Di Blasi 1993 Modelling and Simulation of Combustion Processes of Charring and Non Charring Solid...

Prog. Energy Combust. ScL 1993, Vol. 19, pp. 71 104 0360-1285/93 $24.00 Printed in Great Britain. All rights reserved. ~) 1993 Pergamon Press Ltd

MODELING A N D SIMULATION OF COMBUSTION PROCESSES OF CHARRING AND NON-CHARRING SOLID FUELS

COLOMBA DI BLASI

Dipartimento di Ingegneria Chimica, Unioersitd di Napoli, Piazzale V. Tecchio, 80125 Napoli, Italy

Received 11 February 1993

Abstract--Some of the progress that, owing to modeling and numerical simulation, has been made to the understanding of chemical and physical processes, which occur during combustion of solid fuels, is presented. The first part of the review deals with thermal degradation processes of charring (wood and, in general, cellulosic materials) and non-charring (poly-methyl-methacrylate) materials. Gas-phase combustion processes (ignition, flame spread and extinction) are discussed in the second part of the review. Solid fuel degradation has been described by kinetic models of different complexity, varying from a simple one- step global reaction, to multi-step reaction mechanisms, accounting only for primary solid fuel degradation, and to semi-global reaction mechanisms, accounting for both primary solid degradation and secondary degradation of evolved primary pyrolysis products. Semi-global kinetic models have been coupled to models of transport phenomena to simulate thermal degradation of charring fuels under ablation regime conditions. The effects of bubble formation on the transport of volatiles during thermal degradation of non-charring fuels, described through a one-step global reaction, have also been modeled. On the contrary, very simplified treatments of solid phase processes have been used when gas phase combustion processes are also simulated. On the other hand, the latter have also always been described through one-step global reactions. Numerical modeling has allowed controlling mechanisms of ignition and flame spread to be determined and the understanding of the interaction between chemistry and physics during thermal degradation of solid fuels to be improved. However, the chemical processes are not well understood, the few kinetic data are in most cases empirical and variations of solid properties during degradation are very poorly known, so that even the most advanced models do not in general give quantitative predictions.

CONTENTS

1. Introduction 71 2. Thermal Degradation Processes of Solid Fuels 73

2.1. Charring materials 73 2.2. Kinetic modeling 74

2.2.1. One-step global models 75 2.2.2. One-stage, multi-reaction models 75 2.2.3. Two-stage, semi-global models 76

2.3. Energetics of the pyrolysis reactions 79 2.4. Modeling of chemical and physical processes 80

2.4.1. The equations of wood pyrolysis 82 2.4.2. Numerical simulation of wood pyrolysis 84

2.5. Non-charring materials 85 2.6. Kinetic modeling 86 2.7. Modeling of chemical and physical processes 87

3. Gas Phase Combustion Processes 87 3.1 Modeling and simulation of ignition processes 89 3.2. Flame spread modeling 91

3.2.1. Gas phase models 91 3.2.2. Solid phase models 93 3.2.3. A mathematical model of flame spread 93

3.3. Opposed flow flame spread 94 3.4. Flow assisted flame spread 97 3.5. Microgravity flame spread 99

4. Conclusions and Further Developments 100 Acknowledgements 102 References 102

l. INTRODUCTION sion and to solid municipal waste disposal. It is also Thermal degrada t ion o f solid fuels is a process of interest to safety problems since solid thermal

per t inent to energy recovery th rough biomass conver- degradat ion is the first step of unwanted fire events,

71

72 C. D! BLASl

flaming combustion ~ produce ignition. 3 Under such conditions, degrada- external 1 heating air +l ~ tion processes in an inert atmosphere and in air

/ are not significantly different. A rapid heating of ugh ~,~,~ the solid fuel, to high temperatures, leads, in air,

SOLID ~ thermal degradation - - ~ volatiles + chars ~ to flaming combustion. 4 Even in this case, degra- | / dation of cellulosic materials in air would not be

to~he,t~ ~ ~- very different from that in an inert atmosphere l + air o"

smoldering combustion ~ since, if the flame envelops the degrading solid, the l / diffusion of oxygen into the subsurface layer can be 1 ~ ~ l neglected'5

. . . . . energy feed back .,,._. For subliming or melting solid fuels, such as poly- methyl-methacrylathe (PMMA), processes occurring

Fro. 1. Schematic diagram of combustion processes of char- inside the solid are somewhat simplified since vapori- ring materials.

zation (and pyrolysis) are confined to a thin layer of the fuel sample, at the condensed phase/gas phase

such as smoldering combustion, ignition, flame interface. In the melt layer, bubbles grow and trans- spread and burning. Thus it is very useful to under- port volatiles towards the surface. Thermal degrada- stand the mechanisms controlling the interaction tion processes in an oxidizing environment may be betwen chemical and physical processes and also the different from those occurring in an inert atmosphere. composition of evolved gases. This latter point is Indeed, oxygen may diffuse through the melt layer, important both in the context of maximizing the favored by the large holes left at the surface by yields of chemicals from material conversion and burst bubbles. 6 minimizing air pollution from material burning (incin- Flaming combustion processes are the result of eration and stoves), complex interactions of transport phenomena in

When subjected to external heating, solid fuels the gas phase (momentum, mass and heat transfer) start to decompose, giving a mixture of volatile spe- and in the solid phase, thermal degradation of the cies and, sometimes, a solid carbonaceous residual solid and chemistry of the oxidation of the fuel (char) as products. Combustion processes of charring vapors. materials, exposed in an oxidizing flow environment, Processes which can lead to gas phase ignition could proceed by two alternative pathways involv- include the vaporization of the solid, the formation ing flaming combustion and smoldering (or glow- of a flammable mixture adjacent to the solid surface ing) combustion, as shown, from a qualitative point and the initiation and the sustainment of oxidation of view, by the schematic diagram of Fig. I. Condi- reactions. The characteristics of these processes de- tions of flaming combustion are achieved when the termine whether ignition will occur and the ignition heat released by gas phase combustion of volatile delay time. In general, to get flaming ignition, three products provides the heat flux needed for solid conditions must be met: 7 (1) fuel and oxidizer must fuel degradation and flame spread. When the tem- be available at a proper level of concentration to perature or the intensity of the heat flux are below give a mixture within the flammability limits, (2) certain levels, oxidation of the char could result in the gas phase temperature must attain values suffi- smoldering combustion. Indeed, for porous or fi- ciently high to initiate and accelerate the combus- brous materials, such as wood, air may diffuse tion reaction, and (3) the extent of the heated zone inside the solid matrix and cause slow oxidation: must be sufficiently large to overcome heat losses. the even, low heat release rate, in the absence of The temperature of the mixture above the solid significant radiation heat losses, convection and con- surface plays a key role. Its increase above certain duction, provides the heat flux needed for further levels can occur by heat transfer from the hot charring and propagation of the smoldering combus- degrading surface and/or by devices capable of tion. For charcoal production or biomass gasifica- creating a region of very high temperature in the tion, oxygen flow and other heat and mass transfer gas phase, such as pilot flames, sparks and hot conditions are often adjusted in order to obtain wires (piloted ignition). Ignition can also be caused partial combustion and reaction heat, together with by hot air stream, hot surface and thermal radia- substantial pyrolysis. 1'2 tion (auto-ignition). In the last case, the absorption

Most of the biomass conversion processes are of radiation by the fuel vapors is another very aimed at obtaining solid fuel pyrolysis to volatile important mechanism for increasing the gas phase species and char in a non-oxidizing environment, temperature to levels high enough to produce Analyses of solid pyrolysis in a non-oxidizing environ- ignition. ment are also of interest to combustion processes After ignition, proper conditions may allow flame related to fire safety issues. At intermediate tempera- spread and solid burning. In general, the flame spread tures, gas evolution from cellulosic fuel pyrolysis is rate is determined by the energy feed-back from the sufficiently rapid to prevent significant air diffusion burning region to the unburned solid ahead of the within the solid matrix, yet not rapid enough to flame while the burning rate is determined by the

Combustion processes of solid fuels 73

rate of energy transfer from the flame to the degrad- of wood. The decompositon temperature increases ing solid beneath the flame, a Combustion kinetics from 117°C to 1700C in the order hemicellulose- may also become very important for flame spread < lignin < cellulose. 12 Furthermore the lignin com- processes. It is often very difficult to determine which ponent has a higher tendency for charring, whereas one among the many types of processes is the control- cellulose and hemicellulose readily decompose to vola- ling one. Most analyses have been devoted to the tile products at temperatures above 300°C. determination of the mechanism of energy feed back Pyrolysis products are often grouped into a few from the burning region to the solid ahead of the main components. Each component represents a sum flame. This energy transfer occurs by radiation, con- of numerous species which are lumped together to vection and conduction, the importance of each simplify the analysis. Generally, the product groups mechanism being related to geometrical factors, such considered are: char, gas and tar. Chars are the as the thickness of the solid specimen or the scale of carbon-rich non-volatile residues. Tars are any of the fire, or environmental conditions, such as free or several high molecular weight products (rich in 1,6- forced flow convection, oxygen level etc. For instance, anhydro compounds) that are volatile at the pyroly- radiative heat transfer is controlling for large scale sis temperature but condense near room tempera- turbulent flames whereas gas phase heat conduction ture. 13 Gases include all lower molecular weight is the major heat transfer mechanism for flames products (mainly CO and CO2 and also water), spreading over very thin fuel beds. which have a measurable vapor pressure at room

This review article on modeling and simulation is temperature. divided into two parts, the first dealing with solid Conventional pyrolysis, as usually carried out for phase processes and the second with gas phase proc- conversion purposes, produces gases, tars and chars esses. For the solid phase part, thermal degradation in approximately equal proportions. Also, flash (or of cellulosic materials, which give rise to char forma- fast) pyrolysis,14 based on high heating rates, leading tion, and PMMA, a non-charring material will be to moderate temperatures (from 400°C to 600°C), treated. The analysis is focused on these two types and short residence times of volatiles, is used to of materials because most of the experiments and produce high yields of tars. For both conventional numerical simulations of flame spread over solid fuels and flash pyrolysis, heat transfer occurs from the gas have been carried out with paper, a charring material, film surrounding the solid surface. A variation of fast and PMMA. Modeling and simulation of gas phase pyrolysis is represented by ablative pyrolysis, 15.16 combustion processes (ignition, flame spread and based on direct contact of solid fuel with a high extinction) will be presented in the second part of the pressure, moving, hot surface. Heat transfer occurs review, through a thin film of liquid oil between the hot

surface and the solid fuel. This results in much higher heat transfer coefficients, depending on the pressure

2. THERMAL DEGRADATION PROCESSES OF SOLID and relative velocity of the hot reactor surface. The rUEtS ablation rate and the thickness of the reacting zone

are the two basic parameters of the problem. 16 Ac- In this section the analysis of pyrolysis processes cording to the analyses conducted at the University

in a non-oxidizing environment will be presented of Aston, 17 such a conversion process seems to be since modeling of smoldering combustion has already more promising for obtaining high yields of liquid been treated in an excellent review by Ohlemiller. 9 product than conventional and flash pyrolysis. In Modeling of chemical kinetics and both physical and fact, the higher heat transfer coefficients allow higher chemical processes of solid thermal degradation will reactor specific capacities (smaller equipment sizes) be discussed, and avoid the need for a hot carrier gas as used in

most flash pyrolysis units. In general, two different regimes during cellulosic

2.1. Charring Materials material pyrolysis can be observed, as a result of the relative importance between heat transfer through the

Wood, or more generally cellulosic fuels, are to be degrading medium and the overall chemical reaction considered as the most representative of charring rate. The two regimes which can be established are: (1) materials. Wood has an anisotropic structure with the chemical regime, when the rate of heat transfer is different property (thermal diffusivity, permeability) larger than the overall reaction rate and the thermal values along and cross grain. It is basically composed conversion process is controlled by chemistry and (2) of cellulose (ca. 50~o), hemicellulose (ca. 25~) and the heat transfer controlled or ablation16 regime, when lignin (ca. 25~), the proportion of these constituents the rate of heat transfer is slow with respect to the varying to some extent among species.l°'11 Smaller overall reaction rate and strong temperature gradients amounts of extractive and inorganic compounds are are established along the fuel thickness, as the narrow also present, reaction front propagates. Time evolution of the ther-

Thermo-gravimetric analyses (TGA) indicate that mal degradation is the result of a strong coupling hemicellulose is the least thermally stable component between transport phenomena and chemical reactions.

74 C. DI BLASI

SOLID PHASE chars

primary degradation ~ (cracking - polymerization) CHEMICAL PROCESSES m~ of the solid ~ I

volatiles heat flux ~ solid pre-heating secondary reactions

(heat conduction) ~ I diffnsion and convection

PHYSICAL PROCESSES m~ ~ heat transfer by ~through the hot char layer u

I conductlon, convecti°n I diffnsion and convection ( and radiation I through the virgin solid I pressure gradients /

interior to the degrading solid I condensation

I surface regression crack formation shrinkage and/or swelling

FIG. 2. Schematic diagram of (solid phase) degradation processes of charring materials.

Qualitative descriptions of charring material degra- volatiles inside the porous char matrix and the size dation, caused by a radiative heat flux applied on and the number of surface fissures increase. Thc one side of the fuel sample, under ablation regime increase in the char layer thickness causes a larger conditions, are given by Kanury s't° and Roberts, H mass flow resistance, while the increase of volatile among others, and are summarized in the schematic residence time enhances the possibility for further diagram of Fig. 2. Initially the solid is essentially reactions to occur. The formation of cracks in the interested by transient heat conduction. Then a partially reacted wood naturally reduces the effects region, in the neighborhood of the heated side, under- due to volatile reactions because of the reduced resi- goes thermal degradation. When all the volatiles are dence times (lower resistance to mass flow). It also removed from the solid, a char layer is formed. Two alters the mechanisms of heat transfer, since radiation further spatial zones can be seen: the region where and convective flow of hot gases inside the solid may pyrolysis reactions are active and the virgin wood be enhanced. region. Volatile species, generated in the pyrolysis region, may, because of pressure gradients 18-2°, be forced to flow towards both the unreactcd solid and 2.2. Kinetic Modeling the already charred region. However, because of the much higher char permeability (lower mass flow re- Detailed numerical simulations of solid fuel com- sistance), the flow of products occurs mainly towards bustion are made complex not only by computational the heated surface. As volatile species flow through requirements, but also by the formulation of math- this high temperature region, secondary reactions cmatical models from the complex physical and can occur both homogeneously in the gas phase or chemical processes and by the acquisition of reliable heterogeneously on the surface of the char.t'2 In data.18 The determination of kinetic mechanisms and particular, heterogeneous reactions may give rise to kinetic constants, for cellulosic material degradation, exothermic char gasification by reducing the oxygen- has been pursued mainly under chemical regime con- rich volatile products of primary pyrolysis, ditions (intrinsic kinetics) even though some efforts

Volatile products may also migrate through the have also been devoted to the modeling of chemical unreacted virgin solid where, because of tbe low processes under ablation regime conditions (apparent temperature, they may condense and, subsequently, kinetics). Several studies have been conducted on the as the pyrolysis front progresses, evaporate. The soak- pyrolysis of wood and, in general, on biomass materi- ing of some of the pyrolysis products and the subse- als and their main components, cellulose, hemi- quent redrying cause physical and chemical changes cellulose and lignin. Chemical processes of such of material characteristics, even before the pyrolysis materials can roughly be described as two stages, process starts. 5'1°'~1 related to primary reactions of virgin solid degrada-

Apart from heat, momentum and mass transfer, tion and secondary reactions of evolved degradation changes in the physical structure of the reacting solid products.l'2 are observed with the development of a network of The description of both primary and secondary cracks in the already pyrolyzed region) 1 Surface reactions has been afforded mainly by lumping the regression and internal shrinkage and/or swelling are pyrolysis products into a few main groups (tar, gas also possible. 11.1s.20 and char) and by means of semi-global kinetic mecha-

As the pyrolysis front progresses into the solid, the nisms. Considerable scatter can be observed on the extent of the char layer, the residence time of the reported kinetic data because of ~1 (a) the great vail-


ety of experimental techniques which give rise to where a, b and c are the yield coefficients, expressed different types of pyrolysis on dependence of solid as grams of gas, condensable species and solid per and gas residence times, (b) the type of experiment grams of reacted solid. (isothermal, dynamic), (c) the experimental condi- Table 1, where some data are reported, shows tions (temperature, pressure, heating rate), (d) the large differences in the estimated values of the ki- physical properties of the solid (mainly moisture netic constants. As anticipated, this is due to the content and particle size) and (e) the chemical compo- complex chemistry of the thermal degradation, the sition of the solid (contents of cellulose, hemicellulose, complicated heat, mass and momentum transport lignin and inorganic components), phenomena occurring within the reacting medium

In general, kinetic studies can be classified into and the effects of the size of the particle and envi- three maingroups: ronment (heating rate) conditions. In particular,

(i) one step globalmodels, when a one-step reaction studies have been conducted to analyze the effects is used to describe degradation of the solid fuel by of migration, condensation and regasification of means of the experimentally measured rates of weight volatile products inside the virgin solid on the ap- loss; parent kinetics of degradation. Kanury and Blacks-

(2) one-stage, multi-reaction models, used to corre- hear 32 studied the pyrolysis of large radius, highly late reaction product distributions. These are one- permeable cellulosic cylinders, uniformly heated stage simplified kinetic models, made of several reac- along the surface, and observed that the reaction tions, describing the degradation of the solid to char rate increases, at a particular temperature, passing and several gaseous species; and from the surface to the center of the sample. Regasi-

(3) two-stage, semi-global models, when kinetic fication of condensed pyrolysis products, which mi- mechanisms of solid degradation include both pri- grated in the virgin wood region, was conjectured mary and secondary reactions, to be the cause of this behavior. A further experi-

mental study of the effects of migration, condensation and regasification of volatile species in the

2.2.1. One-stepglobalmodels virgin solid fuel on the apparent kinetics of pyroly-

Studies of group (1) propose a very simple kinetic sis was conducted by Min. 29 He studied the pyroly- scheme to model wood and cellulosic material ther- sis of filter paper and filter paper smeared with con- mal degradation, that is a global, one-step reaction: densable pyrolysis products, heated on one side, the

other being pressed against a permeable chalk (where pyrolysis product could migrate) or an alu-

SOLID k--~VOLATILES + CHAR (AI) minium foil (non-permeable). Condensable species deposition on the virgin solid was seen to reduce

whose rate is proportional either to weight residue or the rate of gaseous species generation and to shift to weight loss after infinite time and presents an the Arrhenius curve towards lower temperatures. Arrhenius law dependence on temperature. Such The trend is similar to that observed by Kanury models have been used to describe the chemistry of and Blackshear, 32 however changes in the apparent solid degradation for conditions of the chemically kinetics were found to be negligible. The different controlled regime as well as the ablation regime, that conclusions reached by the two analyses can be at- is for conditions where secondary reactions have a tributed again to the different experimental condi- significant role. Thus, in the first case, the kinetic tions and thickness of the degrading solid, changing model (AI) describes the primary stage of the degrada- from very thick (cellulosic cylinders) to very thin tion process (gas residence times are very short) (paper sheets)with trasnport phenomena becoming while in the second case, volatiles and char include less important. products proceeding from the initial degradation (primary gases and chars) and those proceeding from the cracking and the repolymerization of primary 2.2.2. One-stage, multi-reaction models

volatiles. Early studies were reviewed by Roberts.11 The studies of group (2) are related to the system- Subsequently, other investigations have been con- atic analyses of the effects of temperature on the ducted, most of them using TGA, 12"22-26 other de- thermal degradation of small particles of wood, 33'34 vices such as fluidized bed reactors, 27 a tube fur- celulose 14'3s'36 and lignin, 37~*° analyzed through nace 2s'29 and other approaches based on in situ product yields and volatile composition. Under high measurement techniques, s.3° heating rates, even though the onset of degradation

Experimental results of solid fuel degradation can and conversion of wood, cellulose and lignin occurs also be interpreted in terms of a single reaction at different temperatures, the same qualitative behav- accounting for the different fractions of gases; tars iour of products, lumped as tar, char and gas, is and chars formed: 3t observed. Tars and gases initially evolve at the same

rate, but tar production becomes much larger as the SOLID k a GASES + b TARS + c CHAR temperature is increased. For even higher tempera-

(AI') tures, tar yield reaches a maximum, then decreases

76 C. DI BLASI

TABLE 1. Kinetic data for one-step global models of charring fuel thermal degradation (X is solid conversion)

Ref. Sample T(K) E(kJ mol-l) A (s- t )

[5] ~t-cellulose 550-1000 79.4 1.7 x 10* [23] Cellulose 600-850 100.5 1.2 x 106 [24] Fir wood 300-1100 101.7 + 142.7X 2.1 x 108 [25] , Cellulose 580-1070 8.8-33.4 0.019-0.14 [27] Beech sawdust 450-700 18 (T < 600) 0.0053 [27] Beech sawdust 450-700 84 (T > 600) 2.3 x 104 [27] Cellulose 450-700 71 6.79 x 103 127] Cellulose 520-1270 139.6 6.79 x 109 [28] Cellulose 520-1270 166.4 3.9 x 1011 [29] Lignin 520-1270 141.3 1.2 x 10 s [29] Hemicellulose 520-1270 123.7 1.45 x 109 [30] Wood 321-720 125.4 1.0 x l0 s [31] Almond shell 730-880 95-121 1.8 x 106

and finally attains an asymptotic value. The decrease are the pre-exponential factor and apparent activa- of the tar yield at high temperatures is due to second- tion energy, respectively. The quantity Vi* is the ary cracking to light volatiles. The total gas yield ultimate attainable yield of the species i, that is, the also increases with temperature reaching a maximum yield at high temperatures for long residence times. in the rate of increase at the temperature of maximum Theoretical curves, obtained by best fit values of tar yield. This is a consequence of secondary reactions, kinetic parameters, correlate well with experimental For temperatures above 800-850 K, tar is the major measurements. However, since at high temperatures pyrolysis product while carbon monoxide dominates and long residence times secondary reactions effects gas yield. Lower amounts of carbon dioxide, meth- are not negligible, a rigorous kinetic model should ane, ethylene and aldehydes are also observed, include multi-step reactions for both the primary and

Product distribution is also dependent on the heat- the secondary stage of the degradation, as well as ing rate. Among others, such effects are presented for transport processes. Therefore the authors 33'35'37 cellulose in Ref. [35]. Instead of the maximum in the pointed out that the values of the kinetic parameters curve of the tar yield as function of temperature are valid only for correlating experimental data under observed for high heating rates, a constant value is the operative conditions from which they were de- obtained for low heating rates (< 100°C s-l). This rived and not representative of the true physico- behavior is believed to occur because volatile resi- chemical processes governing the degradation of solid dence times are shorter than the time required for fuels. the attainment of temperatures sufficiently high for

secondary reactions to occur. Furthermore, for a given 2.2.3. Two-stage, semi-global models temperature, the total volatile yield (tars +gases) increases as the heating rate decreases, as a conse- Studies of group (3) are related to the determina- quence of more time available for thermal conversion, tion of semi-global reaction mechanisms including

Most of the studies of group (2) were mainly the primary and, sometimes, the secondary stage of related to the determination of product distribution the solid degradation process together with the esti- and only very simplified kinetic modeling was pro- mation of kinetic data. Among wood components, posed. Even though secondary reactions were be- cellulose is the one most studied. One of the first lieved to contribute extensively to the overall produc- semi-global models proposed for primary degradation of light gases, such processes as well as transport tion of such a material is due to Kilzer and phenomena were neglected. The proposed models 33- Broido: 41 35.37 assume that the virgin solid fuel (wood or its k, components) decomposes directly to each reaction CELLULOSE ~ ANHYDROCELLULOSE product i, except tar, by a single independent reaction (A3)

according to CELLULOSE - -~ TAR (A4)

k~ VIRGIN FUEL -----, PRODUCT i. (A2) k3

ANHYDROCELLULOSE----o GAS + CHAR. The kinetics are modeled through a unimolecular (A5)

first-order reaction rate which can be expressed as: According to the analyses conducted by Kilzer and

d Vi Broido, 41 thermal degradation of cellulose starts at - - = Ai e xp ( - E i / R T) ( V ~* - VO (1) about 220"C with endothermic intermolecular water dt elimination to produce anhydrocellulose, whereas

where Vi is the yield of the product i, and Ai and Ei the higher temperature (about 280°C), 'unzipping'


(propagation of the reaction chain), more endother- formation of an 'active cellulose', which is essentially mic step results in the formation of volatile ievoglu- the result of a strong reduction in the degree of cosan, the major constituent of tar. The anhydrocellu- polymerization (El = 242.4 kJ moi -1, A ~ = lose undergoes further exothermic pyrolysis to form 2.8 × l019 s-l). The degradation of active cellulose char and gases. Dehydration reactions are predomi- (E2 = 196.5 kJ tool -1, Az = 3.28 x l014 s -1, Ea = nant at low temperatures and lead ultimately to 150.5 kJ mol -~, Aa = 1.3 x l0 ~° s -~) leads to vola- char formation and, in air, to glowing combustion, tile, gas and char formations. Depolymerization reactions, predominant at higher Both mechanisms (A3-A5) and (A6--AS) account temperatures, lead to the formation of volatile tars for the decrease of the char yield as the reaction and, in air, to flaming combustion.a temperature increases indicating, in agreement with

A subsequent study by Arseneau, 42 based on the experiments, 14'aa'aS'37 that the weight loss reactions analysis of thermograms of cellulose and levoglu- (tar and gas formations) are competitive with the cosan, confirmed only partially the interesting study char formation reactions. However, it has been sug- by Kilzer and Broido. 4~ For the case of thin cellulose gested 13 that the ratio of gas to char yield may not samples, only endothermic process were observed, be constant, because low pressure and high tempera- whereas for thick cellulose sample and levoglucosan ture favor cracking reactions of the active cellulose a strong exotherm was observed for the range of to gases, while low temperature favors crosslinking temperature 300-350°C. This behavior led to the and aromatization of the active cellulose to char. In conclusion that the anhydroceIlulose is highly reac- order to examine this point, Agrawal~3 plotted some tive and rapidly undergoes further reactions with data about the ratio of the char yield to the total gas and char formation. However, such processes yield of char and gas as functions of temperature, are not exothermic, while the levoglucosan decom- showing values from 1 (300°C) to 4 (400°C). The poses exothermally. Thus the exotherm observed at conclusion was that if char and gas reactions were high temperatures during the pyrolysis of thick linked this ratio would be independent of tempera- cellulose samples is the result of secondary reac- ture. Consequently, a three-reaction scheme, leading tions and not representative of primary pyrolysis separately to primary tar, char and gas formation processes, was proposed:

The degradation of cellulose was also extensively investigated by Shafizadeh and coworkers L2'43 in CELLULOSE--~ GAS (A9) the temperature range 260-340°C. Similarly to the kinetic scheme (A3-A5), two main pathways were k2 individuated. The first pathway, which dominates at CELLULOSE - -* CHAR (Al0) low temperatures, involves reduction in the degree of polymerization by bond scission; appearance of free k~ radicals; elimination of water; formation of low mo- CELLULOSE - -* TAR. (Al l) lecular weight gases and a char residue. At temperatures of about 300°C, the second pathway starts to The study, ta based on a re-examination of the become competitive and rapidly dominates. The pri- weight loss measurements by Lipska and Parker, 46 mary reaction in this pathway involves depolymeriza- shows how to evaluate the kinetic parameters for tion by transglycosylation, followed by dehydration the reaction scheme (A9-A1 l). Also a comparison and formation of char and gas. As the temperature is is made between the data estimated for the cases increased, the tar forming reactions accelerate rapidly of: and overshadow the formation of char and gases. Interesting details on the chemistry of the process are (linked char and gas formation) given in Refs [1,2] and have also been critically Yc~o analyzed in the review papers by Antal. 44'4s In Refs - 0.35 (2) [1,2,43] the chemical kinetics of cellulose pyrolysis Yc~0 + YGoo are represented by the following scheme: (not linked char and gas formation)

CELLULOSE - -~ ACTIVE CELLULOSE Yc® - - f ( T ) (3)

(A6) }'coo + YGoo

ks ACTIVE CELLULOSE ~ TARS (A7) where f(T) is determined through experimental ob- servation.

The difference between the unmodified (Eq. (2)) k3 ACTIVE CELLULOSE----. CHAR + GASES. and the modified (Eq. (3)) values results in small

(A8) changes only in the amounts of tars and gases. The unmodified assumption overestimates the tar yields

The primary degradation of cellulose is described by at high temperatures and underestimates the tar a first step reaction mechanism accounting for the yields atlowtemperatures. Given the narrow tempera-

78 C. DI BLASI

ture range tested (250-360°C), differences between The second approach considers the fuel as a single the two approaches are not very large. However, homogeneous species which undergoes thermal they may be greater at higher reaction tempera- degradation according to semi-global kinetic tures, schemes.

The interesting feature of the kinetic model (A9- The primary pyrolysis rate of small biomass parti- Al 1) is that formation of tars, chars and gases may cles, in the temperature range 200--700°C, was con- not be entirely linked so that the variation in the sidered to be the sum of the rates of main biomass percentage of volatile products and chars with the components by Koufopanos e t al. 48 Each component operating conditions can be predicted. The model contributes to the formation of the pyrolysis rate to should not be viewed as suggesting that certain experi- an extent proportional to its contribution to the mental conditions permit the entire conversion of composition of the virgin biomass. The interactions cellulose to an individual product species at the ex- among the components as well as the possible bonds pense of the other two species. 13 This is highly un- among them were assumed negligible. The kinetic likely because the rates and the activation energies model 48 for the description of the kinetic rate of each for the formation of various product species are component is schematized as: comparable (the values of the activation energies of primary reactions (A9-AI1) are reported t3 to be VIRGIN M A T E R I A L - ~ INTERMEDIATE 191,211 and 171 kJ mol 1, respectively). (AI5)

Agrawal 4~ also determined the kinetic data for the original Kilzer-Broido model (A3-A5) and a modi- INTERMEDIATE- -~ GASES + TARS fled Kilzer-Broido model with competitive reactions (A16) to form char and gas. It is shown 47 that the modified

INTERMEDIATE --~ CHAR. (A17) Kilzer-Broido model predicts well the experimental weight loss data, confirming that at low temperatures cellulose decomposition is dominated by reactions of The first reaction is similar to that proposed for formation of anhydrocellulose and tar. cellulose 43 and describes the changes in the chemical

A tentative semi-global model for primary lignin structure of the solid fuel observed at low tempera- pyrolysis has been proposed by Anta145 as a result of tures. However, the assumption of linked gas and tar his review of literature data: formation does not come from considerations based

on the chemistry of the process but simply from limitations of the experimental technique (TGA) al-

L I G N I N - - ~ CHAR + GAS (A12) lowing only weight loss measurements. Then, the pyrolysis of different biomass fuels is described ac-

LIGNIN ~-~ TAR (A13) cording to the following rule:

LIGNIN --~ GAS + REACTIVE VAPORS. BIOMASS = ~ CELLULOSE + fl LIGNIN (A 14) + ~, HEMICELLULOSE (A 18)

where ~, fl and ~, represent the contribution of each Low temperature processes (AI2) are essentially rep- component in the biomass composition. The deter- resented by dehydration reactions. At higher tempera- mination of kinetic parameters was achieved by fit- tures, the formation of a variety of lignin monomers ting experimental TGA curves with numerical solu- is described (AI3), which may undergo secondary tions of the mass balance equations for chemical degradation and condensation reactions for tempera- species. tures above 500°C. At very high heating rates, Six independent, first-order reactions for the py- fragmentation reactions are described by a further rolysis of small dry pine wood sawdust, under negligi- pathway (A14) which does not lead to char forma- ble temperature gradients, were presented in Ref. tion. Secondary char formation is, however, possible [49]. Each reaction corresponds to each main wood by the condensation of reactive vapors, component, that is hemicellulose (one reaction), cellu-

Hemicellulose is the less studied wood com- lose (one reaction) and four species describing parts ponent. It is generally believed that its pyrolysis of the lignin macromolecule (or stages in its degrada- mechanism is similar to that of cellulose 17 with the tion). In Ref. [50"1, two sets of wood thermal degrada- levoglucosan replaced by a furan derivative. How- tion data, at subatmospheric pressure, obtained at ever, experimental studies have not yet confirmed constant temperature and at constant heating rate, this supposition, were used to develop a model of weight loss rate,

Two different approaches have been employed in based on the contributions of the three main wood the modeling of the thermal degradation of complex components. Experimental studies have also been solid fuels such as wood and biomass in general. The conducted to determine the reaction rate of wood first approach considers the fuel composed of three thermal degradation, summing reaction rates for cel- chemical components, cellulose, hemicellulose and lulose and a 'second constituent' (hemicellulose and lignin, each of them present in different amounts, lignin), sl


An alternative description of the thermal degrada- for in Refs [54,57]. Diebold Is modeled tar cracking tion of wood and biomass materials considers the as two competitive reactions to form gases and solid as a single homogeneous species. In some cases, secondary tars, while Koufopanos et al. 56 describe only primary 3~'37's2 or secondary s3 reactions have secondary gas, tar and char formations as a result been studied, in other cases, both primary and second- of interactions among primary pyrolysis products. aryreactions ~5'54-57 have beenexamined. Models [53-57] assume first order reactions and

One of the most used primary wood degradation analyses indicate that tar degrades essentially to gas. mechanisms, originally proposed by Shafizadeh and Depending on reaction conditions, intra- and/extra- Chin, s8 is based on the following reactions: particle secondary reactions have a different influence

on the product yields and distributions from wood WOOD k , TAR (A19) pyrolysis. In particular, Boroson et al. 53 observed

that tar conversion is strongly dependent on reaction temperature. For residence times of 1 s, homogeneous

WOOD k2 GAS (A20) conversion is 30 wt% at 600°C and increases to 88 wt% at 740°C. They also analyzed the composition of evolved gases from tar cracking. It was found that

WOOD - - ~ CHAR. (A21) carbon monoxide is the major product at all temperatures, accounting for 50-70 wt% of the tar converted,

Experimental verification of the model and deter- with low amounts of carbon dioxide, ethylene, acety- mination of kinetic parameters require simultaneous lene, ethane and hydrogen.

An approach, similar to that proposed by Die- collection of tar and gas and measurements of bold, ~5 has been used by Anta159 to model the de- wood weight loss rate as a function of time. In Ref. [52] experimental measurements of tar, gas and resi- pendence on temperature and residence times of gas due mass fractions were made for temperatures vary- yields from cellulose- and lignin-derived volatile

matter: ing in the range 300°C-400°C, while the range of evolution time, in the estimation of kinetic param- ~,

VOLATILE ~ PERMANENT GASES eters, was chosen to avoid secondary reactions. (A24) Activation energies (A~ = 1.43 x 104 s ~, A2 =

4.1 x 106 s -1, A3 = 7.4 x l0 s s -1, E1 = 88.6 kJ V O L A T I L E - ~ REFRACTORY CONDENSABLE mo1-1, E2 = 112.7 kJ mo1-1, E3 = 106.5 kJ mol 1) are comparable, indicating only a weak dependence MATERIAL. (A25)

of the distribution of pyrolysis products upon the The first reaction produces more permanent gases pyrolysis temperature, for the small range of values by cracking the reactive material to lighter, less re- considered, active species. The second step produces refractory

Two reactions, the first for tar formation and the condensable materials, which may be a tar or some second for a linked gas and char formation, :5'54's5 combination of water-soluble organic compounds. on the analogy of the active cellulose degradation First order rates were employed and kinetic para- mechanism of Ref. [43], or a single reaction, 57 as the meters were estimated for cellulose. As for lignin, only kinetic scheme (AI'), have also been used to model the difference (El - E2)and the ratio In(A1/A2)were primary wood degradation. Finally, Koufopanos et determined. al. s6 proposed a kinetic scheme accounting for primary and secondary reactions, specifically to describe thermal degradation of large biomass particles under 2.3. Energetics o f the Pyrolysis Reactions ablation regime conditions. The kinetic model in-

eludes two primary reactions for char formation and Differential thermal analysis (DTA) has been linked gas and tar formations, respectively, with rates widely used to investigate the energetics of the ther- showing a power law dependence on virgin solid mal degradation of charring cellulosic materials. concentration and a modified, three parameter Arrhe- Some of the early results have been summarized by nius law dependence on temperature.

In general, secondary reactions describe tar crack- Roberts. 6° In general, it has been found that pyrolysis of hemicelluiose and lignin is an exothermic process,

ing to lighter gases and tar repolymerization to char: while cellulose pyrolysis is an endothermic process 'at

low temperatures and becomes an exothermic process T A R - ~ CHAR (A22) at high temperatures.12'42"49'6° Endothermic as well

as exothermic processes of wood pyrolysis reactions at different temperatures have been found (see, for

T A R - ~ GAS. (A23) example, Refs [10,32,60]). Also very large differences are observed in the measured values for the same

Studies s3'55 only consider tar cracking to light gases, pyrolysis temperature. Tar polymerization to secondary char is accounted The effects of reaction temperature on the ener-

JP£C$ 19:I-F

80 C. DI BLASI

getics of the pyrolysis of large wood samples have tion to improve the understanding of physical and been investigated in Ref. [20]. At low radiative heat chemical processes. fluxes, the process is endothermic ( - 6 1 0 kJ kg -t is Several models of chemical and physical processes the computed value). At high radiative heat fluxes occurring during cellulosic material thermal degrada- (high temperatures), even though no specific value of tion have also been published either related to fire the heat of reaction is given, it appears that the safety issues and to biomass conversion for energy. process is globally exothermic. Also, a dependence of Based on the properties of the Oregon Iodgepole the energetics of cellulose pyrolysis on the sample pine and on the two length scales of interest, that is thickness was found by Arseneau. 42 Thin cellulose the pore diameter (10 /lm), through which volatile samples exhibit endothermic degradation while thick products escape, and the characteristic size of typical samples exhibit endothermicity followed by a signifi- feed particles (1 cm), Chan et al. 64 gave an estimation cant exothermicity, of the order of magnitude of main process character-

The changes in the energetics of cellulosic material istic times, which can be used as a guideline in the degradation, as temperature and size of the sample formulation of a mathematical model. The explicit vary, are believed to be due to the different role effects of temperature on transport characteristic played by primary and secondary reactions. At low times are small while, given the typical values of the temperatures and short residence times of volatiles, activation energy (125-170 kJ mol-~), they are strong only primary (endothermic) reactions are active, on the chemical reaction rate. More complex is the while the high temperatures cause secondary (exother- implicit dependence of transport properties on the mic) reactions. Also, the occurrence of secondary pore distribution which is, in turn, dependent on charring reactions and the lower medium perme- reaction conditions. Following the changes in the ability to gas flow (that is, the increased residence medium density, a global increase in the porosity of times) may cause changes in the global energetics of a factor two is expected. Permeability and effective the process. These findings are also confirmed by a diffusivity, on the other hand, depend on the third 65 recent study s6 where, through measurements of and second order power of porosity. The increase in temperature-time history inside the degrading solid, the medium porosity lowers the transport times and it was shown that the process is initially endothermic increases heat transfer times, unless radiation is im- and then weakly exothermic. Estimation of the heat portant. Also, the volumetric thermal capacity of the of reaction leads to a value of - 2 5 5 kJ k g ~ for solid decreases with temperature because of the de- primary reactions and to a value of 20 kJ kg -1 for crease in the solid density during thermal degrada- secondary reactions, tion. In conclusion, at high temperatures, the heat

transfer rate is several orders of magnitude slower than the chemical reaction rate while, at low tempera-

2.4. Modeling of ChemicalandPhysical Processes tures, the degradation reaction rate is about four times slower than that of heat transfer. For large

Detailed mechanisms controlling transport phe- particles a zone, where the characteristic times of nomena (momentum, heat and mass transfer) as well chemical reactions and heat transfer are comparable, as chemical processes occurring during thermal con- propagates through the particle. Thus in the develop- version of wood and related substances, under abla- ment of a mathematical model both effects should be tion regime conditions, are not yet available to im- accounted for. prove fire prevention and control and to support Another important aspect of the wood degradation chemical reactor design and scale up, where the use is moisture release which is a low temperature phe- of large particle feed is preferred due to the high cost nomenon and affects local thermal properties. From of size reduction. 6~ From a practical point of view, the analysis of characteristic times it is seen that, for processes affecting thermal conversion of particles in dry particles, convective mass transport is faster than biomass reactors are related to temperature and veloc- diffusive transport, indicating that this last effect can ity fields established around the particle. The analysis be disregarded. For wet particles, since moisture in such cases is made complex by the non-uniformity evaporation occurs at temperature values much lower of temperature, species concentrations, velocity and than those allowing pyrolysis, volatile diffusion may pressure profiles and the variation of reaction rate compete with convective flow. Indeed, at this stage of along the particle thickness. In order to study the the process, the porosity and permeability have not thermal conversion from a quantitative point of view yet changed. In general, even for flow parallel to the and more controllable conditions, heating fluxes have wood grain direction where permeabilities are very been varied in the range of values 30-250 kJ m -2 s -~ large, gas velocities are rather low, resulting in gas which are of interest both for simulating fire condi- residence times sufficiently long for secondary reactions and for thermal conversion and combustion of tions to occur. The characteristic time of convective biomass. Measurements of the effects of ambient heat transfer is also very short at the microlevel and, oxygen level and heat flux on wood gasification, 6~-6a given that the solid volumetric heat capacity is about of the application of the heat flux with respect to 600 times larger than that of the gas phase, it may be wood grain direction 2°'6t gave a relevant contribu- assumed that volatile products, as they flow, are


rapidly heated to the temperature of the char (local phase processes is still made, that is the accumulation thermal equilibrium). Consequently a heat flow from of mass and energy of the gaseous species within the the solid phase char to the volatiles occurs and the solid is neglected, the gas density being three orders heat transfer towards the virgin solid region is low- of magnitude lower than that of the solid. This as- ered. sumption is removed in the model by Kansa e ta / . 67

Mathematical models, available to date, use sim- which also accounts for pressure variations inside the plifying assumptions for the description of both porous solid according to the Darcy law. Therefore chemical processes and transport phenomena. As for this model presents a rather complete description of chemical reactions, in most cases, studies of thermal transport phenomena, even though a one-step global degradation of wood and its main components have reaction is still used for the chemistry. been grouped as studies on cellulosic materials and Models accounting for multi-step reaction schemes chemical processes have been modeled according to of wood pyrolysis still make some assumptions in the a one-step, first order, Arrhenius reaction (see, for description of physics. In Ref. (64) the gas is assumed instance, more recent publications66-7°), to flow only towards the heated side of the particle

In a few cases, the description of physical processes and there is no description of mass transfer resistance. is combined with multistep reaction schemes for No convective transport of condensable species, pro- chemical processes. Cellulose decomposition has been ducts of the pyrolysis process, is included, and the modeled in Ref. [71] according to a scheme where volatile release is modeled as instantaneous (dpg/3t = the virgin solid, considered as a single species, decom- 0). Apart from the interesting analysis of the charac- poses by a first reaction into a second solid and a gas teristic time scales of the different phenomena, the and, by a second reaction, into another gas. The model is not used to make extensive simulations solid product of the first reaction may further react of the thermal degradation process. A comparison to give a final (inert) solid and another volatile between the predicted and the measured temperature species. Even though the proposed scheme was not history, at two locations along the particle thickness, based on experimental evidence, the analysis is inter- and pyrolysis product distribution for a couple of esting because it presents the first attempt to account heat flux values and particle sizes are given. for a multi-step reaction scheme in the modeling of The model by Hastouglu and Berruti 73 is quite both chemical and physical processes occurring complete, that is, all of the main chemical and physi- during cellulosic material decomposition, cal processes are included. In particular, it accounts

The assumption that the virgin solid can be de- for the non-isobaric mass transport through the scribed as a single homogeneous species has been porous medium by means of the 'dusty gas' flux made in Refs [64,72-74]. All these analyses include equation. The model also tries to account for the primary and secondary reactions for solid fuel pyroly- fibrous structure of wood by assuming that the react- sis, and use the assumption of lumping the products ing particle is made of hollow cylindrical fibres which, of degradation only into tar, char and gas. Even after pyrolysis, again leave a homogeneous charred though this is still a rough approximation, the up- solid. However the analysis is limited to chemically proach allows main experimental observations to be controlled small particle pyrolysis and only the con- accounted for. The contribution of each wood compo- version time history for several bulk stream tempera- nent is considered in Ref. [75] where kinetics of tures is given. wood pyrolysis, described according to Ref. [49], are More interesting is the analysis presented by Curtis coupled to enthalpy and moisture/vapor balances, and Miller 72 which, even if assumes quasi-steady

A different degree of approximation has also been gas phase equations and constant pressure and is employed in the modeling of transport phenomena, still focused on very small biomass particles (from The problem of the pyrolysis of a wooden sample 5 x l0 -s to 4 x 10 -2 cm), presents parametric results has always been simulated as one-dimensional, since of the effects of particle thickness, total pressure and this condition is often met in the experiments. 2°'62'63 sample heating rate. It is shown that significant gradi- Most of the analyses take the viewpoint that the ents are established within the sample, which affect porosity is fine and uniformly distributed. The mate- product yields. Secondary reactions are negligible rial is considered as a homogeneous medium, with only in the limit of very low total pressure, which specified porosity and permeability, where gas and reduces gas densities and residence times in the region solid are in good thermal contact (solid and gas are of high temperature. Also the role played by radiative at the same temperature). The simplest approach heat transfer and pyrolysis was examined by the use consists of a heat conduction equation with a source of two different models, the first using an effective term accounting for heat release due to chemical thermal conductivity and the second the method of processes, written for a non-porous, constant prop- zones. 76 This effect, for the temperatures considered erty solid. 69 71 An improvement in the description of in the analysis, was found to be negligible. transport phenomena is presented by Kung 66 and The model by Di Blasi et al.74 includes convective Villermaux et. al.,ra who also include convective heat and diffusive heat transfer, unsteady terms in the gas transfer due to the outward flow of volatiles generated phase equations, pressure variations and variable during pyrolysis. The assumption of quasi-steady gas properties. The most restrictive assumption is that of

82 C. DI BLASI

condensed phase tar species. Thermal decomposition (4) no diffusive transport of volatile species, gener- of wood indeed starts at rather high temperatures ated during the reaction process, occurs; (above 550 K), thus tar is present as gas in the (5) condensation of volatile species in the virgin pyrolysis region and in the char layer where even solid region is neglected; higher temperatures are reached. Tar might be (6) kinetic and potential energy are neglected in present as a condensed phase species only in the the energy balance equation and internal energy is virgin wood region where, after migration, volatile replaced by enthalpy; and species may condense because of the low tempera- (7) gases behave according to the ideal gas law. tures. The study was developed with the aim of The energy, chemical species mass, momentum and clarifying the role played by the different assumptions ideal gas law equations and relations giving solid generally made in the formulation of wood pyrolysis volume, porosity and medium property variations mathematical models, that is (1) one-step kinetics, (2) constitute the mathematical description of the prob- quasi-steady gas phase with constant porosity and lem: (3) constant properties. All these assumptions were -mass balance for wood species found to affect even the qualitative behavior of the dpw predictions. - - - (Kx + K2 + K3)pw (4)

The assumption of condensed phase tar has been dt

removed in Refs [77,78]. Apart from the prediction - m a s s balance for char species of the wood thermal degradation, the model has been used to investigate the coupling of heat transfer Opc

- - = K3pw + eKspr (5) and secondary reaction processes to the flow field by 0t varying wood and char permeabilities. Internal flow convection and volatile residence times mainly -mass balancefortarspecies depend on char permeability. As char permeability is decreased, for a fixed wood permeability, larger pres- 0(epT) C3(pTU) sure peaks, ahead of the pyrolysis front, and lower O-----~ + 3x - tOT (6) velocities, in the char region, are observed. Residence times of tar gases inside the char region become - to t a l continuity longer and secondary reactions are favored. The ef- O(eps) Ù(pgu) fects of the application (parallel or perpendicular to + - - = cog (7) wood grain direction) of the radiative heat flux, used dt 0x to cause thermal degradation, have also been investigated.78 - energy conservation

OT The effects of moisture vaporization have been (pwCw + pccc + e(cGp~ + CvPr)) tgt accounted for only by Chan et a1.,64 who describe the process as an additional chemical reaction and by I" OOw Op¢ ecOpC Opt Alvesand Figueiredo75 whoassumethatwatervapori _ + ( T - T o ) ~ C w ~ + Cc-- + - - + e c r - -

dt dt dt by a local moisture-vapor equilibrium relation, zation is controlled by heat supply and can be described 0t de) (

+ (pGc6 + pT)--- + (T-- To) cr + c6 Opru_ Ox /

/ . O T \ 2.4.1. Theequationsofwoodpyrolysis + u(prcT + P~C~)OT=ox Ox~ k ~ x ) + ~ rkAhk

A one-dimensional model of the thermal degrada- k= *.3 tion of a dry wooden slab in inert atmosphere sub- + ~, erkAhk (8) jected on one side to a radiative heat flux has been k=4.5

77 78 recently developed. • Effects of variable properties, - Darcy law unsteady gas phase processes, pressure and velocity

tCap variations and convective transport of tar species u = - - - (9) have been accounted for. Chemical processes have g 0x been modeled according to primary reactions (A19- A21) and secondary reactions (A22-A23). The model - ideal gas law is based on the following assumptions:

(1) the volume occupied by the cell wall sample p = p,RT/W s (10) does not change as the solid undergoes pyrolysis - V s variation (thermal swelling and/or shrinkage and surface regres- Vs (Mw + Me) sion are neglected, that is V = Vs(t) + V~(t) = const); - - = (11)

(2) the gas and the solid matrix are in local thermal Vso Mso

equilibrium; where (3) inertial terms in the momentum balance equa-

tions are negligible; e = Vd V


K = rIKw + (1 - q)Kc

• 1110. d = r /dw + ( I - r /)dc

8°°I- 5 , ' J F / A lO2O. ,1 = Mw/Mwo ~.- 7o0. I- wooo ~ / / / - 1 930.

s ~ " ~ ' ~ - ~ ' - ' C K k = A k e x p ( - - E k / R T ) k = 1,5,

6 0 0 . ~ , , , , 2~ U/__///// ..] 840. '~ Akexp(--Ek/RT)pw k 1,3 5oo. 2, ', ,, £ / / / -t 7 o. - =

8_ 400. ~ " ', "l.,~.~"v/~ /'( / -~ 660. ~ rk = Ak exp(-- Ek/R T)px k = 4 ,5

100. 390. tog = (K~ + K2)pw - eKspT

0. ~ ' ' ' 300. pw = Mw/V, pc = Mc/V .000 .005 .010 .015 .020 .025

pr = Mr~ Vg = MT/(e V), X [m] Pc = M~/VG = M~/(eV), pg = p c +Pr.

FIG. 3. Temperature and wood mass concentration as functions of the sample length from t = 3 rain and with step In the equat ions given above, pw and pc are the

3 rain. apparen t wood and char densities, px, pc and p, are the mass concent ra t ions of volatile species, u the gas

2.00 [ 400. velocity, e the porosity, e the heat capacity, T the temperature, k the thermal conductivity, K the perme-

1.80 [-, 7 - 7 - ~ ~ 360. ,=~ [.,i ,, /l C~A~' l !l i' ~ 320. abil i ty, /z the viscosity, R the universal gas constant , . . . . ~ , , ,~n,~r~, , , a W s the mean molecular weight, V the volume, M the 1.40 t t i j i I 280. ~

1;, , , , , , mass, d the pore diameter, ~ the S te fan-Bol t zmann ~ E 1 2 0 }r- s

J I f j i j - 240. ~ cons tan t and to the emissivity. The subscript 0 refers "~" ~ 1 I I I I I

1 . 0 0 I I I 2 0 0 . ~2~ x u ~ - - ~ , . , . . ~ ~ ~ - - r ~ i '~ to initial condit ions, s to solid phase, g to gas phase, .~ .8o ~ ~ ~ . . \ 16o. ff W to wood, T to tar and C to char. I" .60 ~ ~ ~ N ~ x ~ 120. ~ In the energy balance Eq. (8), the first two terms

.40 80. account for the accumula t ion of the enthalpy of

.20 ~ / 7 , / i .~/' ~~Xk, k~ 40. condensed phase and gas phase species, the th i rd and .00 ~ - " ~"" "~ ~ ~ " ~ " ' ~ ' ~ : 0. four th terms for the convective t r anspor t of the gas

.000 .O05 .010 .015 .02O .025 phase species, the fifth for the conduct ive t r anspor t of heat and the last two for the heat release associated

x [m] with chemical reactions. Radiat ive heat transfer,

FIG. 4. Tar and char mass concentrations as functions inside the solid, is described th rough an effective of the sample length from t = 3 rain and with step 3 radiative cont r ibu t ion to the thermal conductivity. 64

rain. A linear var ia t ion of the conduct ive con t r ibu t ion to effective thermal conductivity, permeabil i ty and pore

.024 30.0 diameter with the medium composi t ion, between the "~=. . p virgin wood value and the char value, is assumed.

".,- * ~.. t=3mln/ -,- - 25.0 Also, the decrease of the solid volume is propor t iona l

r . , , • . to the decrease in the mass of the solid, due to .016 - , ~ ~ ",, • I, , / - 20.0 thermal degradat ion. - . . , . , , . , j /

- - ~ " " ' • ~ * ' * , A / ~ " c ~ In order to define the problem, initial and bound- .012 - ~ ~, ,, '**,, ~ 15.0

- - , ,'. , , ; ~ / ~ . - - z ary condi t ions should also be assigned. Initially (t = - , " - , , " ,~ - 10.0 o. 0) the solid is in a quiescent env i ronment at ambient

z .ooa i ' , " " "~ condit ions: . 0 0 4 i" - " / . ~ - / - - 5.0

-" ~ T = To, p w = p w o , p = p o , u = 0 . (12)

.000 ~ ~ .0 For t > 0, the fuel slab is subjected on one side -.002 I I I I /

.000 •005 .010 .015 •020 .025 (x = L) to an assigned, constant , radiative heat flux, q. At this side, radiant and convective heat t ransfer

X [m] from the surface and cons tan t ambient pressure con-

F~G. 5. Gas velocity and overpressure as functions of the di t ions are used: sample length from t = 3 min and with step 3 min. c3 T

k * - - = q - tr(T 4 - To ~ ) - h . . . . ( T - To); p = p o Ox

k* = k~o. + k,=d (13)

k¢o, = r/kw + (1 - rl)kc + ek, where h . . . . is the convective heat t ransfer coefficient

kraal ---- o'T 3 d/to and tr the Stefan-Bol tzmann constant .

84 C. DI BLASl

.0010 [ 30. primary reactions and by Liden e t al. ss for secondary

.o008 25. reactions.

.00o6 i " ' ' - P 20. The time and space evolution of the pyrolysis o i " ~ process is shown through main variable distributions 0 ,, 15. ,~ .ooo4 i \ ~ ' - (temperature, chemical species concentrations, gas x I ,, 10. E

.o0o2 - / ,, ~ overpressure and velocity) in Figs 3-5, for certain , - / x - 5. ~ times, as a function of the distance from the heated

.o0o0 ~ o. surface. Initially the time evolution of the phenom- -.0002 - NXk, juJ enon is controlled by the increase of the temperature -.0004 j ~ at the surface as a result of the applied radiative heat

2.00 13oo. flux, while chemical species concentrations are constant and equal to the initial values, indicating that

1.60 T / 110o. no reaction takes place. As the surface temperature reaches a value of about 550 K, primary wood decom-

1.2o 9o0. _ position rates start to increase, initiating the pyrolysis x TAR ~" process. Then, for times shorter than 15 min, three w .80 t x 7o0. ~ main regions are present in the computational

I ~ domain: a virgin fuel region, a primary pyrolysis .40 xx - 500. region and a char layer.

In the virgin wood region, due to the low tempera- .o0 ,I I 300. ture values (T < 400 K), reaction rates are negligible.

.010 .015 .020 .025 The boundary between this region and the primary

X [m] pyrolysis region is characterized by a maximum in

FIG. 6. Gas velocity, overpressure, temperature and tar the gas overpressure. The location of the gas overpres- concentration as functions of the sample length for t = 3 sure peak also separates two velocity distributions,

min. one directed towards the cold side of the sample

1.00 800. (virgin wood region), the other towards the irradiated surface (pyrolysis and char regions). The maximum

.90 580. in the pressure distr ibut ion is caused by gas produc-

.80 T '2 560. tion in the very low permeability neighborhood of Lno,.~ .70 , - ' " L=:3min- 540. the boundary between reacting and non-reacting re-

x .80 - ~" 520. gions. Here, both the gas volume and the convective E .50 "~ 5O0. ~ transport are small. This is shown by the magnified

~_..40 480. view of the gas overpressure, velocity, temperature ~ .30 480. and tar concentration distributions for t = 3 min,

.20 440. reported in Fig. 6. Indeed, even though in this zone

.10 420. the temperature is still low, the concentration of gaseous species is found to be about five times larger

.00 I 400. than those in the virgin wood region, immediately

.000 .005 .010 .015 .020 .025 ahead of the maximum pressure. Notwithstanding

X [m] the significant pressure gradients in the virgin wood

FIG. 7. Reaction rate of tar formation and temperature region, only very low gas velocities are computed simulated at the maximum reaction rate position as func- because of the very low values of permeability. The tions of the sample length from t = 3 rain and with step 3 maximum pressure increases slightly with time be-

min. cause of the increased resistance to mass flow. The virgin wood region is followed by the region

On the cold side of the sample (x = 0), convective of primary pyrolysis characterized by temperatures and radiative heat transfer and zero velocity condi- in the range 400 K < T < 700 K. At these tempera- tions are considered: tures, only primary reactions, accounting for wood

k* dT degradation to tar, char and gas, are active. From - - = a ( T 4 - T ~ ) + h . . . . (T - To); u = 0. the solid phase species distribution, it appears that a 8x (14) (primary) pyrolysis wave, about 0.25 x 10 2 m thick,

propagates through the virgin solid with a decreasing

2.4.2. N u m e r i c a l s i m u l a t i o n o f w o o d p y r o l y s i s spread rate (on the average, during pyrolysis of the whole sample, the propagation rate of the reaction

In this section some results of a wood pyrolysis front is about 2 x 10 -5 m s-~). The propagation of simulation, 7a are presented. The radiative heat flux is the (primary) pyrolysis front through the virgin wood 84 kW m 2 and the fuel sample is 0.025 m thick, region is also shown in Fig. 7, where the reaction Property values are taken mainly from Lee e t al., 2° rate of tar formation and the temperature value, kinetic data are those by Thurner and Mann 5z for simulated at the maximum tar reaction rate position,


.40 / 1100. having gone to completion and secondary reactions

.38 t=Bmin~J not active, only heat transfer occurs. Given the rather 1050.

.32 / t high temperature, enhanced by exothermic secondary ~o 10oo. reactions, heat transfer in the char region occurs not

.28

.24 r4 950. only by convection and conduction, but by radiative

m E .20 900. - - From Fig. 4 it appears that primary char formation b--

.16 850. does not lead to the attainment of a constant value

.12 but a slight increase is observed as the pyrolysis front

.08 T 800. extends along the sample length. This is due to

.o4 750. primary reactions occurring at lower temperatures .00 I 700. which favor char formation. Secondary char forma-

.000 .005 .010 .015 .020 .025 tion, shown in Fig. 4, as well as secondary gas formation, are strongly dependent on the residence

X [m] times of the gas phase tar species inside the porous FIG. 8. Reaction rate of tar cracking and temperature solid matrix. Thus, the longer the residence times, the simulated at the maximum reaction rate position as functions greater the extent of secondary reactions. Formation

of the sample length from t = 3 min and with step 3 rain. of secondary char also alters the structure of the solid matrix. Indeed porosity first decreases, due to

as a function of the fuel sample length, for certain the primary wood pyrolysis, and then increases. times, are plotted. As time increases, primary reac- For heating times longer than 15 min, the primary tions occur at lower temperatures and a decreasing reaction front enlarges to the whole sample and the maximum is shown. Indeed, temperature variations decrease of permeability leads to a continuous de- of only 30 K cause strong reductions in the reaction crease in the gas overpressure until the total conver- rate because of the exponential dependence, sion of wood to char and gaseous species (t = 27

Due to the increase in the medium permeability min). along the primary pyrolysis region, the gas velocity Quantitative comparison of numerical predictions starts to increase from zero to positive values, allow- and experimental measurements is difficult because ing convective transport towards the irradiated sur- of the variation of physical properties and kinetic face. The energetics of the conversion process, heat data among cellulosic materials and the dependence convection and conduction determine the tempera- of kinetic data on experimental conditions. A com- ture distribution in this region. Tar species reaches a parison between the predictions of the model pre- maximum, as does the maximum wood decomposi- sented here and experiments by Lee et al. 2° is, tion rate, and goes to zero as the temperature de- however, given by Di Blasi and Russo. 78 Good quan- creases, towards the virgin solid region. A smoother titative agreement is obtained for temperature and decrease in the tar distribution is observed at the pressure distributions for short times as long as boundary between the pyrolysis region and the third variations in the physical structure of the solid are region of the computational domain, the char layer, not significant. Both theory and experiments predict characterized by temperatures larger than 700 K. a maximum overpressure but, whereas the model

Tar concentration values along the char layer are simulates a propagating pressure front with a slightly the result of convective transport, which, given the increasing maximum, in the experiments the propaga- larger permeabilities, is much more active, and of tion of the pressure front occurs with a decreasing secondary reactions. The occurrence of secondary maximum. The char permeability is not constant (as reactions, as volatiles are convected through the al- in the model) but increases with time, due to crack ready charred zone, is confirmed by the distribution formation, and the char layer thickness, due to sur- of reaction rates of tar cracking to lighter gases, face regression and internal shrinkage, is narrower. reported in Fig. 8 for certain times as a function of The decrease of char permeability leads to a decreas- the distance from the irradiated surface. The figure ing maximum overpressure while the reduced char also shows a variation of 150 K in the temperature layer thickness leads, on average, to slightly larger values simulated at the location of the peak in the temperature values. Finally, predictions and measure- reaction rate. As time increases, the secondary reac- ments of the time history of total gas production tion front slowly enlarges through the char layer show fairly good agreement. with a decreasing maximum in the reaction rate and then propagates behind the primary reaction front.

Thus two subregions can be seen in the char layer, 2.5. Non-Charring Materials the first characterized by very high temperatures (800 K < T < 1100 K) where both secondary reac- Complete degradation of some thermoplastic poly- tions and heat transfer take place, and the second mers occurs with breaking of the main chain and no characterized by lower temperatures (700 char formation, so that heat transfer conditions at K < T < 800 K), where the primary reactions the condensed phase/gas phase interface do not

86 C. DI BLASI

change, allowing degradation and pyrolysis processes tion initiation, propagation of reaction chain and to be studied under quasi-stationary conditions, termination. Depolymerization is believed to initiate Quasi-stationary conditions, of course, cannot be at chain ends, at random points along the chain, or established for char-forming polymers because heat at isolated 'weak links'. 81 Free radicals, formed and mass transfer processes are strongly affected by during initiation, give rise to unzipping, that is, the the formation of the char layer. In this review, propagation of the reaction chain. Chemical pro- PMMA degradation will be briefly analyzed because esses at this stage may be characterized by the length this material has been widely used to investigate of the reaction chain, that is the number of monomer flammability limits and flame spread characteristics units produced on average for one initiation. Termina- both experimentally and theoretically. A more exten- tion reactions account for the stabilization of free sive review of thermal pyrolysis of thermoplastic radicals which occurs through the combination with polymers was presented by Khalturiskii and Berlin 79 an H atom. The abstraction of an H atom can occur with reference to experimental techniques, surface either from an inactive chain, thus causing another temperature measurements and modeling of apparent initiation, or at a random point along the chain, or kinetics, from the same chain of the free radical, leading to

On dependence of heating exposure, two types of products larger than the monomer unit. thermal degradation of PMMA can be observed: 79 Kinetic modeling studies of PMMA degradation isothermal bulk degradation and surface degradation can be divided into two main categories: or linear pyrolysis, which, respectively, correspond to (1) One-step global models which employ a one- the chemical regime and the ablation regime, previ- step, global, Arrhenius rate reaction to account for ously introduced for charring materials, all chemical processes. Such an approximation has

When PMMA is exposed to a radiant flux, under been used both with the description of physical pro- linear pyrolysis conditions, a narrow layer, near the esses, to model solid phase processes only, and also heated surface, liquifies. Small clusters of degradation in all computer models which couple solid phase products must escape from the surface. Since the processes (degradation and usually heat transfer) to boiling point of the degradation products is much gas phase combustion and transport phenomena. less than the polymer degradation temperature and Studies on PMMA degradation which model since a significant quantity of only partially degraded chemical processes by means of a one-step global polymer is still available at the surface, the degrada- reaction have been employed both for isothermal tion products are superheated. Consequently they bulk degradation and linear pyrolysis. Explicit rela- nucleate and form bubbles which grow due to mass tions were given between surface regression rate and diffusion through the molten layer, mass vaporization surface temperature, in the limit of large activation and thermal expansion. 6 Furthermore, because of the energies, al This treatment is based on the assumption higher temperatures, the degree of superheating and that the linear pyrolysis mechanism is the same as bubble nucleation rate increase while surface tension that of homogeneous bulk degradation. The study by decreases, as the surface is approached. Transporta- Krishnamurty and Williams 82 makes the same as- tion of bubbles from the interior of the polymer sumption since it uses a pre-exponential factor and towards the surface is also affected by the existence an activation energy, developed for bulk degradation, of viscosity gradients, a° Bubbles very close to the for correlating linear pyrolysis data. The extrapola- surface are able to burst directly through it while tion of the isothermal bulk degradation kinetics data those well below burst through small holes. The size to the range of regression rates observed in the linear and rate of formation of bubbles depend on the pyrolysis is, however, considered invalid. 79 This is polymer characteristics and environmental condi- confirmed by a comparison of the measured time tions, in particular the oxygen level. 6 The presence of evolution of surface temperature and mass loss rate. a3 oxygen in the environment causes a lower viscosity In fact, mass loss rate, for linear pyrolysis, still in- of the molten layer, with higher bubble frequency, creases while the surface temperature reaches a con- Formation of large holes, caused by burst bubbles, stant value. This indicates that the mass loss rate extends the effects of the oxygen level to the interior cannot be related to the surface temperature through of the sample, an Arrhenius expression. Therefore the sub-surface of

Even under conditions of bulk degradation, the the sample contributes to the rate of gasification. gaseous degradation products should escape from (2) Detailed degradation models where kinetic the molten polymer, but experiments are conducted schemes, accounting for chain initiation reactions, with thin samples in order to avoid making transport depropagation reactions and termination reactions, phenomena the rate-controlling step for weight loss. have also been proposed. Such models have never

been coupled to the description of physical processes. Studies belonging to this second group are those

2.6. Kinetic Modeling performed by Kashiwagi et al. s4 as PMMA depolymerization, under vacuum conditions, may initiate

In general, the degradation of PMMA occurs ac- at chain ends or at random points, the former mecha- cording to the following main stages: depolymeriza- nism being favored at low temperatures, the latter at


high temperatures. Possible sources of random scis- tions in the limit of low Reynolds numbers and sion were analyzed in Ref. 1-89]. In Ref. [84] the under the assumption that surface tension forces mechanisms of thermal and oxidative degradation dominate buoyancy forces. After the bubble has nucle- were investigated by measuring the molecular weight, ated, the expression for the growth rate is obtained For both thermal and oxidative degradation, random by an approximate balance between the rate of heat scission is the initiation step. However, the oxidative flow into the bubble from the liquid and the latent environment causes a much faster reduction in the heat required to supply bubble vapor. By means of degree of polymerization, and the activation energy, the translational velocity and the bubble growth rate for random scission of polymer chains, was about expressions, the bubble distribution function is deter- four times lower than that for degradation in nitro- mined. For this derivation it is assumed that bubbles gen. A further study on the effects of oxygen on are spherical and that the rate of binary bubble PMMA degradation was presented in Refs 1,85,86] collisions is negligible. The expression, giving the through the measurements of weight loss and molecu- bubble distribution function, is coupled to the bal- lar weight. Oxygen has a different effect on the tem- ance equations for the melt layer through sink terms perature dependence for polymer degradation: at low which describe, on average, the effects of bubble temperatures the stability to loss of weight is in- distribution on mass, energy and momentum transfer creased whereas at high temperatures random scis- from the liquid to the bubbles. sion is enhanced with a decrease in the polymer Expressions for the regression rate, the non-dimen- stability. A theoretical model of thermal degradation sional melt velocity and the liquid volume fraction of PMMA 87 accounting for three main chain reac- were obtained by means of the method of matched tions: (1) random initiation, (2) depropagation of free asymptotic expansions. The regression rate was the radicals and (3) termination of free radicals, has also result of a balance between the surface heating rate, been proposed. Numerical solutions of a large system the rate of heat removal into the condensed phase of ordinary differential equations allow the changes and the rate at which the monomer is lost from the in the molecular weight distribution and in the polymer with bubble formation. sample volume to be predicted as a function of the initial molecular weight, average zip length, etc. The assumption of a steady state radical concentration 3. GAS PHASE COMBUSTION PROCESSES made in Ref. 1,87] was removed in Ref. 1-88].

A mathematical model of ignition and flame spread over solid fuels should include the description of

2.7. Modeling of Chemical and Physical Processes transport phenomena and chemical processes occurring in the solid and gas phase and should account

Most of the models of thermoplastic polymer degra- for their interaction. Fuel vapors, produced by solid dation, available to date, are based on a simple fueldegradation, mix with air and, under appropriate energy balance equation for the solid with degrada- conditions, form a flammable mixture above the sur- tion localized at the surface, and have been coupled face. At the same time, the gas layer, adjacent to the to gas phase equations for simulating flame spread, surface, is also heated by both heat conduction from The very few models, specifically formulated for im- the solid and, sometimes, the same external source proving the knowledge of solid phase chemical and used to heat the solid. As a consequence of the physical processes, will be reviewed here. heating and the existence of a flammable layer in the

Vovelle et al.S3 proposed a model of the mass loss gas phase, the rate of exothermic gas phase reaction rate of PMMA, subjected to a radiant heat flux, rapidly increases together with the heat release rate. based on a constant property one-dimensional energy A runaway condition can be achieved and ignition equation accounting for in-depth degradation of the occurs (auto-ignitionT), or ignition can be caused by solid. Surface regression was modeled by introducing an external device such as a pilot flame. In this case, the Landau transformation. A comparison of simu- the flame may be quenched by heat losses at the lated and measured temperature profiles shows good surface once fuel vapors have been depleted (flash) or, agreement. Surface temperature is predicted to un- if enough heat is supplied to the solid, it may become dergo a rapid increase followed by the attainment of a sustained diffusion flame (piloted ignition91). a constant value which depends on the incident heat Sometimes ignition is only the first step of further flux. gas phase combustion processes, such as flame

The effects of bubbles inside the molten layer on spread. The exothermicity of gas phase reactions and the steady-state transport ofvolatiles, during degrada- of possible oxidation reactions inside the solid fuel tion of thermoplastic polymers, have been predicted cause a heat flux that, through solid and gas phase by means of a one-dimensional model in Ref. (90). processes, heats the unburned fuel. To have flame The model includes the description of individual spread, the burning region must supply enough heat bubble characteristics in terms of translational veloc- to the unburned solid to cause degradation. At the ity and growth rate. The translational velocity is same time, proper conditions in the gas phase should determined from the steady-state Navier-Stokes equa- be met. In fact, flame spread characteristics are af-

88 C. DI BLASI

fected not only by the mechanisms of solid degrada- Another important factor for flame spread proc- tion but also by other factors, such as the flow esses is fuel thickness. In general the definitions of configuration, oxygen level and orientation of the 'thermally thin' and 'thermally thick' fuel are used. 92 solid fuel. The term thermally thin indicates that the fuel thick-

Flame spread over solid fuels can be classified into ness is small compared to the characteristic thickness two main categories according to flow conditions. 92 of the thermal diffusion layer in the solid, along One mode occurs when flame spread is in the same which no significant variation of solid properties is direction as the oxidizing flow (flow assisted flame observed. Depending on the thickness of the solid spread). The second mode occurs when the flame fuel, the role played by the solid fuel thickness in the spreads against the oxidizing gas flow (opposed flow path for heat transfer, through the solid, to the un- flame spread), burned fuel changes from being of negligible impor-

In the flow-assisted mode of flame spread, the tance for thin fuels to becoming of primary impor- concurrent flow pushes the flame ahead of the vaporiz- tance for thick fuels. If the combustible is thin, flame ing fuel surface. The heat transfer from the hot mix- spread is further characterized by the consumption ture of reacting gases and the combustion products of the solid fuel in the burning region. This produces above the vaporized region to the unburned fuel a propagating burn-out front which affects the flame surface favors the propagation of the flame. The and pyrolysis front propagation. resulting flame spread process is very rapid and conse- Material properties influence the behavior of the quently of great importance to fire safety science. For sample under fire conditions. Most experiments on a very large range of flow velocities and oxygen flame spread over thick solid fuels have been carried concentrations, this phenomenon appears to be con- out with PMMA, a non-charring material, while trolled simply by heat transfer mechanisms. 92 How- experiments related to thin fuels have mainly used ever, the flow remains laminar only in the initial paper, a charring material. stage when heat transfer from the flame to the fuel is Gas phase combustion processes are very compli- due mainly to convection. When the dimensions of cated because of the very high number of chemical the flame increase, the flow becomes turbulent and species evolved from degrading solid both for cellu- flame radiation appears to be the dominant mode of losic materials and thermoplastic polymers. For exam- heat transfer, ple, in the flame above PMMA surfaces, 95 apart from

In the case of opposed-flow flame spread, the heat the fuel monomer, these include hydrogen, methane, transfer to the unburned fuel is more difficult since ethane, ethylene, acetylene, propene, propylene, allene, the flame and pyrolysis fronts are in the same loca- propyne, methanol, formaldehyde, carbon monoxide tion. The opposed flow pushes the flame into the and possibly some fuel-produced carbon dioxide. Few burning region, and heat transfer to the unburned attempts have been made to investigate the detailed fuel, which occurs through solid or gas phase conduc- structure of the flame 95'96 and, for PMMA, to pro- tion, is very slow. The flame front is well defined and pose a detailed mechanism of gas phase thermal generally the size of the fire is easily controlled. The decomposition. 95 On the other hand, numerical mod- phenomenon shows an interesting dependence on eling of hydrocarbon fuel oxidation is becoming possi- environmental conditions: 92 it is dominated by heat- ble for many types of fuels. Reaction mechanisms are transfer mechanisms at relatively low opposed-flow extended over wide ranges of experimental conditions velocities and high oxygen concentrations and by and are being used for problems of much greater chemical kinetics at high flow velocities or low complexity than those addressed previously 97 but oxygen concentrations, numerical models of combustion processes of solid

Ignition and flame spread processes strongly phase fuels have always described gas phase oxida- depend on the presence of gravity and, in a normal tion chemistry by means of a one-step global reaction. gravity environment, on the orientation of the solid. 92 There are two reasons for this simplification. The Upward flame spread, that is, in the direction op- first is that it is generally acknowledged that the posed to the gravity vector, is faster than downward fundamental process of solid fuel combustion is con- flame spread, that is, in the same direction as the trolled more by physical mechanisms (heat transfer gravity vector. In the case of upward flame spread phenomena) than chemical mechanisms. 98 In the the heat transfer from the hot combustible gases to second place, in order to apply detailed kinetic the fuel is enhanced by natural convection while, in models for gas phase combustion, a very accurate the opposite case, natural convection slows the description of the chemistry of solid degradation is spread process, taking away the hot combustion prod- needed, that is accurate predictions of evolved com- ucts from the unburned fuel. Upward and downward bustible volatiles have to become available. In some modes of flame spread show the same characteristics way, solid phase models should give the 'input', of flow-assisted and opposed-flow flame spread. Dif- through the boundary conditions at the solid/gas ferent characteristics of spread are observed 93'94 in interface, for detailed modeling of gas phase combus- microgravity environments when no natural convection processes. However, as stressed in the first part tion is present; radiative heat losses are believed to of this review, only global or semi-global kinetic play an important role. models and composition of evolved gases under speci-


2800.0 tic conditions are available. Recently, an attempt solid f ~ (-'~ gas has been made to estimate the kinetic constants for

pyrolysis, thermal oxidative degradation and char 23oo.o oxidation for cellulosic materials. 99 Yields of CO,

total hydrocarbons, char and products (CO2 and 1800.0 H20) from each reaction have also been evaluated.

T[K] The study is interesting in that it represents the first

~ i l ! i l ~ i ~ ~ step towards the introduction of two gas phase oxida- 1300.0 12.6 " tive reactions, one for total hydrocarbons and the

12.4 other for CO, instead of the one-step reaction usually 12 ~ employed. ooo

The guidelines of this part of the review are essen- . . tially those followed in Ref. [100]. Analyses of recent

300.0 simulation results of auto-ignition as well as piloted -.7 0.0 20.0 40.0 x[cm] ignition will be presented. Then, the characteristics of

computer models of flame spread available to date and FIG. 9. Solid and gas phase temperature as functions of the some results of numerical simulations will be analyzed.

space coordinate for several times (s).

3.1. Modeling and Simulation of lgnition Processes

yl.O 8 ~ [ The simplest mathematical models of ignition only consider one-dimensional solid energy balances and use ignition criteria based on the solid surface reach-

" ing a 'critical' temperature. Asymptotic techniques, valid in the limit of large activation energies, have

i I ~ ~ ~ been applied for the solution of more advanced one- dimensional models, including finite-rate gas phase kinetics. 1°L1°2 A numerical solution of the problem

• is presented in Ref. 1-103]. Although in Refs [101-103] equations both for the

.2 l ~ ~ ' - ) S f / l ~ / ' - solid phase (energy balance) and gas phase (chemical species mass and energy) are solved to model non-

0 0 [6t( ~2"~k-~x'~k'l"~'~'~/~'~ 15 charring solid radiative ignition, the gas phase absorption of radiation is not accounted for and the only

0.0 20.0 40.0 mechanism that can lead to ignition is heat conduc- x[em] tion. Consequently, such models predict ignition only

FIG. 10. Fuel (solid lines) and oxygen (dashed lines) mass if very high surface temperatures are reached or if fractions as functions of the space coordinate for several high reaction rates are simulated. This last condition

times (s). can be achieved only by the use of values for kinetic parameters which are not realistic and thus not useful for comparisons with experimental data. The model

9o.o proposed by Fernandez-Peilo and coworkers t°4 is interesting in that, for the first time, they tried to

75.0 account for gas phase absorption of radiation in an 12.61 oxidizer stagnation point flow. However, solid phase

6o.o processes are not described at all and the temperature u [cm/s] I \ at the solid/gas interface is assumed equal to an

45.0 ~ 3 estimated vaporization temperature. Solid phase processes are described in Ref. [105].

3o.o Thermal radiation is absorbed in-depth by the solid fuel according to the Beers's law. Solid degradation is also an in-depth process, and is modeled with a zero-

15.0 15 order Arrhenius rate reaction. The density and the

5 . solid properties are constant while surface regression 0.0 is described, in the solid energy balance equation, by 0.0 20.0 40.0 a convective term formed by the product of the x[cm] regression rate and the temperature gradient.

FIG. 11. Velocity as a function of the space coordinate for The radiation available for heating the solid fuel several times(s), decreases with time because, as fuel vapors are

90 C. Dl BLASI

produced, they absorb some of the incident radiation, front, giving a premixed zone from t = 12.61 s (Fig. A treatment, valid in the limit of an optically thin 10). As long as a premixed zone exists ahead of the medium, has been applied to describe such a process, flame front, the flame shows a quite high propagation that is the absorbed radiation is proportional to the rate, decreasing with time according to the decrease fuel vapor concentration and the radiation intensity: in the temporal gradient of density, velocity, and

amount of fuel ahead of the flame front. For t > 15

dI~ f f ' t~x -- flpflg = fllopfexp -flpfdx (15) s, the premixed zone ahead of the flame no longer exists and the typical structure of a diffusion flame is observed. As ignition occurs in the gas phase, the

where pf is the partial pressure of fuel vapors and f l a heated layer in the solid increases. constant, global absorption coefficient. The predicted ignition delay time as a function of

The gas phase mathematical model includes one- the intensity of the radiative heat flux shows rather dimensional continuity, mass balances for chemical good agreement with experiments, and gas phase species, an energy balance and the ideal gas law, absorption of radiation is found to play a controlling written under the assumptions of unit Lewis number, role for ignition. The dependence of the ignition constant specific heats, thermal conductivity and pres- phenomenon on kinetic parameters 1°5 has also been sure. A second-order finite rate Arrhenius reaction is simulated. used to model combustion. Numerical solution of A one-dimensional ignition model of PMMA, ex- the problem is simplified through the introduction of posed to a radiatively active high temperature source, a Lagrangian coordinate which uncouples velocity has been proposed by Back and Kim. 1°6 Even from the other unknown variables, though in-depth degradation and surface regression

An example of the simulated ignition phenom- of the solid are neglected, the vaporized fuel absorbs, ena 1°5 for PMMA, radiatively heated with a heat emits and scatters radiation. Ignition delay times are flux of 8.3 W cm -2, is shown through Figs 9-11, found to be dependent on temperature and emissivity where solid and gas temperature, fuel and oxygen of the hot surface but not on the distance between mass fractions and velocity are reported as a function the fuel surface and the hot source. of x for selected times. Until t = 5 s, the solid fuel Gas phase ignition of cellulosic materials has re- absorbs all the external radiation and displays tern- ceived less attention than PMMA. A very simplified peratures higher than those of the gas phase. When description of radiative ignition for such materials is solid phase temperatures larger than 600 K are proposed by Ghandi and Kanury. 1°7 Finite rate py- reached, the degradation process starts and, as the rolysis (first order) and combustion (second order) fuel vapors diffuse, they also absorb some of the reactions are considered. The assumptions of the external radiation in the gas, which shows tempera- Boussinesq approximation (constant gas phase den- tures higher than those of the solid. Because the sity except for variations due to buoyancy) and of a amount of absorbed radiation depends on the thick- well-stirred boundary layer in the longitudinal direc- ness of the fuel layer and the fuel concentration, the tion reduce the mathematical model to the constant temperature in the gas phase shows a maximum at property and constant pressure one-dimensional flow 2.5 cm from the surface for t = l0 s. Until this time, equations. Solid phase processes are described by the the reaction rate is negligible and no disappearance transient one-dimensional heat conduction and mass of fuel and oxygen is observed. Both of them, indeed, balance equations. A mixed analytical/numerical up- give rise to a flammable mixture layer 7.5 cm thick, proach is used for the computation of the solution. Ignition occurs for t = 12.61 s and is characterized The analysis of the simulations has allowed the by a large instantaneous increase in the gas tempera- validity of the ignition criterion based on a reverse in ture (the temporal gradient of gas temperature is the sign of the gas phase temperature gradient at the about 70,000 K s -~) and by a noticeable consumption solid/gas interface to be assessed. of fuel and oxygen. Because ignition occurs in the gas Piloted ignition has been simulated in Ref. [91]. phase (about 3 cm from the surface) and a flammable Solid phase processes are modeled through the formu- mixture layer is present, the propagation of two lation of boundary conditions on temperature and flame fronts, towards the surface and towards the chemical species to describe fuel injection through a unreacted gases, is observed. Oxygen, close to the porous plate at a known temperature. The problem surface and in the whole mixture layer, is burned is thus described through one-dimensional gas phase very fast. Then the former flame front approaches the equations accounting for combustion processes by surface and the latter continues to propagate. The means of a second order, one-step irreversible Arrhen- thickness of the fuel layer under the propagating ius reaction. Simulations of piloted ignition show a flame front increases and absorption of external radia- time evolution of main variables in some way similar tion makes the temperature rise. Ignition is also to that observed for auto-ignition with a premixed characterized by strong temporal gradients of density flame, propagating both towards and away from the that cause high gas phase velocities, as shown in Fig. porous plate. Furthermore, the effects of the ignition ! 1. High gas velocity and spatial fuel concentration source location, the fuel flow rate and the tempera- gradients, push fuel ahead of the propagating flame ture at the surface have been investigated.


3.2. Flame Spread Modeling terms, when momentum balance equations are included in the mathematical formulation of the prob-

In order to simplify the mathematical treatment of lem, is neglected. Pressure variations in space are the problem, early studies of flame spread employed very small and, since in general the system is open, several assumptions. The most commonly used ap- the mean pressure reduced to the specified ambient proximations are constant surface temperature of the pressure. As in Ref. I-112], the pressure excess with solid during thermal degradation, a flame sheet and respect to the ambient value is neglected in the state a boundary layer. The assumption of constant vapori- equation, while it is retained in the momentum equa- zation temperature has been criticized since, although tions. The decoupling of the momentum equations solid fuel reaches constant surface temperature in the from the state equations cuts off the acoustic waves pyrolysis zone during the vaporization process, this and the determination of the pressure field becomes value depends on material properties, ambient pres- an elliptic problem. Apart from Ref. [113-1, no model sure and temperature, solid fuel thickness and heating of flame spread accounts for gas phase heat radiation conditions. The flame sheet assumption implies the losses. existence of an infinite gas phase reaction rate, To date, flame spread models numerically solved whereas boundary layer theory assumes that diffusive and treated the velocity field differently. The simplest processes along the streamwise direction are less models consider the solution of species and energy important than those occurring in the cross direction, equations assuming that the gas density and pressure However, at the flame leading edge, both for opposed are constant and the velocity field is known.l ~4-12~ flow and flow assisted flame spread, and at the flame The streamwise component of velocity is assigned tip, for flow assisted flame spread, the assumptions of according to a chosen profile, while the effects of the infinitely fast kinetics and boundary layer are not jus- mass outflow from the vaporizing surface on the tifiable, a°° velocity field are neglected. Consequently, these

Extensive literature on simplified models, reviewed models account essentially for thermo-diffusive as- in Refs [8,108,109], is available. Sometimes explicit pects of flame spread phenomena. The computational expressions for spread rates have been obtained. Gen- costs are very low and have therefore been widely erally, these formulae are able to describe qualita- used. Predicted values of the opposed-flow spread tively the dependence on environmental conditions rate depend strongly on the velocity profile used in and property values of the solid fuel, when phenom- the computations. However, the use of flow fields ena are controlled by heat transfer mechanisms, assigned according to the Oseen hypothesis (uniform Simplified models of flow assisted flame spread, velocity profile) and to the Hagen-Poiseuille profile still based on the boundary layer and infinite (parabolic velocity profile) do predict the same func- kinetics assumptions, have also been recently tional dependence of the spread rate on the maximum proposed. 1 lO.111 oxidizing flow velocity 122 as observed in the experi-

More comprehensive mathematical models include ments. balance equations for both gas and solid phases and A second type of model, 123 which has been used to remove some approximations. These more complete simulate flame spread, assumes the Boussinesq ap- models are not amenable to analytical solutions and proximation for the formulation of the momentum it is necessary to use numerical approaches. Detailed equations. With this approximation, the pressure can mathematical models, solved numerically, do not give be decoupled from the velocity field if the unsteady explicit expressions for global parameters. On the Navier-Stokes equations are expressed in vorticity contrary, these can be derived from the predicted and stream function transport form and the continu- time and space evolution of the phenomenon, often ity equation is identically satisfied. by means of the same approaches used in experi- The most complete models are those which con- ments, sider the solution of the full Navier-Stokes equations

with density and pressure variations. 113. ! 24-131

3.2.1. Gas phase models As for the numerical techniques, all differential models of flame spread have been approximated to

Models of flame spread are two-dimensional bal- systems of algebraic equations by means of finite ance equations for the gas phase coupled through differences. Details on the numerical schemes and the boundary conditions at the interface to solid solution proceduresaregiven in Ref. [100-1. phase balance equations. As for the gas phase, most Models of flame spread essentially differ in that advanced models published to date, include momen- they use either steady l13-115A24-129'lal or turn, energy and chemical species mass balance equa- unsteady~ tr-tz3,130 formulations of the gas phase tions. All analyses are for laminar flow, and finite equations. They can be roughly classified as: (a) rate combustion kinetics are described through an quasi-steady, constant spread rate models, (b) quasi- overall, second order reaction: F + voO ~ vpP. Vis- steady, variable spread rate models and (c) unsteady cous dissipation and compressive work are neglected, models. Furthermore, the coupling between the momentum Quasi-steady, constant spread rate models. From a equations and the state equation due to pressure rigorous point of view, flame spread is an unsteady

92 C. DI BLASI

phenomenon. However, a quasi-steady treatment of ment of the coupling between pressure and velocity, the gas phase equations can be used, based on the which is the most critical aspect to be faced in the fact that the characteristic evolution times of the computation of the numerical solution, can be solid are much longer than those of the gas phase, avoided. Compressible Navier-Stokes equations may given that the flame spread rate is much smaller than be again formulated in terms of two equations for the gas velocity. In this approach, gas phase condi- the vorticity ~ and the stream function ~,: tions can be considered as a series of steady states resulting from small changes in the solid.~ 14 Besides ~ux = pu ~u r = - p v ~ = uy - ux.

the assumption of a steady gas phase, if a reference In this way the continuity equation is identically frame attached to the flame front is employed, the satisfied even though the gas density varies with flame becomes stationary, while the oxidizing environ- temperature. The calculation of the pressure field is ment and the solid fuel move towards the flame with not required for the computation of the velocity field: velocity equal to the spread rate. It should be ob- if desired it can be readily computed from a Poisson served that such a formulation is possible only under equation, obtained by taking the divergence of the the assumption of constant spread rate. The flame momentum equations. spread rate becomes an eigenvalue of the problem Unfortunately, apart from the model in Ref. [131], and it is not known a priori. From a computational all models of flame spread, based on the assumption point of view, a reference velocity is introduced as an of quasi-steady gas phase processes, do not use the initial guess, then its value is continuously adjusted compressible vorticity-stream function formulation in order to meet the true value of the spread rate. of the Navier-Stokes equations. Numerical methods Most of the numerical models of flame spread belong used to solve the momentum equations account for to this category. ~13'~24 129 Also, the models of Refs the pressure-velocity coupling by iterating the solu- [132-135], used to predict the thermal and convective tion for each time step, according to the SIMPLE structure of a diffusion flame in a counterflow environ- and SIMPLER approaches.137 Iteration procedures ment, can be included in this category. In these are not only very expensive in terms of computer models, only the gas phase equations are solved and time but convergence is not always guaranteed, unless solid phase processes are described by boundary a d h o c u n d e r r e l a x i n g f a c t o r s a r e u s e d . 138'139 conditions at the solid/gas interface. Using this ap- Unsteady spread rate models. The problem becomes proach, the most important feature in the modeling more complex from a numerical point of view when of flame spread, that is, the coupling between the the full unsteady Navier-Stokes equations with den- degradation of the solid fuel and the gas, is not sity and pressure variations are to be considered. described. However, interesting information has been Such a formulation is the proper one to be used for obtained on the extinction and blowoff of diffusion highly unsteady gas phase combustion processes such flames, as ignition and, sometimes, extinction. The coupling

Quasi-steady, variable spreadratemodels . The math- between pressure and velocity cannot be avoided, ematical formulation of model equations adopted in however an effective technique which avoids itera- Refs [113,124-129"1 allows only predictions of con- tions by splitting computational operations into few stant spread rate problems. However the spread rate steps, was proposed by lssa for non-reacting is not always constant. For example, in concurrent flOWS. 138'139 This technique, named PISO (Pressure- flame spread over thin solid fuels, an asymptotic Implicit with Splitting Operators), has been applied value of the spread rate is achieved only after a for simulating opposed flow flame spread. ~3° relatively long accelerative stage. 136 Of course, The PISO technique is an extension of classical models [113,124-129] cannot predict such behavior, splitting procedures used to solve discretized equa- To retain the unsteady character of the spread rate, tions, such as ADI, to the treatment of the coupling however, it is sufficient to use a fixed coordinate between pressure and velocity in the momentum system, that is to write unsteady balance equations equations by predictor-corrector steps. One predictor for the solid phase only, by making use of the quasi- and two corrector steps are considered. Starting from steady approximation for the gas phase. Thus, as the a known pressure field, the velocity distribution is solution in the solid is advanced of a time step, a new computed by an implicit solution of momentum equa- distribution of gas phase variables is determined. The tions (predictor step). In general, this velocity field spread rate does not appear any longer in the balance does not satisfy the continuity equation. Hence a equations and can be determined from the distribu- corrector step is performed where a new pressure tion of simulated time evolution of the main variables distribution is computed by means of the latest avail- (for instance, from the different positions of the flame able velocities. Then the flow velocities are updated leading edge). This approach has been used in early and temperature and species mass fractions are also thermo-diffusive models by T'ien ~ ~4.115 and, more computed. At this point, the continuity equation is recently, in the formulation of a more advanced satisfied but to improve the accuracy of the solution, model, including the Navier-Stokes equations. T M An- a new corrector step for pressure and velocities is other very important point to be observed is that, if performed. It is possible to demonstrate that solu- the steady gas phase equations are written, the treat- tions obtained with one predictor and two corrector


steps are second-order accurate in time. ~ss'139 A cal reaction. On the contrary, the model proposed by higher formal order of accuracy can be reached by Kung 66 for wood pyrolysis, was adapted to describe increasing the number ofcorrector steps, thin paper degradation in Refs [121,131]. As the

solid pyrolyzes, the density, specific heat and thermal 3.2.2. Solidphase models diffusivity change from their initial values to their

final values for the char. The fuel vapors, flowing out From a mathematical point of view, models of of the solid immediately after vaporization, are in

thermally thin fuels can take advantage of the uni- thermal equilibrium with the char. Also, the char formity along the fuel thickness, observed in the surface is at the same location where the virgin solid experiments, and use one-dimensional balance equa- surface was, but the burn-out front propagates as tions. However fuel consumption (burn-out) cannot burning occurs. The energy balance accounts for the be neglected. Two-dimensional heat transfer must be variation of the solid fuel enthalpy, energy convection taken into account for thermally thick fuels but, in due to the flow of volatile gases through the porous this case, fuel consumption is generally neglected, solid, heat diffusion along the direction of flame Modeling fuels of intermediate thickness is very diffi- propagation, and energy release due to the pyrolysis cult and both two-dimensional and solid consump- reaction. tion effects are important.

The complex models of chemical and physical pr0c- 3.2.3. A mathematical model of flame spread esses presented for thermal degradation of charring

materials have never been used together with gas An example of a mathematical model accounting for phase models to simulate flame spread. Also, the main chemical and physicalprocessesofflame spread models of flame spread over PMMA do not account over thermally thick solid fuels, based on unsteady for the effects of bubble formation in the degrading gas phase equations, has been proposed in Ref. [130]. solid. Very simple descriptions for the solid phase Apart from basic assumptions, already outlined in processes have been used. Thermally thick materials Section 3.2.1, constant thermal properties and vis- were modeled by neglecting in-depth mass transfer cosity and validity of the ideal gas law are assumed. and the regression rate, by describing the chemical Gas phase equations are written for: kinetics with a one-step Arrhenius reaction, and including heat transfer. 116 12o,122,123,13o,131 In the -cont inui ty

modeling of cellulosic materials, char formation was Op O(pu) O(pv) described in a very simple fashion and only for thin - - + + = 0 (16) fuels.113 115,121,124 131 0t 0x dy

Thermally thick fuel models assume that the heated - momentum along the x direction

polymeric fuel remains solid until it finally gasifies at the surface according to a zero-order Arrhenius pyroly- (On uOu your= ~p fOZu ~2u~ sis reaction giving the corresponding monomer. In P ~t + --t3x + 0y/ ' ---63x + /.t k~xx 2 + ~y2] such a way, the use of a vaporization temperature is p 3 (On O~y) not needed and the temperature at the interface, which + 3 ~x \~xx + - g(p - po) sin 0 (17) depends on fuel properties and environmental condi-

tions, is found as a result of the solution. The external - momentum along the y direction thermal radiation, which is used to cause ignition, is absorbed by the solid fuel according to Beer's law. (Or uOv vOv'] Op fO2v 02v " ] Heat capacity, thermal conductivity and density are P ~t + --Ox + Oy / = ---Oy q- II ~ X 2 + 0y2, ] assumed constant. Processes related to surface con- p~(Ou O~y) sumption of the solid fuel are neglected. By these + - + - g ( P - po)cos0 (18) hypotheses, and bearing in mind that pyrolysis is a 3 ~y \Ox surface process and must be taken into account through - chemical species the boundary conditions, the mathematical model for

( t3 Yi uO Y, vO Y, ~ the solid phase can be expressed by a simple two- + - - + = wi dimensional heat conduction equation. Properties of P\ Ot Ox t3y / the solid and kinetic data have been chosen to describe [- 0 / t3 Yi'X O f 6 ~ Yi'~7 PMMAXlS and cellulosic materials.116-12o,131 + L ~x?D~x) + ~y~pD~y)J (19)

The models for thermally thin fuels assume that variable distributions across the solid thickness are i = O , F uniform. For chemical processes, only pyrolysis is described: S---, vGG + vcC with kinetics expressed - ene rgy according to a first-order Arrhenius law. Most of the (OT uOT vOT') (O2T 02T " ) models [113-115,124-129] only consider two ordi- PCv Ot + - - + = q + k + nary differential equations describing solid density Ox Oy f \OX 2 Oy2 f and temperature changes associated with the chemi- (20)

94 C. DI BLAS!

(26) -- state equation The cross component of velocity is given by a balance

p T = cos t. (21) of mass fluxes:

The solid phase model, for thermally thick fuels, pv = m (27)

includes a balance equation for: while for the streamwise component a no-slip condi-

- energy tion is usually assigned. Downstream of the leading edge of the flame, the

c~Ts f~ZTs ~ T s ~ (22) boundary layer approximation is adequate and conse- -Ctsk~Sx2 + ~y2 j " quently the first derivatives along the streamwise

Chemical production terms are expressed as: direction are zero. The remaining boundary conditions are based on the physical problem to be mod-

exp ( - E ' ~ YoYvp 2 ---viMi i -- O, F. eled (open boundaries or walls). The treatment of the W i = ~ A

\ R T J MF far field boundary conditions is particularly complicated for the velocity components. In some cases

q = - w F A H . these conditions are derived from the solution of

In Eqs (16-21), u and v are the longitudinal and simplified mathematical models; that is mixed humeri- normal velocity components, # the viscosity, Y the cal/analytical solutions of simplified theories are used species mass fraction, p the density, D the diffusion as far field boundary conditions for the solution of coefficient, cp the specific heat at constant pressure, T more complete mathematical models. Examples of the temperature, k the thermal diffusivity, g the accel- such an approach can be found in the numerical eration due to gravity, 0 the angle of solid fuel prediction of the burning of vertical cellulosic cylin-

ders 14° or in the modeling of free convection along a orientation with respect to gravity, A and E the pre- exponential factor and the activation energy i~, the heated vertical plate (see for example Ref. [141]) gas-phase reaction, AH the heat of combustion, R where the Ostrach's 142 laminar flow solution is used. the universal gas constant, v the stoichiometric coeffi- In most cases, zero normal gradients for the veloc- cient and M the mean molecular weight. The sub- ity components and other main variables are specified script 0 refers to initial conditions and i to chemical at the far field boundary, lt3'lls'119'132 134 On the species: F (fuel), O (oxygen), I (inert), P (product). In other hand, for the prediction of laminar free convec- the solid phase energy balance (22), ~s is the thermal tion in a heated cavity, it has been shown 143 that, diffusivity and Ts the temperature, while for a realistic simulation of the far field flow

The initial conditions correspond to ambient condi- pattern, proper specification of the far field boundary tions, with ignition caused by an external radiative condition is required, the characteristics of the flow heat source. 13° In order to describe ignition and inside and immediately in front of a cavity do not flame spread over solid fuels, Eqs (16)-(21) must be differ from those simulated through the specification coupled to the solid phase balance Eq. (22) through of zero normal gradient along the far field boundary.

boundary conditions at the solid-gas interface. Usu- ally, the changes in the shape of the degraded solid

3.3. Opposed Flow Flame Spread behind the flame are neglected and the boundary conditions are obtained by writing species mass flux and heat flux balances. For the chemical species, the An example of the predicted flame structure, for mass fluxes of species i convected out and diffused opposed flow flame spread over PMMA (property out must be equal to the mass flux of species i values and kinetic data are those reported in Ref. generated on the surface: [144]), as computed with the model presented above

is given in Fig. 12, showing the solid and gas phase pD ~ YF = m(Yv -- 1) (23) temperatures, vector velocity field and the chemical

?~y species mass fractions. Opposed flow flame spread is dominated by the interaction of fluid-dynamics,

pD t3Y° = m Yo. (24) chemical reactions and heat transfer at the flame ~y leading edge (position of the maximum heat flux

from the flame to the fuel), where a combustible For thermally thick fuels, the heat flux balance is expressed as: mixture is established. Downstream of this position,

the flame structure is that typical of a diffusion flame _ k oT _ks &Ts = + mQ (25) in a counterflow environment: isolines of reaction

~y Oy rate correspond to the flame position characterized

where Q is the heat of pyrolysis and ks the solid by the maximum temperature and the minimum fuel thermal conductivity, and oxygen mass fractions. From the vector velocity

At each instant at the solid-gas interface, the solid field, two main flows appear, one of vapor fuels from temperature must be equal to the gas temperature: the pyrolyzing surface and the other of air at ambient

conditions from the inlet. From Fig. 13, where the T = Ts. heat flux from the flame to the solid and the surface


and the flame. The opposed velocity goes to zero on f A the surface, facilitating this fuel transport upstream.

.730 In addition, this process is favored by the very steep gradients of fuel mass fraction in this region, while it

I~m .610 does not appear to depend on the surface temperature "~ ~ ~ gradient. This mechanism of flame spread has also

.490 been predicted by early numerical analyses. 114,115

.370 An important effect is the existence of a region of elevated pressure upstream of the flame leading edge,

250 ' caused by gas expansion. It causes the outward deflec- t__= _~ _ _-- ~ .~ _ z z - - - t i o n o f t h e f l o w n e a r t h e f l a m e f r o n t a n d a r e d u c t i o n

.850 . . . . . . _ _" _" ." . "[3 of the gas velocity encountered by the flame at its

.730 -- -- - leading edge. .61~1 ~ ~ ~ _ _ . - - Studies of flame stabilization at the leading edge of

- - --- : a fuel plate have contributed to the understanding of . 4 ~ ~ ' ~ ~ chemical and physical mechanisms controlling flame

spread. The by Mao et al. 132 the first paper presents .37 " z detailed description of the convective and thermal

"a- - -- - ~ ! " - structure of the flame leading edge over a solid 2~5 L=n,i ~ / / combustible surrounded by inert material. The elimi- 125 nation of inert material allowed blowoff phenomena

to be predicted by Chen and T'ien 133 as the velocity .000 ' I , of the oxidizing flow opposing the flame is increased.

.000 200 .400 .f:~0 .800 1.000 The transition from envelope diffusion flames (high Damk6hler numbers) to open-tip flames (critical

x 1~] Damk6hler number) up to blowoff is also predicted. Fro. 12. Opposed flow flame spread structure and vector Comparison between theoretical and experimental velocity field: (A) fuel mass fraction (solid lines): 0.0002, extinction limits is presented by Kodama et al., 134 as 0.075 and then with step 0.075, and oxygen mass fraction opposed velocity and oxygen concentrations are (dashed lines) from 0 with step 0.033 and (B) gas phase varied. Flame stabilization mechanisms at the leading temperature (K) from 300 with step 250 and solid phase temperature (K) from 300 with step 50; maximum inlet edge o f a fuel plate, under free convection, as gravity

velocity 35 cm s -1. level and oxygen concentration are varied, are presented in Ref. [135]. At very low gravity, the flame extinguishes while a blowoff limit is predicted at very

2.2 .0050 high gravity levels with the flame changing from 2.0 ~ - '~t qs .0045 envelope to open-tip configuration. A blowofflimit is 1.8 - ~ : ' . 0 0 4 0 also determined at very low oxygen concentrations.

~" 1.6 ~ l , .0035 ~ Further investigation on the effects of gravity level t'M

1.4 ~' .oo3o 'E on flame spread over thin cellulosic materials is • 1.2 o o .0025 ~ presented in Ref. [128].

1.0 ' ' The first computer model of flame spread is a .8 / .0020 u')

, .0015 x quasi-steady, variable spread rate model, based on cr .6 , - E the thermo-diffusive equations. It4 It has been used

.4 . . . . - " ~ , .0010 to analyze the dependence of spread on gas phase

.2 , . o o 0 5 parameters 1 ~4 and solid temperature for thermally

.0 I I I I .0000 thin fuels. Unsteady thermo-diffusive models have .000 200 .400 .600 .800 1.000 also been used to analyze flame spread characteristics

x [era] over thermally thick fuels. ~t6-tts Particularly interesting is the prediction of the dependence of the

FIG. 13. Heat flux and surface pyrolysis mass flux as func- flame spread rate on the velocity and oxygen tions of the x coordinate.

concentration of the opposed gas flow. The spread rate for thick PMMA, as measured x45 and predicted

pyrolysis mass flux as functions of the specimen by a thermo-diffusive model, lxa are reported in Fig. length are reported, it is worth observing that the 14 as a function of the opposed-flow velocity and for pyrolysis mass flux, proportional to the normal com- several values of the oxygen mass fractions. The ponent of velocity at the interface, reaches the highest analysis, which qualitatively describes the experimen- values behind the flame leading edge. Consequently, tal results, predicts a spread rate that varies with the the formation of the upstream combustible mixture flow velocity for fixed oxygen concentration. This comes from fuel diffusion from the flame zone spread rate first increases and then decreases as the through a quenching layer between the solid surface flow velocity increases. For a given flow velocity, the

d1~¢$ 19: I '~

96 C. DI BLAS1

the momentum equations, formulated according to F~ 0.3 ¥oo the Boussinesq approximation, have been made 123 in \ , ~ 3 3 z O • order to analyze extinction caused by high flow veloci- U . 3 2 9

n • ~ ties or low oxygen concentrations. Although the > 0.e4 A • . 2 3 o

• . aao A~× ~. E÷6 ( f fw mechanisms which lead to extinction are very differ- O O ent for the two cases, extinction can always be related

to a continuous decrease of the ratio of the flow time 0.18 O(/U 2 to the chemical time pg/wr, that is, the Damkrh-

~ ~ 1 1 O ler number. In both extinction cases simulated, the 0~2 flame leading edge recedes with respect to the heated

solid fuel, thus the solid heat conduction is not controlling at near-extinction conditions. The interac-

0.0E • O O tions between fluid dynamics and chemical processes j M n l l ~ O in the gas phase, which are much faster than in

the solid phase, are responsible for extinction. In the • ,,.~ ~ , ,,~11~ ,,L former case, when the flow velocity is increased, 0 [ 1 k I I i i i t l l i I I I I ~ l

~0 ° to 1 t? ~0 3 M the slight decrease in the chemical time, due to the increase in the fuel concentration, is much lower than

UMAX [CM/S] that in the flow time. Thus the Damkrhler number

FIG. 14. Predicted I ,s (full symbols) and measured 145 (empty at the flame leading edge continuously decreases, symbols) spread rates for opposed flow flame spread over leading to extinction. In the latter case, the flow time

PMMA. is unchanged, but the strong increase in the chemical time, due to the decrease of the reaction rate, again

spread rate increases with the oxygen concentration gives decreasing values of the Damk6hler number and the location of the maximum is also displaced and extinction occurs. towards the higher-velocity region as the oxygen In conclusion, if the chemical time is much smaller concentration increases. The major quantitative dis- than the flow time, the spread of the flame will be crepancies between theory and experiment occur in controlled by the rate of fuel gasification, that is by the very low and very large velocity regions where the heat transfer from the flame to the fuel. On the the approximations of the thermo-diffusive model other hand, if the chemical time is of the same order are not valid. Indeed, at low flow velocities, the as the flow time, the spread of the flame will be phenomenon is controlled by buoyancy, not ac- controlled by the rate at which the fuel can be counted for in the model, while at high flow velocities, consumed, that is by chemical kinetics. the flame structure is very sensitive to the gas velocity More recent simulations of flame spread, including profile, not well described in the model. For intermedi- momentum transfer, are based on the assumption of ate gas flow velocities, the flame spread rate is control- quasi-steady, constant spread-rate equations. The ef- led by the transfer of heat from the flame to the solid, fects of the gas velocity on the opposed flow flame which is less sensitive to the relatively small varia- spread over thin paper have been presented in Ref. tions of the velocity profile. Thus, in this range of 1-126]. In qualitative agreement with experiments, the velocities, the analysis of the spread of the flame is flame spread rate decreases astheopposed ftowvelocity quantitatively better, is increased. The equations do not account for buoy-

The results of numerical analyses 116-x18 have also ancy terms, thus the region of constant spread rates, been employed to determine the controlling mech- observed in the experiments ~45 at low opposed anisms of flame-spread over thick solids and thus to velocities, is not predicted. The extinction limit is verify the phenomenological arguments used to ex- associated with small Damkrhler numbers. The more plain the experimental results in terms of thermally interesting result of the analysis is that solid phase and chemically controlled mechanisms. Both the heat conduction, which does not play any role at high maximum surface heat flux and maximum surface Damk6hler numbers, becomes dominant near the temperature increase with the oxygen concentration blowoff limit. Flow recirculation is predicted ahead and the flow velocity. The increase with the oxygen of the flame leading edge, caused by thermal expan- concentration is due primarily to the increase in the sion of hot product gases, producing high pressure flame temperature. The increase with the flow veloc- inside the flame. The model is not able to identify ity is due to the flame moving closer to the surface, the quenching limit in the slow opposed flow regime, Both of these effects increase the heat transfer from observed under microgravity conditions. the flame to the fuel and the gasification rate of the The downstream spread over thin paper as the solid combustible. Consequently they would tend to gravity level is varied is presented in Ref. [127]. The increase the spread rate for all values of flow veloc- same qualitative behavior as for the case of forced ity. flow conditions is predicted. Even in this case the

Detailed simulations of the flame-spread process model is not capable of predicting an extinction limit over thick solids by a more advanced model including at low gravity level. The only significant difference


. 7 5 0

t=0.05s

. 2 5 O oOOO . 4 0 0 . 8 0 0 1 . 2 0 0 1 . ( 5 0 0 2 . 0 0 0

. 7 5 0

- .

. 2 5 O . 0 0 0 . 4 0 0 . a O 0 1 . 2 0 0 : t . .00O 2 . 0 0 0

. 7 5 0

= o

. 0 0 0 . 4 0 0 ~ 1 . 2 0 0 ] , . (~30 2 . 0 0 0

. 7 5 0

.OOO . 4 0 0 . O O 0 = , . 2 0 0 1 . 0 0 0 2 . 0 0 0

x I~1

FIG. 15. Dynamics of the gas phase temperature (K) fields for flow assisted flame spread, from 300 with step 250 (maximum concurrent velocity 35 cm s -1).

with respect to the case of forced flow is that the As time increases, a rapid propagation of the flame flame, in the natural-convective environment, is front followed by a slower advancement of the pyroly- weaker (lower spread rates) and no recirculation sis front is observed. The gas phase isotherms and ahead of the flame leading edge is predicted. Inclusion contours of equal species concentrations show that of surface radiation in the mathematical model ~2s the flame, except at its upstream leading edge and allows an extinction limit to be predicted at low tip, has a diffusional character with a relatively large gravity levels, while radiative processes are unimpor- reaction rate. Also, the characteristic shape associated tant at high opposed flow velocities, with a diffusion flame over a pyrolyzing surface in a

concurrent environment is shown: the hot gases (react- 3.4. Flow Assisted Flame Spread ing species and combustion products) are pushed

downstream in the direction of the propagating py- Only thermo-diffusive models have been used to rolysis front. Three regions exist in the integration

simulate flow-assisted flame spread over thick ~ ~ 9.~ 2o domain: the vaporization (or pyrolysis) region, the and thint21 fuels. The dynamics of the early stage of 'combusting plume', and the 'thermal plume'. The concurrent flame spread, over thick solids, are shown pyrolysis region is characterized by surface tempera- in Figs 15 and 16 through the gas phase temperature tures larger than 600 K. In this region, an almost and fuel and oxygen mass fraction distributions. Ini- constant value of the surface temperature is reached tially, the solid is at ambient conditions and igni- and maxima of gas temperature and reaction rate are tion is caused by an external radiative heat source, computed. At the flame leading edge there is a

98 C. DI BLASI

. 7 ~ O t = O . O S S

.OOO . 4 0 0 ., . 8 0 0 " i 2 0 0 1 . 6 0 0 2 . 0 0 0

. 7 5 0 . . . .

t=O.O75s

. s o o / f ~ ~ - . = _- - - - - -~ - ' > . " -

, , , , ,

. 0 0 0 . 4 0 0 .O00 1 . 2 0 0 :1.,600 2 . 0 0 0

. 7 5 0

7 t - - O . l s

\ ( . ~ _ - - - - - - - . _ - ~ - - - < . . . . . , . /

- . - - - . . , , , , ~ 5 0 , I ,% %1% %%,%%%~ I ~, I, [ f d ' / ~ f _ - .

. 7 5 0 . 0 0 0 . 4 0 0 - 8 0 0 1 , 2 0 0 aL , (~00 2 . 0 0 0

x [o.]

FIG. 16. Dynamics of fuel (solid lines) and oxygen (dashed lines) mass fraction distributions for flow assisted flame spread, from 0 with step 8.9 x 10 -2 (fuel) and from 0 with step 2.3 x 10 2 (oxygen);

maximum concurrent velocity 35 cm s-L

premixed zone similar to that shown in opposed-flow The predicted flame and pyrolysis spread flame spread, where the flame is thick. In the combust- rates, 119'12° in general agreement with experi- ing plume region, the surface pyrolysis rate is negligi- ments,146 increase with oxygen concentration and ble. The fuel vapors, however, are pushed beyond the flow velocity and vary over a very large range of vaporization region by the external flow rate, and values. Both the increase of oxygen concentration burn, giving high gas temperatures. The consequent and concurrent flow velocity increase the heat flux high values of the heat flux at the surface heat the from the flame to the fuel and the spread rate is solid fuel which also reaches rather high tempera- enhanced. This indicates that, unlike the opposed- tures. In the final part of the combusting plume flow case, flow-assisted flame spread is controlled region, due to the proximity of the flame to the surface essentially by heat transfer. The effects due to finite- and to the relatively low surface temperatures, the rate kinetics are of increasing importance as extinc- reaction rate assumes low values, indicating that the tion is approached, as a consequence of low oxygen flame sheet approximation is not valid here. The last concentrations or very large flow velocities. These zone at the left of the flame tip is the so-called effects appear mainly at the flame leading edge. Here thermal plume. Because of the absence of fuel vapors the extinction length, that is, the distance of the in this zone, the reaction rate is zero. The species flame leading edge from the edge of the fuel slab, present are essentially the oxidizer and the combus- increases as the flow velocity is increased or the tion products at a fairly high temperature, oxygen concentration is lowered. Again, the extinc-


tion process can be explained in terms of a decrease, equations, are all based on the formulation of quasi- below a critical value, of the Damk6hler number at steady, constant spread rate equations and also the flame leading edge. The flame counteracts the consider thermally thin fuels. 113.124-126 Also, simula- decrease by moving into a zone of high fuel tions of flame stabilization at the leading edge of a concentration. The extinction process begins in this fuel plate 13s present conditions of interest to micro- way, but the downstream spread process goes on gravity studies. By lowering the gravity level, the increasing flame and pyrolysis lengths as long as the flame size increases with a decrease of the heat flux pyrolysis spread rate is greater than the upstream to the solid. Different possible explanations of the extinction rate. Complete extinction occurs when the weakness of the flame at low gravity level were given. extinction distance extends to the position of the The first was a reduction in the fuel supply rate pyrolysis front. 12° below a limit value, so that the flame cannot be

The characteristics of flame structure predicted for sustained. The second suggests a reduction in the thin fuels T M are qualitatively similar to those com- oxidizer supply rate to the flame, due to the absence puted for the case of thermally thick fuels, except for of an external driving force: the rate of oxidizer the presence of a burn-out region. The predicted T M depletion is larger than the feeding rate and the and measured 136 variation with time of the flame, flame extinguishes. Also, heat radiation losses are pyrolysis, and burn-out distances to the location of supposed to plan an important role. the flame spread initiation under several flow condi- In Ref. [124], Bhattacharjee et al. used both finite tions are in good agreement. The spreading process and infinite rate kinetics to model flame spread over initially accelerates and then tends towards a steady a thermally thin fuel in a quiescent environment at state as the flame spreads over the solid surface, zero gravity. The flame structure is similar to that

predicted for opposed flow flame spread. For the case of infinite kinetics, the premixed zone disappears

3.5. Microgravity Flame Spread and higher temperatures are observed at the flame leading edge. The increased gas temperature leads to

Studies of flame spread under microgravity condi- higher heat fluxes and consequently to larger spread tions have been greatly increased in the last few years rates. A comparison between predicted and measured because of the revived interest in fire-safety concerns spread rates is also presented. Even for the case of in spacecraft and for the space shuttle. In a micrograv- finite gas phase kinetics, spread rates two or three ity environment, in the absence of forced flow, the times larger than the measured values are predicted. velocity distribution is mainly determined by the fuel Furthermore, in disagreement with experiments, only vaporization at the surface, possible pressure gradi- a weak increase of the spread rate with pressure is ents and flow induced by the flame motion with observed. Simulations of flamespread over thin paper respect to the solid and the quiescent environment, for very low opposed velocities 126 and in a quiescent Among the experimental studies on microgravity environment, 127 in the absence of or at very low flame spread, those conducted by Olsen et al.,93'94 gravity, show the common feature of being incapable where the flame propagation over a thin paper sheet of predicting the quenching limit observed in the under quiescent and slow forced flow conditions is experiments. The reason for such disagreement, as investigated, are very interesting. As a result of the well as for those in Ref. [124], was attributed to the analyses, besides flame structure, an extinction limit neglect of radiation in the gas phase and the solid at very low opposed flow velocities was determined, phase equations. Very low propagation rates and flame shapes, differ- The model in Ref. [124] was modified to include the ent from those at normal gravity, with larger stand- effects of radiative heat transfer from the fuel sur- off distances, were observed, face. 125 Spread rates are predicted as a function of the

Early thermo-diffusive models of flame spread do solid fuel emittance and oxygen level. For any oxygen not include momentum equations and buoyancy level, the spread rate is found to decrease as the solid terms, consequently, in principle, they can be consid- emittance is increased, with a higher rate of decrease ered as microgravity models. Almost all simulations at lower oxygen levels and higher values of the emit- have been performed for conditions dominated by tance. Changes, as the surface emittance increases, are the assigned forced flow, however, simulations of also shown in the flame structure. Indeed, the gas flame spread over thermally thick PMMA at low phase temperature decreases and the flame shrinks in opposed flow velocities, as the oxygen level is varied, size and is located closer to the fuel surface. Near-limit have been presented in Ref. [l 18]. The unsteady flame spread is believed to be controlled by the ratio mathematical model is able to predict an extinction of radiation loss to conductive heat flux to the surface. limit at very low opposed velocities and oxygen The extinction is still due to chemical kinetics but concentrations above ambient conditions (see Fig. reaction rate slows down through temperature reduc- 14). Also, a reverse U-shape curve of the spread rate tion as a result of radiative heat losses. In other words, as a function of the opposed flow velocity is pre- the extinction is caused by a strong decrease in the dicted, surface temperature with the consequent reduction of

More recent studies, including momentum balance the fuel supply rate which attains very low values.

100 C. D! BLASl

A further improvement is presented in Ref. [113] is made more complex by gas phase turbulence. where gas phase radiation effects have been included Detailed modeling of combustion processes of char- in the modeling of flame spread over thermally thin ring and non-charring solid fuels is a formidable task fuels at low gravity. Radiation is coupled to hydro- and models available to date only partially describe dynamics using the emission approximation through the problem. A one-step global reaction is the most three simple parameters: a Planck mean absorption widely suggested kinetic model for the thermal degra- coefficient, the fraction of total emission directed dation of both charring and non-charring solid fuels. towards the surface and a shape function that repre- It is the simplest but offers only a very rough descrip- sents the distribution of gas-to-surface radiation. In tion of the problem with reaction products (usually order to study the effects of radiation on the predic- volatiles and chars) accounting both for primary and tions of flame spread, a set of simulations, made secondary chemical processes. This approach might in a 50Y/o oxidizer ambient, with different models: (a) suffice for fire safety issues, however it is certainly not no heat radiation, (b) surface heat radiation losses appropriate when the study of solid degradation is only, (c) gas phase heat radiation losses only and (d) aimed at obtaining information on the yields of corn- gas phase and solid phase heat radiation losses and bustible components evolved from reaction products. gas to surface radiative heat flux, has been performed. Multi-step, one-stage models have made a signifi- At high opposed velocities, a decrease of the spread cant contribution to the understanding of the ele- rate is observed for the cases (a), (b) and (c), indicat- mental composition of the reaction products from ing that gas phase kinetics are the controlling factor, cellulosic material pyrolysis. However, their validity At low opposing velocities, the flame becomes control- is limited to the range of experimental conditions led by radiation. It appears that only models under which they have been determined, and usually including radiation effects 113"128"131 can predict the their role has been that of correlating the experimen- increase of the spread rate as the opposed velocity is tal data. The chemistry of the depolymerization proc- increased from zero to a limit value with the inverted ess has also been studied for the case of non-charring 'U ' shape of the spread rate curve as a function of the materials. Notwithstanding the noticeable effort un- opposed velocity observed in the experiments. A para- dertaken in this direction, due to complexity of the metric study of the coupled effects of surface emission chemical mechanisms, it is unlikely that in a short and absorption of radiation is also available, t13 time such a type of models can be coupled to solid Finally, the model,~ 13 with only gas phase radi- and/or gas phase transport phenomena to have great ation heat losses, has been used 129 to predict the insight into solid fuelcombustion. structure of the flame leading edge which compares Two-stage, semi-global models for thermal degrada- favorably with that experimentally observed, tion of charring fuels are based on lumping the

reaction products into three main components: gases, tars and chars. As both primary and secondary reac-

4. CONCLUSIONS AND FURTHER DEVELOPMENTS tions are modeled, they are, in some way, the most

useful and advanced models to be used together with Combustion of solid fuels is the result of complex the description of physical processes for predicting

interactions among many chemical and physical pro- product yields from solid fuel thermal degradation. cesses. For the solid phase, these include heat and However, despite the limited number of chemical mass transfer, chemistry of homogeneous and hetero- species used, there is large uncertainty in the kinetic geneous reactions interior to the solid (thermal schemes, mainly in the kinetic data. For the primary degradation and oxidation) and surface regression, stage of wood (or biomass) degradation, a different Furthermore, for PMMA, internal absorption of evolution of tar, char and gas yields, as functions of radiation and formation of bubbles in the melt layer temperature, has been observed. Thus, on a very are also to be accounted for, while, for celluloic general basis, in the group of two-stage, semi-global charring materials, evaporation of absorbed water, models, the three-reaction model accounting separ- pressure variations, cracks caused by thermal stresses ately for gas, tar and char formation from the com- in the char layer, internal shrinkage and/or swelling, plex chemistry of wood could be the most general. and migration of volatiles in the virgin solid region However, few estimations of kinetic data are available are other important processes to be considered. For and their validity is strongly impugned by the very the gas phase, processes include convection and narrow range of temperature variation considered in diffusion of mass, momentum and energy, combus- the experiments and by the assumption of isothermal tion reactions, ignition and flame propagation, radia- conditions, no longer verified during the heating tion absorption by the degradation products, and period, and by a final char yield not depending on heat transfer by radiation. Processes occurring at the temperature. solid-gas interface include convection and diffusion Another drawback in the estimation of kinetic of mass, momentum and energy, reradiation from parameters is that the data are determined and are the surface, and heterogeneous reactions between the valid only for the specific wood considered. The gas phase and the solid phase. In some situations, alternative approach, based on the contribution of especially when the scale length is large, the problem the reaction rate of cellulose, hemicellulose and lignin


to the primary reaction rate of the wood, seems to be of the feed heterogeneity on the pyrolysis of biomass more general. Once the amounts of components par- fuels. Such results could be useful to suggest poss- ticipating in the composition of the specific wood are ible pretreatments to improve process control and determined, the degradation rate of every type of product quality. The analysis of the external condi- wood may, in principle, be determined. The role tions, in particular of the heating level, could played by possible interactions among the wood corn- also be of great importance to fire safety science. ponents as well as possible bonds among them, how- As for non-charring materials, only one-step ever, should be investigated, kinetic models have been coupled with physical

Extensive studies on cellulose have been conducted modeling, which in most cases is only a simple heat and there is some agreement about a semi-global conduction equation. Indeed, apart from the analyti- primary pyrolysis mechanism which considers two cal work in Ref. [90], no effort has been made to competitive pathways leading, respectively, to tar bring together chemical processes, heat transfer and formation and to a linked char and gas formation, bubble formation effects. Kinetic data for such a mechanism have also been Ignition simulations have been made mainly for estimated. A tentative, two-stage, semiglobal model non-charring fuels by means of one-dimensional has been proposed for lignin pyrolysis, but kinetic models. Flame spread has been simulated through constants are not available. Less information is avail- two-dimensional models accounting for momentum, able on hemicellulose. Therefore the approach based mass and heat transfer. In all cases, gas phase combus- on the contribution of the single components to tion and solid phase pyrolysis processes have been model wood or biomass degradation rate also re- described according to one-step global reactions. The quires further study on the kinetics of each compo- predictions of ignition delay times and spread rates nent. are in qualitative agreement with experiments under

Further investigation is needed in the analysis of almost all conditions, and, in some cases, in quantita- secondary reactions. Almost all authors agree that tive agreement, indicating that mathematical models tar degradation to gases and chars occurs. Several could be a powerful tool for the analysis of control- estimations of kinetic data for tar cracking to light ling mechanisms, provided all main chemical and gases, considered only as preliminary, have been physical processes are taken into account even if made, while no quantitative measurement of the sec- with some simplifications. An improved description ondary reaction rate of tar deposition to char has of the chemistry can of course give more information ever been attempted. The role of heterogeneous reac- on the details of ignition and extinction and the tions of char gasification, due to volatile products of emission of gaseous species (mainly CO and CO2) primary pyrolysis, should also be studied, useful for toxicity evaluations.

Models describing both chemical and physical pro- Among the physical processes, deserving an im- cesses of charring material degradation and account- proved treatment, there is radiation transport which ing for transport phenomena generally use a very is believed to play a controlling role for microgravity simplified description of chemistry (one-step global flame spread. pyrolysis reaction), whereas models accounting for Solid phase degradation is very important not pyrolysis through two-stage, semi-global models, only for conversion of biomass fuels to energy, but it often do not describe other important aspects of the is also the first step in the complex phenomena of phenomenon such as property variations, convective gas phase combustion. However, while it is well transport of gaseous species or momentum transfer, known that under ablation regime conditions physi- In the last few years, models accounting for both the cal processes are controlling and that the details of main chemical and physical processes have been pro- the chemistry of solid phase degradation are very posed. They have proved capable of predicting the important for wood and biomass conversion pro- proper trend of product yields to the changes in the cesses, it is not yet sufficiently clear how these aspects reaction conditions (heating, solid and gas residence of solid phase process can affect gas phase flaming times), combustion.

Quantitative agreement between predictions and The coupling of solid and gas phase processes experiments is believed to be very difficult to achieve occurs through the boundary conditions at the inter- due to the lack of reliable data and the dependence face, that is through the solid surface temperature, of the data on operating conditions and type of the blowing velocity due to the devolatilization pro- wood. Under ablation regime conditions, for very cess and the chemical composition of the mixture large samples subjected to high radiative heat fluxes, adjacent to the solid surface. Chemical and physical structural changes may be important. In this case, processes occurring inside the solid are, to a signifi- even the qualitative agreement with experiments may cant extent, responsible for the surface conditions be lost because no model accounts for volume varia- and composition of the evolved gases. Particularly tion effects. Mathematical models have not yet been interesting is a pioneering work by Martin t47 where widely used to perform systematic studies of the the implications of the details of the temperature influences of the heating level, particle size, moisture evolution along cellulose samples radiatively heated content, etc., which are useful to evaluate the effects and the transients and the chemical composition of

102 C. DI BLASI

primary and secondary pyrolysis products on the gas solid degradation, were available. Once the sub- phase ignition processes are presented. For a wide models were validated, they could be included in a range of radiative heat fluxes, the surface is always general, comprehensive model. The complexity of the well-charred before ignition. It was observed to be a complete problem and the more detailed descriptions site for secondary reactions (tar degradation and of physical processes require the use of advanced char gasification) which generate a low, but abruptly numerical techniques and high-speed computers, lm- increasing, concentration of reactive substances provement in quantitative predictions, however, do which lead to ignition. This seems to indicate that not depend only on the availability of comprehensive secondary reactions play an important role not only models, efficient numerical solution techniques and for the yields of products from biomass thermal high-performance machines, but also on the determi- degradation but also for the flammability characteris- nation of reliable data from experimental investiga- tics of charring materials, tions.

Formation of char make the solid phase processes highly transient and affects heat transfer processes Acknowledgements--The work was supported by the Euro- with changes in the amount of combustible volatile pean Economic Community under Contract Joule No. 0035

and by the National Research Council of Italy under Contfi- species generated. The assumption that the pyrolysis butions N.90/4100 and N.91/68. is a surface process, made in the models of flame spread over thick charring and non charring materials, is not confirmed by experimental measurements REFERENCES which show that the mass loss rate still increases even though a constant surface temperature is 1. SHAFIZADEH, F., In: The Chemistry of Solid Wood, R.

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Di Blasi 1993 Modelling and Simulation of Combustion Processes of Charring and Non Charring Solid...

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