Three-dimensional vortex analysis and aeroacoustic source characterization of jet core breakdown

Abstract

The three-dimensional behavior of jet core breakdown is investigated with experiments conducted on a free water jet at Re = 5000 by time-resolved tomographic particle image velocimetry (TR-TOMO PIV). The investigated domain encompasses the range between 0 and 10 jet diameters. The characteristic pulsatile motion of vortex ring shedding and pairing culminates with the growth of four primary in-plane and out-of-plane azimuthal waves and leads to the formation of streamwise vortices. Vortex ring humps are tilted and ejected along the axial direction as they are subjected to higher axial velocities. By the end of the potential core, this process causes the breakdown of the vortex ring regime and the onset of streamwise filaments oriented at 30°-45° to the jet axis and “C” shaped peripheral structures. The latter re-organize further downstream in filaments oriented along the azimuthal direction at the jet periphery. Instead, in the vicinity of the jet axis the filaments do not exhibit any preferential direction resembling the isotropic turbulent regime. Following Powell's aeroacoustic analogy, the instantaneous spatial distribution of the acoustic source term is mapped by the second time derivative of the Lamb vector, revealing the highest activity during vortex ring breakdown. A three-dimensional modal analysis of velocity, vorticity, Lamb vector, and Lamb vector second time derivative fields is conducted by proper orthogonal decomposition (POD) within the first 10 modes. The decomposed velocity fluctuations describe a helical organization in the region of the jet core-breakdown and, further downstream, jet axis flapping and precession motions. By the end of the potential core, vorticity modes show that vortex rings are dominated by travelling waves of radial and axial vorticity with a characteristic 40°-45° inclination to the jet axis. The Lamb vector and the Lamb vector second time derivative modes exhibit similar patterns for the azimuthal component, whereas the vortex ring coherence is described by the radial and the axial components. While velocity, vorticity, and Lamb vector modes are typically associated with Strouhal numbers (St) smaller than 0.9, the modes of the Lamb vector second time derivative are also related to higher frequencies (1.05 ≤ St ≤ 1.9) ascribed to the three-dimensional travelling waves. Far-field acoustic predictions are obtained on the basis of direct evaluation of Powell's analogy with TR-TOMO PIV data. The spectral analysis returns peaks at pairing (St = 0.36) and shedding (St = 0.72) frequency. A broader distribution with a hump between St = 1 and 2.25 is observed, which corresponds to the breakdown of ring vortices.