Three-dimensional density field of a screeching under-expanded jet in helical mode using multi-view digital holographic interferometry

A synchronised multi-axis digital holographic interferometry set-up is presented for the study of 3-D flow fields with large density gradients. This optical configuration provides instantaneous interferograms with fine spatial resolution in six directions of projection. A regularised tomographic approach taking into account the presence of possible shock waves is furthermore considered to reconstruct 3-D density fields. Applied to a screeching under-expanded supersonic jet with helical dynamics, this set-up is used to provide dense optical phase measurements in the initial region of the jet. The jet mean density field is shown to be satisfactorily estimated with sharply resolved density gradients. In addition, an approach based on azimuthal Fourier transform and snapshot proper orthogonal decomposition (POD) applied to the instantaneous flow observations is proposed to study the main coherent dynamics of the jet. Relying on a cluster analysis of the azimuthal POD mode coefficients, a reduced dynamical model in the POD mode phase space is used as an approximation of the two observed limit cycles. A clear 3-D representation of the density field of a helical instability associated with screech mode C is then evidenced, with two equally probable directions of rotation. Switching between the two directions is reported, highlighting intermittency in the feedback loop. This helical structure is particularly seen to extend to the jet core, driving its internal dynamics and inducing out-of-phase density fluctuations between the outer and inner shear layers. These out-of-phase motions are related to the non-uniform radial distribution of fluctuation phase associated with the outer-layer Kelvin-Helmholtz instability wave.

Automated summary

This study presents a synchronised multi-axis digital holographic interferometry set-up for studying 3-D flow fields with large density gradients. The set-up provides instantaneous interferograms with fine spatial resolution in six directions of projection and uses a regularised tomographic approach to reconstruct 3-D density fields. It is applied to a screeching under-expanded supersonic jet with helical dynamics and successfully estimates the jet mean density field with sharply resolved density gradients. A method based on azimuthal Fourier transform and snapshot proper orthogonal decomposition (POD) is proposed to study the coherent dynamics of the jet. A reduced dynamical model in the POD mode phase space is used as an approximation of the observed limit cycles. The study shows a clear 3-D representation of the density field of a helical instability associated with screech mode C.