Extended proper orthogonal decomposition: Application to jet/vortex interaction

The Proper Orthogonal Decomposition (POD) is used in the present work to study the interactions between different regions of a flow. The standard analysis would select structures that are best correlated with the entire fluctuating velocity field. It is therefore not helpful if one flow region S of interest contains only a small percentage of the total kinetic energy. Using POD modes computed in the sub-domain S only, extended modes are introduced using the method of snapshots. We demonstrate that they provide a decomposition of the velocity field in the whole domain and that the extended mode number p provides the only local contribution to the velocity field correlated with the projection of the velocity field on POD mode p in S. This method is general and can be applied to either experimental or numerical velocity fields. As an example, it is applied to the analysis of an internal turbulent flow in a model engine cylinder with tumble. Data are obtained at a given phase with Particle Image Velocimetry. We focus our analysis on the middle of the intake stroke when the energy containing intake jet rolls up to feed a large vortex structure. Preferred directions of the jet/vortex interaction are clearly identified.