LDA Application Methods: Laser Doppler Anemometry for Fluid Dynamics (Experimental Fluid Mechanics)

✍ Scribed by Zhengji Zhang

• Publisher: Springer
• Year: 2010
• Tongue: English
• Leaves: 274
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Preface
Contents
Symbols
Subscript
1 Introduction
1.1 Flows and Flow Measurements
1.2 Traditional Methods of Flow Measurements
1.3 Laser Methods and Laser Doppler Anemometry (LDA)
1.3.1 Developments of LDA Fundamentals and Instrumentations
1.3.2 Developments of LDA Application Methods
1.4 Purposeful Flow Measurements and Rational Measurement Evaluations
1.5 Purposes of this Book
2 Specifications of Engineering Turbulent Flows
2.1 Turbulent Flow Properties
2.1.1 Statistical Views of Flow Turbulences
2.1.2 Isotropic and Anisotropic Turbulences
2.2 Reynolds Turbulent Stresses
3 LDA Principles and Laser Optics
3.1 Light Wave and Its Propagation
3.2 The Doppler Effect
3.3 Superposition of Two Plane Light Waves
3.4 LDA Principle
3.5 Fringe Model on the Light Interference
3.6 Frequency Shift Method to Resolve the Flow Direction
3.6.1 Fringe Shift Speed
3.7 Gaussian Beam Properties
3.7.1 Geometrical Specifications of the Gaussian Beam
3.7.2 Transmission Performance of the Gaussian Beam
3.8 Measurement Volume Size
4 LDA Systems
4.1 Hardware and Optical Components
4.2 Specification of LDA Measurement Volumes
5 Basic Data Processing Methods in LDA Measurements
5.1 Direct Data Processing for Mean Velocities and Velocity Fluctuations
5.2 Weighting Facilities of Mean Velocity and Fluctuations
6 Linear Transformation of Velocities and Turbulent Stresses
6.1 Orthogonal Linear Transformation
6.1.1 Velocity Transformation
6.1.2 Turbulent Stress Transformation
6.1.3 Directional Distribution of Turbulent Stresses
6.1.3.1 On the Basic Parameters σxx, σyy and τxy
6.1.3.2 On the Basic Parameters σ11 and σ22
6.1.3.3 Approximation ϕm ≈ ϕ and Simplifications
6.2 Non-orthogonal Transformation
6.2.1 Velocity Transformation
6.2.2 Turbulent Stress Transformation
6.3 Graphical Presentation of Turbulent Stresses
6.3.1 Ellipse Form of the Turbulence Distribution
6.3.2 Expressions of Turbulent Stresses in Mohr's Stress Circle
7 Tracer Particles and Particle Motion Equations
7.1 Effective Forces Exerted on the Particle in the Flow
7.1.1 Viscous Drag Force
7.1.2 Gravitational and Lift Forces
7.1.3 Pressure Force
7.1.4 Force from Added Mass
7.2 Particle Motion Equation
7.3 Particle Motion in the Straight Flow of Constant Velocity
7.4 Particle Motion in Nozzle and Diffuser Flows
7.4.1 Nozzle Flow
7.4.2 Diffuser Flow
7.5 Particle Motion in the Oscillation Flow
7.5.1 Particle Flows of Small Stokes Numbers
7.5.2 Particle Flows of Large Stokes Numbers
8 Zero Correlation Method (ZCM)
8.1 Shear Stress Measurements with Non-coincident LDA
8.2 Basics of ZCM
8.3 Extension of ZCM
8.3.1 Non-orthogonal Velocity Components
8.3.2 Three-Dimensional Flow Turbulence
8.4 Restriction and Validation of ZCM
9 Dual Measurement Method (DMM)
9.1 Possibility of Resolving the Secondary Flow
9.2 DMM in Basic Form
9.3 DMM with Coordinate Transformation
9.4 Extension of DMM
9.4.1 Direct Component Measurements
9.4.2 Method of Using Coordinate Transformation
10 Symmetrical Method of 3D-Velocity Measurements
11 Non-stationary Turbulent Flows
11.1 Non-stationary Turbulent Flows in the Practice
11.2 Time-Resolved Non-stationary Turbulent Flows
11.2.1 Method of Linear Least Squares Fitting
11.2.2 Linear Trend of the Velocity and the Calculation Method
11.2.3 Time-Dependent Flow Turbulences
11.3 Phase-Resolved Non-stationary Turbulent Flows
11.3.1 Method of Linear Least Squares Fitting
11.3.2 Linear Trend of the Velocity and the Calculation Method
11.3.3 Phase-Dependent Flow Turbulences
12 Turbulent Flow with Spatial Velocity Gradient
12.1 Apparent Turbulence Intensity and Related Quantities
12.2 Combined Velocity Bias Effect
12.2.1 Mean Velocity
12.2.2 Turbulent Normal Stress
12.2.2.1 Uniform Velocity Distribution
12.2.2.2 Negligible Turbulent Flow Fluctuations
12.3 Method of Resolving the Non-uniform Velocity Distribution
13 Flow Measurements Behind the Plane Window: On-axis
13.1 Fringe Spacing
13.2 Shift of the Measurement Volume
13.3 Optical Dispersion and its Negligible Effect
14 Flow Measurements Behind the Plane Window: Off-axis
14.1 Off-axis Measurements and Velocity Transformation
14.2 Fringe Spacing in Measurement Volume and Velocity Corrections
14.3 Refraction of Optical Axis and Orientation of the Measurement Volume
14.4 Two-Dimensional Shift of the Measurement Volume
14.5 Astigmatism and its Presence in Transmitting Optics
14.6 Astigmatism at the Focused Laser Beam Bundle
14.6.1 One-time Refraction of a Focused Beam Bundle
14.6.2 Multiple Refraction of a Focused Beam Bundle
14.7 Measurement Volume and Its Distortion
14.7.1 Single Refraction of Laser Beams
14.7.2 Multiple Refractions of Laser Beams
14.7.3 Astigmatism at the On-axis LDA Alignment
14.8 Signal Qualities and the Lens Dependence
14.8.1 Deterioration of Signal Qualities and Strengths
14.8.2 Lens Dependence of Signal Qualities and Strengths
14.9 Error Sensitivities in Forming the Measurement Volume
14.9.1 Beam Separation in the Test Medium
14.9.1.1 Beam Separation Due to the Bias Angle ψ
14.9.1.2 Beam Separation Due to the Bias Angle δ
14.9.1.3 Statement Regarding the Inaccurate Laser Beam Alignment
14.9.2 Beam Separation After Multiple Refractions
14.9.3 Possible Impact on PDA Measurements
14.10 Method for Compensation of Astigmatism
15 Flow Measurements in Circular Pipes
15.1 Measurements of Axial Velocities
15.2 Measurements of Tangential Velocities
15.2.1 Basic Geometrical Relationships
15.2.2 Simplifications of Calculations
15.2.3 Fringe Spacing and Velocity Corrections
15.3 Measurements of Radial Velocities
15.3.1 Accurate Positioning of the Measurement Volume
15.3.1.1 Determination of Intersection Points ya and yb
15.3.1.2 Simplifications of Calculations
15.3.1.3 Necessary Movement xr and yr of Laser Beam Pair
15.3.2 Laser Beam Intersection Angle
15.3.3 Fringe Spacing and Velocity Corrections
15.3.4 Orientation of the Measurement Volume
15.3.5 Determination of Radial Velocities
15.3.6 Remarks on the Method
15.4 Optical Aberrations and Measurement Volume Distortion
15.4.1 Optical Aberrations in Transmitting and Receiving Optics
15.4.2 Dislocation of Laser Beam Waists from the Measurement Volume
15.4.2.1 Laser Beam Waists in Measuring the Tangential Velocities
15.4.2.2 Laser Beam Waists in Measuring the Radial Velocities
16 Fringe Distortion Effects
16.1 Linear Longitudinal Distribution of the Fringe Spacing
16.2 Fringe Distortion Number and the Apparent Mean Velocity
16.3 Overestimation of the Flow Turbulence
17 Velocity Bias Effects
17.1 Velocity Bias as a Flow Phenomenon
17.2 Velocity Bias and the Momentum Flow Rate
17.3 Velocity Bias in One-Dimensional Flow Fluctuations
17.4 Velocity Bias in Two- and Three-Dimensional Flow Fluctuations
17.4.1 Velocity Bias in Mean Velocities
17.4.1.1 Two-Dimensional Flow Fluctuations
17.4.1.2 Three-Dimensional Flow Fluctuations
17.4.2 Velocity Bias in Turbulent Normal Stresses
17.4.2.1 Two-Dimensional Turbulence
17.4.2.2 Three-Dimensional Turbulence
17.4.3 Velocity Bias in Turbulent Shear Stresses
18 LDA Application Examples
18.1 High Speed Water Jet Flow in a Pelton Turbine
18.2 Measurements of Warp Yarn Speed in a Weaving Machine
18.3 Verification of the Shift Frequency in the Laser Beam
Appendix A Off-axis LDA Alignment and Measurement Volume Displacement
A.1 Laser Beams in the Meridian Plane
A.2 Laser Beams in the Sagittal Plane
A.3 Combination
Appendix B Laser Beam Orientation Under the Effect of the Bias Angle δ
Appendix C Coordinate Transformation of the Reynolds Stress Matrix
References
Index