Spatio-temporal dynamics of an acoustically forced cryogenic coaxial jet injector

Abstract

This study focuses on the application of dynamical systems theory to characterize the local susceptibility of a nonreacting, cryogenic, coaxial-jet, rocket injector to transverse acoustics. This is achieved using trajectories of the phase space obtained from high-speed imaging data, which reveal the underlying dynamical states of the system. Recurrence analysis is then used to obtain regular patterns in low-dimensional sub-space plots and provide a measure of the local response through recurrence quantification analysis. Of particular interest is quantification of the spatio-temporal coupling of the jet with the external acoustics as a function of the relative momentum flux ratio between the outer and inner jets. At lower outer-to-inner jet momentum flux ratios (J < 1), the jets have a relatively strong local response to acoustic coupling in the near field. This is followed by a sharp drop in this response further downstream where a broad range of instabilities indicates turbulent breakdown of the acoustic mode. This is in contrast to higher outer-to-inner jet momentum flux ratios (J > 1), for which the jets are intermittently coupled to the acoustic mode throughout the entire axial domain due to the presence of a second harmonic or natural instability mode. These dynamical systems analysis tools are used in conjunction with wavelet filtering to improve the utility of high-speed backlit images and are qualitatively consistent with wavelet analysis of the acoustic mode within the flow. The utility of these methods for quantifying the local susceptibility of turbulent coaxial jets to acoustic perturbations can provide powerful insight for the design and optimization of passive or active control systems for bipropellant rocket injectors and other potential propulsion applications.