Frequency Reconstruction and Scalability of Periodic Flows Using POD

Abstract

*† This article deals with some issues regarding the Proper Orthogonal Decomposition (POD) method application on periodic flows. The first issue is to study the frequency content of the POD temporal modes. The second issue is the reconstruction of frequency and amplitude maps from the flow variables data set as a function of the number of POD modes. In this study, the data sets used are extracted from the numerical solutions of flow over a triangular bluff body. Several cases with different inlet conditions have been solved. The effect of extracting the mean value of the POD has been studied. Three different approaches to developing a new solution from existing numerical solutions have been investigated. Two of these ideas relate to using the POD modes, while the third is based on linear interpolation. A general POD solution has been obtained to represent the flow trends over a triangular bluff body. Error maps has been drawn to investigate the distribution of the errors between the numerical solution and the scaled one. It is found that extracting the mean value from the data set of the periodic flow variables shifts the modes just one step. The energetic modes that are needed to accurately construct the frequency and amplitudes maps may be higher than that required reconstructing the flow variable itself. Using either 15 POD modes (data reduction is 84%) or linear interpolation prove to give good results (maximum error is less than 5%). The scalability based on the general POD solution gives a maximum error of about 10%.