Numerical Study Of Smoldering Combustion Propagation And Characteristics Of Ignition-Extinguishing And Transition To Flaming In A Horizantal Packed Bed

Smoldering combustion is defined as a heterogeneous, slow surface combustion reactionwithout flame in the interior of porous medium. The smoldering involves many complexprocesses related to fluid flow, heat and mass transfer in a porous medium, together withsurface chemical reactions. The interactions between these thermo-physical and chemicalprocesses determine the final characteristics of the smoldering reaction. The smolderingcombustion is of particular interest in the fire safety field because of its role as a potential fireignition source. Firstly, smoldering reactions can produce more toxic combustion products toresult in severely impair than those of open flames. Secondly, it is very difficult to detectbecause smoldering combustion is a weakly reacting phenomenon that can propagate slowlyfor a long period of time through the interior of porous combustible material. Thirdly, andperhaps, more importantly, smoldering reactions may transition to flaming reactions initiatinga rapidly propagation and potentially hazardous fire. At the same time, this phenomenon has awide range of technological relevance, as in the control of fire spread in permeable solids, thegasification process of porous solid materials, the packed bed incineration of municipal solidwaste, the incineration of hazardous solid waste, dealing with the combustion of biomass, theheating technology of fire pit, etc. Therefore, it is very significative to study the propagationprocess, extinguishing conditions and transition to flaming of smoldering of combustiblematerials for the fire safety science, heat energy utilizing and gasification engineering.Smoldering combustion is generally classified into forward and reverse configurations.In forward smolder, the reaction zone propagates in the same direction as the inlet airflow. Inreverse smolder, the fresh airflow enters the reaction zone from opposite direction ofsmoldering wave propagation. Forward smolder is unsteady and moves at a higher rate, andcan eventually transit to flaming combustion as increasing smoldering velocity due toincreased inlet air velocity or oxygen concentration. Reverse smolder is characterized by asteady propagation velocity and can't transit into flaming.Inthe numerical study, the COMSOL Multiphysics, a special software package based onthe proven finite element method, is employed to resolve the governing equations rearrangedand discretized in space for modeling the smoldering propagation based on partial differentialequations (PDEs). The solvers including direct and iterative method are written to adopt the advanced computation technology based on the C++ program language, and the softwareincludes the advanced multilevel preprocessor, efficient time-step operating rule and intrinsicmodel. In this paper, the heat transfer and chemical engineering modules are called to bulidthe mathematical model including the energy, gaseous species, momentum and overall massconservation equations. The method to solve the equations is iterative and the correspondingsolver, GMRES, is selected. The packed bed of fuel is divided into triangle meshes to performcalculations by employing self-adapting mesh generator.Firstly, in this paper, the forward and reverse smoldering propagations are numericallystudied for the typical porous materials including combustible cellulosic fuel andpolyurethane foam.(1) Based on a three-step kinetic mechanism, a two-dimensional, time dependent,numerical model is presented for the forward smoldering propagation in a horizontally packedbed of fuel. The kinetic processes include pyrolysis of fuel, oxidation of fuel and oxidation ofchar. Heat transfer between solid and gas is taken into account, and radiative transfer isincluded using the diffusion approximation. The diffusion coefficient varies with temperature.Predicted profiles of solid temperature as well as evolutions of gaseous species, solidcompositions, gaseous density and velocity and heat release are presented and analyzed. Theeffects of airflow velocity and oxygen concentration are numerically simulated on smolderingvelocity and average maximum temperature of smoldering fuel, and the results show that thesmoldering velocity linearly varies with increasing airflow velocity and mass fraction ofoxygen. The computational results are compared with the experimental data available fromthe literature, and a general agreement is reached. Simultaneously, the effects of fuelproperties (including thermal conductivity, specific heat, density and pore diameter) arestudied on the smoldering propagation. The fuel density is the most important factor indetermining smoldering propagation, the second is specific heat, and the least is thermalconductivity. Radiation has a non-negligible role on the smoldering velocity for larger porediameters of porous material. By varying the frequency factors (including fuel pyrolysis, fueloxidation and char oxidation), the simulations show that smoldering velocity increases withincreasing fuel oxidation, but decreases with fuel pyrolysis and char oxidation. The heatreleases of three reactions are analyzed and it is shown that the fuel oxidation is the mostimportant energy to maintain the smoldering propagation.(2) Based on a two-step kinetic mechanism (including pyrolysis and oxidation of fuel), atwo-dimensional, time dependent, numerical model is presented for the reverse smolderingpropagation in a horizontally packed bed of fuel. The model takes the radiation heat transferinto account by using the diffusion approximation, and the diffusion coefficient of gas varieswith the temperature in the porous medium. Predicted profiles of solid temperature as well as evolutions of gaseous species, solid compositions, gas density and heat release are presentedand analyzed. The effects of airflow velocity are numerically simulated on smolderingvelocity and average maximum temperature of smoldering fuel by using the model. Withincreasing airflow velocity, the smoldering velocity increases to a maximum and decreasesuntil quenching occurs at the maximum inlet airflow velocity. However, the inlet gas velocityhas little effect on the average maximum temperature. The concentration of oxygen has animportant effect on the characteristics of smoldering propagation. The smoldering velocitylinearly increases with increasing mass fraction of oxygen.Secondly, based on a one-step kinetic mechanism as Dosanjt et al. employed, aone-dimensional, unsteady, numerical model is presented for reverse smoldering propagationin a packed bed. Using asymptotic method and simplifying the model parameters theequations are obtained to qualitatively depict the reverse smoldering propagation. Matlab7.0.1language is adopted to compute the propagation progress of reverse smoldering of fuel. Theanalytic solutions show that the smoldering temperature increases with increasing the gaseousmass flux, but the increase in the amplitude is reduced due to enhancing the convectivecooling of preheat zone. With increasing the gaseous mass flux, the smoldering velocityincreases to a maximum and decreases until quenching occurs at the maximum inlet airflowvelocity. The analytical results are compared with the numerically computed results for thefuel mass flux and smoldering temperature with various gas mass flux, and the correct trend ispresent. The computed result also shows that a weak smoldering propagation can be obtainedat zero gaseous flux. The smoldering velocity and temperature are analytically solved whenthe gaseous flux is zero, namely M_g=0. And the smoldering temperatures and gaseous massfluxes are also solved when the smoldering velocity reaches the maximum and zero.Simultaneously, the effects of oxygen concentration, pre-exponential frequency factors,porosity and fuel properties (including density, specific heat, conductivity, activation energy,heat of reaction) are studied on the reverse smoldering propagation.Lastly, based on the theoretical analysis and simplified physical model, the mathematicalmodel for the transition to flaming from smoldering combustion is presented in a horizontalpacked bed of fuel. The ignition and extinction of smoldering and transition to flaming arestudied by employing the bifurcation theory. The Frank-Kamenetskii parameter,β₁, isselected as the control parameter and the other parameters (including Pe₁, Pe12,α₁,α₂,ε,Le)are fixed, the bifurcation characteristics of ignition and extinction of smoldering andtransition to flaming are detailedly discussed and analyzed. The computed curve has twobifurcations and both of them show S-shaped. The bifurcation curve is obviously divided intotwo reaction zones of solid phase and gas phase. Each of bifurcation includes three branchesof steady ignited branch, extinguished branch and unstable steady branch. Simultaneously, The effects of other parameters (including Pe₁, Pe₂,α₁,α₂,ε, Le) are studied on the ignitionand extinction of smoldering and transition to flaming. Moreover, the effects of activationenergy and heat release of gas-phase reaction are presented on the vanishing of critical state ofgas-phase reaction.