Tomographic Particle Image Velocimetry - Developments and applications to turbulent flows
Creators: name: Discetti, Stefano
Publisher: name: Università degli Studi di Napoli Federico II
Year: 2013

description: Tomographic Particle Image Velocimetry is a velocity measurement technique, based on the reconstruction of the volumetric pattern of light intensity scattered by seeding particles illuminated by a pulsed light, simultaneously recorded from several viewing directions. The reconstructed distributions at different time instants are then interrogated by a 3D cross-correlation algorithm to determine the three-components velocity field. Even though only recently developed, Tomo-PIV is quite well assessed in the measurement of turbulent flows. Nevertheless, the introduction of a new piece in the chain of the well-assessed PIV measurement procedure, i.e. the tomographic reconstruction, and the extension to the 3D scenario of the cross-correlation interrogation algorithms raise new questions and introduce new difficulties. 
The aim of the first part of the thesis is to address these topics; in particular, the following themes are of crucial importance:
- Computational cost of the tomographic reconstruction. The tomographic reconstruction procedure with the widely used Multiplicative Algebraic Reconstruction Technique can be very intensive. In this thesis a Multi-Resolution version of MART is proposed, leading to a remarkable processing time reduction (up to 20 times) over a wide range of seeding densities.
- Accuracy: Due to the limited available number of simultaneous views, the problem of the tomographic reconstruction is underdetermined, i.e. different particles distributions can satisfy the set of projections. In this thesis a variation of MART is proposed, based on properly oriented artificial diffusion applied on the particles distributions in the iterative procedure. The technique, named SFIT (Spatial Filtering Improved Tomography), allows an improvement of the quality of the reconstruction without increasing the computational cost.
- Computational cost of the 3D-PIV: Memory storage issues and large computational cost are the most relevant problems in the 3D extension of PIV. An efficient algorithm, based on multi-resolution interrogation, sparse direct cross-correlation and reduction of the number of redundant operations is proposed in the present thesis.
- Hardware cost: differently from the case of planar PIV, the requirement of double-shutter cameras is much easier to be removed. A low-cost approach, based on two (or more) independent tomographic systems (composed by cheap cameras working in single-frame mode) is proposed, allowing for a reduction of the hardware cost of up to 10 times. 

In the second part of the thesis the focus is on two possible applicative scenarios of the technique. In the first application the nearly isotropic and homogeneous turbulence generated by square fractal grids (i.e. grids with a square pattern repeated at different scales) is investigated. Tomographic PIV is certainly well suited for the assessment of homogeneity and isotropy (at least at large scales); conversely, it is extremely challenged by the small scales measurement, and in particular the dissipation is difficult to be estimated as it requires spatial resolution down to the Kolmogorov scale. 
In the second application the Tomographic PIV exhibits its great potential in the field of 3D quantitative visualization of the organization of coherent structures. The evolution of a circular jet after a sudden expansion in a cylindrical chamber is investigated. The flow organization is extremely complex, as it intermittently switches between two working conditions, i.e. a quasi-axisymmetric expansion within the chamber and an asymmetric configuration with reattachment point precessing in a gyroscopic like motion. The Proper Orthogonal Decomposition is applied to the 3D data in order to isolate the main features of the outflow mode; furthermore, since the flow field is dominated (energetically speaking) by a significant periodic component, a low order reconstruction, obtained combining the most energetic modes, is implemented to observe the key dynamics of the large structures.