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Volumetric 3-Component Velocimetry (V3V)

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Volumetric 3-Component Velocimetry (V3V)

• Individual laser pulses illuminate a volumetric measurement region

• 3-aperture camera probe captures images of tracer particle locations at each laser pulse, through each imaging aperture

• 3-dimensional particle positions are calculated based on information from each aperture

• Flow velocity is measured based on individual particle displacements in the time between laser pulses

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V3V Operation•3D3C Imaging Technique

–Based on DDPIV (Gharib – Caltech)

•Illumination

–Laser illuminates tracers in a volume up to 140 x 140 x 100 mm

–2 pulses (like PIV)

•3D Camera

–3 apertures view measurement region from 3 different perspectives

–3D particle locations determined based on information from each aperture

•Algorithm

–2-Frame Particle Tracking

–Velocity is based on individual particle displacements in the time between laser pulses

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• 3-Aperture Camera

•Measurement Volume defined by overlap of 3 viewing angles

•Combined information from the 3 apertures yields a particle ‘triplet’ for each particle in the common viewing area.

3D Imaging

MeasurementVolume

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Principle of ‘Triplets’

FocalPlane

FocalPlane

2 eyes

3 apertures ‘Triplet’

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3D Camera Calibration

• Automated Multi-plane Calibration • Capture calibration target images in z-planes parallel to the camera.

– Find the target center in each plane to correct misalignment error

– Find dewarping polynomials in each plane to correct lens distortion

– Find pixel adjustment factor in each plane to correct pinhole deviation.Triplet size at each calibration plane

© 2010, TSI Incorporated

Validation Part I: Camera Calibration

• Camera Calibration is used to correct the discrepancy between a real camera and a perfect camera.

Real Camera

Perfect Camera

Mechanical misalignment error

Optical aberration and distortion

Deviation from pinhole optics (e.g. lens, pixels,

aperture locations)

Adjusting reference distance and pixel size

Multi-plane Dewarping

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Validation Part II: 3D Position Measurement

• Grid points on reconstructed calibration targets in multiple z planes

-0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.20

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Error (mm)

Pro

ba

bili

ty D

en

sity

xy error xy error fit (t location-scale)z error z error fit (t location-scale)

xy 1.4 m 8.2 m 3.24z 2.6 m 37.2 m 5.00

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V3V Data Processing

Right A

Left A Top A Right B

Left B Top B

Frame A

2D Particle ProcessorIdentify particles in images

Frame B

Right A

Left A Top A Right B

Left B Top B

Triplet ProcessorFind particles in 3D space

Velocity ProcessorTrack particles in 3D space

TIFF Image

3D Velocity Field

P2D File

P3D File

PV3D/GV3D File

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2D Particle Identification Algorithm

• 2D Gaussian fit of particle image intensity distribution

• Using the Levenberg-Marquardt algorithm for non-linear optimization

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Triplet Search Algorithm

• A particle in the top image defines a ray in the left and right images

• Algorithm searches along these rays for potential matches

• Coarse Search (within 1 pixel)

• Fine Search (0.5 pixels)

Calibration planesCoarse search planesFine search planes

From: Sharp et al. (2009) Exp in Fluids, in Press.

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3D Particle Tracking

• 3D particle cloud at t• 3D particle cloud at t + Δt

• Relaxation Method for Particle Tracking– See for example: Ohmi, Li (2000) Meas. Sci. Tech.– Particles divided into clusters (similar to interrogation region in PIV)– Probability-based matching

From: Sharp et al. (2009) Exp in Fluids, in Press.

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Velocity on Rectangular Grid

• Randomly Spaced Vector Field to Rectangular Grid

• Gaussian-weighted Interpolation

(Slice)

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Example Experimental Setup

Cylinder

Laser

3D Camera Mirror

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Data

Flow over a Cube

From: Pan et al. (2007) V3V: A New Tool for 3D Flow Measurement, APS 2007

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Data

Bluegill Fish Wake Vorticity Isosurfaces colored by Streamwise Velocity

Courtesy: George Lauder, Harvard University

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Data

Vortex Ring from Inclined ExitRe = 2500

From: Troolin, Longmire (2009) Volumetric Velocity Measurements of Vortex Rings from Inclined ExitsExp in Fluids, In Press.

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Propeller Measurements

Tip velocity = 3.2 m/s

Courtesy of INSEAN, Italy

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Mixer with Rushton Turbine

Courtesy of Penn State U

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Wake flow behind a sphere

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Measurement of Vortex Ring Impinging on a Plate

1” injector

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Vortex Ring Impinging on a Plate

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Vortex Ring Impinging on a Plate

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Vortex Ring Impinging on a Plate

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Vortex Ring Impinging on a Plate