*2.4. Grid Independence Analysis*

When FDS is used for fire simulation, the mesh size has a greater impact on the experimental results. The smaller the mesh size, the smaller the numerical fluctuation of the simulation results, the more accurate the experimental results, and the longer the simulation time. Thus, it is very important to select the appropriate mesh size for fire simulation. The dimensionless expression *D*\* = *δ<sup>x</sup>* is given in the FDS Operation Manual [16], and *δ<sup>x</sup>* is the nominal size of the grid cell. Its definition formula is as follows:

$$D^\* = \left[\frac{Q}{\rho\_0 c\_p T\_0 \sqrt{g}}\right]^{2/5} \tag{1}$$

where *D*\* is the characteristic diameter of fire, m; *Q* is the heat release rate, kW; *g* is the acceleration of gravity, m/s<sup>2</sup> ; *ρ*<sup>0</sup> is the ambient air density, 1.29 kg/m<sup>2</sup> ; *c<sup>p</sup>* is the specific heat capacity at constant pressure, 1.005 kJ/(kg·K); *T*<sup>0</sup> is the ambient air temperature, 293 K. Taking the heat release rate of 1.5 MW as an example, the characteristic size of the fire is *D*\* = 1.09 m. It is generally believed that when the ratio of characteristic diameter to grid is 4~16, the simulation results are more accurate, that is, the grid size is 0.27~0.06 m. Due to the large volume of the physical model, the grid size of the atrium is assumed to be 0.3 m, which basically meets the operation conditions. *Fire* **2023**, *6*, x FOR PEER REVIEW 6 of 19

**Figure 4.** Schematic diagram of numerical model of a building complex. **Figure 4.** Schematic diagram of numerical model of a building complex.

### *2.4. Grid Independence Analysis 2.5. Experimental Verification of Numerical Simulation Results*

When FDS is used for fire simulation, the mesh size has a greater impact on the experimental results. The smaller the mesh size, the smaller the numerical fluctuation of the simulation results, the more accurate the experimental results, and the longer the simulation time. Thus, it is very important to select the appropriate mesh size for fire simulation. The dimensionless expression \* = is given in the FDS Operation Manual [16], and is the nominal size of the grid cell. Its definition formula is as follows: 2/5 \* *Q D c T* = (1) As is can be seen from Figure 5, under the same working conditions, the experimental results are in good agreement with the numerical simulation results. However, the experimental temperature data will drop sharply at a certain moment Through observing the experimental video, we know that the phenomenon is caused by the phenomenon of flame fusion and separation during the experiment, so that the temperature data of the measurement point in the center will fluctuate greatly, which is a normal phenomenon. From the overall temperature change trend, this effect can be ignored, and the data error is within an acceptable range. Therefore, we believe that the calculation results of the numerical simulations in this paper are trustworthy. *Fire* **2023**, *6*, x FOR PEER REVIEW 7 of 19

0 0

*p g*

; is the specific heat

measurement point in the center will fluctuate greatly, which is a normal phenomenon. From the overall temperature change trend, this effect can be ignored, and the data error is within an acceptable range. Therefore, we believe that the calculation results of the nu-**Figure 5.** Comparison of temperature change between experiment and numerical simulation of measuring point 1 in Case 1. **Figure 5.** Comparison of temperature change between experiment and numerical simulation of measuring point 1 in Case 1.

Analyzing the two sets of data of numerical simulations and experiments for vari-

the corresponding degrees of freedom are r − 1, n − r, n − 1, thus determining the mean square MSA, MSE and MST between groups. The required test statistics F can be obtained by the ratio of MSA and MSE, F = MSA/MSE. Based on significance level *α*, compare *F* and *Fα*(r − 1, n − r) [17]. The calculation results of analysis of variance are shown in Table 2.

**Squares Freedom Mean** 

differences 2.08291 × 10<sup>6</sup> <sup>1</sup> 2.08291 × 10<sup>6</sup> 113.26094 3.85

By calculation, it can be seen that at the significance level of 0.05, F is significantly greater than *Fα*,

A large amount of smoke and heat generated during a fire will form a hot smoke stream. The flow direction of the smoke is often the direction of the fire spread, and the flow speed of the smoke is often the fire spreading speed [18]. The smoke will gradually collect over the atrium, and the smoke layer will continue to settle, which will continuously reduce visibility, affect the visual range of evacuees and then affect the evacuation

According to the principle of fire dynamics, the development of fire goes through three stages named accelerated combustion, stable combustion and the extinguishing stage. The spread of smoke in each stage is also different. In the stage of accelerated flame combustion, fire smoke is generated and continues to spread upwards and accumulates, reaching the ceiling and continuing to spread around. The fire has developed into a stable combustion stage, and a large amount of smoke generated before has accumulated in the

. The total deviation squared sum SST = SSA + SSE, and

**Square** *<sup>F</sup> <sup>F</sup>α***(r <sup>−</sup> 1, n** <sup>−</sup> **r)** 

2

differences 2.21971 × 10<sup>7</sup> <sup>1027</sup> 18390.333

**3. Analysis and Discussion of Numerical Simulation Results**

( )

*ij*

*x*

merical simulations in this paper are trustworthy.

1 1

**Table 2.** Calculation results of analysis of variance.

Sum 2.428 × 10<sup>7</sup> 1028

*3.1. Analysis of Smoke Spread in Atrium Fire*

showing a significant difference between the two sets of data.

= =

*i j*

=

*r n*

( )

Intergroup

Intragroup

speed.

*i*

 −

*x x*

1 1

*i j*

=

= =

*r n*

SSA

2

,

**Error Source Sum of** 

SSE

Analyzing the two sets of data of numerical simulations and experiments for variance, the sum of three squared errors was calculated to construct the test statistic: SSA = *r* ∑ *i*=1 *n* ∑ *j*=1 *x<sup>i</sup>* − *x* 2 , SSE = *r* ∑ *n* ∑ *xij* − *x<sup>i</sup>* 2 . The total deviation squared sum SST = SSA + SSE, and the

*i*=1 *j*=1 corresponding degrees of freedom are r − 1, n − r, n − 1, thus determining the mean square MSA, MSE and MST between groups. The required test statistics F can be obtained by the ratio of MSA and MSE, F = MSA/MSE. Based on significance level *α*, compare *F* and *Fα*(r − 1, n − r) [17]. The calculation results of analysis of variance are shown in Table 2.



By calculation, it can be seen that at the significance level of 0.05, F is significantly greater than *Fα*, showing a significant difference between the two sets of data.
