Nonlinear Analysis of Shear Coaxial Jets with Transverse Acoustic Forcing

In this paper, we detail the use of nonlinear data analysis tools such as phase space and recurrence-based analysis to investigate the dynamics of nonreacting cryogenic coaxial nitrogen jets characterized by the outer-to-inner jet momentum flux ratios (J) and perturbed by transverse acoustic waves. The shapes of the raw and wavelet-filtered phase space trajectories provide insight into the periodic or chaotic system dynamics, and recurrence analysis enables further study of the phase space portraits for higher dimensional systems via low-dimensional sub-space plots. Leveraging these nonlinear tools, the interaction between the transverse acoustic waves and the shear layer instabilities of coaxial jets has been analyzed. It is observed that at low J the flow is strongly coupled with the acoustic forcing frequency and the dynamics are characterized by low-dimensional behavior that approaches limit-cycle oscillations. At high J, the flow is more susceptible to natural instabilities and experiences intermittent weak coupling with the acoustic perturbation. The utilities of these dynamic tools are discussed for understanding the local response of bipropellant injectors subjected to acoustic perturbation using high-speed imaging data.