Characterization of the primary instability on atomizing jets using dynamic mode decomposition

Abstract

Numerical methods have advanced to the point that many groups can perform detailed numerical simulations of atomizing liquid jets and replicate experimental measurements. However, the simulation results have not lead to a substantial advancement to our understanding of these flows due to the massive amount of data produced. In this work, a tool is developed to extract the physics that destabilize the jets liquid core by leveraging dynamic mode decomposition (DMD). DMD takes ideas from the Arnoldi method as well as the Koopman method to evaluate a non-linear system with a low-rank linear operator. The method reduces the order of the simulation results from all the original data through time to a few key pieces of information. Most important of these are the dynamic modes, their time dynamics, and the DMD spectra. In this case, DMD is applied to the jets liquid core outer radius, which is computed at streamwise and azimuthal locations, i.e., R(theta; x). With the DMD data, we obtain the dominant spatial and temporal modes of the system and their characteristics. The dominant modes provide a useful way to collapse the large data set produced by the simulation into a length and timescale that can be used to initiate reduced-order models and numerically categorize the instabilities on the jets liquid core.