On the use and interpretation of proper orthogonal decomposition of in-cylinder engine flows

The proper orthogonal decomposition (POD) has found increasing application for the comparison of measured and computed data as well as the identification of instantaneous and time varying flow structures, particularly cyclic variability in reciprocating internal combustion engines. The patterns observed in the basis functions or modes are sometimes interpreted as coherent structures, though justification of this is not obvious from the mathematical derivations. Similarly, there is no consensus about whether or not the ensemble mean should be subtracted prior to performing POD on a data set. Synthetic flow fields are used here to reveal POD properties otherwise ambiguous in real stochastic flow data. In particular, each POD mode includes elements of all flow structures from all input snapshots and in general, several modes are needed to reconstruct physical flow structures. POD analysis of two experimental in-cylinder engine data is done: one flow condition where every cycle resembles the ensemble-averaged flow pattern, and the other with large cyclic variability such that no cycles resemble the ensemble average. The energy and flow patterns of the POD modes, derived with and without first subtracting the mean, are compared to each other and to the Reynolds decomposed flow to reveal properties of the POD modes.