Interactions between upstream-propagating guided jet waves and shear-layer instability waves near the nozzle of subsonic and nearly ideally expanded supersonic free jets with laminar boundary layers

Abstract

The interactions between upstream-propagating guided jet waves and shear-layer instability waves near the nozzle of subsonic and nearly ideally expanded supersonic, isothermal free jets are investigated for jets at Mach numbers between 0.50 and 2 with fully laminar exit boundary layers of different thicknesses. The velocity spectra in the shear layers downstream of the nozzle exhibit strong narrow peaks for the first azimuthal modes, associated with growing Kelvin–Helmholtz instability waves. The frequencies of the predominant peaks are close, but not necessarily equal, to those of the most amplified instability waves predicted from the mean flow fields using linear stability analysis. They also fall in most cases within or very near the allowable frequency bands of the free-stream upstream-propagating guided jet waves obtained using a vortex-sheet model and jump from one band to another as the Mach number increases. At these frequencies, moreover, high levels organized into elongated stripes are found in the jet potential core and standing-wave patterns are visible at the edges of the shear layers in the power spectral densities of pressure and velocity fluctuations. Therefore, the free-stream upstream-propagating guided jet waves appear to interact with and excite the instability waves near the nozzle of the present jets, as in screeching and impinging jets. This explains the disparities of the frequencies and azimuthal modes of the instability waves dominating early on in the shear layers of initially laminar jets and their discontinuous changes and staging behaviours as the jet velocity varies.

Noise mitigation in rectangular jets through plasma actuator-based shear layer control

“…Here is the non-dimensional frequency in terms of Strouhal number scaled with the exit momentum thickness of the nozzle boundary layer. This is consistent with the dominant shear layer spectrum for the thin boundary layer of a Mach circular jet, reported by Bogey (2022). On both planes, the peak N factor decreases with increasing frequencies.…”

“…Here St θ is the non-dimensional frequency, Strouhal number, based on the momentum thickness at the nozzle exit, θ. Recent studies by Bogey (2022) have also shown that for an axisymmetric nozzle with laminar exit conditions, the most amplified instability varies with Mach number between St θ = 0.018 for M = 0.5 to St θ = 0.0025 for M = 2.0. The azimuthal mode of the instability was also observed to be sensitive to the jet Mach number.…”

Influence of the boundary-layer thickness on the generation of tonal noise components by subsonic impinging jets

“…For the free jets, in figures 11(d)-11( f ), several high-energy spots are found around specific frequencies. They result from the coupling between the free-stream upstream-propagating GJWs and the shear-layer instability waves near the nozzle, as shown by Bogey (2022a) for free jets with fully laminar exit boundary layers. For a thicker boundary layer, they are located farther downstream, due to the reduction of the peak instability growth rate.…”

“…The spectra of the radial velocity fluctuations of aerodynamic nature obtained for the three impinging jets and the corresponding free jets (Bogey 2022a) for n θ = 0 at r = r 0 are For the impinging jets, the frequencies of the jet initial most-amplified instability waves obtained at z = 0.1r 0 for n θ = 0 using LSA, half of these frequencies, and the frequencies of the small peaks found in the near-nozzle spectra for M06BL10 and M06BL20, are also depicted. For the free jets, in figures 20(d)-20( f ), the highest levels are found in two spots centred, e.g.…”

“…Some of the guided jet waves (GJWs), called free-stream GJWs (Towne et al. 2017; Bogey 2021, 2022 a ), propagate upstream at a velocity close to the speed of sound and have significant amplitudes outside the jet column. They are allowed only in narrow frequency bands, in which the tone frequencies obtained in the upstream direction of high subsonic free jets (Schmidt et al.…”