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Experimental analysis of high-speed helium jet flow using four-dimensional digital speckle tomography

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Abstract

A high-speed and initial helium jet flow has been analyzed by a developed four-dimensional digital speckle tomography. Multiple high-speed cameras have been used to capture movements of speckles in multiple angles of view simultaneously because a shape of a nozzle for the jet flow is asymmetric and the initial jet flow is fast and unsteady. The speckle movements between no flow and helium jet flow from the asymmetric nozzle controlled by a solenoid valve have been obtained by a cross-correlation tracking method so that those distances can be transferred to deflection angles of laser rays for density gradients. The four-dimensional density fields for the high-speed helium jet flow have been reconstructed from the deflection angles by a developed real-time tomography method.

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Abbreviations

b :

Basis function

C :

Multiplicative correction vector

f :

Actual field

\(\ifmmode\expandafter\hat\else\expandafter\^\fi{f} \) :

Guessed or intermediate objective function to be optimized

\(\ifmmode\expandafter\bar\else\expandafter\=\fi{f} \) :

Average value of phantom field f

G :

Gladstone–Dale constant

J :

Equally spaced points in x direction

K :

Equally spaced points in y direction

L :

Equally spaced points in z direction

n :

Index of refraction

n air :

Refractive index of ambient air

n helium :

Refractive index of pure helium

l :

Distance between the test section and the viewing screen

O j :

Height coefficient of j-th basis function

q :

Iteration number

s :

Coordinate on the projection plane, perpendicular to the ray direction

t :

Coordinate parallel to the ray direction

W :

Projection matrix

W i,j :

Weighting factor of MART

w i :

i-th Row of projection matrix

(x, y, z):

Objective field coordinate

α :

Line-of-sight beam deflection angle

δ :

Speckle displacement

Φ :

Reconstruction error

λ :

Laser wave length

θ :

Angle of projection

ρ :

Density

ρ*:

Relative density

ρ air :

Ambient air density

ρ h :

Partial density of helium in mixture

ρ helium :

Pure helium density

\( \ifmmode\expandafter\hat\else\expandafter\^\fi{\psi } \) :

Virtual projection of guessed field

ψ IF :

Interferometric projection of actual field

ψ SP :

Digital speckle projection of actual field

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Acknowledgements

This work was performed at Nuclear Engineering Research Laboratory of the University of Tokyo. This work was also partially supported by the Korea Research Foundation Grant funded by the Korean Government (No. R08-2003-000-10030-0).

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Authors and Affiliations

  1. School of Mechanical Engineering, Sungkyunkwan University, 300 ChunChun-Dong, JangAn-Gu, Suwon, 440-746, KyungGi-Do, Korea

    Han Seo Ko & Yong-Jae Kim

  2. Ibaraki College of Technology, Ibaraki, Japan

    Koh Ikeda

  3. Department of Mechanical Engineering, The University of Ryukyus, Okinawa, Japan

    Masaaki Ishikawa

  4. Department of Quantum Engineering and Systems Science, University of Tokyo, Tokyo, Japan

    Koji Okamoto

Authors
  1. Han Seo Ko
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  2. Koh Ikeda
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  3. Masaaki Ishikawa
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  4. Koji Okamoto
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  5. Yong-Jae Kim
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Correspondence to Han Seo Ko.

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Ko, H.S., Ikeda, K., Ishikawa, M. et al. Experimental analysis of high-speed helium jet flow using four-dimensional digital speckle tomography. Exp Fluids 40, 442–451 (2006). https://doi.org/10.1007/s00348-005-0083-8

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  • DOI: https://doi.org/10.1007/s00348-005-0083-8

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