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High-speed particle image velocimetry for the efficient measurement of turbulence statistics

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Abstract

A high-frame-rate camera and a continuous-wave laser are used to capture long particle image sequences exceeding 100,000 consecutive frames at framing frequencies up to 20 kHz. The electronic shutter of the high-speed CMOS camera is reduced to \(10\,\upmu\)s to prevent excessive particle image streaking. The combination of large image number and high frame rate is possible by limiting the field of view to a narrow strip, primarily to capture temporally resolved profiles of velocity and derived quantities, such as vorticity as well as higher order statistics. Multi-frame PIV processing algorithms are employed to improve the dynamic range of recovered PIV data. The recovered data are temporally well resolved and provide sufficient samples for statistical convergence of the fluctuating velocity components. The measurement technique is demonstrated on a spatially developing turbulent boundary layer inside a small wind tunnel with \(Re_\delta = 4{,}800,\, Re_\tau = 240\) and \(Re_\theta = 515\). The chosen magnification permits a reliable estimation of the mean velocity profile down to a few wall units and yields statistical information such as the Reynolds stress components and probability density functions. By means of single-line correlation, it is further possible to extract the near-wall velocity profile in the viscous sublayer, both time-averaged as well as instantaneous, which permits the estimation the wall shear rate \(\dot{\gamma }\) and along with it the shear stress \(\tau _w\) and friction velocity \(u_\tau\). These data are then used for the calculation of space-time correlation maps of wall shear stress and velocity.

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Notes

  1. Displacements larger than \(\frac{1}{2}\)IW are recoverable with advanced PIV processing methods but impose other restrictions.

Abbreviations

\(c_\mathrm{f}\) :

Friction coefficient

\(f\) :

Focal length

\(f_\#\) :

f-Number (lens aperture)

IW:

Interrogation window size

\(M\) :

Magnification

\(N\) :

Number of samples

\(R_{ij}\) :

Space-time correlation function of scalar quantities \(i,j\)

\(Re_\delta\) :

Reynolds number based on \(U_{\mathrm {99}}\) and \(\delta _{99}\)

\(Re_{\delta ^*}\) :

Reynolds number based on \(U_{\mathrm {99}}\) and \(\delta ^*\)

\(Re_\theta\) :

Reynolds number based on \(U_{\mathrm {99}}\) and \(\theta\)

\(Re_\tau\) :

Reynolds number based on \(u_\tau\) and \(\delta _{99}\)

\(S\) :

Shape factor, \(\delta ^*/\theta\)

\(t\) :

Time

\(u,v,w\) :

Streamwise, wall-normal and spanwise velocity components

\(u',v',w'\) :

Fluctuating velocity components

\(u_\tau\) :

Skin friction velocity

\(U_{cl}\) :

Center line velocity

\(U_{99}\) :

\(0.99\, U_{\mathrm {cl}}\)

\(x,y,z\) :

Streamwise, wall-normal and spanwise coordinates

\(x^+, y^+, z^+\) :

Distances in wall units based on \(u_\tau\)

\(\delta _{99}\) :

Boundary layer thickness at 99% \(U_{{\mathrm {cl}}}\)

\(\delta ^*\) :

Boundary layer displacement thickness

\(\Delta t\) :

Time delay between two illumination pulses

\(\Delta x, \Delta y\) :

Streamwise and wall-normal displacement in pixels

\(\lambda\) :

Wavelength of light

\(\nu\) :

Kinematic viscosity

\(\theta\) :

Boundary layer momentum thickness

\(\dot{\gamma }\) :

Wall shear rate \(\equiv {\partial u / \partial y}_{y=0}\)

\(\tau _w\) :

Wall shear stress

\(\omega _x,\omega _y,\omega _z\) :

Streamwise, wall-normal and spanwise vorticity components

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Acknowledgments

The author would like to thank his colleagues J. Klinner, M. Schroll and M. Beversdorff for their assistance in the wind tunnel setup and PIV measurements. Further acknowledgment goes to N. Buchmann for his valuable comments while preparing the manuscript. Finally, the support of PCO GmbH is gratefully acknowledged who provided the Dimax-HS4 high-speed camera for evaluation purposes. The recommendations by the anonymous reviewers significantly improved the overall quality of the manuscript.

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  1. German Aerospace Center (DLR), Institute for Propulsion Technology, 51170, Cologne, Germany

    Christian E. Willert

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Willert, C.E. High-speed particle image velocimetry for the efficient measurement of turbulence statistics. Exp Fluids 56, 17 (2015). https://doi.org/10.1007/s00348-014-1892-4

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