Fire Dynamics of Mass Timber Compartments with Exposed Surfaces: Development of an Analytical Model

Abstract

Exposed timber in buildings has proven to have a positive effect on the building’s sustainability, occupant wellness, and increases the aesthetic appeal of the building but is currently limited by most building codes mainly due to fire safety concerns. While compartment fire testing can be carried out to prove a design performance, this approach is costly and time consuming. Models predicting the fire dynamics inside mass timber compartment with exposed surfaces were developed over the last years. The charring rate of the timber elements, in these models, is either the charring rate of timber when exposed to standard fire or the displacement of the 300°C isotherm using finite element analysis involving several parameters to be determined. Furthermore, using the 300°C isotherm does not account for the impact of the oxygen concentration on the charring rate. In this study, a two-zone model has been developed to estimate the heat release rate (HRR), the upper-layer temperature and oxygen concentration, and the char depth of the exposed timber elements during compartment fires. The charring rate is determined as a function of the incident heat flux impinging on the surface and the oxygen concentration. Comparing the model predictions to 20 experimental compartment fires with and without exposed timber surfaces shows that the model captures well the general fire dynamic, i.e., HRR and temperature. The char depth predictions are close to the experimental data, while being mostly conservative. Seven limitations and improvements have been discussed and will be considered in future versions of this model.

Appendix

1.1 Nomenclature

${A}_{F}$:

Floor area, m²,

${A}_{i}$:

Area of the surface “$i$”, m²,

${A}_{v}$:

Opening area, m²,

${C}_{D}$:

Flow coefficient,

$g$:

Acceleration due to gravity, $g=$ 9.81 m/s²,

${H}_{c}$:

Heat of combustion, MJ/kg,

${h}_{v}$:

Opening height, m,

${\dot{m}}_{a}$:

Mass flow of air, kg/s,

${\dot{m}}_{{O}_{2}\_a}$:

Mass flow of air entering the compartment, kg/s,

${\dot{m}}_{{O}_{2}\_c}$:

Mass of oxygen required for the combustion inside the compartment, kg/s,

${\dot{m}}_{p}$:

Mass flux in the fire plume entering the upper layer, kg/s,

$\dot{Q}$:

Heat release rate, kW.

${\dot{Q}}^{^{\prime\prime} }$:

Heat release rate per unit area, kW/m²,

${\dot{q}}^{^{\prime\prime} }$:

External heat flux, kW/m²,

${\dot{Q}}_{c}$:

Fuel-controlled heat release rate, kW,

${\dot{Q}}_{dec}$:

Heat release rate at the beginning of the decay, kW,

${\dot{Q}}_{v}$:

Heat release rate limited by the ventilation, kW,

${\dot{Q}}_{R}$:

Energy lost by radiation, kW,

${\dot{Q}}_{TOTAL}$:

Sum of the heat release rate of the movable fuel load and the exposed timber elements, kW,

${\dot{Q}}_{W}$:

Energy lost by conduction, kW,

$RR$:

Reduction rate factor, accounting for the combustion efficiency of timber in oxygen-poor environment,

${RR}_{C}$:

Reduction rate factor for the ceiling surface,

${T}_{0}$:

Ambient temperature,°C or K,

${T}_{f}$:

Upper-layer temperature,°C or K,

$t$:

Time, s,

${t}_{dec}$:

Time when the decay begins, s,

W:

Opening width, m,

${H}_{l}$:

Height of the lower end of the opening, m,

x:

Variable to be determined,

y:

Variable to be determined,

z:

Plume height, m,

$\left[{O}_{2}\right]$:

Oxygen concentration, kg/kg of air

1.2 Greeks

$\alpha$:

Fire growth rate, kW/s²,

${\alpha }_{1}$:

Flow rate coefficient, kg/(s m^5/2),

${\alpha }_{fo}$:

Decreasing rate of the fully developed phase, kW/s²,

$\beta$:

Charring rate, mm/min,

${\beta }_{i}$:

One-dimensional charring rate of the surface “$i$”, mm/min,

$\Delta P$:

Pressure difference across the opening

$\varepsilon$:

Emissivity,

${\rho }_{w,0}$:

Oven dry density of wood, kg/m³,

${\rho }_{0}$:

Air density at ambient temperature, kg/m³,

${\rho }_{s}$:

Smoke density, kg/m³,

$\sigma$:

The Stefan-Boltzmann constant, $\sigma =$ 5.67 × 10^–11 kW/(m²K⁴),

$\Phi$:

View factor