Mathematical Model of Smoldering Combustion in a Carbonaceous Porous Medium Part 1 – Development of Pyrolysis and Combustion Models for a Cylindrical Geometry

Abstract

In Part 1 of this two-part paper on the development of pyrolysis and combustion models for a carbonaceous porous medium, the methodology for elucidating the smoldering mechanism in a carbonaceous porous medium is described. The smoldering process was segregated into two major reaction zones – a pyrolysis zone and a combustion zone. Two independent models for a cylindrical geometry were developed: a steady-state two-dimensional model for the pyrolysis zone resulting in char formation, and a steady-state two-dimensional model for the combustion zone, i.e., char oxidation. The interface temperature between the two zones is defined as the temperature at which the pyrolysis is complete or the residual char ignites, which can be determined experimentally. In order to analyze the mechanism of smoldering combustion, the heat flux required for the smoldering to proceed in the pyrolysis zone (Q_req) and the heat flux (Q_sup) fed from the combustion zone into the pyrolysis zone were obtained from the models developed for any linear burn rate (LBR). Like temperature, these heat fluxes must be balanced at the interface between the two zones. The LBR corresponding to the intersect of Q_req and Q_sup can be used to determine the LBR, temperature and density profiles of the smoldering combustion of a cylindrical geometry.

Keywords

smoldering combustion porous medium mathematical model

Get full access to this article

View all access options for this article.

References

Baker, R.R. (1975). Temperature variation within a cigarette combustion coal during the smoking cycle. High Temperature Science, 7: 236.

Baker, R.R. and Kilburn, K.D. (1973). The distribution of gases within the combustion coal of cigarette. Beitr. Tabakforsch., 7: 79.

Baker, R.R. and Robinson, D.P. (1990). Tobacco combustion–the last ten years. Rec. Adv. Tob. Sci., 16: 3.

Calingaert, G. and Davis, D.S. (1925). Pressure–temperature charts – extended ranges. Ind. Eng. Chem., 17: 1287.

DiBlasi, C. (1993). Analysis of convection and secondary reaction effects within porous solid fuels undergoing pyrolysis. Combust. Sci. and Tech., 90: 315.

Mitler, H.E. and Walton, G. (1993). Modeling the Ignition of Soft Furnishings by a Cigarette. NIST Special Publication 852, Gaithersburg, MD: National Institute of Standards and Technology.

Moussa, N.A. , Toong, T.Y. and Garris, C.A. (1976). Mechanism of smoldering of cellulosic materials. Sixteenth Symposium (International) on Combustion. Pittsburgh, PA.: The Combustion Institute. p. 1447.

Muramatsu, M. (1981). Studies on the transport phenomena in naturally smoldering igarettes. Sci. Papers Cent. Res. Inst., Apan Tobacco and Salt Monop. Corp. (in Japanese), 123: 9.

Muramatsu, M. , Umemura, S. and Okada, T. (1979). A mathematical model of evaporation-pyrolysis processes inside a naturally smoldering cigarette. Combust. Flame, 36: 245.

10.

Ohlemiller, T.J. (1985). Modeling of smoldering combustion propagation. Prog. Energy Combust. Sci., 11: 277.

11.

Ohlemiller, T.J. (1995). Smoldering combustion. The SFPE Handbook of Fire Protection Engineering, 2nd edn. Quincy, MA: National Fire Protection Association. p. 2171.

12.

Patankar, S.V. (1980). Numerical Heat Transfer and Fluid Flow. New York: Hemisphere Publishing Co.

13.

Sandusky, H.W. (1976). A computer-simulated cigarette model for the use in the development of less hazardous cigarettes. PhD Dissertation, Dept. of Aerospace and Mechanical Engineering, Princeton University, Princeton, NJ.