A practical guide for using proper orthogonal decomposition in engine research

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((R)) 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.