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 jet's 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.Comment: submitted to the Journal of Fluid Mechanic

Vortex Breakdown in a Swirling Jet with Axial Forcing

A swirling jet has been generated in water by passing the fluid through a rotating honeycomb and discharging it into a water tank. Experiments were conducted at 3000 < Re < 7000 and 1.15 < S < 1.5. In addition, axial periodic perturbations were applied in order to excite the shear layer by an axisymmetric mode m=0. The amplitudes of the forcing were in the range 4% < A < 44%. Quantitative measurements were carried out by using STEREO-PIV. Experiments show that at higher Reynolds numbers the vortex breakdown does not occur abruptly as often mentioned in the literature. Instead, all mean quantities which characterize the vortex breakdown show a continuous change with increasing swirl. The high turbulence level may explain the differences to former studies. Velocity contours of the cross-sectional view indicate azimuthal modes that decrease from m=4 close to the nozzle to m=2 near the vortex breakdown. Phase-locked data show that the location of vortex breakdown alternates with the forcing frequency without a significant mean displacement, whereas for a certain combination of frequency and amplitude it sheds downstream while losing its intensity

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 fail 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 system 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

Excitation of the precessing vortex core by active flow control to suppress thermoacoustic instabilities in swirl flames

In this study, we apply periodic flow excitation of the precessing vortex core at the centerbody of a swirl-stabilized combustor to investigate the impact of the precessing vortex core on flame shape, flame dynamics, and especially thermoacoustic instabilities. The current control scheme is based on results from linear stability theory that determine the precessing vortex core as a global hydrodynamic instability with its maximum receptivity to open-loop actuation located near the center of the combustor inlet. The control concept is first validated at isothermal conditions. This is of utmost importance for the proceeding studies that focus on the exclusive impact of the precessing vortex core on the combustion dynamics. Subsequently, the control is applied to reacting conditions considering lean premixed turbulent swirl flames. Considering thermoacoustically stable flames first, it is shown that the actuation locks onto the precessing vortex core when it is naturally present in the flame, which allows the precessing vortex core frequency to be controlled. Moreover, the control allows the precessing vortex core to be excited in conditions where it is naturally suppressed by the flame, which yields a very effective possibility to control the precessing vortex core amplitude. The control is then applied to thermoacoustically unstable conditions. Considering perfectly premixed flames first, it is shown that the precessing vortex core actuation has only a minor effect on the thermoacoustic oscillation amplitude. However, we observe a continuous increase of the thermoacoustic frequency with increasing precessing vortex core amplitude due to an upstream displacement of the mean flame and resulting reduction of the convective time delay. Considering partially premixed flames, the precessing vortex core actuation shows a dramatic reduction of the thermoacoustic oscillation amplitude. In consideration of the perfectly premixed cases, we suspect that this is caused by the precessing vortex core-enhanced mixing of equivalence ratio fluctuations at the flame root and due to a reduction of time delays due to mean flame displacement.DFG, 414044773, Open Access Publizieren 2019 - 2020 / Technische Universität Berli

On the impact of swirl on the growth of coherent structures

Dieser Beitrag ist mit Zustimmung des Rechteinhabers aufgrund einer (DFG geförderten) Allianz- bzw. Nationallizenz frei zugänglich.This publication is with permission of the rights owner freely accessible due to an Alliance licence and a national licence (funded by the DFG, German Research Foundation) respectively.Spatial linear stability analysis is applied to the mean flow of a turbulent swirling jet at swirl intensities below the onset of vortex breakdown. The aim of this work is to predict the dominant coherent flow structure, their driving instabilities and how they are affected by swirl. At the nozzle exit, the swirling jet promotes shear instabilities and, less unstable, centrifugal instabilities. The latter stabilize shortly downstream of the nozzle, contributing very little to the formation of coherent structures. The shear mode remains unstable throughout generating coherent structures that scale with the axial shear-layer thickness. The most amplified mode in the nearfield is a co-winding double-helical mode rotating slowly in counter-direction to the swirl. This gives rise to the formation of slowly rotating and stationary large-scale coherent structures, which explains the asymmetries in the mean flows often encountered in swirling jet experiments. The co-winding single-helical mode at high rotation rate dominates the farfield of the swirling jet in replacement of the co- and counter-winding bending modes dominating the non-swirling jet. Moreover, swirl is found to significantly affect the streamwise phase velocity of the helical modes rendering this flow as highly dispersive and insensitive to intermodal interactions, which explains the absence of vortex pairing observed in previous investigations. The stability analysis is validated through hot-wire measurements of the flow excited at a single helical mode and of the flow perturbed by a time- and space-discrete pulse. The experimental results confirm the predicted mode selection and corresponding streamwise growth rates and phase velocities

Stability Analysis of Time-averaged Jet Flows: Fundamentals and Application

We report on experimental and theoretical investigations of shear flow instabilities in jet flows. Linear stability analysis is applied to the time-averaged flow taken from experiments, contrasting the ‘classic’ stability approach that is based on a stationary base flow. To some extend, mean flow stability eigenmodes may deal as a model for instability waves at their nonlinearly saturated state, which is typically encountered in experiments. The capability of mean flow stability models is first demonstrated on laminar oscillating jets where the primary interaction takes place between the mean flow and the instability wave. We then focus on turbulent swirling jets where additional interactions occur between the fine-scale turbulence and the instability waves. Swirling flows are widely used in combustion applications where the associated high turbulence levels and internal recirculation zones (vortex breakdown bubble) are exploited for flame stabilization. We demonstrate the application of mean flow stability analysis on the flow field of a industry- relevant swirl-stabilized flame. We show that the flame response to acoutstic perturbations is closely linked to the flow receptivity predicted from linear stability analysis, which suggests that the adopted theoretical framework is very useful for thermoacoustic modeling