# Tomographic Particle Imaging Velocimetry (Tomo-PIV)

The Tomographic Particle Image Velocimetry method is a relatively new extension of the PIV measurement technique with the specific ability to determine three-dimensional velocity vector fields [1]. Analogous to the planar PIV technique the principle of Tomo-PIV is based on the calculation of the velocity vector field in a flow from the displacement of imaged tracer particles (s.c. seeding) on two subsequently captured images of the region of interest. With a planar stereoscopic PIV set-up it is possible to determine instantaneous velocity vector fields with all three components in a two dimensional plane (2D-3C). Furthermorer, Tomo-PIV enables the determination of an instantaneous velocity vector volume (3D-3C).

The method is making use of the *tomographic reconstruction* of an instantaneous particle distribution based on the projections of this distribution onto several cameras: tiny tracer particles are added to the flow of interest and illuminated with a short laser light pulse in a volume with a rectangular base area. The light scattered by the particles is captured by several (ca. 3 to 6, typically 4) cameras applying the Scheimpflug condition. In that way weighted projections of the instantaneous particle distribution are received by the camera sensors from different viewing directions (see Fig. 1 [3]). The information about the lines of sight of each camera pixel through the investigated volume is described by a polynomial approximation achieved from a 3D-calibration procedure.

In a second step the original three-dimensional particle distribution has to be (re-)calculated from the projections to the cameras. Therefore the MART (Multiplicative Algebraic Reconstruction Technique) method is used, introduced by Herman und Lent [2]. The problem of reconstruction is converted into an under-determined system of equations, which can be solved in a converged approximation using algebraic methods. At the end of the reconstruction process a digital representation of the volume in the shape of a *voxel space (deduced from pixel = picture elements -> volume elements)* is obtained, in which intensity values virtually describe the original particle distribution.

The illumination and imaging of the volume within the flow is carried out at two subsequent time steps and a tomographic reconstruction for both time steps is performed. By calculating the *three-dimensional cross-correlation* of the obtained voxel-spaces locally on a regular grid a displacement vector field of the reconstructed particle distributions can be achieved analogous to the 2D-PIV evaluation process. A sketch summarizing the Tomo-PIV method is shown in Fig. 2 (after F. Scarano, TU Delft).

### Applications

Tomo-PIV can be applied in air as well as in water. Like for planar PIV time-resolved experiments can be performed using high speed-cameras and –lasers. The fluid structure distributions are visualized e.g. by selected vector planes and 3D-iso-contour surfaces of the vorticity.

In case a time-resolved measurement is not necessary or higher spatial resolution is desired the application of high resolution double-frame cameras enables a measurement of instantaneous velocity distributions containing several scales within a complex flow simultaneously. Fig. 3 shows a result from an experiment in which four 16-Megapixel-cameras have been used for the imaging of a volume of 100 x 70 x 8 mm³ size in a transitional shear flow behind a Backward-Facing-Step. Vector fields with a spatial resolution of 1.1 independent vectors per mm³ have been achieved (resulting in a total number of more than 3.5 mio vectors per measurement point at 75 % overlap).

Future applications of Tomo-PIV in industrial wind tunnels will most likely be restricted to so called Fat-Sheet Tomo-PIV due to the influences of long viewing distances and vibrations of the cameras. With such a set-up it is possible to correct for the line-of-sight variations between the cameras by volume self-calibration [4] from single simultaneous images of each camera. The light sheet thickness is only slightly increased compared to a Stereo-PIV set-up, but results of a Fat-sheet Tomo-PIV measurement can deliver the complete instantaneous velocity gradient tensor in a “thick plane”.

### Literature

[1] Elsinga G.E., Scarano F., Wieneke B. and van Oudheusden B.W. (2006); *Tomographic particle image velocimetry*. Exp Fluids 41:933-947(15)

[2] Herman G.T., Lent A.; *Iterative reconstruction algorithms*. Comput Biol Med 6:273–294, 1976

[3] Schröder A., Geisler R., Elsinga G.E., Scarano F., Dierksheide U. (2008); *Investigation of a turbulent spot and a tripped turbulent boundary layer flow using time-resolved tomographic PIV.* Exp Fluids 44:305–316

[4] Wieneke B. (2008); *Volume self-calibration for 3D particle image velocimetry*. 549-556, Exp Fluids 45:549–556