Feasibility Of Multi-Aperture µPTV For Wall Shear Stress Measurements

Abstract

We present a feasibility study on 3d 3c micro PTV for boundary layer flows using a single high-speed camera with a microscope lens. Multi-aperture µPTV (MA-µPTV) relies on the “defocusing” concept (Willert & Gharib, 1992) and determines the wall distance of a particle from the size of projected particle image triplets generated by placing an triplet aperture on the entrance pupil of a microscope objective. Illumination with a high-speed pulsed laser is introduced through the same window used for imaging. The calibration of the orientation and size of the particle image triplets is described and accounts for variation of both with lateral image position and wall distance. Geometrically constrained templates of 2d Gaussians are used to provide least square fitting of triple image intensities, thereby iteratively improving the initial centers and depth position of each particle. In addition to Gaussian weighting, the convolution of a Gaussian and a Lorentzian is studied, that latter of which is considered promising for modeling defocused particle images at large distances from the focus. Lagrangian particle tracks are reconstructed from 3d particle positions using state-of-the-art tracking procedures. Comparative profile-PIV measurements provide reference measurements including estimates of the wall shear stress. A comparison with PIV flow statistics is possible by bin-averaging the velocities of the particle tracks in the wall-normal direction. Mean wall shear rates obtained from MA-µPTV and using single-line cross-correlation on the PIV data are in good agreement and within the uncertainty of the flow parameters. Statistics from bin-averaged velocities of all tracked particles indicate consistency with profile-PIV and agree well with DNS data up to wall distances of 30 wall units.