Near-field coherent structures in circular and fractal orifice jets

Abstract

To investigate the influence of the orifice geometry on near-field coherent structures in a jet, Fourier proper orthogonal decomposition (Fourier-POD) is applied. Velocity and vorticity snapshots obtained from tomographic particle image velocimetry at the downstream distance of two equivalent orifice diameters are analyzed. Jets issuing from a circular orifice and from a fractal orifice are examined, where the fractal geometry is obtained from a repeating fractal pattern applied to a base square shape. While in the round jet energy is mostly contained at wave number m = 0, associated to the characteristic Kelvin-Helmholtz vortex rings, in the fractal jet modal structures at the fundamental azimuthal wave number m = 4 capture the largest amount of energy. In addition, energy is scattered across a wider range of wave numbers than in the round jet. The radial Fourier-POD profiles, however, are nearly insensitive to the orifice geometry, and collapse to a universal distribution when scaled with a characteristic radial length. A similar collapse was recently observed in POD analysis of turbulent structures in pipe flow. However, unlike in pipe flow, the azimuthal-toradial aspect ratio of the Fourier-POD structures is not constant and varies greatly with the wave number. The second part of the paper focuses on the relationship between streamwise vorticity and streamwise velocity, to characterize the role of the orifice geometry on the lift-up mechanism recently found to be active in turbulent jets [P. Nogueira, A. Cavalieri, P. Jordan, and V. Jaunet, Large-scale streaky structures in turbulent jets, J. Fluid Mech. 873, 211 (2019)]. The averaging of the streamwise vorticity conditioned on intense positive fluctuations of streamwise velocity reveals a pair of vorticity structures of opposite sign flanking the conditioning point, inducing a radial flow towards the jet periphery. This pair of structures is observed in both jets, even if the azimuthal extent of this pattern is 30% larger in the jet issuing from the circular orifice. The coupling between streamwise vorticity and velocity motions is also examined using Fourier-POD. The analysis reveals that in the jet with a circular orifice lower wave-number modes, corresponding to structures at larger scales, capture a larger fraction of the vorticity-velocity coupling. This evidences that the orifice geometry directly influences the interaction between velocity and vorticity.

Large-scale streaks in a turbulent bluff body wake

“…We find that the lift-up mechanism is active in turbulent wakes, similar to wall-bounded shear flows (Abreu et al 2020) and turbulent jets (Nogueira et al 2019;Lasagna et al 2021). Conditional averaging and SPOD analysis demonstrate clearly that streamwise vortices lift up low-speed fluid from the wake's core and push down high-speed fluid from the outer wake.…”

“…2019; Lasagna et al. 2021). Conditional averaging and SPOD analysis demonstrate clearly that streamwise vortices lift up low-speed fluid from the wake's core and push down high-speed fluid from the outer wake.…”

“…Pickering et al (2020) analysed a turbulent jet large eddy simulations (LES) database, finding that the response modes of these lift-up-dominated optimal forcing modes indeed take the form of streamwise streaks. While these studies focused on circular jets, Lasagna, Buxton & Fiscaletti (2021) found that the lift-up mechanism is active in the near field of fractal jets as well.…”

Jet noise predictions by time marching of single-snapshot tomographic PIV fields

“…Commendable efforts have been directed to the understanding of relationship between the dominant structural modes in the flow. For example, works utilizing POD (Glauser and George 1987;Citriniti and George 2000;Jung et al 2004;Tinney et al 2008;Lasagna et al 2021) revealed that "volcano-like" and short-duration eruptions of high-strain turbulent flow co-exist with the streamwise vortices and that they are most intense after the collapse of the potential core. Other works have also confirmed through correlation-based techniques that the shear layer comprises long streaky structures and series of toroidal shear-layer vortices in the outer regions of the jet (Iqbal and Thomas 2007;Nogueira et al 2019;Samie et al 2021).…”