# Theoretical and Numerical Simulation Research on Fire of Large-Span Spatial Structures
## 3 Temperature Field Analysis of Structure Under Different Fire Conditions
### Axis Temperature and Velocity of Axisymmetric Flame Plume of the Structure
(6) Weak plume velocity formula [50]:  
\[\Delta T=5.0(\frac{T_{0}}{gc_{P}^{2}\rho_{0}^{2}})^{1/3}\dot{Q}_{c}^{2/3}z^{- 5/3} \tag{2}\]2  
The simulated plume center temperature is compared with the [PERSON] model, [PERSON] model, McCaffrey model, and [PERSON]'s formula, as shown in \[\Delta T=5.0(\frac{T_{0}}{gc_{P}^{2}\rho_{0}^{2}})^{1/3}\dot{Q}_{c}^{2/3}z^{- 5/3} \tag{2}\]3 The temperature in the upper intermittent flame zone begins to decrease due to the weakening of the combustion reverse and the cooling of the entrained air. The total heat release rate \(Q\) of fire source in fire can be divided into convective heat flow \(Q_{\rm c}\) and radiative heat flow \(Q_{\rm r}\). When porous fuels (such as wood) are fully burned, part of the total heat generated during the combustion process is absorbed by unburned fuels. Due to the effects of convection and radiation, the other part escapes from the fuel in the form of convection or radiation energy flow. The heat flux \(Q_{\rm c}\) is only equivalent to 60-70% of the total heat release rate. The convective heat flux \(Q_{\rm c}\) is taken away by the fire plume above the flame, while the remaining radiative heat flux \(Q_{\rm r}\) radiates to the surrounding environment. \[\Delta T=5.0(\frac{T_{0}}{gc_{P}^{2}\rho_{0}^{2}})^{1/3}\dot{Q}_{c}^{2/3}z^{- 5/3} \tag{2}\]4 Temperature at the center of a fire plume. The three models are based on the natural diffusion flame model [50]. The total heat release rate of the fire source is divided into convective heat flow and radiant heat flow, namely: \(Q=Q_{\rm c}+Q_{\rm r}\). For the top opening of the building fire, the fire plume and the smoke plume flow directly out of the outdoor. The total heat release rate of the fire source is divided into convective heat flow and radiant heat flow and the heat flow taken away by the gas flowing out of the opening, namely, \(Q=Q_{\rm c}+Q_{\rm r}+Q_{\rm e}\). From the simulation results (Table 6), most of the heat flows out at the top opening. The proportion of \(Q_{\rm e}\) is in the range of about 72-82%, and its convective heat flow is smaller than that of the three models. Therefore, the theoretical calculation results of the axial temperature rise of the centerline of the three classical plume models are quite different from the simulated calculation values, but with the increase, the theoretical calculation results are closer to the simulated calculation values. The axial temperature of the plume centerline calculated by the McCaffrey model is generally larger than the experimental data. The axial temperature of the plume centerline calculated by the Heskestad model is higher than the experimental data, but the theoretical calculation results and the experimental data can be maintained in a reasonable range. The maximum relative error between the theoretical calculation results and the experimental data is only 4.9%. It can also be found that the plume model for traditional structures is not suitable for the prediction and analysis of fire temperature field of large spatial structures. Meanwhile, with the increase of the area of the air supply port, the temperature at the fire source gradually increases, but with the increase of the height from the combustion surface, the temperature of the plume centerline gradually tends to be consistent. The supplementary air volume of CASE1 and CASE2 is suitable, and it will not significantly strengthen the combustion at the fire source. The temperature increase is relatively slow, and the highest temperature reached after the combustion is stable is basically the same. The supplemental air volume of CASE3 and CASE4 is too large, and the supplemented air provides a large amount of oxygen for the combustion of the fire source and strengthens the combustion, so that the flame temperature increases rapidly, and the maximum temperature reached after the combustion is stable is also higher. The change trend of temperature calculated by [PERSON]'s formula is completely different from the simulation results.