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Validating under-resolved turbulence intensities for PIV experiments in canonical wall-bounded turbulence

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Abstract

The discrepancy between measured turbulence intensity obtained from experiments in wall-bounded turbulence and the fully resolved reference results (usually from DNS datasets) are often attributed to spatial resolution issues, especially in PIV measurements due to the presence of spatial averaging within the interrogation region/volume. In many cases, in particular at high Reynolds numbers (where there is a lack of DNS data), there is no attempt to verify that this is the case. There is a risk that attributing unexpected PIV statistics to spatial resolution, without careful checks, could mask wider problems with the experimental setup or test facility. Here, we propose a robust technique to validate the under-resolved PIV obtained turbulence intensity profiles for canonical wall-bounded turbulence. This validation scheme is independent of Reynolds number and does not rely on empirical functions. It is based on arguments that (1) the viscous-scaled small-scale turbulence energy is invariant with Reynolds number and that (2) the spatially under-resolved measurement is sufficient to capture the large-scale energy. This then suggests that we can estimate the missing energy from volume-filtered DNS data at much lower Reynolds numbers. Good agreement is found between the experimental results and estimation profiles for all three velocity components, demonstrating that the estimation tool successfully computes the missing energy for given spatial resolutions over a wide range of Reynolds numbers. A database for a canonical turbulent boundary layer and associated MATLAB function are provided that enable this missing energy to be calculated across a range of interrogation volume sizes, so that users do not require access to raw DNS data. This methodology and tool will provide PIV practitioners, investigating canonical wall-bounded turbulent flow with a convenient check of the effects of spatial resolution on a given experiment.

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Acknowledgments

The authors gratefully acknowledge the financial support of the Australian Research Council. The authors also wish to thank Dr J. A. Sillero and Professors J. Jiménez and R. D. Moser for making the DNS dataset publicly available.

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Authors and Affiliations

  1. Department of Mechanical Engineering, University of Melbourne, Parkville, VIC, 3010, Australia

    J. H. Lee,  Kevin, J. P. Monty & N. Hutchins

Authors
  1. J. H. Lee
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  2. Kevin
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  3. J. P. Monty
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  4. N. Hutchins
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Correspondence to J. H. Lee.

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Appendix

Appendix

For a turbulent boundary layer, a database of the missing energy profiles for u, v and w components with various spatial resolutions (listed in Table 2) is provided as supplementary information. This database is in the form of a .mat file (348_2016_2209_MOESM1_ESM.mat) which contains missing u, v and w energy (SR_u_DB, SR_v_DB, SR_w_DB) in the form of 4D matrices (1000, 6, 6, 6) which have data pertaining to (\(z^+\), \(\Delta x^+\), \(\Delta y^+\), \(\Delta z^+\)). An example MATLAB function below provides an example of how this database can be used to estimate the missing energy due to a given spatial resolution. SRdiff is the missing energy \(\Delta \overline{u^2}^+|_{SR^+}\) (or the other components) estimated for a given resolution (SR_x, SR_y, SR_z = \(\Delta x^+, \Delta y^+, \Delta z^+\)) at given wall heights (zexp which is a vector of \(z^+\) locations at which SRdiff is required).

The following is an example matlab script

figure a

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Lee, J.H., Kevin, Monty, J.P. et al. Validating under-resolved turbulence intensities for PIV experiments in canonical wall-bounded turbulence. Exp Fluids 57, 129 (2016). https://doi.org/10.1007/s00348-016-2209-6

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  • DOI: https://doi.org/10.1007/s00348-016-2209-6

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