Flow dynamics and azimuthal behavior of the self-excited acoustic modes in axisymmetric shallow cavities

This study presents the interplay of flow and acoustics within tandem deep cavities, focusing on the resonance mechanism occurring between turbulent shear layers and acoustic eigenmodes. The arrangement inside the tandem deep cavities includes both close and remote configurations. A combined fully coupled and decoupled aeroacoustic simulation strategy was devised. Employing an advanced high-order spectral/hp element method in conjunction with implicit large eddy simulation, the nonlinear compressible Navier–Stokes equations were solved to acquire internal flow–acoustic resonant field. In parallel, the linearized Navier–Stokes equations were tackled to determine coherent shear layer perturbations with external acoustic forcing. Based on acoustic measurements, the mainstream Reynolds number approaches approximately $R{e_{in}} = {O}({10^5})$ , where we identified the presence of frequency lock-in and a resonance range. Aeroacoustic noise sources were examined by implementing spectral proper orthogonal decomposition to decompose the pressure fields into hydrodynamic and acoustic components. As feedback intensified, the flow characteristics by the acoustic forcing effect and the flow-interactive effect were categorized according to the development of concurrent turbulent shear layers. Subsequently, the alternating and synchronous behaviours of concurrent shear layers resonated with the out-of-phase and in-phase acoustic eigenmodes were identified, and the corresponding large-scale counter-rotating vortex pairs and co-rotating vortex structures at the cavity entrances were extracted. The acoustic power generated by the Coriolis force was calculated using Howe's vortex-sound analogy, and the aeroacoustic energy transfer mechanism between large-scale shear layer vortices with acoustic eigenmodes was further explored. Finally, a linear response of coherent perturbations of the concurrent shear layers by external acoustic forcing was established. The amplification of flow in the streamwise direction toward the main duct led to the formation of coherent vortex structures, accompanied by separation bubbles into the main duct.

Section: Introductionmentioning

confidence: 73%

Section: Introductionmentioning

confidence: 78%

Flow–acoustic resonance mechanism in tandem deep cavities coupled with acoustic eigenmodes in turbulent shear layers

Wang,

Jia,

et al. 2024

“…Nakiboğlu, Manders & Hirschberg (2012) used Howe's vortex sound theory (Howe 2002) and simulations of the incompressible unsteady Reynolds-averaged Navier–Stokes (RANS) equations of a harmonically forced axisymmetric cavity to predict at which forcing frequency the peak whistling is maximal, depending on the mean flow profile in the pipe and the cavity's aspect ratio. Compressible large eddy simulations (LES) by Wang & Liu (2020) and Abdelmwgoud, Shaaban & Mohany (2020) allowed them to identify the structure of the hydrodynamic fluctuations associated to standing and spinning aeroacoustic modes in axisymmetric cavities. The latter study revealed different vorticity patterns associated with standing and spinning modes.…”

Section: Introductionmentioning

confidence: 99%

Self-sustained azimuthal aeroacoustic modes. Part 1. Symmetry breaking of the mean flow by spinning waves

Faure-Beaulieu,

Xiong,

Pedergnana

et al. 2023

In this paper, we study the aeroacoustic instability which occurs in a deep axisymmetric cavity in a turbulent pipe flow. This phenomenon is the axisymmetric counterpart of the classical whistling of a rectangular deep cavity subject to a grazing flow. The whistling of such axisymmetric cavity originates from the interaction of the coherent fluctuations of the vorticity at the cavity's opening with one of its trapped azimuthal or radial acoustic modes. We focus here on the situation involving the first pure azimuthal mode, which is trapped in the cavity. As a consequence of the rotational symmetry of the configuration, azimuthal modes are actually pairs of degenerate eigenmodes, or almost degenerate in the presence of small asymmetries. Therefore, the aeroacoustic instabilities exhibit more complex mechanisms than in the case of a rectangular deep cavity. In particular, we show that self-sustained spinning modes induce a symmetry breaking of the mean flow and we will elucidate the details of this phenomenon. To that end, simultaneous acoustic and time-resolved stereoscopic particle image velocimetry (PIV) measurements are performed. They reveal that when large-amplitude aeroacoustic waves spin around the cavity, a quasi-steady mean flow starts whirling slowly in the opposite direction to the wave propagation. A linear perturbation analysis around an axisymmetric mean flow confirms the experimental observations: although the incoming pipe flow is not swirling, the hydrodynamic component of the aeroacoustic wave induces such whirling motion of the mean flow because of the forcing from the steady part of the coherent Reynolds stress tensor.

“…2021), and also in the case of axisymmetric cavities (e.g. Aly & Ziada 2010; Nakiboğlu, Manders & Hirschberg 2012; Oshkai & Barannyk 2013; Abdelmwgoud, Shaaban & Mohany 2020; Wang & Liu 2020). In the latter situations, and when the cavity is deep, as in the present work, the first azimuthal acoustic modes are often involved.…”

Section: Introductionmentioning

confidence: 99%

“…These azimuthal aeroacoustic instabilities can be a critical problem in the design of piping systems, valves, turbomachines, boilers or heat exchangers. Moreover, they exhibit strong similarities to thermoacoustic instabilities in annular and axisymmetric combustors, where the driving mechanism originates from the unsteady heat release rate of the flames instead of the unsteady vorticity: in both types of systems, high-amplitude azimuthal oscillations can develop in the form of spinning, standing, mixed or beating acoustic waves (see for instance the papers from Aly & Ziada 2011;Abdelmwgoud et al 2020;Faure-Beaulieu et al 2021;Indlekofer et al 2021).…”

Section: Introductionmentioning

confidence: 99%

Self-sustained azimuthal aeroacoustic modes. Part 2. Effect of a swirling mean flow on the modal dynamics

Faure-Beaulieu,

Pedergnana,

Noiray

2023

The whistling induced by a low-Mach turbulent flow through a deep axisymmetric cavity in a duct is investigated theoretically and experimentally. The experiments include acoustic measurements and stereoscopic particle image velocimetry (PIV). The paper focuses on the effect of a mean swirl on the dynamics of the azimuthal aeroacoustic modes. The mean swirl in the cavity has two origins: one component is imposed by a controlled tangential air injection upstream of the cavity, and the other component spontaneously arises under the action of the self-sustained azimuthal aeroacoustic mode, as explained in the companion paper, Part 1 (Faure-Beaulieu, Xiong, Pedergnana & Noiray, J. Fluid Mech., vol. 971, 2023, A21). Experiments show that the dynamics of the aeroacoustic wave is influenced by the imposed swirl. In particular, the spinning wave propagating against the swirl is promoted. To explain this, a linear perturbation analysis is performed around an incompressible mean swirling flow obtained from RANS simulations. It reveals that the dominant shear layer modes of azimuthal order 1 and −1 involved in the whistling phenomenon are helical modes winding respectively with and against the swirl, and spinning respectively in counterswirl and co-swirl directions. The counterswirl hydrodynamic mode is the least damped of the two, which is in agreement with the experimental observations. Finally, a low-order model based on the wave equation is derived. With only a few parameters, it fully reproduces the experimental observations for a wide range of imposed swirl intensity in the duct flow, and it allows us to disentangle the mechanisms responsible for this complex aeroacoustic instability.