1. 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

2. Lecture 19. Laser Doppler velocimetry

3. Laser Doppler velocimetry
Doppler effect

4. 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 

5. 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:

6. 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

7. Laser Doppler velocimetry
Scattered light intensity of moving particle

8. 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

9. Laser Doppler velocimetry
LDV measuring system

10. 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

11. 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

12. 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

13. Homework
- Read textbook on page
Questions and Problems: 8 on page 286
- Due on 10/10