On the accuracy of one-point and two-point statistics measured via high-speed PIV

Abstract

Spatial and temporal velocity gradients as well as one-point and two-point statistical quantities like space-time correlations are of great interest for many fields of research in fluid dynamics in general. The here presented study is motivated by an approach to investigate and contribute to the understanding of aeroacoustic theory, where the knowledge of such quantities is needed. Flow measurements via high-speed particle image velocimetry (PIV) provide a non intrusive method to obtain temporal and spatial resolved velocity fields and Wernet already calculated two-point statistics from high-speed PIV data. One goal of the here presented study is to investigate the accuracy of the described quantities determined via the PIV technique while a special attention is turned on the influence of the interrogation window size for the PIV analysis. High speed PIV measurements with a sample frequency of 20 kHz are conducted in order to characterize the temporal and spatial response of such a system. The limits and drawbacks associated with the PIV measurement technique regarding one-point and two-point statistical quantities like the space-time correlations of the obtained velocity time series are investigated. Hot wire measurements are performed for comparison. As a test case, the near wake behind a cylinder at a Reynolds number of Re = 10; 000 is chosen for the here presented study. The spatial filter effect which is inherent in the PIV method due to the averaging over the interrogation window was experimentally investigated by Foucaut et al. . They considered the wave-number spectrum of a turbulent flow and evaluated how the spectrum depends on the size of the interrogation window. Previous studies have shown that the measurement noise, which is part of the PIV-process chain, can be formally split in two parts. The first part is assumed to consist of random fluctuations which are uniformly distributed in space and simply added to the actual flow field. These fluctuations appear as white noise in the wave-number spectrum and are attenuated by the PIV averaging like the fluctuations in the flow field. The second part of the noise is assumed to be additional white noise which is not affected by the spatial filter.