Kilian Oberleithner

Formation of Turbulent Vortex Breakdown: Intermittency, Criticality, and Global Instability

This study provides quantitative insight into the formation of vortex breakdown and the onset of global instability in a turbulent swirling jet. A water jet is guided through a rotating honeycomb that imparts the rotational motion, passed through a contraction, and discharged into a large water tank. The flow states evolving at increasing swirl are mapped out via time-resolved particle image velocimetry. The experimental results scale properly with the swirl number based on the axial momentum flux when the commonly used boundary-layer approximations are omitted. The instantaneous velocity field reveals that vortex breakdown occurs intermittently at a wide range of swirl numbers before it appears in the mean flow. At this intermittent state, the evolving breakdown bubble oscillates heavily between two streamwise locations where the vortex core is subcritical. Upon further increasing the swirl, the breakdown oscillations decay and a region of reversed flow appears in the mean flowfield. The formation of this socalled axisymmetric breakdown state is accompanied by a supercritical-to-subcritical transition of the inflowing vortex core. The reversed flow region is found to grow linearly with increasing swirl until the flow undergoes a supercritical Hopf bifurcation to a global single-helical mode, and vortex breakdown adopts a spiral shape. The global mode shape is extracted from the particle image velocimetry snapshots by means of proper orthogonal decomposition and Fourier analysis. The present experiment reveals that, at gradually increasing swirl, the jet first transitions to an axisymmetric breakdown state that remains globally stable until a critical swirl number is exceeded. This sequence of flow states agrees well with the transient formation of vortex breakdown observed in laminar flows.

Impact of Steam-Dilution on the Flame Shape and Coherent Structures in Swirl-Stabilized Combustors

Humidified gas turbines and steam-injected gas turbines are promising technologies to lower the emissions and increase the efficiency and fuel flexibility of gas turbines. In the current study, the influence of steam-dilution on swirl-stabilized methane and hydrogen-fired flames is experimentally investigated at Reynolds numbers in the range of 22,000 to 32,000. Velocity fields and flame positions were measured using high-speed particle image velocimetry and OH* chemiluminescence. An extension of the quantitative light sheet technique was employed to estimate the temperature fields. The combined results reveal strong changes in the flame position, the velocity field, and the temperature field with increasing rates of steam dilution. In particular, three different flow and flame patterns are encountered: At dry conditions, a V-shaped flame stabilizes in a broad inner recirculation zone with low local turbulent kinetic energy; at moderate steam content, the flame changes into a trumpet-like shape; and at very high rates of steam-dilution, the flame detaches and shows an annular shape. The associated coherent flow structures are extracted from the particle image velocimetry data employing proper orthogonal decomposition. The isothermal flow is dominated by a helical instability arising near the combustor inlet. This structure is completely suppressed for the dry flame and reappears for the heavily steam-diluted detached flame with a similar shape and frequency as for the isothermal case. The flow field of the trumpet-like flame at intermediate to high steam dilution rates features a helical instability of lower frequency that is located further downstream than in the isothermal and very wet case. A conceptional explanation is presented that relates the suppression of the helical instability to the specific encountered temperature fields and flame shapes.

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.

Why nonuniform density suppresses the precessing vortex core

Linear stability analysis is applied to a swirl-stabilized combustor flow with the aim to understand how the flame shape and associated density field affects the manifestation of self-excited flow instabilities. In isothermal swirling jets, self-excited flow oscillations typically manifest in a precessing vortex core and synchronized growth of large-scale spiral-shaped vortical structures. Recent theoretical studies relate these dynamics to a hydrodynamic global instability. These global modes also emerge in reacting flows, thereby crucially affecting the mixing characteristics and the flame dynamics. It is, however, observed that these self-excited flow oscillations are often suppressed in the reacting flow, while they are clearly present at isothermal conditions. This study provides strong evidence that the suppression of the precessing vortex core is caused by density inhomogeneities created by the flame. This mechanism is revealed by considering two reacting flow configurations: The first configuration represents a perfectly premixed steam-diluted detached flame featuring a strong precessing vortex core. The second represents a perfectly premixed dry flame anchoring near the combustor inlet, which does not exhibit self-excited oscillations. Experiments are conducted in a generic combustor test rig and the flow dynamics are captured using PIV and LDA. The corresponding density fields are approximated from the seeding density using a quantitative light sheet technique. The experimental results are compared to the global instability properties derived from hydrodynamic linear stability theory. Excellent agreement between the theoretically derived global mode frequency and measured precession frequency provide sufficient evidence to conclude that the self-excited oscillations are, indeed, driven by a global hydrodynamic instability. The effect of the density field on the global instability is studied explicitly by performing the analysis with and without density stratification. It turns out that the significant change in instability is caused by the radial density gradients in the inner recirculation zone and not by the change of the mean velocity field. The present work provides a theoretical framework to analyze the global hydrodynamic instability of realistic combustion configurations. It allows for relating the flame position and the resulting density field to the emergence of a precessing vortex core.

Mean flow stability analysis of oscillating jet experiments

Linear stability analysis is applied to the mean flow of an oscillating round jet with the aim to investigate the robustness and accuracy of mean flow stability wave models. The jets axisymmetric mode is excited at the nozzle lip through a sinusoidal modulation of the flow rate at amplitudes ranging from 0.1 % to 100 %. The instantaneous flow field is measured via particle image velocimetry and decomposed into a mean and periodic part utilizing proper orthogonal decomposition. Local linear stability analysis is applied to the measured mean flow adopting a weakly nonparallel flow approach. The resulting global perturbation field is carefully compared to the measurements in terms of spatial growth rate, phase velocity, and phase and amplitude distribution. It is shown that the stability wave model accurately predicts the excited flow oscillations during their entire growth phase and during a large part of their decay phase. The stability wave model applies over a wide range of forcing amplitudes, showing no pronounced sensitivity to the strength of nonlinear saturation. The upstream displacement of the neutral point and the successive reduction of gain with increasing forcing amplitude is very well captured by the stability wave model. At very strong forcing (>40%), the flow becomes essentially stable to the axisymmetric mode. For these extreme cases, the prediction deteriorates from the measurements due to an interaction of the forced wave with the geometric confinement of the nozzle. Moreover, the model fails far downstream in a region where energy is transferred from the oscillation back to the mean flow. This study supports previously conducted mean flow stability analysis of self-excited flow oscillations in the cylinder wake and in the vortex breakdown bubble and extends the methodology to externally forced convectively unstable flows.

Vortex Breakdown Types and Global Modes in Swirling Combustor Flows with Axial Injection

This paper presents the results of a combined experimental, numerical, and analytical study of the occurrence of different vortex breakdown types and helical instabilities in realistic swirling combustor flows with axial air injection through a centerbody. A parametric study of the isothermal flowfield inside the combustion chamber and in the mixing tube upstream of the combustor is carried out in a water-tunnel test facility. Selected configurations were further assessed under reacting conditions. Next, a large-eddy simulation was conducted and successfully validated with the experimental data. The isothermal and reacting results show a strong effect of the inflow parameters on the type of the vortex breakdown and the frequency, amplitude, and shape of the global mode. Linear local hydrodynamic stability analyses, carried out on the time-average measured and simulated velocity data, yield the absolutely unstable domain inside the flowfield. Axial injection is shown to impede a zone of absolute instabilit...

On the Impact of Shear Flow Instabilities on Global Heat Release Rate Fluctuations: Linear Stability Analysis of an Isothermal and a Reacting Swirling Jet

The prediction of large-scale flow structures in combustor flows and their impact on the flame dynamics is of great importance to avoid thermoacoustic instabilities in modern gas turbine design. The streamwise growth of these so-called coherent structures depends on the receptivity of the shear layers, which can be predicted numerically by means of linear stability analysis. We demonstrate this approach on an isothermal swirling jet that is dominated by a self-excited helical mode that features a precessing vortex core, showing that this theoretical concept successfully predicts the frequency, the source, and the shape of this mode. The analysis is further applied to a reacting flow with a swirl-stabilized flame, pointing out important connections between the shear layer receptivity and the measured amplitude dependence of the flame transfer function. The theoretical findings suggest that the saturation of the global heat release rate fluctuations observed at moderate forcing amplitudes is caused by vanishing shear layer receptivity.Copyright

Impact of Shear Flow Instabilities on the Magnitude and Saturation of the Flame Response

Amplitude-dependent flame transfer functions, also denoted as flame describing functions, are valuable tools for the prediction of limit-cycle amplitudes of thermoacoustic instabilities. However, the effects that govern the transfer function magnitude at low and high amplitudes are not yet fully understood. It is shown in the present work that the flame response at perfectly premixed conditions is dominated by the growth rate of vortical structures in the shear layers. An experimental study in a generic swirl-stabilized combustor was conducted in order to measure the amplitude-dependent flame transfer function and the corresponding flow fields subjected to acoustic forcing. The applied measurement techniques included the Multi-Microphone-Method, high-speed OH*-chemiluminescence measurements, and high-speed Particle Image Velocimetry. The flame response and the corresponding flow fields are assessed for three different swirl numbers at 196 Hz forcing frequency. The results show that forcing leads to significant changes in the time-averaged reacting flow fields and flame shapes. A triple decomposition is applied to the time-resolved data, which reveals that coherent velocity fluctuations at the forcing frequency are amplified considerably stronger in the shear layers at low forcing amplitudes than at high amplitudes, an indicator for a nonlinear saturation process. The strongest saturation is found for the lowest swirl number, where the forcing additionally detached the flame. For the highest swirl number, the saturation of the vortex amplitude is weaker. Overall, the amplitude-dependent vortex amplification resembles the characteristics of the flame response very well. An application of linear stability analysis to the time-averaged flow fields at increasing forcing amplitudes yields decreasing growth rates of shear flow instabilities at the forcing frequency. It therefore successfully predicts a saturation at high forcing amplitudes and demonstrates that the mean flow field and its modifications are of utmost importance for the growth of vortices in the shear layers. Moreover, the results clearly show that the amplification of vortices in the shear layers is a dominant driver for heat release fluctuations and their saturation.Copyright

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.

Global and Local Hydrodynamic Stability Analysis as a Tool for Combustor Dynamics Modeling

Coherent flow structures in shear flows are generated by instabilities intrinsic to the hydrodynamic field. In a combustion environment, these structures may interact with the flame and cause unsteady heat release rate fluctuations. Prediction and modeling of these structures is thereby highly wanted for thermo-acoustic prediction models. In this work we apply hydrodynamic linear stability analysis to the time-averaged flow field of swirl-stabilized combustors obtained from experiments. Recent fundamental investigations have shown that the linear eigenmodes of the mean flow accurately represent the growth and saturation of the coherent structures. In this work biglobal and local stability analysis is applied to the reacting flow in an industry-relevant combustion system. Both the local and the biglobal analysis accurately predicts the onset and structure of a self-excited global instability that is known in the combustion community as a precessing vortex core (PVC). However, only the global analysis accurately predicts a globally stable flow field for the case without the oscillation, while the local analysis wrongly predicts an unstable global growth rate. The predicted spatial distribution of the amplitude functions using both analysis agree very well to the experimentally identified global mode. The presented tools are considered as very promising for the understanding of the PVC and physics based flow control.Copyright