填充床内阴燃传播的数值模拟及阴燃着火—熄火、向明火转捩特性分析
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摘要
阴燃是在多孔介质内发生异相反应并能自维持进行的无焰缓慢燃烧形式，其中包括许多复杂的热物理和化学过程(如流体流动、多孔介质传热、传质过程、表面化学反应等)，这些过程之间的关系决定了阴燃反应的最终特性。阴燃是诱发火灾的重要因素，其主要的危害表现在：①阴燃比通常的有焰燃烧释放的有毒产物更多，对人造成危害更大；②它发生在火灾初期，不易被人发现，因此潜在危险性很大；③如果条件适宜，如随着供氧量的增大，阴燃会发生气相反应而转捩成有焰燃烧诱发火灾，会带来更大破坏和损失。同时，燃料阴燃也具有广泛的科技实用性，如在控制多孔可燃材料的燃烧速度、固体物质的气化工程、城市垃圾焚烧、有害固体废物的燃烧、处理生物量燃烧及燃池采暖技术等。所以，研究可燃物阴燃的传播蔓延过程、熄灭条件及其向明火的转捩，对于火灾安全科学、热能源利用、气化工程等方面都具有重要的应用价值。
阴燃一般分为正向阴燃和反向阴燃。正向阴燃是指阴燃波的转播方向与来流方向相同；而反向阴燃是指阴燃波的传播方向与来流方向相反。正向阴燃在外界条件的改变(如增大风流或氧气含量等)易转捩成明火，而反向阴燃传播则相对比较稳定。
在数值模拟中，本文采用一个专业有限元数值分析软件包—COMSOL Multiphysics(FEMLAB)对燃料阴燃传播的控制方程，即对偏微分方程组(PDEs)，进行建模、离散求解。该软件的求解器是基于C++程序采用最新的数值计算技术编写而成，包括最新的直接求解和迭代求解方法、多级前处理器、高效的时间步用算法则和本征模型。本文对燃料阴燃的数值模拟计算中，主要调用了软件包模型库中的热传递模块和化学工程模块，对能量守恒方程、质量守恒方程、气体组分扩散、动量方程等进行了建模，选用迭代求解方法，使用GMRES求解器，采用自适应网格生成器将填充床划分为多个三角形网格单元。
首先，本文以两种典型的多孔介质材料(松散的纤维质材料和多孔骨架结构的聚胺脂泡沫)为式样，数值模拟了燃料正向阴燃和反向阴燃传播过程：
(1)基于燃料阴燃三步反应动力学机理，建立了2D非稳态纤维质材料填充床正向阴燃的数学模型。阴燃的化学动力过程包括燃料热解、燃料放热氧化及焦炭的放热氧化。该模型考虑了固-气之间的热交换及气体在多孔介质内扩散系数的变化。数值模拟了燃料正向阴燃的温度分布、固体成分和气体组分的变化、气流密度和气流速度的变化、反应释热分析等；模拟了来流速度、氧气浓度对阴燃速度及平均最高温度影响，证明阴燃速度与来流风速和氧气浓度基本上呈线性关系变化，模拟结果与实验进行了对比，吻合较好；模拟了燃料特性参数(如燃料导热率、比热、密度等)对燃料阴燃传播的影响，其中燃料的密度对燃料的阴燃传播影响较大，其次是比热，而燃料导热率的影响是很小的；通过模拟多孔介质的孔径的影响，发现对于小孔隙直径，模型中可以忽略辐射传热，而随着孔隙直径的增大，辐射换热的作用逐渐加强，理论模型中要考虑辐射的传热作用；模拟反应指前频率因子来考察燃料阴燃的传播特性；通过模拟分析了燃料阴燃三个反应过程的释热情况，证明燃料氧化是维持阴燃传播的重要动力。
(2)对于反向阴燃传播，采用两步反应动力学模型，即包括燃料热解和燃料氧化两个反应，建立了二维非稳态燃料反向阴燃传播数学模型。模型中考虑了辐射换热以及气体扩散系数随温度的变化。数值模拟了燃料反向阴燃传播的温度分布、气体组分变化、固体成分变化、气流密度的变化以及反应热释放情况；模拟了来流速度对燃料阴燃传播的影响，随着来流速度的增大，阴燃传播速度呈现出先增大后减小直至熄灭的变化趋势，对阴燃温度的影响相对较小；模拟发现氧气浓度对燃料阴燃传播特性具有重要的影响，其关系粗略呈线性增长，且对燃料阴燃的最高温度也有一定的影响。
其次，基于Dosanih et al．的单步反应机理，建立了一维非稳态燃料填充床反向阴燃的数学模型，通过大活能渐进分析和参数简化得出了定性描述燃料反向阴燃传播的方程。采用采用Matlab7.0.1计算了燃料反向阴燃的传播过程。计算结果表明：燃料的阴燃温度随着气体流量的增大而增大，但随着反向气流对流冷却作用的加强，阴燃温度的增长幅度是逐渐减小的；阴燃传播速度却呈现出先增大后减小直至熄灭的变化趋势。反向阴燃固相质量通量和阴燃温度随气流质量通量变化的解析解与数值解进行了对比，其变化趋势基本一致。通过定性分析反向阴燃得出；在气体流量为零的情况下，燃料仍然可以发生阴燃，且求得来流速度为零的阴燃速度和阴燃温度。同时，分析了氧气浓度、指前频率因子、孔隙率、燃料特性参数(包括密度、比热、导热率、活化能、放热量)等对反向阴燃熄灭的影响。
最后，通过理论分析和物理动力学模型简化，建立了燃料阴燃向明火转捩的数学模型，采用分岔理论对燃料阴燃着火-熄火及向明火转捩过程进行了研究和探讨。以Frank-Kamenetskii参数β_1为分岔参数，详细讨论了阴燃着火及向明火转捩的分岔特性。整个分岔曲线出现了二次分岔特点，明显地分为固相反应区和气相反应区。在每一个反应区，分岔曲线均呈现S型，其中包含有三个分支：稳定的着火分支、熄火分支及非稳定状态分支。同时，研究了方程中的其他控制参数(如Pe_1、Pe_2、α_1、α_2、ε和Le)的变化对燃料阴燃着火-熄火及及向明火转捩的影响。此外，也分析了气相反应活化能和放热量的变化对气相反应临界状态消失的影响。
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,β_1, isselected as the control parameter and the other parameters (including Pe_1, Pe12,α_1,α_2,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 Pe_1, Pe_2,α_1,α_2,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.
阴燃一般分为正向阴燃和反向阴燃。正向阴燃是指阴燃波的转播方向与来流方向相同；而反向阴燃是指阴燃波的传播方向与来流方向相反。正向阴燃在外界条件的改变(如增大风流或氧气含量等)易转捩成明火，而反向阴燃传播则相对比较稳定。
在数值模拟中，本文采用一个专业有限元数值分析软件包—COMSOL Multiphysics(FEMLAB)对燃料阴燃传播的控制方程，即对偏微分方程组(PDEs)，进行建模、离散求解。该软件的求解器是基于C++程序采用最新的数值计算技术编写而成，包括最新的直接求解和迭代求解方法、多级前处理器、高效的时间步用算法则和本征模型。本文对燃料阴燃的数值模拟计算中，主要调用了软件包模型库中的热传递模块和化学工程模块，对能量守恒方程、质量守恒方程、气体组分扩散、动量方程等进行了建模，选用迭代求解方法，使用GMRES求解器，采用自适应网格生成器将填充床划分为多个三角形网格单元。
首先，本文以两种典型的多孔介质材料(松散的纤维质材料和多孔骨架结构的聚胺脂泡沫)为式样，数值模拟了燃料正向阴燃和反向阴燃传播过程：
(1)基于燃料阴燃三步反应动力学机理，建立了2D非稳态纤维质材料填充床正向阴燃的数学模型。阴燃的化学动力过程包括燃料热解、燃料放热氧化及焦炭的放热氧化。该模型考虑了固-气之间的热交换及气体在多孔介质内扩散系数的变化。数值模拟了燃料正向阴燃的温度分布、固体成分和气体组分的变化、气流密度和气流速度的变化、反应释热分析等；模拟了来流速度、氧气浓度对阴燃速度及平均最高温度影响，证明阴燃速度与来流风速和氧气浓度基本上呈线性关系变化，模拟结果与实验进行了对比，吻合较好；模拟了燃料特性参数(如燃料导热率、比热、密度等)对燃料阴燃传播的影响，其中燃料的密度对燃料的阴燃传播影响较大，其次是比热，而燃料导热率的影响是很小的；通过模拟多孔介质的孔径的影响，发现对于小孔隙直径，模型中可以忽略辐射传热，而随着孔隙直径的增大，辐射换热的作用逐渐加强，理论模型中要考虑辐射的传热作用；模拟反应指前频率因子来考察燃料阴燃的传播特性；通过模拟分析了燃料阴燃三个反应过程的释热情况，证明燃料氧化是维持阴燃传播的重要动力。
(2)对于反向阴燃传播，采用两步反应动力学模型，即包括燃料热解和燃料氧化两个反应，建立了二维非稳态燃料反向阴燃传播数学模型。模型中考虑了辐射换热以及气体扩散系数随温度的变化。数值模拟了燃料反向阴燃传播的温度分布、气体组分变化、固体成分变化、气流密度的变化以及反应热释放情况；模拟了来流速度对燃料阴燃传播的影响，随着来流速度的增大，阴燃传播速度呈现出先增大后减小直至熄灭的变化趋势，对阴燃温度的影响相对较小；模拟发现氧气浓度对燃料阴燃传播特性具有重要的影响，其关系粗略呈线性增长，且对燃料阴燃的最高温度也有一定的影响。
其次，基于Dosanih et al．的单步反应机理，建立了一维非稳态燃料填充床反向阴燃的数学模型，通过大活能渐进分析和参数简化得出了定性描述燃料反向阴燃传播的方程。采用采用Matlab7.0.1计算了燃料反向阴燃的传播过程。计算结果表明：燃料的阴燃温度随着气体流量的增大而增大，但随着反向气流对流冷却作用的加强，阴燃温度的增长幅度是逐渐减小的；阴燃传播速度却呈现出先增大后减小直至熄灭的变化趋势。反向阴燃固相质量通量和阴燃温度随气流质量通量变化的解析解与数值解进行了对比，其变化趋势基本一致。通过定性分析反向阴燃得出；在气体流量为零的情况下，燃料仍然可以发生阴燃，且求得来流速度为零的阴燃速度和阴燃温度。同时，分析了氧气浓度、指前频率因子、孔隙率、燃料特性参数(包括密度、比热、导热率、活化能、放热量)等对反向阴燃熄灭的影响。
最后，通过理论分析和物理动力学模型简化，建立了燃料阴燃向明火转捩的数学模型，采用分岔理论对燃料阴燃着火-熄火及向明火转捩过程进行了研究和探讨。以Frank-Kamenetskii参数β_1为分岔参数，详细讨论了阴燃着火及向明火转捩的分岔特性。整个分岔曲线出现了二次分岔特点，明显地分为固相反应区和气相反应区。在每一个反应区，分岔曲线均呈现S型，其中包含有三个分支：稳定的着火分支、熄火分支及非稳定状态分支。同时，研究了方程中的其他控制参数(如Pe_1、Pe_2、α_1、α_2、ε和Le)的变化对燃料阴燃着火-熄火及及向明火转捩的影响。此外，也分析了气相反应活化能和放热量的变化对气相反应临界状态消失的影响。
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,β_1, isselected as the control parameter and the other parameters (including Pe_1, Pe12,α_1,α_2,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 Pe_1, Pe_2,α_1,α_2,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.
引文
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