ISBN-10:
3642135137
ISBN-13:
9783642135132
Pub. Date:
08/31/2010
Publisher:
Springer Berlin Heidelberg
LDA Application Methods: Laser Doppler Anemometry for Fluid Dynamics / Edition 1

LDA Application Methods: Laser Doppler Anemometry for Fluid Dynamics / Edition 1

by Zhengji Zhang

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Product Details

ISBN-13: 9783642135132
Publisher: Springer Berlin Heidelberg
Publication date: 08/31/2010
Series: Experimental Fluid Mechanics
Edition description: 2010
Pages: 272
Product dimensions: 6.10(w) x 9.25(h) x 0.03(d)

About the Author

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. He is currently an engineer at the Oberhasli Hydroelectric Power Company (KWO), working on hydraulic designs and optimizations of hydraulic machineries. He is the author of the monograph «Freistrahlturbinen» 2009.

Table of Contents

1 Introduction 1

1.1 Flows and Flow Measurements 1

1.2 Traditional Methods of Flow Measurements 2

1.3 Laser Methods and Laser Doppler Anemometry (LDA) 2

1.3.1 Developments of LDA Fundamentals and Instrumentations 4

1.3.2 Developments of LDA Application Methods 5

1.4 Purposeful Flow Measurements and Rational Measurement Evaluations 8

1.5 Purposes of this Book 9

2 Specifications of Engineering Turbulent Flows 11

2.1 Turbulent Flow Properties 11

2.1.1 Statistical Views of Flow Turbulences 11

2.1.2 Isotropic and Anisotropic Turbulences 13

2.2 Reynolds Turbulent Stresses 15

3 LDA Principles and Laser Optics 19

3.1 Light Wave and Its Propagation 19

3.2 The Doppler Effect 22

3.3 Superposition of Two Plane Light Waves 24

3.4 LDA Principle 27

3.5 Fringe Model on the Light Interference 29

3.6 Frequency Shift Method to Resolve the Flow Direction 32

3.6.1 Fringe Shift Speed 34

3.7 Gaussian Beam Properties 35

3.7.1 Geometrical Specifications of the Gaussian Beam 35

3.7.2 Transmission Performance of the Gaussian Beam 38

3.8 Measurement Volume Size 39

4 LDA Systems 41

4.1 Hardware and Optical Components 41

4.2 Specification of LDA Measurement Volumes 44

5 Basic Data Processing Methods in LDA Measurements 47

5.1 Direct Data Processing for Mean Velocities and Velocity Fluctuations 47

5.2 Weighting Facilities of Mean Velocity and Fluctuations 51

6 Linear Transformation of Velocities and Turbulent Stresses 53

6.1 Orthogonal Linear Transformation 53

6.1.1 Velocity Transformation 53

6.1.2 Turbulent Stress Transformation 55

6.1.3 Directional Distribution of Turbulent Stresses 55

6.2 Non-orthogonal Transformation 61

6.2.1 Velocity Transformation 62

6.2.2 Turbulent Stress Transformation 63

6.3 Graphical Presentation of Turbulent Stresses 65

6.3.1 Ellipse Form of the Turbulence Distribution 65

6.3.2 Expressions of Turbulent Stresses in Mohr's Stress Circle 66

7 Tracer Particles and Particle Motion Equations 69

7.1 Effective Forces Exerted on the Particle in the Flow 70

7.1 1 Viscous Drag Force 70

7.1.2 Gravitational and Lift Forces 71

7.1.3 Pressure Force 72

7.1.4 Force from Added Mass 73

7.2 Particle Motion Equation 74

7.3 Particle Motion in the Straight Flow of Constant Velocity 75

7.4 Particle Motion in Nozzle and Diffuser Flows 76

7.4.1 Nozzle Flow 78

7.4.2 Diffuser Flow 80

7.5 Particle Motion in the Oscillation Flow 82

7.5.1 Particle Flows of Small Stokes Numbers 86

7.5.2 Particle Flows of Large Stokes Numbers 88

8 Zero Correlation Method (ZCM) 89

8.1 Shear Stress Measurements with Non-coincident LDA 89

8.2 Basics of ZCM 90

8.3 Extension of ZCM 93

8.3.1 Non-orthogonal Velocity Components 93

8.3.2 Three-Dimensional Flow Turbulence 93

8.4 Restriction and Validation of ZCM 94

9 Dual Measurement Method (DMM) 97

9.1 Possibility of Resolving the Secondary Flow 97

9.2 DMM in Basic Form 99

9.3 DMM with Coordinate Transformation 103

9.4 Extension of DMM 105

9.4.1 Direct Component Measurements 106

9.4.2 Method of Using Coordinate Transformation 109

10 Symmetrical Method of 3D-Velocity Measurements 113

11 Non-stationary Turbulent Flows 117

11.1 Non-stationary Turbulent Flows in the Practice 117

11.2 Time-Resolved Non-stationary Turbulent Flows 119

11.2.1 Method of Linear Least Squares Fitting 119

11.2.2 Linear Trend of the Velocity and the Calculation Method 121

11.2.3 Time-Dependent Flow Turbulences 123

11.3 Phase-Resolved Non-stationary Turbulent Flows 126

11.3.1 Method of Linear Least Squares Fitting 127

11.3.2 Linear Trend of the Velocity and the Calculation Method 128

11.3.3 Phase-Dependent Flow Turbulences 130

12 Turbulent Flow with Spatial Velocity Gradient 133

12.1 Apparent Turbulence Intensity and Related Quantities 135

12.2 Combined Velocity Bias Effect 140

12.2.1 Mean Velocity 141

12.2.2 Turbulent Normal Stress 142

12.3 Method of Resolving the Non-uniform Velocity Distribution 145

13 Flow Measurements Behind the Plane Window: On-axis 147

13.1 Fringe Spacing 147

13.2 Shift of the Measurement Volume 148

13.3 Optical Dispersion and its Negligible Effect 149

14 Flow Measurements Behind the Plane Window: Off-axis 151

14.1 Off-axis Measurements and Velocity Transformation 152

14.2 Fringe Spacing in Measurement Volume and Velocity Corrections 153

14.3 Refraction of Optical Axis and Orientation of the Measurement Volume 155

14.4 Two-Dimensional Shift of the Measurement Volume 156

14.5 Astigmatism and its Presence in Transmitting Optics 159

14.6 Astigmatism at the Focused Laser Beam Bundle 163

14.6.1 One-time Refraction of a Focused Beam Bundle 163

14.6.2 Multiple Refraction of a Focused Beam Bundle 169

14.7 Measurement Volume and Its Distortion 170

14.7.1 Single Refraction of Laser Beams 172

14.7.2 Multiple Refractions of Laser Beams 173

14.7.3 Astigmatism at the On-axis LDA Alignment 174

14.8 Signal Qualities and the Lens Dependence 175

14.8.1 Deterioration of Signal Qualities and Strengths 175

14.8.2 Lens Dependence of Signal Qualities and Strengths 176

14.9 Error Sensitivities in Forming the Measurement Volume 179

14.9.1 Beam Separation in the Test Medium 179

14.9.2 Beam Separation After Multiple Refractions 185

14.9.3 Possible Impact on PDA Measurements 185

14.10 Method for Compensation of Astigmatism 186

15 Flow Measurements in Circular Pipes 191

15.1 Measurements of Axial Velocities 193

15.2 Measurements of Tangential Velocities 197

15.2.1 Basic Geometrical Relationships 197

15.2.2 Simplifications of Calculations 198

15.2.3 Fringe Spacing and Velocity Corrections 199

15.3 Measurements of Radial Velocities 200

15.3.1 Accurate Positioning of the Measurement Volume 200

15.3.2 Laser Beam Intersection Angle 205

15.3.3 Fringe Spacing and Velocity Corrections 206

15.3.4 Orientation of the Measurement Volume 207

15.3.5 Determination of Radial Velocities 208

15.3.6 Remarks on the Method 208

15.4 Optical Aberrations and Measurement Volume Distortion 209

15.4.1 Optical Aberrations in Transmitting and Receiving Optics 210

15.4.2 Dislocation of Laser Beam Waists from the Measurement Volume 211

16 Fringe Distortion Effects 219

16.1 Linear Longitudinal Distribution of the Fringe Spacing 220

16.2 Fringe Distortion Number and the Apparent Mean Velocity 221

16.3 Overestimation of the Flow Turbulence 224

17 Velocity Bias Effects 227

17.1 Velocity Bias as a Flow Phenomenon 227

17.2 Velocity Bias and the Momentum Flow Rate 229

17.3 Velocity Bias in One-Dimensional Flow Fluctuations 231

17.4 Velocity Bias in Two- and Three-Dimensional Flow Fluctuations 235

17.4.1 Velocity Bias in Mean Velocities 236

17.4.2 Velocity Bias in Turbulent Normal Stresses 238

17.4.3 Velocity Bias in Turbulent Shear Stresses 241

18 LDA Application Examples 243

18.1 High Speed Water Jet Flow in a Pelton Turbine 243

18.2 Measurements of Warp Yarn Speed in a Weaving Machine 247

18.3 Verification of the Shift Frequency in the Laser Beam 249

Appendix A Off-axis LDA Alignment and Measurement Volume Displacement 253

A.l Laser Beams in the Meridian Plane 254

A.2 Laser Beams in the Sagittal Plane 255

A.3 Combination 257

Appendix B Laser Beam Orientation Under the Effect of the Bias Angle δ 259

Appendix C Coordinate Transformation of the Reynolds Stress Matrix 263

References 267

Index 271

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