Evaluation of turbulent jet characteristic scales using joint statistical moments and an adaptive time-frequency analysis

This paper presents an analysis of turbulence characteristic scales and eddy convection velocity of jet flows computed using joint statistical moments, digital filters, and a modified version of the empirical mode decomposition (EMD). The ongoing aim of this study is to develop semi-empirical space-time cross-correlation models based on stationary statistics and jet physical lengths. Multivariate statistics are used to correlate jet properties to one-dimensional time series. The data available to this study were recorded from single-point and two-point hot-wire anemometry experiments carried out for a range of jet Mach numbers (0.2≤M≤0.8). Firstly, the jet eddy convection velocity, turbulence length, and time scales are computed using space-time cross-correlation functions. Isotropic flow and frozen turbulence hypothesis are then used to estimate the joint moments from single-point statistics in the fully developed turbulence region. An EMD-based decomposition method is presented and assessed in both the Gaussian and non-Gaussian signal regions. It is demonstrated that the artificially filtered signal reconstructs the physical properties of single and multi-point jet statistics. The relationship between central moments and joint moments presented here focuses on the region of high turbulence levels, which generates the vast majority of jet mixing noise produced by turbofan engines. Further analysis is required to extend this investigation to intermittent zones and other jet noise sources, such as jet-surface installation noise.