7FR-75 Topic: Fire 8 th U. S. National Combustion Meeting Organized by the Western States Section of the Combustion Institute and hosted by the University of Utah May 19-, 13 Numerical Study of Solid Fuel Pyrolysis under Time Dependent Radiant Heat Flux Conditions Zohreh Ghorbani 1, rnaud Trouvé 1 1 Department of Fire Protection Engineering, University of Maryland, College Park, MD 74 The present study examines the effect of time dependent irradiation on pyrolysis processes. The pyrolysis process generally takes place in a strongly unsteady environment and consequently the gas-to-solid rate of heat transfer features strong unsteady variations. The variations of the gas-to-solid heat flux may result in some cases in significant variations of the fuel mass loss rate. This aspect is usually overlooked in experimental, theoretical or numerical analysis in hich a quasi-steady point of vie is often adopted. We examine in the present study the effects of fluctuations in incident radiant heat exposure on the pyrolysis processes taking place inside solid flammable materials. The study uses a simple one-dimensional numerical model. The pyrolysis model formulation is based on standard conservation statements for heat and mass, coupled ith a global one-step finite-rate decomposition chemistry model that can be applied to both non-charring and charring materials. The model allos for constant or time-varying radiant exposures. We consider in the present study harmonic periodic variations in irradiation characterized by a mean value, an amplitude and a frequency. The response of polymethyl methacrylate (PMM) and polyvinyl chloride (PVC) samples is analyzed in terms of the amplitude of the fluctuations in both solid temperature and fuel mass loss rate. Results indicate that the response of charring and non-charring materials is quite different. In the case of PMM, the effects of time-varying radiant exposure are pronounced during the entire pyrolysis process, from ignition to burn-out. In contrast, in the case of PVC, the effects of time-varying radiant exposure are only pronounced during a limited time; this limited time corresponds to a regime in hich the pyrolysis front is ithin a certain spatial distance of the exposed surface of the material. The analysis leads to an evaluation of the importance of unsteady heat flux effects on pyrolysis processes. 1. Introduction The advent of computer simulation provides an excellent tool in predicting flame spread and fire groth in real-orld geometries. No, there is a significant interest in the fire community to use CFD-based fire simulation as it provides a cost-effective alternative to expensive full-scale fire tests and can provide a fundamental understanding of material flammability and fire groth [1]. ccurate predictions of the fuel mass loss rate are essential for CFD-based fire groth modeling because the amount of gaseous fuel generated by solid fuel determines in turn the intensity of the combustion process. In fire applications, solid pyrolysis corresponds to the transformation of carbon and hydrogen matter from solid to gas phase and thereby controls the rate of formation of flammable vapors that fuels the combustion process. Pyrolysis is driven by the gas-to-solid heat transfer process also called the thermal feedback hich includes convection and thermal radiation components. significant amount of experimental and theoretical studies have been conducted over the past fe decades for the analysis and prediction of pyrolysis processes of both charring and non-charring materials [1-8]. Pyrolysis models feature a variety of approaches and may be categorized as: 1) fully empirical models in hich the evolution of the fuel mass loss rate is prescribed based on data obtained in reference bench-scale or furniture calorimeter experiments; ) semi-empirical or comprehensive models that are based on detailed descriptions of the many physical 1
and chemical processes that occur inside solid fuel sources in response to the gas-to-solid thermal loading [1-6]. Semiempirical models correspond to an intermediate approach based on simplified descriptions of in-solid heat transfer and chemical processes [4-6]. These cost-effective models rely on a number of simplifications, e.g. infinitely fast or global single-step pyrolysis chemistry, the assumption of a single-phase homogeneous medium, etc. The pyrolysis process generally takes place in a strongly unsteady environment and consequently the gas-to-solid rate of heat transfer features strong unsteady variations. The variations of the gas-to-solid heat flux may result in some cases in significant variations of the fuel mass loss rate. This aspect is usually overlooked in experimental, theoretical, or numerical analysis in hich a quasi-steady point of vie is often adopted. In the present study, the effect of fluctuations in incident radiant heat exposure on the pyrolysis processes as examined. The paper is organized as follos: Section 1 contains a brief description the pyrolysis model employed in this study. The pyrolysis model formulation is based on standard conservation statements for heat and mass, coupled ith a global onestep finite-rate decomposition chemistry model that can be applied to both non-charring and charring materials. The pyrolysis model allos for constant or time-varying radiant exposures. The material properties and chemical reaction parameters used in the pyrolysis model have been previously calibrated based on an optimization technique to represent thermal degradation of polymethyl methacrylate (PMM) and polyvinyl chloride (PVC). mathematical solution to a reference analog problem corresponding to heat conduction in a semi-infinite solid thermally loaded by an unsteady heat flux is used as the basis for data analysis. Section 3 contains the study of the pyrolysis behavior of PMM and PVC here the radiation intensity is excited. The response of the PMM and PVC samples under harmonic periodic variations in irradiation as analyzed in terms of the magnitude of the fluctuations in both solid temperature and fuel mass loss rate. In Section 4, the findings of this study and plans for future ork are summarized.. Methods.1 Pyrolysis Model The present study considers a classical pyrolysis model that is similar to the experimental configuration studied in cone calorimeter tests. The pyrolysis model treats the thermal degradation across a solid as a local one-dimensional problem in the direction normal to the exposed solid surface. The model formulation is based on the classical conservation statements for heat and mass and is adopted from Ref [4]. n rrhenius-like thermal degradation chemistry is assumed based on a global one-step pyrolysis reaction ith virgin solids transformed into volatiles and char. The main equations of the model formulation based on finite volume formulation are: sy sgy (1) t syi y ( f - d ) i y () t scstsy k t y s Ts f d yh y ( - ) R (3) here s, cs, ks and T s designate the mass density, heat capacity, thermal conductivity and temperature of the solid material, y the spatial coordinate normal to the exposed surface, y the cell height, the volumetric formation rate of volatiles from the condensed phase (i.e. the amount of virgin solid mass transformed into gas by pyrolysis processes per unit time per unit volume), fi and di are the volumetric formation and destruction rate of condensed species (virgin material or char) and H R the heat of pyrolysis. Equation (1) and equation () describe the solid phase mass conservation equation and solid phase mass species conservation equation. Equation (1) together ith equation () describes solid mass loss due to phase change and the associated production of flammable vapors. Equation (3) represents the conservation of energy for the condensed phase. sg
The total destruction rate of solid material as formulated using an rrhenius-like expression, shon in equation (4a). In equation (4a), T thr is the threshold temperature, Yvs the mass fraction of the solid material, a pre-exponential factor and E activation energy. The formation rate of char, at hich the solid mass converted to char, and the formation rate of volatiles from the condensed phase are: Y exp( E / RT ) (4a) d s vs sc SF d s (4b) sg ( 1 SF) d (4c) 1 vs SF 1 (1 ) (4d) Note vs c c, designate the mass density of the virgin solid material and char, and is a user defined parameter that controls shrinkage and selling. The fuel mass loss rate (per unit exposed surface area) is by definition the mass flux of volatiles from the exposed surface of the solid material and may be expressed as: L m ( t) ( x, t) dy (4) f sg here L is the sample thickness. Note that Eq. (4) neglects any possible gas transport effect from the depth of the solid sample to the exposed surface. The solid material is treated as optically opaque. The heat flux at the exposed surface of the solid material (at x = ) is: 4 4 ( q t) G ( Ts, T ) h( Ts, T ) radiation convection Note is the surface emissivity, G the irradiation from the radiant panel, the Stefan-Boltzmann constant, (5) T s, the solid surface temperature (at x ), T the ambient gas temperature, and h the convective heat transfer coefficient. The model allos for constant or fluctuating radiant exposures. The back surface (at x L ) as assumed to be adiabatic. Equations (1)-(3) are coupled partial differential equations; these equations ere numerically solved using a fully implicit algorithm (second-order technique for spatial discretization time integration).. Pyrolysis Material Property The flammable materials examined in the present study are polymethyl methacrylate (PMM) and polyvinyl chloride (PVC). The pyrolysis model necessitated a large number of unknon coefficients (material properties and parameters of the chemical reactions), hich needed to be determined for each material. To achieve this, the pyrolysis model as coupled to an automated optimization scheme hich uses a genetic algorithm (G). This optimization scheme adjusts the material properties in an iterative process based on evolutionary principles to obtain optimal agreement beteen the model and experimental data, typically coming from thermo-gravimetric and/or cone calorimeter experiments. Test data needed for non-charring and charring polymers ere obtained from Ref. [4-5]. Table 1 presents value of material properties and reaction parameters for non-charring and charring material. The value of parameter 1 as considered for both PMM and PVC..3 Mathematical Theory.3.1 mplitude of Temperature Fluctuation The case of a one dimensional semi-infinite solid slab made of a homogenous material ith constant properties as considered. The slab as assumed to be at a constant initial temperature, T, and the surface as subjected to an oscillatory heat flux. In this section, the mathematical models used to predict the thermal behavior of the problem ill be developed. heat balance over the body leads to the folloing ell knon transient heat equation: 3
T t T x (6) here is the thermal diffusivity. The boundary condition is q(, t) q sin( t). The classical solution found in the literature is in the form of: q T( x, t) T k e x It can be seen in the steady state solution x t q x sin( t x ) cos( ( )) exp( ) 4 t k 4 4 q k x e represents the amplitude of oscillation at point x, and ( x ) 4 in the sine function represents the phase delay of oscillation at the point x relative to the oscillation of the surface temperature. It is apparent that the amplitude of the oscillation decreases as x increases, and the phase of oscillation delays ith increasing x. The oscillation at x is not as strong as that at the surface and there is a delay from the time that the surface temperature changes to the time that the temperature at x responds to such change. The amplitude of temperate oscillation at the front surface may be ritten as: T q k The sudden surface temperature change gradually propagates into the semi-infinite slab. The heat is conducted inside the material, developing to different sections: the heated region, hich the temperature is affected by the surface imposed heat and the virgin region here the material has not felt the presence of the surface heating, remaining at the initial temperature. The distance beteen the surface of the material and the front end of the regions named as the heat penetration depth, 4 t. The avelength of the heat equation analytical solution, the distance over hich the t aves shape repeats, is given by. k Table 1. Synthetic data non-charring and charring material. Virgin Material Properties Residue Material Properties Reaction Parameters PMM PVC PMM PVC PMM PVC ρ(kg/m 3 ) 119.8 179.75 ρ(kg/m 3 ) - 397.84 ΔHp(kJ/kg) 91E+3.9E+5 c(j/kg/k) 1311.3 1111.3 c(kj/kg/k) - 3894.3 (s -1 ) 1.9E+11.98E+13 k(w/m/k).7.17 k(w/m/k) -.1 E(kJ/mol) 1.53E+5 1.93E+5 ε.9.9 ε -.9 Tthr(ºC) - 3.9 χ 1 1 η.3.3. Pyrolysis Front Thickness The heat transferred from the external radiation source to the surface of the material slab develops a thermal ave traveling through the material. In addition, as heat penetrates, a pyrolysis front develops and propagates inside the virgin material ith time. In other ords, upon the incoming heat flux, a thermal ave develops and travels through the material, folloed by the pyrolysis front. t steady state, chemical time scales and diffusion time scales have the same order of magnitude. This leads to an expression for pyrolysis front thickness. (7) (8) chemical diffusion E exp( RT s ) (9) Where, E and Ts are a pre-exponential factor, activation energy and solid temperature, R the gas constant. 3. Results and Discussion 4
It as assumed that the sample thickness is 5 mm and that the convective heat loss at the surface of the samples is negligible. Harmonic variations in irradiation ere used in the form G Gmean G sin( f t).note Gmean, G, f are the mean irradiation from panel, forcing irradiation amplitude, and forcing frequency. These variations in gas-to-solid heat loading induce oscillations in solid temperatures. To provide a qualitative analysis of the effect of external heat flux on pyrolysis of charring and non-charring plastic, a sinusoidal thermal load ith mean radiation intensity of 5, 75 K/m and 1 K/m, forcing radiation amplitude of 5, 1 and K/m, and frequency of.1-1 Hz as considered. Figure 1 presents representative results in the form of a comparison beteen the simulated fuel mass loss rate and front surface temperature obtained ith a steady and unsteady radiant heat flux. The PVC slab as subjected to incident radiation value of G 75K/m, G K/m, f.1hz. The harmonic variation in thermal load, shon in figure mean 1, induced oscillations in burning rate and front surface temperature. The back all surface temperature as not affected by the excited exited radiant heat exposure. It is expected that for a thermally thin sample, an oscillatory behavior ould be observed at the back all surface. The oscillatory behavior in the burning rate of PVC is damped out after seconds. The magnitude of the burning rate oscillation varied ith time before it reached the steady state. Figure 1. Time variation of the fuel mass loss rate (left) and front surface temperature (right): Case of a PVC sample subjected to a constant (blue line) and time-varying (red dots) radiant heat flux. G 75K/m, G K/m, f.1hz mean Figure shos the reaction rate and temperature profile inside the PVC slab at 3 seconds for one cycle. The heat transferred from the harmonic radiation panel to the surface of the PVC layer causes pyrolysis of PVC and hence the formation of a pyrolysis front and its movement inside the virgin material ith time. The pyrolysis front propagating through the solid separates char from the virgin material, indicated in figure. In addition, profiles shon in figure indicate that the position of the pyrolysis front, as an interface beteen char zone and virgin zone, and pyrolysis front thickness (pyrolysis zone) varies in time. The temperature oscillation inside the solid is confined ithin a small region and does not penetrate throughout the PVC sample. The characteristic length scale, l, is.531 mm and gives the distance at hich oscillatory external heat flux takes place and consequently influences the behavior of both mass loss rate and front surface temperature. In other ords, as long as the reaction front ave is inside of the reaction zone, the effect of oscillations in irradiation ill be pronounced in the pyrolysis model calculation. The temperature characteristics versus time and depth, and thus the burning characteristics during the pyrolysis process, depend on both the material properties and the external parameters. The groing char layer formed a high thermal resistant layer beteen the front surface and the pyrolysis front ave, and, acting like a damper, damped out the thermal oscillatory ave propagating from the front surface toard the solid slab. 5
Temp(K) Temp(K) Reaction Rate(kg/m 3 /s) Reaction Rate(kg/m 3 /s) 15 1 Oscillatory Thermal Load T = 36. s T = 38.5 s T = 41. s T = 43.5 s T = 46. s 1 1 8 6 Constant Thermal Load T = 36. s T = 38.5 s T = 41. s T = 43.5 s T = 46. s 5 4 1 1 3 9 8 7 6 5 4 Oscillatory Thermal Load T = 36. s T = 38.5 s T = 41. s T = 43.5 s T = 46. s 9 8 7 6 5 4 1 3 Constant Thermal Load T = 36. s T = 38.5 s T = 41. s T = 43.5 s T = 46. s 3 3 1 3 1 3 Figure. Reaction rate and temperature distribution inside 5 mm PVC sample subjected to harmonic irradiation G 75K/m, G K/m, f.1hz mean Figure 3. Time variation of the fuel mass loss rate (left) and front surface temperature (right): Case of a PMM sample subjected to a constant (blue line) and time-varying (red dots) radiant heat flux Gmean 75K/m, G K/m, f.1hz. Figure 3 shos a comparison beteen the simulated fuel mass loss rate and the front surface temperature obtained ith a steady and unsteady radiant heat flux for PMM. The PMM slab as subjected to incident radiation value of 6
Temp(K) Temp(K) Reaction Rate(kg/m 3 /s) Reaction Rate(kg/m 3 /s) Gmean 75K/m, G K/m, f.1hz. s indicated in the figure, the harmonic behavior in the fuel mass loss curve remains until the burn out time. The back all temperature, not shon here, as affected by the exited thermal load at 1 seconds. The magnitude of the burning rate oscillation for PMM remains constant hereas this varies ith time for PVC material. The chemical process during the pyrolysis results in shrinkage of the PMM material hich results in steeper temperature gradients and increased heat transfer ithin the particle. Hoever, for PVC, the formation of the char acts like a thermal barrier and as a result the oscillation in radiant panel ill not propagate toard the solid sample. 5 4 3 Oscillatory Thermal Load T = 53. s T = 55.5 s T = 58. s T = 6.5 s T = 63. s 3 5 15 1 Constant Thermal Load T = 53. s T = 55.5 s T = 58. s T = 6.5 s T = 63. s 1 5 7 65 6.5 1 1.5 Oscillatory Thermal Load T = 53. s T = 55.5 s T = 58. s T = 6.5 s T = 63. s.5 1 1.5 Constant Thermal Load 7 T = 53. s T = 55.5 s 65 T = 58. s T = 6.5 s T = 63. s 6 55 55.5 1 1.5 Figure 4. Reaction rate and temperature distribution inside 5 mm PMM sample subjected to harmonic and constant radiationg 75K/m, G K/m, f.1hz. mean.5 1 1.5 Figure 4 shos the temperature profile and reaction rate at 53seconds for one cycle inside the PMM solid sample. Fluctuations appeared in the traces of temperature profile and reaction rate. The characteristic length scale, l, for PMM has the value of.768 mm. The pyrolysis front is ithin the characteristic distance of the exposed surface in hich the incoming heat flux is exited, and therefore the effects of time-varying irradiation are pronounced. Figure 3 together ith figure 7 indicate that the response of charring and non-charring materials is different. The pyrolysis front thickness at time 1, 37, 65, 9, and 1 seconds is.5,.6, 1., 1.85 and.5 mm respectively. The theoretical 7
T (K) T (K) pyrolysis thickness is calculated from equation (9) is 1.6 mm. It appears the predicted pyrolysis thickness and the values obtained from the pyrolysis model are of the same order of magnitude. The amplitude of temperature fluctuation at the front surface for PMM and PVC solid sample is compared ith the theoretical expression, shon in equation (8) at different frequencies and forcing amplitudes of 5 kw/m. The theoretical predictions match the model at frequencies of.5 and 1 Hz. Hoever at lo values of frequency the theory over predicts the oscillation amplitude for PVC (PMM) by about 15 %( %3) PVC PMM 5 4 X:.1 Y: 41.1 Model Theory 35 3 5 Model Theory 3 15 1 1.1.5 1 5.1.5 1 f(hz) f(hz) Figure 5. The amplitude of temperature fluctuations for 5 mm PVC (left) and PMM (right) slab: theoretical (black diamond), model (circle). G 75K/m, G K/m mean 4. Conclusions The general objective of the present study is to evaluate the pyrolysis process of both charring and non-charring material under a time-varying thermal load. The flammable solids considered for the present study ere PMM and PVC. general pyrolysis model as developed based on conservation of mass, species and energy. The model allos for material shrinkage and transient thermal load. The pyrolysis parameters needed for pyrolysis modeling ere estimated based on a genetic algorithm technique. mathematical expression as developed based on a simple one dimensional heat equation to predict the fluctuation magnitude of the front surface temperature. comparison of predictions made by the pyrolysis models under harmonic radiant exposure for PMM and PVC as presented. The response in fuel mass loss rate and back all temperature as different for each flammable material. In the case of PMM, the effects of timevarying radiant exposure ere pronounced during the entire pyrolysis process, from ignition to burn-out. In contrast, in the case of PVC, the effects of time-varying radiant exposure ere only pronounced during a limited time; this limited time corresponds to a regime in hich the pyrolysis front is ithin a certain spatial distance of the exposed surface of the material. The analysis led to an evaluation of the importance of unsteady heat flux effects on pyrolysis processes. Continuing ork on this topic is planned and summarized as follos: (1) continued development of a mathematical model to accurately predict the effect of harmonic radiant exposure on pyrolysis process, () elaborate on an adequate technique to calculate the ratio of the reaction production and solid temperature, (3) a better understanding of char formation on impact on propagation of pyrolysis front under harmonic incoming heat flux, and (4) analyze the fuel mass rate fluctuation amplitude under transient thermal load to determine a systematic approach to differentiate charring and non-charring material. References 1. C. Di Blasi, Modeling and simulation of combustion processes of charring and non-charring solid fuels, Progress in Energy Combustion science 19 (1993) 71-14. B., Moghtaderi, The state-of-the-art in pyrolysis modeling of lignocellulosic solid fuels, Fire and Materials 3 (6) 1-34. 8
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