Moritz Sieber

Spectral proper orthogonal decomposition

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.

The impact of heating the breakdown bubble on the global mode of a swirling jet: Experiments and linear stability analysis

This study investigates the dynamics of non-isothermal swirling jets undergoing vortex breakdown, with an emphasis on helical coherent structures. It is proposed that the dominant helical coherent structure can be suppressed by heating the recirculation bubble. This proposition is assessed with Stereo Particle Image Velocimetry (PIV) measurements of the breakdown region of isothermal and heated swirling jets. The coherent kinetic energy of the dominant helical structure was derived from PIV snapshots via Proper Orthogonal Decomposition. For one set of experimental parameters, mild heating is found to increase the energy content of the dominant helical mode. Strong heating leads to a reduction by 30\% of the coherent structures energy. For a second set of experimental parameters, no alteration of the dominant coherent structure is detectable. Local linear stability analysis of the time-averaged velocity fields shows that the key difference between the two configurations is the density ratio at the respective wavemaker location. A density ratio of approximately 0.8 is found to correlate to a suppression of the global mode in the experiments. A parametric study with model density and velocity profiles indicates the most important parameters that govern the local absolute growth rate: The density ratio and the relative position of the density profiles and the inner shear layer.

On the control of global modes in swirling jet experiments

The aim of this work is to control the self-excited global mode that concomitants vortex breakdown in turbulent swirling jets. This mode is characterized by a co-rotating counter winding single helical instability wave that originates from the jet center. Experiments show that the amplitude of this global mode is effectively reduced by exciting a double-helical mode in the outer shear layer. This mode is shown to be convective unstable at growth rates that are well predicted by spatial linear stability analysis. The dampening of the global mode occurs through an energy transfer between the inner and the outer shear layer. In preparation of closed-loop experiments, a reduced order model of the flow dynamics is developed based on five leading POD modes. The model is calibrated to flow–transients recorded via time-resolved PIV. A state estimator is designed that predicts the flow state from two hotwire probes. The performance of the estimator is validated in open-loop experiments. First results support the design of the model and state estimator.

Experimental Study Of Transient Mechanisms Of Bi-Stable Flame Shape Transitions In A Swirl Combustor

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. [DOI: 10.1115/1.4037724]

Methods for the Extraction and Analysis of the Global Mode in Swirling Jets Undergoing Vortex Breakdown

Swirling jets undergoing vortex breakdown are widely used in combustion applications, due to their ability to provide aerodynamic flame stabilization. It is well known that vortex breakdown is accompanied by a dominant coherent structure, the so called precessing vortex core (PVC). Reports on the impact of the PVC on the combustion process range from beneficial to detrimental. In any event, efficient methods for the analysis of the PVC help to increase the benefit or reduce the penalty resulting from it. This study uses Particle Image Velocimetry (PIV) measurements of a generic non-isothermal swirling jet to demonstrate the use of advanced data analysis techniques. In particular, the Finite Time Lyapunov Exponent (FTLE) and local linear stability analysis (LSA) are shown to reveal deep insight into the physical mechanisms that drive the PVC. Particularly, it is demonstrated that the PVC amplitude is strongly reduced, if heating is applied at the wavemaker of the flow. These techniques are complemented by the traditionally used Proper Orthogonal Decomposition (POD) and spatial correlation techniques. It is demonstrated how these methods complement each other and lead to a comprehensive understanding of the PVC that lays out the path to efficient control strategies.Copyright

The Impact of an Inhomogeneous Temperature Field on the Precessing Vortex Core in Swirling Jets Undergoing Vortex Breakdown

The vast majority of modern gas turbines employ swirling jets undergoing vortex breakdown in their burners. Usually, the vortex breakdown is accompanied by a large scale coherent structure, the so called precessing vortex core (PVC). It is known that under isothermal conditions the PVC always occurs in the natural flow, if the swirl number is sufficiently large. Nevertheless, it has been observed that the PVC may be suppressed in the reacting flows of gas turbine combustors, even though, the swirl number would allow for the occurrence of a PVC under isothermal conditions. Therefore, this study investigates the influence of a non-homogeneous temperature distribution in a non-reacting flow on the PVC. In order to isolate the influence of the temperature, a heated generic swirling jet is considered. This eliminates the need to consider the much more complex flow field of gas turbine combustors, where the PVC may be influenced by the confinement, the chemical reaction and thermoacoustics. The flow field of the generic swirling jet is investigated at a fixed Reynolds number and for different swirl numbers by means of Stereo Particle-ImageVelocimetry (SPIV). The temperature distribution is imposed by a heating element in the flow. Proper-Orthogonal-Decomposition (POD) is applied to the measured data to gain insight into the energy content and spatial structure of the PVC. Linear hydrodynamic stability analysis is used as an analytical tool to investigate the growth or dampening of the PVC. It is shown that the simplifications described above are justified. A heated generic swirling jet is a suitable model to investigate the basic phenomena that lead to the suppression of the PVC in non-isothermal swirling jets. The decisive factor for the suppression of the PVC in non-isothermal, non-reacting flows is the temperature gradient in the vicinity of the upstream stagnation point.

Poster: A graphical representation of the spectral proper orthogonal decomposition

We consider the spectral proper orthogonal decomposition (SPOD) for experimental data of a turbulent swirling jet. This newly introduced method combines the advantages of spectral methods, such as Fourier decomposition or dynamic mode decomposition, with the energy-ranked proper orthogonal decomposition (POD). This poster visualizes how the modal energy spectrum transitions from the spectral purity of Fourier space to the sparsity of POD space. The transition is achieved by changing a single parameter – the width of the SPOD filter. Each dot in the 3D space corresponds to an SPOD mode pair, where the size and color indicates its spectral coherence. What we notice is that neither the Fourier nor the POD spectrum achieves a clear separation of the dynamic phenomena. Scanning through the graph from the front plane (Fourier) to the back plane (POD), we observe how three highly coherent SPOD modes emerge from the dispersed Fourier spectrum and later branch out into numerous POD modes. The spatial properties of these three individual SPOD modes are displayed in the back of the graph using line integral convolution colored by vorticity. The first two modes correspond to single-helical global instabilities that are well known for these flows. Their coexistence, however, has not been observed until now. The third mode is of double- helical shape and has not been observed so far. For this considered data set and many others, the SPOD is superior in identification of coherent structures in turbulent flows. Hopefully, it gives access to new fluid dynamic phenomena and enriches the available methods.

The influence of the inner shear layer on the suppression of the global mode in heated swirling jets

The vast majority of modern gas turbines employ swirling jets undergoing vortex breakdown in their burners. Usually, the vortex breakdown is accompanied by a large scale coherent structure, the so called global mode. It is known that under isothermal conditions the global mode always occurs in the natural flow, if the swirl number is sufficiently large. Nevertheless, it has been observed that the global mode may be suppressed in the reacting flows of gas turbine combustors, even though, the swirl number would allow for the occurrence of a global mode under isothermal conditions. Therefore, this study investigates the influence of a non-homogeneous temperature distribution in a non-reacting flow on the global mode. In order to isolate the influence of the temperature, a heated generic swirling jet is considered. This eliminates the need to consider the much more complex flow field of gas turbine combustors, where the global mode may be influenced by the confinement, the chemical reaction and thermoacoustics. The flow field of the generic swirling jet is investigated by means of Stereo Particle-Image-Velocimetry (SPIV) at various levels of heating. The temperature distribution is imposed by a heating element in the flow. Analysis of the experimental data suggests that a sufficient amount of heating hinders the synchronization of the inner and outer shear layer, a feature otherwise typical of the global mode. The authors propose that the applied heating leads to an altered growth of the inner shear layer, thus altering the stability characteristics of the flow in the vicinity of the wave-maker. Linear stability analysis is used to conduct a model study, in order to investigate the parametric influence of the shear layer thickness on the stability characteristics of a heated swirling jet.