Proper Orthogonal Decomposition and Dynamic Mode Decomposition of Under-Expanded Free-Jets with Varying Nozzle Pressure Ratios

This paper provides an overview of the progress made in a study of the coherent structures of feedback loops found in under-expanded free-jets. In order to gain a better understanding of the topology and dynamics of these structures the proper-orthogonal decomposition (POD) and dynamic mode decomposition (DMD) techniques will be applied to high resolution numerical datasets. We consider a purely convergent under-expanded free jet with nozzle pressure ratios \({NPR}=\left\{ 2.2,2.6\right\} \) and a nozzle lip thickness \(t_n/d=1/3\) where \(d=15\,{\text {mm}}\) is the nozzle diameter. The analysis has shown that DMD is more capable than POD in extracting the structure of instabilities from small datasets which correspond well to the experimental observations.