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Experiments in Fluids

, Volume 41, Issue 3, pp 499–511 | Cite as

A further assessment of interpolation schemes for window deformation in PIV

  • Byoung Jae Kim
  • Hyung Jin SungEmail author
Research Article

Abstract

We have evaluated the performances of the following seven interpolation schemes used for window deformation in particle image velocimetry (PIV): the linear, quadratic, B-spline, cubic, sinc, Lagrange, and Gaussian interpolations. Artificially generated images comprised particles of diameter in a range 1.1 ≤ d p ≤ 10.0 pixel were investigated. Three particle diameters were selected for detailed evaluation: d p = 2.2, 3.3, and 4.4 pixel with a constant particle concentration 0.02 particle/pixel2. Two flow patterns were considered: uniform and shear flow. The mean and random errors, and the computation times of the interpolation schemes were determined and compared.

Keywords

Particle Image Velocimetry Random Error Shear Flow Interpolation Scheme Uniform Flow 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

List of symbols

a

parameter in the cubic interpolation

C

particle density (particle/pixel2)

d

arbitrary value between 0 and 1 (pixel)

dp

particle diameter (pixel)

f

spatial frequency (pixel−1)

f(x,y)

intensity data interpolated from the original image

f1 (x,y)

intensity data of the first image

f2 (x,y)

intensity data of the second image

G0 (x,b)

Gaussian function

GP (x,b)

Pth derivative of the Gaussian function

h(x)

one-dimensional impulse response function of a reconstruction filter

h2D (x,y)

two-dimensional impulse response function of a reconstruction filter

H(f)

Fourier transform of the one-dimensional impulse response function of a reconstruction filter

i

integer horizontal position in the image (pixel)

j

integer vertical position in the image (pixel)

k

iteration number

M

total number of vectors

N

kernel size of an interpolation (pixel)

U

horizontal displacement in the uniform flow (pixel)

\(\bar{U}\)

mean of the measured displacements in the uniform flow (pixel)

Uexact

exact displacement on the image for the uniform flow (pixel)

Uc

horizontal displacement in the shear flow (pixel)

\(\bar{U}_{c}\)

mean of the measured displacements in the shear flow (pixel)

Uc,exact

exact displacement on the image for the shear flow (pixel)

\(\vec{V}(i,j)\)

velocity vector at the (i,j) location (pixel, pixel)

W

size of a square interrogation window (pixel)

γ2

parameter used in the second-order Gaussian interpolation

γ6

parameter used in the sixth-order Gaussian interpolation

Δx

horizontal value to be determined through cross-correlation (pixel)

Δy

vertical value to be determined through cross-correlation (pixel)

σ

random error (pixel)

ω

shear rate (pixel/pixel)

ω (i,j)

two-dimentional Gaussian windowing mask

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Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringKorea Advanced Institute of Science and TechnologyYuseong-guSouth Korea

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