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Open-cavity flows are known to exhibit a few well-defined peaks in the power spectral distribution of velocity or pressure signals recorded close to the impinging corner. The measured frequencies are in fact common to the entire flow, indicating some global organisation of the flow. The modal structures, i.e. the spatial distribution of the most characteristic frequencies in the flow, are experimentally investigated using time-resolved particle image velocimetry. Each spatial point, of the resulting twodimension-two-component (2D-2C) velocity fields, provides time-resolved series of the velocity components V x and V y , in a (x, y) streamwise plane orthogonal to cavity bottom. Each local time-series is Fourier-transformed, such as to provide the spectral distribution at any point of the PIV-plane. One finally obtains the spatial structure associated with any frequency of the Fourier spectrum. Some of the modal spatial structures are expected to represent the nonlinear saturation of the global modes, against which the stationary solution of the Navier-Stokes equations may have become linearly unstable. Following Rowley et al. (J Fluid Mech 641:115-127, 2009), our experimental modal structures may even correspond to the Koopman modes of this incompressible cavity flow.

Side-band frequencies in an incompressible flow past a rectangular cavity are characterized through their space-time coherent structures. A parametric study over a range of dimensionless cavity length L/θ 0 has been carried out in the incompressible regime. It yields the general evolution of self-sustained oscillations, for which primary characteristics match results in the literature. The modulating frequencies associated with side-band frequencies are usually imputed either to the two-dimensional (vortexedge) interaction at the impingement or to three-dimensional dynamics induced by centrifugal instabilities in the inner-flow. However, secondary order features sometimes depart from commonly accepted scheme. In addition to the salient features of the flow, our observations bring to light another modulation, which may be related to the main recirculation inside the cavity. That modulation even becomes predominant for peculiar configurations. The present work focuses on such a configuration with a cavity length/depth ratio L/D = 1.5 and dimensionless cavity length L/θ 0 = 76. Based on time-resolved velocity measurements, the extensive analysis is concerned with the non-linear interactions within the flow. Using laser Doppler velocimetry and time-resolved particle image velocimetry in two planes, this multi-modulated regime is so addressed through both local and global aspects. Time-resolved velocity fields provide space-time coherent data that are analysed using transfer functions, space-time diagrams, and space-extended time-Fourier decomposition.

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Abstract

In this paper we propose a method to reconstruct the flow at a given time over a region of space using partial instantaneous measurements and full-space proper orthogonal decomposition (POD) statistical information. The procedure is tested for the flow past an open cavity. 3D and 2D POD analysis are used to characterize the physics of the flow. We show that the full 3D flow can be estimated from a 2D section at an instant in time provided that some 3D statistical information—i.e., the largest POD modes of the flow— is made available.

The transition to unsteadiness of a three-dimensional open cavity flow is investigated using the joint application of direct numerical simulations and fully three-dimensional linear stability analyses, providing a clear understanding of the first two bifurcations occurring in the flow. The first bifurcation is characterized by the emergence of Taylor–Görtler-like vortices resulting from a centrifugal instability of the primary vortex core. Further increasing the Reynolds number eventually triggers self-sustained periodic oscillations of the flow in the vicinity of the spanwise end walls of the cavity. This secondary instability causes the emergence of a new set of Taylor–Görtler vortices experiencing a spanwise drift directed toward the spanwise end walls of the cavity. While a two-dimensional stability analysis would fail to capture this secondary instability due to the neglect of the lateral walls, it is the first time to our knowledge that this drifting of the vortices can be entirely characterized by a three-dimensional linear stability analysis of the flow. Good agreements with experimental observations and measurements strongly support our claim that the initial stages of the transition to turbulence of three-dimensional open cavity flows are solely governed by modal instabilities.

Experiments were conducted with air-water flow in a horizontal 0.095-m pipeline at atmospheric pressure to examine the mechanism by which slugs form in a stratified flow. A specially designed entrance box was used to avoid disturbances. In these experiments, at superficial gas velocities less than 3 m/s, the slugs are found to evolve from waves, with a length of about 0.085 m, that are generated by a Jeffreys mechanism. These waves grow in height and eventually double in wavelength by a nonlinear resonance mechanism. Depending on the height of the liquid, the growth can lead to a breaking wave or to a wave that fills the whole pipe cross section. At superficial gas velocities equal to or greater than 4 m / s capillary-gravity waves with a wide range of lengths are generated by a linear Kelvin-Helmholtz mechanism. These rapidly evolve into long waves outside the range of linear instability. If the liquid height is large enough, these waves can form slugs through a nonlinear KelvinHelmholtz instability that is aided by wave coalescence.