A novel method for correction of temporally- and spatially-variant optical distortion in planar particle image velocimetry

Abstract

In-cylinder flow measurements are necessary to gain a fundamental understanding of swirl-supported, light-duty Diesel engine processes for high thermal efficiency and low emissions. Planar particle image velocimetry (PIV) can be used for non-intrusive, in situ measurement of swirl-plane velocity fields through a transparent piston. In order to keep the flow unchanged from all-metal engine operation, the geometry of the transparent piston must adapt the production-intent metal piston geometry. As a result, a temporally- and spatially-variant optical distortion is introduced to the particle images. To ensure reliable measurement of particle displacements, this work documents a systematic exploration of optical distortion quantification and a hybrid back-projection procedure that combines ray-tracing-based geometric and in situ manual back-projection approaches. The proposed hybrid back-projection method for the first time provides a time-efficient and robust way to process planar PIV measurements conducted in an optical research engine with temporally- and spatially-varying optical distortion. This method is based upon geometric ray tracing and serves as a universal tool for the correction of optical distortion with an arbitrary but axisymmetric piston crown window geometry. Analytical analysis demonstrates that the ignorance of optical distortion change during the PIV laser temporal interval may induce a significant error in instantaneous velocity measurements. With the proposed digital dewarping method, this piston-motion-induced error can be eliminated. Uncertainty analysis with simulated particle images provides guidance on whether to back-project particle images or back-project velocity fields in order to minimize dewarping-induced uncertainties. The optimal implementation is piston-geometry-dependent. For regions with significant change in nominal magnification factor, it is recommended to apply the proposed back-projection approach to particle images prior to PIV interrogation. For regions with significant dewarping-induced particle elongation (Ep > 3), it is recommended to apply the proposed dewarping method to the vector fields resulting from PIV interrogation of raw particle image pairs.