Fluid Mechanics of Flow Metering (eBook)

Preface 5
Contents 7
1 Fully Developed Turbulent Pipe Flow 12
1.1 Basic Equations 12
1.2 Two-Layer Structure for Ret .8 15
1.3 Wall Layer 15
1.4 Core Region 16
1.5 Friction Law for Given Volume Flux 19
1.6 Velocity Distribution 20
1.7 Influence ofWall Roughness 24
1.8 Low Reynolds Number Pipe Flow 29
References 31
2 Decay of Disturbances in Turbulent Pipe Flow 34
2.1 Introduction 34
2.2 Basic Equations 35
2.3 Fully Developed Pipe Flow 40
2.4 Eigenvalue Problem 45
2.5 Comparisons with Experimental Results 53
References 57
3 Optimal Characteristic Parameters for the Disturbances in Turbulent Pipe Flow 60
3.1 Introduction 60
3.2 Objective 61
3.3 Formulae for the Optimal Characteristic Parameters 61
3.4 Fully Developed Flow 63
3.5 Minimal Program 64
3.6 Example 67
3.7 Experimental Determination of the Characteristic Parameters ( Minimal Program) 67
References 70
4 Measurement of Velocity and Turbulence Downstream of Flow Conditioners 72
4.1 Introduction 72
4.2 Experiments 73
4.3 Results and Discussion 76
4.4 Conclusion 86
References 88
5 Signal Processing of Complex Modulated Ultrasonic Signals 90
5.1 Introduction 90
5.2 Cross-Correlation Measurements 91
5.3 Demodulation by Digital Undersampling 92
5.4 Digital Hilbert-Transform 94
5.5 Phase Reconstruction 99
5.6 Phase Demodulation with Kalman Filter 100
5.7 Analog Signal Processing 102
5.8 Conclusion 104
References 105
6 Vortex-Shedding Flow Metering Using Ultrasound 106
6.1 Introduction 106
6.2 Physical Background 107
6.3 Measurement Principle and Test Arrangement 108
6.4 Simulations 108
6.5 Comparisons of Pressure and Ultrasonic Signals 109
6.6 Experiments 110
6.7 Influence of Disturbances 119
6.8 Conclusion 120
References 121
7 Ultrasonic Gas-Flow Measurement Using Correlation Methods 122
7.1 Introduction 122
7.2 Determination of Traveling Time by Cross-Correlation Functions 124
7.3 Physical Quantity Measured by Cross-Correlation Functions 125
7.4 Measurements 127
7.5 Multipath Arrangement 135
7.6 Tomographic Reconstruction of Flow Profile 136
7.7 Conclusion 137
References 138
8 Ultrasound Cross-Correlation Flow Meter: Analysis by System Theory and Influence of Turbulence 140
8.1 Introduction 140
8.2 Experiments 142
8.3 System-Theoretical Model 144
8.4 Comparison of Theoretical and Experimental Results 152
8.5 Conclusions 158
References 158
9 Effect of Area Changes in Swirling Flow 160
9.1 Introduction 161
9.2 Physical Background 162
9.3 Mathematical Formulation of the Problem 164
9.4 Results and Discussion 171
References 174
10 Errors of Turbine Meters Due to Swirl 176
10.1 Introduction 177
10.2 Physical and Mathematical Background 179
10.3 Experiments and Data Reduction 190
10.4 Discussion 194
10.5 Conclusions 194
References 195
11 Investigation of Unsteady Three-Dimensional Flow Fields in a Turbine Flow Meter 196
11.1 Introduction 196
11.2 Theory of Operation 197
11.3 Numerical Tools: Fluent and ACHIEVE 199
11.4 Three-Dimensional Simulations: Geometry and Setup 199
11.5 Discussion of Results 201
11.6 The Pressure Shift 207
11.7 Secondary Flow 209
11.8 Summary 210
References 211
12 How to Design a New Flow Meter from Scratch 212
12.1 Introduction 212
12.2 Measuring Principle 213
12.3 Setup and Calibration 217
12.4 Results for Installations 219
12.5 Conclusions 220
References 221
13 Effects of Disturbed Inflow on Vortex Shedding from a Bluff Body 222
13.1 Introduction 222
13.2 Numerical Algorithm 223
13.3 Results 227
13.4 Conclusions 232
References 232
14 Correction of the Reading of a Flow Meter in Pipe Flow Disturbed by Installation Effects 234
14.1 Introduction 234
14.2 Characterization of the Disturbed Flow 236
14.3 Experiments 237
14.4 Relationship Between Error Shift and Flow Disturbance 242
14.5 Results 243
14.6 Conclusions 247
References 248
15 How to Correct the Error Shift of an Ultrasonic Flow Meter Downstream of Installations 250
15.1 Introduction 250
15.2 Experimental Setup 251
15.3 Experiments 255
15.4 Correction 258
15.5 Results 261
15.6 Conclusion 263
References 263
Index 266