Novel ex-situ calibration procedure for Tomographic PIV in a confined environment: application to a single-cylinder optical engine

International audienceFor over a decade, Tomographic PIV has been rapidly developing and is now applied in a wide range of domains in fluid mechanics [1]. This progress has been very rapid, especially thanks to the knowledge acquired during the last twenty years in the development of the PIV technique. This 3D optical measurement technique appears to be of high interest in fluid mechanics due to its ability to investigate complex 3D flow structures. However, in many situations relevant to fluid mechanics, its application is complex and inaccurate or even unthought-of without new developments. Among the most critical experiments, we can mention confined configurations where the maximum magnitude of the view angles of the cameras is limited and not optimal for Tomo-PIV reconstruction as well as experiments with local optical index variations induced by flat or curved glass windows [2] and/or by the flow itself [3][4] (combustion, thermal flow). In the present work, the applicability and improvement of the Tomographic PIV technique to investigate in-cylinder flow in a single-cylinder optical engine is addressed. The process can then be applied to other comparable configurations with glass windows. The engine test bench consists in a mono-cylinder GDI engine (AVL) with a displacement volume of 450 cm 3 (Figure 1-a), a compression ratio of 8.5 and a maximum rpm of 3000 rpm in firing conditions. The engine is equipped with a single transparent quartz liner that has an 82 mm bore and an 86 mm stroke (Figure 1-b). In such a configuration, for the Tomo-PIV technique, the two major difficulties are the optical arrangement which has to deal with strong geometrical constraints inducing limited angles of view (columns, timing belt…) and the imaging system viewing throughout a thick curved window producing image distortions and optical aberrations (Figure 1-b). In addition to the previous remarks, the difficulty concerns the calibration step of the investigation volume. Indeed, in-situ calibration is much more complex with the quartz liner than in an opened space, especially to obtain an accurate positioning of the calibration grid in different planes. The camera model has also to take into account the strong image distortions as a function of the 3D coordinate system X/Y/Z. For the image acquisition part, we developed an original optical arrangement (Figure 1-c) based on four 12 bits Hamamatsu cameras (C9300-4M pixels) equipped with PC-E Micro NIKKOR (45mm f/2.8D) lenses with perspective control including both tilt and shift corrections. With this configuration in place, the X/Y dimension of the investigation domain images the whole cross-section of in-cylinder volume with four independent angles of views ranging between 20° and 30°. The experiment was optimised using shift and translation settings to maximise the angles and the field of view without introducing optical blocking from external parts of the engine. Compared to previous optical arrangement proposed in the literature [2], our approach improves the volumetric reconstruction from four fully independent angles of view. For the calibration, our objective in this work is to transpose a multiplanes 3D calibration done without the quartz liner onto the configuration with the liner presence, using like in classic PIV, only a single fixed view of the calibration target recorded with the glass liner and located at the centre of the investigation volume. Comparison of the middle plane images with and without quartz liner allows us to evaluate the optical distortion introduced by the cylinder and compensate them in the ex-situ calibration model