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

Abstract

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.

The screeching jet, seen from all sides

“…The dominance of the mode in the results of Léon et al. (2022) provides at last this rigorous proof. Through the application of proper orthogonal decomposition, the authors then demonstrated that the helicity changes sign frequently during the continuous operation of the jet.…”

“…Léon et al. (2022) combined an experimental set-up of significant complexity with elegant mathematical techniques to educe not only the time-averaged flow structures of such a jet, but also the three-dimensional structure of the leading azimuthal Fourier modes of the flow. The authors implemented a TDHI technique based on an arrangement of six Mach–Zehnder interferometers.…”

“…While for now there may be few research groups with the necessary skillset to reproduce the approach of Léon et al. (2022), the remarkable quality of the results might be enough to see the technique take its place in the standard set of diagnostic tools for high-speed flows.…”

“…The tomographic digital holographic interferometry (TDHI) technique of Léon et al. (2022) shown in figure 1 has the potential to do exactly that.

Figure 1.The TDHI set-up from Léon et al.

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“…If experimental techniques are to provide more than simple validation for numerical codes, then they will need to be able to provide high-resolution measurements of three-dimensional structures in complex flows, flows that are challenging to simulate. The tomographic digital holographic interferometry (TDHI) technique of Léon et al (2022) shown in figure 1 has the potential to do exactly that.…”