Effects of the spatial resolution of planar PIV on measured turbulence multi-point statistics

Particle Image Velocimetry (PIV), in particular planar PIV, has been widely implemented in the experimental study of statistical characteristics of turbulence because of its maturity in technology and capability to provide instantaneous flow fields. The spatial resolution of PIV measurement, i.e., the smallest scale of the flow field resolvable by PIV, is determined by the size of the Interrogation Window (IW) during image processing. Hence, small-scale turbulence fluctuations might not be accurately resolved, which leads to deviations in measured turbulence multi-point statistics, such as velocity structure functions, turbulent dissipation rate and so on. To quantify this deviation, we model the effect of PIV measurement on the instantaneous single-point velocity vectors as spatial filtering, which allows the change of the velocity structure functions and the turbulent dissipation rate measured by PIV with filter size to be derived. To check these predictions, synthetic PIV image pairs were generated based on simulated tracer particle motions following the velocity fields from direct numerical simulation (DNS) of isotropic turbulence, which were then processed by a standard PIV algorithm. Turbulence statistics obtained from such measured velocity fields were then compared with those from the exact DNS data to evaluate quantitative deviations. The results show that our model captures the effect of spatial resolutions on turbulence statistics in PIV measurement. Experimentally, planar PIV measurements were carried out in the center of a von Kármán swirling flow device, where the turbulence is nearly homogeneous and isotropic. The deviation between measured velocity structure functions and the K41 theory was also analyzed and corrected using the aforementioned model prediction. This work provides a theoretical guidance for examing turbulence statistics measured by PIV, especially multi-point statistics at small scales.