# Theoretical and Numerical Simulation Research on Fire of Large-Span Spatial Structures
## 2 Numerical Simulation Model Verification and Fire Source Condition Setting  
### Numerical Analysis Method Validation  
#### 2.1.1 Fire Test and Finite Element Model  
[PERSON] et al. [44; 45] investigated the fire resistance of aluminum alloy single-layer reticulated shells through scale model fire tests, which were designed to encompass varying fire source powers, positions, and ventilation conditions. The test model, depicted in Figure 3a, consisted of an aluminum alloy spherical reticulated shell with a span of 8 m and a height of 0.5 m, covered with fireproof and ceramic fiber fabric, and a lower supporting structure. This structure was anchored by fixed hinges and included a load-bearing steel framework and masonry infill walls. The heat release rates for the fire tests were 143.11 kW and 357.77 kW, corresponding to fire areas of approximately 0.25 m\({}^{2}\) and 0.49 m\({}^{2}\) for medium and high power fires, respectively  
Conducted under near windless conditions, the fire test suite encompassed two oil pan combustion characteristic assessments and eight structural non-destructive fire evaluations. To ascertain the air temperature within the model, as illustrated in Figure 3b,c, fifteen 3 mm-diameter thermocouples were strategically positioned along the axes 1 and 4, with each sensor placed 50 mm from the nearest component or wall surface. Tests 1 and 4 were chosen for numerical simulation comparison, with detailed parameters outlined in Table 1. The aluminum alloy shell before and after the fire test are shown in Figure 4a,b, and the phenomena observed during the stable combustion phase are depicted in Figure 4c,d. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Label** & **Fire Power** & **Q/kW** & **Fire Location** & **Remarks** \\ \hline Test 1 & Medium & 143.11 & Center & Only doors open \\ \hline Test 4 & High & 357.77 & Center & Windows and doors open \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Details of the fire tests. Figure 3: The enclosure system and the placement of temperature sensors [44]. (**a**) The enclosure system; (**b**) The temperature sensors for air temperature (elevation view); (**c**) The temperature sensors for air temperature (top view). Building upon the experimental data, FDS was utilized to model the air temperature field within the shell structure under fire conditions and to perform a subsequent field simulation analysis. The FDS model is briefly described as follows:  
(1) Fluid dynamics model: Generally, there are two numerical simulation methods, namely direct numerical simulation (DNS) and large eddy simulation (LES). Due to the defects of DNS itself, large eddy simulation is generally used in FDS calculation. (2) Combustion model: LES adopts a mixed fraction model, DNS adopts a finite reaction model. (3) Thermal radiation model: FDS generally adopts the finite volume method (FVM). The physical meaning of the discrete equations obtained by this method is clear, and the conservation characteristics of the whole region can be guaranteed. (4) Boundary conditions: all solid medium surfaces in FDS need to define corresponding material combustion characteristics and thermal boundary conditions, which can be directly called from the software database when modeling; for the wall heat exchange LES simulation, the empirical formula is generally used, and the DNS is directly solved by the theoretical method. The numerical model depicted in Figure 5 aligns with the experimental setup in terms of fire source location and size. In order to take into account the computational efficiency and accuracy, the entire model space corresponding to the +3.200 m elevation plane is divided into two regions for meshing. The mesh size of the lower region is 0.2 m \(\times\) 0.2 m \(\times\) 0.2 m, and the mesh size of the upper region is 0.1 m \(\times\) 0.1 m \(\times\) 0.1 m. The total number of elements of the numerical model is 120,000. Figure 4: The stable combustion stage of the tests [44].