Short Time Proper Orthogonal Decomposition for State Estimation of Transient Flow Fields

Proper Orthogonal Decomposition (POD) has been used extensively in the past for estimation and low dimensional modeling of both steady and time periodic flow fields. We demonstrate how POD can be successfully applied to transient flow fields by using snapshots acquired over short time periods. Using snapshot ensembles of exactly one cycle of the dominant flow field frequency in length, it is possible to correctly model and estimate transient flow fields. The onset of vortex shedding in a circular cylinder wake simulation as well as a feedback controlled cylinder wake flow are used to demonstrate the capabilities of this short time proper orthogonal decomposition (SPOD) procedure. In comparison to traditional and recently published modified POD methods, SPOD improves the estimation accuracy while reducing the number of sensors employed from 35 to 8.