Feasibility of multi-aperture micro-PTV for wall shear stress measurements

Abstract

We present a feasibility study on 3d-3c micro particle tracking velocimetry (µPTV) for boundary layer flows using a single high-speed camera with a microscope lens. Multi-aperture micro-PTV (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 a triplet aperature on the entrance pupil of the microscope lens. 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 lateral image position as well as 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, 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. The measurement technique is demonstrated in a developing turbulent duct flow of a small wind tunnel up to Re_tau = 836 for a wall-bounded volume up to 1.7x1.3x1 mm^3 (in viscous units 52x40x31). Comparative profile-PIV measurements provide reference measurements including estimates of the wall shear stress. A comparison with flow statistics obtained with 2d-2c PIV is made possible by bin-averaging the velocities of the particle tracks in the wall-normal direction at a resolution of 10-16 µm. Mean wall shear rates obtained from MA-µPTV and single-line cross-correlation on the PIV data are in good agreement. The fluctuations in wall shear rate are consistent with correlations found in the literature. Statistics from bin-averaged velocities of all tracked particles indicate consistency with profile-PIV and are in agreement with DNS data up to wall distances of 28 viscous units.