Mathematical Modeling & Simulation of Pyrolysis ...

Bergische Universität Wuppertal

Mathematical Modeling & Simulation of Pyrolysis & Flame Spread in OpenFOAM Master Thesis submitted for the degree of

M.Sc. Computer Simulation in Science

Ashish Davinderkumar Vinayak Matriculation Number: 1426291

supervised by Dr. rer. nat. Lukas Arnold Dr.-Ing. Stephan Kelm

October 30, 2017

Declaration I hereby declare that this dissertation towards the completion of my master thesis is a result of my own independent work. I have exercised reasonable caution towards acknowledging the work of others wherever such a situation has occurred. Additionally, I hereby give consent for my dissertation, if accepted, to be available freely for distribution and understand that any reference to or quotation of this work will receive an acknowledgement. Wuppertal, October 30, 2017

................................................. Ashish Davinderkumar Vinayak

Code developed for this work is available at: https://github.com/ashishvinayak/fireFoamBoundaryConditions

Abstract This thesis investigates the numerical modeling and simulation of pyrolysis and flame spread using OpenFOAM. For the purpose of simulation, the large eddy simulation solver FireFOAM developed by FM Global was used. A major portion of the thesis involves the coupling of mass and energy transfer across the fluid and material domains, to achieve radiant heating of Polymethyl methacrylate (PMMA), which serves as the dominant mode of energy transfer during the flaming combustion of PMMA. Ongoing research at Bergische Universität Wuppertal (BUW) with Cone Calorimeter-like experiments (ISO-17554) is used to validate the results of the simulation. The investigation consists of 5 setups, wherein simulated setup consists of a horizontal and vertical placed PMMA blocks, that are heated using a fixed incident flux at various angles. In the initial stage, simulations were carried out in an uncoupled manner to achieve convergence in either regions of the mesh. Increasing in complexity, several boundary conditions were developed, to realize the idea of mass, momentum and energy transfer across the interface boundary. The thesis provides a method to obtain mass loss rate (MLR) of any arbitrary material when it is subject to radiant heat at its surface. The addition of radiation to an already burning material increases the mass loss rate (MLR) of the material. This is demonstrated through the development of a new boundary condition that applies a fixed radiant heat with the addition of a surface radiation source term from the flame. For obtaining a proof of concept, a minimum residual optimization was carried out for three parameters, namely, heat of volatilization, the pre-exponential factor and the activation energy ratio, the latter of which are the Arrhenius parameters. The optimization of single parameters shows that the activation energy ratio and heat of volatilization is a highly sensitive parameters, greatly affecting the magnitude of mass loss rate of the material. For the first simulation, on which the optimization was carried out, the simulated results show good agreement with the experimentally obtained values. For the remaining 4 simulations, the mass loss rate and flame spread velocity were computed. The mass loss rates show parallel gradients i.e they are shifted in time to the experimentally obtained values. This in turn causes the predicted values of flame spread velocity to be higher than the experimental results. Thus, the idea of using one set of optimized parameters for all simulations could not be confirmed. It would therefore be possible to obtain exact curves for the other simulations by further optimization.

Keywords Pyrolysis, CFD, OpenFOAM, FireFOAM, flame spread, fire modeling, multi-region simulation, radiation heat transfer

Preface This report in Pyrolysis and Flame Spread Modeling was written as a part of a master thesis at the Bergische Universität Wuppertal (BUW) in cooperation with Forschungszentrum Jülich in Germany for a period of 6 months starting February 2017. Acknowledgment I would firstly like to thank my supervisors Dr. rer. nat. Lukas Arnold and Dr.-Ing. Stephan Kelm who provided me with the right amount of guidance each time I faced difficulties and pushed me in the right direction. Their help has been very consequential for me to develop a right mindset for entry into the field of simulation research. Additionally, I would like to thank Manohar Kampili whose expertise in OpenFOAM has been essential especially during the starting phase of the thesis. I would also like to thank Forschungszentrum Jülich to allow me complete access to use their supercomputing resources. Finally, I would like to thank the staff at Civil Security and Traffic group at Forschungszentrum Jülich who kept me motivated during the entirety of my thesis. Wuppertal, October 30, 2017

................................................. Ashish Davinderkumar Vinayak

Contents 1 Introduction 1.1 The need of pyrolysis modeling 1.2 Objectives

1 1 2

2 Theoretical Background 2.1 Transport Phenomena in Pyrolysis 2.1.1 Solid Phase Heat Conduction 2.1.2 Radiation 2.1.3 Convection and Advection 2.1.4 Other Transport Phenomena 2.2 Pyrolysis Models 2.3 Measurement Methods 2.3.1 Cone Calorimetry 2.3.2 Thermogravimetric Analysis 2.4 Inverse Modeling of Experiments 2.4.1 Parameter Optimization 2.5 Flame Spread

3 4 4 4 5 5 5 7 8 8 9 10 10

3 CFD and Fire Simulation 3.1 Computational Fluid Dynamics 3.2 Conservation Equations 3.2.1 Solid Region 3.2.2 Fluid Region

12 12 12 12 14

4 Simulation of Pyrolysis and Combustion 4.1 Experimental Setup 4.2 Simulation Setup 4.3 Boundary Conditions 4.3.1 Pyrolysis Boundary Conditions 4.3.2 Fluid Boundary Conditions 4.4 Simulation Results 4.4.1 Simulation Description 4.4.2 Lack of Conservation 4.4.3 Development of Boundary Conditions 4.4.4 Coupling Flame Radiation 4.4.5 Parameter Optimization

16 16 18 19 19 21 23 23 23 25 26 26

4.4.6 4.4.7 4.4.8

Results - Mass Loss Rate Results - Flame Spread Visualizations - Flame Spread

28 31 34

5 Conclusions 5.1 Boundary Conditions 5.2 Possibility of Surface Re-radiation 5.3 Flame Spread 5.4 Future Work

38 38 38 38 39

Appendix A Boundary Conditions A.1 Angled Radiant Flux Boundary Condition

40 40

Appendix B Simulation Parameters

43

Appendix C Material Data

44

List of Figures 2.1 2.2 2.3

Schematic– Energy feedback loop for sustained burning TGA curves for PMMA under various atmospheric conditions Flame spread.

3 9 11

4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 4.10 4.11 4.12 4.13 4.14 4.15 4.16 4.19 4.17 4.18 4.20 4.21 4.22 4.23 4.24 4.25 4.26 4.27 4.28 4.29 4.30

General schematic of experimental setup Horizontal Experiment (Angle of inclination = 60◦ ) Vertical Experiment (Angle of inclination = 30◦ ) Simulation Setup in OpenFOAM Configuration for flame spread experiment Mass Loss Rate from Solid Mass Flux by using the debugSwitch tool in OpenFOAM ParaView- Mass Integration over Time Mass conservation holds true with new boundary conditions Radiation simulation results Sensitivity of mass loss rate to pre-exponential factor A Sensitivity of mass loss rate to activation energy ratio Ta Sensitivity of mass loss rate to heat of volatilization Simulation 1 (horizontally incident radiation) results over time Fluctuation of mass of system (g) vs. time (s) Simulation 2 (horizontal plate, θ = 30o ) results over time Simulation 5 (vertical plate, θ = 60o ) results over time Simulation 3 (horizontal plate, θ = 60o ) results over time Simulation 4 (vertical plate, θ = 30o ) results over time Configuration 2- Flame spread velocity (m s−1 ) as a function of time (s) Configuration 3- Flame spread velocity (m s−1 ) as a function of time (s) Configuration 4- Flame spread velocity (m s−1 ) as a function of time (s) Configuration 5- Flame spread velocity (m s−1 ) as a function of time (s) Experiment 3 - Effect of blower on flame spread Experiment 5 - Top of image shows heat transfer from flame to atmosphere Simulation 5 - Flame is confined to the geometry in the top half Simulation 2 - Temperature profiles during initial flaming period Simulation 3 - Temperature profiles during initial flaming period Simulation 4 - Steady state temperature profile Simulation 5 - Steady state temperature profile

16 17 17 18 19 24 24 25 25 26 27 27 28 28 29 29 30 30 30 31 31 32 32 33 34 34 35 36 37 37

A.1 2-Dimensional radiation schematic A.2 Heat exchange between two bodies

40 41

List of Tables 2.1 2.2 2.3

Temperature dependent specific heat [1] Temperature dependent thermal conductivity [2] Temperature dependent density [2]

4.1 4.2 4.3 4.4 4.5 4.6

Details of experimental configurations Boundary Conditions- Pyrolysis Boundary Conditions- Species Mass Fractions Boundary Conditions- Fluid Properties Boundary Conditions- Turbulence & Radiation Predicted average flame spread velocities

B.1 List of parameters used in the pyrolysis simulation

4 4 4 18 19 21 21 21 32 43

Nomenclature ρ c κ t A Ea Tcrit Yi hs u e p¯ µ µsgs fk Y Dk ¯˙ 000 ω k fs h P rt 00 q¯˙r 00 q¯˙c m ˙ exp m ˙ num Hvol ∆hf Q σ R Ta = Ea /R

Density of solid [kg m−3 ] Specific heat of solid [J/kgK] Thermal conductivity of solid [W/mK] Total emissivity of material Pre-exponential factor for Arrhenius equation [s−1 ] Activation energy [J mol−1 ] Critical temperature of solid K Species mass fractions Sensible enthalpy [kJ kg−1 ] Fluid velocity [m s−1 ] Fluid pressure [N m−2 ] Dynamic viscosity of fluid [N s m−2 ] Subgrid-scale viscosity [N s m−2 ] Mass fraction of species k Mass diffusivity of species k [m2 s−1 ] Reaction rate of the species [kg/m3 s] Sensible enthalpy [kJ kg−1 ] Turbulent Prandtl number Radiative flux [W m−2 ] Combustion source term [W m−2 ] Experimental mass loss rate [kg s−1 ] Numerical mass loss rate [kg s−1 ] Heat of volatilization (standard) [J/kgm3 ] Heat of volatilization (OpenFOAM) [J/kgm3 ] Heat flux [W m−2 ] Stefan-Boltzmann constant [W/m2 K4 ] Ideal gas constant [J/molK] Activation energy ratio (OpenFOAM) [K] List of variables used

1 | Introduction 1.1

The need of pyrolysis modeling

General fire modeling does not consider the initiation phase of a fire. We instead prescribe a set of initial conditions such as inlet mass flux of gaseous species, or a heat release rate, and measure the consequence of these parameters on the volume domain under consideration. Thus the way in which these gases are generated, namely pyrolysis is not considered [3]. While this method of modeling has its benefits towards the design of a building and evaluating it’s fire hazard, the actual development of fire is not a subject of consideration. In general, accurate fire modeling involves the coupling of many non-linear coupled phenomena on a broad range of length and time scales. During the pyrolysis of PMMA for example, a large number of combustible transient gases are released adding to the complexity of the fire [4]. The composition of the gaseous volatiles is a matter of primary importance, since it determines the stability of the flame and the amount of soot that a flame will produce. In order to accurately predict the fire development using a simulation, in the first step the coupling of the condensed phase (solid phase pyrolysis) model with the gas phase model must be achieved. Due to increase in computing power, it is now possible to achieve a coupling between the solid and fluid phase. Another important problem with pyrolysis modeling is that much of the prescriptive models rely on the use of data obtained from bench scale tests such as cone calorimeter, thermogravimetric analysis, etc. While this data must not be viewed in negative light, it does have its limitations in terms of accurately being able to predict the thermal stability of solids. The long term goal in fire research is to use material property data as direct input in fire simulations [5]. Fire draws a lot of parallels with combustion and the application Navier-Stokes equations have been understood to a large extent in relation to fire modeling. Much of the development towards fire modeling also comes as an extension from modeling of combustion. Pyrolysis modeling, however, is lagging behind with the models only being able to simulate elementary single-step reactions, over a narrow range of materials (namely, wood and thermoplastics). This lag becomes even bigger when we use these simplified pyrolysis models simulate pyrolysis of complex materials. Speaking generally, even though the level of complexity achieved using these single-step reactions is not very high, it serves as a good approximation as well as a starting point towards the study of pyrolysis modeling. It also necessitates the need for a proper analysis of the physical phenomena to understand where simplifications may be applied. For the purpose of this study, the open-source CFD software OpenFOAM was used, which provides a good balance between modeling simplifications as well as simulation complexity.

1

1.2

Objectives

The objectives of this master thesis are as follows: • Understand pyrolysis and fire modeling in the OpenFOAM framework. • Simulation of pyrolysis and combustion of PMMA with FireFOAM solver. • Validate the use of the current models with experimental data. • Suggest improvements in the current model. The thesis is organized as follows: Chapter 1 introduces the topic and gives the motivation behind the thesis. Chapter 2 delves further into the topic of pyrolysis modeling giving some background information about the research that has been carried out in the field, as well as some of the essential literature. Chapter 3 introduces the FireFOAM solver and the equations relevant to pyrolysis and fire modeling. Chapter 4 uses the developed ideas to simulate pyrolysis and combustion of PMMA, and further discusses the obtained results. Chapter 5 presents the concluding remarks from the thesis and provides suggestions for further development of the solver.

2

2 | Theoretical Background Pyrolysis, as used in the fire research community refers to the thermal decomposition and degradation of a material in the presence of applied heat. According to the American Society for Testing and Materials (ASTM), thermal decomposition is defined as extensive chemical change of material caused by heat. Thermal degradation is defined as a process whereby the action of heat or elevated temperature causes a loss of physical, mechanical or chemical properties. In terms of fire, both of these processes play a significant role. For example, a polymeric material will melt on heating to form a pool of fuel, which will lead to a larger pool fire. Although, both these processes are important in the context of a fire, only thermal decomposition leads to the formation of gaseous volatiles, which in turn leads to fire [6]. For the decomposition to be self-sustainable, the burning gases must provide sufficient heat in terms of a feedback mechanism back to the surface of the solid material. Thus a continuous loop is formed (figure 2.1), wherein the heat from the flame around the material is provided back to the material which in turn results in the formation of more gaseous volatiles and increase of mass loss from the material.

Figure 2.1: Schematic– Energy feedback loop for sustained burning The production of volatiles in polymers is generally much more complicated than that of flammable liquids. In the case of flammable liquids, gasification process simply consists of evaporation. However, polymers in their canonical form are simply non-volatile and energy is required to break up the solid molecules into shorter molecules i.e monomers. However, at high surface temperatures, polymers break down into a large number of gaseous species such as hydrogen as well as complex molecules of higher molecular weight such as methane [7].

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2.1

Transport Phenomena in Pyrolysis

Various physical phenomena take place within the solid material as it undergoes thermal decomposition. A pyrolysis model must account for these phenomena up to a desired level of complexity, specifically by making simplifications that reduce the computational time of the simulation yet it must sufficiently predict the pyrolysis behavior. A brief description of these transport phenomena is made below.

2.1.1

Solid Phase Heat Conduction

With regard to the solid phase heat conduction, the thermophysical properties such as specific heat, density, thermal conductivity are temperature dependent. These can be accommodated by the use of thermophysical models. The density of polymers generally reduces by as much as 20% from room temperature to ignition temperature (Tig = 360 K). The temperature dependent specific heat, density and thermal conductivity of PMMA are given in tables 2.1, 2.2, 2.3. T [◦C] c [J/kg · K]

17 1434

47 1564

77 1694

97 1781

107 2180

167 2333

227 2486

277 2613

Table 2.1: Temperature dependent specific heat [1]

T [◦C] κ [W/m · K]

0 0.2

105 0.2

275 0.16

Table 2.2: Temperature dependent thermal conductivity [2]

T [◦C] ρ [kg m−3 ]

40 1181

80 1171

120 1153

160 1126

200 1097

220 1082

240 1067

260 1052

Table 2.3: Temperature dependent density [2]

2.1.2

Radiation

Radiation from a fire serves as the largest source of heat transfer into a material during flaming [8]. Moreover, since the absorption of radiation into the material is wavelength dependent, we must understand the radiation properties of a material sufficiently well in order to make the necessary simplifications during modeling. At certain wavelengths, some solids are semi-transparent and absorb radiation in-depth. This causes the peak temperature to occur within the material instead of on the surface. The absorption of radiant heat into the material is controlled by its absorptivity κ which is strongly wavelength dependent. For example, in case of clear PMMA the absorptivity within 1 µm is almost zero whereas above 3 µm, it approaches unity [3]. It is possible to model in-depth radiation by an additional source term in the energy conservation equation of the condensed phase. Contrary to semi-transparent materials, opaque materials do not absorb radiation in-depth but within 1 µm of the surface depth. This simplifying assumption is generally used in case of 4

fire modeling. In case of PMMA, the absorption of radiation in-depth is generally less than 1 mm [9] and hence, radiation absorption can be treated as a surface phenomenon. In terms of modeling, the common way to achieve radiative feedback is by directly prescribing a known value of flame radiation on the surface of the material. For example, in case of PMMA, during the steady state burning, the radiant heat contribution due to flaming is up to 30 kW m−2 [3], [10]. However, this shifts the onus of modeling from prediction to prescription. As will be seen later, the thesis investigates the possibility of using radiation models to be able to predict the radiant flux from the flame at the surface instead of manually prescribing a known value on the surface.

2.1.3

Convection and Advection

Convection refers to the heat transfer between gases and solid material within the material itself. Within the solid, gases are generated in-depth (for example due to in-depth radiation absorption). As the volatiles escapes to the surface, they transfer energy to the material that may be at a temperature lower than the gases itself. Since the solid material has an effective temperature that is lower than the escaping gases, the overall result is a cooling effect within the material, which is due to convective heat transfer. Advection refers to the bulk motion of the condensed phase species. Escaping gases from inside the material, result in the creation of voids within the material. Surrounding molten material fills these voids, thereby causing the thickness of the solid to reduce. This is also termed as surface regression. Surface regression is not investigated in this work.

2.1.4

Other Transport Phenomena

Several other transport phenomena occur during the thermal decomposition of PMMA. Primary among them are melting, bubbling and momentum transport. The decomposition of polymers occurs over a range of temperatures [7]. During pyrolysis, PMMA will first undergo melting at a temperature lower than the vaporization temperature. This melting of PMMA in turn influences its combustion behavior since heat is absorbed by the material to cause phase change into gaseous state. Melting also results in the entrainment of oxygen into the material which further results in bubbling. The presence of gas phase oxygen within the solid causes a loss in viscosity of molten polymer and increases the frequency with which bubbling occurs. Bubbles that are formed on the surface break, causing small holes in the material. Bubbles are also formed in-depth, resulting in vicious spewing of material into the gas phase and creation of neck-like holes in the material. However, at high irradiation levels, bubbles are smaller and closer to the surface [9]. Melting is not treated as it greatly increases the modeling complexity. Additionally, it is assumed that all products formed inside the material are released spontaneously at the surface. Physically, this means that any gaseous products formed during pyrolysis receive negligible resistance in their path up to the surface. Thus, the momentum equation is not solved, which further reduces the modeling complexity.

2.2

Pyrolysis Models

A pyrolysis model is a mathematical model that quantifies the mass loss rate of a material when the material is thermally stimulated by some kind of incident heat flux. This mass loss data can optionally further be used as a inlet flux boundary condition in a computer fire model. Much literature is available regarding pyrolysis modeling [11] [12]. This text gives a brief description of 5

the types of pyrolysis models available currently. Particularly the transport equations relevant to pyrolysis modeling in OpenFOAM are described in section 3.2.1. Pyrolysis models for polymers such as PMMA can be divided into two types, namely, semiempirical models and comprehensive models. Semi-empirical Pyrolysis Models Semi-empirical models provide a macroscale description of the fire phenomena wherein they relate burning or flame spread rates directly to bench scale test data. Microscale contribution of the fire is not considered in this case. A fire test apparatus usually measures the mass loss rate (MLR) and the heat release rate (HRR) of small samples that are exposed to radiant heating. The idea of semi-empirical models is to formulate the conservation equations such that available material property data from bench scale tests can directly be used. For example in one modeling approach, it is assumed that the mass loss rate of a material is zero until it reaches a pyrolysis temperature (Tp ) which is usually the ignition temperature of the material (Tig ). The time at which the pyrolyzing material reaches the pyrolysis temperature is determined by solving the transient heat conduction equation. One method of doing so, is by assuming the material to be a constant property, semi-infinite solid and applying Duhamel’s theorem [3]: ( ” R t q˙net,mod (τ ) 1 √ dτ for t < tp T0 + √πkρc τ =0 t−τ (2.2.1) Ts (t) = Tp for t ≥ tp In equation 2.2.1, Ts is the surface temperature, T0 is the initial temperature of the solid and ” q˙net,mod is the net heat flux to the surface of the material calculated by the model. tp is the time at which the surface reaches the pyrolysis temperature Tp , and kρc is the apparent thermal inertia. The heat of gasification ∆Hg is the amount of heat required to generate unit mass of pyrosylate gas at temperature Tp from unit mass of solid at temperature T0 . Thus, if the solid ignites at temperature Tp with heat of combustion ∆Hc , the heat release rate from the model is given as: ( 0 if t < tp (2.2.2) Q˙ ”mod = ∆Hc ” q ˙ if t ≥ tp ∆Hg net,mod ∆Hc The ratio ∆H is a material fire property called as combustibility ratio. The equation 2.2.2 is g strictly valid for non-charring, thermally thick, ablative (evaporating) solids. A clear limitation exists in the above model. Experimental measurements have shown that burning temperatures of materials is generally higher than the ignition temperature Tig . However, all the input parameters required such as ∆Hc , ∆Hg , kρc, Tig is available directly from bench scale fire test data.

Comprehensive Pyrolysis Models Comprehensive models are further divided into two types– ablation models and finite rate pyrolysis models. The simplest class i.e ablation models, the temperature profile of the surface is determined by using finite difference methods or by using integral methods instead of using Duhamel’s theorem. The mass loss rate from the material is assumed to be zero unless the critical temperature Tp is reached upon which the surface is maintained at Tp . Thus the pyrolysis kinetics are considered to be infinitely fast, and heat diffusion is the limiting process. The temperature distribution in the solid T (z, t) is calculated using a one-dimensional heat conduction equation for a constant

6

density, opaque solid: ∂T ∂ ρc = ∂t ∂z

∂T k ∂z

(2.2.3)

One initial condition and two boundary conditions are required to completely prescribe the above equation. The initial condition specifies the temperature of the solid at time t = 0. The boundary conditions are applied at the front and back face. The front face boundary condition depends on the condition of the material i.e whether it has ignited, whereas the back face boundary condition describes the rate of heat transfer from it as a function of temperature. The following boundary conditions can be applied to the front face based on the state of the material: −κ

∂T ” = q˙net ∂z

T = Tp

for t < tp

(2.2.4)

for t = tp

(2.2.5)

∂T ” = q˙net −m ˙ ” ∆Hvol for t ≥ tp (2.2.6) ∂z The ablation model mentioned above is only slightly more complex than equation 2.2.1. Despite this fact, it is capable of successfully reproducing bench scale fire tests. One important disadvantage of this method is that individual thermophysical property data such as density, specific heat, etc. are required but not available from bench scale tests. Furthermore, it assumes that the temperature on the surface remains constant as Tp which is not the case. Since no mechanism is included to account for surface regression, the results from the model deviate during the last phase of pyrolysis due to insulating effect of substrate and decreasing thickness of solid [3]. The next level of complexity is the finite-rate comprehensive pyrolysis model which assumes an n-th order Arrhenius reaction rate. Generation of gaseous products can occur only at the surface or in-depth due to radiation absorption. The decomposition of the polymer is characterised by three parameters, the pre-exponential factor, the activation energy and the order of reaction (n), which is usually taken as one. This is also the model described in section 3.2.1. A major drawback of this approach is that the action of oxygen concentration on pyrolysis is not considered. Oxygen plays a large effect on the thermal decomposition kinetics, and in a real fire scenario, material is usually subject to varying amounts of oxygen concentration. For example, [9] has demonstrated that the mass loss rate of PMMA increases with increases amount of oxygen concentration [13] (see figure 2.2). −κ

2.3

Measurement Methods

The heat release rate (HRR) from a material is the single most important parameter in a fire hazard [14]. Since assessment of hazards in case of compartment fires is the primary application in fire science, it is important to have proper techniques to measure the HRR and in turn, the mass loss rate (MLR) from the material in question. In general, there exist two methods by which this can be achieved. One of them is by performing full scale tests in an experimental setting. This usually involves multiple large-scale fire tests which consider all the scenarios related to the fire. The second approach involves using small scale data (small sample of material) to calculated the required unknowns and then estimate results in case of large scale fire scenarios using this data. The second approach is both time and cost effective and hence, has become the preferred approach over time.

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2.3.1

Cone Calorimetry

The heat release rate from a material can be determined by using a cone calorimeter. A specimen size of 0.1 m x 0.1 m is placed onto a load cell and exposed to well ventilated conditions of ambient air. Two configurations of the material are possible, usually the specimen is placed horizontally to measure HRR and the vertical configuration is usually used for exploratory studies [15]. The specimen is positioned approximately 25 mm below the bottom plate of the cone heater when in the horizontal orientation. The products of combustion are exhausted using a circular opening at the top of the heater. In cone experiments, a radiant heating of up to 100 kW/m2 is applied and the material is ignited using an ignition pilot such as an electric spark placed between the cone heater and the specimen. Measurement: In 1917, it was shown by Thornton that for a large variety of fuels, the net amount of heat released per unit mass of oxygen consumed is nearly constant. Thus, if we are able to measure the amount of oxygen consumed during a flaming experiment, it is possible to measure the heat release rate as well. This method of measuring the HRR is used in the cone calorimeter and is known as the Oxygen Consumption Method. It is now recognized as the most accurate method of measuring HRR for both small-scale and large-scale fire tests. According to Thornton’s rule, Q˙ = c · m ˙ O2 The constant of proportionality c, is the heat release per unit mass of oxygen consumed, has been measured to be 13.1 MJ kg−1 with a deviation of ±5%. It is thus possible to calculate the heat release rate of a material if the mass of oxygen consumed, (m ˙ O2 ) is known.

2.3.2

Thermogravimetric Analysis

A solid potential to undergo combustion is controlled by the amount of mass that decomposes when an external heat flux is applied to the surface. Thus, it in turn depends on the magnitude of heat flux that has been applied. There are several measurement methods available to measure the thermal stability of solids such as Thermogravimetric Analysis (TGA), Differential Scanning Calorimetry (DSC), etc. The TGA experiment involves applying a constant or linearly increasing radiant heat flux to the surface of the solid material. During the experiment the material is thermally activated causing a release of gaseous volatiles thereby causing a reduction in its mass. A high precision measuring scale is used during the experiment, to measure the mass loss of the material under the influence of applied heat. The TG curve is a plot of α vs. temperature (T). The objective of the TGA is the determination of the kinetic triplet namely, the pre-exponential factor (Z), the activation energy (E) and the order of reaction (n). The mass loss data from TGA is analyzed using a kinetic model given in equation 2.3.1. E dα n = Zexp − (1 − α) (2.3.1) dt RT where, the conversion α is defined as, [3] α=

m0 − m m0 − m∞

Several techniques exist in order to extract the kinetic triplet from TGA data. They involve a non-linear curve fitting between the equation 2.3.1 and the experimental data obtained from TGA. 8

The application of TGA data to real fires is questionable primarily because the heating rates encountered in real fires are much higher than typical TGA experiments. Furthermore, several limitations exist in determining kinetic triplet data from TG curves. There has been significant debate regarding the physical significance of the Arrhenius parameters. Several authors suggest that both, the pre-exponential factor (Z) as well as the activation energy (E) have no physical meaning and must be treated as adjustable model parameters [16] [17]. Despite these limitations, the Arrhenius parameters have been adequately used to reproduce TG data for single step decomposition. Additionally, the decomposition kinetics of materials are sensitive to the presence of oxygen in the environment (see figure 2.2). Due to these sensitivities, it might be useful for kinetic model equations that account for the presence oxygen have also been suggested in research settings [3].

Figure 2.2: TGA curves for PMMA under various atmospheric conditions

2.4

Inverse Modeling of Experiments

As stated earlier, there is an increasing need in fire modeling to change an approach from prescribing a fire scenario (such as HRR) towards actually predicting it. The use of accurate physical properties of material in order to correctly predict the fire is thus a prime objective. However, there are several limitations in porting material property data directly from literature and bench scale fire tests for use in simulations. Physical constants of materials (such as density, specific heat etc.) are inherently variable in nature and in most cases, cannot be prescribed directly from literature. Moreover, during a fire scenario, the values of these physical quantities are subject to change, further complicating the issue. As will be seen later, kinetic parameters from TGA data do not largely influence mass loss rates after the initial period. The mass loss rate of a material is strongly sensitive to reaction enthalpies (for example, ∆Hvol ), which again cannot be directly estimated from bench scale tests. Simplifications made in numerical modeling of pyrolysis further limit the use of physical

9

constants from literature. Due to the apparently unrealistic nature of results obtained from bench scale fire tests, the approach of parameter optimization serves as a good method towards achieving plausible simulation results.

2.4.1

Parameter Optimization

The idea of inverse modeling is to treat physical properties of materials such as density, kinetic triplet, emissivity, etc. as model parameters whose values can be varied over a certain plausible range. This idea of parameter estimation can thus be treated as a purely mathematical problem of optimization. Several methods such as Genetic algorithms, Shuffled Complex Evolution algorithm, etc. exist wherein the aim of the optimization procedure, is to find an optimum set of parameters that minimize an ’objective function’. The objective function is one that estimates the fitness of the numerically obtained results with the experimentally obtained value. The idea is to generate a population of model parameters around a starting value (3 parameters, pre-exponential factor, activation energy ratio, heat of volatilization are optimized in this work) using uniformly distributed pseudo random numbers (r). A set of simulations is then performed based on this population. At the end of the simulation cycle, the residual is computed and the model parameters exhibiting the lowest residual are withheld. The process is then repeated with the best estimate of model parameters a multiple number of times to arrive at the required accuracy. Any model parameter φ is calculated based on a required minimum φ%−min and maximum fraction φ%−max value as given in equation 2.4.1. φ = φo + φo [φ%−min + r ∗ (φ%−max − φ%−min )]

(2.4.1)

For the purpose of this thesis, optimization was performed using a simple minimal residual approach that minimizes the error between experimentally recorded mass loss rate and its numerical value. The residual is computed based on the work of Lautenberger et al. [3]. The residual Em˙ is given in 2.4.2 for approaching an ideal mass loss rate. m ˙ exp 1 X (2.4.2) Em˙ = n∆t |m ˙ num − m ˙ exp | + m˙ m ˙ exp It is important to note that inverse problems are ill-posed. Furthermore, it may be unstable to small changes in input value. While a near-optimal agreement between experimental and numerical results will be obtained, the final solution may not be absolute. In other words, for such an inverse problem, multiple solutions do exist and we may obtain any one of them. It is thus important that we choose a feasible range for model parameters.

2.5

Flame Spread

Flame spread refers to the process of movement of flame in the vicinity of a pyrolyzing region, which causes further heating of the material, due to direct or remote heat transfer between flame and pyrolyzing material [18]. The distribution of flame on a surface occurs after an initially pyrolysed material has already caught fire. Thus, if the fire sustains long enough, the heat transfer from the flame back to the surface will result in further release of unburnt volatiles, causing the flame to spread. The concentrations of fuel and oxygen also strongly affect flame spread. The growth of fire is directly responsible towards the destiny of materials and thus it’s evaluation forms an integral part of evaluating fire hazard. 10

The speed of spread and its sustainability are controlled by the heat balance of surface heating and flame temperature. Flame spread in the direction of mean flow of air is known as wind-aided or concurrent spread whereas, in the direction opposite to mean flow is know as counter-flow spread. Wind-aided spread tends to accelerate the spread of the flame. Additionally, the orientation of the pyrolyzing material and the size of the initial flame, will also determine if the flame will accelerate or extinguish. Figure 2.3b shows the effect of orientation of material on the flame spread. On a horizontal surface, the flame remains confined to a certain length, however as the angle of inclination increases the flame begins to ’crawl’ over the surface thereby speeding up pyrolysis of the material downstream. This is usually expected in wind-aided spread. [18]

(a) Schematic - Upward flame spread

(b) Effect of orientation of material on flame spread

Figure 2.3: Flame spread. Measurement: Figure 2.3a shows a typical schematic of a buoyancy aided flame spread. Flame spread can be measured in two ways, namely, by measuring the distance the flame has travelled or by measuring the distance of pyrolysed material from a datum. The latter of the two i.e the rate of movement of the ignition front is usually defined as the flame spread velocity [18]. The location of the ignition front is the point on the surface where the surface temperature front has crossed the ignition temperature.

11

3 | CFD and Fire Simulation 3.1

Computational Fluid Dynamics

CFD has emerged as a major tool in terms of analysis and prediction of flow systems. While the zone modeling approach was developed by the fire community itself, the CFD modeling approach has been imported into it rather recently, and is very much an active area of research, through the use of solver codes like FireFOAM and FDS. A major advantage of using CFD rather than zone models is that, in a general sense, it is possible to use CFD codes to solve a multitude of problems, and it can be demonstrated that the same solution methods are applicable to model fire related problems. FireFOAM is a Large Eddy Simulation (LES) solver that uses a finite volume approach towards the modeling and discretisation of conservation equations. Several considerations must be made in order to achieve a satisfactory solution some of which include uncertainity related to turbulence modeling, combustion, heat transfer at the boundary etc. In case of pyrolysis modeling, it is essential that the radiation at the boundaries is correctly modeled, as the radiation feedback serves as a major source of heat back to the fire.

3.2

Conservation Equations

This section describes the conservation equations from the FireFOAM solver- a CFD code, based on OpenFOAM developed by FM Global for modeling fire phenomena [19]. Furthermore, a brief introduction is given to the various sub-models that have been used for the task of modeling:

3.2.1

Solid Region

Mass Conservation The mass conservation for the condensed phase species is given as: ∂ρ = −RRg ∂t

(3.2.1)

Here, RRg stands for the total release rate of the gas (defined on a per volume basis). Physically, the equation states that the mass loss rate of the condensed phase species is equal to the total mass generation rate of the gaseous phase species. It solves for the density of condensed phase species. The release rate RRg has been computed using an Arrhenius equation as given in equation (3.2.2). Reaction rate, E −T a = Z · exp − (3.2.2) RRg = A · exp T RT 12

The reaction rate as computed by the Arrhenius equation (3.2.2) is in per second (s−1 ) basis. RRg has been defined in terms of mass concentration of the species, thus accommodating multiple species is possible. RRg must thus be computed based on concentration of each condensed phase species. The discretized form of the equation (3.2.1) is an Euler implicit scheme, that is first order accurate in time. Species Conservation The species conservation equation for condensed phase species can be given as follows: ∂(ρi Yi ) = RRs (Yi ) ∂t

(3.2.3)

Physically, this implies that the concentration of each specie is equal to the rate of generation of the solid species. Since the total concentration of the species Yi must be equal to unity, this equation is solved for (n-1) species. Energy Conservation The energy conservation equation for the condensed phase species can be given as follows: 000 ∂(ρhs ) + O · (κOT ) = Q˙ s ∂t

(3.2.4)

Due to the modular nature of OpenFOAM, it is possible to select source terms based on the 000 complexity required. In total 4 source terms i.e Q˙ s , the latter of the two can be optionally switched. They are: 000

1. The heat added to the system to cause phase change (Q˙ a ). 000

2. The heat lost from the system from escaping gases (Q˙ g ). 000 3. Source term due to gas flux into the cell towards fluid region (Q˙ v ). 000 4. In-depth radiation source term (Q˙ r ). 000 Q˙ a (J/m3 .s) is the product of heat of volatilization and the reaction rate of the solid. It can be thought of as the sum of energy required to break the chemical bonds and further to vaporize the decomposition products. By convention, for an endothermic reaction, ∆Hf is taken 000 as positive. Thus, Q˙ a is also positive when the reaction is endothermic. It is given as a sum over all condensed phase species i as follows: X 000 Q˙ a = − ∆hf (i)RRs (i) (3.2.5)

i 000

Q˙ g = (RRg ) ∗ h is a sink term, which represents the heat lost due to release of pyrolysis gases. Since it appears on the right hand side of the equation, and is negative (gases are leaving the surface), it is treated implicitly in OpenFOAM for better stability. During the pyrolysis reaction, the gas flux moves across the control volumes towards the fluid region. This addition of heat energy across the cells is accounted for by the divergence of the sensible enthalpy gas flux φhs : 000 Q˙ v = O.φhs (3.2.6)

13

000

The in-depth radiation source term Q˙ r , is the radiation that propagates from the material surface inwards, and is dependent on the absorptivity of the material, the initial value of radiation at the surface, distance away from the surface. An exponential distribution of in-depth radiation has been assumed. Furthermore, the distribution of radiation within the material is one-dimensional. The in-depth source radiation is given as: Ra (3.2.7) Q˙ r (a) = O. Qr (0)e− 0 k(x)dx where, Qr (0) is the radiation source at the surface and a is the distance into the material at which the value is desired. In the pyrolysis region the following equation is solved: P M M A → gas

(3.2.8)

The gas mass flux is then transferred to the fluid region wherein combustion takes place. The solid region assumes an opaqueSolid radiation model which does not create an additional source term in equation (3.2.4). However, the transfer of radiation from the fire back to the source material is handled by the feedback boundary condition described in (4.3.1).

3.2.2

Fluid Region

After solving the conservation equations in the pyrolysis region, the fluid region is evolved using the following equations in FireFOAM: Mass Continuity: ∂ ρ¯ + ∇ · ρ¯u e=0 ∂t

(3.2.9)

∂ ρ¯u e + ∇ · (¯ ρu eu e) = −∇¯ p + ∇ · (µ + µsgs ) ∇e u + ∇e uT + ρ¯g ∂t

(3.2.10)

Momentum Continuity:

Species Mass Fraction Transport Equation: For species k = 1, ..., Ns − 1 fk ∂ ρ¯Y νsgs f f ¯˙ k000 + ∇ · ρ¯u eYk = ∇ · ρ¯ Dk + ∇Yk + ω ∂t Sct

(3.2.11)

Energy Equation: fs ∂ ρ¯h fs = Dp¯ + ∇ · ρ¯ Dth + νsgs ∇h fs − ∇ · q¯˙00 + q¯˙00 + ∇ · ρ¯u eh r c ∂t Dt P rt

(3.2.12)

P rt is the turbulent Prandtl number taken as 1. [20] notes that the Lewis number, Le, which is the ratio of thermal diffusivity to mass diffusivity is 1 for methane combustion. This is also the assumption made by FireFOAM as noted by [21]. Thus, the thermal diffusivity Dth in equation 3.2.12 equals Dk i.e the mass diffusivity. Finally, the Schmidt number is also implemented as Sct = 1 in FireFOAM [21]. 14

For simulation of the fire, all the modeling decisions from the previous simulations were retained [22]. One equation eddy-viscosity model is chosen as the LES model chosen for the simulation. The oneEqEddy model uses a modeled balance equation for the SGS turbulent energy k to simulate the behaviour of the SGS turbulent energy. The model equations are described in [23]. The default combustion model in FireFOAM is infinitelyFastChemistry. This assumes that combustion is infinitely fast compared to mixing of the species i.e fuel and oxidiser cannot co-exist in the same space. In the experiment, a pilot flame is used to ignite the initially released fuel of ’activated’ PMMA, the effect of which is reproduced by this combustion model. The radiation modeling is simulated using the P1 model with constant absorption and emission coefficients. The P1 model been noted to be satisfactory for combustion simulations as noted in [24]. After one evolution of the conservation equations, the density is corrected using the ideal gas equation.

15

4 | Simulation of Pyrolysis and Combustion 4.1

Experimental Setup

Five experiments were performed at Bergische Universität Wuppertal based on the standard ISO 17554 to measure mass loss rate and flame spread of PMMA. The basic pyrolysis and flaming experiment as shown in figure 4.1 (experiment no. 1) is a slab of PMMA (surface area= 100 cm2 , 20 mm thick) placed horizontally. It is ignited using a pilot flame after an initial period of time where its surface is heated using a cone shaped radiator. The shape of the cone is such that it incorporates an exhaust chimney, and the gases of combustion are moved away from the experiment. The flame spread setup (experiment nos. 2-5) consists of small slabs of PMMA (surface area= 200 cm2 , 20 mm thick) placed in horizontal and vertical positions. Figures 4.2 and 4.3 show the actual setups for the horizontal and vertical configurations respectively.

Figure 4.1: General schematic of experimental setup During the initial period the surface of PMMA is ’activated’, which results in the release of gaseous volatiles from its surface. These gaseous volatiles are then ignited using the spark ignitor. The mass loss rate of the specimen is then measured using a sensitive weighing scale placed under the burning sample.

16

Figure 4.2: Horizontal Experiment (Angle of inclination = 60◦ )

Figure 4.3: Vertical Experiment (Angle of inclination = 30◦ ) Various details about the experimental configurations are summarized in table 4.1. The experiment work sheets are also included in appendix C.

17

No. 1 2 3 4 5

Material Placement Horizontal Horizontal Horizontal Vertical Vertical

Incident Angle 0o 30o 60o 30o 60o

Experimental Time 802 sec 346 sec 459 sec 954 sec 780 sec

Compute Time 2 days 1.5 days 2 days 3 days 2 days

Table 4.1: Details of experimental configurations

4.2

Simulation Setup

The simulation setup simplifies the experimental setup described above as shown in the figure 4.4. The mesh consists of two regions, namely the fluid region (white wireframe in figure 4.4), and the material region (red wireframe in figure 4.4). A homogeneous heat flux of 50 kW m−2 is applied horizontally at the top of the material in the first simulation. For the remaining four simulations, there exists horizontal and vertical configurations of PMMA (see figure 4.5). For these simulations, heat flux of 50 kW m−2 is applied at angle of 30 ◦ and 60 ◦ . This creates a non-homogenous distribution of heat on top of the surface of the material, thus the region of material closer to the radiator will receive more heat than the region further away. The Feedback boundary condition developed in this work is not dependent on gravity. As a result, it is possible to the achieve vertical PMMA simulations (figure 4.5b) by changing the direction of the gravity vector from (0, 0, −9.81) to (−9.81, 0, 0).

(a) Perspective View

(b) Front View

Figure 4.4: Simulation Setup in OpenFOAM The fluid region as well as the material region consist of regular hexahederal meshes that are coupled together at the interface using coupling boundary conditions as described in section 4.3. The fluid region is divided into a set of 30 x 30 x 30 cells. The mesh at the wall is further refined, halving its original size. The region at the wall is fine enough and does not warrant the use of wall functions. Within the material region, conservation equations are applied along only one dimension, in a direction normal from the surface to the bottom of the material. The material region assumes an infinitely long domain, thus number of one dimensional layers (nLayers) is in-effect irrelevant. Additionally, surface regression is not modelled. Finally, all the numerical schemes used in the simulation reflect the ’best practise schemes’ supplied by FM Global [22].

18

(a) Simulation 2 and 3 (side view)

(b) Simulation 4 and 5 (top view)

Figure 4.5: Configuration for flame spread experiment

4.3

Boundary Conditions

4.3.1

Pyrolysis Boundary Conditions

The following boundary conditions have been defined in the pyrolysis region: internalField

PMMA uniform 1

uncoupledPatch

zeroGradient

coupledPatch sides

zeroGradient empty

T uniform 294 fixedValue value 294 (see below) empty

Qr uniform 0

Y0default uniform 0

zeroGradient

zeroGradient

zeroGradient empty

zeroGradient empty

Table 4.2: Boundary Conditions- Pyrolysis Temperature Boundary Conditions on Coupled Patch Three boundary conditions were developed in this work as given below for the coupled temperature patch field. The Feedback boundary conditions achieve a multi-region coupling for the transfer of energy and consider the contribution of radiative heat flux from the flame back to the surface. These are described below: 1. compressible::fixedIncidentRadiationCoupledMixedFeedback – This boundary condition uses the radiant heat flux Qr based on gas combustion within the fluid region as a surface flux input into the solid region. Thus, it is possible to achieve a radiant heat transfer contribution back into the pyrolysis region. The following equation is used to compute the temperature gradient in the material region and is given as: ∂T t = (Qri + Qr − σ · T 4 ) (4.3.1) ∂z κ Qri is the heat flux to the surface provided by the radiator. Qr is the feedback of radiant heat available on the coupled surface. In the fluid region, a zero gradient boundary condition is set.

19

2. angledFixedIncidentRadiation – This boundary condition has been created to account for the incidence of heat radiation supplied at an angle. It models a pseudo-view factor for each patch face based on an angle provided using the following equation: Z Z 1 cosβi cosβj dAi dAj (4.3.2) Fij = Ai A i A j πs2ij where i indexes the faces of the pseudo radiator and j indexes the faces of the pyrolysis surface. The gradient of temperature at each face is then calculated the view factor vector contributions as follows: ∂T t = (Qri · F − σ · T 4 ) (4.3.3) ∂z κ In the fluid region, a zero gradient boundary condition is used. Additional notes on the same can be found in appendix A.1 3. compressible::coupledAngledFixedIncidentRadiationFeedback – This is a coupled boundary condition and hence must be provided on both sides on the interface. This uses equations (4.3.1) and (4.3.3) together, achieving angular incident radiation as well as radiant heat feedback. The gradient in the solid region is given as: t ∂T = (F · Qri + Qr − σ · T 4 ) ∂z κ In the fluid region, a zero gradient boundary condition is set.

20

(4.3.4)

4.3.2

Fluid Boundary Conditions

The following boundary conditions have been set within the fluid region: internalField sides front&Back top coupledPatch

CH4 uniform 0 inletOutlet inletOutlet inletOutlet (see below)

O2 uniform 0.23301 inletOutlet inletOutlet inletOutlet zeroGradient

N2 uniform 0.76699 inletOutlet inletOutlet inletOutlet zeroGradient

H2O uniform 0 inletOutlet inletOutlet inletOutlet zeroGradient

Table 4.3: Boundary Conditions- Species Mass Fractions p p_rgh T U internalField uniform 1e5 uniform 1e5 uniform 294 uniform (0 0 0) sides calculated totalPressure inletOutlet (see below) front&Back calculated totalPressure inletOutlet (see below) top calculated zeroGradient inletOutlet zeroGradient coupledPatch calculated fixedFluxPressure (see below) (see below) Table 4.4: Boundary Conditions- Fluid Properties alphaSgs muSgs G internalField uniform 0 uniform 0 uniform 0 sides zeroGradient zeroGradient zeroGradient front&Back zeroGradient zeroGradient zeroGradient top zeroGradient zeroGradient zeroGradient coupledPatch zeroGradient zeroGradient zeroGradient

Ydefault uniform 0 inletOutlet inletOutlet inletOutlet inletOutlet

Table 4.5: Boundary Conditions- Turbulence & Radiation Gas Boundary Condition- CH4 To achieve a mass flux transfer between the two regions, a new boundary condition namely, totalFlowRateAdvectiveDiffusiveCoupled is developed. At the end of a pyrolysis solving cycle, the mass flux leaving the boundary is available at each face. This mass flux is then available at the coupled patch, driven by the velocity field in the fluid region. The boundary condition computes the mass fraction entering in the fluid region from the pyrolysis region through the coupled patch. Temperature Boundary Conditions on Coupled Patch Similar to the description made earlier, the temperature field at the boundary is set based on the type of experiment. Thus, for the first simulation we use the boundary condition, compressible::fixedIncidentRadiationCoupledMixedFeedback and for the remaining four simulations we use the boundary condition, compressible::coupledAngledFixedIncidentRadiationFeedback.

21

Velocity Boundary Conditions 1. flowRateInletVelocityCoupled – At the coupled patch, the available mass flux to compute an inlet velocity. The inlet velocity is calculated based on the flow rate equation: Ui =

m ˙ Aρ

where Ui is the inlet velocity, ρ is the density of fluid, m ˙ is the mass flux, and A is the patch area. 2. pressureInletOutletVelocity – At the boundaries - front&Back and sides – this velocity inlet/outlet boundary condition is applied, where the pressure is specified. A zero gradient condition is applied for outflow (as defined by the flux); for inflow, the velocity is obtained from the patch-face normal component of the internal-cell value [25]. Thus, it acts as a zeroGradient boundary condition. Pressure Boundary Conditions 1. fixedFluxPressure – This boundary condition adjusts the pressure gradient such that the flux on the boundary is that specified by the velocity boundary condition. 2. totalPressure – This boundary condition computes the total pressure at the boundary based on the following equation: pt = po + 0.5|U |2

22

4.4

Simulation Results

4.4.1

Simulation Description

Multiple number of simulations were performed in an increasing order of complexity. The case study used for all the initial test simulations was Simulation 1 (see 4.1). A small description related to the complexity of the simulations is given below: 1. Set 1 – In the first simulation set, the least complex of all, the fluid and pyrolysis region are simulated with the best available boundary conditions in the current FireFOAM release (fireFOAM-2.4.x). The idea behind doing this set of simulations was to only understand the difficulties associated with multi-region coupling, and possible lack of boundary conditions thereof. It then became clear that mass, momentum and energy boundary conditions need to be developed in order to achieve the required objective. 2. Set 2 – During the second simulation set, the default boundary condition provided by FireFOAM, namely, compressible::fixedIncidentRadiationCoupledMixed was used. The boundary condition achieves a coupling within the two regions for energy transfer. Two boundary conditions were developed to achieve mass and momentum transfer across the boundary – • totalFlowRateAdvectiveDiffusiveCoupled • flowRateInletVelocityCoupled Using the FireFoam default boundary condition, compressible::fixedIncidentRadiationCoupledMixed, it was realized that radiation coupling due to flame is not achieved at the interface boundary. A comparison for this is shown in figure 4.10a. 3. Set 3 – In this set, radiation coupling at the boundary due to the flame is achieved using a newly developed Feedback boundary condition. These boundary conditions are described in section 4.3.1. 4. Set 4 – After developing the boundary conditions, a 3 parameter optimization was performed using Arrhenius parameters, and heat of volatilization. In this case, we treat the thermophysical properties of the material as model parameters, which can be adjusted to achieve a close correlation between experimental and simulation results.

4.4.2

Lack of Conservation

In simulation set 1, it was investigated whether conservation of quantities across the interface holds when there is no combustion. This implies that any pyrolysis gases released due to incident heat must pass into the fluid region and the mass loss rate from the pyrolysis region must coincide with the rate of mass increase in the fluid region. The following boundary conditions are relevant at the interface of solid and fluid regions: • totalFlowRateAdvectiveDiffusive is applied to the CH4 field. The mass fraction inlet is set as 1. • fixedValue is applied to the velocity field with a uniform initial condition of (0 0 0). • fixedIncidentRadiation is applied to the temperature field surface of the solid region. 23

Figure 4.6 shows the mass loss rate from the solid domain due to pure pyrolysis for a time period of 200 sec.

Figure 4.6: Mass Loss Rate from Solid We will then monitor the mass in the fluid region by two methods: One method uses a debugSwitch for totalFlowRateAdvectiveDiffusive, which recomputes the mass flux from the mass fraction at the boundary. Figure 4.7 shows the mass flux through the debugSwitch method. As can be seen, the mass flux is zero. This is because the velocity field is set as uniform (0 0 0). Thus, even if a mass fraction exists at the boundary it is not transported, since the fluid is not moving at the boundary.

Figure 4.7: Mass Flux by using the debugSwitch tool in OpenFOAM The second method, by using ParaView, integrates the value of pyrolysis gases within the control volumes and then plots the time average of the mass of CH4 over the entire region. Figure 4.8 shows this; the amount of gas seems to be increasing almost linearly with time initially, after which it starts reducing. The initial peak occurs due to the setting the mass flux fraction of CH4 as 1 as mentioned above. The reduction occurs at steady state since at the walls of the fluid, an inletOutlet type boundary condition has been set.

24

Figure 4.8: ParaView- Mass Integration over Time The main takeaway here is that even though there is no mass flux as shown by figure 4.7, ParaView indicates a presence of methane within the fluid region. Hence, it is necessary to develop the boundary condition that will correctly model the mass conservation across the interface. This is achieved using the totalFlowRateAdvectiveDiffusiveCoupled and flowRateInletVelocityCoupled boundary conditions.

4.4.3

Development of Boundary Conditions

In simulation set 2, boundary conditions were developed to achieve correct mass transfer across the solid-fluid interface. In the simulation, we assume that only pyrolysis gases enter the fluid region upon pyrolysis and no gases from the atmosphere enter at the interface. Thus, if the boundary condition totalFlowRateAdvectiveDiffusive takes in a constant mass flux fraction value of 1, the velocity at the interface must be determined by the mass loss rate exiting the solid surface. This is achieved by using the two boundary conditions, totalFlowRateAdvectiveDiffusiveCoupled and totalFlowRateInletVelocityCoupled. The inlet velocity at each time step is then determined by the mass flux entering at the interface boundary as described by the velocity boundary conditions in 4.3. The plot in figure 4.9 shows a comparison of the pure pyrolysis mass loss rate and the debugSwitch of totalFlowRateAdvectiveDiffusiveCoupled. Mass is thus conserved.

Figure 4.9: Mass conservation holds true with new boundary conditions 25

4.4.4

Coupling Flame Radiation

As stated earlier, any radiation from the flame must ideally cause an increase of the mass loss rate from the surface. The easiest way to accomplish this is by considering radiation input at the surface as a sum of incident radiation and flame radiation. The Feedback boundary conditions described in section 4.3.1 were developed to achieve just this purpose. Figure 4.10b shows the time history of feedback radiative flux due to flame on the surface. A slightly overpredicted value of 35 kW is added to the system. This value is expected to improve on further refining the mesh. However, it shows an adequate correlation with experimentally obtained values as stated in section 2.1.2. The increase in mass loss rate due to radiation feedback is captured in figure 4.10a.

(a) Comparison of mass loss rate with and (b) Simulated radiant heat flux feedback without radiation feedback on the surface

Figure 4.10: Radiation simulation results

4.4.5

Parameter Optimization

With the entire system now working, in simulation set 4, an optimization procedure was carried out on only a single PMMA simulation, namely simulation 1 wherein the flux is incident horizontally. Optimized Values of Arrhenius parameters was obtained by performing a simple minimal residual optimization, wherein it was noticed that the sensitivity of MLR to changing the pre-exponential factor is not very high. The MLR is sensitive to the change of activation energy, thereby causing a change in the mass loss rate curve itself. This can be seen from figure 4.11 and figure 4.12 respectively. The solution also shows high sensitivity at lower values of activation energy as shown by the green curve in figure 4.12.

26

Figure 4.11: Sensitivity of mass loss rate to pre-exponential factor A

Figure 4.12: Sensitivity of mass loss rate to activation energy ratio Ta Eventually, the heat of volatilization was added as an optimization parameter. The mass loss rate of thermoplastics once ignited is not largely sensitive to Arrhenius parameters but to the enthalpies of the material under consideration, its thermal conductivity and the net heat input at the surface. At typical temperatures of flaming combustion, the decomposition kinetics are so fast that they are no longer a limiting factor [3]. Figure 4.13 shows that the mass loss rate is very sensitive to heat of volatilization after the initial period where decomposition kinetics i.e Arrhenius parameters control the state of the system. It must also be appreciated that the mass loss rate in figure 4.14a is shifted in time i.e the loss of mass begins marginally earlier than the experimental value. The reason for this is that there are two more parameters which may be included in the optimization procedure, namely the thermal conductivity of the material and the emissivity– thereby a total optimization of 5 input parameters must be performed. The thermal conductivity in this case would be the primary optimization parameter to obtain the correct value of time. As a proof of concept, it is sufficient to show that the trend is followed correctly.

27

Figure 4.13: Sensitivity of mass loss rate to heat of volatilization

4.4.6

Results - Mass Loss Rate

The results for simulation 1 (table 4.1) show an extremely good coincidence with respect to the experimentally obtained values. This is shown in figure 4.14a.

(a) Mass loss rate [g s−1 ]

(b) Mass [g] of system

Figure 4.14: Simulation 1 (horizontally incident radiation) results over time Importantly, it can also be seen that the final peak of mass loss rate of the system is not captured. The reason for this is that the material in question is modeled to have semi-infinite mass. Additionally, as the material burns away, its thickness reduces and thus, an additional advection term must be added to account for surface regression. The insulating effect of the substrate and reducing thickness of solid is responsible for the final peak (at 700s) in the experimental results, which is not captured by the simulation. The fluctuation of experimentally obtained mass loss rate in figure 4.14a is also not captured. A primary reason for this is melting, which results in the formation of a heat shield, thereby causing a temporary reduction in mass loss rate [3]. However, the cumulative mass loss (figure 4.14b) coincides well to the experimentally obtained values. The cumulative mass of the system 28

also exhibits fluctuations, as shown in figure 4.15, which will again not be captured by the simulation.

Figure 4.15: Fluctuation of mass of system (g) vs. time (s) This leads us to the remaining 4 experiments– The simulations wherein flux is incident at an angle also show good trends for MLR which are shifted in time, however, they do not show an appreciation for the optimized parameters obtained from the first simulation. While it was originally hypothesized that the optimized parameters would work for all five simulations, no information about the material was available to further pursue the reason why this isn’t the case. Another possible reason for the same is possibly the mesh resolution at the boundary which in turn changes the view factors at the surface. However, this is also not pursued at the moment. The figures below show all the trends.



Figure 4.16: Simulation 2 (horizontal plate, θ = 30o ) results over time

29



Figure 4.19: Simulation 5 (vertical plate, θ = 60o ) results over time



Figure 4.17: Simulation 3 (horizontal plate, θ = 60o ) results over time



Figure 4.18: Simulation 4 (vertical plate, θ = 30o ) results over time

30

4.4.7

Results - Flame Spread

Flame spread is captured as follows- The temperature at the surface of PMMA is monitored at all time steps. A region is said to be pyrolysed it crosses the critical temperature of 360 K. Thus, one can measure the length, from the origin, up to the point of pyrolysis as a function of time. The first derivative of the graph of length vs time then results in the flame spread velocity. The figures 4.20, 4.21, 4.22, 4.23 show the flame spread rate as a function of time for all angular four configurations (i.e Experiments 2 - 5). Right on the onset it is clear that in case of vertical configurations, the flame spread velocity is higher, and the material pyrolysis completely within a short amount of time. Flame spread for horizontally placed configurations tend to be relatively slow as compared to the vertical counter parts. The reason for this is that the radiation from flame upstream affects the downstream virgin material at a faster rate in case of a vertical configurations.

(a) Experiment

(b) Simulation

Figure 4.20: Configuration 2- Flame spread velocity (m s−1 ) as a function of time (s)

(a) Experiment

(b) Simulation


31

(a) Experiment

(b) Simulation


(a) Experiment

(b) Simulation

Figure 4.23: Configuration 5- Flame spread velocity (m s−1 ) as a function of time (s) In the case of angular configurations, the predicted mass loss rate is larger than its experimentally obtained value. This will also be reflected in flame spread as shown in the figures. In case of all experiments it is seen that starting from a high value of flame spread velocity, each experiment approaches a flame spread velocity of approximately 0.005 m s−1 . Although the values predicted by the simulation are higher, it does capture a similar trend. The fluctuation in velocity should ideally reduce with increasing mesh size for this result to be confirmed. The table 4.6 shows the average velocities have been computed by the simulations: Configuration No. 2 3 4 5

Predicted velocity [m s−1 ] 0.06 0.065 0.1 0.08

Table 4.6: Predicted average flame spread velocities In the case of the vertical simulations (figures 4.22, 4.23), the entire surface reaches a state of 32

pyrolysis faster than in the the horizontal simulations. This also makes intuitive sense. However, the results of flame spread are not in good agreement with the experiments and cautions should be exercised when interpreting these values. There are several reasons for this phenomenon. Since inverse modeling the experiment does not result in a unique result, the values of Arrhenius parameters obtained are lower than those that would correctly predict a realistic flame spread rate. A correct way to achieve ’good’ modeling parameters would be to include a weighting function that includes the effect of experimentally obtained mass loss rate as well as flame spread velocity in the residual equation. Furthermore, the experiment includes a exhaust blower whose effect is not captured in the simulation. The figure 4.24 shows that the blower results in a counter-flow spread which thereby retards the spread of the flame.

Figure 4.24: Experiment 3 - Effect of blower on flame spread Two further problems exist: Firstly, for simulating the experiments an extremely simple geometry was used. Compared to the experiments, there is a large amount of loss of information at the boundary. This can be seen in the figure 4.25, wherein we see that a portion of the flame transfers heat to the surrounding. However, in the case of the simulation result (figure 4.26), we lose this information. This geometry simplification further leads to another problem. It results in an over-prediction of radiation flux at the boundary thereby causing an increase in the mass loss rates and thereby the flame spread.

33

Figure 4.25: Experiment 5 - Top of image shows heat transfer from flame to atmosphere

Figure 4.26: Simulation 5 - Flame is confined to the geometry in the top half

4.4.8

Visualizations - Flame Spread

The temperature profile of the simulation captures the effective flame travel at various time steps (figures 4.27, 4.28). In case of simulation 2 and 3, it would be beneficial to increase the height of the computational domain, to determine whether this increase has any effect on the flame spread velocity. Furthermore, stricter boundary conditions will be essential to capture the effect of the blower. Since the effect of heat transfer from flame downstream to atmosphere has an effect on on the overall mass loss rate, it would also be beneficial to improve the initial setup in case of vertical simulations, to include a fluid region downstream [26].

34

Figure 4.27: Simulation 2 - Temperature profiles during initial flaming period

35

Figure 4.28: Simulation 3 - Temperature profiles during initial flaming period

36

Figure 4.29: Simulation 4 - Steady state temperature profile

Figure 4.30: Simulation 5 - Steady state temperature profile

37

5 | Conclusions A series of simulations were conducted to explore the possibility of multiregion pyrolysis and flame spread for Cone Calorimeter type experiments using the OpenFOAM solver, FireFoam.

5.1

Boundary Conditions

Exploration in the territory of pyrolysis and flame spread led to the development of a total of four new boundary conditions to achieve the various experimental requirements. These are: • totalFlowRateAdvectiveDiffusiveCoupled – to achieve mass transfer. • flowRateInletVelocity – to achieve momentum transfer. • fixedIncidentRadiationCoupledMixedFeedback – to achieve energy transfer. • angledFixedIncidentRadiationCoupledMixedFeedback – to achieve energy transfer. It was confirmed that it is possible to couple the two regions of scalar transport. For one of the simulations, parameter optimization was performed, thus obtaining reasonable equivalence between simulation and experimental results. It was also recognized that within the context of modeling within the pyrolysis region, the heat of volatilization is a highly sensitive parameter and is largely responsible for changes of mass loss rate during the period of flaming.

5.2

Possibility of Surface Re-radiation

The possibility of re-radiating the surface of pyrolyzing material by the use of radiation models instead of directly prescribing a value was realized. The additional radiant heat results in an increase of mass loss rate from the material which is confirmed by comparison (fig. 4.10a). The radiated flux from the flame to the surface is slightly over-predicted. A mesh sensitivity analysis would conclusively determine whether the fluctuation of radiative flux obtained reduces with increasing mesh resolution.

5.3

Flame Spread

Flame velocity is over-predicted in all angular configurations which coincides with the overprediction of mass loss rates. Additional heat transfer from the flame within the simplified geometry would result in higher mass loss rates, thus a more complex geometry is required to accurately predict mass loss rate and in turn, the flame spread velocity. 38

5.4

Future Work

The pyrolysis model and boundary conditions developed desire much more room for improvement. Firstly, a mesh sensitivity analysis must be performed to evaluate the fluctuation of numerically obtained values of mass loss rate for increasing mesh resolution. With regard to the pyrolysis model, the conduction of heat within the material takes place only in the direction of depth. It may not capture the complete detail of heating when the radiator is positioned at an angle. A 2D model for heat conduction would be beneficial to perform a comparative study with the present model. The boundary conditions developed for the purpose of this thesis also require further work. Firstly, they must work in case of parallel computation. This would reduce the computation time drastically. In the case of the newly developed angled radiant boundary condition, the view factors have been manually bounded at the maximum value of one. Although the trends in mass loss rate are captured correctly, there is a need to investigate this further.

39

A | Boundary Conditions A.1

Angled Radiant Flux Boundary Condition

angledFixedIncidentRadiation computes the effective contribution from a pseudo-heat radiator inclined at an angle θ to the base of the material. The schematic for a 3-element discretization is shown in figure A.1:

Figure A.1: 2-Dimensional radiation schematic

40

Figure A.2: Heat exchange between two bodies Consider 2 elements belonging to large black bodies as shown in the figure A.2. The net heat exchange in this case can be given as: Z Z cosβ1 cosβ2 4 4 Qnet = σ T1 − T2 dA2 dA1 (A.1.1) πs21−2 A2 A1 We also have the following two relations: Qnet = F1−2 A1 σ T14 − T24

and, F2−1 A2 = F1−2 A1 Using these relations, we can determine F2−1 , which is: Z Z cosβ1 cosβ2 1 dA2 dA1 F2−1 = A2 A2 A1 πs21−2

(A.1.2) (A.1.3)

(A.1.4)

As a first approximation to modeling, we assume that the pseudo-heat radiator is divided into small elements of area dA. The equation A.1.4 in discrete form can then be given as: F2−1 =

1 X cosβ1 cosβ2 dA2 dA1 dA2 πs21−2

(A.1.5)

A1

where, β1 and β2 is determined separately for each patch face of pyrolysis material. Extrapolating this idea, we can find the relative contribution of each discrete heat radiating element to the patch faces. The algorithm to do so is given below. The view factor contributions are stored in the diagonal of the shape matrix:

41

Data: Incident Heat Radiation Qr, angle of incidence θ Result: View Factor Matrix F base ← P atchF aceCenters; angle ← ConvertT oRadians; (sine, cosine) ← sin(angle), cos(angle); rotM at ← Store rotation matrix based on rotation axis; locationOf F luxer ← rotM at ∗ base; foreach Patch Face Center(pfc) j ∈ base do foreach Ghost Face Center(gfc) i ∈ locationOf F luxer do sij = locationOf F luxerij − baseij; beta1ij ← 0; beta2ji ← 0; sij .n1 scalarangle1 = arccos √ sij ; beta2ij = cos angle − angle1 ∗ Apf c ; cos angle1∗Agf c ; beta1ji = π∗sij end end 1 M atrixshape ← Agf ∗ beta1 ∗ beta2 c Algorithm 1: View Factor Algorithm

42

B | Simulation Parameters ρ c κ t A Ta = Ea /R Tc rit ∆hf

1190 [kg m−3 ] 1063 [J/kgK] 0.139 [W/mK] 0.99 4.50603 [s−1 ] 4584.52 [K] 360 K -1.86378e6 [J/kgm3 ]

Table B.1: List of parameters used in the pyrolysis simulation

43

C | Material Data NOTE: Material data is organized based on 4.1. There is an error in the data 2-5, Area = 200cm2 . The material data follows from the next page.

44

Report produced with the Fire Testing Technology MLCCalc software

page 1

Mass Loss Calorimeter Test Report Report name Specimen description Material name/ID Laboratory name Operator Data filename

PMMA_50 PMMA_50 PMMA ABS Corinna Trettin C:\MLCCALC\DATA\16070043.PRN

Specimen information Thickness 18.2 mm Initial mass 217.35 g Surface area 100 cm² Conditioned? Yes Temperature 22°C RH 62% Test Standard used Date of test Time of test Date of report Sampling interval Test times Time to ignition Time to flameout End of test time (for calculations)

ISO 17554 12 July 2016 18:21 12 July 2016 1s

Specimen number Manufacturer Sponsor Edge frame used? Fixed to substrate? Substrate

48

Heat flux Separation HRR Calibration filename

50 kW/m² 25 mm N/A (Thermopile not collected)

No No N/A

Test results (between 0 and 802 s) Total heat release no thermopile data Initial mass 217.4 g Mass at EOT 1.8 g Mass lost 215.5 g Specific mass lost 21.55 kg/m² Percentage mass lost 99.1 %

30 s 799 s 802 s

Test results (between 30 and 802 s) Total heat release Mass at sustained flaming Mass at EOT Mass lost Specific mass lost Percentage mass lost Average specific MLR

no thermopile data 218.1 g 1.8 g 216.2 g 21.62 kg/m² 99.2 % 28.98 g/(m²·s)

Heat release rate (kW/m²) Effective heat of comb. (MJ/kg) Mass loss rate (g/s)

Mean Peak at time (s) no thermopile data no thermopile data 0.280 1.053 126

Test averages from ignition to ignition plus... Heat release rate (kW/m²) Effective heat of comb. (MJ/kg) Mass loss rate (g/s)

180 s 300 s no thermopile data no thermopile data 0.242 0.248

The test results relate to the behaviour of the test specimens of a product under the particular conditions of the test; they are not intended to be the sole criterion for assessing the potential fire hazard of the product in use.


page 1


Fichte_FS PMMA_Flame spread_1_horizontal PMMA_50_Zündung_6 mm ABS Corinna Trettin C:\MLCCALC\DATA\16040036.PRN

Specimen information Thickness 20 mm Initial mass 493.05 g Surface area 100 cm² Conditioned? Yes Temperature 21°C RH 36% Test Standard used Date of test Time of test Date of report Sampling interval Test times Time to ignition Time to flameout End of test time (for calculations)

ISO 17554 23 April 2016 19:20 23 April 2016 1s


1



No No N/A


37 s s 346 s









page 1


PMMA_FS PMMA_Flame spread_1_horizontal_60 PMMA_50_Zündung_3 mm ABS Corinna Trettin C:\MLCCALC\DATA\16050017.PRN


ISO 17554 18 May 2016 18:50 18 May 2016 1s


1



No No N/A


36 s s 459 s









page 1


PMMA_FS PMMA Flame spread_4 Fichte_50_Zündung_6 mm ABS Corinna Trettin C:\MLCCALC\DATA\16040008.PRN


ISO 17554 3 April 2016 17:43 3 April 2016 1s


4



No No N/A


42 s s 954 s









page 1


PMMA_FS PMMA_Flame spread_1_60 PMMA_50_Zündung_6 mm ABS Corinna Trettin C:\MLCCALC\DATA\16040026.PRN


ISO 17554 12 April 2016 06:37 12 April 2016 1s


1



No No N/A


39 s s 780 s








Bibliography [1] D.I.T. Steinhaus and Md.). Department of Fire Protection Engineering University of Maryland (College Park. Evaluation of the Thermophysical Properties of Poly(methyl Methacrylate): A Reference Material for the Development of a Flammability Test for Micro-gravity Environments. University of Maryland, College Park, 1999. [2] Robert A. Orwoll. Densities, Coefficients of Thermal Expansion, and Compressibilities of Amorphous Polymers, pages 93–101. Springer New York, New York, NY, 2007. [3] C.W. Lautenberger. A Generalized Pyrolysis Model for Combustible Solids. University of California, Berkeley, 2007. [4] W. R. Zeng, S. F. Li, and W. K. Chow. Review on chemical reactions of burning poly(methyl methacrylate) pmma. Journal of Fire Sciences, 20(5):401–433, 2002. [5] Louis A. Gritzo, Paul E. Senseny, Yibing Xin, and J. Russell Thomas. The international forum of fire research directors: A position paper on verification and validation of numerical fire models. Fire Safety Journal, 40(5):485 – 490, 2005. [6] M.J. Hurley, D.T. Gottuk, J.R. Hall, K. Harada, E.D. Kuligowski, M. Puchovsky, J.L. Torero, J.M. Watts, and C.J. Wieczorek. SFPE Handbook of Fire Protection Engineering. Springer New York, 2015. [7] Craig L Beyler and Marcelo M Hirschler. Thermal decomposition of polymers. SFPE handbook of fire protection engineering, 2:111–131, 2002. [8] John De Ris. Fire radiation—a review. In Symposium (International) on Combustion, volume 17, pages 1003–1016. Elsevier, 1979. [9] A study of oxygen effects on nonflaming transient gasification of pmma and pe during thermal irradiation. 19:815 – 823, 1982. [10] D. Drysdale. An Introduction to Fire Dynamics. Wiley, 2011. [11] G. Cox. Combustion Fundamentals of Fire. Combustion treatise. Academic Press, 1995. [12] M. Faghri and B. Sundén. Transport Phenomena in Fires. Developments in heat transfer. WIT, 2008. [13] Jeffery D Peterson, Sergey Vyazovkin, Charles A Wight, et al. Stabilizing effect of oxygen on thermal degradation of poly (methyl methacrylate). Macromolecular rapid communications, 20(9):480–483, 1999.

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[14] Marc Janssens. Calorimetry, pages 905–951. Springer New York, New York, NY, 2016. [15] Vytenis Babrauskas. The Cone Calorimeter, pages 952–980. Springer New York, New York, NY, 2016. [16] Peter Šimon. Single-step kinetics approximation employing non-arrhenius temperature functions. Journal of thermal analysis and calorimetry, 79(3):703–708, 2005. [17] WJ Parker. Prediction of the heat release rate of douglas fir. Fire Safety Science, 2:337–346, 1989. [18] Yuji Hasemi. Surface Flame Spread, pages 705–723. Springer New York, New York, NY, 2016. [19] Karl Meredith. Firefoam is a cfd code for modeling fire suppression based on openfoam, 2015. [20] A.J. Aspden, M.S. Day, and J.B. Bell. Lewis number effects in distributed flames. Proceedings of the Combustion Institute, 33(1):1473 – 1480, 2011. [21] Tue Emil Skydt. CFD modelling of flame spread in corner fires. PhD thesis, Department of Civil Engineering, Technical University of Denmark, 2017. [22] Karl Meredith. Pyrolyis case study - firefoam, 2016. [23] Villiers Eugene. The potential of large eddy simulation for the modeling of wall bounded flows, 2006. [24] Alexey Vdovin. Radiation heat transfer in openfoam, 2017. [25] OpenFOAM-C++ Source Guide. [26] ZHENGHUA Yan and GORAN Holmstedt. Cfd simulation of upward flame spread over fuel surface. Fire Safety Science, 5:345–356, 1997.

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