Zhengji LDA Application Methods

Laser Doppler Anemometry for Fluid Dynamics
1. Auflage 2010
ISBN: 978-3-642-13514-9
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 272 Seiten

Reihe: Experimental Fluid Mechanics

This technical book considers the application side of LDA techniques. Starting from the basic theories that are crucial for each LDA user, the main subject of the book is focused on diverse application methods. In details, it deals with universal methodical techniques that have been mostly developed in the last 15 years. The book thus gives for the first time an application reference for LDA users in improving the optical conditions and enhancing the measurement accuracies. It also provides the guidelines for simplifying the measurements and correcting measurement errors as well as for clarifying the application limits and extending the application areas of LDA techniques. Beside the treatments of some traditional optical and flow mechanical features influencing the measurement accuracies, the book shows a broad spectrum of LDA application methods in the manner of measuring the flow turbulence, resolving the secondary flow structures, and quantifying the optical aberrations at measurements of internal flows etc.. Thus, it also supports the further developments of both the hard- and software of LDA instrumentations.

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.

Autoren/Hrsg.

Zhang, Zhengji

Inhaltsverzeichnis

1;Preface;5
2;Contents;7
3;Symbols;12
3.1;Subscript;14
4;1 Introduction;15
4.1;1.1 Flows and Flow Measurements;15
4.2;1.2 Traditional Methods of Flow Measurements;16
4.3;1.3 Laser Methods and Laser Doppler Anemometry (LDA);16
4.3.1;1.3.1 Developments of LDA Fundamentals and Instrumentations;18
4.3.2;1.3.2 Developments of LDA Application Methods;19
4.4;1.4 Purposeful Flow Measurements and Rational Measurement Evaluations;22
4.5;1.5 Purposes of this Book;23
5;2 Specifications of Engineering Turbulent Flows;24
5.1;2.1 Turbulent Flow Properties;24
5.1.1;2.1.1 Statistical Views of Flow Turbulences;24
5.1.2;2.1.2 Isotropic and Anisotropic Turbulences;26
5.2;2.2 Reynolds Turbulent Stresses;28
6;3 LDA Principles and Laser Optics;31
6.1;3.1 Light Wave and Its Propagation;31
6.2;3.2 The Doppler Effect;34
6.3;3.3 Superposition of Two Plane Light Waves;36
6.4;3.4 LDA Principle;39
6.5;3.5 Fringe Model on the Light Interference;41
6.6;3.6 Frequency Shift Method to Resolve the Flow Direction;44
6.6.1;3.6.1 Fringe Shift Speed;46
6.7;3.7 Gaussian Beam Properties;47
6.7.1;3.7.1 Geometrical Specifications of the Gaussian Beam;47
6.7.2;3.7.2 Transmission Performance of the Gaussian Beam;50
6.8;3.8 Measurement Volume Size;51
7;4 LDA Systems;53
7.1;4.1 Hardware and Optical Components;53
7.2;4.2 Specification of LDA Measurement Volumes;55
8;5 Basic Data Processing Methods in LDA Measurements;58
8.1;5.1 Direct Data Processing for Mean Velocities and Velocity Fluctuations;58
8.2;5.2 Weighting Facilities of Mean Velocity and Fluctuations;62
9;6 Linear Transformation of Velocities and Turbulent Stresses;64
9.1;6.1 Orthogonal Linear Transformation;64
9.1.1;6.1.1 Velocity Transformation;64
9.1.2;6.1.2 Turbulent Stress Transformation;66
9.1.3;6.1.3 Directional Distribution of Turbulent Stresses;66
9.1.3.1;6.1.3.1 On the Basic Parameters sxx, syy and txy ;66
9.1.3.2;6.1.3.2 On the Basic Parameters s11 and s22 ;71
9.1.3.3;6.1.3.3 Approximation .m ˜ . and Simplifications;72
9.2;6.2 Non-orthogonal Transformation;72
9.2.1;6.2.1 Velocity Transformation;73
9.2.2;6.2.2 Turbulent Stress Transformation;74
9.3;6.3 Graphical Presentation of Turbulent Stresses;76
9.3.1;6.3.1 Ellipse Form of the Turbulence Distribution;76
9.3.2;6.3.2 Expressions of Turbulent Stresses in Mohr's Stress Circle;77
10;7 Tracer Particles and Particle Motion Equations;79
10.1;7.1 Effective Forces Exerted on the Particle in the Flow;80
10.1.1;7.1.1 Viscous Drag Force;80
10.1.2;7.1.2 Gravitational and Lift Forces;81
10.1.3;7.1.3 Pressure Force;82
10.1.4;7.1.4 Force from Added Mass;83
10.2;7.2 Particle Motion Equation;84
10.3;7.3 Particle Motion in the Straight Flow of Constant Velocity;85
10.4;7.4 Particle Motion in Nozzle and Diffuser Flows;86
10.4.1;7.4.1 Nozzle Flow;88
10.4.2;7.4.2 Diffuser Flow;90
10.5;7.5 Particle Motion in the Oscillation Flow;92
10.5.1;7.5.1 Particle Flows of Small Stokes Numbers;96
10.5.2;7.5.2 Particle Flows of Large Stokes Numbers;98
11;8 Zero Correlation Method (ZCM);99
11.1;8.1 Shear Stress Measurements with Non-coincident LDA;99
11.2;8.2 Basics of ZCM;100
11.3;8.3 Extension of ZCM;103
11.3.1;8.3.1 Non-orthogonal Velocity Components;103
11.3.2;8.3.2 Three-Dimensional Flow Turbulence;103
11.4;8.4 Restriction and Validation of ZCM;104
12;9 Dual Measurement Method (DMM);107
12.1;9.1 Possibility of Resolving the Secondary Flow;107
12.2;9.2 DMM in Basic Form;109
12.3;9.3 DMM with Coordinate Transformation;113
12.4;9.4 Extension of DMM;115
12.4.1;9.4.1 Direct Component Measurements;116
12.4.2;9.4.2 Method of Using Coordinate Transformation;119
13;10 Symmetrical Method of 3D-Velocity Measurements;122
14;11 Non-stationary Turbulent Flows;126
14.1;11.1 Non-stationary Turbulent Flows in the Practice;126
14.2;11.2 Time-Resolved Non-stationary Turbulent Flows;128
14.2.1;11.2.1 Method of Linear Least Squares Fitting;128
14.2.2;11.2.2 Linear Trend of the Velocity and the Calculation Method;130
14.2.3;11.2.3 Time-Dependent Flow Turbulences;132
14.3;11.3 Phase-Resolved Non-stationary Turbulent Flows;135
14.3.1;11.3.1 Method of Linear Least Squares Fitting;136
14.3.2;11.3.2 Linear Trend of the Velocity and the Calculation Method;137
14.3.3;11.3.3 Phase-Dependent Flow Turbulences;139
15;12 Turbulent Flow with Spatial Velocity Gradient;141
15.1;12.1 Apparent Turbulence Intensity and Related Quantities;143
15.2;12.2 Combined Velocity Bias Effect;148
15.2.1;12.2.1 Mean Velocity;149
15.2.2;12.2.2 Turbulent Normal Stress;150
15.2.2.1;12.2.2.1 Uniform Velocity Distribution;152
15.2.2.2;12.2.2.2 Negligible Turbulent Flow Fluctuations ;153
15.3;12.3 Method of Resolving the Non-uniform Velocity Distribution;153
16;13 Flow Measurements Behind the Plane Window: On-axis;155
16.1;13.1 Fringe Spacing;155
16.2;13.2 Shift of the Measurement Volume;156
16.3;13.3 Optical Dispersion and its Negligible Effect;157
17;14 Flow Measurements Behind the Plane Window: Off-axis;159
17.1;14.1 Off-axis Measurements and Velocity Transformation;160
17.2;14.2 Fringe Spacing in Measurement Volume and Velocity Corrections;161
17.3;14.3 Refraction of Optical Axis and Orientation of the Measurement Volume;163
17.4;14.4 Two-Dimensional Shift of the Measurement Volume;164
17.5;14.5 Astigmatism and its Presence in Transmitting Optics;167
17.6;14.6 Astigmatism at the Focused Laser Beam Bundle;171
17.6.1;14.6.1 One-time Refraction of a Focused Beam Bundle;171
17.6.2;14.6.2 Multiple Refraction of a Focused Beam Bundle;177
17.7;14.7 Measurement Volume and Its Distortion;178
17.7.1;14.7.1 Single Refraction of Laser Beams;180
17.7.2;14.7.2 Multiple Refractions of Laser Beams;181
17.7.3;14.7.3 Astigmatism at the On-axis LDA Alignment;182
17.8;14.8 Signal Qualities and the Lens Dependence;183
17.8.1;14.8.1 Deterioration of Signal Qualities and Strengths;183
17.8.2;14.8.2 Lens Dependence of Signal Qualities and Strengths;184
17.9;14.9 Error Sensitivities in Forming the Measurement Volume;187
17.9.1;14.9.1 Beam Separation in the Test Medium;187
17.9.1.1;14.9.1.1 Beam Separation Due to the Bias Angle . ;190
17.9.1.2;14.9.1.2 Beam Separation Due to the Bias Angle d ;191
17.9.1.3;14.9.1.3 Statement Regarding the Inaccurate Laser Beam Alignment;193
17.9.2;14.9.2 Beam Separation After Multiple Refractions;193
17.9.3;14.9.3 Possible Impact on PDA Measurements;193
17.10;14.10 Method for Compensation of Astigmatism;194
18;15 Flow Measurements in Circular Pipes;198
18.1;15.1 Measurements of Axial Velocities;200
18.2;15.2 Measurements of Tangential Velocities;204
18.2.1;15.2.1 Basic Geometrical Relationships;204
18.2.2;15.2.2 Simplifications of Calculations;205
18.2.3;15.2.3 Fringe Spacing and Velocity Corrections;206
18.3;15.3 Measurements of Radial Velocities;207
18.3.1;15.3.1 Accurate Positioning of the Measurement Volume;207
18.3.1.1;15.3.1.1 Determination of Intersection Points ya and yb ;209
18.3.1.2;15.3.1.2 Simplifications of Calculations;210
18.3.1.3;15.3.1.3 Necessary Movement xr and yr of Laser Beam Pair;212
18.3.2;15.3.2 Laser Beam Intersection Angle;212
18.3.3;15.3.3 Fringe Spacing and Velocity Corrections;213
18.3.4;15.3.4 Orientation of the Measurement Volume;214
18.3.5;15.3.5 Determination of Radial Velocities;215
18.3.6;15.3.6 Remarks on the Method;215
18.4;15.4 Optical Aberrations and Measurement Volume Distortion;216
18.4.1;15.4.1 Optical Aberrations in Transmitting and Receiving Optics;217
18.4.2;15.4.2 Dislocation of Laser Beam Waists from the Measurement Volume;218
18.4.2.1;15.4.2.1 Laser Beam Waists in Measuring the Tangential Velocities;219
18.4.2.2;15.4.2.2 Laser Beam Waists in Measuring the Radial Velocities;222
19;16 Fringe Distortion Effects;225
19.1;16.1 Linear Longitudinal Distribution of the Fringe Spacing;226
19.2;16.2 Fringe Distortion Number and the Apparent Mean Velocity;227
19.3;16.3 Overestimation of the Flow Turbulence;230
20;17 Velocity Bias Effects;233
20.1;17.1 Velocity Bias as a Flow Phenomenon;233
20.2;17.2 Velocity Bias and the Momentum Flow Rate;235
20.3;17.3 Velocity Bias in One-Dimensional Flow Fluctuations;237
20.4;17.4 Velocity Bias in Two- and Three-Dimensional Flow Fluctuations;241
20.4.1;17.4.1 Velocity Bias in Mean Velocities;242
20.4.1.1;17.4.1.1 Two-Dimensional Flow Fluctuations;242
20.4.1.2;17.4.1.2 Three-Dimensional Flow Fluctuations;243
20.4.2;17.4.2 Velocity Bias in Turbulent Normal Stresses;244
20.4.2.1;17.4.2.1 Two-Dimensional Turbulence;245
20.4.2.2;17.4.2.2 Three-Dimensional Turbulence;246
20.4.3;17.4.3 Velocity Bias in Turbulent Shear Stresses;247
21;18 LDA Application Examples;248
21.1;18.1 High Speed Water Jet Flow in a Pelton Turbine;248
21.2;18.2 Measurements of Warp Yarn Speed in a Weaving Machine;252
21.3;18.3 Verification of the Shift Frequency in the Laser Beam;254
22;Appendix A Off-axis LDA Alignment and Measurement Volume Displacement;257
22.1;A.1 Laser Beams in the Meridian Plane;258
22.2;A.2 Laser Beams in the Sagittal Plane;259
22.3;A.3 Combination;261
23;Appendix B Laser Beam Orientation Under the Effect of the Bias Angle d;263
24;Appendix C Coordinate Transformation of the Reynolds Stress Matrix;266
25;References;269
26;Index;273