Lagrangian acceleration evaluation for tomographic PIV : a particle - tracking based approach

The evaluation of the instantaneous three-dimensional pressure field from tomographic PIV data relies on the accurate estimate of the Lagrangian acceleration. To date, techniques to reconstruct the Lagrangian trajectories from velocity fields obtained by Tomo-PIV have been used. Nevertheless, the reconstruction of relatively long trajectories, beneficial for the reduction of the precision error in the acceleration evaluation, suffers from truncation errors introduced both during the trajectory reconstruction and by the evaluation of the derivative with finite differences. On the other hand, 3D particle tracking velocimetry (3D-PTV) allows for the accurate reconstruction of single particle trajectories over a long observation time providing an accurate evaluation of the Lagrangian properties. Since particles are identified and tracked on the camera images, ambiguities can raise by overlapping particles which limit the range of applicable seeding density, typically one order of magnitude less than Tomo-PIV, therefore providing highly sparse information. In the present study a technique to combine the higher spatial resolution of tomographic PIV and the accurate trajectory reconstruction of PTV is proposed (Tomo-3D-PTV), which provides accurate material acceleration information over a dense regular grid, condition needed for the evaluation of the pressure field. The particle tracking algorithm is applied over reconstructed objects by tomographic PIV; ambiguities in the particle identification over subsequent recordings are avoided given the relatively large distance between particles in the 3D domain. The use of polynomial functions to fit the tracked particle position leads to the reduction of errors in the peak location potentially introduced by tomographic reconstruction. The Lagrangian acceleration is obtained analytically by the polynomial fit which largely reduces truncation errors. The analysis of computer generated data of an advecting vortex ring shows that a reduction up to a factor 2.5 of the precision error in the material acceleration can be achieved when a long sequence is considered (e.g. 15-20 recordings); moreover, the truncation error introduced by the PIV based technique is almost completely compensated for. The Lagrangian acceleration information obtained on scattered locations in the 3D domain is fitted to a regular grid by means of a second order spatial regression without significantly affect the accuracy of the acceleration evaluation. The application of the technique to data from a Tomo-PIV experiment of a transitional jet in water confirms its potential to reduce the precision error by means of large observation time without introducing important truncation effects.