On the modulating effect of three-dimensional instabilities in open cavity flows

Abstract

Open cavity flows are known to select and enhance locked-on modes or tones. High-energy self-sustained oscillations arise within the shear layer, impinging onto the trailing edge of the cavity. These self-sustained oscillations are subject to amplitude modulations (AMs) at multiple low frequencies. However, only a few studies have addressed the identification of the lowest modulating frequencies. The present work brings to light salient AMs of the shear layer waves and identifies their source as three-dimensional dynamics existing inside the cavity. Indeed, the recirculating inner flow gives rise to centrifugal instabilities, which entail broad-band frequencies down two orders of magnitude lower than those of the self-sustained oscillations. Using timeresolved PIV (TRPIV) in two planes, the nonlinearly saturated dynamics is analysed in both space and time by means of proper orthogonal decomposition, global Fourier decomposition and Hilbert-Huang transforms. The inner flow can be decomposed as three-dimensional waves carried by the main recirculation. Bicoherence distributions are computed to highlight the nonlinear interactions between these spanwise-travelling waves inside the cavity and the locked-on modes. The modulated envelope of the shear layer oscillations is extracted and investigated with regards to the inner-flow dynamics. Strong cross-correlations, in time rather than in space, reveal a global coupling mechanism, possibly related to the beating of the spanwise-travelling waves.

Identification of the formation of resonant tones in compressible cavity flows

“…This area, which reflected the interaction of M with all other modes present in the spectrum, indicated a strong correlation between the lowest modulating frequency and all the other characteristic modes induced by shear layer fluctuations. As pointed out by Basley et al[15] this was the influence of the centrifugal instabilities along the recirculating flow inside the cavity. The fact that the IWBC indicated that the low Strouhal number interaction persisted for the whole temporal evolution of the signal is important because, even if in particular time samples the main Rossiter-Heller modes were not active, the instabilities persisted and continued to exchange energy across a wideband spectrum.…”

Centrifugal instabilities in an experimental open cavity flow

“…Despite this fact, considering their decisive impact upon the amplitude modulation of the self-sustained oscillations of the flow, as was shown in Brès & Colonius (2008), Basley et al (2014), these centrifugal instabilities can arise as the determining effects behind the disturbing consequences of cavities, for instance in transport.…”

“…However, it has been recently shown that the first instability does not occur in the shear layer but inside the cavity, as shown in Brès & Colonius (2008), Meseguer-Garrido et al (2011), Alizard, Robinet & Gloerfelt (2012). As reported in these studies, frequencies associated with the inner-flow structures are approximately two orders of magnitude smaller than the dominant (shear-layer) frequencies (see also Basley et al 2013Basley et al , 2014). Indeed, fluid particle trajectories are bent when entering the recirculating flow inside the cavity, which may lead to the development of centrifugal instabilities.…”

“…Such a regime was identified in Faure et al (2009) as a so-called 'turbulent' regime. Note that, for this regime, as well as for Re D = 3000, the shear-layer self-oscillations couple to the inner-flow dynamics, as shown in Basley et al (2014). The fine details of the route to space-time chaos in this system would require a study of its own, which is beyond the scope of this paper.…”

Investigation of fundamental flow mechanisms over a corrugated waveform using proper orthogonal decomposition and spectral analyses

“…They reported consistency between the POD modes and the vortices in the wake of the jet and argued that first few modes are typically associated with large-scale flow structures. Basley et al [21] and Podvin et al [22] also reported direct relation between the POD modes and the prominent flow structure.…”