Spatial Stability Analysis of Subsonic Jets Modified for Low-Frequency Noise Reduction

Abstract

This study performs a spatial stability analysis of several jets that have previously been investigated in terms of their noise radiation. The cases include a round jet and two chevron nozzle jets with varying penetration angle. The instability wave evolution in the near-nozzle region is examined to seek for clues as to how and why the mean flow azimuthal inhomogeneity introduced by chevrons modifies the low-frequency noise component. A biglobal stability analysis is performed to determine the most unstable modes on an initial plane. The downstream evolution of the most unstable modes is then computed via three-dimensional parabolized stability equations. The azimuthal mean flow inhomogeneity introduced by chevrons is found to modify instability wave growth rates and phase speeds. Findings indicate that the near-field hydrodynamic pressure oscillations of round jet instability modes are suppressed by chevron jets. For the same modal excitation amplitude at the inlet, the two chevron jets generate considerably lower pressure fluctuations than the round jet. It is also shown that the chevron jet with the lowest hydrodynamic pressure fluctuation levels is the jet with the lowest far-field low-frequency noise output among the three jets. Nomenclature

Parabolized stability analysis of jets from serrated nozzles

“…In particular, the normally three-dimensional PSE problem for serrated jets is simplified to a coupled set of two-dimensional ones. Recently, Uzun et al (2015) revisited the two-dimensional version of the inviscid LST and the three-dimensional version of the inviscid PSE problem for serrated jets. Our formulation here allows significant simplification but is otherwise equivalent, except for viscous effects.…”

Instability waves and low-frequency noise radiation in the subsonic chevron jet

“…[9,10]. For simplicity, we only take the frequency St = 0.5 as an example, in which three types of most unstable modes are found at z = 0.5r 0 , and the real parts of eigenfunctions of pressure are plotted in Fig.…”

“…3.2, we have identified that the growth rates and phase speeds of the chevron jet are both lower than that of the round jet as z 2r 0 . It has been argued that the higher growth rate and closer to sonic of phase speed, the higher acoustic radiation efficiency of wavepackets [8,10]. This has been suggested as one reason of the low-frequency noise reduction in chevron jets.…”

“…In their subsequent studies [9], spatial instability waves were analyzed, and they found that the peak growth rates shift to lower frequencies in the chevron jet. Very recently, Uzun et al [10] and Sinha et al [11,12] further analyzed the spatial stability of chevron jets at the low frequency and investigated the influence of the chevron parameters. Additionally, Sinha et al [13] studied the instability waves in the downstream region and found a good match between the instability waves and the hydrodynamic fluctuations in the near field.…”

Analysis of Coherent Structures in Circular and Chevron Jets

“…Кроме первичных структур (вихрей Кельвина -Гельмгольца) также обнаруживаются вторичные структуры в виде продольных вихрей с ненулевой осевой завихренностью. На основе результатов анализа линейной устойчивости полей средней скорости в работе [11] сделан вывод о том, что инкременты пространственного роста доминирующих азимутальных мод в шевронных струях оказываются существенно ниже, чем для осесимметричных струй, а пики дисперсионных кривых смещены в область более низких частот.…”