Proper orthogonal decomposition has been utilized for well over a decade to study turbulence and cyclic variation of flow and combustion properties in internal combustion engines. In addition, proper orthogonal decomposition is useful to quantitatively compare multi-cycle in-cylinder measurements with numerical simulations (large-eddy simulations). However, the application can be daunting, and physical interpretation of proper orthogonal decomposition can be ambiguous. In this paper, the mathematical procedure of proper orthogonal decomposition is described conceptually, and a compact MATLAB® code is provided. However, the major purpose is to empirically illustrate the properties of the proper orthogonal decomposition analysis and to propose practical procedures for application to internal combustion engine flows. Two measured velocity data sets from a motored internal combustion engine are employed, one a highly directed flow (each cycle resembles the ensemble average), and the other an undirected flow (no cycle resembles the average). These data are used to illustrate the degree to which proper orthogonal decomposition can quantitatively distinguish between internal combustion engine flows with these two extreme flow properties. In each flow, proper orthogonal decomposition mode 1 is an excellent estimate of ensemble average, and this study illustrates how it is thus possible to unambiguously quantify the cyclic variability of Reynolds-averaged Navier–Stokes ensemble average and turbulence. In addition, this study demonstrates the benefits of comparing two different samples of cycles using a common proper orthogonal decomposition mode set derived by combining the two samples, the effect of spatial resolution, and a method to evaluate the number of snapshots required to achieve convergence.

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.

Ultraviolet-visible absorption spectral slope ratios S R (slope in 275-295 nm divided by slope in 350-400 nm) and humification index (HIX, integrated fluorescence emission in 435-480 nm divided by that in 435-480 and 300-345 nm) were compared when characterizing chromophoric dissolved organic matter (CDOM) in three humic acids and 44 whole water samples. HIX increased with increasing pH for humic acids, while their S R showed much more complicated dependencies on pH. There was a negative correlation between S R and HIX. S R increased in the order terrestrial coal/peat \ terrestrial soil/ river \ seawater, while HIX increased in the order seawater \ terrestrial soil/river \ terrestrial coal/peat. The comparative study in this work indicates that terrestrially derived CDOM has higher HIX and lower S R than marine CDOM. Investigators may potentially use these two indices to compare qualitatively the character of CDOM in different sources (e.g., terrestrial vs. marine).

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This paper presents a novel approach to analyze the cycle-to-cycle variations of pulsing spray characteristics. The purpose is to quantify the cycle-to-cycle variations of the macroscopic characteristics of spark-ignition direct-injection (SIDI) fuel injector spray, so that improvements of air-fuel mixture formation can be made to enhance the combustion efficiency and reduce emissions of SIDI engines. The experiments were carried out using an eight-hole SIDI fuel injector under a controlled ambient environment with an extended range of test conditions. Using a strobe light as an illumination source, multiple cycles of macroscopic spray structure images at a fixed injection delay time were taken by a CCD camera. The proper orthogonal decomposition (POD) technique was implemented to analyze the cycle-to-cycle characteristics of spray variation. In addition, the effects of injection pressure, ambient pressure, and fuel type on spray variation were also investigated. POD analysis reveals that the mode 1 pattern captured the ensemble-averaged spray shape, the mode 2 pattern provided quantification of spatial fuel distribution variations of different cycles of spray, and higher mode patterns further quantified the finer details of the variations surrounding the well-atomized periphery of the spray structure. POD analysis also quantitatively confirms that better-atomized sprays led to slightly higher variations of finer structures along the spray boundary. Overall, this study demonstrates that POD analysis can be used as a novel approach to quantify the cycle-to-cycle variation of pulsing spray characteristics.