# Performance-Based Analysis of Single-Layer Cylindrical Steel Reticulated Shells in Fire
## 3 Air Temperature Field Analysis During a Fire  
In this paper, we used the FDS (Fire Dynamics Simulator) software developed by the National Institute of Standards and Technology (NIST) to simulate fire. FDS is a software for calculating fire dynamics problems, and it is mainly used to simulate and analyze fire problems in three-dimensional space. It has an open program system and good post-processing functions, and it is widely used in the field of fire safety structural engineering. Our calculation results were also experimentally verified. A mesh setting is an essential part of FDS simulation calculations. All FDS calculations must be carried out based on meshing generation. Further, the size of the grid settings controls the accuracy of the simulation calculations and the length of the calculation time.  
A proper mesh setting size is significant for simulations in FDS in order to minimize the calculation time and obtain the required calculation precision. The simulation accuracy of can be obtained by setting close or consistent length of mesh size in three directions of coordinate axis. The mesh size in FDS can be determined based on the numbers of grid respectively in x, y, and z directions, which are supposed to meet the module requirements of 2\({}^{u}\), 3\({}^{v}\) or 5\({}^{w}\). The coefficients of u, v, and w are integers. According to the instructions of FDS, the mesh size is determined according to the following empirical Equation (3), which is the function of initial condition and heat release rate.  
\[D^{\prime\prime}=\left(\frac{Q}{\rho_{\infty}\cdot c_{\infty}\cdot T_{\infty} \cdot\sqrt{g}}\right)^{2/5} \tag{3}\]  
\(D^{\prime\prime}/\delta_{x}\in(4,16)\), \(D^{\prime\prime}/\delta_{y}\in(4,16)\), \(D^{\prime\prime}/\delta_{z}\in(4,16)\) where  
\(D^{\prime\prime}\)-equivalent fire source diameter (m);  
Q----heat release rate of fire source (kW);  
g----gravitational acceleration, which is 9.8 m/s\({}^{2}\);  
\(\rho_{\infty}\)----initial environment air density, which is 1.290 kg/m\({}^{3}\);  
\(c_{\infty}\)----initial value of heat capacity, which is \(1.4\times 103\) J.(kg\(\cdot\)K);  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Types of Fire** & **Maximum Heat Release Rate \(Q_{s}\)/MW** \\ \hline Small power fire & \multicolumn{2}{c}{\(<\)3.5} \\ \hline Middle power fire & 3.5–15 & \\ \hline Large power fire & \multicolumn{2}{c}{\(>\)15} \\ \hline \hline \end{tabular}
\end{table}
Table 1: Types of heat release rate.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \(Q_{max}\) (MW) & HRRPUA (kW/m\({}^{2}\)) & \(A\) (m\({}^{2}\)) & \(\alpha\) (kW/s\({}^{2}\)) & \(t_{g}\) (s) \\ \hline
10 & 1000 & 2.0 \(\times\) 5.0 & 0.04689 & 461 \\
15 & 1000 & 3.0 \(\times\) 5.0 & 0.04689 & 565 \\
16 & 1000 & 3.2 \(\times\) 5.0 & 0.04689 & 584 \\
17 & 1000 & 3.4 \(\times\) 5.0 & 0.04689 & 6\(T_{\infty}\)-initial environment temperature, which is 293 K;  
\(\delta_{x},\delta_{y},\delta_{z}\)-mash size in \(x\), \(y\), and \(z\) direction, respectively.  
In order to ensure the accuracy of the calculation results and reduction of the calculation time, the mash size is designated to be \(0.2\) m \(\times\) 0.2 m \(\times\) 0.2 m in this paper. When the maximum heat release rate of fire source is 20 kW, the availability of the mash size can be proved based on the Equation (3) as follows:  
\[D^{\prime\prime}=\left(\frac{Q}{\rho_{\infty}C_{p}T_{\infty}\sqrt{g}}\right)^ {2/5}=\left(\frac{20000}{1.29\times 1.4\times 293\times\sqrt{9.8}}\right)^{2/5}=2.71,\]  
\[\frac{D^{\prime\prime}}{\delta x}=\frac{2.71}{0.2}=13.55\in[4,16]\]