Instructor: Lichuan Gui lichuan-gui@uiowa.edu http://lcgui.net Measurements in Fluid Mechanics 058:180:001 (ME:5180:0001) Time & Location: 2:30P - 3:20P MWF 218 MLH Office Hours: 4:00P – 5:00P MWF 223B-5 HL Instructor: Lichuan Gui lichuan-gui@uiowa.edu http://lcgui.net

Lecture 19. Laser Doppler velocimetry

Laser Doppler velocimetry Doppler effect

Laser Doppler velocimetry Doppler shift of light frequency - monochromatic, coherent, linearly polarized, and collimated laser with wavelength  and frequency  - transmitted through a fluid seeded with particles of velocity 𝑉 - particle adsorbs some of the light and reemits light following Mie-scattering laws - photodetector receives the scattered light with frequency +D from view angle  Doppler frequency: 𝑒 𝑖 – unit direction vector of incident light 𝑒 𝑠 – unit direction vector of scattered light 𝑉  – projection of velocity vector on the direction normal to the bisector of angle 

Laser Doppler velocimetry Dual-beam LDV - laser beam split into two parallel beams - focused at measuring volume with angle  - small particles with velocity 𝑉 in measuring volume - scattered lights collected with lens and superimposed on photodetector - received light intensities: 𝐴 1 sin2𝜋 𝜈+ 𝜈 𝐷1 𝑡 𝐴 2 sin2𝜋 𝜈+ 𝜈 𝐷2 𝑡 - output voltage: - Doppler frequency difference: - photodetector output (Doppler signal) : - flow velocity component:

Laser Doppler velocimetry The measuring volume - Gaussian intensity distribution across laser beam - beam diameter 𝑑 𝑒 determined at 13.5% of maximum intensity - focused beam diameter: 𝑓 𝑇 - focal distance of the lens - measuring volume with an ellipsoidal shape Fringe model - fringes in measuring volume with fringe spacing - fringe number in measuring volume

Laser Doppler velocimetry Scattered light intensity of moving particle

Laser Doppler velocimetry Directional ambiguity / Frequency shift - Particles moving in either the forward or reverse direction will produce identical signals and frequencies. - With frequency shift (w. Bragg cell) in one beam relative to the other, the interference fringes appear to move at the shift frequency. - The fringe moving speed is subtracted from measured velocity. - With frequency shifting, negative velocities can be distinguished. 8

Laser Doppler velocimetry LDV measuring system

Laser Doppler velocimetry - spatial coherent cross-correlation between two points has only 1 value at all times Laser, characteristics and requirements Monochrome - light of a narrow frequency Coherent - temporal coherent perfectly correlated at one location between any two different times Linearly polarized Laser Low divergence (collimator) Gaussian intensity distribution Laser

Laser Doppler velocimetry System configurations Forward scatter and side scatter (off-axis) Difficult to align, Vibration sensitive Backscatter Easy to align User friendly Receiving optics with detector Transmitting optics Flow with Detector Flow Laser Bragg cell Detector Transmitting and receiving optics

Laser Doppler velocimetry Multicomponent LDV systems Two-component system - two pairs of laser beams create two groups of fringe planes perpendicular to each other to measure two velocity components - different wavelength for each pair of beams e.g. Argon-ion laser spectral peaks at =514.5nm (G) and =488 nm (B) - optical filters used to separate signals Three-component system - add a third pair of laser beams for 3D velocity measurement

Homework - Read textbook 11.2-11.3 on page 264 - 275 Questions and Problems: 8 on page 286 - Due on 10/10