涡流火焰中速度场,OH-PLIF检测方案(粒子图像测速)

智能文字提取功能测试中

Combustion and Flame 199 (2019) 267-278Contents lists available at ScienceDirect 268Q. An and A.M. Steinberg/Combustion and Flame 199 (2019) 267-278 ARTICLE INF O Article history：Received 1 July 2018Revised 6 August 2018Accepted 23 October 2018Available online 3 November 2018 Keywords： Swirl flamesFlame blow-offHydrodynamic instabilityPrecessing vortex coresFlame extinction Laser diagnostics ABSTRAC T The coupling between fluid strain rate， local flame extinction， hydrodynamic instability， and flame liftoff was studied in premixed swirl flames using multi-kHz repetition-rate OH* chemiluminescence (CL)，OH planar laser induced fluorescence (PLIF)， and stereoscopic particle image velocimetry (S-PIV). Over 50different combinations of fuel composition (CH4/H2 ratio)， equivalence ratio， and reactant preheat temper-ature were studied， allowing systematic variation of the reactant-to-product density ratio， laminar flamespeed， and Lewis number. Depending on the test conditions， the flame could either be stably attachedto the nozzle， stably lifted， or intermittently transitioning between attached and lifted states. Transitionbetween stabilization states was linked with the transition between convective instability and absoluteinstability at the flame base； formation of an m=1 (m denotes the azimuthal wavenumber) globally un-stable wave was associated with the lifted flame， which was manifested by a helical precessing vortexcore (PVC). The minimum bulk velocity at which the flame was stably lifted was linearly correlated withthe laminar flame extinction strain rate， while none of the other commonly reported key parameters gov-erning hydrodynamic instability was able to collapse the data alone. Hence， lift-off was associated with arelatively constant Damkohler number based on the bulk fluid strain rate and extinction strain rate.Theroles of local strain and extinction on the transition process were further elucidated by the cases with in-termittent lift-off/reattachment. The probability of the flame being in the lifted state was roughly linearlycorrelated with the degree oflocal extinction at the flame base while the flame was still in the attachedstate. Moreover， this probability also was linearly related to the ratio of fluid-dynamic strain rate to ex-tinction strain rate， but not the fluid-dynamic strain rate itself. These results demonstrate the importanceof predicting extinction and hydrodynamic stability for predicting the attachment state of swirl flames. O 2018 The Combustion Institute. Published by Elsevier Inc. All rights reserved. 1. Introduction Swirling flows are extensively used in gas turbine combustorsfor flame stabilization. At a sufficiently high swirl number， the ra-dially expanding swirl flow issuing from a nozzle forms a cen-tral recirculation zone (CRZ) due to vortex breakdown， providing afavourable environment for the fresh reactants to be continuouslyignited by the recirculated hot products [1-3]. Swirling flows oftenare accompanied by coherent flow structures featuring precessionof the vortex axis coupled with helical vortices， commonly giventhe term precessing vortex cores (PVC) in the literature [4-6]. The presence or absence of a PVC plays a significant role in de-termining the global configuration of a swirl flame， i.e. whether it ( * Corresponding author. ) ( E-mail a ddresses： qia n ga n @ut i as.utoronto.ca ( Q. An)， adam.steinberg@gatech.edu (A.M. Steinberg). ) attaches to the nozzle， is lifted， or blows out. For example， Gal-ley et al. [7] studied fuel and air mixing in a partially premixedswirl flame using planar laser induced fluorescence (PLIF) of bothOH and acetone. The PVC was observed to enhance mixing， therebyhelping stabilize the flame. In an experimental study on lean blow-out (LBO) of partially premixed swirl flames， Stohr et al. [8] linkedLBO， local extinction， and the PVC. While the flame could be sus-tained during frequent short-duration extinction events， LBO oc-curred if the entire flame root was extinguished for more thanone period of the PVC oscillation. An et al. [9] recently reportedthat premixed swirl flame lift-off was associated with the onsetof a PVC， whereas the PVC was suppressed when the flame wasattached to the nozzle. The formation of the PVC appeared to betriggered by local extinction events near the flame base. PVC formation is closely related to the transition between con-vective instability and absolute instability， and therefore can beframed in the larger context of hydrodynamic stability of jetsand wakes [10，11]. The former instability mode corresponds to situations in which local disturbances are convected away by themean flow， leaving the entire flow field ultimately undisturbed.The latter corresponds to local disturbances influencing the en-tire flow field by spreading both downstream and upstream. Whileboth are local concepts， they are linked to the global profile ofthe velocity field through the fact that the existence of a localabsolutely unstable region is necessary for the development of aglobal mode， viz. self-sustained oscillations without external forc-ing. Specifically， PVC formation has been reported to be associatedwith an m=1 (m denotes the azimuthal wavenumber) globallyunstable wave [12-14]. For instance， Liang and Maxworthy[12] ex-perimentally demonstrated that， after the strongly swirling jetsunderwent vortex breakdown， an m=1 spiral mode became thedominant flow structure while the previously existing small-scalevortices were suppressed. The occurrence of this spiral mode wasaccompanied by an absolutely unstable region located near the tipof the CRZ， which served as the wavemaker by imposing its fre-quency on the whole flow. This topic has been extensively investigated through linear sta-bility analysis (LSA)， which usually linearizes the Navier-Stokesand mass conservation equations about a steady base flow [11，15].When exploring the hydrodynamic instability mechanism of inertjets and wakes using LSA， Yu and Monkewitz [16] found that wakeswith lower density than the main flow attenuated or eliminatedthe absolute instability that would otherwise have been presentin a uniform density flow. This was consistent with experimen-tal observations of wakes behind heated bluff bodies， wherein theasymmetric von Kárman vortex streets (absolute instability) gradu-ally transitioned to a symmetrical vortex shedding pattern (convec-tive instability) as the heating was increased [17]. Manoharan andHemchandra [18] probed the convective/absolute instability transi-tion mechanism for a backward facing step combustor using LSA.They concluded that absolute instability could be suppressed if thevelocity gradient of the base flow was co-located with the den-sity gradient. Another study by Manoharan et al.[19] performedan LSA on a base flow model representing swirl flow (i.e. the mod-ified ‘Monkewitz profile'[20-22]) along with an assumed densityprofile， from which the boundary between convective and absoluteinstability was identified in a parameter space consisting of a localswirl number and a backflow ratio. The transition between the twowas found to be strongly affected by the density gradient and itsdisposition relative to the shear layers. Oberleithner et al. [23] conducted a local LSA on a swirl com-bustor that was very similar to the one used in our current study.The density field near the combustor nozzle was found to be criti-cal in determining the existence of the PVC. That is， for attachedV-flames without the PVC， the growth rate and frequency pre-dicted by LSA could match the experimentally measured valuesonly when a radially stratified density field， rather than a ho-mogeneous one， was adopted. Tammisola and Juniper [24] imple-mented a global LSA on the non-reacting flow in an industrially-relevant combustor， from which the calculated spatial structureand frequency of the PVC well matched the instability propertiesof the DNS results， and the region most sensitive to perturbations(i.e. wavemaker) was identified downstream of the tip of the CRZ.While the traditional use of LSA is limited to the mean flow， Rukeset al. [25] recently proposed a transient LSA， and applied it to theevolution of an m=1 global mode in swirling jets measured us-ing high-speed diagnostics. This allowed them to track the locationof the wavemaker and growth rate of the global mode during theconvective/absolute instability transition. Emerson et al. [26] conducted a systematic experimental in-vestigation on hydrodynamic instability in bluff-body stabilizedflames. Specifically， they confirmed the role of density ratio be-tween unburnt reactants and burned products， Dr= pu/Pb， in con-vective/absolute instability transition (pu and ph are the unburnt and burnt gas densitites， respectively). While high and low Drvalues corresponded to an asymmetrically oscillatory flame anda symmetrically stable flame， respectively， transition between thetwo did not occur at a fixed density ratio； instead， intermittenttransitions were observed at multiple intermediate pulpb values. The dynamics of bluff-body flame structure transition fromthe convectively unstable (symmetric or varicose) mode to theabsolutely unstable (asymmetric or sinuous) mode was furtherexplained in Refs. [27-29] using high-speed laser measurementtechniques. As lean blow-out was approached， localized holesdeveloped on the flame sheet when the instantaneous strain rateexceeded the extinction strain rate. Subsequent entrainment ofcold reactants into the hot wake through these holes led to moreasymmetry in the flame and flow， followed by further flame frag-mentation and the eventual blow-out. This conclusion is analogousto the swirl flame lift-off mechanism proposed in our previousstudy [9]， which was characterized by a highly coupled processinvolving local flame extinction， density field variation， increasedflow field asymmetry， flame lift-off， and development of full PVC.Local extinction is crucial here in the sense that it actually initiatesthe transition between the two different instability mechanisms.By studying the dynamics of local extinction in partially premixedswirl flames， Boxx et al. [30] argued that these events werestrongly related to the persistent presence of high 2-D principalcompressive strain near the reaction zone. The picture emerging from the aforementioned studies is that(a) PVC formation is linked to the transition between convec-tive and absolute instability； (b) reduced density in the wake orrecirculation zone can suppress this transition or， alternatively，increasing the density of a low-density wake/CRZ can trigger thetransition； (c) local extinction plays a role around the transitionconditions. However， there remains a lack of systematic studiesthat unravel the parameters controlling the transition point be-tween the convective and absolute instability，particularly in swirlflames. Understanding these parameters is critical for predict-ing whether a system will exhibit a PVC， which may determinewhether the flame lifts- or blows-off. This paper investigates suchtransitions over a wide range of parameters in a well-characterizedswirl combustor. 2. Experimental setup 2.1. Combustor and test matrices The swirl burner used here (Fig. 1) has been the subject ofmany previous experimental and numerical studies， e.g. [31-34].Premixed fuel and air were fed through a plenum (78 mm diame-ter， 100 mm length) that had a radial swirler with 12 vanes and anozzle (27.85 mm diameter) with a conical center body. The swirlnumber was around 0.55， which was measured immediately abovethe burner nozzle using the velocity data by neglecting the pres-sure term and assuming constant density within the radius of thenozzle. This swirl number was sufficiently high to induce a strongCRZ after vortex breakdown for all the conditions studied in thiswork. There were two minor changes to the combustor comparedto the original work of Meier et al. [31]. Firstly， the optically acces-sible combustion chamber， consisting of four pieces of fused sil-ica glass， had a dimension of 97×97×114 mm’(as opposed to85×85×114 mm3). Secondly， the downstream end of the com-bustion chamber did not contract to an exhaust tube， in order toreduce the occurrence of thermoacoustic oscillations. The axial， ra-dial， and azimuthal axes of the chamber were defined as x， y， andz， respectively， with their corresponding velocity components beingu， v， and w. The reactants were metered using calibrated electromechanicalmass flow controllers (Brooks) with an accuracy of ±1%of rate Fig. 1. Schematic of the swirl burner used in this study. (for flows 20%-100% full scale) or ±0.2% of full scale (for flows2%-20% full scale)， where the former was the limiting factor fornearly all the flow rates in these experiments. Air was preheatedusing an in-line electric air heater (Farnam Heat Torch 200) to atemperature slightly greater than the target reactant temperature(Tr) and then mixed with fuel about 1 m upstream of the plenum.The mixture temperature was monitored in the plenum using atype K thermocouple， where it was maintained at Tr. The uncer-tainty of Tr was estimated to be ±2 K. The combustor was operated across a range of fuel composi-tions (different CH4：H2 ratios)， Tr， and equivalence ratios (中). Aswill be described below， these parameters were varied to system-atically adjust different combinations of the laminar flame speed(s[)， Dr， and the Lewis number (Le) while keeping the other param-eters constant. The laminar flame speed is important for kinematicbalance between fluid velocity and flame propagation， which mayinfluence flame transition.As described above， Dr is considered akey parameter for determining hydrodynamic instability. The Lewisnumber was investigated to determine if preferential diffusion hada distinct impact on flame transition that was not otherwise cap-tured [35]. Furthermore， blends of CH4 and H2 are of interest ascomponents of alternative fuels for gas turbines， e.g. Refs.[36-38]. The three fuel compositions used in the experiments corre-sponded to CH4：H2 of 100：0 (F1)， 90：10 (F2)， and 80：20 (F3)in terms of volume fraction. The values of effective Le of thethree fuel compositions were calculated to be 0.98， 0.91， and 0.84，respectively， using the volume-based calculation method (Ley =XcH xLecHa +XH，×LeH2， with X， being the mole fraction of i)[39]， where LecH and Le， were taken to 0.98 and 0.29， respec-tively [40]. The use of relatively low proportions of H2 was basedon the consideration of H2 enriched fuels of interest in power-generation gas turbine applications， as well as the fact that evensmall amounts of H2 greatly enhanced the flame stability [41]， aswill be demonstrated below. For all test cases， sp was calculatedusing the FreeFlame model in Cantera [42] with the GRI 3.0 mech-anism [43]. Four sets of tests were performed， designated T1-T4， in whichdifferent combinations of thermo-chemical parameters were heldconstant or varied； a total of 52 different combinations were stud-ied. Each test case within a set represents fixed thermo-chemicalconditions， viz. fuel composition， ， and Tr (and hence Le， s， and Dr). For each such case， the flame was ignited at a sufficiently lowbulk velocity U (volumetric flow rate divided by nozzle exit area)that the flame was stably anchored at the conical center bodyin the burner nozzle. Then， both air and fuel flow rates were in-creased in a simultaneous and incremental fashion while keepingthe thermo-chemical parameters constant. As the flow rate in-creased， the flame began to intermittently lift-off from the nozzleand reattach. In Ref. [9]， it was shown that the transition fromattached-to-lifted flames was associated with the development ofa PVC， whereas the PVC disappeared during flame reattachment.As the flow rates were further increased， the percentage of timespent in the lifted state also increased， until the flame statisticallydetached from the nozzle and became aerodynamically-stabilizedat a bulk velocity of U. Table 1 shows the test matrix for T1， in which Dr and Le werefixed at various levels. The purpose of designing T1 was to deter-mine if the transition point between stably attached flames (withonly convectively unstable flow) to fully lifted flames (with onlyglobally unstable flow) was characterized by Dr. It is noted thatCases T1D3F1 and T1D5F1 are not included， because fully attachedflames could not be achieved even at the lowest U achievable bythe mass flow controllers. It was found that Dr was unable to collapse the lift-off lim·its， and hence did not collapse the conditions at which the steadyglobal instability occurred (see Section 3.2). Additionally， variationof s in T1 was concurrent with changes in both Dr and Le. There-fore， another three sets of tests (T2， T3， and T4) were designedto allow further variation of the thermo-chemical parameters. Thetest matrices of T2-T4 are shown in Tables 2-4. T2 includes fivedifferent groups of three cases， with each group having a fixedvalue of Dr and Le， but different s. T3 also includes five groupsof three cases， each having a fixed Dr and s， but different Le. InT4， three groups were performed， varying Dr with fixed Le and sp. 2.2. Diagnostic techniques The test matrices described above include 52 different combi.nations of thermo-chemical parameters. For each such combina-tion， measurements were made at a variety of different flow ratescorresponding to the attached state， various degrees of intermit-tent lift-off and reattachment， and the first flow rate at which theflame was never attached， viz. U.OH* chemiluminescence (CL)measurements were made at each such condition at a repetitionrate of 1 kHz. Furthermore， simultaneous 10 kHz OH planar laserinduced fluorescence (PLIF) and stereoscopic particle image ve-locimetry (S-PIV) measurements were made at select conditions. The layout of the 10 kHz simultaneous OH PLIF and S-PIV sys-tem is shown in Fig.2. The OH PLIF excitation system consisted ofa diode-pumped， solid-state， Nd：YAG pump laser (Edgewave IS16II-E) and a frequency-doubled dye laser (Sirah Credo). The pumplaser delivered laser pulses at 532 nm with 8 mJ/pulse at 10 kHzand a pulse duration of 10 ns. After frequency doubling， the dyelaser was tuned to excite the Q(7) line of the A-X(v'=1，v"=0)transition of OH at 283.2 nm. The dye laser delivered an aver-age output power of 2.5 W or 0.25 mJ/pulse. The laser beam wasformed into a collimated sheet with a height of about 40 mm us-ing three cylindrical lenses， which was passed along the combus-tion chamber centerline. The OH PLIF signal was acquired using a lens coupled and elec-trically synchronized image intensifier (Invisible Vision UVi， 100 nsgate) and high-speed CMOS camera (Photron SAZ). An OH band-pass filter (center wavelength 310±5 nm， transmission >90%) wasplaced in front of the UV lens (Sodern Cerco， f=45 mm， f/#=1.8) mounted on the intensifier to capture OH emission from theflame. The PLIF images were corrected for the vertical mean lasersheet intensity profile using the signal from a uniform acetone Table 1Test conditions for T1. Case # Tad (×103K) Tr±2(×102 K) Dr XAir XcHa XH， T1D1F1 1.77 3.0 5.9 0.66 0.94 0.064 0 T1D1F2 1.77 3.0 5.9 0.65 0.93 0.062 0.0069 T1D1F3 1.77 3.0 5.9 0.65 0.93 0.059 0.015 T1D2F1 1.75 4.0 4.4 0.60 0.94 0.060 0 T1D2F2 1.75 4.0 4.4 0.60 0.94 0.058 0.0064 T1D2F3 1.75 4.0 4.4 0.60 0.93 0.055 0.014 T1D3F2 1.70 5.0 3.4 0.53 0.94 0.052 0.0057 T1D3F3 1.70 5.0 3.4 0.53 0.94 0.049 0.012 T1D4F1 1.75 6.0 2.9 0.52 0.95 0.052 0 T1D4F2 1.75 6.0 2.9 0.52 0.94 0.050 0.0056 T1D4F3 1.75 6.0 2.9 0.52 0.94 0.048 0.012 T1D5F2 1.70 7.5 2.3 0.43 0.95 0.042 0.0047 T1D5F3 1.70 7.5 2.3 0.43 0.95 0.040 0.010 Table 2Conditions for T2， varying s at fixed Dr and Le. Dr=5.0， Le=0.98 Dr=5.0， Le =0.91 Dr=5.0， Le =0.84 Dr =4.5， Le=0.91 Dr=3.5， Le =0.91 Tad (×103K) 1.75 1.83 1.90 1.75 1.83 1.90 1.75 1.83 1.90 1.69 1.76 1.82 1.70 1.75 1.80 Tr±2(×102K) 3.5 3.7 3.8 3.5 3.7 3.8 3.5 3.7 3.8 3.8 3.9 4.1 4.9 5.0 5.2 s (m/s) 0.18 0.24 0.31 0.19 0.25 0.32 0.21 0.27 0.34 0.18 0.23 0.30 0.28 0.34 0.42 Table 3Conditions for T3， varying Le at fixed D， and sj. Dr=4.5， sp~0.17 m/s Dr=4.0， sj~0.24 m/s Dr=4.0， sj~0.31 m/s Dr=4.0， sj~0.38 m/s Dr=3.5， sj~0.40 m/s Tad (×10 K) 1.69 1.68 1.67 1.73 1.72 1.70 1.80 1.78 1.77 1.86 1.84 1.82 1.81 1.79 1.77 Tr±2(×10K) 3.8 3.7 3.7 4.3 4.3 4.3 4.5 4.5 4.4 4.7 4.6 4.6 5.2 5.1 5.1 Le 0.98 0.91 0.84 0.98 0.91 0.84 0.98 0.91 0.84 0.98 0.91 0.84 0.98 0.91 0.84 Table 4Conditions for T4， varying Dr at fixed Le and sj. Le =0.98， s~0.18 m/s Le =0.91， si≈0.24 m/s Le=0.84， sj≈0.30 m/s Tad (x10 K) 1.68 1.71 1.74 1.75 1.79 1.83 1.82 1.85 1.90 Tr±2(×102 K) D. 49 3.8 58 40 28 40 21 Fig. 2. Schematic of the simultaneous 10 kHz S-PIV and OH PLIF system. field that was doped into the combustion chamber. The imagesalso were corrected for the intensifier white-field response. The two-dimensional， three-component S-PIV system consistedof a dual-cavity， diode-pumped， solid-state， double-pulse， Nd：YAGlaser (Quantronix Duo Hawk) and two high-speed CMOS cameras(Photron SA5) equipped with Scheimpflug adapters and commer-cial camera lenses (Tokina， f= 100 mm， f/#=2.8). The PIV laserdelivered laser pulse pairs at 532 nm with an average outputof 6 mJ/pulse. The separation time between the two pulses was between 8-22 us， depending on the U of a specific test condition.The laser beam was formed into an approximately 40 mm tallsheet and overlapped with the PLIF laser sheet. TiO2 particles witha nominal diameter of 1 um were used to seed the flow. The two PIV cameras were placed in a forward scatter con-figuration， with an angle of about 115 degrees between them.The lenses were tilted by adjusting the Scheimpflug adapters tomeet the Scheimpflug criterion. As shown in Fig. 1， the field ofview of S-PIV was slightly off-center to avoid obstruction from the (a) Stably attached state (b) Fully lifted state Fig. 3. A typical instantaneous OH intensity field overlaid with the corresponding vector field， representing the stably attached state and the fully lifted state， respectively，extracted from Case T1D1F1 at U=7.7 m/s. The white dot denotes the LSP. combustion chamber corner posts. The cameras were operated ata frame rate of 20 kHz (frame straddling mode) and imaged a fieldof view of about 40 mm x50 mm. After pre-processing using bothtemporal and spatial filters， vector fields were calculated from thespatial cross-correlation using the adaptive evaluation algorithm ina commercial software package (LaVision DaVis 8.3). A final inter-rogation window size of 32×32 pixels was used， with an over-lap of 75%.This led to a vector-field spatial resolution of 2.76 mmwith a vector spacing of 0.69 mm. The main purpose of using thestereoscopic system in the experiments was to increase the accu-racy of the in-plane vector calculations for the swirling flow. All the equipment was triggered by an external pulse generator(BNC 575) and timing was monitored on an oscilloscope (LeCroyWavejet 354A). The PLIF laser pulse fell in between the S-PIV laserpulse pair constituting a velocity measurement. 15，000 measure-ments (duration 1.5 s) were obtained at each test condition. Cal-ibration images of a 3D dot target (LaVision 058-5) were used tomap the fields of view from the raw PLIF and PIV pixel coordinatesto the same world coordinate. OH* CL measurements were conducted separately as a qualita-tive indicator of the line-of-sight integrated heat release rate. Thecamera/lens/filter configuration was identical to that used in theOH PLIF system， but the gate duration was set to 60 us. Imageswere taken with a field of view that covered almost the entirecombustion chamber at a frame rate of 1 kHz. 3. Results 3.1. Convective instability and global instability Two flame stabilization modes were observed from the experi-ments， each of which exhibited distinct flow dynamics. When theflame was in the attached state， as in Fig. 3a， the instantaneousOH radical distribution was approximately axisymmetric and theflame front was mostly stabilized along the inner shear layer (ISL).The combustion products within the CRZ were recirculated all theway back into the nozzle. ISL roll-up occurred as a result of theKelvin-Helmholtz (K-H) instability； the flow was convectively un-stable but globally stable. Note that although both axial and az-imuthal shear existed， the flow field in this state was dominatedby the K-H instability that was primarily induced by shear in theaxial direction [2]. Figure 4a shows the 2-D out-of-plane vortic-ity field(ωz) at the same instant shown in Fig. 3a， with the over-laid black curves denoting the flame topology. The flame topology algorithm utilized the magnitude， gradient， and curvature of theOH field to identify burning segments [44]. The flame front wasessentially contiguous for y≤20 mm， thus providing a high ra-dial density gradient in the vicinity of the burner nozzle [23]. Thisacted to suppress the absolute instability region that would other-wise appear for non-reacting flows in this burner， thereby prevent-ing the formation of the global hydrodynamic instability. However， convective instability can transition to absolute instability， either by changing the test condition， or spontaneously ata fixed operating condition [9，45-47]. Such transition also largelydictates the lift-off process of these swirl flames [9]. Subsequentto this transition， large-amplitude flow oscillations were estab-lished at the global scale and exhibited limit-cycle features， asshown in Figs. 3b and 4 b. The PVC structure is clearly seenin Fig. 4b， manifested by the zig-zag distribution of the vorticityfield. The shear layers after flame lift-off were qualitatively differ-ent than before lift-off， featuring a high degree of fragmentation.The high strain associated with the asymmetric flow field nearthe nozzle prevented flame attachment. Observation of the OH*CL and isothermal-flow dynamics confirmed that the lifted state(M-shaped flame) and non-reacting conditions exhibited the m=1globally unstable mode across all the test matrices， whereas theattached state (V-shaped flame) did not show this mode. (a) Stably attached state (b) Fully lifted state Fig. 4. A typical instantaneous 2-D out-of-plane vorticity field (ωz， s-) for the stably attached state and the fully lifted state， respectively， extracted from Case T1D1F1 atU=7.7 m/s. The overlaid black curves represent flame topology. (a) t= 0.0 ms (b)t=1.0 ms (c)t =2.1 ms Fig. 5. Evolution of the vorticity field for Case T1D1F3 at U=22.4 m/s， reconstructed using the 0-10th modes of POD. ωz shown here ranges from -20000 s-1 (dark) to20000 s-1 (light). Solid and dashed lines roughly represent precession close to and away from the viewer. This process is highly analogous to the previously described obser-vations made during transition of bluff-body flames， representing asignificant linkage between the hydrodynamics of swirl flames andbluff-bodyflames. In order to further identify the PVC structure for flames at thelifted state in a more quantitative way， a proper orthogonal decom-position (POD) analysis was conducted. POD is a common tech-nique used for extracting coherent structures in turbulent flows[44]. A k-mode POD representation of a dataset is given by where i represents the time instant of the original data， j the modenumber， M；(x，y) the jth spatial eigenmode， and a (t) the temporalcoefficient of the jth mode.POD provides optimal energy conver-gence， thus allowing the energetic flow features to be described bya small number of modes. In the current analysis， POD was implemented on the vorticity(wz) field. The Oth POD mode corresponded to the mean vortic-ity field. Evolution of the PVC was reconstructed using the 0-10thmodes of POD； an example of this using Case T1D1F3 at U =22.4m/s is shown in Fig. 5. As can be seen， one revolution of the PVCtook about 2.1 ms. Figure 6 shows the power spectral density (PSD) plots obtainedfrom a fast Fourier transform (FFT) implemented on the temporalcoefficient a(t) for two U conditions in Case T1D1F3， represent-ing the stably attached and lifted states. No dominant frequency Fig. 6. Normalized PSD of a(t) for two U conditions from Case T1D1F3， repre-senting a stably attached condition (U=15.3 m/s) and a stably lifted condition(U=22.4 m/s)， respectively. is found in the attached flame. On the other hand， a distinct peakoccurs at approximately 480 Hz for the lifted state， which corre-sponds well to the PVC revolution period shown in Fig. 5. The PVCfrequency was found to be a linear function of U， as illustrated inFig. 7 using a number of conditions that all exhibited steady globalinstability. This is in agreement with previous studies， e.g. Ref. [49]. To quantitatively show that the identified PVC was an m=1global mode， two points located symmetrically about the y axis of 40 Fig. 7. Relationship between identified PVC frequency and U for various conditionsexhibiting steady global instability. (a) Magnitude-squared coherence (b) Phase lag Fig. 8. Results of cross spectrum analysis for Case T1D1F3 at U = 22.4 m/s. the combustion chamber， viz. point 1 (x≈-10 mm，y~5 mm) andpoint 2 (x≈10 mm， y~5 mm)， were selected.Cross-spectral analy-sis was then performed on the radial velocity components at thesepoints. Figure 8a shows the magnitude-squared coherence of thesetwo signals extracted from Case T1D1F3 at U =22.4 m/s. The peakat around 480 Hz， which matches the one shown in Fig. 6， sug-gests that there exists significant coherence between the two timeseries at this PVC frequency. Figure 8b shows that the phase lagbetween the two signals corresponding to 480 Hz is roughly n， in-dicating that the global hydrodynamic instability occurring at thelifted state indeed featured an anti-symmetric m=1 mode. Fig. 9. Flame detachment probability plotted against bulk velocity for three testcases in T1D1. 3.2. Statistics of flame lift-off Based on the dynamical flame/flow behaviors described in theprevious section， all the test conditions studied could be dividedinto three categories as U was increased， namely steadily attached，intermittent (and apparently random) attached/lifted transitions，and steadily lifted. In the dynamical systems sense， each of theserepresents a dynamically stable state. That is， the attached andlifted classes are aperiodic and periodic attractors in the phasespace， respectively， and the intermittent regime features switchingback and forth between these attractors. This scenario is similar tothat of hydrodynamic instability of bluff-body flames studied bySuresha et al. [46]， where the features of and transition betweenthe two attractors were confirmed using a recurrence quantifica-tion analysis. It is important to acknowledge that intermittencyshould not be viewed as a trivial phenomenon [50]； An et al.[9] showed that varying degrees of intermittency could occur overa relatively wide range of conditions. This also is demonstrated inFig. 9， which shows the percentage of time spent in the lifted state(defined as DP) as a function of U for a few typical test cases. A consideration of primary interest is the combination(s) offluid and thermo-chemical parameters that control the transitionto the dynamically stable lifted state， i.e. U. This represents thelower boundary of the flame stabilization regime having a contin-uous global hydrodynamic instability. U therefore was determinedfor each test case from the OH* CL measurements. The relationship between U and Dr for the test cases in T1 isshown in Fig. 10a. Within each group of data points having thesame Dr， U increased with increasing s and decreasing Le. Further-more， cases with lower Dr had higher values of U. That is， lowerDr required higher velocities before the onset of steady global hy-drodynamic instability. This is in contrast to what may be expectedfrom heated non-reacting flows， in which a lower density ratio be-tween the cold and hot fluids is usually associated with increasedoccurrence of global instability. Specifically， using combustion asthe heat source results in additional coupling between the the fluidmechanics and heat added to the flow compared to what wouldoccur， e.g. behind a heated bluff-body [16]. However， as mentioned， T1 involved two parameters simulta-neously being changed at different fixed values of Dr. This makesit difficult to isolate the critical parameters characterizing the (a) T1 (c) T3 (d) T4 Fig. 10. The experimentally identified bulk velocity at statistical lift-off for each test case in T1-T4， respectively， plotted against a thermo-chemical parameter. flow/flame interaction. Hence， T2-T4 were performed to help iso-late the different effects. U of each test case in T2 is plotted as a function of Dr inFig. 10b. With a fixed combination of Dr and Le， U increased withincreasing sp. For the three groups with Le=0.91， Uwas high-est for Dr=3.5， lowest for Dr=4.5， and in between for Dr =5.0.The three groups with the same Dr and different Le generallyhad increasing U with decreasing Le. However， this decreasing Lealso was associated with an increase in s； U increased essentiallymonotonically with sp over all cases in T2 (not shown). The relationship of U with s is further elucidated in Fig. 10c，which shows this relationship for all cases in T3. At a given valueof s and Dr， U increased with decreasing Le. Furthermore， for afixed value of Le (e.g. the lower-most symbols in each type)，U in-creased roughly linearly with sj. Hence， there is a clear dependencyof lift-off and global instability on s， but there also is a chemicaleffect that is not captured by sj. Figure 10(a) and (b) demonstrated that Dr does not well charac-terize the onset of steady global instability/statistical lift-off. This isfurther elucidated by Fig. 10d， which shows U versus s for T4. Ata fixed fuel composition (or Le) and sj， U was not strongly affectedby Dr；there was only a slightly increasing trend with increasing Dr.This plot also highlights the linear relationship between U and sj. In summary， Fig. 10 shows that (a) the flame lift-off limits andthe associated onset of steady global hydrodynamic instability arenot characterized by Dr； (b) for a given fuel composition， Uscalesroughly linearly with s； (c) there is a fuel effect that is not cap-tured by sp， in which increasing the hydrogen content (or decreas-ing Le) increased U at a fixed sj. Based on the observations of Anet al. [9]-and other similar observations [23] - that intermittentlift-off and growth of the global instability was linked to local ex-tinction near the flame base， it was hypothesized that the lift-off Fig. 11. IdentifiedU of each test case in T1-T4 plotted against the correspondingextinction strain rate. limit may be linked to the susceptibility of the reactants to strain-based extinction. That is， the combined effects of fuel composition，equivalence ratio，and preheat temperature (or s， Le， and Dr) maybe linked to the extinction strain rate. Hence， the steady extinctionstrain rate (ate) was calculated for each reactant mixture using theExtinction of Premixed or Opposed Flow Flame reactor model inChemkin. Figure 11 shows U versus at， e for all cases across T1-T4. Thereis a clear linear trend， with a fitted equation of U =0.049ate +8.6 Fig. 12. Daj versus at， e for all test cases in T1-T4. in m/s. That is， the flame lift-off limit and the onset of steadyglobal hydrodynamic instability are linearly correlated with the ex-tinction strain rate. Although the above discussed thermo-chemicalparameters (i.e. Dr， s， and Le) are all significant in determiningflame/flow transition boundaries， none of them can collapse thedata alone in the same way that at， e is capable of. This linear cor-relation implies a relatively simple means of predicting how thetransition limits will depend on fuel composition and operatingconditions in swirl flames. Note that the y-intercept of this lineis not at U=0， indicating that even weakly flammable mixturescan produce attached flames. The specific y-intercept and slope ofthe U versus at， e relationship are expected to be geometry depen-dent， potentially depending on swirl number， confinement， and/orother features. Nevertheless， the results indicate that test over arelatively small parameter space could be sufficient to enable pre-diction of the transition behavior in a given geometry. The linear trend also indicates that the transition occurs at arelatively constant Damkohler number， defined as where Rn is the nozzle radius and Uio=8.6 m/s is the y-interceptof the linear fit in Fig. 11. The fluid timescale (Rn(U-Ulo)) ismeant to describe the mean shear rate， which is expected to be thefluid mechanical property characterizing strain-based extinction. Figure 12 shows Da versus at，e for all cases， demonstrating arelatively constant value. The mean value was Daj=0.29， with astandard deviation of 0.034 or 12%. The majority of the deviationoccurred for the weaker flames having the lower calculated at，e. Reasons for this increased scatter may be due to inaccuracies inthe at， e computation and/or the fluid timescale description. Re-garding the latter， it is possible that using a length scale that char-acterizes the shear layer width more accurately for each individualcase would provide a better collapse. However， this would requirevelocity measurements for each case， which would not be viablefor practical systems. As an additional note， the use of Uro in thecurrent definition of Da is necessary as it plays a role in accu-rately characterizing the transition dependence on at， e. Otherwise，a constant Daj may not be achieved [9]. The scaling based on extinction strain rate demonstrated aboveshares remarkable similarity with a recent study by Taamallahet al. [51]， where they experimentally investigated the macro flamestructure transition from ISL stabilization to ISL & outer shear layer(OSL)/outer recirculation zone (ORZ) stabilization. Above a criticalequivalence ratio for a specific fuel composition， such flame shapetransition would occur if a flame kernel was entrained into theORZ and not extinguished. All the transition points of various op-erating conditions were collapsed through a linear relationship be-tween a characteristic flow time scale and the inverse of extinctionstrain rate， resulting in， analogously， a roughly constant Karlovitznumber in their case. Hence， extinction strain rate may play a uni-versally important role in flame shape transitions in different con-figurations of swirl combustion. 3.3. Role of local extinction The above results demonstrated that transition from the at.tached state - with convectively unstable flow - to the detachedstate - with globally unstable flow - is closely linked with ex-tinction. This indicates that reducing the density ratio betweenthe recirculating flow and inflow is more controlled by entrain-ment of cold reactants into the recirculation zone through localflame holes than by changing the thermo-chemistry and assum-ing adiabatic combustion. Hence， the degree of local extinction atthe flame base would determine the susceptibility to transition be-tween convective instability and absolute instability， thereby indicating how likely it is that a global instability mode will be formedafter a strong wavemaker is established in this region. To assess this idea， we analyzed the linkages between local ex·tinction at the flame base when the flame was attached and theprobability of being in the attached state. Note that the analy.sis was performed on conditions with intermittent attached/liftedtransitions， but with the results conditioned on instants that theflame was attached (defined as at least one flame segment at theflame base). The region in the ISL between the nozzle exit and EE Table 5Summary for the flame extinction length analysis. Test condition # DP ext Sn (×103s-1) ate(×10s-1) Sn/at.e Bmax T1D4F2 @U= 14.0 m/s 0.09 0.35 3.1 3.8 8.3 0.50 T1D1F1 @U=7.7 m/s 0.31 0.41 1.4 1.1 13 0.54 T1D2F2 @U= 16.1 m/s 0.47 0.52 2.7 1.8 15 0.51 T1D1F3 @ U=17.5 m/s 0.65 0.61 3.2 1.7 18 0.50 T1D1F2 @ U=14.9 m/s 0.93 0.66 3.2 1.4 24 0.55 Fig. 14. Flame extinction length calculation for Case T1D1F2 at U = 14.9 m/s. Fig. 15. A typical instantaneous 2-D strain rate field (unit： s-) at the stably at-tached state， extracted from Case T1D1F2 at U=14.9 m/s. The red rectangle showsthe region from which Sn is calculated. (For interpretation of the references to colorin this figure legend， the reader is referred to the web version of this article.) y=8 mm was analyzed， as this is the region expected to containthe wavemaker [23]. The roughly V-shaped flame was divided intoleft and right branches. Then， the linear length of the gaps betweenconsecutive segments of both branches， indicative of local extinc-tions， were summed to compute the total flame extinction lengthof the current snapshot (lext) as demonstrated in Fig. 13. If no flamesegment at all was detected at one branch， this branch was as-sumed to contribute 8 mm to lext. Then lext was normalized by theprobe box height (8 mm) to a dimensionless number lext； hence，o≤ lext <2. As an example， Fig. 14 shows the calculation result for CaseT1D1F2 at U=14.9 m/s using 500 consecutive OH PLIF snapshotshaving attached flames. The temporal evolution of l fluctuatessignificantly， with a mean of lw=0.66. A summary of the calcu-lated let for several test conditions belonging to the intermittentregime is shown in Table 5. Operating conditions with a higheramount of local extinction while the flame was in the attachedstate correspond to a higher probability of the flame being in thethe lifted state (i.e. higher DP)； Fig. 16 shows that the relationshipis approximately linear. That is， the flame is more susceptible to Fig. 16. 1 and Sn/at.e plotted against DP for various intermittent conditions. the development of a global hydrodynamic instability mode， evenwhile the flame is still attached. Note that DP was calculated fromthe corresponding OH* CL datasets， because they had longer du-ration (5 s) than the OH PLIF data (1.5 s)， giving better convergedstatistics. Our aim nowisto link10extwith the fluid mechanics.Figure 15 shows a typical instantaneous 2-D fluid dynamic strainrate magnitude field (norm of the principal strain values) at theattached state， extracted from Case T1D1F2 at U=14.9 m/s. Tocharacterize the fluid dynamic strain acting on the flame base，the mean strain rate in a region spanning -10 ≤x≤ 10 mm and0≤y≤5 mm was calculated at every time instant. The time aver-age of these values (Sn) then was used to link the fluid dynam-ics to extinction. Sn and the ratio Sn/at，e are shown in Table 5；Sn/at，e is plotted against DP in Fig. 16. While Sn does not corre-late with lxt or DP， Sn/at，e monotonically - and roughly linearly -increases with both. This clearly demonstrates the causal relation-ship between strain rate， local extinction， and flame lift-off [9，30]. As a final note， we consider whether the backflow ratio cor-relates with the probability of lift-off. The backflow ratio， p， isdefined at each axial location based on the mean axial velocityfield as the ratio between the absolute value of axial velocity onthe centerline and the maximum axial velocity of the reactant jet.The last column of Table 5 shows the maximum backflow ratio，βmax， for each condition considered here. While previous studies(e.g. Ref.[26]) experimentally showed that Bmax was a critical fac-tor controlling convective/absolute instability transition， the valuesobtained in our current analysis did not exhibit a clear trend withDP. It was noticed that Btypically reached its maxima at aroundy=20 mm. Therefore， one potential explanation for this discrep-ancy is that the wavemaker in Ref. [26] was identified at axial lo-cations that were more than one hydraulic diameter away from thecombustor inlet， whereas the wavemaker of the presently studiedburner was located near the nozzle exit [23]. In other words， ifBmax occurs at a location that is far from the wavemaker， it maynot be an appropriate parameter for characterizing the underlyingphysics of instability transition in this situation. In addition， Bmaxis a fluid mechanical measure that represents how strongly pertur-bations can travel upstream. However， as we showed in Table 5，simultaneous consideration of both turbulence and chemistry is 4. Conclusion A systematic study was performed to explore the links betweenflame properties， local extinction， fluid strain rate， hydrodynamicstability， and lift-off of swirl flames. The main conclusions are asfollows. 1. The correspondence between flame lift-off/reattachment andthe formation/suppression of a PVC-type global hydrodynamicinstability was confirmed. This included dynamically stablestates in which the flame intermittently lifted and reattached. 2. The velocity at steady lift-off conditions was linearly correlatedwith the extinction strain rate across the full range of fuel com-positions， equivalence ratios， and reactant temperatures tested.The data did not collapse based on other flame properties，such as the density ratio or laminar flame speed. Steady lift-offtherefore was characterized by a relatively constant Damkohlernumber as defined by Eq. (2). 3. For conditions exhibiting intermittent lift-off， the probability ofbeing in the lifted state correlated linearly with the amount oflocal extinction at the flame base and the ratio of fluid-dynamicstrain rate to extinction strain rate while the flame was at-tached. These results demonstrate that simulations must accuratelypredict flame extinction due to turbulent straining and hydrody-namic instability in order to accurately predict the stabilizationconfiguration of swirl flames. 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The coupling between fluid strain rate, local flame extinction, hydrodynamic instability, and flame lift- offwas studied in premixed swirl flames using multi-kHz repetition-rate OH ∗chemiluminescence (CL), OH planar laser induced fluorescence (PLIF), and stereoscopic particle image velocimetry (S-PIV). Over 50 different combinations of fuel composition (CH 4 /H 2 ratio), equivalence ratio, and reactant preheat temper- ature were studied, allowing systematic variation of the reactant-to-product density ratio, laminar flame speed, and Lewis number. Depending on the test conditions, the flame could either be stably attached to the nozzle, stably lifted, or intermittently transitioning between attached and lifted states. Transition between stabilization states was linked with the transition between convective instability and absolute instability at the flame base; formation of an m = 1 ( m denotes the azimuthal wavenumber) globally un- stable wave was associated with the lifted flame, which was manifested by a helical precessing vortex core (PVC). The minimum bulk velocity at which the flame was stably lifted was linearly correlated with the laminar flame extinction strain rate, while none of the other commonly reported key parameters gov- erning hydrodynamic instability was able to collapse the data alone. Hence, lift-offwas associated with a relatively constant Damköhler number based on the bulk fluid strain rate and extinction strain rate. The roles of local strain and extinction on the transition process were further elucidated by the cases with in- termittent lift-off/reattachment. The probability of the flame being in the lifted state was roughly linearly correlated with the degree of local extinction at the flame base while the flame was still in the attached state. Moreover, this probability also was linearly related to the ratio of fluid-dynamic strain rate to ex- tinction strain rate, but not the fluid-dynamic strain rate itself. These results demonstrate the importance of predicting extinction and hydrodynamic stability for predicting the attachment state of swirl flames.