260
21.2 Reynolds Number and Jet Impact Force 261
References 262
Chapter 22: Sand Abrasion and Particle Motion in the Bucket Flow 263
22.1 Jet Spreading and Water-Sheet Flow in the Bucket 266
22.2 Motion Equation of Sand Particles 267
22.3 Application Example 271
22.3.1 Pelton Turbine and Bucket Form 271
22.3.2 Flow Distribution in the Bucket 273
22.3.3 Particle Motion in the Bucket 278
22.3.4 Extended Example 281
22.4 Simplification of Calculations 282
References 284
Chapter 23: Bucket Mechanical Strength and Similarity Laws 285
23.1 Dynamic Tension in the Bucket Root Area 285
23.2 Similarity Laws in the Bucket Mechanical Loading 289
Appendix A: Nomenclature 293
Symbols 293
Indices 296
Appendix B: Definition of Derived Parameters 297
Appendix C: Specific Speed and Application in Pelton Turbines 298
Appendix D: Specification of the Jet Piece for a Bucket 300
Appendix E: Specification of the Bucket Positions 303
Appendix F: Particle Motion Along the Streamlines in the Pelton Bucket 306
References 310
Index 311

Produkt-Details

• Erscheint lt. Verlag: 13.6.2016
• Zusatzinfo: XIII, 311 p. 130 illus., 6 illus. in color.
• Verlagsort: Cham
• Sprache: englisch
• Themenwelt: Technik ► Maschinenbau
• Schlagworte: abrasive erosions • high-speed water jet • hydraulic design • Pelton bucket • Pelton turbine hydraulics • Pelton wheel • water industry and water technology
• ISBN-10: 3-319-31909-4 / 3319319094
• ISBN-13: 978-3-319-31909-4 / 9783319319094