A Practical Model on Flame Spreading over Materials

Flame spreading is a very important phenomenon in the hazard assessment for fire, which is a key element in providing fire safety in buildings with engineering performance-based fire codes. A mathematical model is presented in this paper to predict the flame spreading of materials using the experimental data from cone calorimeter. Numerical prediction of the flame front position and flame spreading velocity of the ASTM LIFT test are generated The heat flux from the external radiation panel, irradiance from the burning part of the sample and convective heat loss to the ambient air were included to model the total net heat flux incident on the specimen. A two dimensional radiation model, together with a simplified model of luminous flame emissivity, are used to characterize the radiative transfer from the flame to the sample. Simulation results agree well with the experimental data, giving confidence that the model is reliable. Radiation is identified as an important mechanism affecting the flame spread behavior. This model can be taken as the first step for modeling flame spreading over materials for implementing engineering performance-based fire codes. 1 Copyright © 2003 JSME NOMENCLATURE a Absorption coefficient b Width of the specimen c Specific heat capacity of specimen (J/kgK) C2 Second radiation constant D Flame thickness (m) dA The area receiving the radiative feedback from the flame fv particulates volume fraction Fdx-f Configuration factor between the top of the flame to a differential area element, dx, at x (Eq. (8)) Fdx-L Configuration factor between a horizontal plane of length L to a differential area element, dx, at x (Fig. 2) Fdx,g Exchange factor between the flame at a differential area element, dx, at x F(x) Distribution factor of external radiative heat flux on specimen h Total heat loss coefficient (W/mK) hc Convective heat transfer coefficient (W/mK) k Conductivity of specimen (W/mK) " av q& Average value of heat release rate of material under 25 kW/m within time period, td (W/m) " c q& Convective heat loss along specimen surface (W/m) " cr q& Critical irradiance for ignition (W/m ) ) ( " x qe & External irradiance on x mm position of speciman from radiation panel (W/m) " f q& Radiative feedback from burning part of the specimen (W/m) " max q& Maximum heat release rate of specimen (W/m) " t q& Total net heat flux on the specimen (W/m ) S2(x) 2-dimensional radiation function t Time (s) t0 Preheat time measured in LIFT tests tig Ignition time (s) td Time period within which the heat release rate is greater than 60% of the material in the cone calorimeter (s) " max q& td,c Flame duration from cone calorimeter data (s) tph Preheat time (s) tph, min Minimum preheat time (s) Ts Surface temperature of specimen (K) T∞ Initial / ambient temperature (K) Tf Flame temperature (K) Tig Critical surface temperature for ignition (K) xH Flame front position, (m) xL Flame end position, (m) y Coordinate in the span wise direction of the sample z Coordinate in the direction perpendicular to the sample ρ Density of the material (kg/m) kρc Thermal inertia of the material (Ws/mK) ε Emissivity of surface of the material εf Emissivity of the radiating plane used in ref. [12] σ Stefan-Boltzmann constant α Absorptivity of fuel surface κ empirical constant used in Eq. (11) INTRODUCTION For providing adequate fire safety in buildings, partition walls for compartmentation must be designed to withstand an accidental fire over a finite time period. A good understanding on flame spreading over wall materials including paint coatings is important for the design development. Flame spreading also plays an important role in the understanding of other fire assessment parameters such as heat release rate of the room, time to flashover in the compartment and the available safe egress time for occupants. This is very important when implementing engineering performance-based fire codes [1]. As reviewed [2,3], only the old bench-scale test [4] was specified in the Hong Kong fire codes [5-7] for assessing the flame spreading behavior of materials. This approach is not adequate for assessing wall structures made of more than one material such as sandwich panels in actual fires. Full-scale room corner fire test [8], on the other hand, is too expensive to be a practical assessment tool. The development of a mathematical model based on bench-scale test results to assess the flame spreading of materials is thus an important task to the industry. There are many models for various aspects of fire available in the industry such as zone models, field models and airflow network models, etc. However, very few [9,10] of them include a good prediction for flame spreading [11]. Many of the existing models still require further experimental verification and thus have uncertain accuracy. There is a need for developing a suitable model for flame spreading. Reviews of models reported in the literature had identified an approach of using bench-scale testing data to predict the flame spreading results [12] such as those generated by the ASTM Lateral flame spread and ignition test (LIFT) [13]. Cone calorimeter [14] results including ignition time, critical surface temperature for ignition, heat release rate, and flame duration are used as input data to predict the test results. Assumptions were made for particular flame configuration, flame duration and emissivity. The heat flux from the external radiation panel, irradiance from the burning part of the sample and convective heat loss to the ambient air were included to model the total net heat flux incident on the specimen. The transient surface temperature of the sample was calculated and data 2 Copyright © 2003 JSME