Research Papers

Spatial Spectrum From Particle Image Velocimetry Data

[+] Author and Article Information
Daniel Duda

Department of Power System Engineering,
University of West Bohemia,
Univerzitní 22,
Pilsen 306 14, Czech Republic
e-mail: dudad@kke.zcu.cz

Vaclav Uruba

Department of Power System Engineering,
University of West Bohemia,
Univerzitní 22,
Pilsen 306 14, Czech Republic;
Department of Fluid Dynamics,
Institute of Thermomechanics,
Czech Academy of Sciences,
Dolejškova 5,
Prague 182 00, Czech Republic
e-mail: uruba@kke.zcu.cz

Manuscript received November 16, 2018; final manuscript received February 26, 2019; published online April 16, 2019. Assoc. Editor: Martin Schulc.

ASME J of Nuclear Rad Sci 5(3), 031901 (Apr 16, 2019) (7 pages) Paper No: NERS-18-1116; doi: 10.1115/1.4043319 History: Received November 16, 2018; Revised February 26, 2019

We present a simple method of obtaining the turbulence kinetic energy spectrum from spatially resolved particle image velocimetry (PIV) data without need of use of Taylor hypothesis of frozen turbulence. Additionally, this method allows us to extract the velocity field components related to individual length scales resolved in the spectrum. We convolute the measured PIV velocity field with a band-pass filter, i.e., a difference of two Gauss functions with different widths, and the energy content of a such product we relate to the relevant length-scale of the used band. This is a “kind of wavelet transformation”, which, in respect to Fourier transformation, gives a good physical meaning to individual components.

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Grahic Jump Location
Fig. 1

The main result of our study, left: the energy spectra at four different locations in the jet shear layer (first number in the legend) and at three different velocities (second number in the legend is the corresponding Reynolds number (k plays for ×103)), right: the same data divided by k−5∕3 in order to highlight the difference from the universal behavior (i.e., k−5∕3 is just a horizontal line)

Grahic Jump Location
Fig. 2

Left is a sketch of the location of 2 of 4 sample fields of view used in this work in respect to the jet nozzle. Right panels show the mean velocity magnitude in both drawn FoVs at the jet velocity 50.4 m/s, Re = 1.7 × 105. The remaining FoVs are located 0.17 and 0.235 m from the jet nozzle.

Grahic Jump Location
Fig. 3

Illustration of the extraction of the length-scale dependent signal in a single snapshot. First panel: original data taken 0.235 m from the jet nozzle at Re = 1.6 × 104. Second panel: the convolution with Gaussian of halfwidth 4 IA = 1.1 × 10–3 m keeps the mean flow. Note that the energy is almost equal to that of original data (difference hidden in next digit). Third panel shows the subtraction of data smoothed over 1 IA = 2.8 × 10−4 m and 4 IA = 1.1 × 10−3 m highlighting structures of this size interval. The velocity scale of the plot is 10 × smaller. The last panel shows the rest of this decomposition: structures uncorrelated in the length-scale 1 IA = 2.8 × 10−4 m. Coordinates and halfwidths of Gaussians are in 10−3 m.

Grahic Jump Location
Fig. 4

The same data as in Fig. 3 filtered by using different band-pass-filters. Coordinates and the values of Gaussian halfwidths are in 10−3 m.

Grahic Jump Location
Fig. 5

The length-dependent turbulence kinetic energy at the shear layer close to the nozzle of the jet for three jet velocities (a) 4.8 m/s, Re = 1.6 × 104, (b) 16.1 m/s, Re = 5.4 × 104 and (c) 50.4 m/s, Re = 1.7 × 105. The color of each IA is composed of three colors: red for TKE at length-scale (3–4) × 10−4 m, green for (8–11) × 10−4 m, and blue for (2.2–3.3) × 10−3 m. The outer quiet fluid is at the left-hand side of each figure and the jet core at the right-hand side. Coordinates are in 10−3 m counted from the origin of the FoV.

Grahic Jump Location
Fig. 6

(a) The energy spectrum normalized by k– 5∕3, for the sake of simplicity, only data 7.5 × 10−2 m from the nozzle are displayed. The red dashed line shows geometrically the method for estimation of instrumental noise. The orange triangles represent the spectrum of one cleaned dataset, namely in the distance 7.5 × 10−2 m at Re = 1.7 × 105. (b): effect of the cleaning, i.e., removing frames with significantly higher energy than the average at small scale. These points are corrupted probably during the PIV analysis—wrong correlation peak has been selected. The colormap is same as in Fig. 5.

Grahic Jump Location
Fig. 7

Comparison of fluctuation decompositions of instantaneous velocity field of dataset 1.75 × 10−1 m, 5.4 × 105: (a) shows the convolution with band-pass-filter with σL = 2.8 × 10−4 m and σH = 1.7 × 10−3 m and (b) is standard Reynolds decomposition, i.e., subtraction of time-averaged velocity field, smoothed over 2.8 × 10−4 m. Coordinates are in 10−3 m. Color shows the vorticity ωz=∇×u.



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