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The transient, one-dimensional, thermally thick, noncharring solid material version of a numerical thermal degradation model is used to analyze the thermal degradation process of poly(methyl methacrylate) when subjected to a radiation source from a graphite plate. A theory is developed to account for oxygen-sensitive thermal degradation, which is based on differences in polymer degradation behavior in inert and non-inert environments. The model includes condensed phase heat transfer, in-depth thermal and oxidative decomposition, advective mass transfer, and in-depth absorption of radiation. It is found that an increase in gas-phase oxygen concentration decreases the surface temperature and increases the gasification rate substantially. The predictions yield physically realistic results when compared with published experimental data for an external radiation source with flux of 17 kW·m m 2 .

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... It simulates the process up to the threshold of ignition, and solves sequentially in solid and gas phases. Esfahani [10,11] reported a transient, onedimensional, thermally thick thermal degradation model to analyze the thermal degradation process of polymethylmethacrylate (PMMA). It has been assumed that the solid phase exchanges energy with the adjacent gas phase and can be described by a Newtonian cooling term. ...

... In the present work, a degradation model has been improved to analyze the effect of oxygen on the route of thermal degradation mechanisms. Our work differs significantly from the previous one [10,11] by the care taken to simulate a two-dimensional thermal and flow field around the sample. Contrary to the previous sub-model [4], this new one simulates the process simultaneously in solid and gas phases, and includes the oxygen effect on chemical reaction rate. ...

... The two-dimensional type of continuity, momentum, and energy equations are solved for the fluid phase of the domain The flow is assumed incompressible with constant properties and the viscous dissipation is neglected. In the solid phase of the computational model, the main feature of the mathematical model follows closely that reported by Esfahani [10,11]. The model includes a global finite-rate thermal degradation model for the solid, as well as in-depth absorption of radiation. ...

In the present work, numerical computations of the flow and thermal fields have been carried out for a transient, two-dimensional model of thermal and oxidative degradation of polymethylmethacrylate (PMMA) subjected to a monochromatic, radiant heat flux. An external thermal radiation source is used to simulate the primary mode of energy transfer in a room fire. An incompressible SIMPLE code is used with a staggered grid arrangement. The equations for the fluid and solid (fuel) phases are solved simultaneously using a segregated technique. At the outlet of the computational domain, a convective boundary condition is compared with a traditional Neumann condition. The convective boundary condition is shown to be more effective in reducing the CPU time. A study in the effects of spatial resolution and different time steps are provided. A theory is developed to account for thermal and oxidative degradation. The theory is based on differences in polymer degradation behavior in inert and non-inert environments. A number of quantities such as surface temperature and mass flux of PMMA are calculated by an external source of 40 kW/m2. The predictions of the model are in a good agreement with the experimental results. It is found that an increase in gas-phase oxygen concentration obviously decreases the surface temperature and increases the gasification rate of PMMA.

... The previous numerical works of Esfahani [6,7] illustrated the ignition of solid fuel. In Esfahani's other numerical task [8] the oxygen-sensitive thermal degradation of PMMA was considered for the first time, where the oxygen concentration on the irradiated surface is assumed the same as the concentration in the far ambient in order to skip the complexity of oxygen diffusive-volatile advective behavior. ...

... The purpose of the present work is to extend the earlier task [8] to make a better understanding of thermal behavior and the details of involved mechanisms. Thus, penetration of the oxygen and the counter flow of released volatiles have been simulated by utilizing a one-dimensional model for the gas phase in addition to all features of the previous solid phase model such as in-depth absorption of radiation, in-depth degradation, etc. Esfahani et al. [9] presented a two-dimensional model with the similar framework to this task, but the high numerical cost and the long run time of multi-dimensional codes, made the authors to apply new ideas in a simpler one-dimensional model, i.e., the present work and [10]. ...

... The mathematical model follows the framework of Esfahani et al. [1,8,20] to simulate Kashiwagi and Ohlemiller's experimental studies [3] and is largely based on the model proposed by Ohlemiller [21]. According to Kashiwagi's findings [3] the rate of transient gasification cannot be described simply as a function of surface temperature or proportional to energy input, in addition a model for predicting the gasification rate should include condensed phase oxidative chemical reactions. ...

A transient, one-dimensional model has been presented to formulate the substantial role of polymer gasification in the early
stages of fire growth. The present model comprises the interaction between the oxygen diffusion and the released volatiles
on the rate of polymer gasification, when the polymeric sample is subjected to an external radiative source. The model also
includes different mechanisms affecting the degradation process such as in-depth thermal and oxidative decomposition, in-depth
absorption of radiation and heat and mass transfer in the both gas and solid phases. The results for two different radiative
heat sources (17 and 40kWm−2) are reported and yielded realistic results, comparing to the published experimental data. It was found that an increase
in the oxygen concentration will lead to a considerable decrease in the surface temperature as well as significant increase
of gasification rate at 17kWm−2; nevertheless this effect is less apparent at 40kWm−2.

... Prior numerical studies in flammability of solid fuels have been mainly divided into two groups: those that only solve the solid-phase decomposition (Esfahani, 2002;Linteris, 2011) and those that contain the coupled reaction process of both the solid and gas phase (Fereres et al., 2015;Peng et al., 2015). Esfahani (2002) developed a one-dimensional (1-D) model only including solid-phase to study the influence of oxygen concentration on thermal decomposition of polymethyl methacrylate (PMMA). ...

... Prior numerical studies in flammability of solid fuels have been mainly divided into two groups: those that only solve the solid-phase decomposition (Esfahani, 2002;Linteris, 2011) and those that contain the coupled reaction process of both the solid and gas phase (Fereres et al., 2015;Peng et al., 2015). Esfahani (2002) developed a one-dimensional (1-D) model only including solid-phase to study the influence of oxygen concentration on thermal decomposition of polymethyl methacrylate (PMMA). Afterwards, Esfahani and Kashani (2006) analyzed the effects of oxygen concentration and external radiation based on the previous 1-D model on the ignition of PMMA through solving simultaneously the solid and gas phase equations. ...

Purpose
This study aims to investigate the controlling mechanisms of ambient oxygen and pressure on piloted ignition of solid combustibles under external radiant heating.
Design/methodology/approach
The numerical simulation method was used to model the influence of ambient oxygen concentration on the piloted ignition of a thermally irradiated solid sample in reduced pressure atmospheres. The solid phase decomposition and gas phase kinetics were solved simultaneously.
Findings
It was determined that the elevated oxygen atmospheres resulted in a higher flame temperature and a thicker temperature profile over the solid surface. Also, increasing oxygen and reducing pressure had a similar effect in the decrease of the ignition delay time. The shorter ignition time in reduced pressure was mainly because of the decreasing of convective heat losses from the heated solid. As oxygen was reduced, however, ignition occurred later and with a greater mass loss rate because more volatiles of solid fuel at transient ignition were required to sustain a complete reaction under an oxygen-poor condition.
Research limitations/implications
The results need to be verified with experiments.
Practical implications
The results could be applied for design and assessment of fire-fighting and fire prevention strategies in reduced pressure atmosphere.
Originality/value
This paper shows the effect mechanism of ambient oxygen and pressure on piloted ignition of solid combustibles.

... Flame spread over solid fuel sur faces has been a sub ject of in ten sive ex per i mental and the o ret i cal in ves ti ga tions [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15] due to its im por tance to fire safety. A re view of mod el ing and sim u la tion of com bus tion pro cesses of char ring and non-char ring solid fuels was be done by Di Blasi [1]. ...

... Sousa and Esfahani [14] also stud ied by nu mer i cal meth ods the ig ni tion of PMMA which induced by mono chro matic ra di a tion. In re cent work, Esfahani [15][16][17] stud ied the ef fect of ox y gen con cen tra tion on the deg ra da tion of PMMA by nu mer i cal meth ods. ...

The present work is addressed to the numerical study of the transient laminar opposed-flow flame spread over a solid fuel in a quiescent ambient. The transient governing equations-full Navier-Stokes, energy, and species (oxygen and volatiles) for the gas phase, and continuity and energy equations for the solid phase (fuel) with primitive variables are discretized in a staggered grid by a control volume approach. The second-order Arrhenius kinetics law is used to determine the rate of consumption of volatiles due to combustion, and the zero-order Arrhenius kinetics law is used to determine the rate of degradation of solid fuel. The equations for the fluid and solid phases are solved simultaneously using a segregated technique. The physical and thermo-physical properties of the fluid (air) such as density, thermal conductivity, and viscosity vary with temperature. The surface regression of the solid fuel is modeled numerically using a discrete formulation, and the effect upon the results is analyzed The surface regression of the solid fuel as shown affects on the fuel surface and gas temperature, mass flux and velocity of volatiles on the top surface of fuel, total energy transferred to the solid phase, etc. It seems the results to be realistic.

... In Eq. (8) the gradient temperature in the Z direction can be neglected because the thickness of the solid is very thin. The major part of heat transfer through the pyrolysis region takes place in the first 2 mm distance ahead of the flame [24][25][26][27], and therefore the order of δ approximately equals the order of b(b≈ 2 mm) . If δ<<w, the first term in energy balance can be neglected. ...

The combustion process of polymer is a complex coupling of energy feedback from a flame to the polymer surface with gasification of the polymer to generate combustible degradation products. In this paper the effect of the dimension of the polymer sheets upon the downward flame spread is studied by theoretical and experimental methods. In the theoretical method the effect of the dimensions of the solid fuel on the energy balance in the solid phase is studied by scale up method. This study show that the flame spread over the solid fuel is independent of the width of the sample if the ratio of the width to the thicknes s of the solid is higher than ten. The experimental results confirm the theoretical results.

... For comparison between the effect of all dependent parameters on main model responses consist of temperature, catalytic heat transfer, surface mole fraction and fuel conversion, the sensitivity analysis can be attained. In line with [20] this can be characterized by the ratio of percentage changes in model response, DU, to value of dependent parameter, DE, therefore the normalized differential sensitivity is defined as follows: ...

In the present work the effect of catalytic surface reaction on non-reactive bulk flow in micro-channel is investigated. The reaction surface is analyzed with assumption of constant wall temperature. To solve this problem, the energy, mole fraction and catalytic reaction equations are solved by trial and error process. The analysis show that most sensitive parameter is fuel conversion and the sensitivity of hydraulic diameter is more than longitude coordinates.

... Despite the potentially significant effect of oxidative pyrolysis on a material's overall reaction to fire, modeling the effect of oxygen concentration on the decomposition of a thermally stimulated solid fuel slab has been infrequently explored. Reaction kinetics and thermodynamics of polymer oxidative pyrolysis have been directly related to the freestream oxygen concentration [6,7]. However, the oxygen concentration at the exposed surface may be reduced due to blowing, and this effect cannot be captured with this modeling approach. ...

A generalized pyrolysis model (Gpyro) is applied to simulate the oxidative pyrolysis of white pine slabs irradiated under nonflaming conditions. Conservation equations for gaseous and solid mass, energy, species, and gaseous momentum (Darcy's law approximation) inside the decomposing solid are solved to calculate profiles of temperature, mass fractions, and pressure inside the decomposing wood. The condensed phase consists of four species, and the gas that fills the voids inside the decomposing solid consists of seven species. Four heterogeneous (gas/solid) reactions and two homogeneous (gas/gas) reactions are included. Diffusion of oxygen from the ambient into the decomposing solid and its effect on local reactions occurring therein is explicitly modeled. A genetic algorithm is used to extract the required material properties from experimental data at 25 kW/m² and 40 kW/m² irradiance and ambient oxygen concentrations of 0%, 10.5% and 21% by volume. Optimized model calculations for mass loss rate, surface temperature, and in-depth temperatures reproduce well the experimental data, including the experimentally observed increase in temperature and mass loss rate with increasing oxygen concentration. (author)

... Like the effect of highenergy g-radiation on PMMA, the summary here is not exhaustive. For example, the literature related to the topics of flammability or spot-specific (laser) heating (some of which are identified in [303]) will not be examined. Table 6 summarizes prominent studies examining the thermal degradation and thermal oxidation of PMMA. ...

The durability of Fresnel lenses used in the concentrating photovoltaic (CPV) application is reviewed from the literature. The examination here primarily concerns monolithic lenses constructed of poly(methyl methacrylate) (PMMA), with supplemental examination of silicone-on-glass (SOG) composite lenses. For PMMA, the review includes the topics of: optical durability (loss of transmittance with age); discoloration (the wavelength-specific loss of transmittance); microcrazing and hazing; fracture and mechanical fatigue; physical aging, creep, shape change, buckling, and warping; and solid erosion. Soiling, or the accumulation of particulate matter, is examined in the following contexts: its magnitude of reduction in transmittance; variation with time, module tilt, and wavelength; the processes of adhesion and accumulation; particle size, distribution, composition, and morphology; and its prevention. Photodegradation and thermal decomposition, mechanisms enabling aging, are examined relative to the CPV-specific environment. Aspects specific to SOG lenses include: solarization of the glass superstrate; corrosion of glass; delamination of the silicone/glass interface; change in focus due to thermal misfit between the laminate layers; and the chemical stability of poly(dimethylsiloxane) (PDMS). Recommendations for future research are provided, based on the most important and the least explored topics.

... Other controlling parameters of flame spread are related to the environmental conditions, such as the oxygen concentration or the direction of the gas flow relative to the direction of flame spread. Esfahani [13] studied the effect of oxygen concentration on the degradation of polymethyl methacrylate (PMMA) by numerical methods. There is an interest in using numerical methods to investigate details of fire initiation and spread on solid fuels. ...

To explore the flame spread mechanisms over noncharring material, downward flame spread over polymethyl methacrylate (PMMA) sheets from 1.5 to 10mm thick is studied experimentally in the quiescent air in an open space.The experimental results show that the flame spread rate decreases with increasing thickness of sheet and it tends to a constant value for thick samples. Also the angle of the pyrolysis region is roughly constant for different sheet thicknesses.In this study, a heat transfer model is proposed to examine the rate of heat transfer for noncharring materials. Based on this model and the experimental results, a correlation between the flame spread rate and thickness is derived, in which the flame spread rate is inversely proportional to the sheet thickness. The proposed model estimated the convection heat flux and the gradient of temperature in the solid and gas phases. The experimental data are in good agreement with the results of the theoretical model.

... Flame spread over solid fuel surfaces has been a subject of intensive experimental and theoretical investigations [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15] due to its importance to fire safety. A review of modeling and simulation of combustion processes of charring and non-charring solid fuels was be done by Di Blasi [1]. ...

Purpose
To show the effect of radiation from the heat source and the variation of fluid properties on the laminar natural convection induced by a line heat source.
Design/methodology/approach
The governing equations – Navier‐Stokes and energy equation are discretized in a staggered grid by a control volume approach, and they are solved using a segregated technique. The equations for the fluid and solid (line heat source) phases are solved simultaneously. The three sides of the computational domain are open boundary. Some of the physical and thermo‐physical properties of the fluid (air) such as density, thermal conductivity and viscosity were considered to vary with temperature.
Findings
The present predictions are compared with those using the Boussinesq approximation, with the results for the boundary layer equations, and with the experimental results. The present predictions reveal considerable departure from the Boussinesq‐based solution and from the boundary layer results. This study also shows the radiation exchange between the heat source and surrounding has major effect in the results. Thus, the departure between the experimental and analytical results can be explained by the effect of radiation exchange.
Research limitations/implications
In this work, just studied steady‐state laminar thermal plume with the effects of radiation from heat source and the variation of air properties with temperature while it is propose to extend this work to transient and/or turbulent flow.
Originality/value
The effect of radiation from a line heat source on the flow filed around the source and offers enhancement of design to thermal engineers.

... is concerned with smoldering combustion through porous media essentially emanating from fire related problems. Blasi (1993), Kashiwagi (1994) and Kashiwagi and Ohlemiller (1982) have examined the condensed phase processes with polymers such as polymethylmethacrylate and polyethylene including the role of oxygen in the gas phase on the gasification. Esfahani (2002) has proposed a model for the thermal behavior in an oxidative environment for non-charring polymers such as PMMA. Calculations are made for the in-depth thermal profile with impinging heat flux from thermal radiation and these are shown to be in reasonable agreement with measurements of Kashiwagi (1994) and others. Olsen and T'ien (2000 ...

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... Although this model like the previous work of Esfahani [8] utilizes a transient one-dimensional formulation, it also simulates gas region interactive mechanisms. Although the details of advanced two-dimensional models such as [10] and [9] are more reliable and accurate, the present formulation has the advantage of having a low run cost and faster achievement of results, these results at least can be applied as a first guess to predict the ignition of PMMA by considering a reasonable safety factor. ...

A transient one-dimensional model is applied to study degradation and combustion of a poly methyl methacrylate (PMMA) sample.
Ignition of PMMA is a complex interaction among different mechanisms, including solid fuel degradation, heat transfer, in-depth
absorption of radiation, surface regression, gas-phase advective heat/mass transfer, and combustion. The present task has
the significant feature of coupling the solid and gas phases. Besides the mathematical model has been solved numerically by
using a fast iterative method and has yielded realistic results.

... Moreover, because the radiant energy emitted from the hot surface is quite small compared with the incident radiation, absorption of the emission from the hot surface by MMA is neglected. Solid phase [11][12][13][14] c S specific heat [kJ/(kg K)] Boundary conditions are imposed as zero gradients of temperature, species concentrations, and dynamic pressure to simulate the open boundaries, except at the y = 0 plane (symmetric) and the PMMA surface (interfacial). At the PMMA surface, the dependent variables are solved with interfacial boundary conditions [9]. ...

Nonpiloted ignition processes of a thin poly(methyl methacrylate) (PMMA) sheet (0.2 mm thick) with a laser beam as an external radiant source are investigated using three-dimensional, time-dependent numerical calculations. The effects of sample orientation angle on ignition delay time in quiescent air in a normal-gravity environment and of imposed velocity in a microgravity environment are determined. The numerical model includes heat and mass transport processes with global one-step chemical reactions in both gas and solid phases. A simple absorption model based on Beer's law is introduced and bulk absorption coefficients are applied to the solid PMMA and evolved methylmethacrylate (MMA). The PMMA sample surface is kept normal to the incident radiation at all sample orientation angles. In a zero gravity environment, ignition delay time increases with an increase in imposed flow velocity. In quiescent normal gravity, ignition delay time has a strong dependency on the sample orientation angle due to a complex interaction between the buoyancy-induced flow containing evolved MMA and the incident laser beam. Without absorption of the incident radiation by the evolved MMA, ignition is not achieved. The most favorable ignition configuration is the ceiling configuration (downward-facing horizontal sample irradiated by upward laser beam). The formation of a hole through the thin sample due to consumption has two counteractive effects on the ignition process: one is a reduction in the fuel supply rate, and the other is an increase in the air supply from the side opposite to the irradiated side by the buoyancy-induced flow through the hole.

... A one-step pyrolysis reaction is considered for the PMMA decomposition reaction to form MMA [10]. The thermal properties of PMMA are given as functions of temperature [11] and surface radiative properties are from [12]. The absorption coefficient of PMMA at 10.6 lm is 175 cm À1 (measured using FTIR). ...

Numerical computations and a series of experiments were conducted in microgravity to study the ignition characteristics of a thin polymethylmethacrylate (PMMA) sheet (thicknesses of 0.2 and 0.4 mm) using a CO2 laser as an external radiant source. Two separate ignition events were observed, including ignition over the irradiated surface (frontside ignition), and ignition, after some delay, over the backside surface (backside ignition). The backside ignition was achieved in two different modes. In the first mode, after the laser was turned off, the flame shrank and stabilized closer to the fuel surface. This allowed the flame to travel from the frontside to the backside through the small, open hole generated by the laser’s vaporization of PMMA. In the second mode, backside ignition was achieved during the laser irradiation. The numerical calculation simulating this second process predicts fresh oxygen supply flows from the backside gas phase to the frontside gas phase through the open hole, which mixes with accumulated hot MMA fuel vapor which is ignited as a second flame in the frontside gas phase above the hole. Then, the flame initiated from the second ignition travels through the hole to ignite the accumulated flammable mixture in the backside gas phase near the hole, attaining backside ignition. The first backside ignition mode was observed in 21% oxygen and the second backside ignition mode in 35%. The duration of the laser irradiation appears to have important effects on the onset of backside ignition. For example, in 21% oxygen, the backside ignition was attained after a 3 s laser duration but was not observed after a 6 s laser duration (within the available test time of 10 s). Longer laser duration might prevent two-sided ignition in low oxygen concentrations.

The problem of simulating the thermomechanical behavior of composites under high temperatures is complex because it straddles many fields: thermal physics, thermal chemistry, solid mechanics, etc. Since concepts such as thermodecomposition and ablation are new to mechanicians calculating microstresses in composites, we define the principal ideas of physico-chemical transformations in this chapter. A schematic classification of the most wide-spread types of high-temperature effects on composite structures is given, and their principal types (aerodynamical heating, gas-dynamical heating, heating in energetic devices, action of a fire and technological heating) are considered in detail. Furthermore, a classification of ablation processes in composites is suggested, and main types of volumetric ablation (pyrolytic thermodecomposition (TD) and thermo-oxidative decomposition (TOD)) and surface ablation (evaporation, chemical reactions with the surroundings (mainly, combustion), melting and thermomechanical erosion) are defined. In addition, the principal phenomena caused by high-temperature effects in composite materials and composite structures are enumerated, and a physical model of ablative composite is suggested.

The experiments of downward flame spread over poly(methyl methacrylate) sheets with different dimensions were conducted in this study. In comparison with flame spread over samples under infinite width condition, lateral air entrainment shows significant influence on downward flame spread of finite width. The characteristic angles, defined as those produced on sample residues in a steady-state stage, are constant for different dimensions. Based on the characteristic angles and with reasonable assumptions, a three-dimensional theoretical model is proposed to illustrate the experimental results. Width effects on downward flame spread over thicker samples are more obvious and they fade away with gradual increase in width. Moreover, the heat flux penetrating through the solid surface at the front of the pyrolysis region is higher than that in the two-dimensional case. The flame height correlates well with mass loss rate as an exponential function with a mean power value of 0.79.

In the present study, the surface catalytic reaction in a microchannel with nonreactive hydrogen-air flow is investigated. Here, the microchannel wall is coated with a catalyst. A solution to the catalytic microchannel flow is gainedbyapplyinganiterative methodtosolve the energy, mole fraction, and catalytic reaction equations.To validate the model, the results of fuel conversion are compared with the results of experimental studies available in the literature, and a good agreement between them is achieved. Moreover, the results show that increasing the hydraulic diameter of the microchannel decreases normalized temperature of the mixture and catalyst heat transfer. Steeper variations are observed in the case of dh/L < 0.2. Furthermore, when the wall-to-inlet-temperature ratio is smaller than 2.5, the fuel conversion is very small; and for TW/Ti > 3.5, the fuel is fully converted. © 2012 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

To explore the flame spread mechanisms over the solid fuel sheets, downward flame spread over vertical polymethylmethacrylate sheets with thicknesses from 1.75 to 5.75 mm have been examined in the quiescent environment. The dependence of the flame spread rate on the thickness of sheets is obtained by one-dimensional heat transfer model. An equation for the flame spread rate based on the thermal properties and the thickness of the sheet by scale lip method is derived from this model. During combustion, temperature within the gas and solid phases is measured by a fine thermocouple. The pyrolysis temperature, the length of the pyrolysis Zone, the length of the preheating zone, and the flame temperature are determined from the experimental data. Mathematical analysis has Welded realistic results. This model provides a useful formula to predict the rate of flame spread over any thin solid fuel.

This paper reports 2D CFD-based computer modeling of opposed flow flame spread over thick samples of polymethylmethacrylate (PMMA). Model predictions are compared with experimental data from normal-gravity experiments at multiple forced flow velocities and KC-135 parabolic flight microgravity experiments. For the normal gravity experiments, good agreement between the model predictions and experimental data is obtained at one oxygen level, but flame spread rates at other oxygen levels are not well predicted. Of the four microgravity data points, the model underpredicts the spread rate of two of the data points by 35% or less. However, the model overpredicts the other two data points by almost a factor of two. Potential reasons for the discrepancies between the model predictions and the experimental data are discussed.

The effect of catalytic surface reaction on non-reactive flow in micro-channels is investigated. The hydraulic diameter of the channel is considered within the range of 0.2–1.2 mm, and the channel length is considered to be 5 mm. The whole length of the channel wall is coated with a catalyst. The sensitivity analysis shows that the effect of normalized hydraulic diameter is more than the normalized longitude coordinates in accordance with the existence of the large ratio of surface area to volume in the micro-channel. For validation of this model, the variation of fuel conversion is compared with the published experimental data and shows an acceptable agreement.

An experimental investigation of smoldering combustion of teak wood and cow dung particles has been carried out. Fuel characterization analysis in terms of the calorific value and fhermo-gravimetric data has been performed with both fuels. Sieved particles of biomass are stacked into a thin paper tube, in which, the smoldering combustion is studied by igniting one end of the tube and by recording the rate of regression of the tube length. The paper tube has been kept in 3 orientations with respect to normal gravity (vertical) direction and smoldering rates for each orientation have been measured using both fuels. The results show that, based on the fuel characteristics, orientation plays an important role in deciding the smoldering rate.

A transient one dimensional model has been presented to simulate degradation and gasification of polyethylene, in early stage of fire growth. In the present model effect of oxygen on degradation and rate of polymer gasification while the sample is subjected to an external radiative heat source is numerically investigated This model includes different mechanism, which affect the degradation process, such as in depth thermal oxidative decomposition, in depth absorption of radiation, heat transfer, volatiles advection in solid phase and convective heat transfer on surface. Also effects of radiative parameters, due to formation of char layer such as surface reflectivity and absorptivity on thermal degradation of polyethylene are investigated The results for 40 kW/m(2) heat source are reported and yielded realistic results, comparing to the published experimental data. The results show that an increase in oxygen concentration leads to considerable increase in gasification rate and also leads to sharp increase of surface temperature.

The experiment which have been made clear the effect of turbulence caused by combustion analyzed in the second paper was done by this paper. The experiments let equivalence ratio of supplied air-fuel mixture, pressure, configuration of combustion chamber and location of ignition plug change using constant volume combustion chamber. As a result of experiments, it became clear that the turbulence caused by combustion was in proportion to the density of supplied air-fuel mixture and mean velocity of flame propagation. The empirical formula is shown next. u^^^'0≈0.058ρ0.440V0.40fm The calorific value calculated using this empirical formula became small around 8% value with mean than theoretical calorific value. And also it became clear that the dispersion of estimation was small comparatively because a value of correlation coefficient was 0.98.

In the present work, numerical computations of the flow and thermal fields have been carried out for a transient, two-dimensional model of thermal and oxidative degradation of polymethylmethacrylate (PMMA) subjected to a monochromatic, radiant heat flux. An external thermal radiation source is used to simulate the primary mode of energy transfer in a room fire. An incompressible SIMPLE code is used with a staggered grid arrangement. The equations for the fluid and solid (fuel) phases are solved simultaneously using a segregated technique. At the outlet of the computational domain, a convective boundary condition is compared with a traditional Neumann condition. The convective boundary condition is shown to be more effective in reducing the CPU time. A study in the effects of spatial resolution and different time steps are provided. A theory is developed to account for thermal and oxidative degradation. The theory is based on differences in polymer degradation behavior in inert and non-inert environments. A number of quantities such as surface temperature and mass flux of PMMA are calculated by an external source of 40 kW/m2. The predictions of the model are in a good agreement with the experimental results. It is found that an increase in gas-phase oxygen concentration obviously decreases the surface temperature and increases the gasification rate of PMMA.

A transient one-dimensional model is applied to study degradation and combustion of a poly methyl methacrylate (PMMA) sample.
Ignition of PMMA is a complex interaction among different mechanisms, including solid fuel degradation, heat transfer, in-depth
absorption of radiation, surface regression, gas-phase advective heat/mass transfer, and combustion. The present task has
the significant feature of coupling the solid and gas phases. Besides the mathematical model has been solved numerically by
using a fast iterative method and has yielded realistic results.

A time-dependent, three-dimensional model is under development to predict the temperature field, burning rate, and bubble bursting characteristics of burning thermoplastic materials in microgravity. Model results will be compared with experiments performed under microgravity and normal gravity conditions. The model will then be used to study the effects of variations in material properties and combustion conditions on burning rate and combustion behavior.

Mixing and combustion characteristics of propane in supersonic air streams is investigated numerically. The configuration used in the study features the existence of a generic rearward-facing step in the upper longitudinal wall. The step is swept from both end sides. Sonic pilot propane is injected at the step base parallel to the incoming supersonic air. The main propane is injected from the upper wall normal to the incoming air with sonic speed. Sweeping the step from both end sides creates a good combustible mixture zone at the step base that initiates and stabilizes the combustion of the main propane injection. It also enhances the fuel-air mixing in the far field domain. The 3-D version of Fluent CFD code is used in the present study. The current work is a step towards an ongoing research work aiming at examining the combustion characteristics of a variety of hydrocarbon fuels. The current work is still underway to complete studying the combustion flowfield of liquid kerosene injection with pilot hydrogen as a comprehensive study to address the possibility of using hydrocarbon fuels in the mid-speed range of the hypersonic flight.

An experimental program is reported in which a specially designed ignition cabinet was used to measure the piloted ignition times of commercial polymer samples at incident irradiances up to 3. 5 cal/sq cm-sec using both benzene flame radiation and tungsten lamp radiation. Spectral absorptances were measured for each sample. A simple mathematical model served as the basis of a correlation of the ignition data.

We consider a mathematical model of thermal degradation of thick solids which is formulated in terms of a general kinetic rate law. The model is applicable to many fire-test situations, notably the standard cone calorimeter test where a horizontal sample is exposed to a uniform heatllux. The model incorporates a mechanism for the transfer of mass through the material as vaporisation occurs - a feature neglected in many mathematical models published to date. Attention is focused on a single-step nth. order Arrhenius reaction for the thermal degradation. Results are presented which quantify the effects of incident heat flux, heat losses and kinetic mechanism on the temperature distribution in the solid and the mass loss rate. In particular we demonstrate that thermal history strongly affects mass loss rate for materials that degrade according to reactions of non-unitary order. The consequences of this and other effects on the ignition characteristics of solids are briefly discussed.

A new edition of the bestseller on convection heat transfer A revised edition of the industry classic, Convection Heat Transfer, Fourth Edition, chronicles how the field of heat transfer has grown and prospered over the last two decades. This new edition is more accessible, while not sacrificing its thorough treatment of the most up-to-date information on current research and applications in the field. One of the foremost leaders in the field, Adrian Bejan has pioneered and taught many of the methods and practices commonly used in the industry today. He continues this book's long-standing role as an inspiring, optimal study tool by providing: Coverage of how convection affects performance, and how convective flows can be configured so that performance is enhanced How convective configurations have been evolving, from the flat plates, smooth pipes, and single-dimension fins of the earlier editions to new populations of configurations: tapered ducts, plates with multiscale features, dendritic fins, duct and plate assemblies (packages) for heat transfer density and compactness, etc. New, updated, and enhanced examples and problems that reflect the author's research and advances in the field since the last edition A solutions manual Complete with hundreds of informative and original illustrations, Convection Heat Transfer, Fourth Edition is the most comprehensive and approachable text for students in schools of mechanical engineering.

Thermal degradation of PMMA subjected to a radiant heat flux was studied both experimentally and numerically. Very accurate measurements of mass loss rate and temperature profiles were performed for three constant heat fluxes: 1.5,2.3 and 3.0 W·cm-'. The results show that the mass loss rate cannot be directly related to the surface temperature and a contribution of the sub-surface region of the sample to the rate of gasification must be taken into account in a thermal degradation odel. A heat source term was introduced in the conduction equation and a kinetic equation was used to locally calculate the mass loss rate in each slab of the solid. The density and the thermal conductivity of the material were assumed temperature independent while for the specific heat the values measured by differential scanning calorimetry in the range 20-400·C were retained. The predictions of the model are in very close agreement with the experimental results for the evolution with time of both the temperature profile in the solid and the mass loss rate.

PRINCIPLES OF HEAT TRANSFER was first published in 1959, and since then it has grown to be considered a classic within the field, setting the standards for coverage and organization within all other Heat Transfer texts. The book is designed for a one-semester course in heat transfer at the junior or senior level, however, flexibility in pedagogy has been provided. Following several recommendations of the ASME Committee on Heat Transfer Education, Kreith, Manglik, and Bohn present relevant and stimulating content in this fresh and comprehensive approach to heat transfer, acknowledging that in today's world classical mathematical solutions to heat transfer problems are often less influential than computational analysis. This acknowledgement is met with the emphasize that students must still learn to appreciate both the physics and the elegance of simple mathematics in addressing complex phenomena, aiming at presenting the principles of heat transfer both within the framework of classical mathematics and empirical correlations.

The heat of gasification is often considered as a fundamental property of solids and is used to estimate burning rates at specific heat fluxes in engineering calculations. For solids which sublime at a critical temperature, there is no problem with this approach. However, how valid is the concept of heat of gasification for real polymers? The exploration of this question starts with an analysis of the usual method for estimating the heat of gasification of solids due to Tewarson & Pion. This method is then compared with specific calculations for PE and PMMA. Finally, a new degradation model based on population balance equations is used to calculate heat of gasification for PMMA under a variety of conditions.

A one-dimensional model describing the melting, degradation, and bubbling behavior of polypropylene exposed to a high heat flux is presented. The region of vigorous bubbling observed in experiment is represented as a mixed layer of uniform temperature. Temperature profiles and thicknesses of solid, melt, and mixed layers are determined by solving conservation equations supplemented by simple models of turbulent mixing. The results of the model with and without a mixed layer are compared with experiment.

The combustion process of polymers is a complex coupling of energy feedback from a flame to thepolymer surface with gasification of the polymer to generate combustible degradation products. Although there are extensive studies of the effects of wind velocity, gas phase oxygen concentration, external thermal radiation, and gravity on the combustion of polymers, the effects of polymer characteristics on combustion and flammability are not nearly as well understood as those in the gas phase. At present, detailed governing equations for continuity, momentum, energy, and chemical species concentration in the gas phase can readily be written with appropriate boundary conditions, and their solutions can be derived for various cases. However, even those governing equations cannot be derived for the condensed phase without understanding of the governing chemical and physical processes that control the gasification of polymers. This paper concentrates on describing various observed phenomena in polymers (which have been often ignored or neglected) during their combustion, some or all of which might have significant effects on the burning rate and flammability properties. Because of a lack of understanding of the basic combustion mechanisms of polymers, theoretical models able to predict combustion phenomena and flammability properties are not available. In order to overcome this problem, global material characteristics are currently measured by well-defined test methods, and the results are used as inputs to fire growth models intended to predict behavior of the materials in specific fire scenarios. To improve the fire performance of polymers, a nonhalogenated char-forming flame-retardant approach is suggested, and its benefits are discussed.

A multiple-step pressure correction algorithm, similar in spirit to the PISO algorithm, has been developed for the calculation of viscous flows in nonorthogonal curvilinear coordinates. The resulting pressure correction equations arc solved using a multigrid correction scheme. These developments were pursued because the pressure correction equation is the most time-consuming part of a Navier-Stokes flow calculation and because of the effect of the coupling between the pressure and velocity variables on the convergence rate. The new algorithm does improve the convergence rate for laminar flows or flows calculated on nearly orthogonal meshes. However, for turbulent or reacting flows, or flows computed on highly nonorthogonal meshes, there is little or no improvement in the convergence rate, and the CPU time is generally higher than for a single-step algorithm. A suitable balance between updating the velocity and static pressure variables is important, since a tightly converged pressure field can exaggerate the changes in the velocity field and cause the overall convergence rate to worsen. Although the multigrid scheme does a much better job of solving the pressure correction equation to high accuracy than a single-grid method, this limits the improvement of the overall algorithm that is possible. These results indicate that a multiple-step pressure correction algorithm does not have a decisive advantage over a single-step algorithm for many practical flows.

Smoldering combustion of various natural and synthetic solid materials constitutes a substantial fire hazard; the process itself produces copious toxic gases and it can lead to flaming combustion. This review focuses on the coupled chemical and physical processes involved in self-sustained propagation of smoldering. The potential heat sources (gas-phase oxidation, oxidative polymer degradation. char oxidation) are examined, along with the heat sinks (polymer pyrolysis, water vaporization). It is concluded that, even for the most-studied case of cellulose, the chemical mechanisms involved in these processes are both too complex and too poorly understood to be included in a smolder propagation model. Greatly simplified kinetic schemes are currently inevitable; the kinetic parameters are empirical and of restricted usefulness. A general model of the thermophysics of propagation (for arbitrary chemistry) is presented as a benchmark against which to compare existing models. The general case, with gradients both on the scale of the particles that comprise the fuel and on the scale of the overall combustion wave moving through the fuel bed, is too complex to be tractable. The general model equations are non-dimensionalized: simplifications are noted in the limit of small or large values for certain dimensionless groups. Existing smolder propagation models in the literature are reviewed; all represent great simplifications of the general case and none closely describes a realistic smoldering fire hazard. The principal usefulness of existing models is in rationalizing certain experimentally-observed trends. Truly useful predictive models of realistic hazard situations remain to be developed.

The classical model on erosion combustion of energetic materials explains the phenomenon of increasing the combustion rate with growing an external hot flow speed only by heat effects caused by turbulence of the flow. However, experiments with flammable materials show that combustion in high-speed and high-enthalpy flows is accompanied with mechanical erosion, i.e., with dispersing the surface particles. In the present paper a new model of erosion combustion is suggested that describes an influence not only of turbulence but also of mechanical destruction (dispersing) of the material on the combustion rate of energetic materials. The experiments conducted for combustion of polysiloxane rubbers in high-enthalpy flows showed a good agreement of theoretical and experimental results.

The primary achievement in this work has been the discovery that turbulent upward flame spread on noncharring materials (for pyrolysis lengths less than 1.8 m) can be directly predicted by using measurable flammability parameters. These parameters are: a characteristic length scale which is proportional to a turbulent combustion and mixing related length scale parameter (q̇″net (ΔHcΔHv))2, a pyrolysis or ignition time τp, and a parameter which determines the transient pyrolysis history of a non-charring material: λ = Lc ΔTp = ratio of the latent heat to the sensible heat of the pyrolysis temperature of the material. In the length scale parameter, q̇″net is the total net heat flux from the flames to the wall (i.e., total heat flux minus reradiation losses), ΔHc is the heat of combustion and ΔHc is an effective heat of gasification for the material. The pyrolysis or ignition time depends (for thermally thick conditions) on the material thermal inertia, the pyrolysis temperature, and the total heat flux from the flames to the wall, q̇″fw. The present discovery was made possible by using both a numerical simulation, developed earlier, and exact similarity solutions, which are developed in this work. The predictions of the analysis have been validated by comparison with upward flame spread experiments on PMMA. The present results are directly applicable for pyrolysis lengths less than 1.8 m over which experiments in practical materials show that the total (radiative and convective) heat flux to the wall from the flames is a function of the height normalized by the flame height (ZZf) having a maximum value that is nearly constant for many materials; this profile is approximated in the work by a uniform profile of constant heat flux over the flame length, without loss of generality or violation of the physical situation. As the pyrolysis length increases (> ∼ 1.8 m), radiation dominates and a different total wall heat flux distribution applies. For this case a numerical simulation, such as FMRC's upward Flame Spread and Growth (FSG) code, can be used to predict upward flame spread rates while the present correlations can provide an upper bound for the flame spread rate.

Experimental results relating flame radiation feedback mechanisms to the burning behavior of 51 mm-thick, solid, horizontal, square, polymethyl methacrylate (PMMA) pools are discussed. Data for sizes ranging from 25 mm × 25 mm to 1.22 m × 1.22 m show that the burning rate per unit surface area of plastic pool fires increases with scale and is dominated, at the larger scales, by thermal radiation from the flames. The total radiative power output of the flames represents 42% of total heat release rate of the larger PMMA fires. Local burning rates for the larger plastic pools are maximum at pool center, corresponding to maximum radiative heat transfer from the flames, and decrease monotonically to the edge of the pool. Relatively long time periods are required to establish steady burning in the intermediate sized pools. The long “burn-in” time to reach steady state is associated with increasing radiative heat flux from the flames to the pool with time. The magnitude of the time-dependent radiative heat flux to the pool is calculated on the basis of a one-dimensional analysis for a semi-infinite slab. The variation of local burning rates along the pool surface is formulated in terms of a cylindrical flame model. Physical implications of the assumptions made in the analysis and their limitations are reviewed critically.

The oxidative degradation of poly(methyl methacrylate), PMMA, has been investigated at temperatures up to 320°C. Molecular oxygen protects PMMA against depolymerization at temperatures below about 220°C. At higher temperatures oxidative main-chain scission becomes very important as evidenced by molar mass determinations. By GC-MS analysis it was found that the condensable volatile products contained as major compounds, apart from monomer, 2-methyl-oxirane carbonic acid methyl ester (I), methyl pyruvate (II), dimethyl itaconate (V) and acetaldehyde. According to our proposed mechanisms the formation of I is indicative of main-chain scissions due to the decomposition of oxyl-radicals which are formed by H-abstraction from backbone carbons and the subsequent reaction of the carbon-centered radicals with O2. II is traced back to oxy-radicals formed by reaction of O2 with carbon-centered terminal radicals generated by cleavage of CC bonds in the backbone. The rather high product yield ratio indicates that at T<320°C and in the presence of O2 main-chain cleavage is mainly due to H-abstraction from backbone carbons.

The effects of gas phase oxygen on the rate of gasification and surface temperature of PMMA and low density PE samples (4 X 4 cm) were investigated under transient, nonflam ing heating by thermal radiation. Five different ambient gas mixtures, 100% nitrogen, 5% 02/95% N2, 10% 0';90% N2, 20% 0';80% N2, and 40% O2/60% N2, were used. The ver tically oriented samples were subjected to two different radiant fluxes, 1. 7 and 4.0 W /cm2. For PMMA, large bubbles are formed in the hottest, near-surface layer in a nitrogen en vironment; these bubbles are smaller and more frequent in oxygen-containing environments. It appears that the molten surface layer of PMMA becomes less viscous in an oxygen-con taining environment and this enhances bubbling mass transfer of in-depth-decomposition products to the surface; the bubbles in turn affect the depth to which oxygen alters the decomposition process. The surface of PE turns brown in oxygen-containing environments, increasing the local absorption coefficient and hence increasing the rate of heating. An in crease in gas phase oxygen concentration increases the gasification rate of PMMA and PE substantially. With PMMA, when the rate of gasification becomes substantial, the effect of oxygen on the gasification process is reduced; the counterflow of gases from the surface apparently serves to reduce the oxygen supply rate to the condensed phase. An increase in oxygen concentration significantly decreases the surface temperature of PMMA and even more significantly increases that of PE. Neither polymer gasifies like a liquid in the sense of having constant surface temperature and mass flux proportional to energy input.

This work presents experimental and numerical results for the autoignition and pilot ignition of horizontal black polymethylmethacrylate (PMMA) plates in a cone calorimeter. Experimentally, the histories of plate surface temperature as well as ignition times have been measured for various radiative heating fluxes. Numerically, a two-dimensional axisymmetric model is proposed to simulate the transient processes in the gas and the solid plate. The radiative absorption by the gas phase monomer is considered in a simplified way. With a set of parameters for the one-step Arrhenius kinetics for the gas-phase reaction and a set of parameters for PMMA pyrolysis, the numerical results of surface temperatures and ignition times agree well with the experimental data for both autoignition and pilot ignition. Both experimental and numerical results indicate that while the pilot ignition is pyrolysis-controlled, the autoignition process depends not only on PMMA pyrolysis but also on gas-phase reaction, especially for lower heating fluxes. According to the numerical calculations for autoignition, the ignition times of thermally thin plates are significantly shorter than those of thermally thick plates. For pilot ignition, there exists a linear 1/tig − qrad relation for thermally thick plates, as indicated in the literature.

In a book designed for the engineer to acquaint him with the phenomena occurring in combustion, the emphasis is placed upon the chemical and physical processes occurring and their interactions in flames. The topics discussed are the chemistry of combustion, physics of combustion, kinetically controlled combustion phenomena, diffusion flames in liquid fuel combustion, combustion of solids, combustion of gaseous jet fuels, and flames in premixed gases. The thermodynamics, thermochemistry, and equilibria of reactive mixtures are presented in appendices. (JSR)

Explicit expressions are obtained for the surface regression rates of pyrolyzing vinyl polymers. Thermal degradation of the polymer in a subsurface reaction zone is assumed rate limiting. Emphasis is placed on determination of the proper degradation mechanism (e. g. , mode of initiation and magnitude of the kinetic chain length compared to the degree of polymerization), development of kinetic data, and derivation of corresponding expressions for the rate of mass loss. The method of calculation is based on a matched asymptotic expansion scheme, with the nondimensional activation energy treated as the expansion parameter.

The effects of gas-phase oxygen on the weight loss of poly(methyl methacrylate) (PMMA) were studied by comparing weight loss behavior of PMMA degraded in nitrogen with that of PMMA degraded in air. Thermogravimetry (TG) and isothermal heating experiments were conducted to obtain kinetic constants for the degradation of PMMA. The results show that there are two distinct effects of oxygen on the weight loss of PMMA; one is an increase in PMMA stability at low temperatures and the other is a destabilization of PMMA at high temperatures by enhanced random scission. There are two reaction stages for the weight loss from PMMA degraded in nitrogen and four reaction stages for PMMA degraded in air. These four reaction stages are, however, caused mainly by impurities in the sample. The effects of purification of the commercial PMMA on the weight loss are small for samples degraded in nitrogen, but they are significant for samples degraded in air.

This work investigates experimentally and theoretically the downward spread of a flame over a thick polymethylmethacrylate (PMMA) slab with an opposed flow of air. Simulation results, using an unsteady combustion model with mixed convection, indicate that the ignition delay time increases with a decreasing opposed-flow temperature or increasing velocity. The ignition delay time is nearly constant at a low opposed flow velocity, i.e., . Experiments were conducted at three different opposed flow temperatures and velocities, namely, , and 353 K and , respectively. Measurements included the flame-spread rate and temperature distributions, using thermocouples and laser-holographic interferometry. The qualitative trends of the flame-spread rate and thermal boundary layer thickness, as obtained experimentally and from numerical predictions, were identical. For a quantitative comparison, the predicted and experimental flame-spread rates correlated well with each other, except at the lowest velocity . The discrepancies between the measured and predicted thermal boundary layer thicknesses decreased with an increasing flow velocity. The quantitative agreement with a high velocity indicates that the spread of an opposed flame is mainly controlled by the flame front, whereas the discrepancies at low flow rates demonstrate the importance of radiation, the finite length of the fuel, and also three-dimensional effects, which were not considered in the model. The temperature profiles around the flame front measured by interferometric photographs indicate a recirculation flow there, as predicted by the simulation.

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 (2ood 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.

The effects of sample orientation on autoignition delay times and the minimum external radiant flux for autoignition were studied using a CO2 laser and a gas fired radiant panel as external radiant sources with PMMA and red oak as samples. Ignition delay times were shorter with the horizontal sample than with the vertical one at the same external radiant flux. The minimum external radiant flux for ignition was also less with the horizontal sample. The absorption of external radiation by the boundary layer of decomposition products for the vertical orientation is significant, although its amount is less than the absorption through the plume for the horizontal orientation. Surface temperature at ignition is higher with vertical sample orientation than with horizontal at the same external radiant flux. A theoretical calculation of the surface temperature history with endothermic gasification significantly underestimates the experimental results; this raises a question of the applicability of regression rate expression derived from steady state experiments to the dynamic heating condition.

A one-dimensional unsteady mathematical model of solid fuel ignition is presented. The solid fuel is heated by an external radiative heat source. Some radiation is absorbed in depth by the solid fuel and some by the decomposition products in the gas phase. Solid fuel degradation occurs according to a zero-order Arrhenius pyrolysis reaction and gas-phase combustion according to a second-order Arrhenius reaction. Gas-phase heat and mass transfer and solid phase heat transfer are described by differential balance equations that are coupled through the boundary conditions at the interface. The solution is computed numerically by an implicit finite difference method. PMMA radiative ignition is simulated by varying the intensity of the radiative heat flux and predictions show quite good agreement with experiments. The ignition process oceurs in the gas phase in a premixed fashion, rapidly followed by the transition to a diffusion flame. As the radiative heat flux is increased, higher surface temperatures and pyrolysis mass fluxes are reached, ignition occurs closer and closer to the fuel surface, and ignition delay times decrease. Gas-phase absorption of radiation plays a fundamental role in the predicted ignition phenomenon and ignition delay times. In particular, with realistic data and no absorption of radiation in the gas phase, ignition does not occur at all. Finally, a parametric study is performed in order to analyze the dependence of the predicted ignition phenomenon on key parameters used to model degradation and combustion processes, such as preexponential factors and activation energies of the reactions.

Nonpiloted ignition processes of a thin poly(methyl methacrylate) (PMMA) sheet (0.2 mm thick) with a laser beam as an external radiant source are investigated using three-dimensional, time-dependent numerical calculations. The effects of sample orientation angle on ignition delay time in quiescent air in a normal-gravity environment and of imposed velocity in a microgravity environment are determined. The numerical model includes heat and mass transport processes with global one-step chemical reactions in both gas and solid phases. A simple absorption model based on Beer's law is introduced and bulk absorption coefficients are applied to the solid PMMA and evolved methylmethacrylate (MMA). The PMMA sample surface is kept normal to the incident radiation at all sample orientation angles. In a zero gravity environment, ignition delay time increases with an increase in imposed flow velocity. In quiescent normal gravity, ignition delay time has a strong dependency on the sample orientation angle due to a complex interaction between the buoyancy-induced flow containing evolved MMA and the incident laser beam. Without absorption of the incident radiation by the evolved MMA, ignition is not achieved. The most favorable ignition configuration is the ceiling configuration (downward-facing horizontal sample irradiated by upward laser beam). The formation of a hole through the thin sample due to consumption has two counteractive effects on the ignition process: one is a reduction in the fuel supply rate, and the other is an increase in the air supply from the side opposite to the irradiated side by the buoyancy-induced flow through the hole.

The effect of atmospheric oxygen on the thermal decomposition of poly(methyl methacrylate), PMMA, in a slab-like configuration was investigated. Blackbody irradiation of 12 mm thick PMMA slabs on one side was used to simulate the thermal decomposition and gasification of the polymer in a fire environment. Results are reported for chain scission number obtained from molecular weight measurements and for residual monomer content at various levels below the slab surfaces irradiated at 17 and 30 kW/m2 in atmospheres containing 0, 10, 21, and 41% oxygen in nitrogen.The scission number and polydispersity of surface layers, about 0.1 mm thick, were found to increase linearly with the mole fraction of oxygen in nitrogen. Over this range (0 to 41% O2) the scission number increased from 1.5 to 5.0 and the polydispersity increased from 3.6 to 11.3 when the PMMA was degraded at the lower flux, while at the higher flux, the scission number increased from 5.0 to 14.4 with a concomitant polydispersity change from 2.0 to 4.5. These results show that gas phase O2 reacts with the polymer chains, enhancing random scissions and generating functional groups from which depropagation is initiated. This enhanced decomposition increases the transient gasification rate leading to ignition and flame spread.

The transient, two dimensional non-charring materials version of a numerical model developed to study the ignition of charring and non-charring materials is used to analyse the ignition process of epoxy when subjected to a monochromatic radiation source. The model has the significant feature of coupling the solution for the solid and gas phases through the boundary conditions at the gas/solid interface along with a global finite-rate thermal degradation for the solid phase. The predictions yield physically realistic results, and predicted ignition delays present a maximum deviation of 7.56% when compared with published experimental data for an external radiation source with fluxes ranging from 1 MW·m−2 to 4 MW·m−2.RésuméOn a analysé le processus d'ignition de l'époxy lorsque celui-ci est soumis à une source radiative monochromatique. Pour ce faire, on a utilisé un modèle numérique transitoire et bidimensionnel applicable à des matériaux sans résidue. Ce modèle constitue une version d'un modéle plus général conçu pour des matériaux avec et sans résidu. Le modèle possède la caractéristique particulière de pouvoir coupler les solutions pour les phases solide et gazeuse par l'intermédiaire des conditions frontières à l'interface gaz-solide. II permet, de plus, de tenir compte de la cinétique globale de la dégradation thermique de la phase solide. Les prédictions obtenues sont réalistes: les délairs d'ignition calculés présentent une différence maximale de 7,56%, si on les compare aux données expérimentales de la littérature pour le cas d'une source radiative externe produisant des flux entre 1 et 4 MW·m−2.

Advances in modeling soot formation and burnout in combustion systems are surveyed. The types of models are divided up into three classes: empirical, semi-empirical and detailed. Empirical models use correlations of experimental data to predict trends in soot loadings. Semi-empirical models solve rate equations that are calibrated against experimental data. Detailed models seek to predict the concentrations of all the important species in a flame, from fuel to polyaromatic hydrocarbons to soot. The three classes of models have demonstrated success in predicting soot concentrations. However, our knowledge of some of the fundamental underlying is still open to question and the success of the models has been obtained to some degree by adjustments to fit measurements.

Contenido: Conceptos básicos de corrientes de fluidos; Introducción a los métodos numéricos; Métodos de diferencia finita; Métodos de volumen finito; Solución de sistemas de ecuaciones lineales; Método de problemas inestables; Solución de la ecuación de Navier-Stokes; Geometrías complejas; Flujos turbulentos; Flujo comprensible; Eficiencia y mejora de la exactitud; Cuestiones especiales; Apéndices.

Thesis (Ph. D.)--University of New Brunswick, 1998. Includes bibliographical references.

Analytical studies of the transient and steady-state combustion processes in a hybrid rocket system are discussed. The particular system chosen consists of a gaseous oxidizer flowing within a tube of solid fuel, resulting in a heterogeneous combustion. Finite rate chemical kinetics with appropriate reaction mechanisms were incorporated in the model. A temperature dependent Arrhenius type fuel surface regression rate equation was chosen for the current study. The governing mathematical equations employed for the reacting gas phase and for the solid phase are the general, two-dimensional, time-dependent conservation equations in a cylindrical coordinate system. Keeping the simplifying assumptions to a minimum, these basic equations were programmed for numerical computation, using two implicit finite-difference schemes, the Lax-Wendroff scheme for the gas phase, and, the Crank-Nicolson scheme for the solid phase.

Principle of Heat Transfer Thermal degradation kinetics and surface pyrolysis of vinyl polymers

- F Kreith
- M S Bohn

Kreith, F. and Bohn, M.S. (1997) Principle of Heat Transfer, 5th ed., PWS Publishing Company, Minneapolis. Lengelle, G. (1982) Thermal degradation kinetics and surface pyrolysis of vinyl polymers. AIAA J., 8, 1989–1996.

Numerical modeling of ignition by radiation for a cellulosic material Computational Modelling of Free and Moving Boundary Pro-blems III

- J A Esfahani
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- A M G Lopes

Esfahani, J.A., Sousa, A.C.M., and Lopes, A.M.G. (1995) Numerical modeling of ignition by radiation for a cellulosic material. In L.C. Wrobel, B. Sarter, C.A. Brebbia (Eds.) Computational Modelling of Free and Moving Boundary Pro-blems III, Computational Mechanics Publications, Southampton, U.K., pp. 327–334.

Numerical Studies of the Ignition Process of Charring and Non-Charring Solid Materials. Ph.D. Dissertation, Dept. of Mechanical Engineering Ignition of epoxy by a high radiation source. A numerical study

- J A Esfahani

Esfahani, J.A. (1998) Numerical Studies of the Ignition Process of Charring and Non-Charring Solid Materials. Ph.D. Dissertation, Dept. of Mechanical Engineering, University of New Brunswick, Canada. Esfahani, J.A. and Sousa, A.C.M. (1999) Ignition of epoxy by a high radiation source. A numerical study. Int. J. Therm. Sci., 38, 315–323.

Behavior of Charring Materials in Simulated Fire Environments

- E M Suuberg
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Suuberg, E.M., Milosavljevic, I., and Lilly, W.D. (1994) Behavior of Charring Materials in Simulated Fire Environments. NIST-GCR-94-645.

Numerical Modelling of PMMA Igni-tion Induced by Monochromatic Radiation. 17th UIT National Heat Transfer Conference

- A C M Sousa
- J A Esfahani

Sousa, A.C.M. and Esfahani, J.A. (1999) Numerical Modelling of PMMA Igni-tion Induced by Monochromatic Radiation. 17th UIT National Heat Transfer Conference, Unione Italiana Di Thermofluidodinamica, Ferrara, Italy, pp. 409–420.

Radiative Heat Transfer Modelling of smoldering combustion propagation

- M F Modest
- Mcgraw
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- T J Ohlemiller

Modest, M.F. (1993) Radiative Heat Transfer, McGraw–Hill, Singapore. Ohlemiller, T.J. (1985) Modelling of smoldering combustion propagation. Prog. Energy Combust. Sci., 11, 277–310.

Parameter Estimation in Engineering and Science Di Blasi, C. (1993) Modeling and simulation of combustion processes of charring and non-charring solid fuels Numerical model of ignition processes of polymeric materials including gas-phase absorption of radiation

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Beck, J.V. and Arnold, K.J. (1977) Parameter Estimation in Engineering and Science, John Wiley & Sons, New York. Di Blasi, C. (1993) Modeling and simulation of combustion processes of charring and non-charring solid fuels. Prog. Energy Combust. Sci., 19, 71–104 Di Blasi, C., Crescitelli, S., Russo, G., and Cinque, G. (1991) Numerical model of ignition processes of polymeric materials including gas-phase absorption of radiation. Combust. Flame, 83, 333–344.

A numerical model for combustion of bubbling thermoplastic materials in microgravity, Fire Research Division, Building and Fire Research Laboratory, National Institute of Standards and Technology

- Km Butler

Butler KM (2002) A numerical model for combustion of bubbling
thermoplastic materials in microgravity, Fire Research Division,
Building and Fire Research Laboratory, National Institute of
Standards and Technology, Gaithersburg, MD 20899–8665

Introduction to combustion phenomena Gordon and Breach Science Publishers, USA 29 Study of pressure correction methods with multigrid for viscous flow calculation in non orthogonal curvilinear coordinates

- Am Kanury

Kanury AM (1982) Introduction to combustion phenomena, 3rd
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Interactive effect of oxygen diffusion-volatile advection on the rate of gasification for poly methyl methacrylate (PMMA): a numerical study

- A Kashani

Kashani A (2004) Interactive effect of oxygen diffusion-volatile
advection on the rate of gasification for poly methyl methacrylate
(PMMA): a numerical study, Masters of Science Thesis,
Department of Mechanical Engineering, Ferdowsi University of
Mashhad, Iran

Numerical studies of the ignition process of charring and non-charring solid materials, PhD Dissertation Modeling of smoldering combustion propagation

- Ja Esfahani

Esfahani JA (1998) Numerical studies of the ignition process of
charring and non-charring solid materials, PhD Dissertation,
Department of Mechanical Engineering, University of New
Brunswick, Canada
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propagation. Prog Energy Combust Sci 11:277–310