*3.2. Vertical Smoke Temperature Distribution in Atrium*

The fire produces a large amount of smoke, and releases huge heat to produce a high temperature. A high temperature environment and toxic smoke will bring difficulties to the safe evacuation of trapped people. Long-term exposure to smoke will seriously damage people's physical functions, and they may lose the ability to escape. The study of the temperature distribution law of smoke in an atrium can not only provide a reference for building fire design, but also provide guidance for personnel evacuation during a fire. Figures 7–11 are the variation charts of vertical smoke temperature in the atrium under five different working conditions, and six measurement points at different positions are selected as analysis objects in the vertical direction: V1 (17.3 m), V4 (14.3 m), V7 (11.3 m), V10 (8.3 m), V13 (5.3 m), V16 (2.3 m). *Fire* **2023**, *6*, x FOR PEER REVIEW 8 of 19 ceiling and formed a stable smoke layer, which continues to settle. Until the extinguishing phase, smoke is continuously generated and fills the entire atrium. Figure 6 shows the schematic diagram of smoke spread under working Cases 1~5.

Case 1

1.

0

0

100

200

300

Temperature/℃

2.

400

500

20 s 100 s 300 s selected as analysis objects in the vertical direction: V1 (17.3 m), V4 (14.3 m), V7 (11.3 m),

> V1 V4 V7 V10 V13

V16

**Figure 6.** Comparison of smoke layer thickness at different times in Cases 1~5. **Figure 6.** Comparison of smoke layer thickness at different times in Cases 1~5. V10 (8.3 m), V13 (5.3 m), V16 (2.3 m).

sonable smoke exhaust system. **Figure 7.** Temperature variation of measuring points at different heights above the atrium in Case **Figure 7.** Temperature variation of measuring points at different heights above the atrium in Case 1.

100 200 300 400 500 600 700

Time/s

**Figure 8.** Temperature variation of measuring points at different heights above the atrium in Case

100 200 300 400 500 600 700 800 900

**Figure 7.** Temperature variation of measuring points at different heights above the atrium in Case

V16 (Case1)

Time/s

*3.2. Vertical Smoke Temperature Distribution in Atrium*

V10 (8.3 m), V13 (5.3 m), V16 (2.3 m).

0

0

100

200

300

Temperature/℃

1.

2.

3.

4.

4.

0

0

0

0

50

50

100

100

150

150

Temperature/℃

Temperature/℃

5.

5.

200

200

250

250

400

500

The fire produces a large amount of smoke, and releases huge heat to produce a high temperature. A high temperature environment and toxic smoke will bring difficulties to the safe evacuation of trapped people. Long-term exposure to smoke will seriously damage people's physical functions, and they may lose the ability to escape. The study of the temperature distribution law of smoke in an atrium can not only provide a reference for building fire design, but also provide guidance for personnel evacuation during a fire. Figures 7–11 are the variation charts of vertical smoke temperature in the atrium under five different working conditions, and six measurement points at different positions are selected as analysis objects in the vertical direction: V1 (17.3 m), V4 (14.3 m), V7 (11.3 m),

> V1 V4 V7 V10 V13

**Figure 8.** Temperature variation of measuring points at different heights above the atrium in Case **Figure 8.** Temperature variation of measuring points at different heights above the atrium in Case 2.

V1

**Figure 9.** Temperature variation of measuring points at different heights above the atrium in Case **Figure 9.** Temperature variation of measuring points at different heights above the atrium in Case 3. 3.

**Figure 10.** Temperature variation of measuring points at different heights above the atrium in Case **Figure 10.** Temperature variation of measuring points at different heights above the atrium in Case 4.

100 200 300 400 500 600

100 200 300 400 500 600

**Figure 11.** Temperature variation of measuring points at different heights above the atrium in Case

**Figure 11.** Temperature variation of measuring points at different heights above the atrium in Case

Time/s

Time/s

**Figure 10.** Temperature variation of measuring points at different heights above the atrium in Case

 V1 V4 V7 V10 V13

 V1 V4 V7 V10 V13

Time/s

0 100 200 300 400 500 600 700 800

Time/s

V16 (Case4)

100 200 300 400 500 600 700 800

**Figure 10.** Temperature variation of measuring points at different heights above the atrium in Case

Time/s

**Figure 9.** Temperature variation of measuring points at different heights above the atrium in Case

V16 (Case3)

 V1 V4 V7 V10 V13

 V1 V4 V7 V10 V13

0

50

100

150

Temperature/℃

3.

0

0

50

100

150

Temperature/℃

4.

200

250

200

250

**Figure 11.** Temperature variation of measuring points at different heights above the atrium in Case **Figure 11.** Temperature variation of measuring points at different heights above the atrium in Case 5.

5. It can be seen that the change trend of smoke temperature rise under different working conditions is basically similar. Regardless of the heat release rate and whether the smoke exhaust system is turned on, the rise of smoke temperature has successively experienced the three stages of rise, fluctuation within a certain range and decrease, which is consistent with the three stages of occurrence and development of fire explained by combustion theory. In the stable combustion stage of the ignition source, the smoke temperature will fluctuate within a certain range, and we regard it as the stable stage of the smoke temperature rise (Figures 7–11). Under different working conditions, the stabilization stage of smoke temperature rise is different, which is mainly reflected in the stable value of smoke temperature rise and the time when the stable section disappears.

When a fire starts, the heat released by the fire is limited, and the rise of smoke temperature is relatively slow. Then, the fire becomes violent, and the temperature gradient increases rapidly and it quickly reaches the maximum temperature. Comparing Figures 7, 9 and 10, it can be seen that under the same natural filling conditions, the temperature stability values of the measurement point closest to the fire source under different heat release rate in Case 1 (1.5 MW), Case 3 (0.7 MW) and Case 4 (0.34 MW) decrease sequentially. This indicates that the greater the heat release rate is, the greater the average temperature of the smoke in the atrium is. The greater the distance between the smoke and the fire source above the atrium, the lower the temperature of the smoke is; that is, the thermocouple closest to the fire source has the highest temperature and the thermocouple farthest away has the lowest temperature. As the smoke moves far away in the upper layers, heat is gradually dissipated. However, the time it takes for the smoke temperature stabilization to disappear is not much different. When the natural smoke exhaust mode (Cases 1 and 2) is turned on, it mainly has a greater impact on the smoke temperature on the upper floor of the atrium, and has little impact on the smoke temperature near the fire source. This is because the natural smoke exhaust strategy only opens the top glass window of the atrium to accelerate the flow of smoke near it, so that the heat exchange is accelerated, while the position near the fire source far from the glass window receives little impact. After turning on the mechanical smoke exhaust system (Cases 4 and 5), the temperature decreases, which also causes the temperature stability section to disappear earlier.

Figure 12 shows the change of the average temperature of the vertical smoke stabilization section of the atrium with the height of the fire source center under the conditions of Cases 1~5. It can be clearly known that the uniform temperature of the smoke stabilization section is directly related to the heat release rate of the fire. In addition, the use of natural smoke exhaust (Cases 1 and 2) or mechanical smoke exhaust (Cases 4 and 5) also has an impact on the uniform temperature of the smoke stabilization section. Turning on the

smoke exhaust system will accelerate the heat exchange between the smoke and outside, so that the smoke cooling temperature is reduced. However, from Figure 12, the magnitude of this temperature reduction is not obvious, indicating that a single smoke exhaust mode has a poor effect on the flow control of smoke. *Fire* **2023**, *6*, x FOR PEER REVIEW 13 of 19300 350 Case 1 Case 2 Case 3 Case 4 Case 5

*Fire* **2023**, *6*, x FOR PEER REVIEW 13 of 19

250

400

**Figure 12.** Variation of vertical smoke average temperature in atrium with height from fire source center in Cases 1~5. **Figure 12.** Variation of vertical smoke average temperature in atrium with height from fire source center in Cases 1~5. In orderto describe the distribution of vertical smoke temperature in the atrium more intuitively and accurately, we introduced the McCaffrey plume model [19]. The McCaf-

In orderto describe the distribution of vertical smoke temperature in the atrium more intuitively and accurately, we introduced the McCaffrey plume model [19]. The McCaffrey plume model is a semi-empirical formula, which is fitted by a large number of experimental results. It is applicable to the calculation of plume mass flow under the condition of both small area fires and large area fires, maintaining certain universality. It is widely used to study the flame plume in building fires [20–23]. The expression is as follows: In order to describe the distribution of vertical smoke temperature in the atrium more intuitively and accurately, we introduced the McCaffrey plume model [19]. The McCaffrey plume model is a semi-empirical formula, which is fitted by a large number of experimental results. It is applicable to the calculation of plume mass flow under the condition of both small area fires and large area fires, maintaining certain universality. It is widely used to study the flame plume in building fires [20–23]. The expression is as follows: frey plume model is a semi-empirical formula, which is fitted by a large number of experimental results. It is applicable to the calculation of plume mass flow under the condition of both small area fires and large area fires, maintaining certain universality. It is widely used to study the flame plume in building fires [20–23]. The expression is as follows:2 2 1 z *TT* − =

$$
\Delta T = \left(\frac{\kappa}{0.9 \cdot \sqrt{2\text{g}}}\right)^2 \left(\frac{\text{z}}{\text{\textdegree\%}}\right)^{2\eta - 1} \cdot T\_{\infty} \tag{2}
$$

$$
\text{\textdegree \dots \text{\textdegree} \dots \text{\textdegree} \dots \text{\textdegree} \dots \text{\textdegree}} \tag{3}
$$

2/5

(2)

20

**[m/kW2/5]**

**[m/kW2/5]**

ambient temperature, K; *g* is the acceleration of gravity, 9.81 m/s<sup>2</sup> ; *Q* is the heat release rate of the fire, kW; z is the height, m; *T* is the ambient temperature, 293 K. The three zones of the axisymmetric buoyant plume are shown in Figure 13. The values of κ and η of the McCaffrey plume model are shown in Table 3. where ∆*T* represents the difference between the temperature at appointed altitude and the ambient temperature, K; *g* is the acceleration of gravity, 9.81 m/s<sup>2</sup> ; . *Q* is the heat release rate of the fire, kW; z is the height, m; *T*<sup>∞</sup> is the ambient temperature, 293 K. The three zones of the axisymmetric buoyant plume are shown in Figure 13. The values of κ and η of the McCaffrey plume model are shown in Table 3. rate of the fire, kW; z is the height, m; *T* is the ambient temperature, 293 K. The three zones of the axisymmetric buoyant plume are shown in Figure 13. The values of κ and η of the McCaffrey plume model are shown in Table 3.

where ∆*T* represents the difference between the temperature at appointed altitude and the

**Table 3.** Values of and .

**Zone**

**Zone**

**Table 3.** Values of and .

**Figure 13.** The three zones of the axisymmetric buoyant plume. **Figure 13.** The three zones of the axisymmetric buoyant plume. **Figure 13.** The three zones of the axisymmetric buoyant plume.

2/5 *z Q*

2/5 *z Q*

Intermittent flame zone 0.08–0.2 1.9 [m/kW1/5 s] 0

Plume zone >0.2 1.1 [m4/3/kW1/3 s] −1/3

Continuous flame zone <0.08 6.8 [m1/2/s] 1/2 Intermittent flame zone 0.08–0.2 1.9 [m/kW1/5 s] 0

Plume zone >0.2 1.1 [m4/3/kW1/3 s] −1/3



However, considering the factors of multi-fire flame fusion, air flow and smoke exhaust system in this working condition, the McCaffrey plume model above needs to be corrected. We still use *z*/ . *Q* 2/5 as the independent variable to draw the scatter diagram of smoke temperature rise changing with the vertical height and the heat release rate of the fire source, and then carry out subsection fitting correction, as shown in Figure 14. However, considering the factors of multi-fire flame fusion, air flow and smoke exhaust system in this working condition, the McCaffrey plume model above needs to be corrected. We still use 2/5 *z Q* as the independent variable to draw the scatter diagram of smoke temperature rise changing with the vertical height and the heat release rate of the fire source, and then carry out subsection fitting correction, as shown in Figure 14.

**Figure 14.** Variation of smoke temperature rise with 2/5*z Q* . **Figure 14.** Variation of smoke temperature rise with *z*/ . *Q* 2/5 .

The modified *κ* and *η* values are shown in Table 4. The modified *κ* and *η* values are shown in Table 4.

**Table 4.** Modified values of and . **Table 4.** Modified values of *κ* and *η*.

where

0 *T*

*T*

of atrium, 19.8 m.


### *3.3. Horizontal Smoke Temperature Distribution under the Ceiling of the Atrium 3.3. Horizontal Smoke Temperature Distribution under the Ceiling of the Atrium*

The temperature distribution below the atrium ceiling is similar to ceiling jet. The smoke rises from the atrium fire source to the ceiling, and then spreads around, filling the entire atrium. Under all cases, the smoke temperature reached a maximum value directly above the fire source, and decreased on the east and west sides as it moved away from the center point, showing an exponential attenuation mode. The temperature attenuation rate is not only directly related to the heat release rate, but also has a certain relationship with the smoke exhaust system. In order to analyze this attenuation relationship more intuitively and qualitatively, we make the average temperature of the smoke under the atrium ceiling dimensionless according to the following equation [24],The temperature distribution below the atrium ceiling is similar to ceiling jet. The smoke rises from the atrium fire source to the ceiling, and then spreads around, filling the entire atrium. Under all cases, the smoke temperature reached a maximum value directly above the fire source, and decreased on the east and west sides as it moved away from the center point, showing an exponential attenuation mode. The temperature attenuation rate is not only directly related to the heat release rate, but also has a certain relationship with the smoke exhaust system. In order to analyze this attenuation relationship more intuitively and qualitatively, we make the average temperature of the smoke under the atrium ceiling dimensionless according to the following equation [24],

0

represents the temperature at the center position directly above the fire source, °C;

distance from fire source; *x* is the distance from the center point, m; *H* is the clear height

represents the temperature of the measurement point in the '*x*' direction, °C;

$$
\Delta T/\Delta T\_0 = e^{-a\mathbf{x}/H} \tag{3}
$$

where ∆*T* represents the temperature of the measurement point in the '*x*' direction, ◦C; ∆*T*<sup>0</sup> represents the temperature at the center position directly above the fire source, ◦C; *α* is the attenuation coefficient of dimensionless smoke temperature rise with dimensionless distance from fire source; *x* is the distance from the center point, m; *H* is the clear height of atrium, 19.8 m. *Fire* **2023**, *6*, x FOR PEER REVIEW 15 of 19 Figure 15 shows the variation of the horizontal dimensionless smoke temperature

> Figure 15 shows the variation of the horizontal dimensionless smoke temperature rise ∆*T*/∆*T*<sup>0</sup> with the dimensionless distance *x/H* from the fire source at the height of 18.3 m below the atrium ceiling under various working conditions. The correlation coefficient of the fitting curve reaches more than 0.95 under all cases, indicating that the consistency between the data and the model was good. Table 5 shows the attenuation coefficient of dimensionless smoke temperature rise with dimensionless distance from the fire source. rise 0 *T T* / with the dimensionless distance *x/H* from the fire source at the height of 18.3 m below the atrium ceiling under various working conditions. The correlation coefficient of the fitting curve reaches more than 0.95 under all cases, indicating that the consistency between the data and the model was good. Table 5 shows the attenuation coefficient of dimensionless smoke temperature rise with dimensionless distance from the fire source.

**Figure 15.** *Cont*.

*Fire* **2023**, *6*, x FOR PEER REVIEW 16 of 19

**Figure 15.** Variation of dimensionless smoke temperature rise 0 *T T* / under atrium ceiling with **Figure 15.** Variation of dimensionless smoke temperature rise ∆*T*/∆*T*<sup>0</sup> under atrium ceiling with dimensionless distance from fire source *x/H* in Cases 1~5.

dimensionless distance from fire source *x/H* in Cases 1~5.


**Table 5.** Attenuation coefficients of dimensionless smoke temperature rise with dimensionless distance from fire source.

It can be seen from Figure 15 that the variation of lateral dimensionless smoke temperature rise under the atrium ceiling with the distance between dimensionless and fire source has a greater relationship with the heat release rate. The larger the heat release rate is, the higher the smoke temperature in the atrium is, and the greater the mass flow rate is, also the faster the smoke spreads, resulting in a smaller attenuation coefficient. The smoke temperature shows a trend of attenuation from the central position to both sides, and the left and right sides are basically symmetrically distributed, but there are still slight differences. Possibly because the east side of the building has a protruding space, as well as the obstruction of the smoke barrier, the east side of the smoke accumulates in a small area, and the heat is not dispersed, resulting in a smaller attenuation rate than the west side. Analyzing the influence of different experimental scenarios, it is found that the dimensionless temperature rise attenuation rate is also related to the use of the smoke exhaust system. Specifically, after opening the natural smoke exhaust vents (Cases 1 and 2) and turning on the mechanical smoke exhaust (Cases 4 and 5), the smoke flow is accelerated, and the heat exchange with the external environment is promoted, bringing the cooling effect to the smoke. Therefore, it will lead to the increase of the attenuation coefficient, which means that the attenuation rate also increases. Additionally, the effect of mechanical smoke exhaust is better than that of natural smoke exhaust.
