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Tomographic spatial filter velocimetry for three-dimensional measurement of fluid velocity

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Abstract

Spatial filter velocimetry (SFV) is extended to three-dimensional three-component velocimetry by coupling the SFV processing with a tomographic technique, which reconstructs three-dimensional particle distributions from stereoscopic particle images recorded by two cameras. Since time duration of a ghost particle traveling through an interrogation area of SFV is shorter than the transit time of a real tracer particle, a validation method of velocity data based on a particle transit time is used to eliminate ghost particles generated in the particle reconstruction process. Effect of a ghost particle on velocity evaluation is not significant due to the short transit time of a ghost particle. The developed system is applied to a free jet, and an impinging jet discharged from a circular pipe. Three-dimensional distributions of time-averaged velocity vectors of the jets are successfully measured by the developed tomographic spatial filter velocimetry (Tomo-SFV) in spite of using only two cameras. The peak-locking errors, which are apt to occur in particle image velocimetry measurements, do not appear in Tomo-SFV measurements.

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Abbreviations

A :

Offset matrix

D :

Inner diameter of nozzle (m)

F SF :

Spatial filter function

f :

Frequency (Hz)

I :

Intensity

I SF :

Integrated intensity

L :

Wavelength of spatial filter (m)

M :

Magnification matrix

q :

Flow rate (m3/s)

r :

Coordinate in radial direction (m)

t :

Time (s)

U :

Axial mean velocity (m/s)

u :

Instantaneous axial velocity (m/s)

V :

Mean velocity vector (m/s)

v :

Velocity (m/s)

x :

Coordinate in vertical direction (m)

y :

Coordinate in width direction (m)

z :

Coordinate in depth direction (m)

Δx, Δy, Δz :

Size of interrogation area in x, y and z directions (m)

λ :

Wavelength (m)

ν :

Kinematic viscosity (m2/s)

θ :

Volume of a voxel (m3)

C :

Center

i :

Camera number

max:

Maximum value

r :

r direction

x :

x direction

xi :

ith direction

y :

y direction

z :

z direction

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Acknowledgments

The authors gratefully acknowledge the support on the high-speed camera by Photron Ltd. This work has been partly supported by the Japan Society for the Promotion of Science (Grants-in-aid for scientific research (C) No. 22560167 and (B) No. 25289033).

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Authors and Affiliations

  1. Department of Mechanical Engineering, Graduate School of Engineering, Kobe University, 1-1 Rokkodai, Nada, Kobe, Hyogo, 657-8501, Japan

    Shigeo Hosokawa, Takaaki Matsumoto & Akio Tomiyama

Authors
  1. Shigeo Hosokawa
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  2. Takaaki Matsumoto
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  3. Akio Tomiyama
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Corresponding author

Correspondence to Shigeo Hosokawa.

Additional information

This article is part of the Topical Collection on Application of Laser Techniques to Fluid Mechanics 2012.

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Hosokawa, S., Matsumoto, T. & Tomiyama, A. Tomographic spatial filter velocimetry for three-dimensional measurement of fluid velocity. Exp Fluids 54, 1597 (2013). https://doi.org/10.1007/s00348-013-1597-0

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  • DOI: https://doi.org/10.1007/s00348-013-1597-0

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