The Spectral Response of Time-Resolved PIV in a Turbulent Boundary Layer

Abstract This study presents the application of time-resolved particle image velocimetry (TR-PIV) to measure the mean and fluctuating velocity components in a turbulent boundary layer (TBL) over an axisymmetric body of revolution. A narrow wall-normal strip of the flow was captured using a synchronised high-speed laser and camera at a recording frequency of up to 80~kHz. The resulting streamwise and wall-normal velocity TR-PIV data were validated against hot-wire anemometry measurements and direct numerical simulations (DNS) of a flat plate under matched flow conditions. The mean flow results showed good agreement between all methods, while the expected attenuation due to the spatial averaging was found in the TR-PIV turbulence statistics closer to the wall. A key outcome of this study is the establishment of an effective laser sheet thickness for the TR-PIV using DNS as a reference. This study fills a gap in understanding the spectral response and limitations of TR-PIV in such complex flows, particularly how spatial resolution and noise influence the accuracy of turbulence measurements. As such, the TR-PIV streamwise velocity energy spectra were compared with DNS data that were spatially filtered to match the resolution of the TR-PIV and hot-wire. A transfer function was derived to determine cut-off wavelengths as a function of wall-normal distance. The cut-off wavelengths enabled the quantification of the resolvable turbulence scales within the TBL, revealing that the spatial resolution, in particular the spanwise resolution, is a limiting factor for TR-PIV. The theoretical Nyquist, particle response, and interrogation window cut-off wavelengths were found to be outside the main energetic length scales. This methodology was applied to locations with zero and favourable pressure gradients, providing insights into how pressure gradients influence spectral content and the limitations of TR-PIV in capturing the full range of turbulence scales. The outlined methodology is applicable more broadly and can be used to enhance the accuracy of experimental techniques in future boundary layer investigations.