Three-dimensional numerical simulations of cellular jet diffusion ames
C. E. Frouzakisa, , A. G. Tomboulidesb , P. Papasc , P. F. Fischerd , R. M. Raisa , P. A. Monkewitze , K. Boulouchosa
Aerothermochemistry and Combustion Systems Laboratory Swiss Federal Institute of Technology Zurich (ETHZ) CH-8092 Zurich, Switzerland Department of Energy Resources Management and Engineering Aristotle University of Thessaloniki, 50100 Kozani, Greece c Division of Engineering Colorado School of Mines, Golden CO 80401, USA d Mathematics and Computer Science Division Argonne National Laboratory, Argonne IL 60439, USA e Fluid Mechanics Laboratory Swiss Federal Institute of Technology Lausanne (EPFL) CH-1015 Lausanne, Switzerland
Abstract Recent experimental investigations have demonstrated that the appearance of particular cellular states in circular non-premixed jet ames depends signicantly on a number of parameters, including the initial mixture strength, reactant Lewis numbers, and proximity to the extinction limit (Damk hler number). For CO2 -diluted H2 /O2 jet o diffusion ames, these studies have shown that a variety of different cellular patterns or states can form. For given fuel and oxidizer compositions, several preferred states were found to co-exist, and the particular state realized was determined by the initial conditions. In order to elucidate the dynamics of cellular instabilities, circular nonpremixed jet ames are modeled with a combination of three-dimensional numerical simulation and linear stability analysis (LSA). In both formulations, chemistry is described by a single-step, nite-rate reaction, and different reactant Lewis numbers and molecular weights are specied. The three-dimensional numerical simulations show that different cellular ames can be obtained close to extinction and that different states co-exist for the same parameter values. Similar to the experiments, the behavior of the cell structures is sensitive to (numerical) noise. During the transient blow-off process, the ame undergoes transitions to structures with different numbers of cells, while the ame edge close to the nozzle oscillates in the streamwise direction. For conditions similar to the experiments discussed, the LSA results reveal various cellular instabilities, typically with azimuthal wavenumber m = 1 6. Consistent with previous theoretical work, the propensity for the cellular instabilities is shown to increase with decreasing reactant Lewis number and Damk hler number. o
Keywords:Cellular ame, diffusion ame instability
1. Introduction Experimental evidence dating back many decades [1] has shown that cellular instabilities exist for gaseous diffusion ames. The experiments of Chen et al. [2] clearly demonstrated the importance of relatively low Lewis and Damk hler numbers on the o occurrence of cellularity in Wolfhard-Parker burner ames. More recent experimental work on cell formation in non-premixed axisymmetric jet ames, identied the variety of spatio-temporal patterns forming near the extinction limit [3]. In addition to the importance of low reactant Lewis numbers, these experiments demonstrated the importance of the initial mixture strength [3, 4], with the propensity for cellularity increasing with decreasing initial mixture strength. The initial mixture strength is dened here as the ratio of the fuel mass fraction supplied in the fuel stream to the oxidizer mass fraction supplied in the oxidizer stream normalized by the stoichiometric ratio. For premixed ames, many studies can be found in the literature that deal with cell formation in circular burners. These patterns include uniformly rotating ring(s) of cells [5], and ratcheting or chaotic motions [6]. Theoretical studies [7] have well established that the formation of cellular structures in premixed ames arises from thermo-diffusive instabilities that occur when a weighted Lewis number is sufciently low [7]. Since three-dimensional numerical simulations have been too expensive in the past, simple phenomenological models have been developed to replicate the cellular patterns [8]. Recent theoretical work has shown that the formation of cellular structures in diffusion ames can also be attributed to thermo-diffusive instabilities [9 11]. The stability analysis performed by Cheatham and Matalon [10], for example, demonstrated that the propensity for the formation of cellularity increases with increasing heat loss and decreasing reactant Lewis numbers, Damk hler number, and inio tial mixture strength. Numerical simulations of counterow diffusion ames have also demonstrated that transitions from cellular states with narrow stripes to wider stripes occur as the Damk hler number is o reduced [12]. Cell formation in non-premixed circular jet ames involves a large number of physical effects and parameters; consequently, both experimental and numerical information will be required to elucidate the underlying physics. Such information is still incomplete. For example, the dynamics and types of cellular patterns as well as the parameter space in which these different cell patterns develop in non-premixed ames have not been fully investigated. The current study investigates cellular instabilities occurring in non-premixed circular jet ames near the extinction limit. In order to elucidate the physics behind recent experimental ndings [3, 4], three-dimensional numerical simulations have been undertaken in combination with linear stability analysis. In this paper, we start with a brief review of the

recent experimental investigations into cell formation in circular jet ames near extinction. We then present the results obtained with three-dimensional numerical simulations of the experimental system. Finally, we briey discuss the results from a linear stability analysis, elucidating the inuence of the reactant Lewis numbers and the Damk hler number on the different o azimuthal modes near extinction. 2. Experimental observations A recent publication [3] reported a systematic experimental investigation of cell formation in CO2 diluted H2 -O2 circular jet non-premixed ames. Since numerical simulations of these experiments are the focus here, a brief description of some results from this publication will be given. The EPFL jet ame facility [3, 13] consists of a free jet apparatus, oriented vertically up and mounted on a precision traverse, together with PC-based data acquisition and control systems. An intensied CCD camera with 14-bit resolution was used to record images of the streamwise integrated chemiluminescence emission from above the ame tip. The ow rates of the hydrogen, oxygen, and (diluent) carbon dioxide gases to the jet apparatus were set with fully automated ow controllers. The gaseous fuel passed through a mufer, a settling chamber with honeycomb straighteners and screens, and nally through a contoured axisymmetric contraction with an area ratio of 100:1. The diameter of the circular fuel nozzle was D = 0.75 cm. A uniform co-ow of a O2 -CO2 mixture was introduced through a porous plate of 7.5 cm diameter surrounding the fuel nozzle. The uniform fuel velocity was UF = 76 cm/s, and the co-owing oxidizer stream velocity, UO , was xed at 4 cm/s. The parameter space near the extinction limit was investigated by xing the fuel composition (H2 -CO2 mixture) and then systematically lowering the O2 concentration in the co-owing O2 -CO2 stream. The O2 concentration was lowered in decrements of less than 0.1% (by volume) until a transition to cellular ames was rst observed, and then further until the extinction limit was reached. The conditions for these near-extinction experiments covered a range of reactant Lewis numbers, based on the overall fuel-oxygen mixture at 300 K of [1.1-1.2] for oxygen and [0.250.29] for hydrogen, and initial mixture strength m from 0.08 1.34. Figure 1 shows the various types of cellular modes observed at a xed jet fuel composition (22.5% vol. H2 , except for the last image (f) observed for 21.5% H2 ) and various oxygen concentrations above the extinction limit of 23.2% O2. These images were taken from above the ame, and the false-color scale is related to the intensity of the chemiluminescence, integrated in the streamwise direction over the entire length of the ame. In the terminology of [5], the cellular states in these images are classied by the number of cells, followed by the letters R or S for rotating and stationary states, respectively. When

visualized in the dark laboratory with the naked eye, all these ames revealed distinctively cellular ame structures that varied little in the streamwise direction. The ame height for these ames was less than three jet diameters. The experiments showed that cellular ames occur near the extinction limit, and the parameter space for cellularity was found to increase with decreasing initial mixture strength. For xed initial fuel and oxygen concentrations in their respective reactant streams, several cellular states were found to co-exist, and the particular state realized was determined by the initial conditions and the path adopted in parameter space to reach the experimental condition. Mode switching could also be induced by suitable perturbations such as noise, transient perturbations of the jet ow eld, or introduction of bluff bodies at the jet exit. With all other conditions xed, the transitions between cellular ames with different number of cells were also studied for a 22.5% H2 -77.5% CO2 fuel mixture. The composition of the oxidizer stream was carefully varied between 35% and the extinction value of 23.2% O2. Within this range, hysteretic transitions between ames with one to ve cells were observed, and the range of oxidizer compositions over which the different ame structures were stable was identied. The number of cells in the preferred states observed was found to decrease with decreasing oxygen concentration (Damk hler number). o 3. Numerical simulations 3.1. Problem formulation The conservation equations of mass, momentum, species and energy in the low Mach number limit were integrated with a parallel, spectral-element based code. The spectral element method is a highorder weighted residual technique that couples the efciency of global spectral methods with the geometric exibility of nite elements methods. Locally, the mesh is structured, with the data and geometry expressed as sums of N th -order tensor product polynomials [14]. Globally, the mesh is an unstructured array of deformed hexahedral elements. Temporal discretization is based on a second-order, operatorsplitting formulation for low speed compressible reacting ows that permits large time steps. The code uses scalable domain-decompositionbased iterative solvers with efcient preconditioners. The parallel implementation is based on the standard message-passing Single Program Multiple Data (SPMD) mode, where contiguous groups of elements are distributed to processors and the computation proceeds in a loosely synchronous manner; communication is based on the MPI standard. More information about the numerical algorithms can be found in [14 17]. The code exhibits very good parallel efciency and scalability properties, sustaining high MFLOPS, on a number of distributed-memory platforms.

The computational domain was a cylinder with diameter equal to ve times the jet diameter, D=0.75 cm, and height equal to 10D. The fuel stream was f CO2 -diluted H2 (XHuel = 0.215) that enters the 2 domain with a top-hat velocity prole of UF = 76 cm/s at T =300K. The oxidizer was a O2 -CO2 mixox ture (XO2 = 0.50), with a uniform velocity prole of UO = 4 cm/s, and T =300K. To avoid numerical discontinuities, the exit velocity proles were approximated by a steep hyperbolic tangent prole (see description in the linear analysis section). For the species, ux (mixed) boundary conditions (BC) were used on the nozzle plane, and zero-Neumann BC on the rest of the domain boundaries. On the outer cylinder boundary, the slip wall BC with axial velocity equal to UO was used for the momentum, and xedtemperature BC for the energy. On the outow boundary, zero normal stress BC were used for the momentum equation, and zero-Neumann BC for the rest of the variables. Although the temperature variation of the transport properties was taken into account, the non-dimensional parameters Reynolds, Re, Prandtl, P r, and Lewis, Lei , were kept xed at Re = 517, P r = 0.52, LeH2 = 0.26, LeO2 = 1.15, LeH2 O = 1.12, and LeCO2 = 1.7. These values were calculated with the Chemkin [18] routines, using as reference quantities the properties of the overall fueloxidizer mixture. Other reference variables used in the non-dimensionalization were Tref = TF = 300 K, Uref = UF , and tref = D/UF = 9.9 ms. The chemistry was described by a single-step reaction, 2H2 + O2 H2 O, with reaction rate expression r = A T n exp(Ta /T ) [H2 ]2 [O2 ]. The reaction rate parameters were taken from [19] as n = 0.91, Ta =27.7 , and the dimensionless heat of reaction was equal to Hr =44.12. The initial non-dimensional pre-exponential factor was A = 1.33 109. Theoretical and stability analysis of diffusion ames usually employ a Damk hler number that includes the expoo nential term at the adiabatic ame temperature and the initial fuel and oxidizer mass fractions (e.g. [10]). A similar approach was adopted in the experiment, where the Damk hler number was changed by modio fying the initial composition of the oxidizer stream. In the simulations, the pre-exponential factor was directly lowered to bring the system close to the extinction limit. Two grids were employed with 1166 and 2376 elements and interpolating polynomial orders of 6 N 8 and N = 4 in each of the three spatial directions, respectively. The largest simulation had a total of about 600,000 points, corresponding to more than 5 million unknowns. All computations were performed on a 64-CPU Linux cluster. 3.2. Numerical results For the conditions described above, the initial value A = 1.resulted in a stable ame without cells that was anchored at the nozzle. The factor A was then lowered until ame extinction was observed for A = 1.7 108. Extinction in this case

corresponded to blow-off as the ame was lifted from the jet exit. In all cases considered (1.< A < 1.), the fuel was fully consumed in the numerical domain, and the ame was lifted from the jet exit. Cells at the edge of the ame close to the jet exit appeared at A = and persisted all the way down to extinction. The lifted edge of the ame was no longer at the same height at different locations along the azimuthal direction but attained a wavy structure. The high-temperature regions with the cell-like structure did not persist all the way to the outow. Overall, cellular ames with 6-, 4-, 3- and 2-cell structures were observed (Fig. 2). The 6-cell structure was obtained for A = , whereas 4-cell and fewer cell structures were obtained for A 2.5 108. It was found that, similar to the experiments, the transition to the different cellular ames is sensitive to (numerical) noise. In some cases, this noise was enough to produce an unsteady solution (periodic with very small amplitude and low frequency) and in other cases to cause a transition from one state to another. The 2cell structures were observed only during the transient extinction process of the ame at A = 1., described below. We note that the symmetry of the obtained structures is not related to the symmetry of the computational grid (which was four fold for the 1166element grid and eight fold for the 2376-element grid, i.e. the grids were divided into four or eight sections in the azimuthal direction). 3.3. Flame structure The structure of the 4-cell ame was analyzed by extracting the temperature, species, reaction rate and mixture fraction proles along one-dimensional cuts at different ame heights. The mixture fraction was f uel ox ox dened as = sYH2 YO2 + YO2 /(sYH2 + YO2 ), where s = H2 WH2 /(O2 WO2 ) = 8 is the mass stoichiometric ratio, and Wi represent species molecular weights. The stoichiometric mixture fraction for these f uel ox conditions was then st = 1/(1 + sYH2 /YO2 ) = 0.809. Despite the unequal Lewis numbers, the diffusion ame was, to a good approximation, located close to the stoichiometric mixture fraction surface [10]. At A = 1., the diffusion ame was lifted from the nozzle exit. The isocontours of the reaction rate (Fig. 2(g)) show a triple ame structure, with a weak diffusion ame tail located around the stoichiometric mixture fraction isoline plotted with the dotdashed line. The heights where the ame structure was extracted are indicated by the solid lines marked 1, 2, and 3 at z=1.0, z=3.0, and z=3.5, respectively, and the corresponding ame structures are plotted in Fig. 4(a-c). For the proles at z=1.0, signicant leakage of fuel and oxidizer through the reaction zone can be observed, and the ame has an essentially premixed character (the fuel-rich branch of the triple ame). At z=3.0 and z=3.5, the signicantly lower reaction rate prole acquired a second peak associated with the dif-

fusion ame tail, while the rst peak was from the fuel-lean premixed ame branch of the triple ame. Similar to the experiment, co-existence of two different cellular structures was observed at the same parameter values. Figures 2(a) and 2(b) show the stationary 3- and 4-cell ame computed for A = 1.8 108. The 4-cell ame was obtained rst with the 1166-element simulation for polynomial order N = 8. The result was then interpolated onto a 2376element grid with N = 4 (corresponding, overall, to a lower resolution because of the lower order of the interpolating polynomials). The integration of the conservation equations with the interpolated elds as initial condition, resulted, after the initial transient, in a ame with three cells. In other words, the numerical noise introduced by the interpolation and the lower resolution was enough to perturb the system to the stationary 3-cell state. The resulting elds were then interpolated back to the high-resolution grid; the 3-cell state remained stable, obviously showing that it is also a stable ame structure for A = 1.8 108. The co-existence of two stable steady states at the same parameter values shows that the hysteretic transition between different cellular structures observed experimentally is also reproduced by the simulations. 3.4. Flame extinction Starting with the 4-cell state for A = 1.as initial condition, the pre-exponential factor was reduced to A = 1.7 108. The ame went through a sequence of transitions with different number of cells (the 4-, 3-, and 2-cell ames observed are shown in Fig. 3), while the edge of the ame close to the nozzle oscillated with a growing amplitude. Eventually, the ame blew off. The four-cell ames persisted for a long time from the start of the calculation (about 200 non-dimensional units). During this period, two of the four cells located opposite from each other had higher temperature, reaction rate and size than the other two. The pair of cells burning stronger changed from upper-left/lower-right (Fig. 3(a)) to upper-right/lower-left (Fig. 3(b)). The maximum temperature and the ame height (determined from the location where the temperature was twice that of the inlet streams) during the extinction process are plotted in Fig. 5; both variables oscillated as the ame blew off. 3.5. Stability analysis To elucidate the stability characteristics for axisymmetric ames, a viscous linear stability analysis was employed using a nite rate, one-step reaction model. A brief description will be given below. Details about the axisymmetric jet ame analysis can be found in [20, 21]. A similar methodology was also followed in a recent publication considering the instabilities of planar diffusion ames [11]. The undisturbed basic state considered is a reacting axisymmetric jet surrounded by a co-owing ox-

idizer stream a diffusion ame formed between two parallel streams of hydrogen-water and oxygen. Unless otherwise indicated, the parameters chosen to model this ame are specied in the Problem formulation section. The mean proles were taken to be frozen in the streamwise direction (parallel ow assumption). The mean velocity prole was represented with a hyperbolic tangent prole [22]: U = 0.5{1 + tanh[0.25(R/)(R/r r/R]}, where R is the jet radius and the momentum thickness. The mean temperature and mean mass fractions were determined using a methodology discussed in [11, 21]. The linearized continuity, momentum, energy, species, and state equations, including reaction and diffusion terms, were obtained with the following assumptions: body forces (e.g. gravity) and bulk viscosity were neglected; the ow was assumed to be low subsonic; the multi-component gas mixture properties (thermal conductivity, specic heat at constant pressure, and viscosity) were assumed equal for all species (unity Prandtl numbers); the mass diffusion coefcients (dened by Ficks law) were assumed equal to the binary mass diffusivity of all species pairs. Finally, the terms in the energy equation due to viscous stresses, radiative heat transfer, interdiffusion, and the Dufour effect were neglected. As in the formulation for the numerical simulations, the nondimensionalization of the governing equations was based on the reference quantities of the fuel stream. The viscosity , thermal conductivity , and densityweighted mass diffusivity (D) were all assumed to follow Chapmans law ( = = Di = T in nondimensional form). Different Lewis numbers Lei = 0 /cp,0 (Di ) were specied for the reactants, with the subscript 0 denoting properties of the fuel stream at r = 0. Once the basic state was computed, temporal stability computations were performed. The perturbations were in the form of normal modes q (r, x, , t) = q (r) exp i(x + m t), where is the complex frequency, m the azimuthal wave number, and the complex wave number. The resulting eigenvalue problem was solved with a shooting method, starting the numerical integration from both sides of the mixing layer with asymptotic solutions valid for vanishing radial gradients of the base ow. Although not all parameters of the threedimensional simulations were matched, most of the parameters used in the stability analysis correspond closely to the simulations. Similar to the numerical simulations, R/ = 20 was chosen which has been shown to correspond to experimental conditions [20]. The far-eld temperatures of both reactant streams were taken to be equal. The initial mixture strength m and the Reynolds number were xed at 0.5 and 500, respectively. Finally, the niterate hydrogen-oxygen reaction was characterized by a non-dimensional activation energy Ta = 30, normalized by the fuel free stream temperature. The molecular weights for hydrogen and product were taken to be 2 and 18, respectively, and the quiescent oxidizer

stream was chosen to be pure oxygen. Also, the appropriate heat release parameter was chosen to obtain a maximum (normalized with the fuel centerline temperature) temperature Tmax = 6.0 at the ame-sheet limit for unity Lewis numbers (cf. Ref. [11]). Temporal stability calculations were performed for this representative H2 -O2 ame over a range in Damk hler number, Da, close to its extinction limit, o DaE. The fuel and oxidizer Lewis numbers were xed at LeH2 = 0.3 and LeO2 = 1.0, respectively. Figure 6 shows the maximum temporal growth rate i,max as a function of Da for the azimuthal modes m = 1 6. The gure reveals several interesting features. First, the different azimuthal modes become unstable over different and overlapping intervals of the Damk hler number just prior to the o extinction limit at DaE = 1.098 103. Second, the respective maximum growth rates of each azimuthal mode m = are relatively close, and progressively increase with decreasing Da. The Da value where a particular azimuthal mode rst becomes unstable is designated as Da (m), and corresponds to Da (m) = 2.49, 2.45, 2.42, 2.10, 1.90, and 1.for the m = 1, 2, 3, 4, 5, and 6 modes, respectively. A plot of i,max as a function of Da Da (m) is shown in the upper right-hand corner of Fig. 6, where the different Da (m) values for the azimuthal modes are specied above. Figure 6 illustrates that the dominant mode changes with Damk hler number, and the m = 1 mode is dominant o just prior to the extinction condition. 4. Conclusions With single-step chemistry and constant but unequal reactant Lewis numbers, the three-dimensional simulation of a CO2 -diluted H2 jet diffusion ame showed cell ame structures similar to the ones observed experimentally. Flames with different numbers of cells were obtained close to extinction. The transient extinction process itself showed transitions to cellular states containing different number of cells. These transient ame structures oscillated in various ways, and the entire ame eventually blew off. Similar to the experiments, the cellular states were found to be sensitive to noise, which was enough to lead from a 4- to a 3-cell ame structure for the same parameter values. This coexistence of different cellular ames was also observed experimentally. The cellular ames were found to be associated with a large leakage of reactants through the reaction zone, and exhibit a triple ame structure at the ame base near the jet exit. Given the simplications of a linear stability analysis, comparisons between experiments, as well as direct numerical simulations, can only be qualitative; however, linear stability theory has provided many insights into the physics behind cell formation. Previous research [9, 10] on thermo-diffusive instabilities in non-premixed ames has shown that both reactant Lewis numbers, LeF and LeO , are important parame-

ters. At Damk hler numbers near the extinction limit, o cellular instabilities for axisymmetric jet ames have been shown to be dominant at relatively low Lewis numbers, while axisymmetric pulsations can dominate at relatively high Lewis numbers [21]. For a representative H2 -O2 jet diffusion ame, the linear stability results reported here show that multiple azimuthal modes, which become destabilized near the extinction limit, have comparable growth rates for a given Damk hler number. The overlapping intervals o in Damk hler number where these unstable modes o appear is consistent with the co-existence of multiple states observed both in the experiments and the numerical simulations near the extinction limit. For the conditions of this study, the linear stability calculations [21] also indicate that the various azimuthal modes, which are thermo-diffusive instabilities, are absolute instabilities; however, further work will be required to elucidate their relevance to actual ame dynamics. Currently, numerical work is underway to identify the range of parameter values over which the different ame structures are stable, and study the transition between these different structures. Acknowledgments The nancial support from the Swiss Ofce of Energy (BfE) for CEF and KB, the Swiss National Science Foundation (grants NF20-61887.00 and NF57100.99) for PP and RMR, a SNSF grant (number PIOI2-103091) for AGT, and from the U.S. Department of Energy (Contract W-31-109-Eng-38) for PFF is gratefully acknowledged. The authors are also grateful to Prof. M. Matalon for many fruitful discussions. References
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[14] M.O. Deville, P.F. Fischer, E.H. Mund, High-Order Methods for Incompressible Fluid Flow. Cambridge University Press, 2002. [15] P.F. Fischer, H.M. Tufo, in Parallel Computational Fluid Dynamics: Towards Teraops, Optimization and Novel Formulations. D. Keyes, A. Ecer, N. Satofuka, P. Fox, and J. Periaux (eds.) North-Holland, 2000, p. 17-26. [16] A.G. Tomboulides, J. Lee, S. A. Orszag, J. Sci. Comp., 12(2) (1997) 139167. [17] A.G. Tomboulides, and S.A Orszag, J. Comp. Phys., 146(2), 691706, (1998). [18] R.J. Kee, G. Dixon-Lewis, J. Warnatz, M.E. Coltrin, J.A. Miller, A Fortran Computer Code for Evaluation of Gas-Phase Multicomponent Transport Properties, Report No. SAND86-8246, Sandia National Laboratories, 1986. [19] A. Beccantini, H. Paill re, R. Morel, F. Dabbene, 17th e International Colloquium on the Dynamics of Explosions and Reactive Systems, July 25-30, 1999, Heidelberg, Germany. [20] M. F ri, P. Papas, R.M. Rais, P.A. Monkewitz, Proc. u Combust. Inst. 29 (2002) 16531661. [21] R.M. Rais. Investigations of diffusion ame instabilities, PhD thesis no. 2700, Swiss Federal Institute of Technology Lausanne (EPFL), (2002). [22] A. Michalke, Prog. Aerospace Sci. 21:159-199 (1984).
1.4 1.2 flame height [] 1 Tmax flame height

5.2 5.1 Tmax []

5.0 4.9 4.4.7 500

0.8 0.6 0.4

Fig. 5: Maximum ame temperature and ame height during the transient extinction process
2 m=6 m=5 m=4 m=3 m=2 m=1 1.1

0 -1.5

[Da-Da*(m)] x 1000

(Da) x 1000

Fig. 6: Maximum temporal growth rate i,max as a function of the Damk hler number Da for the different azimuthal o wave numbers m = 1 6. The results for m = 0 are not shown.

(a) 1R-cell

(b) 2R-cell

(c) 3R-cell

(d) 4S-cell

(e) 5S-cell

(f) 6S-cell
Fig. 1: Streamwise integrated chemiluminescence images taken from the downstream jet axis of a 22.5% H2 (78.5% CO2 ) jet ame burning in (a) 24.6% O2 (75.4% CO2 ) co-ow; (b) 26.0% O2 co-ow; (c) 27.5% O2 co-ow; (d) 31.0% O2 co-ow, (e) 40.0% O2 co-ow, and (f) 21.5% H2 (79.5% CO2 ) jet ame burning in 70.0% O2 co-ow. R designates rotating and S stationary cell patterns. Fuel centerline and oxidizer velocities are UF = 76 and UO = 4 cm/s, respectively. [Figs. (a)-(e) taken with permission from Ref. [3]]

0 -1 -2 -2

0 -2 -2 -2

0 -1 -2 -2 -1 2

0 -1 -2 -2 -1 0X 1 2
(d) (e) (f) Fig. 2: Isocontours of temperature of (a) the 3- (A = 1., at z = D), (b) the 4- (A = 1., at z = 0.8D), and (c) the 6-cell ame (A = 2., at z = 0.5D); (d)-(f) corresponding fuel mass fraction; (g) heat release rate for the 4-cell ame. Scales are from blue (low) to red (high): 1 T 5, 104 YF 1., and 0 reaction rate 0.12.

Fig. 3: Temperature isocontours showing the different cell structures observed during ame blow off for A = 1.(from left to right: t=100, 165, 340, 445, 480 non-dimensional time units, at heights 0.9, 0.95, 1.3, 1.5, and 2.0 nozzle diameters, respectively). Scales are from blue (low) to red (high): 1 T 5.

1.0 0.8

T/5 8*YH YO
0.6 0.4 0.2 0.0 0.0 0.4 0.8 1.2 1.6

0.6 0.4 0.2

YH O 50*r

0.0 0.0

Fig. 4: Flame structure of the 4-cell ame at (a) z=1.0, (b) z=5.0, and (c) z=3.5 (A = 1.).