TomoPIV setup for the investigation of a turbulent spot in the 1mwindtunnel of DLR Göttingen 
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Essential steps for TomoPIV: Exposure of doubleframe particle images, tomographic reconstruction of intensities and threedimensional crosscorrelation 
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Transitional flow structures behind a BackwardFacingStep with 6 mm height at U=6.6 m/s visualized by 3Dvorticity isocontour surfaces (blue) and one horizontal vector plane at 3.5 mm height with instantaneous 3Cvelocity vectors colour coded by the wallnormal component (flow from left) 


The Tomographic Particle Image Velocimetry method is a relatively new extension of the PIV measurement technique with the specific ability to determine threedimensional velocity vector fields [1]. Analogous to the planar PIV technique the principle of TomoPIV 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 setup it is possible to determine instantaneous velocity vector fields with all three components in a two dimensional plane (2D3C). Furthermorer, TomoPIV enables the determination of an instantaneous velocity vector volume (3D3C).
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 3Dcalibration procedure.
In a second step the original threedimensional 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 underdetermined 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 threedimensional crosscorrelation of the obtained voxelspaces locally on a regular grid a displacement vector field of the reconstructed particle distributions can be achieved analogous to the 2DPIV evaluation process. A sketch summarizing the TomoPIV method is shown in Fig. 2 (after F. Scarano, TU Delft).
Applications
TomoPIV can be applied in air as well as in water. Like for planar PIV timeresolved experiments can be performed using high speedcameras and –lasers (e.g. turbulent boundary layers flows). The fluid structure distributions are visualized e.g. by selected vector planes and 3Disocontour surfaces of the vorticity.
In case a timeresolved measurement is not necessary or higher spatial resolution is desired the application of high resolution doubleframe 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 16Megapixelcameras have been used for the imaging of a volume of 100 x 70 x 8 mm³ size in a transitional shear flow behind a BackwardFacingStep. 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 TomoPIV in industrial wind tunnels will most likely be restricted to so called FatSheet TomoPIV due to the influences of long viewing distances and vibrations of the cameras. With such a setup it is possible to correct for the lineofsight variations between the cameras by volume selfcalibration [4] from single simultaneous images of each camera. The light sheet thickness is only slightly increased compared to a StereoPIV setup, but results of a Fatsheet TomoPIV measurement can deliver the complete instantaneous velocity gradient tensor in a “thick plane”.
Reference
[1] Elsinga G.E., Scarano F., Wieneke B. and van Oudheusden B.W. (2006); Tomographic particle image velocimetry. Exp Fluids 41:933947(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 timeresolved tomographic PIV. Exp Fluids 44:305–316
[4] Wieneke B. (2008); Volume selfcalibration for 3D particle image velocimetry. 549556, Exp Fluids 45:549–556