Three-component micro-PIV using the continuity equation and a comparison of the performance with that of stereoscopic measurements

Abstract

Recently, a number of techniques have been presented for the determination of the third “out-of-plane” velocity component in micro particle image velocimetry (micro-PIV) data. In particular, the conventional macroscopic stereo-PIV technique has been converted to the micro scale by the use of stereo-microscopy. In this work a different technique is investigated, which uses conventional, two-component micro-PIV to generate velocity data on a number of planes. The in-plane velocity gradients are then calculated, which can be used in the continuity equation to produce the out-of-plane velocity gradients. These, together with the no-penetration boundary condition, can then be used to calculate the out-of-plane velocities. An algorithm is presented that is capable of handling up to one invalid vector per column of data by using a combination of first order and second order projections of the velocity. The advantage of the continuity based technique is that it uses the existing two-component micro-PIV technology, which at present is in a more advanced stage of development then stereo-microscopy based micro-PIV. The technique is investigated using a flow similar to one used previously to assess stereoscopic micro-PIV (Meas Sci Technol 17:2175–2185, 2006). This allows a comparison of the performance of the two techniques. The results show that the continuity based data agrees well with an independent computational fluid dynamics solution and has a smaller experimental uncertainty than the stereoscopic technique at a better spatial resolution. There are, however, potential limitations to the continuity based technique. These include the two-dimensionality of the data, which is limited to the planes on which the original images were taken, and the dependence of the technique on the data close to surfaces, where the experimental errors are often greatest. Stereoscopic micro-PIV does not have these limitations so, whilst at present it appears that continuity based techniques may be more accurate, there is sufficient potential for stereoscopic techniques to justify their further development.