Transactions of the Korean Society of Mechanical Engineers B (대한기계학회논문집B)

The Korean Society of Mechanical Engineers (대한기계학회)
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Theoretical Analysis on Bifurcation Behavior of Catalytic Surface Reaction on Nonadiabatic Stagnation Plane

비단열 정체면에서 촉매 표면반응의 천이 거동에 대한 이론적 해석

  • 이수룡 (서울산업대학교 자동차공학과)
  • Published : 2004.06.01
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Abstract

Bifurcation behavior of ignition and extinction of catalytic reaction is theoretically investigated in a stagnation-point flow. Considering that reaction takes place only on the catalytic surface, where conductive heat losses are allowed to occur, activation energy asymptotics with a overall one-step Arrhenius-type catalytic reaction is employed. For the cases with and without the limiting reactant consumption, the analysis provides explicit expressions, which indicate the possibility of multiple steady-state solution branches. The difference between the solutions with and without reactant consumption is in the existence of an upper solution branch, and the neglect of reactant consumption is inappropriate for determining extinction conditions. For larger values of reactant consumption, the solution response is all monotone, suggesting that multiple solutions are not possible. It is shown that bifurcation Damkohler numbers increase (decrease) with increasing of conductive heat loss (gain) on the catalytic surface, which means that smaller (larger) values of the strain rate allow the surface reaction to tolerate larger heat losses (gains). Lewis number of the limiting reactant can also significantly affect bifurcation behavior in a similar way to the effect of heat loss.

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References

  1. Sea, Y. S., Shin, H. D. and Kang, S. K., 1998, 'Combustion Characteristics of Lean Premixed Mixture in Catalytic Combustors,' Transactions of the KSME, Vol. 22, No. 12, pp. 1681-1690
  2. Hwang, C. H., Lee, C. E. and Jeong, Y. S., 2001, 'Numerical Studies on Combustion Characteristics of a Hybrid Catalytic Combustor,' Transactions of the KSME, Vol. 25, No. 4, pp. 583-592
  3. Law, C. K. and Sivashinsky, G. I., 1982, 'Catalytic Extension of Extinction Limits of Stretched Premixed Flames,' Combust. Sci. Technol. Vol. 29, pp. 277-286 https://doi.org/10.1080/00102208208923602
  4. Warnatz, J., Allendore, M. D., Kee, R. J. and Coltrin, M. E., 1994, 'A Model of Elementary Chemistry and Fluid Mechanics in the Combustion of Hydrogen on Platinum Surfaces,' Combust. Flame, Vol. 96, pp. 393-406 https://doi.org/10.1016/0010-2180(94)90107-4
  5. Deutschmann, D., Schmidt, R., Behrendt, F. and Warnatz, J., 1996, 'Numerical Modeling of Catalytic Ignition,' Proceedings of the Combustion Institute, Vol. 26, pp. 1747-1754 https://doi.org/10.1016/S0082-0784(96)80400-0
  6. Maruta, K., Takeda, K., Ahn, J., Borer, K., Sitzki, L., Ronney, P. D. and Deutschmann, O., 2002, 'Extinction Limits of Catalytic Combustion in Microchannels,' Proceedings of the Combustion Institute, Vol. 29, pp. 957-963 https://doi.org/10.1016/S1540-7489(02)80121-3
  7. Margolis, S. B. and Gardner, T. J., 2002, 'Extinction Limits of Nonadiabatic, Catalyst-Assisted Flames in Stagnation-Point Flow,' Combust. Theory Modelling, Vol. 6, pp. 19-34 https://doi.org/10.1088/1364-7830/6/1/302
  8. Margolis, S. B. and Gardner, T. J., 2003, 'An Asymptotic Model of Nonadiabatic Catalytic Flames in Stagnation-Point Flow,' SIAM J. of Appl. Math., Vol. 63, No.3, pp. 1083-1103 https://doi.org/10.1137/S0036139902402452
  9. Song, X., Williams, W. R., Schmidt, L. D. and Aris, R., 1991, 'Bifurcation Behavior in Homogeneous-Heterogeneous Combustion : II. Computations for Stagnation-Point Flow,' Combust. Flame, Vol. 84, pp. 292-311 https://doi.org/10.1016/0010-2180(91)90007-X
  10. Schlichting, H. and Gersten, K., 1999, Boundary Layer Theory, Springer
  11. Linan, A. and Williams, F. A., 1979, 'Ignition of a Reactive Solid Exposed to a Step in Surface Temperature,' SIAM J. of Appl. Math., Vol. 36, No. 3, pp. 587-603 https://doi.org/10.1137/0136042
  12. Chaudhary, M. A. and Merkin, J. H., 1994, 'Free-Convection Stagnation-Point Boundary Layers Driven by Catalytic Surface Reactions : I. the Steady States,' J of Engineering Math., Vol. 28, pp. 145-171 https://doi.org/10.1007/BF00127583
  13. Ablow, C. M., Schechter, S. and Wise, H., 1980, 'Catalytic Combustion in a Stagnation Point Boundary Layer,' Combust. Sci. Technol. Vol. 12, pp. 107-117 https://doi.org/10.1080/00102208008952376
  14. Fernandes, N. E., Park, Y. K. and Vlachos, D. G., 1999, 'The Autothermal Behavior of Platinum Catalyzed Hydrogen Oxidation : Experiments and Modeling,' Combust. Flame, Vol. 118, pp. 164-178 https://doi.org/10.1016/S0010-2180(98)00162-X