Extinction strain rate suppression of the precessing vortex core in a swirl stabilised combustor and consequences for thermoacoustic oscillations
Introduction
The lean premixed mode of operation of gas turbine combustors has been developed as a means of meeting NOx reduction requirements. The technology aims to reduce the formation of thermal NOx by introducing a surplus of air in relation to the stoichiometric requirement for complete fuel consumption [1], which reduces the adiabatic temperature of combustion. However, this mode of operation is inherently susceptible to triggering of thermoacoustic instabilities [2], wherein the thermal field couples with an acoustic eigenmode of the geometry of the combustor, into a self amplification feedback loop that eventually results in the establishment of an operational dynamic state known as limit cycle [3]. Thermoacoustic instabilities feature high amplitude dynamic pressure and heat release rate fluctuations that may prove detrimental to the combustor [4].
Gas turbine combustors employ a swirling flowfield to secure adequate residence timescales for the flame to anchor. High levels of swirl induce a vortex breakdown that results in the establishment of a closed recirculation zone, that features a streamwise downstream stagnation point [5]. The recirculation zone features inner and outer shear layers at the vicinity of which the flame may stabilize. An inherent characteristic of the non reacting swirling flowfields, which may be encountered under reacting conditions as well, is the development of a helical coherent structure surrounding the recirculation zone, that lies in the vicinity of the outer shear layer and the free stream region, usually stemming from the root of the combustor [6]. The recirculation zone under the effect of the coherent structure may precess around the cylindrical axis of symmetry introducing a precessing vortex core (PVC) phenomenon. These helical waves are characterized by azimuthal asymmetry, thereby they appear as vortical structures breaking the rotational symmetry of a recirculation zone.
The conditions under which helical asymmetries were established in isothermal swirling flowfields were studied in [7], [8] by considering the linear stability of swirl model flows. Their results were confirmed experimentally in [9]. The authors suggested that on increasing swirl an azimuthal helical wave of first order was stabilized, counter-rotating in respect to the azimuthal direction of the swirling flow. For lower swirl numbers, instead of a helical wave, a vortex ring was established of zero azimuthal wavelength. The authors concluded that the PVC was a global self-excited mode of the swirling flow, which was driven by a wavemaker region of absolute instability. Linear stability analysis was introduced as a means of predicting the growth rate and the frequency of coherent structures in confined environments resembling the geometry of a combustor in [10]. The author reported that one was able to identify via linear stability considerations convectively or absolutely unstable regions of the flow, as well as study the stability properties of azimuthal disturbances of the first azimuthal wavenumber. It was further reported that a central recirculation zone was strongly absolutely unstable and resulted in the establishment of a vortex breakdown zone in the region between the introduction of swirling jet streams.
The current article examines the interaction of limit cycle thermoacoustic instabilities with the PVC under reacting conditions. The PVC in [11] introduced azimuthal disturbances that were not captured however in the integral heat release rate spectra, because of cancellation effects. The authors suggested that cancellation effects were caused by the first order nature of the azimuthal helical wave associated with the PVC. In [12], the authors reported that PVC is associated to enhanced mixing that assisted to securing a strongly anchored flame. In [13], the authors suggested that the scanning of the reaction zone by a coherent structure such as the PVC may result in increased combustion efficiency via increased turbulent intensities. However the potential introduction of heat release rate asymmetries may result in resonance with an acoustic eigenmode. The PVC-flame interaction of the self-excited helical structures while the combustor demonstrated thermoacoustically unstable oscillations was reported in [11], [14], however its origins were interpreted via aerodynamic considerations in the former and via nonlinear flow-flame interactions in the latter. In both of these works, a coherent structure-flame interaction frequency was identified at the difference between the thermoacoustic and the PVC frequency. In [14], it was observed that the PVC’s streamwise extent was contracting and expanding at the thermoacoustic frequency, while at the same time the centroid of the heat release rate was moving radially at a rate equal to the interaction frequency. In [11], the value of the interaction frequency, with respect to the value of the fundamental thermoacoustic frequency was interpreted via a G-equation analysis of the flame-helical wave interaction. The authors concluded that the superposition of the helical wave and the flame necessarily led to the appearance of the observed interaction component. They concluded that nonlinear flame dynamics must be associated with the emergence of this interaction frequency.
Even though the helical structure is inherently unstable to high swirl numbers, it is not always present in model gas turbine combustors, since PVC suppression or excitation rather appears to demonstrate dependency on the operating conditions [11], [15], [16], [17]. In recent years, significant progress has been made into understanding the flowfield parameters under which the PVC affects the combustion characteristics. In [18], the authors conducted a linear stability analysis on reacting swirling flow fields for an attached to and a detached from the centerbody flame. A spatio-temporal analysis was conducted on the linearised incompressible Navier–Stokes equations of motion, which described the coherent component of the interaction between the mean flowfield and the coherent superimposed disturbance. The effect of radial stratification of the temperature and density flowfield was introduced in the equations of motion as a parameter in the pressure term and in the Reynolds number which scaled the viscous terms. Whether the PVC was amplified depended upon the density and temperature gradients at the region of the inner shear layers of the recirculation zone. A strong density gradient induced by enhanced combustion close to the centerbody of the combustor was expected to suppress the swirling jet, whereas a lifted flame was expected to be susceptible to the demonstration of the coherent helical structure instability. The authors supported their argument in [19] by examining a lifted M-shaped flame (it is characterized as annular) and an attached V-shaped flame. The latter flame, whose core anchored close to the centerbody did not demonstrate PVC excitation, whereas the flowfields of the former case demonstrated a coherent helical structure. In the same work, it was suggested that the PVC was able to homogenize the temperature field and smooth out gradients, thus cooling the inner recirculation zone and promoting reattachment of the lifted flame.
In [15], the authors linked the flame shape directly with the excitation or suppression of the PVC. They studied three flames, namely an attached V-shaped, a lifted M-shaped and a transitional flame that demonstrated intermittently either a V or an M shape. The transitional flame bifurcated from V to M shape through a stochastic event of a high strain rate pulse at the inlet of the combustor that extinguished the flame from the inlet and allowed the formation of a temperature profile suitable for the excitation of the PVC. It effectively caused the flame to expand in the outer recirculation zone in their geometry assuming a lifted M shape. This observation is consistent with the one reported in [20], where the authors noticed a persistent compressive two dimensional strain that was able to extinguish the flame at the root and enhance the PVC formation. In [17], the authors further confirmed the density and temperature stratification at the inlet of the combustor, as the dictating factor of whether the flame excited or suppressed the PVC, via determination of the density field through Mie intensity images acquired with the purpose of conducting Particle Image Velocimetry (PIV) measurements. Further to that observation, they also reported that a random extinction event at the flame root excited the PVC. However, in their own geometry they presented a V-shaped flame for both PVC excited and suppressed conditions. In [21], a linear stability analysis and a spectral decomposition method were applied to the PIV measurements of a bistable flame that was intermittent between a V and an M shape. They studied the mechanism of formation of the PVC, while a V-flame was established. Slow density drifts caused by temperature variations lead to an increase of the helical structure’s initially negative growth rate which approached zero. A random turbulent event further increased the growth rate to positive values. Once the PVC was strongly established, the growth rate noticeably increased through a self-amplification process, which effectively led to a thermoacoustic limit cycle. A lower stagnation point in the recirculation zone extinguished the flame from the inlet and from then on the growth rate saturated until a lifted M-shaped flame was formed. During the limit cycle, periodically formed symmetric vortex rings suppressed the PVC whose power was gradually decreased. On decaying PVC power, the limit cycle dynamic pressure amplitude decayed as well, before a quiescent V-shaped flame was established.
The mentioned works showed that strong evidence exists with regards to the relevance of the density and temperature stratification in the flowfield downstream the combustor inlet and the PVC excitation. To summarize the argument encountered in relevant literature, [15], [22], [23], [24], [25] density stratification may affect the stability and the growth rates of coherent structures. More specifically, radial density gradients that are sign-commensurate to axial velocity radial gradients may damp the helical instability. Hence, in swirl-stabilized combustors, higher density swirling jets introduced in the vicinity of a flame attached close to the combustor inlet damps the helical motion. Another issue, that has been addressed in the literature rather ambiguously, is the flame shape under PVC excitation. In most works the M-shaped flame, when lifted from the burner centerbody was associated with the establishment of the PVC, whereas the V-shaped flame, attached to the centerbody was associated with its suppression. Nevertheless, the mechanism that causes flame shape changes is not necessarily related to the PVC establishment, since there have been suggested different flame shape transition mechanisms that did not feature a PVC mechanism. In [26], transitions from V-shaped to M-shaped flames were explained via considerations of the spatial distribution of the ratio of the flow imposed to the extinction strain rate. The flame assumed an M-shape, on increasing the extinction rate of the mixture, while exhibiting enhanced thermoacoustic amplitudes. The reason for this is that the flame became more robust to straining, and was even able to penetrate through high straining flow topologies thus shifting the global flame shape. A different approach to the flame shape bifurcation is presented in [27], wherein regulating the wall temperature distribution dictated the flame anchoring regions. Colder wall temperatures did not prompt flame anchoring at the outer recirculation zones (ORZ) in their geometry, whereas a ramp in the thermal load of the combustor inhibited the expansion of the flame in the outer recirculation zone, where an M-shape was observed. An intermittent expansion towards the outer recirculation zone and an effective transition from a V- to an M-shaped flame was observed in [28]. The expansion was associated with a Karlovitz number based criterion that related the possibility of flame expansion in the outer recirculation zone to the inverse of a local flow time scale associated to the swirling scanning frequency of the azimuthal dimension of the duct by the flow that defined an azimuthal strain rate in the ORZ to the extinction strain rate of the mixture. Granted that the flame was able to survive increased stretching in the ORZ, enhanced combustion was sustained in that region as well, hence the flame assumed an M-shape.
The motivation of the current research is to examine the triggering/suppression PVC mechanisms for an M-shaped flame under limit cycle operation as a function of increased resistance to extinction as one increases the equivalence ratio, while the flow Reynolds number remains constant. Previous research related to the current combustor geometry [29], showed that the flame behaviour was affected by extinction strain rate adjustments. In that research, the extinction strain rate was regulated by preheating the premixture. On increasing the preheat temperature, the flame anchored closer to the quarl of the combustor and its length decreased.
The contribution of the current work is twofold. First and in accordance with literature, a V flame, that is encountered at the leaner of the equivalence ratios of this study, does not feature a helical instability, whereas an M-shaped flame at an intermediate equivalence ratio lifts off the centerbody at the moment of maximum dynamic pressure. This aids the PVC excitation. We show that the lift-off is caused by local extinction linked to aerodynamic straining. On further increasing the equivalence ratio, an already M-shaped flame suppresses the PVC. The richer mixture features increased extinction resistance, hence the flame is able to sustain increased straining at the inner shear layers and it eventually propagates along the inner shear layers and flashes back. It is thereby shown that an M-shaped flame may suppress or excite the PVC, based on the relative ratio of the flow imposed strain rate to the flame extinction strain rate in the region of the inner shear layers.
Second, we show that in contrast to the experimental work in [11] and the analytical work in [30], in the current configuration, the PVC contributes in the global heat release rate and dynamic pressure spectra at both the interaction and the aerodynamic frequency. In other words, the PVC-induced heat release rate disturbance does not neutralize its contribution to the heat release rate spectra (reported as cancellation effects in [11]). The differentiating factor from [11], [30] is that the PVC is excited and interacts with the flame, while the flame’s intensity is strongly dissipating towards zero values.
The structure of the rest of this paper is as follows. Section 2 describes the experimental configuration and the measurement techniques employed to characterize the flowfield and the flame shape. Section 3.1 describes the effect of PVC establishment on the locus of attraction in phase space of the dynamic pressure signal. Section 3.2 presents the phase resolved flow field structure, as well as the phase resolved anchoring locations of the flame for different equivalence ratios. Section 3.3 describes the flow-flame interactions by applying DMD on the PIV measurements and high speed flame images. Finally, the mechanism of PVC excitation/suppression under limit cycle oscillations is identified. Two premixing states are considered, namely an industrially relevant, technically premixed state in Section 3.4 and a fully premixed state in Section 3.5. The paper ends with a summary of the main findings.
Section snippets
Experimental configuration and analytical methods
We provide an overview of the experimental configuration that is used in the current study in Figs. 1 and 2. The configuration is similar to that of previous works [29], [32], [33]. Compressed air was provided at 4 barg, measured through a thermal mass flow meter (M+W Instruments, Mass Stream D-6280) and controlled through a thermal mass flow controller (M+W Instruments, Mass Stream D-6383). The air flow was regulated through the following equipment. A pressure reducer was installed
Results and discussion
In the current section, we focus on the effects of the establishment of the PVC on the dynamic state of the combustor, the flame shape that its emergence is associated with and the conditions under which it is excited or suppressed. The results presented in Sections 3.1–3.4 feature measurements acquired with the combustor operating in a technically premixed mode, while fully premixed conditions are considered in Section 3.5.
Conclusions
In the current experimental work we investigated flame interactions with the Precessing Vortex Core (PVC) using high speed CH* chemiluminescent intensity and PIV velocity measurements on a swirl stabilized model gas turbine combustor operating under self-excited limit cycle thermoacoustic instabilities. On increasing the equivalence ratio under constant Re, PVC excitation was observed and subsequently PVC suppression. Before the PVC excitation, dynamics were attracted to a period-1 limit cycle,
Acknowledgments
The authors would like to acknowledge support from the Engineering and Physical Sciences Research Council (EPSRC) through grants EP/K21095/1 and EP/M0153001/1. The authors are also grateful to SIEMENS UK Industrial Turbomachinery Ltd. for their support.
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