## 3 Results and Analysis
### Pyrolysis Boundary Evolution and Burning Characteristics  
Upward flame spreading along the FPU board, as an unsteady burning process, showed evident acceleration with enlarged \(\theta\). Figure 2 demonstrates the boundary evolution of the inverse \"V\" shape pyrolysis zone by view angle calibration (case with air pressure 70 kPa and board inclination 60\({}^{\circ}\), for example). To avoid heating or damage by fire within this limited test space, the camera was set in an oblique direction. Time-sequential images of the flame along the whole board by original perspective view were corrected into \"front view\", to show a more precise spreading process based on the linear twist method.  
A \"V\" shape burning area marked by orange color was growing during the flame spreading until the pyrolysis front reached the upper edge of the board, which would then decrease gradually with increasing burnout area marked by red. Nevertheless, the FSR of the pyrolysis front was undoubtedly enhanced by enlarged inclination or pressure. Actually, the increasing length and FSR of the pyrolysis  
Figure 2: Evolution of pyrolysis and burnout zone profiles (typical results under 70 kPa and inclination 60\({}^{\circ}\) condition) during upward flame spread (**b**) by digital image view correction (**a**).  
zone with time history were reproduced by [PERSON]'s model [19] using 2D direct numerical simulation (DNS), which confirmed the importance of flame heat flux into both preheated and pyrolysis zones.  
For a direct comparison with burning characteristics of downward flame spread reported in our study [9], the averaged value of FSR \(V_{p}\), burning rate \(\dot{m}\)and flame length \(L_{f}\) were used as shown in Figure 3.  
The detailed measurement (or, i.e., calculation) method was also described in [9; 20], where the FSR and burning rate were the average values from the same spreading distance of the pyrolysis front within 30-70 cm, and flame length was obtained by the digital image process based on [PERSON]'s definition [20]. Figure 3a-c show the experimental results of \(V_{p}\), \(\dot{m}\) and \(L_{f}\) for both upward and downward flame spread with various inclinations under different pressures. In addition, normalization of these parameters (defined as \(V_{p,d}\)/\(V_{p,0}\), \(\dot{m}_{d}\)/\(\dot{m}_{0}\) and \(L_{f,d}\)/\(L_{f,0}\)) vs. air pressure \(p_{d}\)/\(p_{0}\) is applied to give quantitative effects of pressure as shown in Figure 3d-f, where subscript \(d\) and \(0\) denote decreased pressure and normal pressure (~100 kPa), respectively. The indexes of pressure tagged in Figure 3d-f are fitted by data with inclination from 30\({}^{\circ}\) to 90\({}^{\circ}\) for upward or downward flame spread as overall comparisons.  
It is interesting that the pressure effect on burning characteristics in downward spread showed somehow consistent as,  
\[\left\{\begin{array}{l}V_{p}\sim p^{0.67}\\ \dot{m}\sim p^{0.77}\\ L_{f}\sim p^{0.78}\\ \end{array}\right.,\text{ }for downward\\ \tag{2}\]  
Figure 3: Burning characteristics and related normalization including flame spread rate (FSR) (**a**,**d**), burning rate (**b**,**e**) and flame length (**c**,**f**) for downward and upward flame spread, respectively, with various inclination under different pressures.  
However, for upward flame spread, three indexes are totally distinct from each other,  
\[\left\{\begin{array}{l}V_{p}\sim p^{1.49}\\ \dot{m}\sim p^{1.02}\\ L_{f}\sim p^{0.39}\end{array}\right.,\ for\ upward \tag{3}\]  
Theoretical explanation for these tendencies is proposed hereinafter according to fire dynamic analysis.