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Assessment of dual plane PIV measurements in wall turbulence using DNS data

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Abstract

Experimental dual plane particle image velocimetry (PIV) data are assessed using direct numerical simulation (DNS) data of a similar flow with the aim of studying the effect of averaging within the interrogation window. The primary reason for the use of dual plane PIV is that the entire velocity gradient tensor and hence the full vorticity vector can be obtained. One limitation of PIV is the limit on dynamic range, while DNS is typically limited by the Reynolds number of the flow. In this study, the DNS data are resolved more finely than the PIV data, and an averaging scheme is implemented on the DNS data of similar Reynolds number to compare the effects of averaging inherent to the present PIV technique. The effects of averaging on the RMS values of the velocity and vorticity are analyzed in order to estimate the percentage of turbulence intensity and enstrophy captured for a given PIV resolution in turbulent boundary layers. The focus is also to identify vortex core angle distributions, for which the two-dimensional and three-dimensional swirl strengths are used. The studies are performed in the logarithmic region of a turbulent boundary layer at z + = 110 from the wall. The dual plane PIV data are measured in a zero pressure gradient flow over a flat plate at Re τ = 1,160, while the DNS data are extracted from a channel flow at Re τ = 934. Representative plots at various wall-normal locations for the RMS values of velocity and vorticity indicate the attenuation of the variance with increasing filter size. Further, the effect of averaging on the vortex core angle statistics is negligible when compared with the raw DNS data. These results indicate that the present PIV technique is an accurate and reliable method for the purposes of statistical analysis and identification of vortex structures.

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Acknowledgements

The authors would like to express sincere thanks to Prof. Robert Moser for providing the DNS data for the channel flow. We are indebted to Dr. Bharathram Ganapathisubramani, Pramod Subbareddy and Dr. Nicholas Hutchins for their help in using the PIV and DNS datasets and many discussions during the course of this study. Support from the National Science Foundation through Grant CTS-0324898 and from the David and Lucile Packard Foundation is gratefully acknowledged.

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Authors and Affiliations

  1. Department of Aerospace Engineering and Mechanics, University of Minnesota, 107 Akerman Hall, 110 Union St. SE, Minneapolis, MN, 55414, USA

    Neelakantan Saikrishnan, Ivan Marusic & Ellen K. Longmire

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  1. Neelakantan Saikrishnan
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  2. Ivan Marusic
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  3. Ellen K. Longmire
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Correspondence to Neelakantan Saikrishnan.

Appendix: Effect of filter size on RMS statistics

Appendix: Effect of filter size on RMS statistics

The following section provides plots of the RMS values of velocity, vorticity and the Reynolds shear stress in the logarithmic, viscous buffer and outer regions of a turbulent boundary layer (Figs. 13, 14, 15, 16). These results can be used to estimate the percentage of turbulence intensity or enstrophy captured or lost for a given PIV interrogation resolution across turbulent boundary layers.

Fig. 13
figure 13

Variation of RMS statistics in the viscous buffer region with filter size of a velocity b vorticity. Quantities are normalized by raw DNS values

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Fig. 14
figure 14

Variation of RMS statistics in the logarithmic region with filter size of a velocity b vorticity. Quantities are normalized by raw DNS values

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Fig. 15
figure 15

Variation of RMS statistics in the outer region with filter size of a velocity b vorticity. Quantities are normalized by raw DNS values

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Fig. 16
figure 16

Variation of Reynolds shear stress with filter size, normalized by raw DNS values

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In all of the following plots, the normalization is done using the corresponding RMS value computed from the fully resolved DNS data set. RMS values of the various quantities at different wall-normal locations from the fully resolved DNS data are shown in Table 2. For the calculation of streamwise and spanwise derivatives in the wall-normal direction, a first-order approximation using two planes separated by Δz + = 21 is used, consistent with the description in Sect. 3. It must be noted that at the wall-normal location z + = 15, the effect of spacing between the planes can be seen clearly from the large drop in values of the vorticity components containing wall-normal gradients.

Table 2 RMS statistics at various wall-normal locations for the fully resolved DNS dataset
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Saikrishnan, N., Marusic, I. & Longmire, E.K. Assessment of dual plane PIV measurements in wall turbulence using DNS data. Exp Fluids 41, 265–278 (2006). https://doi.org/10.1007/s00348-006-0168-z

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