The use of microperforations to attenuate the cavity pressure fluctuations induced by a low-speed flow
Introduction
The pressure fluctuations generated by a flow passing over a shallow cavity is a subject of considerable importance for the transportation industry. In aeronautics, landing gears, high-lift flaps and slats are amongst the major contributors to the cavity flow-induced noise that is predominant under approach condition at Mach 0.2 [1]. Flow noise issues also appear in pantograph cavities of high-speed trains [2], in automotive door seals [3] and in solar collectors surrounded by wind barriers to improve their thermal efficiency [4]. The present work is linked to a number of applications in which unbacked micro-perforated panels (MPP) could be used to mitigate the flow-induced pressure fluctuations in shallow cavities. Examples include deployable low-noise high-drag perforated spoilers mounted on aircraft wings [5], perforated cladding panels wrapped around buildings to control light level exposure but prone to generate wind-induced noise over the facade cavities [6] and MPPs inserted within double-glazed ventilation window systems [7].
The objective of the study is to examine the effect of a micro-perforated base wall on the attenuation of the pressure fluctuations induced by a low-speed flow over cavities in transitional regime. When this regime takes place, flow reattachment might occur over the cavity floor. It has been observed for cavities with a length-to-depth ratio [8], but it has not been studied systematically. This regime is intermediate between closed and open cavity flow regimes. A closed cavity flow regime implies the formation of a localized recirculation bubble upstream in the cavity. It occurs in very elongated cavities with a large aspect ratio [4]. In the other limit, an open flow regime takes place when the cavity is separated from the main flow by a shear layer that spans the full cavity mouth. It typically occurs for deep and shallow cavities characterized by a ratio [2,3]. Self-sustained oscillations of the shear layer are present in the open flow regime [9] whereas they do not occur in the closed flow regime.
The pressure fluctuations in each flow regime depend on several parameters related to the cavity geometry, to the aerodynamical properties of the incoming boundary layer and to the surrounding acoustical environment in case of ducted cavities. Rockwell and Naudascher [10] categorized the interaction of the flow with the cavity according to three mechanisms associated to fluid-dynamic, fluid-resonant and fluid-elastic oscillations whereas Wilcox [11] classified the flow regimes as open, closed and transitional at transonic and supersonic flow speed. More recently, Gloerfelt [12] provided an extensive review of the driving mechanisms and leading parameters that govern the dynamics of flow past a cavity together with a state-of-the-art of the theoretical and numerical models that predict the resulting tonal and broadband pressure components. He quoted several works that stressed the importance of tunnel modes in experiments where the cavity is confined by a duct or by wind-tunnel walls. In particular, experimental [13] and simulation studies [14,15] showed that transverse acoustic modes associated with the height of the duct above the cavity dominate the frequency spectra.
Knowledge of these physical mechanisms is of major importance to reduce the pressure fluctuations [16,17]. Passive attenuation techniques have been investigated such as the use of sloped floors [18] or the insertion of spanwise cylinders to break large recirculation bubbles [19]. These techniques mainly concern open cavity flow regimes and may introduce additional drag and weight. In the current work, it is proposed to micro-perforate the floor of cavities in transitional or closed flow regimes. This solution does not add weight and hardly increases the high drag already produced by such very shallow cavities.
When backed by a rigid wall, MPPs constitute fibreless resonance absorbers with sub-millimetric holes diameter that ideally provide high resistance and low reactance [20]. They can be made of lightweight, recyclable materials, eventually transparent. Their absorption properties are caused by the viscous losses on the internal and external parts of the MPP apertures, but also by acoustically induced vorticity, even in case of moderate incident pressure levels due to high particle velocity in the perforations [21]. They are used in room acoustics under diffuse field incidence [20] and in flow duct acoustics as locally reacting liners whose impedance can be optimized to maximize the axial decay rate of the least attenuated mode propagating in the waveguide [22,23]. The influence of a low Mach number grazing-bias flow on the impedance of wall micro-perforations [24] and perforations [25] is the subject of current modelling efforts and experimental characterizations. A set-up made up of a flush-mounted MPP backed by a cavity and exposed to a fully-developed turbulent boundary layer (TBL) has been considered [26]. It was shown that a large part of the power injected by the aerodynamic pressures into the MPP was efficiently dissipated and transmitted through the apertures provided that the hole-based Strouhal number, , stayed lower than 0.1, with the frequency, the holes diameter and the flow free-stream velocity. An alternative configuration is studied in this work with an unbacked MPP constituting the floor of a cavity mounted in a low-speed wind tunnel and undergoing a transitional flow regime. Unbacked MPPs have already been used to suppress self-sustained flow-induced boiler-tones in heat-exchange cavities [27,28] and to damp the first spinning modes when located parallel to the axis of an air conditioning duct [29].
Experimental results are presented in Section 2 on the effect of micro-perforated floors on the wall-pressure fluctuations of very shallow cavities in transitional and closed flow regimes. A numerical study using a Lattice-Boltzmann scheme is described in Section 3 to determine the attenuation mechanisms of the observed dominant peaks by the MPP apertures. Also, the effect of an optimised MPP floor that achieves maximal axial attenuation is assessed.
Section snippets
Experimental study
Experiments have been performed in the closed-loop S1 wind-tunnel of the IRPHE Fluid Dynamics Laboratory (“Institut de Recherche sur les Phénomènes Hors Equilibre”, Marseille, France) in order to determine the effect of micro-perforating the base wall of shallow cavities on the flow noise induced by a low speed TBL. A schematic of the experimental system is shown in Fig. 1. Pictures of the MPP constituting the base wall of the cavity mounted on the top of the test section can be seen in Fig. 1,
Numerical study
A numerical model has been built using the two-dimensional Lattice Boltzmann Method (LBM) to predict the effect on the TC resonances of microperforating the floor of a cavity in transitional flow regime. The program has been implemented in the open access Palabos code.
Conclusions
Numerical and experimental studies have been carried out to evaluate the effect on the pressure fluctuations of microperforating the floor of shallow cavities at low Mach number. Wind-tunnel measurements showed that the amplitude of the first dominant peaks observed in the base wall-pressures towards the leading edge are attenuated by up to 8 dB by the MPP. This is qualitatively supported by aeroacoustic simulations based on the two-dimensional LBM that predicts the pressure and velocity
Acknowledgments
This study has been funded by the Ministerio de Economía y Competitividad in Spain, project TRA2017-87978-R, “Programa Estatal de Investigación, Desarrollo e Innovación Orientada a los Retos de la Sociedad”. The authors were granted access to the High Performance Computing Resources of Aix-Marseille University (Project Equip@Meso, ANR-10-EQPX-29-01, France) for the numerical part of this work. The authors would like to thank the Turbulence Group of IRPHE Laboratory for use of the S1 wind-tunnel
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