Proper orthogonal decomposition (POD) has been proposed as an approach to analyze complex turbulent flows in piston engines, and as a basis for making quantitative, objective comparisons between in-cylinder velocity fields obtained using high-speed optical diagnostics (e.g., particle-image velocimetry - PIV) and numerical simulations (e.g., large-eddy simulation - LES). Here we explore several POD variants that can be used to analyze statistically nonstationary flows in time-varying domains, such as piston engines, in a well-defined and relatively simple geometric configuration. Systematic parametric studies are performed, including sensitivities of POD mode structure and mode convergence rate to spatial and temporal resolution. The use of POD to identify and quantify cycle-to-cycle flow variations is explored, and the ability of POD to distinguish between organized and disorganized flows is demonstrated. The findings are expected to provide guidance to other researchers who apply POD to analyze PIV and LES data for flows in real engines, and who seek to make quantitative comparisons between experimental measurements and simulation data using POD.