Self-similarity for statistical properties in low-order representations of a large-scale turbulent round jet based on the proper orthogonal decomposition

Abstract

This study is an experimental investigation into the self-similarity behavior of first and second order statistical quantities derived from a jet flow based on a) the original data and b) its low-order representations derived from the Proper Orthogonal Decomposition (POD) and c) a comparison of both. The flow under investigation is an air-helium turbulent round jet with Re≈15400 emerging from a tube into an ambient containing identical gas mass fraction and temperature as the jet at a constant pressure. Instantaneous two-dimensional velocity field measurements were obtained for downstream distances of 5.5d to 17.4d in the plane of the axis of the jet, via Particle Image Velocimetry. The snapshot POD algorithm was then applied to this data set to generate low-order representations with rank approximations 1, 5, 10 and 50. These then serve as the basis to derive the respective (rank truncated) statistical properties. All properties are non-dimensionalized with a self-similar framework as obtained from the original jet data. It is found that the statistical properties obtained from the low-order representations a) resemble in shape the asymptotic outline of the original jet and b) that the maximum values (for a given low-order representation) exhibit asymptotic states with increasing downstream distances. This is a strong indication that i) self-similar behavior is equally found in the low-order representations and that ii) this finding is mainly controlled by the large-scale vortices. The sole exception is the axial velocity root-mean-square values, where a distinct dip in the center line of the flow is found. This dip is successively filled up by smaller-scale turbulence for higher order truncations. Additionally, a new criterion – based on the maximum cross-correlation obtained through successive time traces of the temporal POD modes – is suggested to distinguish physically relevant modes from the POD basis in a more quantitative and explicit manner compared to traditional energy-based criteria.