Analysis of transient and intermittent flows using a multidimensional empirical mode decomposition

TL;DR

This paper compares two advanced modal decomposition techniques, FA-MVEMD and mrDMD, for analyzing unsteady, transient, and intermittent flows, demonstrating that multidimensional EMD offers superior spatial support and frequency characterization.

Contribution

It provides a comparative analysis of FA-MVEMD and mrDMD for flow analysis, highlighting the advantages of multidimensional EMD in capturing transient flow features.

Findings

Multidimensional EMD offers better spatial support than mrDMD.

EMD captures more information within a single intrinsic mode function.

EMD enables characterization of instantaneous frequencies of flow structures.

Abstract

Modal decomposition techniques are important tools for the analysis of unsteady flows and, in order to provide meaningful insights with respect to coherent structures and their characteristic frequencies, the modes must possess a robust spatial support. In this context, although widely used, methods based on singular value decomposition (SVD) may produce modes that are difficult to interpret when applied to problems dominated by intermittent and transient events. Fortunately, specific modal decomposition techniques have been recently developed to analyze such problems. However, a proper comparison between existing methods is still lacking from the literature. Therefore, this work compares two recent methods: the fast adaptive multivariate empirical mode decomposition (FA-MVEMD) and the multi-resolution dynamic mode decomposition (mrDMD). These techniques are employed here for the study of flow databases involving transient and intermittent dynamics. Specifically, the investigated problems include an SD7003 airfoil subjected to deep dynamic stall conditions, and a steady NACA0012 airfoil operating at a transitional Reynolds number. In the former case, the methods are employed to investigate the onset and evolution of the dynamic stall vortex (DSV), while in the latter case, intermittent vortex pairing is analyzed. We show that the combination of a multidimensional EMD with the Hilbert transform provides modes with superior spatial support when compared to the mrDMD, also allowing the characterization of instantaneous frequencies of coherent structures. Moreover, the EMD also condenses a larger amount of information within a single intrinsic mode function (IMF).