Flame dynamics and unsteady heat release rate of self-excited azimuthal modes in an annular combustor

Combustion and Flame xxx (2014) xxx–xxx

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Combustion and Flame j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / c o m b u s t fl a m e

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Flame dynamics and unsteady heat release rate of self-excited azimuthal modes in an annular combustor James R. Dawson a,⇑, Nicholas A. Worth b a b

Department of Energy and Process Engineering, Norwegian University of Science and Technology, N-7491 Trondheim, Norway Department of Engineering, University of Cambridge, Trumpington Street, Cambridge CB2 1PZ, UK

a r t i c l e

i n f o

Article history: Received 27 June 2013 Received in revised form 26 October 2013 Accepted 31 March 2014 Available online xxxx Keywords: Azimuthal instabilities Combustion instabilities Gas turbines Spinning waves Standing waves Flame dynamics

a b s t r a c t This paper presents an experimental study into the structure and dynamics of the phase-averaged heat release rate during self-excited spinning and standing azimuthal modes in an annular combustion chamber. The flame response was characterised using two methods: high-speed OH⁄ chemiluminescence imaged above the annulus to investigate the structure of the phase-averaged fluctuations in heat release rate, and high-speed OH-PLIF measured across the centreline of two adjacent flames to investigate phase-averaged flame dynamics. Two-microphone measurements were obtained at three circumferential locations to determine the modes and the amplitude of the velocity fluctuations. It was found that the flame responds differently to spinning and standing wave modes. During standing wave modes, the amplitude of the unsteady heat release rate of each flame (sector) varied according to its location in the mode shape with maximum fluctuations occurring at the pressure anti-nodes and minimum fluctuations occurring at the pressure nodes. At the pressure anti-nodes, peak fluctuations result from the production of flame surface area by axisymmetric flame motions caused by the modulation of flow at the burner inlet by the pressure fluctuations. However, at the pressure nodes, an anti-symmetric, transverse flapping motion of the flame occurred producing negligible unsteady heat release rate over the oscillations cycle via the mechanism of cancellation. During spinning modes, the structure of the heat release rate was found to be asymmetric and characterised by the preferential suppression of shear layer disturbances depending on the spin direction. Ó 2014 The Combustion Institute. Published by Elsevier Inc. All rights reserved.

1. Introduction Most combustion systems in modern gas turbines for power and propulsion use annular combustion chambers. Self-excited thermoacoustic instabilities are a well known and recurring problem in the development of new combustion systems. In annular combustion chambers these instabilities tend to excite azimuthal modes as the circumference typically forms the longest dimension [1]. These instabilities occur when acoustic waves propagating azimuthally around the combustion chamber constructively interact with fluctuations in the heat release rate generating pressure fluctuations which grow in amplitude until a limit-cycle is reached. Recent numerical computations of an annular combustor by Wolf et al. [2] showed that over the simulation time, the selfexcited azimuthal modes switched back and forth between spinning and standing wave modes. Similar observations have been reported in experiments by Worth and Dawson [3] and Bourgouin ⇑ Corresponding author. Fax: +47 735 935 80. E-mail address: [email protected] (J.R. Dawson).

et al. [4] in simple laboratory-scale annular combustion chambers. In geometrically symmetric annular geometries, acoustic waves that travel in the clockwise (CW) and anti-clockwise (ACW) azimuthal directions are not coupled with each other. This is because there is no wall or sudden change in impedance to break the symmetry and couple the azimuthal waves. Consequently, self-excited azimuthal modes exhibit time-varying amplitude and phase and are therefore rarely pure rotating or standing wave modes but a mix or composite of the two. Constructing probability density functions (p.d.f.s) of the amplitudes Aþ and A of the azimuthal waves, Worth and Dawson [3] showed that a statistical prevalence for spinning or standing modes depended on the flame separation distance when all burners were equipped with swirlers having the same sign. When alternating burners were fitted with swirlers of opposite sign to eliminate bulk swirl, a statistical preference for standing wave modes was observed in all cases. Bourgouin et al. [4] proposed a spin ratio SR (see Section 2.3) to characterise azimuthal modes, a simple but elegant normalisation of the difference between the magnitude of the amplitudes of the clockwise and anti-clockwise acoustic waves divided by their conjugate, such

http://dx.doi.org/10.1016/j.combustflame.2014.03.021 0010-2180/Ó 2014 The Combustion Institute. Published by Elsevier Inc. All rights reserved.

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that SR ¼ 0 corresponds to a perfect standing mode and SR ¼ 1 correspond to perfect spinning modes in either direction. A p.d.f. of SR from their experiments showed a statistical preference for a weak CW spinning mode. Prior to these recent studies, our understanding of azimuthal modes has predominantly relied on linear stability analyses within simplified acoustic network descriptions of the combustion system [5–9]. The non-linear flame response is then modelled, usually using a flame transfer/describing function (FTF/FDF) based on an equivalent single, typically axisymmetric flame. This relates normalised global fluctuations in heat release rate q0 =Q produced at each burner to the normalised axial velocity fluctuations u0 =U at the burner inlet over a range of frequencies and amplitudes, usually with the addition of a time-delay. The important concept is that the flame response is assumed to be invariant and therefore always have the same FTF/FDF. A corollary of this is that interactions with neighbouring flames does not occur. The LES of an annular helicopter engine by Staffelbach et al. [10] is one case where these assumptions have been demonstrated sufficient. In that study, the self-excited azimuthal mode was mixed but can be considered closer to a spinning mode than a standing mode as ratio of amplitudes of the CW and ACW waves was A =Aþ ¼ 0:33. During spinning modes, where SR ! 1, velocity fluctuations through each burner are driven by the pressure nodes travelling around the annulus at the speed of sound, c. Generality would require these assumptions to be demonstrated sufficient for standing wave and all composite modes where SR takes on intermediate values. Despite numerical and experimental evidence to the contrary [2–4,11], most models ultimately predict that only spinning modes give rise to stable limit cycle oscillations in symmetric annular combustion chambers, i.e. identical burners that are evenly spaced around the annulus and assumed to have the same FTF [8,12,13]. As a means of controlling instabilities, Noiray et al. [13] investigated the effect of asymmetric heat release rate around the annulus by introducing a non-uniform distribution of FTFs. Depending on the degree of asymmetry, their model predicted that standing wave or composite modes were stable. More recently, Noiray and Schuermans [14] added stochastic forcing in the form of broadband noise into their model with symmetric heat release rate around the annulus, in an effort to reconcile differences between their predictions and the simulations of Wolf et al. [2]. They found that noise can cause the modes to jump back and forth between the two spinning modes but stable standing wave modes, as reported in the symmetric annular configurations [2–4], were not found. Currently, most thermo-acoustic models cannot explain why standing modes in symmetric annular chambers should be stable, despite being observed in both experiments and numerical simulations. However, a recent study by Ghirardo and Juniper [15] extended the model of Noiray et al. [13] to include interactions between the azimuthal acoustic velocity and the unsteady heat release rate and found that standing, spinning and mixed modes can be stable. One of main challenges is to develop physics based descriptions of the unsteady heat release rate during spinning, standing and composite self-excited azimuthal modes. This requires experimental or numerical data which has only recently started to become available. Worth and Dawson [3] observed that the unsteady heat release rate around the annulus was different for spinning and standing wave modes. During spinning wave modes, the amplitude of q0 =Q produced by each burner around the annulus was approximately constant consistent with the findings of Staffelbach et al. [10]. However, during standing wave modes the amplitude of heat release rate fluctuations varied spatially around the annulus with peak fluctuations produced at the pressure anti-nodes and negligible fluctuations produced at the pressure nodes. Within a onedimensional framework, in the absence of velocity fluctuations at the pressure nodes, i.e. u0 =U ! 0, flames should be steady with a

constant heat release rate q0 =Q ! 0. However, recent studies of transversely forced flames have shown that complex flame dynamics actually occur at pressure nodes and yet produce negligible q0 =Q . Connor and Lieuwen [16] investigated the flow field response of an annular jet at a pressure anti-node and node under cold flow and reacting conditions using two-dimensional particle image velocimetry (PIV). At the pressure anti-node, transverse velocity fluctuations, v 0 , were small, and an axisymmetric response was observed which is consistent with the flame dynamics from longitudinal forcing, see Refs. [17,18] for two examples. At the pressure node, v 0 components of  30  40% of the bulk velocity was reported causing adjacent sides of the annular jet to oscillate in anti-phase which they suggested was due to the amplification of helical modes. A recent paper by Lespinasse et al. [19] considered the effect of transverse forcing of a conical laminar flame when placed at different locations between the pressure node and antinode. They also observed that v 0 is amplified at the acoustic velocity anti-node inducing transverse flame motions. Using a different acoustic forcing arrangement, transverse forcing in the plenum upstream of a flame positioned at a pressure node (acoustic velocity anti-node), Hauser et al. [20] also observed a strong asymmetric flame response. Together these studies indicate that v 0 plays a mechanistic role in ensuring that q0 =Q ! 0 at pressure nodes. Previous studies focused on the effect of flame spacing on the global heat release response of ACW spinning modes [11] and the time-varying amplitude and phase behaviour of self-excited azimuthal modes [3], however this paper investigates the unsteady flame dynamics during spinning and standing wave modes in an effort to improve our understanding of the physical mechanisms that drive the unsteady heat release rate for azimuthal modes. To do this, the flame response is characterised using two methods; high-speed chemiluminescence imaging and high-speed OH-PLIF. Combined, these measurements provide new physical understanding of the structure of the heat release rate and the local flame dynamics. In the next section the apparatus, operating conditions, and measurement techniques are presented. In Section 3 the effect of flame spacing on the mean flame structure is described. In Section 4, the phase-averaged structure of the global heat release rate during spinning and standing wave modes viewed from above the annulus is presented and discussed. The phase-averaged planar flame dynamics are then presented in Section 5.

2. Experimental methods 2.1. The model annular combustor The annular combustor has been described previously in Refs. [3,11]. As shown in Fig. 1, it consists of 12, 15, or 18 equidistantly spaced bluff-body stabilised turbulent premixed flames arranged around a circle of diameter Da ¼ 170 mm. Each flame is supplied from a cylindrical plenum chamber of length Lp ¼ 200 mm having an inner diameter of Dp ¼ 212 mm. Inside the plenum a honeycomb flow straightener, a layer of wire wool, a series of grids, and a hemispherical body of diameter Dh ¼ 140 mm are used for flow conditioning and acoustic damping. Premixed C 2 H4 /air flows from the plenum into 150 mm long circular tubes having an inner diameter D ¼ 18:9 mm fitted with a centrally located conical bluffbody of diameter dbb ¼ 13 mm. The bluff bodies are mounted flush with the combustion chamber resulting in a blockage ratio of 50%. The inlet tubes were fixed between upper and lower plates, which could be changed to 12, 15 or 18 flame configurations corresponding to non-dimensional flame separation distances of S ¼ 2:33D; S ¼ 1:87D and S ¼ 1:56D, where S is defined as the arc distance between the bluff-body centres described in Fig. 1(b). Each bluff body was fitted with a six-vane swirler with a vane angle of 60°

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Fig. 1. The annular combustor: (a) general schematic, (b) overhead schematic illustrating key dimensions, pressure transducer locations, and sector dimensions used for data analysis, and (c) overhead schematic illustrating local and bulk swirl directions.

positioned 10 mm upstream. A detailed schematic of the swirler was provided in [3]. In the present investigation, all swirlers imparted azimuthal velocity components in the anti-clockwise (ACW) when viewed from overhead. After passing through the swirler the flow encounters a favourable pressure gradient due to the area reduction from the bluff body which will reduce the level of swirl. Two co-ordinate systems are referred to in the paper, one based on the annular dimensions, and the other based on individual burner dimensions. The annular coordinate system is shown in Fig. 1(b) whereas the local burner coordinate system is shown in Fig. 12(c). In general, the annular co-ordinate system and geometry in Fig. 1(b) uses h for azimuthal angle/annular position and uppercase letters for key dimensions, i.e. R; S; D. Whereas the burner coordinate system uses b and lower case letters, r; d. The annular combustion chamber consisted of inner and outer steel tubes of Di ¼ 127 mm and Do ¼ 212 mm with lengths of Li ¼ 130 and Lo ¼ 300 mm respectively. The mismatch between Li and Lo aided in the self-excitation of azimuthal modes as reported in [3,11]. Bourgouin et al. [4] also found that a mismatch between Li and Lo helped to obtain self-excited azimuthal modes in their annular combustion chamber. Using a Helmholtz solver they also point out that the self-excited modes are more correctly described as a 1A 1L mode, i.e. the first azimuthal, first longitudinal mode. A longitudinal component exists along the length of the combustor since it is open to the atmosphere and not choked as it would be in a gas turbine combustor. However, the combustor is long compared with the flame length and the corresponding variation in the longitudinal pressure is negligible in the flame and immediate post-flame regions. As such the longitudinal dependence of the mode is neglected in the analysis and is treated as an azimuthal mode only. A 50 mm long section of the outer stainless steel tube was replaced with a quartz glass window to provide optical access and visualise the flames. Two different window configurations were used, a complete quartz glass cylinder as shown in Fig. 1, and a quartz window with the same radius of curvature which provided optical access to flames over a single quadrant. 2.2. Operating conditions and instrumentation A pair of mass flow controllers were used with ranges of 0– 2000 lpm for air and 0–100 lpm for C 2 H4 were used. Their measurement accuracy was 0.8% of the reading ±0.2% of the full scale. A constant time-average bulk velocity of U ¼ 18 m=s was maintained during all experiments corresponding to a Reynolds number of Re ¼ 15; 000 based on the bluff-body diameter. Hot wire measurements were made at 4 quadrant locations to ensure bulk flow

uniformity to within 1%. The equivalence ratio was varied between / = 0.85–1 in order to promote self-excited oscillations. To characterise the instability modes, the inlet velocity fluctuations u0 were measured using the two-microphone technique at three locations around the annulus, P1, P2, and P3, each being 120° apart, see Fig. 1. At each location, a pair of Kulite XCS-093 pressure transducers with a sensitivity of 4.2857  103 mV/Pa, range of 0.35 atm, and accuracy of 0:15% full scale were positioned along the inlet pipes. Each microphone was mounted flush with the inside walls of the inlet tubes. Since the flow is low-Mach number, the modes and amplitudes can be determined. The pressure signals were acquired at 30 kHz with sample lengths of 4.3 s and a minimum of 10 runs were used to analyse the time-varying behaviour of the modes. The signals were amplified and filtered before being digitised using a National Instruments 16 bit PCI 6251 card. 2.3. Mode characterisation and phase-averaging Previous studies [2–4] have shown that the instability mode rapidly switches back and forth between spinning and standing modes. Therefore, conditional averaging methods were applied to the pressure time-series to characterise the azimuthal modes by calculating the amplitudes of the ACW and CW waves. To determine the modes, the pressure fluctuations, pk , at any azimuthal location in the annulus hk can be written as:

  pk ¼ Aþ eiðhk v h t=RÞ þ A eiðhk þv h t=RÞ eixt ;

ð1Þ

where Aþ and A are the amplitudes in either azimuthal direction, is the azimuthal velocity component of the mean flow, R is the radius of the annulus, and x is the angular frequency. When jAþ j ¼ jA j the mode is a standing wave, when jAþ j ¼ 0 or jA j ¼ 0 spinning waves in either direction occur. We can also define the spin ratio, SR, proposed by Bourgouin et al. [4] as:

vh

SR ¼

jAþ j  jA j : jAþ j þ jA j

ð2Þ

When the SR ! 0 a perfect standing mode is approached and as SR ¼ 1 perfect spinning modes are approached in either direction. However, the time-varying amplitude behaviour of degenerate modes means that the SR varies in time and forms a population. The distribution of this population is an indicator of whether the mode is predominantly standing or spinning in nature. In previous work [3] we used the ratio, Aþ =A , to categorise how strongly spinning or standing the mode was. To solve for Aþ ; A , and v h t=R, the pressure time-series data measured at P1, P2 and P3 were summed together to construct a

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mode indicator, CðtÞ, used by Wolf et al. [2], which can be written as:

This combines the three time-series measured at P1, P2 and P3 into a single time-series, CðtÞ. The method of least squares was then applied to local intervals of CðtÞ, (approximately 6 cycles) from which Aþ ; A , and v h t=R were determined. This enabled the SR to be calculated and the orientation of the nodes, v h t=R. For standing wave modes, conditional averaging on the orientation v h t=R, i.e. the location of the nodes, was particularly important. To illustrate this point, consider a time-series where a standing wave mode occurs at time t1 for a number of cycles, before becoming a spinning mode at time t 2 for a number of cycles, and then returning to a standing mode at time t 3 bearing in mind that the SR is also timevarying. In an annular combustion chamber, the pressure and velocity nodes can be positioned anywhere within the annulus so at t 1 lets consider that they are located at 12 and 6 o’clock. Marching forward in time to t 1 þ dt they have slowly rotated a given number of radians due to the azimuthal velocity component of the mean field, v h , noting that v h =R  x. This continues until t 2 when a spinning mode is established. However, when the standing mode is re-established at t 3 the nodes may now be located at completely different locations, say 10 and 4 o’clock. Conditional averaging on mode type enables phase-averages of the heat release rate to be compiled via simultaneous acquisition of the pressure time-series with the high-speed chemiluminescence and OH-PLIF measurements. The mode types were classified according to their SR. Phase-averages of spinning and standing wave modes were then compiled by identifying the amplitude peaks from one of the sensor locations at P1, P2, and P3 and normalising by the local period of the oscillation, T. The heat release rate data was divided into 18 equal time bins, t, and normalised by T giving a non-dimensional cycle time s ¼ t=T. Each normalised time bin was populated with a minimum of 200 OH⁄ chemiluminescence or OH-PLIF images. When SR ! 0, the heat release rate data was also conditioned on mode orientation yielding the phase-averaged heat release rate of flames at different locations within the standing wave mode, i.e. the flame response due to its relative location to the pressure nodes and anti-nodes. P.d.f.s of the SR are plotted in Fig. 2. These show that the selfexcited azimuthal modes are strongly influenced by large-scale flame-flame interactions. When S ¼ 2:33D the flames behave independently with a skewed distribution in favour of CW spinning modes. A more Gaussian shaped distribution is found for S ¼ 1:87D with a weaker preference for amplifying CW spinning modes. A bimodal distribution is found for S ¼ 1:56 with peaks near standing modes and ACW modes. These figures are included to aid the discussion on the response of the heat release rate. For details regarding the statistical aspects of azimuthal modes we refer the reader to Ref. [3]. 2.4. High-speed chemiluminescence imaging The annular combustion chamber was visualised from overhead by placing an air cooled mirror immersed in the exhaust gases at an angle of 45°. High-speed OH⁄ chemiluminescence images were captured using a Photron SA1.1 high-speed CMOS camera having a 10242 maximum pixel resolution coupled with a LaVision IRO high-speed two-stage intensifier, fitted with a Cerco 2178 UV lens 100F/2.8 and a UV filter (270–370 nm). During the self-excited cases 14,328 images (full buffer) were captured at a frame rate of 14,400 fps at a pixel resolution of 628  640. A calibration plate was used for image de-warping to minimise perspective effects.

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Fig. 2. Probability density functions of spin ratios, SR, for each flame separation distance, S.

The phase-averaged fluctuations in the global heat release rate for 18 non-dimensional time-steps were calculated by q0s ¼ ðq0  Q Þ=hQ i where q0 and Q , are the phase-averaged fluctuations and the time-averaged mean evaluated at each pixel respectively. The denominator, hQ i, is the global time-average evaluated over the whole annulus. When considering global fluctuations in the heat release rate, hq0s i, the numerator was evaluated over single sectors defined of size (360/N)° where N is the number of flames, as shown in Fig. 1(b). Global quantities are denoted by hi of time-averaged values. 2.5. High-speed hydroxyl planar laser induced fluorescence Time-resolved OH-PLIF was used to provide a measure of the flame structure. The imaging system consisted of a 15W JDSU Q201-HD laser, which was used to pump a high-speed Sirah Credo 2400 dye laser, achieving an average of approximately 60 lj per pulse at 5 kHz. A series of optics were used to produce a thin 25 mm high sheet whose path traversed the centres of two bluff bodies (as shown in Fig. 3). The position and angle of annular burner with respect to the incoming light sheet was varied to remove the effect of refraction through the curved quartz glass outer enclosure, and ensure the beam passed through the bluff body centrelines. The camera, intensifier and lens described in Section 2.4 were fitted with a bandpass OH filter (300–325 nm), and 8900 images were obtained. After correcting for beam profile inhomogeneities the flame surface area (FSA) was computed

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Fig. 5. Schematic of the FSA integration regions. Fig. 3. OH-PLIF imaging setup schematic.

following a similar approach to Balachandran et al. [17], using an interrogation window size of 5 pixels. It should be noted that due to the light sheet alignment with the bluff body centrelines, the relative position of the illuminated regions changes with the number of flames. The maximum disparity occurs at the mid point between the two bluff body centre locations, with the distance from the geometric annular radius, R ¼ Da =2, scaling with flame separation angle as, Rð1  cosðh=2ÞÞ. This gives rise to disparities of 1.3, 1.9, and 2.9 mm for the S ¼ 1:56D; 1:87D and 2:33D cases respectively. The alignment of the light sheet through the centreline of two bluff bodies permits investigation of the flame structure and dynamics in the interacting region between these two bluff bodies. However, it is more difficult to interpret the results from illuminated regions outside of the bluff bodies, where the light sheet cuts the interacting region off-centre (as shown in Fig. 3). Therefore, the images are cropped and only the central region between the two bluff bodies is retained. Although the imaging location was fixed, conditioning on the orientation during standing wave modes, made it possible to reconstruct pseudo-spatial FSA distributions of the flame dynamics from the pressure node to the anti-node. However, this could only be realised for certain cases and was not experimentally controllable due to degeneracy. This approach provides FSA distributions which are readily comparable with the twin flame measurements of Worth and Dawson [21], and illustrate the spatial dependence of the flame dynamics in a manner similar to figures more easily accessible to LES [2,10]. The stitching process described in Fig. 4 shows that the phase averaged FSA distributions are first cropped and then stitched together with another phase-averaged FSA distribution offset by the orientation, v h R=t. Only orientations that are very close the flame spacing S=D were used. This could also be done for the spinning wave cases by conditioning on the normalised cycle location rather than orientation, however, little insight is provided by

doing this since the flame dynamics during spinning waves are time-dependent and not spatially dependent on the mode. In order to assess the effect of the flame dynamics on the spatial heat release response the FSA was also integrated over selected areas of interest, reducing the FSA to a 1D signal in these regions. This can be used to quantify the phase of the heat release rate on both sides of the flame, along the flame length, and the effect of large-scale flame-flame interactions which has been previously shown to dominate the heat release response [21]. As shown in Fig. 5, regions on the left and right are integrated separately and the extent of the flame is split into 4 different downstream regions, to capture both the merged and unmerged flame dynamics.

3. Mean flame structure The effect of S on the mean flame surface area under stable operating conditions is shown in Fig. 6. The mean flame surface area is calculated from 1000 OH-PLIF images showing that the mean flame height is  1:8D for each S. As found in previous work on two interacting premixed flames [21], large-scale merging of adjacent flames occurs further upstream as S is decreased leading to a complex three-dimensional asymmetric flame structure [22]. The effect of this large-scale merging is replicated around the annulus [3,11]. When spaced apart a suitable distance only the tips of the turbulent flame brush interact with adjacent flames as shown in Fig. 6(b). For all S the flames are anchored along the inner shear layers however, as S is decreased, an increasing amount of flame is stabilised along both the outer and inner shear layers. In Fig. 6(c) flame surface area along the outer shear layers fully extends across the whole merging region with the adjacent flame in a continuous structure. These changes to the flame structure caused by large-scale flame merging are indicative of changes to the mean flow structure compared to the axisymmetric flame structure of Fig. 6(a).

Fig. 4. Schematic of the image cropping and stitching.

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shows how the amplitude of the velocity fluctuations Au ¼ ju0 j=jUj varies around the annulus for each flame separation distance reconstructed from the two-microphone measurements conditionally averaged at a given mode orientation. The amplitude of the global fluctuations in heat release rate around the annulus,

y (mm)

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Aq ¼ jhq0s ij=jhQ ij, is also plotted. Three important effects are observed in these figures: firstly peak Aq occurs at flames nearest to the pressure anti-nodes, where Au reaches a maximum, secondly, negligible Aq is produced by flames near or at pressure nodes where Au is a minimum, and thirdly flame merging increases Aq . The structure and dynamics of the heat release rate that give rise to these global effects are discussed in the following sections. To examine the response at the pressure anti-node and node in more detail for S ¼ 2:33D, a zoomed in phase-averaged sequence of q0s at L1 and L2 is shown in Fig. 9. A SR ¼ 0:049 shows that this is close to a pure standing wave mode. The non-dimensional timesteps s are denoted in the lower left hand side of the images. In Fig. 9(a), the structure of q0s is characterised by the formation of concentric regions of heat release rate that originate near the bluff-body and advect downstream. Closer inspection shows approximately three distinct concentric-like regions of q0s of alternating colour indicating the phase of the fluctuations vary along the flame length. The inner regions show the footprint of the 6vaned swirler which becomes smoothed out downstream. Peak values of q0s occur at the top of the flame and take the form of large concentric rings. Overall, the zoomed in views clearly show the structure of the heat release rate is essentially axisymmetric at the pressure anti-node and evolves independently for each flame when S ¼ 2:33D. We note that the structures are not fully axisymmetric due to the effect of the swirler and also very close to the inner annular wall due to confinement effects. Figure 9(b) shows that the structure of q0s is completely different at the pressure node, L2. A highly organised structure in the form of concentric semi-circles of minimum and maximum q0s are formed expanding radially outwards from the bluff body about a diagonal symmetry plane in alternating phase. Each half of the flame about the diagonal plane, which extends from approximately 11 to 5 o’clock, shows the same structure but oscillates in anti-phase over the cycle. The response of the heat release rate can be described as an anti-symmetric transverse flapping motion where each half of the flame undergoes coherent, transverse motions driven by transverse velocity fluctuations, v 0 as u0 ! 0 (see Fig. 8(a)). The anti-symmetric transverse flapping motion of the flame results in cancellation and explains why, on average, negligible fluctuations are produced at the pressure node, i.e. over a single sector the integrated value of hq0s i ! 0. This anti-symmetric structure of the heat release rate is distinctly different from spiral-like structure of the unsteady heat release rate produced by a helical or precessing

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Fig. 6. Mean FSA distribution calculated from 1000 OH-PLIF images for each separation distance, / ¼ 0:80 and Re ¼ 15; 000 based on the bluff-body diameter.

4. Phase-averaged heat release rate 4.1. Global heat release rate of standing wave modes The effect of flame separation distance on the structure of the phase-averaged global heat release rate during a standing wave mode visualised from above the annulus is shown in Fig. 7 at an arbitrary non-dimensional time-step, s. After identifying the different modes following the procedure briefly outlined in Section 2.3, the phase-averaged structure of the fluctuations, q0s ¼ ðq0  Q Þ=hQ i were calculated. L1 and L2 correspond to flames in the closest proximity to a pressure anti-node and node respectively. Figure 8

L2

L1

L1

L1 L2

L2

Fig. 7. The effect of flame separation distance, S, on the structure of the phase-averaged global heat release rate during a standing wave mode viewed from above the annulus at an arbitrary normalised time step s. L1 and L2 denote flame locations closest to a pressure anti-node and node locations respectively. The corresponding spin ratios are: (a) SR ¼ 0:048, (b) SR ¼ 0:149, and (c) SR ¼ 0:179.

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Fig. 8. Amplitude of the unsteady velocity fluctuations, Au , and global fluctuations in heat release rate, Aq , around the annulus for each flame separation distance, S. Measured values of Au using the two-microphone technique are denoted by , interpolated values of Au at other burners were obtained from a least squares fit based on the mode shape. Aq is measured at each sector around the annulus – see Fig. 1(b). Sector locations are expressed in terms of the azimuthal angle, h along the circumference R. The spin ratios are the same as Fig. 7.

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vortex core (PVC) [16,20,23–26]. In such cases, a planar slice through the flame will also show out-of-phase disturbances along the flame front. PVC type instabilities occur more frequently in swirling flames that are aerodynamically stabilised where the recirculation zone is turbulent and only exists as a well defined flow structure in an averaged sense. In these experiments, the wake or recirculation zone is formed by flow separation at the bluff body and is comparably more stable and swirl primarily controls the spreading rate of the annular jet. Further structural details of the anti-symmetric transverse flapping motion is shown by the planar flame dynamics presented in Section 5.1. The effect of flame separation distance on the structure of q0s at the node and anti-node positions is shown in Figs. 10 and 11. The formation of concentric regions of q0s at L1 are still evident in Fig. 10 even though large-scale merging between adjacent flames occurs. At the pressure node, L2, large-scale interactions between flames affects the symmetry of the flapping mode, however large portions of the unsteady heat release remains in anti-phase. In the case of S ¼ 1:56D in Fig. 11 merging occurs at lower flame lengths (see Fig. 6) and obscures the inner structure of q0s bearing in mind these data are line-of-sight measurements. As such these views predominantly describe the merged structures. Peak oscillations of q0s are dominated by large interconnected regions along the outer annular wall spanning approximately half of the annulus. During maximum and minimum heat release at s ¼ 1=6 and s ¼ 4=6, large fluctuations reappear in the merging region between adjacent flames which are at low levels for the remainder of the cycle. However, the phase-averaged flame dynamics presented in Section 5.1 will show that even in the presence of flame merging, upstream the flame exhibits an axisymmetric response at L1 and the anti-symmetric transverse flapping mode at L2. Putting aside the more complex effects that flame separation distance introduces, further analysis of the node and anti-node positions for the S ¼ 2:33D case is worthwhile. To further elucidate the structure of q0s at the node and anti-node locations, radial profiles of the phase of q0s from the edge of the bluff body, r ¼ rbb , to r ¼ 0:85D were extracted every b ¼ 20 around the flames at L1 and L2 and plotted in Fig. 12. Here, b is the local azimuthal angle as denoted in Fig. 12(c). At L1, the pressure anti-node, the phase of q0s initially decreases linearly until r  13 mm before levelling

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Fig. 9. Phase-averaged global heat release rate at a pressure anti-node (L1) and pressure node (L2) during a standing wave mode for S ¼ 2:33D with a spin ratio, SR ¼ 0:049. The normalised cycle time, s, is indicated in the lower left hand side of each image.

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Fig. 10. Phase-averaged global heat release rate at a pressure anti-node (L1) and pressure node (L2) during a standing wave mode for S ¼ 1:87D with a spin ratio, SR ¼ 0:149. The normalised cycle time, s, is indicated in the lower left hand side of each image.

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Fig. 11. Phase-averaged global heat release rate at a pressure anti-node (L1) and pressure node (L2) during a standing wave mode for S ¼ 1:56D with a spin ratio, SR ¼ 0:179. The normalised cycle time, s, is indicated in the lower left hand side of each image.

off towards constant phase. The important feature of this plot is that the phase for all radial profiles are similar and consistent with the advection of axisymmetric disturbances along the flame front. The fact that both sides do not fully collapse is because the pressure anti-node is not positioned exactly at the bluff body centre. On the other hand, L2 exhibits bimodal behaviour with a linear decrease in phase along the flame but with phase shift of p either side of the diagonal axis depicted Fig. 12(c). This bimodal response is what is expected from anti-symmetric transverse flame motions. Note that only a few profiles in each case actually deviate from the general trends due to the effect of swirl and the starting position from which the profiles are taken relative to where the diagonal plane of the flapping modes was assigned. 4.2. Global heat release rate of spinning wave modes The structure of q0s during spinning modes does not exhibit the same spatial dependence as the standing wave modes. This is

shown in Fig. 13 which shows the amplitude variation of u0 =U and hq0s i over the annulus. Unlike standing wave modes, where the pressure and velocity nodes have a fixed phase relationship in space, during spinning modes pressure and velocity nodes travel around the annulus in the clockwise (CW) or anti-clockwise (ACW) direction at the speed of sound. This is shown by the approximately constant values of Au and Aq . The spin ratio in this case is SR ¼ 0:676 which gives rise to the low amplitude modulation of Au (if the SR ¼ 1 the Au would be constant). This is distinctly different to the behaviour of standing wave modes as show in Fig. 8. In terms of the phase-averaged structure of the global heat release rate, the effect of S was the addressed in Ref. [11] for ACW spinning modes and therefore only the CW and ACW modes for the S ¼ 1:87D case are presented here to highlight the differences with standing wave modes. Figures 14 and 15 show full annular and zoomed in views at L1 of q0s for both ACW and CW spinning modes. Note that the burner location at L1 in this case serves as an arbitrary reference from

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9

Fig. 12. Radial profiles of the phase of q0s evaluated from r ¼ r bb to r ¼ 0:85D plotted in b ¼ 20 intervals around the flame for S ¼ 2:33D at (a) the pressure anti-node, L1, and (b) the pressure node, L2. (c) shows a schematic of a single sector defining the local azimuthal angle b with red and blue shaded regions (colour online) denoting the diagonal axis about which the anti-symmetric flame motions occur at L2. The red and blue profiles were extracted from the corresponding to the red and blue shaded regions.

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θ (°) Fig. 13. Amplitude of the unsteady velocity fluctuations, Au , and global fluctuations in heat release rate, Aq , around the annulus during an ACW spinning mode for S ¼ 1:87D. As before, measured values of Au from two-microphone measurements are denoted by  and interpolated values of Au at other burners were obtained from a least squares fit based on the mode shape. Aq is measured at each sector around the annulus – see Fig. 1(b). Sector locations are expressed in terms of the azimuthal angle, h, along the circumference at R (see Fig. 1(b)). The spin ratio, SR ¼ 0:495.

L1

L1

Fig. 14. Overhead views of an ACW and CW spinning modes with spin ratios of SR ¼ 0:495 and 0.517 respectively at an arbitrary normalised time step, s. L1 denotes location of zoomed in sequence in following figures.

which the flame response can be described following the convention shown in Fig. 12(c). Worth and Dawson [11] previously showed that the response of isolated flames (S ¼ 2:33D) during

ACW spinning modes were characterised by the formation of large crescent shaped regions of maximum (red) and minimum (blue) values of q0s oriented around the right hand side of each burner. This feature is most obvious by the minimum values at the bottom of the annulus in Fig. 14(a) noting that we denote the 12 o’clock position as the location facing the outer annular wall along R intersecting each bluff body centre. These organised, large-scale fluctuations in q0s extended from the top of the flame along outer annular wall, around the right hand side of the burner, to the merging region between adjacent flames. Similar structures are observed in Fig. 15(a) with the addition of flame merging along the outer annular wall. It is clear that the bulk of the peak q0s occurs in the vicinity of the outer annular wall. However, during CW modes the orientation of the peak q0s is reversed as shown in Fig. 15(b). CW modes see a spatial shift in the peak fluctuations towards the inner annular wall and extend around the left hand side of the burner. Although the structures of q0s appear less organised than the ACW case, careful inspection shows that a larger proportion of the fluctuations occurs in the proximity of the inner annular wall. The main reason why the structures appear less organised may be due to relative change in confinement between the inner and outer annular walls. Overall, there are several interesting results to summarise. First is that the spatial arrangement of q0s is sensitive to the direction of the most amplified wave. The crescent shaped regions of peak q0s are formed on the side where the acoustic wave is incident on the flame. The SR in these cases are of intermediate value and it may be that this preferential suppression of shear layer disturbances may be more amplified if the SR was closer to 1. Second, is that the response of the heat release rate during spinning wave modes is neither axisymmetric or anti-symmetric, as found during the standing wave modes, however the response is repeated by each flame around the annulus with a time-delay. It is important to point out the lack of axisymmetry is not simply a consequence of flame merging. ACW spinning modes for S ¼ 2:33D reported in Ref. [11] also showed a similar asymmetric response when the flames were far apart and independent. A final result of interest, is that if the flame asymmetry results in a greater amplitude of

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Fig. 15. Overhead OH⁄ imaging with magnified view of a single flame over a normalised oscillation cycle for ACW and CW spinning modes. The corresponding spin ratios are: (a) SR ¼ 0:495 and (b) SR ¼ 0:517. The normalised cycle time, s, is indicated in the lower left hand side of each image.

the global unsteady heat release rate Aq in the outer part of the annulus then the mode spins in the ACW direction which coincides with the bulk swirl direction induced at the outer annular wall as shown in Fig. 1(c). If Aq is greater in the inner part of the annulus then the mode spins in the CW direction which coincides with the bulk swirl direction induced along the inner annular wall. This was discussed in more detail in Ref. [3]. In these experiments each burner was equipped with ACW swirlers which results in a mean þv h in the ACW direction along the outer annular wall, and a mean v h in the CW direction along the inner annular wall as shown in Fig. 1(c).

5. Phase-averaged flame dynamics The previous section discussed the phase averaged structures of global heat release rate obtained from high-speed chemiluminescence imaging above the annulus. Further insight can be gained from planar slices through the flame using high-speed OH-PLIF to calculate the flame surface area (FSA) and compile phase-averages of the flame dynamics for standing and spinning wave modes. The methods used to construct phase-averaged sequences are described in Section 2.5. In addition to the high-speed chemiluminescence data, high-speed OH-PLIF offers a more complete picture

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x (mm) Fig. 16. Pseudo-spatial reconstruction of the flame dynamics from a pressure anti-node, near L1, to a pressure node, L2, at three non-dimensional time-steps, s for the S ¼ 1:56D configuration. The average spin ratio was SR ¼ 0:067. The modes shapes for p0 and u0 are plotted at the top. The bluff body centres of consecutive flames are denoted by the azimuthal angle h, each being 20 apart when S ¼ 1:56D. Over the cycle, and prior to flame merging, the flame response nearest to L1 is almost axisymmetric whereas the anti-symmetric flapping mode of the flame is seen at L2. In between L1 and L2 the flame dynamics show a composite response.

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of the flame response, especially for flames that are close together as the merging region disguises the flame structure upstream. Due to the degenerate behaviour of the self-excited modes and experimental constraints, it was not possible to predetermine which modes would be captured during the OH-PLIF measurements for each flame spacing. As such, the flame dynamics for standing wave modes for the S ¼ 1:56D configuration are shown, whereas ACW and CW spinning modes are presented for S ¼ 1:56D and S ¼ 1:87D respectively. Nevertheless, the resulting flame dynamics are fully consistent with the results and interpretations of the previous section and provide additional physical insight in the response of the heat release rate. 5.1. Flame dynamics of a standing wave mode Figure 16 shows the phase-averaged FSA of each flame from a pressure anti-node to a pressure node for the S ¼ 1:56D case at three non-dimensional time-steps during a standing wave mode. This pseudo-spatial distribution was constructed by stitching together the phase-averages at six different standing wave orientations, v h R=t, as described in Section 2.5. This enables the

y (mm)

20

phase-averaged response over a quarter of the annulus to be visualised. The corresponding acoustic mode shape is depicted above the figure with flame locations denoted by azimuthal angle h, which for S ¼ 1:56 means that each flame is h ¼ 20 apart. Note that for S ¼ 1:56D no 4 burners are 90° apart, so the pressure anti-node L1 is actually located at 10° which is in between two burners. For discussion purposes we therefore consider the flame dynamics at L1 to be at 20° and L2 at 80°. It is immediately apparent from these plots that the flame response depends on its location within the mode. Over the three time-steps, s, disturbances advect along the shear layers and generate FSA in an axisymmetric fashion prior to the large-scale interactions that occur at the top of the flame brushes. At L2, flame dynamics of the anti-symmetric transverse mode can be observed as the flame either side of the bluff body flaps from side-to-side, in anti-phase, once per cycle. Another important observation is that flames between L2 and L1 the flame dynamics exhibit a composite response gradually changing from an anti-symmetric transverse mode to an axisymmetric longitudinal mode. To show the flame dynamics at L1 and L2 in more detail 6 nondimensional time-steps, s, are plotted in Fig. 17. From these plots it

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Fig. 17. Phase-averaged flame surface area during a standing wave for S ¼ 1:56D. The corresponding spin ratios are: (a) SR = 0.078 and (b) SR = 0.102. The normalised cycle time, s, is indicated in the top left hand side of each image.

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can be seen that large-scale flame-flame interactions occupy the downstream half of the flames, which explains why the overhead chemiluminescence measurements only captures the phase-averaged behaviour of the merging regions. Despite the added complication of flame merging, the flame response to shear layer disturbances originate at the base of the flame and remain unaffected during their early development. The axisymmetric flame response at L1 shows the formation of vortex structures near the flame base starting around s ¼ 2=6. From s ¼ 2=6 to s ¼ 5=6 the vortex-flame interactions develop along the flame length eventually colliding with neighbouring flames in the merging region between s ¼ 5=6 and s ¼ 0. The collision and interaction with adjacent flames rapidly produces FSA, as shown by the increase in intensity in the merging region between s ¼ 0 and s ¼ 2=6. Overall, the flame dynamics upstream of the merging region at L1 compares well with the forced flame studies in multiple flames [21] and are also generally consistent with longitudinally and forced or self-excited, shear layer stabilised flames [17,18,27]. The flame dynamics at the pressure node, L2, are shown in Fig. 17(b). Disregarding the effects of flame merging for the time being, and concentrating on the upstream flame region, the antisymmetric transverse flapping motion of the flame over the oscillation cycle can be clearly observed. Although the amplitude of u0 =U ! 0 as shown in Fig. 8(c), the flame is clearly not steady and undergoes strong transverse motions. Since the flame is stabilised along the shear layers of the annular jet, a reasonable explanation is that the transverse flame motions result from transverse velocity fluctuations, v 0 , generated at the acoustic velocity antinode as found in Ref. [16,19]. One of the main effects of v 0 is that is modulates the jet efflux angle over the cycle. For example, at s ¼ 0 the annular jet on the right hand side is almost parallel, 0°, but is 45° on the left hand side. Half a cycle later the angles are reversed. It is important to point out that if one only considers the planar FSA data, the flapping response of the flame might appear to be due to a coupling with helical or PVC type instabilities [16,20,23,25]. However, this is not the case, as demonstrated by

the overhead chemiluminescence data shown in Section 4. The anti-symmetric transverse response of the flame observed in these experiments is dominated by the acoustics. To separate out the effects of merging from the axisymmetric and antisymmetric flame modes, the proportion of q0 produced in different regions along the flame front is considered. The flame length was divided into 4 equal sections between 0 < y < 20 mm on both the l.h.s. and r.h.s. of the flame as described in Fig. 5. The global fluctuations in heat release rate, q0c , was calculated from the phase averaged FSA and normalised by the globally integrated heat release rate of the flame, hq0s i over each time-step in the oscillation cycle. The results are plotted in Fig. 18 at L1 and L2. The upstream anti-symmetric flapping motion of the flame persists along the first two panels in Fig. 18(b). Here, the variation of q0c =Q on the l.h.s. and r.h.s. are in anti-phase over the cycle resulting in negligible production of q0 between 0 < y < 10. Downstream of this point, large-scale interactions between adjacent flames occur, which alters the phase between the l.h.s. and r.h.s. of the flame which produces q0 . Moreover, peak fluctuations are generated in the merging region due to the production of FSA [21]. Near L1 in Fig. 18(a), the variation of q0c =Q on both sides of the flame oscillate in phase before and after merging occurs. Again, the production of FSA in the merging region results in peak fluctuations in q0c =Q and also an increase in the amplitude as shown in earlier in Fig. 8. The minor differences between the l.h.s. and r.h.s. of the flame shown in the final panel in Fig. 18(a), which shows the average of q0c =Q over the whole flame, most probably results from the spin ratio being non-zero, SR ¼ 0:0779, and the flame not being centred at the anti-node. The same analysis can be applied to each flame from the pressure node and anti-node as shown in Fig. 16 get a sense of how the phase of the flame response changes within the mode shape. After calculating the phase-averaged FSA of each flame in the same manner as Fig. 18, the phase difference /LR of q0c between the l.h.s. and r.h.s. was estimated by fitting a sinusoid using the method of least squares and plotted in Fig. 19. Because the standing wave

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Fig. 18. Spatial contributions of the phase-averaged FSA along the flame length for the standing wave cases in Fig. 17. The top and bottom rows correspond to the pressure anti-node and node respectively. The normalised cycle time, s, is indicated in the top left hand side of each image.

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y (mm) Fig. 19. The phase difference /LR of the unsteady heat release rate on the l.h.s. and r.h.s. of each flame from a pressure anti-node to a pressure node. Symbols represent the azimuthal position, h, starting from the pressure anti-node, h ¼ 20 as shown in Fig. 16. h ¼ 20 is denoted by ; h ¼ 40 by N; h ¼ 60 by j; h ¼ 80 by }; and h ¼ 100 (pressure node) by .. Corresponding positions in terms of their orientations are: v h R=t ¼ 0; 1=9; 2=9; 3=9; 4=9 when normalised by p.

modes rotate slowly with an azimuthal velocity, v h , the flame positions within the mode were determined by their orientation, v h R=t as described in Section 2.3 and Section 2.5. For discussion

purposes, a more convenient method to compare the flame response is to simply consider the azimuthal location, h, of each flame within the standing wave as shown at the top Fig. 16 where each flame is 20° apart. The pressure anti-node is actually located at h ¼ 10 so we consider the flame response at h ¼ 20 whereas the flame at the pressure node is at h ¼ 100 . Starting at the antinode in Fig. 19, the axisymmetric response is shown by small /LR differences between the l.h.s. and r.h.s. of the flame. Upstream of the merging region between 0 < y < 10 mm, the /LR between the l.h.s. and r.h.s. of consecutive flames progressively increases until each side of the flame is oscillating in anti-phase,  p, at the pressure node. The effect of flame merging, which occurs between 10 < y < 15 mm, acts to smooth out the phase differences in the upstream flame dynamics throughout the mode but does not produce large fluctuations in heat release rate as shown in Fig. 8(c). 5.2. Flame dynamics during a spinning wave mode Figure 20 plots the phase-averaged FSA of a CW and ACW spinning mode for S ¼ 1:87D and 1:56D respectively. The spin ratios are SR ¼ 0:482 and 0:675 respectively. The direction of the pressure wave is indicated at the top of the figure. Unlike standing waves, where the nodes have a fixed orientation in space, during spinning modes the pressure and velocity nodes travel around the annulus Spin Direction

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Fig. 20. Phase averaged FSA for spinning wave cases. The corresponding spin ratios are: (a) SR = 0.482 and (b) SR = 0.676. The normalised cycle time, s, is indicated in the top left hand side of each image.

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at the speed of sound. The result is that the underlying flame dynamics are repeated from flame to flame. Recall from Fig. 15 that the spatial arrangement of q0s was sensitive to the direction of the most amplified wave. Crescent shaped regions of peak q0s were formed on the side of the flame where the acoustic wave was incident. These effects are visualised in a localised way in the phaseaveraged FSA in Fig. 20. At first glance, some similarities with the axisymmetric flame response in Fig. 17(a) can be observed, such as the formation and growth of vortices or disturbances which advect along the shear layers on both sides of the flame. Since the phase difference across the flame is small but finite, the vortex-flame interactions on the incident side of the wave develop more quickly. However, careful inspection reveals that the flame response is not axisymmetric as the formation of vortical disturbances are preferentially suppressed on adjacent shear layers following the direction of the pressure wave. To illustrate this more clearly, Fig. 20 is annotated with white arrows which track the development of the vortexflame interactions along the inner shear layers labelled 1 and 2. The convention adopted is that 1 is assigned to the inner shear layer where the pressure wave is incident to the flame. In both the CW and ACW spinning modes the evolution of shear layer disturbances on the side of the flame labelled 1 are suppressed over the oscillation cycle, whereas shear layer disturbances are unaffected along the flame at 2. This preferential suppression in Fig. 20(a) is slightly less pronounced as the spinning mode is weaker, SR ¼ 0:482. Both cases illustrate a subtle but important difference in the flame response compared with standing wave modes. Based on the data available we can only speculate at the mechanisms responsible, however one possibility is that the transverse velocity component is non-negligible, and results in vorticity cancellation in a phenomenologically similar manner observed during vortex ring formation in the presence of a crossflow [28]. Finally, it is worth pointing out that although that FSA provides physical insight in the flame motions and flame-flame interactions, care must be taken when interpreting the data noting that the overall flame response cannot be considered axisymmetric. The OH⁄ chemiluminescence shows that the unsteady heat release rate exhibits varying degrees of asymmetry depending on flame spacing and spin direction, as discussed in Section 4 and in Refs. [3,11]. Nevertheless, both methods combined has provided new and important insight into the 3D structure of the heat release rate during spinning and standing wave modes and that there are important differences between them. 6. Conclusions The structure and dynamics of the phase-averaged heat release rate from high speed chemiluminescence and OH-PLIF during selfexcited standing and spinning wave azimuthal modes in an annular combustion chamber has been presented. As found in previous studies [2–4], self-excited azimuthal modes are degenerate and exhibit time-varying amplitude and phase causing the modes to switch back and forth between spinning and standing waves. The statistical preference of the modes can be characterised using a spin ratio, SR [4]. In this paper, it was shown that SR distributions are affected by the flame separation distance, S. The SR in conjunction with conditional averaging methods permitted the compilation the phase-averaged heat release rate data. The results showed that the structure of the global heat release rate and planar flame dynamics are different for spinning and standing wave

modes. During standing wave modes, the magnitude of the global heat release rate and flame dynamics were found to be spatially dependent on the mode shape. At the pressure anti-nodes, peak fluctuations in heat release rate result from the generation of flame surface area produced by axisymmetric motions of the flame driven due to the modulation of the inlet flow induced by the pressure fluctuations. On the other hand, flames nearest to the pressure nodes, produced negligible fluctuations in the global heat release rate due to anti-symmetric, transverse, flapping motions of the flame which results in cancellation. The dynamics of flames located between the pressure node and anti-node exhibited a composite of anti-symmetric and axisymmetric response. During spinning modes, the structure of the flame was found to be asymmetric and characterised by the preferential suppression of disturbances along the shear layers incident to the direction of the pressure wave and were different from the standing wave cases. Acknowledgements The authors would like to acknowledge the financial support from the ESPRC. Grant nos. EP/E053866/1 and EP/G035784/1. References [1] W. Krebs, P. Flohr, B. Prade, S. Hoffmann, Combust. Sci. Technol. 174 (2002) 99–128. [2] P. Wolf, G. Staffelbach, L.Y. Gicquel, J.-D. Müller, T. Poinsot, Combust. Flame 159 (2012) 3398–3413. [3] N.A. Worth, J.R. Dawson, Combust. Flame 160 (2013) 2476–2489. [4] J.-F. Bourgouin, D. Durox, J. Moeck, T. Schuller, S. Candel, Self-sustained instabilities in an annular combustor coupled by azimuthal and longitudinal acoustic modes, in: ASME Conference Proceedings GT2013-95010, 2013. [5] U. Krüger, J. Hüren, S. Hoffmann, W. Krebs, P. Flohr, D. Bohn, J. Eng .Gas Turbines Power 123 (2000) 557–566. [6] S. Stow, A. Dowling, Thermoacoustic oscillations in an annular combustor, in: ASME Conference Proceedings GT2001-0037, 2001. [7] S. Evesque, W. Polifke, C. Pankiewitz, Spinning and azimuthally standing acoustic modes in annular combustors, in: 9th AIAA/CEAS Aeroacoustics Conference. [8] B. Schuermans, C. Paschereit, P. Monkewitz, Non-linear combustion instabilities in annular gas turbine combustors, in: 44th AIAA Aerospace Sciences Meeting and Exhibit. [9] J.-F. Parmentier, P. Salas, P. Wolf, G. Staffelbach, F. Nicoud, T. Poinsot, Combust. Flame 159 (2012) 2374–2387. [10] G. Staffelbach, L. Gicquel, G. Boudier, T. Poinsot, Proc. Combust. Inst. 32 (2009) 2909–2916. [11] N.A. Worth, J.R. Dawson, Proc. Combust. Inst. 34 (2013) 3127–3134. [12] S.R. Stow, A.P. Dowling, Low-order modelling of thermoacoustic limit cycles, in: ASME Conference Proceedings GT2004-41669, 2004, pp. 775–786. [13] N. Noiray, M. Bothien, B. Schuermans, Combust. Theory Modell. 15 (2011) 585–606. [14] N. Noiray, B. Schuermans, Proc. R. Soc. A: Math. Phys. Eng. Sci. 469 (2013). [15] G. Ghirardo, M.P. Juniper, Proc. R. Soc. A: Math. Phys. Eng. Sci. 469 (2013). [16] J. O’Connor, T. Lieuwen, Combust. Sci. Technol. 183 (2011) 427–443. 17. [17] R. Balachandran, B. Ayoola, C. Kaminski, A. Dowling, E. Mastorakos, Combust. Flame 143 (2005) 37–55. [18] P. Palies, D. Durox, T. Schuller, S. Candel, Combust. Flame 157 (2010) 1698– 1717. [19] F. Lespinasse, F. Baillot, T. Boushaki, Comptes Rendus Mécanique 341 (2013) 110–120. [20] M. Hauser, M. Lorenz, T. Sattelmayer, J. Eng. Gas Turbines Power 133 (2011) 041501. [21] N.A. Worth, J.R. Dawson, Combust. Flame 159 (2012) 1109–1126. [22] N.A. Worth, J.R. Dawson, Meas. Sci. Technol. 24 (2013) 024013. [23] N. Syred, Prog. Energy Combust. Sci. 32 (2006) 93–161. [24] J.P. Moeck, J.-F. Bourgouin, D. Durox, T. Schuller, S. Candel, Combust. Flame 159 (2012) 2650–2668. [25] I. Boxx, M. Stöhr, C. Carter, W. Meier, Combust. Flame 157 (2010) 1510–1525. [26] A. Steinberg, I. Boxx, M. Stöhr, C. Carter, W. Meier, Combust. Flame 157 (2010) 2250–2266. [27] S.K. Thumuluru, T. Lieuwen, Proc. Combust. Inst. 32 (2009) 2893–2900. [28] R. Sau, K. Mahesh, J. Fluid Mech. 604 (2008) 389–410.

Please cite this article in press as: J.R. Dawson, N.A. Worth, Combust. Flame (2014), http://dx.doi.org/10.1016/j.combustflame.2014.03.021