The spatio-temporal evolution of a turbulent swirling jet undergoing vortex breakdown has been investigated. Experiments suggest the existence of a self-excited global mode having a single dominant frequency. This oscillatory mode is shown to be absolutely unstable and leads to a rotating counter-winding helical structure that is located at the periphery of the recirculation zone. The resulting time-periodic 3D velocity field is predicted theoretically as being the most unstable mode determined by parabolized stability analysis employing the mean flow data from experiments. The 3D oscillatory flow is constructed from uncorrelated 2D snapshots of particle image velocimetry data, using proper orthogonal decomposition, a phase-averaging technique and an azimuthal symmetry associated with helical structures. Stability-derived modes and empirically derived modes correspond remarkably well, yielding prototypical coherent structures that dominate the investigated flow region. The proposed method of constructing 3D time-periodic velocity fields from uncorrelated 2D data is applicable to a large class of turbulent shear flows.

The identification of coherent structures from experimental or numerical data is an essential task when conducting research in fluid dynamics. This typically involves the construction of an empirical mode base that appropriately captures the dominant flow structures. The most prominent candidates are the energy-ranked proper orthogonal decomposition (POD) and the frequency-ranked Fourier decomposition and dynamic mode decomposition (DMD). However, these methods are not suitable when the relevant coherent structures occur at low energies or at multiple frequencies, which is often the case. To overcome the deficit of these 'rigid' approaches, we propose a new method termed spectral proper orthogonal decomposition (SPOD). It is based on classical POD and it can be applied to spatially and temporally resolved data. The new method involves an additional temporal constraint that enables a clear separation of phenomena that occur at multiple frequencies and energies. SPOD allows for a continuous shifting from the energetically optimal POD to the spectrally pure Fourier decomposition by changing a single parameter. In this article, SPOD is motivated from phenomenological considerations of the POD autocorrelation matrix and justified from dynamical systems theory. The new method is further applied to three sets of PIV measurements of flows from very different engineering problems. We consider the flow of a swirl-stabilized combustor, the wake of an airfoil with a Gurney flap and the flow field of the sweeping jet behind a fluidic oscillator. For these examples, the commonly used methods fail to assign the relevant coherent structures to single modes. The SPOD, however, achieves a proper separation of spatially and temporally coherent structures, which are either hidden in stochastic turbulent fluctuations or spread over a wide frequency range. The SPOD requires only one additional parameter, which can be estimated from the basic time scales of the flow. In spite of all these benefits, the algorithmic complexity and computational cost of the SPOD are only marginally greater than those of the snapshot POD.

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Sudden changes of flame shape are an undesired, yet poorly understood feature of swirl combustors used in gas turbines. The present work studies flame shape transition mechanisms of a bistable turbulent swirl flame in a gas turbine model combustor, which alternates intermittently between an attached V-form and a lifted M-form. Time-resolved velocity fields and two-dimensional flame structures were measured simultaneously using high-speed stereo-particle image velocimetry (PIV) and planar laser-induced fluorescence of OH (OH-PLIF) at 10 kHz. The data analysis is performed using two novel methods that are well adapted to the study of transient flame shape transitions: First, the linear stability analysis (LSA) of a time-varying mean flow and second, the recently proposed spectral proper orthogonal decomposition (SPOD). The results show that the transitions are governed by two types of instability, namely a hydrodynamic instability in the form of a precessing vortex core (PVC) and a thermoacoustic (TA) instability. The LSA shows that the V-M transition implies the transient formation of a PVC as the result of a self-amplification process. The V-M transition, on the other hand, is induced by the appearance of a TA instability that suppresses the PVC and thereby modifies the flowfield such that the flame re-attaches at the nozzle. In summary, these results provide novel insights into the complex interactions of TA and hydrodynamic instabilities that govern the shape of turbulent swirl-stabilized flames.

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