## 4 Validation Results  
### Data Processing  
The data of interest for the validation of the zonal model concern the evolution of the average gas and wall temperatures, and the volume concentrations of CO\({}_{2}\) and O\({}_{2}\) in the exhausted gases. The interface of the smoke layer is diffuse and cannot be measured with sufficient reliability, which is why the raw measurements are treated in a specific way.  
The average temperature of the gas in the compartment is obtained by summing the local temperature values measured by the 20 thermocouples placed, as shown in Figure 7a, and dividing by 20. The value obtained is then compared to that calculated from the upper- and lower-layer temperatures and the elevation of the smoke interface predicted by the zone model: \(\overline{T}^{mod}=[(z_{room}-z_{i})T_{u}+z_{i}T_{l}]/z_{room}\).  
Due to the distribution of the thermocouples on the walls of the compartment (Figure 7b), the average temperature of the side walls is calculated as follows:  
\[\overline{T}^{exp}_{sw}=\frac{1}{4}[\overline{T}_{p_{FRONT}}+\overline{T}_{p_ {BACK}}+\overline{T}_{p_{WEST}}+\overline{T}_{p_{EAST}}] \tag{48}\]  
with  
\[\overline{T}_{p_{FRONT}} =\frac{1}{6}[T_{p}(0.5,0,0.5)+T_{p}(2.5,0,0.5)+2T_{p}(1.5,0,1.5)+T _{p}(0.5,0,2.5)+T_{p}(2.5,0,2.5)] \tag{49}\] \[\overline{T}_{p_{BACK}} =\frac{1}{6}[T_{p}(0.5,3,0.5)+T_{p}(2.5,3,0.5)+2T_{p}(1.5,3,1.5)+T _{p}(0.5,3,2.5)+T_{p}(2.5,3,2.5)]\] (50) \[\overline{T}_{p_{WEST}} =\frac{1}{6}[T_{p}(0,0.5,0.5)+T_{p}(0,2.5,0.5)+2T_{p}(0,1.5,1.5)+T _{p}(0,0.5,2.5)+T_{p}(0,2.5,2.5)]\] (51) \[\overline{T}_{p_{EAST}} =\left\{\begin{array}{c}\frac{1}{6}[T_{p}(3,0.5,0.5)+T_{p}(3,2.5,0.5)+2T_{p}(3,1.5,1.5)+T_{p}(3,0.5,2.5)+T_{p}(3,2.5,2.5)]\\ \\ \frac{1}{4}[T_{p}(3,0.5,0.5)+T_{p}(3,2.5,0.5)+T_{p}(3,0.5,2.5)+T_{p}(3,2.5,2.5) ]\end{array}\right.for\text{ }Tests 6\text{ to }10 \tag{52}\]  
It is compared to that obtained from the predicted temperatures of wall segments 2 to 9: \(\overline{T}^{mod}_{sw}=\sum_{\sigma=2}^{9}T_{w}/8\).  
For the ceiling, the average experimental temperature is calculated using a Gaussian profile about the center of the ceiling:  
\[\overline{T}^{\exp}_{ceil}=\frac{2\pi}{A_{w=1}}T_{p}(1.5,1.5,3)\int_{0}^{R} exp\left(-\frac{r^{2}}{\sigma^{2}}\right)rdr \tag{53}\]  
where \(R\) is the equivalent radius of the ceiling deduced from \(R^{2}=x_{room}y_{room}\), and \(\sigma\) is estimated from thermocouple values as follows: \(\sigma^{2}=-2/ln\big{(}\overline{T}_{0.5}/\overline{T}_{p}(1.5,1.5,3)\big{)}\), with \(\overline{T}_{0.5}=0.25\big{[}T_{p}(0.5,0.5,3)+T_{p}(0.5,2.5,3)+T_{p}(2.5,0.5,3) +T_{p}(2.5,2.5,3)\big{]}\). \(\overline{T}^{\exp}_{ceil}\) is then compared with the predicted ceiling temperature \(T_{w=10}\).  
The N-percentage rule by [PERSON] [22] is applied to estimate the smoke layer interface height from the measured vertical temperature profiles. Beforehand, the gas temperatures measured in the four corners at 1.0, 1.5, 2.0, and 2.5 were first averaged to obtain \(\overline{T}_{1.0}\), \(\overline{T}_{1.5}\), \(\overline{T}_{2.0}\), and \(\overline{T}_{2.5}\), as done previously for \(\overline{T}_{0.5}\). Then, they were interpolated between each thermocouple height to refine the temperature profile (e.g., every cm). The interface height \(z_{int}\) is finally determined as the height value satisfying the following condition:  
\[T(z_{int},t)-T_{0}=\frac{N}{100}\big{[}max(\overline{T}_{2.5}(t))-\overline{T}_{ 2.5}(0)\big{]} \tag{54}\]  
The selection of the value of N is quite subjective. Values of 10, 15 and 20 have been suggested by [PERSON] [22]. Here, optimum values in the range of [15-40] are adopted depending on the test under study. Other techniques, namely the maximum gradient method by [PERSON] [15], the Janssens and Tran method [23], and the integral ratio method by [PERSON] et al. [24], have been tested, but they were not able to describe the time evolution of the interface height with decreasing smoke layer thickness, especially at the end of burn.