A cone-beam compensated back-projection algorithm for X-ray particle tracking velocimetry

• Implemented a cone-beam back-projection algorithm for X-ray particle tracking velocimetry.
• Performed a comparison between a parallel-beam and cone-beam back-projection algorithm.
• Demonstrated the applicability of X-ray particle tracking velocity in a granular flow system.

Characterizing multiphase or granular flows is difficult due to the opaque nature of the system. While invasive measurement techniques provide detailed information about a single point, assessing the entire system is a laborious task due to the large number of samples required. Therefore, significant work has gone into developing noninvasive methods of measuring these flow systems. In this study, identical pairs of X-ray source/detector systems are used to provide two simultaneous but independent X-ray radiographic projections, which are then coupled together to perform X-ray stereographic imaging of a granular flow. A cone-beam compensated back-projection algorithm is developed for X-ray particle tracking velocimetry (XPTV). This method accurately corrects for the X-ray׳s cone-beam geometry, which is ignored in parallel-beam back-projection methods. To demonstrate the need for the cone-beam compensation, a direct comparison between the cone-beam and parallel-beam back-projection algorithms is used, and significant differences are presented. These methods are then used to perform XPTV in a double screw mixer, allowing the position and velocity of individual tracer particles to be characterized.

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