jUAA 99-2781 -. Stability-Limit Predictions of ‘-Methane Jet Diffusion Flames .a

F. Takahashi University of Dayton Dayton, OH. .

V.R:Katta . ‘. Innovative Scientific Solutions, Inc. 2766 Indian Ripple Road ‘, Dayton, OH ‘. 1 I

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_- AMA-99-2781

STABILITY-LIMIT PREDICTIONS O F METHANE ,ilET DIFFUSION FLAMES . .

kumiaki Takahashi’ Univers ity of Dayton Research Institute

300 CollegePark : Dayton, Oh io 45469

,.Viswanath R. Kattat Innovative Scientific Solutions, Inc.

2766 Indian Ripple Road Dayton, Oh io, 45440

ABSTRACT An attempt is made to,predict the lifting limit of an

axisymmetric laminar methane jet .diffusion .&me. Computations for solv ing the time-dependent full Navier- Stokes equations with buoyancy were.performed using ,an implic it, third-order accurate numerical scheme- and a semi-detailed C,-chemistry model. The calculated standoff distance of the flame base prior to lifting was comparable to that experimentally observed. As the mean co-flow air velocity was increased at a fixed fuel jet’ velocity toward a lifting limit, the reaction hwnel (peak reactiv ity spot) in the flame base broadened and shifted to a new stabilizing point downstream, where a higher reactiv ity could be obtained to sustain combustion against a higher incoming flow velocity. The reactiv ity augmentation is due to a “blowing effect,” which caused enhanced convective and diffusive fluxes of oxygen into the reaction kernel, :while maintaining the reaction kernel temperature (-1550 K) and equivalence ratio (-0.5) at nearly constant levels. A novel hypothesis for the flame stabilizing mechanism is proposed: that a flame lifts or .blows off if the total oxygen flux feeding into the reaction kernel exceeds -a limit that the reaction kernel can consume by oxidation reactions.

: INTRODtkTION The stability, of diffnsion flames. has long been a

investigations of the flame-base structure and behavior, including experiments [3, 5, 81 and theories [14-161, generally suffered from the lack,of detailed information, particularly on radicals. Diagnostic techniques available to measure var ious species in a small flame-stabilizing region are limited, and theories generally ignore radical species.. As a’ result of recent advances in computational capabilities and chemistry models, a numerical approach- seems most .promising. to obtain comprehensive information on the flame structure.

In .previous papers [ 17, 181, the chemical k inetic structure ‘of the -flame stabilizing region of methane diffusion flames and the role ofchemistry models were reported. In this paper, the effect of co-flow air velocity on a near-lifting-limit flame was investigated to reveal the flame stabilizing mechanism. 3 ,

NUMERICAL METHODS The numerical code (UNICORN) used in this study

was developed by Katta et al. [19] and validated against measurements and flow v isualization of var ious diffusion and premixed flame phenomena; i.e., unsteady characteristics, extinction, and ignition [20,-2’11. The code has also been used in numerical experiments on vortex- flame interactions and attachment mechanisms of methane jet diffusion flames [17, 18, 22, 23J.. T ime- dependent governing equations, expressed in cy lindric’al coordinates, consist of mass continuity, axial and radial full Navier-Stokes momentum conservation, energy conservation, and species conservation equations with the ideal-gas equation of state. A body-force term caused by the gravitational field is included in the axial momentum equation. The momentum equations are integrated using an implic it Q U ICKEST numerical scheme [ 191, which is third-order accurate in both space and time and has a very low numerical-diffusion error. The finite-difference form of the species and enthalpy is obtained using the. hybrid scheme with upwind and central differencing. The coefficients of v iscos ity, thermal conductiv ity, and

fundamental and practical research subject in combustion [l- 131. Local flame-flow phenomena, including tmnsport processes and chemical reactions. around the flame base, control the flame stabilizing mechanism. Therefore,’ to gain in-depth understanding of the subject, detailed flame- base structure resulting from the transport and reaction processes must be revealed: Unfo,rtunately; previous

* Research Engineer, Research Institute, Senior Member AIAA t Senior Research Engineer, Member AIAA Copyright 61999 by the authors. Published by the American Institute of Aeronautics and Astronautics, Inc. w ith permission.

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diffision are estimated using molecular dynamics and mixture rules [24]. The enthalpy of each species is calculated from polynomial curve-fits using the CHEMKIN libraries.

The semi-detailed chemistry model [25] for 24 species and 81 elementary steps is used. The Arrhenius psuTlmeters for the reaction CH, + H + CH, are replaced with those by Wamatz [26]. Otherwise, the extinction limit of counter-flow diffusion flames was predicted at a significantly lower strain rate [27] compared to that determined experimentally by Sung et al. [28], and the jet diffusion flames under consideration prematurely lifted off under conditions below the stability limit obtained experimentally [ 121.

The computational domain of 150 x 60 mm in the axial (x) x radial (r) directions is represented by a mesh system of up to 371 x 101 with clustered grid lines near the jet exit and a minimum spacing of 0.05 mm. The inner diameter (d= 9.5 mm) and lip thickness (0.25 mm) of the fuel tube are close to those used in the previous experiments [ 121. The fuel tube exit plane is placed 10 mm from the inflow boundary. The fully developed pipe flow in the fuel tube and boundary layer velocity profiles outside the burner tube are used. Several cases with various mean co-flow air velocities (UJ at a constant mean jet velocity (Y) are simulated to approach the lifting limit [12]. The initial and boundary conditions for the axial (U) and radial (v) velocities and species and energy at different flow boundaries are the same as the previous work [17]. The outer boundaries of the computational domain are shifted sufficiently far enough to minimize the propagation of disturbances into the region of interest. No-slip boundary conditions are enforced along the burner walls. An extrapolation procedure with weighted zero- and first-order terms is used to estimate the flow variables on the outflow boundary.

RJBULTS AND DISCUSSION Figure 1 shows the two-color particle image

velocimetry (PlV) photographs of the stabilizing region of near-lifting and lifted methane jet diffusion flames. The burner system and the PIV technique used is described elsewhere [ 12, 171. Submicron particles were illuminated by a sheet of green and red pulsed (10 ns) lasers with a known time delay. The high number-density cold airflow, a low number-density hot zone around the flame, and the jet-external dividing streamline were visualized. A time- exposure (1130 s) image of the blue flame zone was also recorded in the photographs. As the lifting condition approached (Figs. la to lb), the flame base shifted gradually away from the burner rim a few millimeters. The outer cold air was entrained into the fuel jet through the dark space between the flame base and the rim. Thus, the flame base (Fig. lb) was thermally disconnected from the burner wall, and the effect of heat losses to the burner

wall vanished before lifting. After lifbng, the flame base was stabilized a few jet diameters downstream. No sign of wings of the triple flame structure [ 11, 14, 16,291 was observed at the base of methane diffusion flames as reported by Chung [ 111.

Figure 2 shows the experimental result [12] of a stability-limit curve and the lift-off height (/zJ at the lifting limit. The critical mean jet velocity at the stability limit decreased monotonously as the mean co-flow air velocity increased, except for low air velocity conditions (U, < 0.1 m/s) under which the outer air tube (26.9 mm i.d.) blocked free air entrainment. The minimum lift-off height was in the range of 0.2 < iJ, < 0.4 m/s.

Figure 3 shows the computational results of the structure of the flame base under a near-lifting condition (U, = 0.8 m/s and vj = 1.7 m/s). Figure 3a shows the calculated velocity vectors (v’ ), isotherms (T), and oxygen mole fiaction (X0*) contours. The flame base resided farther downstream (-10 mm) from the jet exit, compared to the case previously reported (-4 mm) for U, = 0.72 rnk at the same vj using the same C,-chemistry model [ 181. The flame base is anchored in a relatively low-velocity wake region formed by the boundary layers along the burner walls. The velocity vectors and the oxygen mole fraction contours show air penetration onto the fuel side of the flame. As a result, a relatively high oxygen concentration zone surrounds the flame base.

Figure 3b shows a close-up view of the flame stabilizing region, including the velocity vectors, isotherms, and heat-release rate (4 ) contours. The heat- release rate contours show that the reaction kernel (highest reactivity spot) at the flame base was farther broadened outwardly, compared to the lower air velocity case previously studied [ 181. The velocity vectors show the lateral expansion of stream tubes as well as the longitudinal acceleration as the flow approached the hot zone around the flame base due to thermal expansion of gases and the pressure field deformation.

Figure 3c shows the calculated total molar flux vectors of methane (McH~ ) and molecular oxygen

( Go2 ), including both difhrsion and convection terms, contours of the equivalence ratio (4, and the oxygen consumption rate (-wo2). The equivalence ratio was determined from the fuel and oxygen molar fluxes, thus including the dynamic effects of both convection and diffusion. The equivalence ratio based on the fluxes differed from that based on the mole fractions, particularly in the region near the reaction kernel, which is a strong sink of the reactants.

Although the partial premixing of the fuel and oxygen in the dark space progressed further compared to the lower air velocity case [18], the thickness of the mixing layer within the flammability limits (0.5 < I+ ~1.7)

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was -0.8 mm, just below the reaction kernel, which was still less than half the minimum quenching distance ,of 2.2 n-m [ 11. Thus, the mixiig layer was too narrow- foi: aii ordinary premixed flame to propagate through at the laminar burning velocity. More importantly, the reaction kernel was more under fuel-lean conditions and the peak reactivity was obtained at Q x 0.5, unlike the ordinary premixed flames that have the maximum burning velocity at ‘4 = 1. Therefore, the reaction kernel structure is different from ,the ordinary premixed flame- or the fuel- lean branch of the triple-flame structure [l 1,14, 16,291.

Figure 3d shows the calculated total molar flux vectors of atomic hydrogen (6~ ), the mole fraction of molecular oxygen, and the rate of water vapor producnon (w@). Hydrogen atoms diffused dowmvard in every direction into high oxygen concentration region around the reaction kernel,. inducing the most important chain branching reaction H + OZ + OH +- 0. Other radical species (OH, 0, and CH,, etc.) also back-diffused against the convective oxidizing flow, reacted with each other and with oxygen, broadened the reaction zone, and,increased the global reaction rates even at relatively low temperatures (~1600 K).

Figure 4 shows the effects of the mean air velocity on the reaction kernel coordinates (xk, J+,) at the heat-release rate peak and axial and radial velocity components (Ui, VJ, including the previous results (C-chemistry) [17] as well as the current results (C,-chemistry). As the mean air velocity was increased, the axial coordinate (standoff distance) of the reaction kernel increased. dramatically, while the radial distance maintained nearly con&t (Fig. 4a). The C&hem&y. model resulted “in a -longer standoff ,distance as previously reported [IS]. The computational results matched ,very well with the experimental observation of the (visible) flame base location and the lifting limit data (V, = 0.76 m/s and vj = 1.7 m/s [ 121, see Fig. 1). The axial, velocity component of the incoming flow into the reaction kernel also increased rapidly, while the magnitude of the radial velocity component approached zero (vertical flow direction) (Fig. 4b). The current G-chemistry model results almost perfectly matched the previous C,-chemistry results.

In the previous paper [ 171, heuristic correlations valid for both jet- and flat-plate diffusion flames were obtained between the peak heat-release rate; or oxygen consumption rate, and the total velocity at the reaction kernel. The reaction kernel correlations demonstrated that the baseline mechanism responsible for flame stabilization and attachment was identical for both types of diffusion flames. Figure 5 shows the reaction kernel correlation

~plot, temperature and equivalence ratio, including the points for various U, at r/j = 1.7 m/S ,only. Both peak

‘heat-release rate and the oxygen consumption rate increased almost linearly with the magnitude of the

velocity at each peak location in the reaction kernel (Fig: 5a). :Thus, the reaction kernel shifted to a new stabilizing point J&ns,tream, where a higher reactivity could be obtained and withstood a higher incoming flow velocity. The reactivity augmentation was due to increased diffusive and zonvective oxygen fluxes into the reaction kernel caused by, ‘blowing.” -As the incoming velocity was increased, the slopes (4 /Iv’ ] or -wo2/] v’ 1) of the curves became somewhat smaller, while the reaction kernel temperatures and equivalence ratios at both 4 ,and - wo2 peaks remained nearly constit in the ranges of 1500- 1600 K and 0.5-0.6, respectively (Fig. 5b)., Thus, the incoming velocity tended to increase faster than the reactivity increase toward lifting.

6OiCLUSIONS Computations of lam&r methane jet diffusion

flames. revealed the flame structure and behavior of the reaction -kernel (highest reactivity [ 4, -w,+ and ~~~1 spot) in response to &I increase in the co-flow air velocity. The simulated reaction kernel shifted away from the’jet

exit, matching qualitative and quantitative experirnerital observations under conditions toward the, lifting limit. At a downstream location,. the reaction kernel sustained combustion under a higher incoming flow velocity as a result bf a higher reactivity, while the reaction kernel temperature (1500- 1600 K) and equivalence ratio (0.5- 0.6) remained ‘nearly constant during the shifting. The correlations between the heat-release rate or oxygen consumption rate vs. the total velocity at the reaction kernel indicated that the increasing rate of the incoming flow velocity exceeded that of the reactivity. This new finding leads to ‘a hypothesis that lifiing’ occurs if the, fluxes of ‘reactants exceed a limit beyond which the reaction kernel cannot consume them. Consequently, the reaction kernel can no longer find a new ‘stationary stabilizirig location downstream, and the trailing flame drifts away downstream, eventually. leading to lift or blow-off.

ACKNOWLED’GMENT .This work was supported by the U. S. Air .Force

-Research Laboratory, Propulsion Directorate, Propulsion Sciences and Advanced Concept Division, Wright- Patterson Air Force Base, Ohio, under Contract No. F336!5-97-C-2719 (Technical Monitor: C. W. Frayne).

REFERENCES 1. Lewis, B., and von Elbe, G., Combustion, Flames,

and Explosions of Gases, 2nd ed., Academic Press, New York, 1961.

2. Vranos, A., Taback, E. E., and Shipman, C. W., “An Experimental Study of the Stability of Hydrogen-Air Diffision Flames,” Cornbust. Flame 12: 253 (1968).

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3.

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Robson, K., and Wilson, M. J. G., “The Stability of Larninar Diffusion Flames of Methane,” Combust. Flame 13: 626 (1969). Takeno, T., and Kotani, Y., “An Experimental Study on the Stability of Jet Diffusion Flames,” Acta Astronaut. 2: 999 (1975). Kawamura, T., Asato, K., and Mazaki, T., “Structure Analysis of the Stabilizing Region of Plane, Laminar Fuel-jet Flames,” Combust. Sci. Technol. 22: 211 (1980). Takahashi, F., Mizomoto, M., Ikai, S., Futaki, N., “Lifting Mechanism of Free Jet Diffusion Flames,” Twentieth Symposium (International) on Combustion, The Combustion Institute, 1985, pp. 295-302. Eickoff, H., Lenze, B., and Leuckel, W., “Experimental Investigation on the Stabilization Mechanism of Jet Diffusion Flames,” Twentieth Symposium (international) on Combustion, The Combustion Institute, 1985, pp. 311-318. Takahashi, F., Mizomoto, M., and Ikai, S., “Structure of the Stabilizing Region of a Laminar Jet Diffusion Flame,“J. Heat Transfer 110: 182 (1988). Gollahalli, S. R., Savas, 6., and Huang, R. F., and Rodriquez Azara, J. L., “Structure of Attached and Lifted Gas Jet Flames, in Hysteresis Region,” Twenty-First Symposium (International) on Combustion, The Combustion Institute, 1988, pp. 1463-1471. Coats, C. M., and Zhao, H., “Transition and Stability of Turbulent Jet Diffusion Flames,” Twenty-Second Symposium (International) on Combustion, The Combustion Institute, 1989, pp. 685-692. Chung, S. H. and Lee, B. J., “On the Characteristics of Laminar Lifted Flames in a ,Nonpremixed Jet,” Cornbust. Flame 86: 62, (1991). Takahashi, F., and Schmoll, W. J., “Lifting Criteria of Jet Diffusion Flames,” Twenty-third Symposium (International) on ‘ Combustion, The Combustion Institute, 1991, pp. 677-683. Takahashi, F., Durbin, M. D., and Vangsness, M. D., “Stabilization of Hydrogen Jet Diffusion Flames With or Without Swirl,” Transport Phenomena in Combustion (S. H. Chan, ed.), Vol. 1, Taylor & Francis, Washington, D. C., 1996, pp. 593-604. Veynante, D., Vervisch, L., Poinsot, T., Lifian, A., and Ruetsch, G., ‘Triple Flame Structure and Diffusion Flame Stabilization,” Proceedings of the Summer Program, Center for Turbulence Research, Stanford University, Palo Alto, California, 1994, pp. 55-73. Buckmaster, J. and Weber, R., “Edge-flame Holding,” Twenty-Sixth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1996, pp. 1143-l 149.

16. Wichman, I. S. and Ramadan, B., “Theory of Attached and Lifted Diffnsion Flames,” Physics of Fluids 10: 3145-3154 (1998).

17. Takahashi, F. and Katta, V. R., “Attachment Mechanisms of Diffusion Flames,” Twenty-Seventh Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1998, pp. 675-684.

18. Takahashi, F. and Katta, V. R., “A Role of Chemical Kinetics in the Simulation of the Reaction Kernel of Methane Jet Diffusion Flames,” Proc. 5th ASME/JSME Joint Thermal Engineering Conference, San Diego, Paper No. AJTE99-6190, 1999.

19. Katta, V. R., Goss, L. P., and Roquemore, W. M., ‘Numerical Investigations of Transitional H& Jet Diffision Flames,” AI&l J. 32: 84 (1994).

20. Katta, V. R and Roquemore, W. M., “Simulation of Dynamic Methane Jet Diffision Flames Using Finite Rate Chemistry Models,” AL4A J. 36: 2044 (1996).

21. Roquemore, W. M., and Katta, V. R., “Role of Flow Visualization in the Development of UNICORN,” Proceedings of VU-SPIE98, Yokohama, Japan, PaperNo. KL310, 1998.

22. Takahashi, F. and Katta, V. R., “Numerical Experiments on the Vortex-flame Interactions in Jet Diffusion Flames,” J. Propulsion Power 11: 170 (1995).

23. Takahashi, F. and Katta, V. R., “Unsteady Extinction Mechanisms of Diffusion Flames,” Twenty-Sixth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1996, pp. 115 l- 1160.

24. Hirschfelder, J. O., Curtis, C. F., and Bird, R. B., Z%e Molecular Theory of Gases and Liquids, Wiley, New York, 1954.

25. Peters, N., “Flame Calculations With Reduced Mechanisms-An Outline,” Reduced Kinetic Mechanisms for Applications in Combustion Systems (N. Peters and B. Rogg, Eds.), Springer-Verlag, Berlin, 1993, pp. 3-14.

26. Warnatz, J., “Rate Coefficients in the C/w0 System,” Combustion Chemistry (W. C. Gardiner, Ed.), Springer-Verlag, New York, 1984, p. 197-360..

27. Katta, V. R. and Roquemore, W. M., “Extinction in Methane-Air Counterflow Diffusion Flame-a Direct Numerical Study,” Central States/The Combustion Institute Meeting, St. Louis, Paper No. 80, 1996, pp. 449-454.

28. Sung, C. J., Liu, J. B., and Law, C. K., ,“Structnral . Response of Counterflow Diffusion Flames to Strain

Rate Variations,” Cornbust.. Flame 102: 48 1 (1995). 29. Plessing, T., Terhoeven, P., Peters, N., and Mansour,

M. S., “An Experimental and Numerical Study on a Laminar Triple Flame,” Combust. Flame 115: 335 (1998).

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