A critical review of flow field analysis methods involving proper orthogonal decomposition and quadruple proper orthogonal decomposition for internal combustion engines

Experimental techniques like particle image velocimetry provide a powerful technical support for the analysis of the spatial and temporal evolution of the flow field in internal combustion engines. Such techniques can be used to investigate both ensemble-averaged flow structures and their cyclic variations. These last are among the major causes of cycle-to-cycle variability of the engine processes (mixture formation, combustion, heat transfer, emission formation), the reduction of which has become a paradigm recently in engine development. Proper orthogonal decomposition has been largely used in conjunction with particle image velocimetry to analyze flow field characteristics. Several methods involving proper orthogonal decomposition have been proposed in the recent years to analyze engine cycle-to-cycle variability. In this work, phase-invariant proper orthogonal decomposition analysis, conditional averaging and triple and quadruple proper orthogonal decomposition methods are first introduced and applied to a large database of particle image velocimetry data from a well-known research engine. Results are discussed with particular emphasis on the capability of the methods to perform both quantitative and qualitative evaluations on cycle-to-cycle variability. Second, a new quadruple proper orthogonal decomposition methodology is proposed and compared to those available in the literature. All the methods are found to be helpful to identify the turbulent structures responsible for cycle-to-cycle variability. They can be equally applied to both experimental and numerical datasets to analyze turbulent fields in detail and to make comparisons.