Absorption of thermal energy in PMMA by in-depth radiation

Abstract

An experimental technique is developed to quantify the absorption of thermal energy in black PMMA (Polycast) by in-depth radiation in semi-transparent media. In-depth heating occurs when non-reflected incident heat flux enters the solid without first being absorbed at the exposed surface. Transient conduction due to temperature gradients occurs within the solid in response to this in-depth absorption. An analytical model is developed for predicting time to ignition for such in-depth heating situations. Using the measured absorption coefficient, κ, the analytical prediction for time to ignition is found to be in excellent agreement with data from experiments of Saito and Delichatsios.

Introduction

It is well understood in the field of fire science that thermal radiation is the dominant mode of heat transfer in large-scale fires. de Ris [1] provides a well-known review and discussion of flame radiation. The study of the ignition phenomenon by absorption of radiation is, therefore, important for fire spread. The objective of the present study is to characterize the absorption of thermal energy in black PMMA by in-depth radiation.

There have been a lot of recent research works on ignition aimed at understanding the physical processes determining the time to ignition [2], [3], [4], [5], [6], including many experimental and theoretical studies on radiative ignitions of various solid fuels, such as polymers, wood and cellulose materials, etc.

Experiments and analysis conducted by Hallman et al. [7], [8] in the 1970s reached an important conclusion that times to pilot ignition of polymers are strongly affected by the surface absorption. In that study, average surface absorptances were analytically determined for various radiant energy sources, and the ignition time of a number of polymers was measured and evaluated on the basis of surface absorption.

In-depth absorption is quite common, and is also referred to as heat transfer in semi-transparent media [9]. Heat is delivered at significant depth into the interior of the solid instead of effectively being deposited directly on the surface. This reduces the increase in surface temperature and delays time to ignition.

Various theoretical models describing radiative ignition of solid fuels have been established and numerically analyzed [10], [11], [12], in which in-depth absorption of the incident radiation by the solid fuel is considered and modeled as an important contributing factor, in addition to a gas phase reaction and absorption. Among these theoretical works, Linan's study [12] focused on a theoretical determination of conditions necessary for the neglect of the in-depth absorption using an asymptotic analysis.

Additionally, many elegant experimental studies were performed to extend the knowledge of pilot ignition by radiation [13], [14], [15], [16], [17], which mainly involves time to sustained ignition and the corresponding surface temperature. In 1988, Saito et al. [18], [19] at FM Global performed a set of experiments exploring the difference between in-depth absorption and surface absorption by the absence or presence of black carbon powder on the surface. The experiment and results are briefly summarized in Section 5. Based on the available knowledge, the present study focuses on a theoretical explanation of the difference between in-depth and surface absorptances in Saito's experimental results using a simple analytical approach by properly characterizing the in-depth absorption.

Furthermore, in-depth absorption becomes increasingly important at high incident heat fluxes for which the reduced depth of heat penetration by conduction becomes comparable to the depth of heat penetration by in-depth radiant absorption. Under these conditions, the time to ignition no longer follows that of a thermally thick solid. Recently, Beaulieu [20] observed such delays in ignition times at high incident heat fluxes for many materials, including black PMMA, gray PVC, pine, asphalt shingles, plywood, etc. Delays are also commonly observed for foamed plastics whose low densities result in reduced thermal conductivities and a greater penetration depth of radiant heat. The widespread occurrence of this phenomenon involving high radiant fluxes was therefore a further motivation for the present study.

In the present work, the absorption coefficient of black PMMA (Polycast) is experimentally measured. Based on the measurement, the physical processes of in-depth heating by radiation are analyzed by solving the differential governing equations. The preliminary results are then compared with the previous experimental data by Delichatsios and Saito [19] and Beaulieu [20].