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Rotating flow inside an internal combustion engine cylinder is deliberately engineered for improved fuel-air mixing and combustion. The details of the rotating flow structure vary temporally over an engine cycle as well as cyclically at the same engine phase. Algorithms in the literature to identify these structural details of the rotating flow invariably focus on locating its center and, on occasion, measuring its rotational strength and spatial extent. In this paper, these flow structure parameters are evaluated by means of complex moments, which have been adapted from image (scalar field) recognition applications to two-dimensional flow pattern (vector field) analysis. Several additional detailed characteristics of the rotating flow pattern - the type and extent of its deviation from the ideal circular pattern, its rotational and reflectional symmetry (if exists), and thus its orientation - are also shown to be related to the first few low-order complex moments of the flow pattern.

The large-scale rotating flow structure in an engine cylinder exhibits features that can be described in generic terms of tumble and swirl. The structural details, nevertheless, vary from cycle to cycle due to fluctuating initial and boundary conditions of the flow. Typical analysis of the flow field cyclic variability - by simple root-mean-square, or additional spatial or temporal filtering, or proper orthogonal decomposition - is based on pointwise deviation of the instantaneous velocity from the ensemble mean. However, that analysis approach is not amenable to the evaluation of spatial variation of the flow structure, in position and orientation, within the flow field. To this end, other studies in the past focused instead on quantifying the variation of the vortex center for the dominant tumble or swirl pattern within the flow field.

Proper Orthogonal Decomposition (POD) is a useful statistical tool for analyzing the cycle-to-cycle variation of internal combustion engine in-cylinder flow field. Given a set of flow fields (also known as snapshots) recorded over multiple engine cycles, the POD analysis optimally decomposes the snapshots into a series of flow patterns (known as POD modes) and corresponding coefficients of successively maximum flow kinetic energy content. These POD results are therefore strongly dependent on the kinetic energy content of the individual snapshots, which may vary over a wide range. However, there is as yet no algorithm in the literature to define, detect, and then remove outlier snapshots from the dataset in a systematic manner to ensure reliable POD results.