# 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  
Through numerical simulation analysis, the axial temperature and velocity of the axially symmetric fire plume are obtained. As shown in Figure 17, due to the symmetrical distribution of the inlet, the fire plume still presents the characteristics of approximately axisymmetric distribution. Therefore, in the following related research and analysis, the fire plume is analyzed as an axisymmetric fire plume model. Figure 18 shows the schematic diagram of the fire plume generated by the combustion of combustibles [50]. Due to the thermal feedback of the fire, the volatiles generated by  
Figure 17: Velocity distribution at different times. the combustion are mixed with the ambient air to form a diffusion flame. A dotted line stretching upward on both sides of the flame represents the boundary of the plume, that is, the boundary of the entire plume composed of combustion products and entrained air. In order to analyze and verify whether the traditional plume model is suitable for predicting the axial temperature and velocity of the plume under fire in large-span spatial structures, the current mainstream plume model is compared with the numerical simulation results, and the plume model is improved according to the calculation results. The common traditional calculation formulas of plume center temperature and velocity are as follows:  
(1) [PERSON] model [9; 10]:  
In order to further determine the distribution of plume in fire, [PERSON] carried out a large number of fire plume experiments on the basis of the ideal plume theory hypothesis. The ideal plume theory hypothesis is as follows:  
1 It is assumed that all the energy enters the plume from the hot source and maintains energy conservation in the plume. 2 Assume that the density change is very small throughout the plume height, generally considered \(\rho\sim\rho\). Therefore, the ideal plume theory is mainly used to describe the weak plume. 3 It is assumed that the distribution of velocity, temperature, and force has the same form, which is independent of height z. 4 It is assumed that the air is entrained into the plume, and the velocity entering the plume is proportional to the velocity of the plume smoke. During the experiment, the hot smoke layer was kept at a fixed height by controlling the mass flow rate in the smoke hood of the experimental instrument. Based on the above experimental data, the mass flow rate equation of the ideal plume was modified, as shown in Equation (2):  
\[\Delta T=5.0(\frac{T_{0}}{gc_{P}^{2}\rho_{0}^{2}})^{1/3}\dot{Q}_{c}^{2/3}z^{- 5/3} \tag{2}\]  
In the formula, \(\Delta T\) is the difference between the plume temperature and the ambient temperature, K; \(T_{0}\) is the initial temperature of the environment, K; \(g\) is the acceleration of gravity, \(g=9.81\) m/s\({}^{2}\); \(c_{P}\) is the specific constant pressure heat capacity of ambient air, \(c_{P}=1.0\) kJ/(kg \(\cdot\) K); \(\rho_{0}\) is the density of ambient air, \(\rho_{0}=1.2\) kg/m\({}^{3}\); \(\dot{Q}_{c}\) is the convective heat flow, \(\dot{Q}_{c}=0.7\dot{Q}\), kW; \(z\) is the distance to the center of the fire source, m.  
(2) [PERSON] model [11; 12]:  
In order to obtain a more realistic plume temperature distribution in the fire, [PERSON] also relaxes its assumptions on the basis of the ideal plume to make it closer to the real fire. The assumptions are as follows:  
1 The concept of 'virtual source' is introduced, and the relationship between the convective energy release rate port and the parameters of some plumes is considered. 2 The temperature and centerline velocity of the plume centerline are introduced, and the Gaussian distribution which is closer to the actual fire situation is adopted. Figure 18: Fire plume flow. 3 Considering the large density difference inside and outside the plume, his means that \(\rho\
eq\rho\). Therefore, the Heskestad plume mainly describes the strong plume.