IMPACT OF HYDROGEN ADDITION ON THE THERMOACOUSTIC INSTABILITY AND PRECESSINGTEX CORE DYNAMICS IN A CH 4 /H 2 /AIR TECHNICALLY PREMIXED COMBUSTOR

We study the impact of H 2 enrichment on the unsteady ﬂow dynamics and thermoa-coustic instability in PRECCINSTA swirl combustor. The experiments were performed at atmospheric conditions with H 2 /CH 4 fuel mixtures at a global equivalence ratio of 0.65 and a constant thermal power of 20 kW. We analyze data with three fuel compositions: 0% , 20% and 50% H 2 in two operating modes, premixed (PM) and technically premixed (TPM). A new multi-resolution modal decomposition method, using a combination of wavelet transforms and proper orthogonal decomposition (WPOD) is performed on time resolved ﬂow velocity and OHPLIF measurements. Thermoacoustic oscillations are observed in the TPM operating mode alone, indicating that the primary heat release driving mechanism is due to fuel-air ratio oscillations. WPOD results for the 0% H 2 TPM case reveals intermittent helical PVC oscillations along with axi-symmetric hydrodynamic ﬂow oscillations due to the thermoacoustic oscillations. These oscillations cause local ﬂame extinction near the nozzle centrebody resulting in liftoff. A precessing vortex core (PVC) then develops in the ﬂow and enables intermittent ﬂame reattachment. In the 0% H 2 premixed case, the ﬂame remains lifted off the centrebody despite the presence of PVC oscillations. H 2 enrichment results in the suppression of ﬂame lift-off and the PVC in both operating modes. We show from ﬂow strain rate statistics and extinction strain rate calculations that the increase of the latter with H 2 addition, allows the ﬂame to stabilize in the region near the centrebody where the pure CH 4 cases show lift off.


INTRODUCTION
Increased deployment of renewable sources such as solar and wind energy for power generation, presents a challenging problem for power distribution, grid stability and operability, due to fluctuations in solar flux and wind due to both daily and seasonal variations.A possible solution to this problem is to use the available excess power from renewable sources, during periods of low demand, to generate and store hydrogen from electrolysis of water.Then, during periods of high demand that cannot be met by renewable sources, the hydrogen thus generated can be blended with or even replace natural gas from conventional sources as fuel for gas turbine power plants.
This can then facilitate increased adoption of renewable sources, and thus achieve an overall reduction in carbon dioxide emissions.For this reason, combustion of natural gas -hydrogen fuel blends is an emergent technological objective for gas turbine combustion systems.
Combustion instability in gas turbine combustors is a result of coupling between unsteady heat release and combustor acoustic modes, resulting in the amplification of pressure oscillations.
These pressure oscillations, referred to as thermoacoustic oscillations, are undesirable as they can result in hardware damage, unacceptably high levels of pollutant emission and other operability issues [1].Current combustion instability mitigation strategies for gas turbine combustion systems have been developed predominantly for natural gas as fuel with some level of compositional variability.However, the significant change in fundamental combustion parameters such as the flame speed, extinction strain rates etc., with increased levels of hydrogen enrichment, presents new technological challenges from the standpoint of instability mitigation.This is the motivation for the present paper that seeks to clarify the impact of H 2 enrichment of the primary CH 4 fuel in a model gas turbine combustor facility at DLR Stuttgart.
Unsteady heat release oscillations arise from coupling between velocity oscillations [2][3][4] and unsteady fuel-air ratio oscillations [5][6][7][8], with the flame.Velocity oscillations in combustors are produced by the the interaction between acoustic velocity oscillations and hydrodynamic instability modes of the combustor flow [9].These typically result in the generation large length scale coherent structures that may either be self-excited or driven by the acoustic velocity field.When the interaction between the flame and these structures causes the overall burning area to oscil-late, heat release oscillations are caused [3,4,10].Fuel-air ratio oscillations result from oscillatory fuel and air mass flow rates at fuel injectors due to flow oscillations caused by acoustic pressure oscillations.These cause the formation of fluid pockets whose equivalence ratio can be leaner or richer than the nominal value, which are then advected by the flow into the flame and cause heat release oscillations [6,7].This interplay between various fundamental mechanisms driving unsteady heat release and acoustic pressure oscillations, can result in a wide variety of combustor states that may even be chaotic [11].
Most gas turbine combustors use swirl as a means to achieve good fuel-air mixing and reliable flame stabilization [12].Swirl is imparted to air entering the combustor primary zone through one or more nozzles by means of passages or vanes.Sometimes, this air is split into two counter-swirled streams in order to generate regions of high shear that sustain turbulent flow fluctuations [13].The characteristics of these types of flows are determined by the swirl number, S, which is the ratio of the streamwise flux of azimuthal momentum to the streamwise flux of axial flow momentum.For S > 0.6 -typically -a breakdown of the swirl generated axial vortex creates flow structures of many different forms depending on the value of S and boundary conditions [14][15][16][17].Gas turbine nozzles typically operate within the range 0.5 ≤ S ≤ 1. Vortex breakdown in this range typically leads to the formation of a nominally axi-symmetric bubble like recirculation zone in the flow, referred to as bubble vortex breakdown (BVB).At higher S values, a much larger conical structure -referred to as the conical breakdown bubble (CVB) -is formed [18].We will use the term vortex breakdown bubble (VBB) to refer to either type of breakdown in this paper.Flow recirculation creates a low velocity region upstream of the VBB and also brings hot products and reaction intermediates in contact with the fresh unburnt gas.Both of these factors facilitate flame stabilization.
The annular deflection of the oncoming flow by the VBB creates an annular jet surrounding the VBB.Strong shear layers develop between the annular jet and the VBB (inner shear layer), as well as, between the annular jet and the surrounding fluid (outer shear layer).Several past studies have shown that the emergence of the VBB is accompanied by simultaneous self-excited precession of the VBB axis around the geometric axis of the flow [19][20][21].Manoharan et al [21] showed from ab initio analysis, that this precession is due to the emergence of an unstable helical hydrodynamic mode of the flow which results in a stable limit cycle flow oscillation wherein the VBB precesses about the flow axis.Other prior studies [20,22] have also suggested that VBB precession is a stable limit cycle oscillation.VBB precession perturbs the shear layers in a helical fashion and causes them to roll up into a helical vortex structure which rotates with the flow and encircles the VBB.This coherent unsteady flow structure is commonly referred to as the precessing vortex core (PVC) [23].
We analyze time resolved stereoscopic particle image velocimetry (sPIV) and OH planar laser induced fluorescence (OH-PLIF) data, obtained from the combustor at atmospheric pressure for a nominal heat release power output of 20 kW and a nominal equivalence ratio φ = 0.65, with varying levels of H 2 enrichment of the primary CH 4 fuel.We use a recently developed global mode extraction method, referred to in this work as wavelet-POD (WPOD) [29][30][31], to characterize the non-stationary dynamics of the flow.Experiments have been performed in both fully premixed (PM) operating mode and a technically premixed (TPM) operating mode.In the PM cases analyzed, fuel and air are premixed externally before being introduced into the experiment.For TPM cases analyzed, fuel is injected into the air flow via holes positioned within the swirler passages.
Acoustic pressure measurements reveal the presence of thermoacoustic pressure oscillations only in the TPM cases.The pure methane TPM case shows intermittent flame lift-off and reattachment events that are induced by thermoacoustic oscillations.Flame re-attachment occurs due to the emergence of a PVC which then provides a low velocity propagation path for the flame back onto the nozzle centrebody.This type of PVC-flame behaviour has been observed in other prior studies as well [32][33][34][35].With increase in H 2 enrichment in the TPM cases, flame lift-off and the PVC are both suppressed, while sustained thermoacoustic oscillations remain.On the other hand, the PM cases show thermoacoustic pressure oscillations that are negligibly small for the pure CH 4 case which then completely disappear with H 2 enrichment.This shows that thermoacoustic instability in the TPM cases is being driven primarily by the fuel-air ratio oscillation mechanism [5].The pure CH 4 PM case shows a flame that is always lifted-off from the centrebody, while remaining attached when H 2 is added.This suggests that H 2 enrichment increases the flame extinction strain rate (see eg. ref. [32,36]) and thereby, allows it to remain attached.In the pure CH 4 TPM case, spatial fuel-air ratio stratification results in a nominally richer mixture along the centreline which also increases the extinction strain rate of the flame locally.This effect is however smaller than the increase that H 2 enrichment induces [32,36] and results in intermittent flame re-attachment and lift-off due to intermittent thermoacoustic oscillations.
The non-reacting flow at the same mass flow rate conditions as the PM and TPM cases, shows a sustained PVC.Mukherjee et al [37] show in their recent study, that separation between the centrebody wake and the VBB, results in the hydrodynamic VBB precession mode of the flow becoming unstable and causes sustained PVC oscillations.Thus, the presence of a PVC in the non-reacting case suggests that the VBB and centrebody wake are separated in this experiment as well.In the reacting flow cases, when the flame is attached, either a BVB situated further upstream when compared with the non-reacting case or a large CVB is observed.This may be attributed to the combined effect of flow dilatation due to the flame and lateral confinement imposed by the combustor walls.Thus, the disappearance of the PVC maybe attributed to the merger between the BVB and the centrebody wake or the presence of CVB, which may not have a linearly unstable helical hydrodynamic VBB precession mode.That the flame itself doesn't cause suppression of the PVC is suggested by a related prior study of H 2 enriched methane-air premixed flame behaviour in a single nozzle swirl combustor with a deeply recessed centrebody, where, sustained PVC oscillations were observed for all reacting flow conditions [32,38].
The rest of this paper is organized as follows.Section 2 describes the experimental setup and details of the cases studied in this paper.Section 3 describes the data analysis procedures including the relatively recent WPOD procedure used in this paper.Section 4 presents the results of this analysis and section 5 concludes the paper with an outlook on future work.

Datta et al.,GTP-21-1391
The gas turbine model combustor based on the PRECCINSTA design is shown schematically in Fig. 1a.The setup consists of a cylindrical plenum of diameter 78 mm, from where flow is directed to a swirler consisting of 12 radial passages.Below the swirler section, there is a fuel distributor from where fuel with varying levels of H 2 enrichment, can be injected into the swirler passages through 1 mm diameter holes in the technically premixed (TPM) operating configuration.
The swirled flow then passes through a converging nozzle with a conical centrebody and enters the combustor test section.The burner nozzle has an exit diameter of D = 27.85 mm.The test section has a square cross-section of 85 × 85 mm 2 and a height of 114 mm.The flow exits the combustor through a converging conical transition piece into an exhaust duct with a diameter of 40 mm.The lateral walls of the chamber are made with quartz glass so as to provide optical access for laser diagnostic measurements.The origin of coordinates for this study is placed on the nozzle centerline at the combustor dump plane, i.e. at the tip of the centerbody.The y-axis is oriented along the streamwise flow direction and the x axis is along the laser sheet.
Simultaneous stereoscopic PIV (sPIV) and OH planar laser-induced fluorescence (PLIF) measurements were performed at a repetition rate of 10 kHz.The sPIV system includes a dual-cavity, diode-pumped, solid state laser (Edgewave, IS200-2-LD, up to 9 mJ/pulse at 532 nm) and a pair of CMOS cameras (Phantom V1212), stationed on either side of the laser sheet and pointing towards the combustor -see Fig. 1a.A total of 10,000 PIV image pairs were acquired during each run, which corresponds to a time record of 1 second.The laser beam was formed into a sheet using a pair of cylindrical lenses (f = -38 mm and 250 mm) and thinned to a waist using a third cylindrical lens (f = 700 mm).The flow was seeded with titanium dioxide (TiO 2 ) particles of a nominal diameter of 1 µm.Three component velocity measurements were obtained in a plane containing the nozzle centreline using stereoscopic particle image velocimetry (sPIV), over window of size ≈ 2.3D × 1.8D (-32 mm < x < 32 mm and 0 mm < y < 50 mm).The projected pixel size of the PIV system was ca.0.08 mm/pixel while the PIV image resolution was 640 × 800 pixels.
Interframe pulse separation (∆t) was set to 10 µs.A multi-pass, adaptive window offset, crosscorrelation algorithm (LaVision DaVis 10) was used for image mapping, calibration, and obtaining Datta et al.,GTP-21-1391 particle cross-correlations.Interrogation windows with a size of 16 × 16 pixels with an overlap of 50% were used, corresponding to a physical window size of 1.3 mm square and vector spacing of 0.65 mm.Based on the correlation statistics in DaVis, the uncertainties of instantaneous in-plane (u x and u y ) and out-of-plane (u z ) velocity components were estimated to be approximately 0.7 m/s and 1.8 m/s respectively.
The OH-PLIF imaging system used a frequency-doubled dye laser, pumped by high speed, pulsed Nd:YAG laser (Edgewave IS400-2-L, 150 W at 532 nm and 10kHz) -see Fig. 1b.The dye laser system (Sirah Credo), was tuned to excite the Q1(6) line of the band by producing 5.3 -5.5 W at 283 nm and 10 kHz repetition rate (i.e.0.53-0.55mJ/pulse).A photomultiplier tube (PMT) fitted with WG-305 and UG-11 filters and a premixed, laminar reference flame were used to monitor the laser wavelength continuously during the experiments.The 283nm PLIF excitation beam was focused in into a sheet approximately 50 mm (high) × 0.2 mm (thick) using three fused-silica, cylindrical lenses.The lenses were anti-reflective coated in order to maximize transmission.The laser sheets of the OH-PLIF and the sPIV systems were overlapped by passing the (green, 532nm) PIV sheet through the final OH-PLIF turning mirror.The OH-PLIF fluorescence signal was imaged using a highspeed CMOS camera (LaVision HSS6) along with an external two-stage intensifier (LaVision HS-IRO).A 64 mm focal length, f/2 (Halle) UV-objective lens with a high transmission, bandpass interference filter was used with the OH-PLIF camera.
The projected pixel resolution of the camera was ca.0.102mm/pixel, with an array size of 768 × 768 pixels.The OH-PLIF measurement domain overlapped that of the PIV system and was slightly wider overall (≈ 2.87D × 1.8D), spanning approximately -40 mm < x < 40 mm, and 0 mm < y < 50 mm.Pressure signals were recorded using amplitude and phase calibrated microphone probes equipped with B&K Type 4939 condenser microphones.Two of these were placed at a height of y = 20 mm ≈ 0.7D and y = 60 mm ≈ 2.1D from the dump plane in the combustor.A third microphone was placed in the plenum.The signals were measured simultaneously using a multichannel A/D converter with a sampling rate of 100 kHz.OH* chemiluminescence is a commonly used indicator of heat-release.OH* chemiluminescence signal was collected with an Datta et al.,GTP-21-1391 intensified high-speed CMOS camera (LaVision HSS 5 with LaVision HS-IRO) equipped with a fast UV lens (Cerco, f = 45 mm, f/1.8) and a bandpass filter (300-325 nm).The intensifier gate time was between 20 and 50 µs depending on signal strength.Images were acquired for 0.82 s at 10 kHz yielding 8192 frames per imaging run.

Operating conditions
The combustor is operated in two different modes, perfectly premixed mode (PM) and technically premixed mode (TPM).In the first configuration, a fully premixed mixture of fuel and air is supplied through the plenum.In the TPM setup, air is supplied through the plenum while fuel is injected into the swirler passages through the 1 mm diameter ports with high momentum.Sufficient premixing occurs within the nozzle before reaching the combustion chamber.Measurements from all of the experimental cases studied in this paper were obtained with CH 4 /H 2 fuel mixtures at a global equivalence ratio of 0.65, reactant temperature, T u = 300 K and a constant thermal load of 20 kW.This yields an average bulk flow velocity at nozzle exit, U b = 14.3 m/s with a variation of less than 1%, across all cases considered.This yields a flow Reynolds number, Re = U b D/ν ∼ 28, 000, where, ν is the kinematic viscosity of air at T u = 300 K.
We consider three cases with the primary CH 4 fuel, enriched with 0%, 20% and 50% H 2 (by volume) in both PM and TPM configurations.The cases studied in this work are listed in Tab. 1.A description of the overall unsteady flow state with respect to PVC dynamics and thermoacoustic (TA) oscillations is summarized in columns 4 and 5 in Tab.1a-b.The meaning of each of the abbreviations in the columns 4 and 5 are as follows, I = "intermittent", S = "sustained", NP = "not present".The type of flow is mentioned in column 3 where NR = "non-reacting", R = "reacting".
The non-reacting flow case (case 1 in Tab.1a) in which the inflow conditions identical to that of the 0% H 2 PM case, was analyzed to establish a baseline for unsteady flow behaviour in this study.

DATA ANALYSIS
We analyze the sPIV and OH-PLIF data obtained from the various cases in Tab.1a-b in several different ways.Time averaged fields are used to understand broadly, changes in VBB position and flame shape.Spectral proper orthogonal decomposition (SPOD), using the method of Towne et al [39], is used to extract information about global flow oscillations at various oscillation frequencies.SPOD performs a Fourier decomposition on ensembles of consecutive snapshots of flow field measurements and extracts optimal modes using proper orthogonal decomposition (POD) on a set of snapshots at a given frequency.The use of Fourier decompositon implicitly assumes that the frequency content of the flow oscillations is invariant in time.However, in turbulent flows such as considered in this paper, intermittent global flow oscillations can occur due to intermittent changes in flow and flame topology.Therefore, we use a new modal decomposition method which replaces the Fourier decomposition step of SPOD with a time-frequency decomposition of the measured data, using a discretized continuous wavelet transform (CWT).We refer to this modal decomposition technique as wavelet-POD (WPOD) in this paper and is performed as follows.

Wavelet proper orthogonal decomposition (WPOD)
A time-frequency decomposition of snapshots of measured flow field quantities, q(x, y, t) is performed at every spatial point using a discretized continuous wavelet transform (CWT) [40].
Note that this is different from other approaches that use the discrete wavelet transform [30] and the maximum overlap discrete wavelet packet transform [29].The CWT is shift invariant which ensures that shifts in the time domain signal translate into time shifts of the same value in the computed wavelet coefficients.Thus, phase relationships between signals are retained between their CWTs.This makes a time-frequency interpretation of phase relationships between signal features revealed by the CWT meaningful.Further, the scale parameter of the wavelet basis is discretized as 2 j/ν j = 0, 1, 2 . . ., with the parameter choice of ν = 10 for present results.This gives a resolution of 10 frequency bands per octave in the computed CWT, yielding a finer frequency discretization, when compared to discrete wavelet approaches [29,30].Therefore, intermittent flow Datta et al.,GTP-21-1391 oscillation events, characterized by components whose frequency content is limited and occur over short time intervals, can be accurately captured in the CWT frequency-time decomposition.The trade-off however, is the higher computational cost of computing the CWT when compared to discrete approaches.
Next, time series signals isolating intermittent global flow oscillations of interest are reconstructed using only those wavelet components that lie within their frequency band.This process is referred to as wavelet filtering in the present paper.Wavelet filtering, isolating a fixed frequency band, is applied to q(x, y, t) at all spatial points in the measurement domain, yielding waveletfiltered flow snapshots, q(x, y, t).Optimal basis modes and associated temporal variations that reconstruct q(x, y, t) are determined using POD as follows.The instantaneous snapshots q(x, y, t) are rearranged into column vectors.A snapshot matrix S whose columns are comprised of successive flow snapshots is assembled.If there are P spatial points per snapshot and Q snapshots in all, then S is a matrix of size P × Q.A singular value decomposition (SVD) of S yields the following, where, the columns of the matrix Φ (size P × P ) are the WPOD modes φk and the columns of matrix A (size Q × Q), a k (t), sample the temporal variation of q(x, y, t) projected onto φk at each sampling instant.
By construction, it is clear that φk are orthogonal.The matrix Σ is P × Q matrix whose upper square P × P submatrix, Σ P ×P , is a diagonal matrix of singular values, i.e., Σ P ×P = diag[σ 1 , ..., σ P ].The value of σ 2 k quantifies the contribution of the mode φk (x, y) to the total energy in q(x, y, t).The above process orders the modes φk in the descending order of σ 2 k values.Note that the wavelet filtering step ensures that these modes capture signal features that are contained within the chosen frequency band alone.Further, since the above process does not require a k (t) to be have the form of a stationary harmonic oscillation, the decomposition in Eq. 2 naturally recovers global non-stationary oscillatory flow behaviour.We scale a k (t) with the corresponding σk , as is common practice.Thus, the reconstructed flow field data q(x, y, t) can be written in the following form, We use the forward and inverse CWT implementations provided by the 'cwt' and 'icwt' MATLAB functions in this paper for wavelet filtering with the choice of the 'bump' wavelet as the basis of the CWT.

WPOD: example analysis
We now illustrate the WPOD analysis procedure by applying it to the sPIV measurements from the 0% H 2 TPM case (see Tab. 1b)).All quantities have been normalized using the bulk velocity at the nozzle exit for the reacting 0% H 2 PM case, U b = 14.3 m/s and nozzle diameter, D, as velocity and length scales respectively.Figure 2 shows the scalogram of the transverse velocity component Figure 3a shows the modal energy spectrum for the computed WPOD modes (black circles).
Also shown for comparison are modal spectra obtained from application of baseline POD (red squares) (i.e.without any filtering) and SPOD (blue crosses) at St = 0.9, directly to the same dataset.The SPOD results have been obtained using 19 ensembles of 1000 snapshots with 50% overlap between successive ensembles.Due to the mathematical formulation of the SPOD, where POD is applied on complex valued snapshots in frequency space, the procedure yields one complex mode whose real and imaginary parts capture spatial phase relationships associated with the oscillation.
Note that Fig. 3 shows that for both SPOD and WPOD results, most of the energy of the

Datta et al.,GTP-21-1391
oscillations is captured by the first mode and the first two modes respectively.The POD result on the other hand, shows a nearly continuous variation of modal energy across modes.This shows that it does not isolate intermittent flow oscillations as discrete modes in the same way that WPOD does.While the SPOD result prima facie achieves the same result as WPOD (see Fig. 3a, blue '×'), the interpretation that this result provides is that there is a stationary global oscillation of the flow at St = 0.9, associated with the most energetic mode.However, the temporal evolution associated with the first WPOD mode shown in Figs.3b, shows that the oscillations are intermittent and appear in bursts.Figure 3c shows the associated WPOD mode shape, φ1 , which now reveals the the spatial amplitude distribution of these oscillation bursts.
In general, the instantaneous amplitude of a k (t) in Eq. 2, is defined using the magnitude of the Hilbert transform of a k (t) as follows, The thick black curve in Fig. 3b, shows the variation of ã1 (t), which as may be expected, is simply the amplitude envelope of a 1 (t).Hilbert transforms in this study have been computed using the 'hilbert' function provided by MATLAB.Figure 3d shows the trajectory of the flow oscillations due to the first two WPOD modes that clearly dominate the flow dynamics at St = 0.9.This trajectory is shown in a phase space spanned by their respective instantaneous amplitudes, computed using Eq. 3. The excursions towards the origin that this trajectory makes, shows that the instantaneous amplitudes corresponding to both energetic WPOD modes approach zero simultaneously.
This confirms that the flow oscillations are in reality, globally intermittent and not harmonic and stationary as the SPOD result suggests.In the rest of this paper, time averages of instantaneous flow quantities, q, are denoted using the corresponding upper case symbol as, ( Q). Modes obtained from the SPOD and WPOD of q are denoted using symbol modifiers as q and q respectively.

RESULTS AND DISCUSSION
We first show results for time averaged mean flow fields in order to understand how the shape and position of the VBB changes with H 2 enrichment in the non-reacting, PM and TPM cases.
Figures 4a-g show the spatial distribution of Ūy for the cases listed in Tab.1a-b.The time averaged shape of the VBB is shown using the Ūy = 0 contour (solid black curves) in each case.
Figures 4b-g shows that the magnitudes of Ūy in the annular jet are slightly higher in the reacting flow cases when compared with the non-reacting (NR) case in Fig. 4a.This is expected due to the combined effect of gas expansion across the flame, which increases extent of lateral deflection of the oncoming flow and lateral confinement imposed by combustor walls, which causes streamwise flow acceleration.Figure 5 shows the time averaged OH-PLIF signal intensity for the PM (Fig. 5ac) and TPM cases (Fig. 5d-f).The Ūy = 0 contours (solid yellow curves) have been overlaid on these figures for reference.
Bubble type vortex breakdown (BVB) is observed in the NR, 0% H 2 PM and 0% H 2 TPM cases as shown by Figs.4a, b and e respectively.The VBB appears to be positioned further upstream in the TPM case when compared to the PM case -compare Ūy = 0 contours in Figs.4b and e.This is due to the qualitatively different nature of flame attachment in these two cases.This is evident from the time averaged OH-PLIF signal field shown in Figs.5a and d for the 0% H 2 PM and TPM cases respectively.Figure 5a shows a region of strong OH-PLIF signal intensity within the VBB at y/D ∼ 1 when compared to nearly zero values in regions closer to the centrebody.This suggests sustained flame lift off from the centrebody in the 0% H 2 PM case.The corresponding result for the 0% H 2 TPM case in Fig. 5d shows a more uniform distribution of OH-PLIF signal intensity, suggesting qualitatively different flame attachment.This suggests that partial premixing in the 0% H 2 TPM case leads to richer than nominal fuel-air ratios close to the centrebody, thereby, resulting in a time averaged flame structure that is qualitatively different from the corresponding PM case.
In the PM case, SPOD decomposition is performed on three-component velocity datasets obtained from time resolved sPIV measurements using the method of Towne et al [39].These results were evaluated from 10000 flow field snapshots using 19 ensembles with 1000 snapshots per ensemble and 50% overlap between successive ensembles.This yields the same ∆St ∼ 0.0195, as has been used to determine the PSD results in Fig. 6.Figures 7a-c show the results from SPOD for the non-reacting case.Figure 7a and c.The phase of the flow oscillations on the left side of the flow axis relative to the right in these results, shows that the flow oscillations are helical in nature.Further, Fig. 7b shows a strong transverse flow oscillation on the flow centreline at the upstream end of the VBB due to VBB precession about the flow axis.The oscillations along the shear layers show evidence of helical rollup.These results show that a coherent PVC oscillation is present in the flow for the non-reacting case.This is consistent with the prior study of Steinberg et al [26], where, similar PVC oscillations with St ∼ 0.78 were observed under non-reacting flow conditions, for air mass flow rates equivalent to thermal loadings of 10 and 30 kW.This agrees well with the present value of St ∼ 0.86 to within 10%.The weakly non-linear analysis of the flow state bifurcation that results in PVC oscillations by Manoharan et al [21], shows that the PVC St depends on the swirl number alone.For this reason, it is expected that PVC oscillations should occur at nearly the same values of St in all these studies [25][26][27], as well as, the present paper.
Prior work by Mukherjee et al [37] showed that separation between the centrebody wake and the VBB, results in the instability of a linear hydrodynamic oscillation mode of the flow and causes the emergence of stable limit cycle oscillations with the characteristics similar to that shown in Fig. 7b-c.Although not shown here, an ongoing LES study of the present experiment has revealed similar flow characteristics as Mukherjee et al [37].Therefore, we conclude that in the non-reacting case, the VBB is separated from the centerbody in the present experiment, resulting in the emergence of a PVC oscillation.Note that is difficult to show this flow field structure directly from sPIV measurements due to quantitative inaccuracy in measured velocity values close to the nozzle exit due to laser reflection from the wall.-b, the amplitude of the hydrodynamic response in the 0% H 2 TPM case is much smaller than that in the 20% and 50% H 2 TPM cases -see peaks marked with an '×' on the red, green and blue curves in Fig. 8a.Note that these axisymmetric oscillations do impact the heat release response by inducing axi-symmetric wrinkling on the flame surface in the TPM case.However, they are not the primary driving mechanism as the lack of thermoacoustic oscillations in the PM cases shows.This further suggests that the fuelair ratio oscillation mechanism is the primary generator of heat release oscillations in the cases analyzed in this paper.
Next, note that the two TPM cases with H 2 enrichment do not show the presence of PVC oscillations.Since the flame is stabilized in the shear layers for these cases -see Fig. 5e-f -the time averaged density gradient is located away from the flow centreline.Therefore, the impact of flow dilatation and baroclinic torque generated by the density gradient on the vorticity dynamics of the flow would be minimal at the flow centreline.This is where the flow region driving VBB precession is positioned, as shown from linear strucutral sensitivity analysis in prior non-reacting flow studies [21,33,37,42].This suggests that in the 20% H 2 TPM case, the upstream movement of the time averaged VBB position -see Fig. 4f -causes it to merge with the centrebody wake.This stabilizes the hydrodynamic VBB precession mode and suppresses PVC oscillations [37].In the 50% H 2 TPM case, it is likely that the onset of CVB stabilizes the VBB precession mode resulting in the absence of PVC oscillations.
Interestingly, a low amplitude PVC mode is seen at St ∼ 0.9 for the 0% H 2 TPM case in Fig. 8a.This is confirmed by by the spatial amplitude distribution of the ûx and ûy in the SPOD modes at St = 0.9, shown in Fig. 10a-b (real part).Comparing these results with those for the non-reacting flow shown in Fig. 7b-c, confirms that the the flow oscillation at St = 0.9 in 0% H 2 TPM case is a PVC oscillation.Note however, that the modal energy of this St = 0.9 SPOD mode is is smaller by nearly one order of magnitude when compared with the modal energy associated with the PVC in the non-reacting case.The SPOD spectra for the PM cases in Fig. 8b, show a large peak at St ∼ 1 for the 0% H 2 PM case which corresponds to a PVC oscillation.This was confirmed by confirming that the the ûx and ûy components of the associated SPOD mode are qualitatively similar to those shown in Figs.7b and c St ∼ 0.47 and St ∼ 1.5 were confirmed by examining the spatial amplitude distributions of their SPOD modes.These, results are consistent with a recent study [43] which shows theoretically, that these types of oscillations arise due to non-linear coupling between the helical hydrodynamic VBB precession mode that generates the PVC and the axi-symmetric hydrodynamic response to the forcing imposed on the flow by the thermoacoustic oscillation.
Next, we apply WPOD analysis on the 0% H 2 TPM case to show that flow and thermoacoustic oscillations in this case are intermittent.Two typical snapshots of instantaneous OH-PLIF field for this case are shown in Fig. 11 a and b, showing lifted and attached flames respectively.The green contour corresponds to u y = 0 and shows the instantaneous shape of the VBB in each figure.The measurement section used for WPOD analysis of OH-PLIF measurements is shown in both the figures using broken red lines.When the flame is attached to the centrebody, the instantaneous VBB shape appears symmetric and have wider lateral extends near the dump plane (see Fig. 11b) when compared to the lifted flame snapshot (see Fig. 11a).Also note that in latter case, the instantaneous VBB appears to be helical.This qualitatively suggests the presence of a PVC oscillation.WPOD results were obtained using 8000 wavelet filtered velocity field snapshots in two bands of width ∆St = 0.14 centred around St T A = 0.43 and ∆St = 0.25 around St P V C = 0.9.
The OH-PLIF signal within a window of size 1.1D × 0.35D positioned on the dump plane and centered at the nozzle axis -see red broken line box in Fig. 11a-b -was also analyzed similarly, in order to gain insight into the timing of flame lift-off and reattachment events, relative to the flow oscillations for this case.
Figure 12a shows the modal energy spectrum obtained from WPOD analysis on time resolved velocity field measurements in the St = 0.43 and 0.9 bands, corresponding to St T A and St P V C values.The WPOD modal spectrum for the OH-PLIF signal in the St T A band is shown in Fig. 12b.
Note first that the WPOD modal energies of first two velocity WPOD modes in the St T A band are higher than those of the first two WPOD modes in the St P V C band, a result consistent with the SPOD spectrum for the 0% H 2 TPM case. Figure 12a shows that the first WPOD mode dominates the flow oscillations at St T A .The next three modes in Fig. 12b correspond to flow oscillations at , generated by non-linear hydrodynamic mode coupling [43].In the present experiment, the St for this oscillation happens to be very close to St T A and is therefore captured within the wavelet-filtering band around St T A .The modal spectrum at St P V C in Fig. 12a, shows that the two most energetic modes capture most of the flow kinetic energy at St P V C . Figure 12b shows that the flame dynamics at St T A is captured largely by the most energetic mode.
Figure 13a shows the temporal variation associated with the most energetic WPOD mode for the thermoacoustic oscillation (a 1,T A ), PVC (a 1,P V C ) and OH-PLIF (a 1,OH ).These results show intermittent bursts of high amplitude oscillations which suggests that flow oscillations in the 0% H 2 TPM operating mode case are intermittent.Figure 13b  Figure 14a shows the variation of a 1,OH plotted against a 1,T A , where, both quantities have been normalized by their respective peak values.Note that the trajectory is mostly aligned along a line making an angle greater than π/2 with the positive horizontal axis.This shows that a 1,T A

Datta et al.,GTP-21-1391
leads a 1,OH .Also, note that there is a trajectory band on the horizontal axis, i.e.where a 1,OH ∼ 0 showing that the flame is lifted off.These two facts together, show that flame liftoff is initiated by the thermoacoustic oscillation.This is due to local extinction of the flame at the centerbody because of transient high flow strain rates near the centrebody, created by the axi-symmetric flow response to thermoacoustic oscillations which now occurs intermittently because of the presence of turbulence fluctuations.The results for the two cases with H 2 enrichment are shown in Fig. 14b (20% H 2 ) and Fig. 14c (50% H 2 ).In both these cases, the trajectories of a 1,OH vs. a 1,T A , do not pass through the origin, showing that unsteady flame lift-off does not occur.The trajectory shapes again confirm that the thermoacoustic flow oscillation leads the OH-PLIF oscillation in both cases.
Figure 15a shows the evolution of the instantaneous amplitude of the flow oscillations at St T A , ã1,T A , evaluated using Eq. 3, for all TPM cases.Note that the the flow oscillations in the two H 2 enriched cases are stationary and largely coherent as the nearly constant variation of ã1,T A in Fig. 15a for these cases shows.The corresponding result for the 0% H 2 case shows intermittent excursions towards zero.These correspond to the times when the flame shape is transitioning from attached to lifted or vice versa.This intermittent axi-symmetric flow oscillation at St T A , induces intermittent global flame area oscillations [10] which in turn, result in intermittent thermoacoustic oscillations.This can be clearly seen from the scalograms of OH * chemiluminescence and acoustic pressure p in in Figs.15b and c respectively, for the 0% H 2 TPM case.The intermittent nature of both signals at St ∼ 0.43 = St T A is evident.Note also a very weak intermittent oscillation at St ∼ 0.9 in both Figs.15b and c.This result confirms that the intermittent PVC oscillation has a negligible impact on the flame response, even though it causes large scale flame wrinkling [10].
The absence of oscillations in OH * chemiluminescence emission spectra from prior studies in this burner, at frequencies associated with PVC oscillations in the TPM configuration at similar thermal loadings [25], confirm the generality of this result.These intermittent characteristics result in the lower magnitude of the PSD for the 0% H 2 TPM case as shown in Fig. 6a-b (solid curves).The somewhat weaker oscillation relative to the thermoacoustic oscillation at St ∼ 0.9, in Fig. 15c, appears to be the aeroacoustic signature of the intermittent PVC oscillation itself and is unrelated to thermoacoustic coupling.
The bulk flow velocity through the burner is mostly unaffected by H 2 enrichment due to the lower density of H 2 when compared to CH 4 at a given pressure and temperature.This means that the nominal unsteady strain rate field in the flow, emerging from the nozzle is also unaffected by H 2 enrichment.The presence of additional H 2 in the fuel, activates reaction pathways driven by OH and H radicals that are now produced in additional quantities due to the oxidation of the added H 2 [36].This results in an acceleration of the oxidation rate of CH 4 and the reduction in overall flame chemical time.This then results in an increase in the extinction strain rate for all H 2 enriched cases studied in this work.Thus, the reasons for the observed flame stabilization characteristics can be understood by comparing statistics of flow strain rates with the extinction strain rate as follows.
We compare the largest in-plane extensional principal flow strain rate, κ, obtained from experimentally measured velocity fields, with extinction strain rates (κ ext ) determined for axi-symmetric premixed CH 4 /H 2 /air flames in the counterflow configuration.Extinction strain rate calculations were performed using Chemkin-Pro with the GRI-Mech 3.0 [44] chemical mechanism.The inflow radial velocity was set to zero and upto 500 points were used to discretize the domain using an adaptive meshing technique.Boundary conditions for both inflows were set to the unburnt φ = 0.65 mixture composition and temperature of 300 K.The resulting flame structure closely mimics the near adiabatic strained flame condition at the base of the VBB in the present study.The κ ext values were found to be 799 s −1 , 1410 s −1 and 3400 s −1 respectively for 0%, 20% and 50% levels of H 2 enrichment in qualitative and quantitative agreement with prior results [32,36].One additional calculation was performed for pure CH 4 fuel at φ = 0.7, yielding a κ ext = 1120 s −1 .
The principal in-plane hydrodynamic strain rates in the upstream reactant flow, ahead of the flame near the dump plane were determined as follows.The instantaneous snapshots of the OH-PLIF field from the measurement window shown in Fig. 11, were binarized by replacing the measured OH-PLIF signal strength with the values 0 and 1 at points at which the OH-PLIF signal strength are below and above a threshold value.Instantaneous strain rates were computed at all points in the reactants, using velocity components from the corresponding sPIV measurement snapshot.Velocity gradients were determined using second order central differences.Thereafter, the principal in plane strain rate with the maximum magnitude, κ, and its orientation angle, θ, w.r.t the streamwise direction (y axis) are evaluated.The values of κ are normalized using the nominal value of κ ext for the nominal premixed upstream mixture composition in each case and a joint probability density (JPDF) of κ/κ ext and θ for κ > 0 (i.e.extensional strain rate) is constructed.
Figure 16a shows the JPDF for the 20% H 2 TPM case.A shape contour shown in magenta, corresponds to 50% of the maximum JPDF value marked by the cross.Together these two elements characterize the shape and position of the JPDF in the sample space.The broken vertical line corresponds to κ/κ ext = 1.Note that the largest principal extensional strain rate occurs at an angle of about 40 degrees relative to the flow axis.This may be expected as the blockage imposed by the vortex breakdown bubble deflects the oncoming flow by this angle.The flame being stabilized in the inner shear layer therefore, makes the same angle to the oncoming flow near the centrebody as indicated by the time averaged OH-PLIF fields -see Fig. 5.These results are typical and similar characteristics are observed for all other cases as well.Thus, these results show that the flame is positively stretched by the flow near the centrebody.
Figures 16b and c show the change in the shape contours and maximum values (crosses) of the JPDF for PM and TPM cases respectively.The shape contours in these results show that with increasing hydrogen enrichment in both operating modes, the principal extensional flow strain rates become progressively smaller than the nominal extinction strain rate.Note also that this is true for the most probable value of the flow strain rate, shown by the crosses in Fig. 16b-c, which is aligned tangential to the flame as well.These facts show that with increasing H 2 -enrichment, the increase in κ ext allows the flame to remain attached to the centerbody as shown by Fig. 5, because the net flame stretch quantified by the most probable flow principal strain rate is less than Further, note from Fig. 16c that the most probable strain rate in the 0% H 2 TPM case is very close to κ/κ ext = 1.This suggests that the flame would be able to remain attached to the centrebody in this case until the growth of the thermoacoustic oscillation results in instantaneous flow strain rate values exceeding κ ext and causing the flame to lift-off.Prior mixing studies at similar conditions in the same burner [24] show that the local equivalence ratio near the centrebody is higher than the nominal value.The associated local increase in κ ext with φ for the pure methane mixture, enables the flame to propgate back to the centrebody and remain nominally attached, when thermoacoustic oscillation amplitudes are low.Also, the onset of PVC oscillations following flame liftoff provides a low velocity path for the flame to propagate back and re-attach onto the nozzle centrebody, as observed in prior studies of this burner [27].
The role of fuel-air ratio stratification in the 0% H 2 TPM case is consistent with the fact that in the corresponding 0% H 2 PM case, Fig. 16b shows that the most probable flow strain rate is significantly larger than κ ext .This suggests the flame would extinguish as it propagates back towards the centrebody, despite the presence of low velocity regions generated by the PVC and therefore, prevents flame re-attachment to the centrebody.The prior study by St öhr et al [27], for a fully premixed φ = 0.7, 0% H 2 case at the same thermal loading of 20 kW as in the present burner, shows intermittent flame lift-off and reattachment.This is expected due to the increase in κ ext with φ and lends further support to our conclusions about the present dataset.

CONCLUSIONS
The present paper studies the impact of H 2 enrichment of the the primary CH Precessing vortex core (PVC) oscillations are observed in the 0% H 2 cases in both PM and TPM operating configurations, which have flames that are lifted off from the centrebody.PVC oscillations are also observed in the non-reacting case as well.This suggests that the vortex breakdown bubble and the recirculation zone behind the centrebody are separated.This results in the emergence of flow region upstream of the VBB that induces precession, as shown by the recent study from the IISc group [37].Flame lift-off in the reacting flow cases, results in flow characteristics near the centrebody that are nominally similar to the non-reacting case and therefore, shows PVC oscillations.Fuel enrichment with H 2 , results in a significant increase in extinction strain rates due to activation of H 2 oxidation driven chemical kinetic pathways.This allows the flame to remain attached to the centrebody for these cases, in both PM and TPM operating configurations.As a result, the VBB either moves upstream towards the centrebody or is of a fundamentally different conical type.Both of these changes result in PVC suppression.
The 0% H 2 TPM case shows intermittent flame lift-off and reattachment, as opposed to the corresponding PM case where the lift off is sustained.This suggests that fuel-air ratio stratification in the TPM case results in a nominally richer fuel-air ratio at the domain centreline.This then allows the lifted flame to propagate back down along a low velocity path created by the PVC oscillations and re-attach to the centrebody.This is similar to the re-attachment process described in a different burner by Tamallah et al [38], where a similar argument based on extinction strain rate was used to explain the change in the macroscopic flame shape.Thermoacoustic oscillations are observed in both lifted and attached states.This fact, along with the absence of thermoacoustic oscillations in the PM case, further lends support to the conclusion that the fuel-air ratio coupled mechanism [7] is the primary heat-release oscillation generation mechanism in this burner.
of operation at different levels of H 2 enrichment.For all results presented in this paper, velocities and lengths in this paper are normalised using U b for the 0% H 2 PM case and the burner exit diameter D. Accordingly, time and frequency are normalized as t * = tU b /D and St = f D/U b (Strouhal number).The x and y directions are referred Datta et al.,GTP-21-1391 Journal of Engineering for Gas Turbines and Power to as transverse and streamwise directions respectively.
(u x ) at y/D = 0.25 on the nozzle centerline, obtained from the CWT.The field in Fig.2shows the magnitude of the wavelet coefficients, ũx .It is evident from Fig.2that there is an intermittent oscillation at St = f D/U b ∼ 0.9.Therefore, wavelet filtering is applied to isolate the time series within a band of width ∆St = 0.25 around this St value at every point in the measurement domain to determine flow snapshots for the POD step.
The above example thus shows how WPOD analysis can extract spectrally resolved global oscillation features of non-stationary flow oscillations from flow field data, that classical POD and SPOD analyses cannot directly provide.Pointwise wavelet transforms such as the result in Fig.2, are local, i.e. they give qualitative evidence of intermittent behavior at a point.In turbulent flows, this is broadly expected and does not necessarily imply global intermittent behaviour.The WPOD Datta et al.,GTP-21-1391 analysis presented above aids in obtaining this type of insight as WPOD modes and their temporal evolution are determined directly from wavelet filtered time series data with no prior assumptions of stationarity.
Figs. 5e-f show.For the two H 2 enriched cases, Figs.5e and f show a concentration of high time averaged OH-PLIF signal intensity close to the centrebody, y/D < 1, when compared to other regions of the flow.This suggests sustained flame attachment near the centrebody in the two H 2 enriched TPM cases.The more homogeneous spatial distribution of OH-PLIF signal intensitywithin the VBB in the 0% H 2 TPM case, suggests the occurrence of intermittent flame attachment and lift-off events.The difference in the type of vortex breakdown that results from these flame dynamics suggests that the nature of the downstream subcritical flow[14,41] which determines the vortex breakdown mode i.e., BVB or CVB, depends on the time averaged density distribution in the flow that the presence of a flame creates, in addition to the time averaged velocity fields.
Figs.7b and c.The phase of the flow oscillations on the left side of the flow axis relative to the

Figures 8a and b
Figures8a and bshow SPOD modal energy spectra for the most energetic SPOD mode alone, for each of the three TPM and PM cases respectively.The result for the most energetic mode for the non-reacting case from Fig.7ais overlaid for comparison.The peaks marked with '×', correspond to velocity oscillations at St T A and those marked with a filled circle are those corresponding to PVC oscillations.This is ascertained by examining the spatial velocity variation associated with the SPOD modes at each of the peaks seen in the spectra shown in Fig.8a-b as follows.

Figure 9a -
Figure 9a-c shows the variation of ûx (real part) from the SPOD modes at St = St T A for each of the TPM cases.These results show that the flow oscillations between symmetrically positioned points on each side of the flow axis are out of phase.Although not shown here, the corresponding results for ûy , show oscillations that are in phase on either side of the flow axis.Together, these results confirm that the flow oscillations at St = St T A in Fig 8a are the hydrodynamic response to the forcing imposed by the acoustic velocity fluctuations imposed on the flow by the thermoacoustic oscillation.Again, like in the result shown in Figs.6a-b, the amplitude of the hydrodynamic . The shapes and positions of the VBB in the 0% H 2 PM case and the non-Datta et al.,GTP-21-1391 reacting flow case, as suggested by Figs.4a and b, are similar.Additionally, sustained flame lift-off from the centrebody in the 0% H 2 PM case, causes the wavemaker of the VBB precession mode to have similar characteristics as in the non-reacting case, resulting in coherent PVC oscillations.A low amplitude axi-symmetric flow oscillation is also present in the 0% H 2 PM case at its St T A ∼ 0.52 (marked with an '×' in Fig.8b) corresponding to the peak PSD of the acoustic pressure oscillations for this case -see Figs.6a-b.The spatial amplitude distribution of the SPOD modes for this case, confirm that these flow oscillations are axi-symmetric.These correspond to the hydrodynamic flow response to forcing imposed by the very weak thermoacoustic mode in the 0% H 2 PM case at St ∼ 0.52 -see Figs.6a-b.As a result, two additional hydrodynamic responses can be seen in Fig.8bat St ∼ 0.47 and 1.5, corresponding to the sum and difference of the St associated with the PVC and thermoacoustic oscillations.The helical nature of the oscillations at shows the instantaneous amplitude time history corresponding to the temporal variations shown in Fig. 13a between t * = tU b /D = 200 − 300.It is clear that ã1,P V C rises when ã1,OH falls, showing that flame lift-off results in PVC amplitude growth.A transient reduction in ã1,T A when ã1,OH rises or falls, shows that flame lift-off causes the thermoacoustic oscillations to decay before regaining their amplitude due to acousticheat release coupling being re-established with the flame in either the attached or lifted state.This behaviour is typical and is observed in other time intervals showing intermittent bursts as well.

4
figurations.The premixed (PM) operating configuration is when fuel and air are mixed externally and then introduced into the combustor.The technically premixed (TPM) operating configuration is when fuel is injected upstream of the burner through injection holes located within the passages between adjacent swirler blades.Spectral proper orthogonal decomposition (SPOD) and the more recent, wavelet proper orthogonal decomposition (WPOD) techniques are used to gain insight into the global flow oscillation phenomena.Statistics of principal strain rates in the reactant flow and extinction strain rates, determined from laminar counterflow flame computations, are used to gain insight into the impact of H 2 enrichment on flame stabilization.Thermoacoustic oscillations are observed to occur in the technically premixed operating mode while having vanishingly small am-

Fig. 6 :
Fig. 6: Variation of power spectral density of pressure with St = f D/U b for TPM (solid curves) and PM (broken curves) cases, determined from time series pressure measurements in the (a) plenum and (b) test section (at y/D = 0.7).

Fig. 7 :
Fig. 7: SPOD result for the non-reacting case (a) Variation of energy associated with the SPOD modes.Velocity components (real part) from the SPOD mode 1 at St = 0.86 (a) ûx and (b) ûy .

Fig. 8 :
Fig. 8: Variation of the most dominant spectral POD mode with St for (a) technically premixed (TPM) and (b) premixed (PM) cases.The black curve from non-reacting is overlaid on both figures for reference.The crosses and dots mark thermoacoustic and PVC oscillations respectively.

Fig. 11 :
Fig. 11: Instantaneous snapshots of OH PLIF showing typical (a) lifted (t * = 240) and (b) attached (t * = 260) flame states from 0% H 2 TPM case.The green contour corresponds to u y = 0. Red chain lines show the bounds of the window used for WPOD analysis of the OH-PLIF field.

Fig. 16 :
Fig. 16: Variation of the joint probability density function (JPDF) of the largest extensional principal strain rate and its orientation relative to y axis (streamwise direction) (a) JPDF for the 20% H 2 TPM case and 50% of peak probability contours for (b) PM cases and (c) TPM cases.Strain rate are been normalised by extinction strain rate value for the unburnt reactants in each case.The '×' markers in (b) and (c) show the position of the maximum JPDF value.