Approximate Analytical Solutions For The Transient Mass Loss Rate And Piloted Ignition Time Of A Radiatively Heated Solid In The High Heat Flux Limit

Abstract

An approximate closed form solution is developed for the mass loss rate of a semiinfinite solid irradiated by a constant net heat flux. The solution is valid at high heat flux levels where surface losses and the endothermic heat sink due to pyrolysis are small in comparison to the applied heat flux. The expression obtained for the mass loss rate is used to develop an explicit closed form relation for the time to piloted ignition using a critical mass flux as the ignition criterion. The resultant formula is identical to that obtained from the classical thermal ignition theory, with the important difference that the surface temperature at ignition is not constant. Rather, it increases with applied heat flux, mass flux at ignition, and activation temperature, and decreases with increasing density, pre-exponential factor, and thermal conductivity. The model predictions are compared to recent high-heat flux ignition measurements for PMMA.

Generalized pyrolysis model for combustible solids

“…The concept of a 4 critical mass loss rate at ignition was explored theoretically [7], and a theory was developed to explain the experimentally-observed increase in surface temperature at piloted ignition with applied heat flux [8]. The 1D numerical pyrolysis model described in this dissertation has recently been extended to two dimensions and used to simulate two-dimensional smolder structure with complex kinetics [9].…”

Numerical simulations of polymer pyrolysis rate: Effect of property variations

“…In general, two approaches are being taken to supply these parameters: estimating them from the MLR (or temperature) data obtained in the experiments to be modeled themselves [4,7,8] (sometimes with parameter optimization algorithms [13]), or measuring the individual parameters with separate experimental devices [5,6,[9][10][11][12]. In either case, it is of value to understand the sensitivity of the MLR to the individual parameters in the model.…”

An Investigation of the Influence of Heating Modes on Ignition and Pyrolysis of Woody Wildland Fuel

“…A number of previous publications have focused on critical time (Atreya et al, 1986;Babrauskas, 2001;Bilbao et al, 2002;Brescianini et al, 2003;Delichatsios et al, 2003;Moghtaderi et al, 1997;Thomson et al, 1988), heating mode (Babu and Chaurasia, 2003;Frankman et al, 2010;Lizhong et al, 2007;Tan et al, 2009), and mass loss rate (Delichatsios, 2005;Lautenberger and Fernandez-Pello, 2009;McAlister et al, 2012;Shen et al, 2006). Many of these studies were on pyrolysis and/or combustion models with an ignition criterion that utilized a critical surface temperature as the ignition temperature (Atreya et al, 1986;Bilbao et al, 2002;Frankman et al, 2010;Lautenberger and Fernandez-Pello, 2005;Thomson et al, 1988). Experiments of Atreya et al (1986) and Thomson et al (1988) showed that the critical time is approximately the same time at which the surface of the particle begins to undergo pyrolysis.…”

“…In order to model the wind effects, a convective heat transfer coefficient h is considered. The domain is initially at a uniform temperature T 0 = 27 o C. Since we use critical temperature as the ignition criteria, the time at which surface temperature reaches this value T cr = 370 o C (Babrauskas, 2001;Lautenberger and Fernandez-Pello, 2005), is referred to here as critical time and is denoted by t cr . It is noted that in this work, we are not dealing with flaming ignition for which the use of critical fuel mass flux is arguably a better criterion (McAllister et al, 2011;Rasbash et al, 1986).…”