Laser Velocimetry in Fluid Mechanics

Alain Boutier is Assistant of the General Scientific Director at Office National d'Etudes et de Recherches Aerospatiales (ONERA), Palaiseau, France.

Preface xi Alain BOUTIER Intoduction xiii Alain BOUTIER Chapter 1. Measurement Needs in Fluid Mechanics 1 Daniel ARNAL and Pierre MILLAN 1.1. Navier-Stokes equations 2 1.2. Similarity parameters 4 1.3. Scale notion 6 1.4. Equations for turbulent flows and for Reynolds stress tensor 6 1.5. Spatial-temporal correlations 8 1.6. Turbulence models 10 1.6.1. Zero equation model 11 1.6.2. One equation model 11 1.6.3. Two equations model12 1.6.4. Reynolds stress models (RSM, ARSM) 12 1.7. Conclusion 13 1.8. Bibliography . 13 Chapter 2. Classification of Laser Velocimetry Techniques 15 Alain BOUTIER 2.1. Generalities 16 2.2. Definitions and vocabulary 17 2.3. Specificities of LDV 19 2.3.1. Advantages 19 2.3.2. Use limitations 20 vi Laser Velocimetry in Fluid Mechanics 2.4. Application domain of laser velocimeters (LDV, PIV, DGV) 21 2.5. Velocity measurements based on interactions with molecules 22 2.5.1. Excitation by electron beams 22 2.5.2. Laser fluorescence 23 2.5.3. Spectroscopy with a tunable laser diode in the infrared 23 2.5.4. Coherent anti-Stokes Raman scattering technique 24 2.5.5. Tagging techniques 24 2.5.6. Summary 25 2.6. Bibliography 28 Chapter 3. Laser Doppler Velocimetry 33 Alain BOUTIER and Jean-Michel MOST 3.1. Introduction 33 3.2. Basic idea: Doppler effect34 3.2.1. Double Doppler effect 34 3.2.2. Four optical set-ups 36 3.2.3. Comments on the four configurations 39 3.3. Fringe velocimetry theory40 3.3.1. Fringe pattern in probe volume 40 3.3.2. Interferometry theory42 3.3.3. Comparison between the three theoretical approaches 44 3.3.4. SNR 44 3.4. Velocity sign measurement 48 3.4.1. Problem origin 48 3.4.2. Solution explanation 49 3.4.3. Various means to shift a laser beam frequency 51 3.5. Emitting and receiving optics 56 3.5.1. Emitting 56 3.5.2. Probe volume characteristics 61 3.5.3. Receiving part 64 3.6. General organigram of a mono-dimensional fringe velocimeter 67 3.7. Necessity for simultaneous measurement of 2 or 3 velocity components 68 3.8. 2D laser velocimetry 70 3.9. 3D laser velocimetry 71 3.9.1. Exotic 3D laser velocimeters 71 3.9.2. 3D fringe laser velocimetry 72 3.9.3. Five-beam 3D laser velocimeters 73 3.9.4. Six-beam 3D laser velocimeters 74 3.10. Electronic processing of Doppler signal 79 3.10.1. Generalities and main classes of Doppler processors 79 Table of Contents vii 3.10.2. Photon converter: photomultiplier 79 3.10.3. Doppler burst detection 84 3.10.4. First processing units 86 3.10.5. Digital processing units 88 3.10.6. Exotic techniques 102 3.10.7. Optimization of signal processing 103 3.11. Measurement accuracy in laser velocimetry 103 3.11.1. Probe volume influence 104 3.11.2. Calibration 105 3.11.3. Doppler signal quality 112 3.11.4. Velocity domain for measurements 114 3.11.5. Synthesis of various bias and error sources117 3.11.6. Specific problems in 2D and 3D devices 123 3.11.7. Global accuracy 126 3.12. Specific laser velocimeters for specific applications 127 3.12.1. Optical fibers in fringe laser velocimetry 127 3.12.2. Miniature laser velocimeters 132 3.12.3. Doppler image of velocity field 133 3.13. Bibliography 134 Chapter 4. Optical Barrier Velocimetry 139 Alain BOUTIER 4.1. Laser two-focus velocimeter 139 4.2. Mosaic laser velocimeter145 4.3. Bibliography 147 Chapter 5. Doppler Global Velocimetry 149 Alain BOUTIER 5.1. Overview of Doppler global velocimetry 149 5.2. Basic principles of DGV 150 5.3. Measurement uncertainties in DGV 153 5.4. Bibliography 156 Chapter 6. Particle Image Velocimetry 159 Michel RIETHMULLER, Laurent DAVID and Bertrand LECORDIER 6.1. Introduction 159 6.2. Two-component PIV 164 6.2.1. Laser light source 164 6.2.2. Emission optics in PIV 168 6.2.3. Image recording 169 6.2.4. PTV (Particle Tracking Velocimetry) 185 viii Laser Velocimetry in Fluid Mechanics 6.2.5. Measurement of velocity using PIV 192 6.2.6. Correlation techniques 201 6.3. Three-component PIV 233 6.3.1. Introduction 233 6.3.2. Acquisition of the signal from the particles 234 6.3.3. Evaluation of the particles' motion 236 6.3.4. Modeling of sensor 237 6.3.5. Stereoscopy: 2D-3C PIV 252 6.3.6. 2.5D-3C surface PIV259 6.3.7. 3C-3D volumic PIV 261 6.3.8. Conclusion 268 6.4. Bibliography 269 Chapter 7. Seeding in Laser Velocimetry 283 Alain BOUTIER and Max ELENA 7.1. Optical properties of tracers 284 7.2. Particle generators 288 7.3. Particle control 292 7.4. Particle behavior 297 7.5. Bibliography 303 Chapter 8. Post-Processing of LDV Data 305 Jacques HAERTIG and Alain BOUTIER 8.1. The average values 306 8.2. Statistical notions 308 8.3. Estimation of autocorrelations and spectra 314 8.3.1. Continuous signals of limited duration 314 8.3.2. Signals sampled periodically (of limited duration T) 316 8.3.3. Random sampling 318 8.4. Temporal filtering: principle and application to white noise 321 8.4.1. Case of white noise 321 8.4.2. Moving average (MA) 323 8.4.3. Autoregressive (AR) process: Markov 324 8.5. Numerical calculations of FT326 8.6. Summary and essential results329 8.7. Detailed calculation of the FT and of the spectrum of fluctuations in velocity measured by laser velocimetry 330 8.7.1. Notations and overview of results regarding the FT 331 8.7.2. Calculating the FT of a sampled function F(t): periodic sampling 333 8.7.3. Calculating the FT of a sampled function F(t): random sampling 335 Table of Contents ix 8.7.4. FT of the sampled signal reconstructed after periodic sampling 339 8.7.5. FT of the sampled signal, reconstructed after random sampling 341 8.7.6. Spectrum of a random signal sampled in a random manner 345 8.7.7. Application to some signals 352 8.7.8. Main conclusions 356 8.8. Statistical bias 358 8.8.1. Simple example of statistical bias 358 8.8.2. Measurement sampling process 360 8.8.3. The various bias phenomena in laser velocimetry368 8.8.4. Analysis of the bias correction put forward by McLaughlin and Tiederman 369 8.8.5. Method for detecting statistical bias 369 8.8.6. Signal reconstruction methods 372 8.8.7. Interpolation methods applied to the reconstructed signal 374 8.9. Spectral analysis on resampled signals 375 8.9.1. Direct transform 376 8.9.2. Slotting technique 377 8.9.3. Kalman interpolating filter 379 8.10. Bibliography 384 Chapter 9. Comparison of Different Techniques 389 Alain BOUTIER 9.1. Introduction 389 9.2. Comparison of signal intensities between DGV, PIV and LDV 390 9.3. Comparison of PIV and DGV capabilities 394 9.4. Conclusion 396 9.5. Bibliography 397 Conclusion 399 Alain BOUTIER Nomenclature401 List of Authors 407 Index 409