The Variability of Critical Mass Loss Rate at Auto-Extinction

Auto-extinction of burning timber is frequently cited as key to achieving adequate safety in high rise mass timber buildings where elements of the structure are exposed (or become exposed) during a fire [1‐4]. Drysdale [5] noted that ‘it is ‘common experience’ that a thick slab of wood will not burn unless supported by… heat transfer from another source’; early work on the burning and auto-extinction of timber was recently summarised by Bartlett [6]. Auto-extinction occurs when the energy balance on the timber results in insufficient production of pyrolyzate to sustain flaming combustion. In order to determine whether auto-extinction can occur in a given compartment, it is necessary to understand the influence of the thermal and air flow environment on this process. Previous authors have investigated the conditions for auto-extinction of timber and their findings have been captured as the critical heat flux for auto-extinction (\(\dot{q}_{crit}^{\prime\prime}\)) and/or the critical mass loss rate for extinction (\(\dot{m}_{crit}^{\prime\prime}\)) [2, 3, 7, 8]. The critical heat flux for auto-extinction of timber has been reported in the range 30 kW/m² to 45 kW/m², and the critical mass loss rate for auto-extinction has been reported in the range 3.5 g/m²/s to 4.0 g/m²/s. The findings of different authors are summarized in Table 1 with notes about each of the experimental programs. The experimental procedures for this previous work show notable differences. Emberley used the mass loss cone in the vertical orientation and samples were not insulated around the perimeter. Bartlett used the Fire Propagation Apparatus in the horizonal orientation and provided insulation around the perimeter (and base). It is perhaps unsurprising that different experimental arrangements lead to differences in the reported values of \(\dot{q}_{crit}^{\prime\prime}\) and \(\dot{m}_{crit}^{\prime\prime}\). The literature on auto-extinction (and the experimental work presented in this paper) focuses on the cessation of flaming combustion. It should be noted that smouldering combustion may continue even after the end of flaming and, while the mass burning rates associated with smouldering are comparatively lower than for flaming, this may still represent a hazard that should be addressed in the design of mass timber buildings.

Expanding from Emberley [1], the pyrolysis rate per unit area of a sample of timber can be expressed as follows:where \(\dot{m}_{p}^{\prime\prime}\) is defined as the pyrolysis (mass loss) rate, \(\Delta H_{p}\) is the heat of pyrolysis, \(\dot{q}_{inc}^{\prime\prime}\) is the applied heat flux (independent of any heat feedback from the flame),\(\dot{q}_{f}^{\prime\prime}\) is the heat feedback from the flame; \(\dot{q}_{ch}^{\prime\prime}\) is the energy generated due to reaction of the char, \(\dot{q}_{loss}^{\prime\prime}\) is the heat losses from the surface, k is the thermal conductivity of the timber, \(\left. {\frac{dT}{dx}} \right|_{{x = x_{ch} }}\) is the thermal gradient of the heat losses into the virgin timber, \(\delta\) is the thickness of the char layer and \(\left( {\delta q^{\prime\prime\prime}} \right)\) is the energy stored per unit area of the char layer.

The significant differences in \(\dot{q}_{crit}^{\prime\prime}\) observed in the literature suggests that there is variation in the terms of the energy equation between testing programmes. For example, differences may arise in experiments undertaken using the Cone Calorimeter compared to the Fire Propagation Apparatus, due to changes in the convective heat transfer at the edge of the sample, absorptivity of the samples at different wavelengths; or sample size.

Conversely, although the literature shows some variation in \(\dot{m}_{crit}^{\prime\prime}\), this variation is small (~ 13%) compared to the observed variation in \(\dot{q}_{crit}^{\prime\prime}\) (~ 50%). The relative insensitivity of \(\dot{m}_{crit}^{\prime\prime}\) between the experimental programmes suggest that this term may provide a more reliable predictor of auto-extinction than a critical heat flux.

To develop understanding of the robustness of the critical mass loss rate criterion it is necessary to establish the: (1) variability in \(\dot{m}_{crit}^{\prime\prime}\) for a given set of conditions; (2) difference in \(\dot{m}_{crit}^{\prime\prime}\) between different applied heat fluxes; (3) difference in \(\dot{m}_{crit}^{\prime\prime}\) for samples in different orientations; and (4) differences in the burning and extinction behaviour for samples subjected to an imposed flow across the surface.

The experimental programme was undertaken using the mass loss calorimeter. Samples were of solid redwood timber with dimensions 95 × 95 × 95 mm, a density of 488 kg/m³ ± 35 kg/m³, with a conditioned moisture content of 12.5% (as measured on a dry basis). Samples were selected such that there were minimal imperfections or knots on the exposed face; grain orientation was perpendicular to the direction of heating (i.e. heating across the grain). The incident heat flux on the sample surface (25 mm away from the cone heater) was calibrated using a Schmidt-Boelter heat flux gauge and a pilot spark was used. The sample mass was recorded with a frequency of 1 Hz; the duration of flaming was recorded.

To establish a baseline variation that should be expected in the parameters of interest, twelve experiments were conducted under an incident heat flux of 25 kW/m² in the vertical orientation (Fig. 1a). To establish the variability of the mass loss rate and time to extinction under different heat fluxes and orientations, samples were tested in vertical and horizontal orientation (Fig. 1b) under 15, 25 and 35 kW/m². These values of heat flux were chosen to maximize the influence of \(\dot{q}_{f}^{\prime\prime}\) which is expected to be proportionately more significant at low heat fluxes—a minimum of four repetitions were tested for each condition. The vertical orientation was analogous to a ‘wall’ configuration, while the horizontal orientation was analogous to a ‘floor’ configuration—with the cone heater located above the sample.

In the case of the forced flow, a simple arrangement (Fig. 1c) was used to impose the flow over the surface of the sample. The sample was positioned 75 mm away from the cone heater to allow the airflow to be delivered. The impact of this on the burning rate for extinction was characterized.

Four air velocities were imposed across the exposed face of the samples in the upwards vertical direction (i.e. the same direction as the buoyancy induced flow). The velocities were established prior to the experiments, in the absence of heating, using a hot wire anemometer. To establish the characteristic velocity across the surface, measurements were made in front of the sample and at the exit of the duct. The measured flow provides an indication of the free flow velocity in front of the sample. Four characteristic velocities were used as follows: 0.7 m/s, 1.2 m/s, 1.7 m/s, 2.3 m/s. It should be noted that the applicability of these values to full scale compartment fire tests has not been established.

This experimental setup allowed an investigation into the key parameters of interests. However, it should be noted that the scale of the samples is limited. Therefore, while it is possible to make direct comparisons between different variables for this scale, it does not necessarily follow that the conclusions would hold for samples or a larger scale.

Each experiment displayed relatively similar behaviour upon exposure to the incident heat flux. Immediately after ignition, flame lengths were relatively long, and over the duration of the experiment these gradually reduced in length; towards the end of the experiment flaming was localised around either cracks that had formed in the char, or around the edge of the samples. When the final flamelet was no longer visible, this was recorded as extinction. The results of the experiments are presented in three phases as follows: the baseline study of twelve samples; the heat flux/orientation study; and the forced flow study.

The difference between the \(\dot{m}_{crit}^{\prime\prime}\) values obtained and those obtained by Emberley [8] and Bartlett [2], raises a question with regard to the definition of extinction and the degree to which a global mass loss rate per unit area can be used to define local behaviours. For example, where the overall incident heat flux is low, but there are local flamelets—burning may be sustained locally, but the average mass loss rate of the sample may be low. Conversely, where the overall incident heat flux is high, and there are local flamelets prior to extinction—burning may be sustained locally, but the average mass loss rate for the whole sample might be expected to be higher. It is possible that this may explain the differences in the recorded \(\dot{m}_{crit}^{\prime\prime}\) value obtained in this study and in the literature. Species and sample preparation may also contribute to differences.

This suggests that, overall, the global energy balance is not changed significantly between orientations. However, whether this means the contribution of the flame (\(\dot{q}_{f}^{\prime\prime}\)) is unaffected by the sample orientation, or whether any changes to the flame are balanced by similar changes in char oxidation (\(\dot{q}_{ch}^{\prime\prime}\)) and/or additional losses from the surfaces (\(\dot{q}_{loss}^{\prime\prime}\)) cannot be defined based on these experiments. However, what these results demonstrate is that, for this configuration, orientation does not affect the overall mass loss rate of the sample.

Solid timber samples were exposed to a range of heat fluxes, characteristic velocities over the exposed face, and sample orientations. It was found that:

Predicting the extinction of timber is a necessary step to realising the design of compartments with exposed timber surfaces. While designers may be reliant on mass loss rate to predict the auto-extinction of timber, the variation in time to extinction may have a significant impact on the loadbearing capacity of any mass timber elements. It has been found that, as suggested by previous authors, mass loss rate is a reliable metric by which to anticipate auto-extinction of timber. However it is shown that, under constant external heating, the time to auto-extinction and, ultimately, the total mass lost from a sample can vary significantly.

The study on orientation demonstrates that, for the scale of sample studied, the orientation has relatively little impact on the burning rate—but that the critical mass loss rate for auto extinction is higher in the vertical compared to the horizontal orientation. In this study, the horizontal condition represents a “floor” configuration and the vertical condition a “wall” configuration; it does not necessarily follow that the results for a horizontal “ceiling” would show the same behaviour.

The origin of this difference can be attributed to the flow across the sample. The critical mass loss rate was shown to be proportionate to the square of the characteristic flow velocity at the timber surface. Again, in the context of designing compartments to achieve auto-extinction, these results suggest that the orientation and, indeed, length scale may play an important role.

The results demonstrate that extinction is controlled by local conditions close to the timber surface. In particular, application to real compartments will require detailed knowledge of the flow regime in the compartment as this has been shown to be significant in the determination of the critical mass loss rate. This raises the question of how this parameter can be reliably used in design.

The results and analysis both confirm previous findings in the literature and raise a series of issues regarding the application of such data by designers aiming to achieve auto-extinction. Of particular interest is developing a better understanding of how increased length scale may affect these results; identifying the role of orientations other than those tested here (e.g. exposed timber soffits) and evaluating appropriate criteria to capture the local processes which govern auto-extinction.