Heat transfer consequences of condensation during premixed flame quenching

Brief Communication Heat Transfer Consequences of Condensation durl,ag Premixed Flame Quenching O. A. EZEKOYE Department of Mechanical Engineering, University of Texas at Austin, Austin, TX 78712

INTRODUCTION Although unsteady flame quenching is a classical combustion problem, several key features of the process have yet to be fully characterized. As an example, for an unsteadily propagating flame stagnating on a cold wail, there has not been conclusive experimental and theoretical agreement on the effects of varying the thermal boundary conditions on the flame extinction process. Characterization of the flame quenching problem is limited by the length scales over which it occurs. The flame quenching distance for head-on (stagnation) flame quenching at atmospheric pressures is on the order of hundreds of micrometers, and thus few diagnostics can be used to determine the extent to which the flame propagates towards a specified temperature wail. The most meaningful diagnostics to date for such processes have been heat transfer measurements of the wall heat flux as the flame quenches, These diagnostics although second hand, provide information about the flame trajectory during a given quenching process. Single surface laminar quenching flame experiments have been made at elevated wall temperatures by Ezekoye et al. [1] and Connelly et al. [2]. In those studies, the primary diagnostic method was a heat transfer measurement from a laminar quenching flame to a heated wall. Several computational investigations have considered the effects of thermal boundary conditions on the flame quenching process [3-5]. P o p p e t al. [5] simulate the head-on quenching process using detailed chemistry and find that there are differences between results from one step mechanisms and those of detailed mechanisms in evaluating the wall heat flux at temperatures above room 0010-2180/98/$19.00 PII S0010-2180(97)00021-7

temperature. The trends for both detailed chemistry and simplified chemistry simulations are similar and both show deviations from experimental results. Experimentally, a kink exists in the peak heat flux data at approximately 360 K. Computational results have not shown this bend in the peak heat flux. Several l~ossible directions have been pursued to explain the relatively lower temperature quenching processes (300-400 K) from higher temperature results ( > 400 K). While catalytic surR,'e effects have been investigated [5, 6], the effects of water condensation as it affects both gas phase and surface chemistry as well as the wall heat flux measurement are not discussed. In all premixed flame quenching processes a hot gas mixture containing a significant mass fraction of water vapor comes into contact with a relatively colder wall. For isothermal conditions the mass fraction of water vapor at the cold wall is constrained by the saturation vapor pressure at that wall temperature. This implies that subsequent mass transfer is associated with vapor condensation. The flux of some individual species across the reaction zone is quite large given that the burned gas region is generally on the order of 100 ttm from the wall. It is expected then that this gradient will modify the reaction rate as well as the wall he~ ~ flux. Since the wall heat flux has been used in several studies as a diagnostic for the gas side processes, it is important that effects such as condensation be explicitly included into gas side modeling of flame quenching. In general, use of detailed chemistry simulations has not significantly altered the quantitative predictions and qualitative descriptions of flame quenching that have long existed. It appears that the fundamental characterization of this process COMBUSTION AND FLAME 112:266-269(1998)

© 1998by The CombustionInstitute Publishedby ElsevierScienceInc.

PREMIXED FLAME Q U E N C H I N G will be made not only from detailed chemistry studies, but also from well focused reduced chemistry investigations of the process. In this study, the dynamics of a one dimensional flame quenching process are analyzed using a two step chemical mechanism, and the effects of condensation on wall heat flux and the reaction rate are noted.

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THEORY Head-on or planar flame quenching may be modeled by solving the one dimensional conservation equations for ma~.~, species, and energy. Standard equations are utilized and a discussion of the solution procedure can be found in Ezekoye et al. [1]. A two-step global reaction mechanism for p r o p a n e / a i r flames from Westbrook and Dryer [7] is employed in this study and is given by

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CO + }02 ~ CO2. The rate parameters are given in Ref. [7]. The wall is considered to be isothermal, impermeable and noncatalytic. At the initial time a one dimensional flame is ignited several flame lengths from the wall. The flame propagates into an initially quiescent unburned gas mixture. During the quenching process water vapor is allowed to condense at the appropriate wall water vapor partial pressure. RESULTS AND DISCUSSION The temperature profile associated with the quenching process is shown in Fig. 1. For a sufficiently long time before the flame interacts with the wall the characteristic steady flame temperature profile exists. At the time that the flame begins to "feel" the presence of the wall the flame temperature profile steepens in response to the fixed wall boundary condition. The fixed cold wall subsequently modifies the reaction process and quenches the flame. The temperature profile, no longer maintained by flame exothcrmicity, recedes by simple diffusion. For noncondensing gas species the boundary condition at the impermeable

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Fig. I. Spatial profiles of temperature, CO, and H 2 0 prior to and after quenching. Time before quenching (peak heat flux) is considered negative while time after quenching is specified to be positive. The condition shown is for a wall temperature of 300 K and a stoichiometric propane-air flame.

wall is a zero gradient condition. As an example, consider the CO, profile at the time o f flame quenching in Fig. 1. The CO, mass fraction profile exhibits a zero gradient condition at the wall and continuously increases towards its value within the burned gas. For a quenching condition where the wall temperature is fixed below the dew point temperature for the water vapor in the burned gas, the interaction between the water vapor and the wall is somewhat more complicated than that which is specified to occur for the other pro-

268 files (cf. Fig. 1). The water vapor initially maintains a zero flux condition at the wall while the partial pressure of vapor at the wall is below the saturation partial pressure. At the time that the partial pressure reaches the saturation value, a phase change process occurs and the wall value of the partial pressure is maintained at the saturation value. After this point, a thin film of condensed water begins to grow and the vapor partial pressure of water is nearly constant at the saturation value associated with the interface temperature. A gradient is seen in the water mass fraction profile near the wall. Much like the temperature profile, the water vapor profile after the reactions subside influences the water vapor distribution outside of the quenching zone by simple diffusion processes. Simple scaling analysis establishes an order of magnitude estimate for the heat flux associated with water condensation. The most significant parameters appear to be the quench layer thickness (lq = 100 /~m), the difference between the water vapor mass fraction in the burned gas and at the wall (AY ~ 0.08), and the product of the mixture density ( p 1 k g / m 3) and vapor diffusivity (D = 30 × 10 -6 m2/$). The latent heat of vaporization, hr~, for water is approximately 2000 kJ/kg. The maximum heat flux from condensation, pD(AY/lq)hf g, is then approximately 0.05 M W / m z. Altiaough the quench layer thickness decreases with increasing wall temperature, it does not change markedly in the temperature range between 300 and 400 K. The product of mixture density and vapor diffusivity increases with increasing temperature, but similar to the quench distance changes in this parameter are small over the temperature ranges considered. The single most important factor influencing the magnitude of the vapor mass flux in the these low temperature quenching problems is the change in the saturation partial pressure at the wall. For a total pressure of 1 atmosphere, the partial pressure of water vapor in the burned gas is approximately 0.154 atmosphere for the stoichiometric propane-air flames considered in this study. For quenching conditions with a wall saturation partial pressure above the burned gas value there will not be conden-

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wall temperatures.Conventionaltreatment of the quenching processwhich neglects phase change processeswould predict a monotonicincrease in the peak fluxwith increasing temperature.Phase changeprocessesmodifythis result and are in closer agreementwith experimentalresults. sation at the wall. This implies that for wall temperature above approximately 55° C (328 K) these effects will not occur. Associated with the vapor mass flux is a heat transfer rate associated with the latent heat of vaporization. This phase change heat flux, which is assumed to contribute directly to the total wall heat flux, is shown in Fig. 2 with the direct temperature gradient induced heat flux. The maximum phase change heat flux is approximately 5% of the maximum temperature gradient heat flux at the lowest wall tempera-

PREMIXED FLAME QUENCHING ture condition (300 K). While this result it not very large, it has been overlooked in past investigations o f flame quenching and has contributed to systematic errors in interpreting experimental results. In addition to the modification o f the c o m p u t e d heat flux, the monolayer of water vapor deposited on the wall influences any perceived catalytic effects o f the base wall material. Further, the effects of water vapor migration from the quench zone may modify the gas phase chemistry at the time o f quench. F o r the two step mechanism considered, in addition to increases in total heat flux by phase change effects, the t e m p e r a t u r e gradient heat flux itself increases by 7% at 300 K when the condensation process is coupled to the quenching event. The detailed examination o f these issues is beyond the scope o f this study, and should be pursued with more sophisticated treatment of the gas phase chemistry and surface reactions.

REFERENCES I. Ezekoye, O. A., Greif, R., and Sawyer, R. F., Twenty, Fourth Symposium (International) on Combi~ion,

Combustion Institute, Pittsburgh, 1993, p. 1465. 2. Connelly, L., Ogasawara, T., Lee, D., Greif, R., Sawyer, R. F., and Ezekoye, O. A., Fall Meeting Western States Section of the Combustion Institute, WSC! 9"3077, Stanford, CA, Oct. 18-19, 1993. 3. Bush, W. B., Fendell, F. E., and FinL S. F., Combmt. Sci. Technol. 24:53 (1980). 4. Kiehne, T. M., Matthews, R. D., and Wilson, D. E., Combust. Sci. TechnoL 54:! (1987). 5. Popp, P., Smooke, M. D., and Baum, M., Twenly-Sixth Symposium (International) on Combustion, The

bustion Institute, Pittsburgh, 1997. 6. Popp, P. and Baum, M., SAE Technical Paper 952387, Fuels and Lubricants Meeting, Toronto Canada, Oct. 16-19, 1995. 7. Westbrook, C. K. and Dryer, F. L, Combua. 8c/. Technol. 27:31 (1981).

Receit'ed 7 September 1996; accepted 12 February 1997