*3.3. Maximum Temperature Rise Prediction Model for Interconnected Tunnel*

The experimental data were processed by the maximum temperature rise prediction Equation (6) proposed by Li [16]. The sum of the velocities of ramps C and D was used as the characteristic velocity. The maximum temperature rise data fit well, as shown in Figure 10. It demonstrated how the velocities of ramp C and ramp D had an impact on the maximum temperature rise. However, the experimental results were lower than the prediction of Equation (6).

$$
\Delta T\_{\rm m} = \frac{\dot{Q}}{V b\_{fo}^{1/3} H\_{\varepsilon f}^{5/3} \prime} \quad V \prime > 0.19 \tag{6}
$$

$$\begin{aligned} V' &= V'\_{\mathbb{C}+D} = \frac{V\_{\mathbb{C}+D}}{\overline{w}'}\\ w^\* &= \left(\frac{\dot{Q}g}{b\_{fb}\rho\_0 c\_p T\_0}\right)^{1/3} \end{aligned} \tag{7}$$

where:

than Equation (6).

*VC*+*<sup>D</sup>* is the sum of ramps C and D velocity (m/s). resulted in the decrease in the temperature. Therefore, the experiment data were lower

**Figure 10.** Fitting of maximum temperature rise with different blockage ratios: (**a**) = 0%; (**b**) = 10%; (**c**) = 20%; (**d**) = 30%. **Figure 10.** Fitting of maximum temperature rise with different blockage ratios: (**a**) *φ* = 0%; (**b**) *φ* = 10%; (**c**) *φ* = 20%; (**d**) *φ* = 30%.

Figure 11 contrasts the maximum temperature increases with various blockage ratios with the predictions of the Li model. It was discovered that there were no obvious fluctuation tendencies in the distribution under the various blockage ratios. This demonstrates

 **0% 10% 20% 30%**

**0 100 200 300 400 500 600 700 800 900**

**Figure 11.** Comparison of the maximum temperature rise with the prediction equation of Li.

Equation (6) focuses on the maximum temperature rise of the single-pipe tunnel. To better understand the maximum temperature rise during the interconnected tunnel's

1 3 5 3

*/ /*

*Q /V'b <sup>H</sup>fo ef*

 **Blockage ratio**

 **Li et al.**

**600**

**∆***T***m (K)**

This is because the maximum temperature rise prediction equation proposed by Li is based on ventilation tests in the single-pipe tunnel. The maximum temperature rise in this paper was based on the interconnected tunnel. At the same velocity, the tunnel section where the fire source was located was larger than the tunnel section in the Li model, so the air volume was also larger than that in the Li model. Ramp C and ramp D supplied air at the same time, which increased the contact area between the fire plume and the airflow, so the air entrainment of the fire plume in the tunnel section also increased, which resulted in the decrease in the temperature. Therefore, the experiment data were lower than Equation (6). **0 100 200 300 400 500 600 700 800 0** 1 3 5 3 *Q /V'b <sup>H</sup>fo ef / /* **0 100 200 300 400 500 600 700 800 0** 1 3 5 3 *Q /V'b <sup>H</sup>fo ef / /* (**c**) (**d**) **Figure 10.** Fitting of maximum temperature rise with different blockage ratios: (**a**) = 0%; (**b**) = 10%; (**c**) = 20%; (**d**) = 30%.

*Fire* **2023**, *6*, x FOR PEER REVIEW 10 of 15

 **0%**

**0 100 200 300 400 500 600 700 800**

 **20%**

1 3 5 3

*/ /*

*Q /V'b <sup>H</sup>fo ef*

 **Blockage ratio**

 **Li et al.**

 **Blockage ratio**

 **Li et al.**

than Equation (6).

**∆***T***m (K)**

**∆***T***m (K)**

**0**

**100**

**200**

**300**

**400**

**500**

**100**

**200**

**300**

**400**

**500**

resulted in the decrease in the temperature. Therefore, the experiment data were lower

(**a**) (**b**)

**500**

**500**

**∆***T***m (K)**

**∆***T***m (K)**

**0 100 200 300 400 500 600 700 800**

 **30%**

 **10%**

1 3 5 3

*/ /*

*Q /V'b <sup>H</sup>fo ef*

 **Blockage ratio**

 **Li et al.**

 **Blockage ratio**

 **Li et al.**

**0**

**100**

**200**

**300**

**400**

**100**

**200**

**300**

**400**

Figure 11 contrasts the maximum temperature increases with various blockage ratios with the predictions of the Li model. It was discovered that there were no obvious fluctuation tendencies in the distribution under the various blockage ratios. This demonstrates that when the interconnected tunnel was blocked, Equation (6) was not capable of forecasting the increase in temperature. Figure 11 contrasts the maximum temperature increases with various blockage ratios with the predictions of the Li model. It was discovered that there were no obvious fluctuation tendencies in the distribution under the various blockage ratios. This demonstrates that when the interconnected tunnel was blocked, Equation (6) was not capable of forecasting the increase in temperature.

**Figure 11.** Comparison of the maximum temperature rise with the prediction equation of Li. **Figure 11.** Comparison of the maximum temperature rise with the prediction equation of Li.

Equation (6) focuses on the maximum temperature rise of the single-pipe tunnel. To better understand the maximum temperature rise during the interconnected tunnel's Equation (6) focuses on the maximum temperature rise of the single-pipe tunnel. To better understand the maximum temperature rise during the interconnected tunnel's blockage, this paper establishes a suitable maximum temperature rise model for different blockage ratios of the test data. The effects of vehicle blockage, longitudinal ventilation velocity, and HRR on the maximum temperature increase in an interconnected tunnel were studied in this model, where the ventilation velocity of ramp D was directly affected by the vehicle blockage.

In the underground interconnected tunnel, the maximum temperature rise was affected by the velocities of both ramp C and ramp D, while the velocity of ramp D changed with the vehicle blockage ratios. The longitudinal velocity and blocking ratio were combined with interconnected tunnels, and this paper analyzed the smoke mass flow rate to establish a prediction model.

The smoke mass flow was mainly composed of the fuel mass flow and air mass flow in ramp C and ramp D. . . . .

$$
\dot{m}\_s = \dot{m}\_\mathbb{C} + \dot{m}\_D + \dot{m}\_f \tag{8}
$$

The fuel mass flow rate was much lower than that of ramp C and ramp D. Therefore, the mass flow rate of smoke can be expressed by the sums of the longitudinal ventilation velocities of ramps C and D:

$$
\dot{m}\_s = \rho V\_{\mathbb{C}+D} \mathbb{S} \tag{9}
$$

where:

*S* is the tunnel cross-sectional area (m<sup>2</sup> ).

Based on the heat calculation formula, where . *Q<sup>c</sup>* = 0.7 . *Q*: is the tunnel cross-sectional area (m<sup>2</sup> ). Based on the heat calculation formula, where

*Fire* **2023**, *6*, x FOR PEER REVIEW 11 of 15

blockage, this paper establishes a suitable maximum temperature rise model for different blockage ratios of the test data. The effects of vehicle blockage, longitudinal ventilation velocity, and HRR on the maximum temperature increase in an interconnected tunnel were studied in this model, where the ventilation velocity of ramp D was directly affected

In the underground interconnected tunnel, the maximum temperature rise was affected by the velocities of both ramp C and ramp D, while the velocity of ramp D changed with the vehicle blockage ratios. The longitudinal velocity and blocking ratio were combined with interconnected tunnels, and this paper analyzed the smoke mass flow rate to

The smoke mass flow was mainly composed of the fuel mass flow and air mass flow

 *D*

The fuel mass flow rate was much lower than that of ramp C and ramp D. Therefore, the mass flow rate of smoke can be expressed by the sums of the longitudinal ventilation

> *V S*

 +

 *C D*

 +

 *f* (8)

(9)

(10)

(11)

(12)

*m m m m*

*s*

=

*m*

*s*

=

 *C*  +

$$
\dot{Q}\_c = \mathbf{C} \times \dot{m} \times \Delta T\_m \tag{10}
$$

 *Q* :

0.7

*Q*

 *m*

*c*

where *C* is a constant. where *C*is a constant.

where:

*S*

by the vehicle blockage.

establish a prediction model.

velocities of ramps C and D:

in ramp C and ramp D.

The maximum temperature rise is proportional to . *Qc*/ . *m*, as shown in Equation (11): The maximum temperature rise is proportional to /*Qm*, as shown in Equation (11):

*c*

*C D*

> *C D*

 +

 +

$$
\Delta T\_m \propto \frac{\dot{Q}\_c}{\rho V\_{\odot + D} S} \tag{11}
$$

 *c*

When the blockage ratio is 0%, the relation (12) is obtained from Equation (11), which is shown in Figure 12 by fitting the data. When the blockage ratio is 0%, the relation (12) is obtained from Equation (11), which is shown in Figure 12 by fitting the data.

$$
\Delta T\_{m,0 \,\,\%} \propto \frac{\dot{Q}\_{\varepsilon}}{\rho v\_{\odot + D} S} \tag{12}
$$

where: where:

> *C D*

 +

*vC*+*<sup>D</sup>* is the sum of the velocity of ramps C and D when the blockage ratio is 0%. *v*is the sum of the velocity of ramps C and D when the blockage ratio is 0%.

**Figure 12. Figure 12.**  Maximum temperature rise prediction formula ( Maximum temperature rise prediction formula ( *φ* = 0%). 

As can be seen from Figure 12, the prediction equation at 0% blockage is shown in Equation (13), which agrees well with the experimental results.

$$
\Delta T\_{\text{m},0\ \%} = 8.59 \frac{\dot{Q}\_{\text{c}}}{\rho v\_{\text{C}+D}S} - 22.8,\ 0.6 \le v\_{\text{C}+D} \le 1.6\tag{13}
$$

For the velocity sum of ramps C and D, introducing the blockage ratio *φ*, the following relationship can be obtained:

$$V\_{\mathbb{C}+D} = v\_{\mathbb{C}+D} \mathfrak{g}(\mathfrak{\phi}) \tag{14}$$

= 0%).

As the blockage ratio increases in the interconnected tunnel, the sum of the velocities at ramps C and D becomes lower. If the relationship between *VC*+*<sup>D</sup>* and *vC*+*<sup>D</sup>* satisfies Equation (15), the data are fitted by fitting the data as shown in Figure 13.

$$\lg(\phi) = V\_{\mathbb{C}+D} / v\_{\mathbb{C}+D} = (1 - a\phi) \tag{15}$$

**Figure 13.** Variation in velocities with blockage ratio. **Figure 13.** Variation in velocities with blockage ratio.

The relationship between the ratio *VC D*+ and *C D v* + and the blockage ratio can be obtained from Figure 13, as shown in Equation (16). The relationship between the ratio *VC*+*<sup>D</sup>* and *vC*+*<sup>D</sup>* and the blockage ratio can be obtained from Figure 13, as shown in Equation (16).

$$g(\phi) = V\_{\mathbb{C} + D} / v\_{\mathbb{C} + D} = (1 - 0.6\phi), \ 0\% \le \phi \le \Im 0\% \tag{16}$$

As can be seen from Figure 12, the prediction equation at 0% blockage is shown in

 22.8,

 −

 *v g*

 /

 *v*

 +

*C D C D*

+

 *V*

=

=

 *C D* 

 +

As the blockage ratio increases in the interconnected tunnel, the sum of the velocities

*c*

+

*C D*

For the velocity sum of ramps C and D, introducing the blockage ratio

*v S*

*V*

Equation (15), the data are fitted by fitting the data as shown in Figure 13.

( )

*g*

*C D*

+

*Q*

0.6

( )

> (1

 = −  )

 *a*

   *C D*

+

 *v*

 1

  .6

> *VC D*+

and

(13)

(14)

(15)

(16)

(17)

satisfies

, the fol-

*C D v* <sup>+</sup>

Equation (13), which agrees well with the experimental results.

=

at ramps C and D becomes lower. If the relationship between

8.59

, 0 %

*m*

*T*

lowing relationship can be obtained:

Equations (13) and (16) may be used to derive the link (11) between the maximum temperature rise and velocity and blockage ratio, and the data are fitted, as shown in Figure 14. The test data under different blockage ratios of the interconnected tunnel fit well with the prediction formula, while Li's [22] formula cannot predict it well, as shown in Figure 15. The prediction formula is shown in Equation (17). This formula applies to in-Equations (13) and (16) may be used to derive the link (11) between the maximum temperature rise and velocity and blockage ratio, and the data are fitted, as shown in Figure 14. The test data under different blockage ratios of the interconnected tunnel fit well with the prediction formula, while Li's [22] formula cannot predict it well, as shown in Figure 15. The prediction formula is shown in Equation (17). This formula applies to interconnected tunnel blockage rates between 0% and 30%.

> (1 0.6 )

−

*C D*

+

*v*

$$
\Delta T\_{\rm II} = 8.59 \frac{\dot{Q}\_{\rm I}}{\rho v\_{\rm C+D} (1 - 0.6 \phi) S} - 22.8, \ 0.6 \le v\_{\rm C+D} \le 1.6\tag{17}
$$

  *m*

**Figure 14.** Maximum temperature rise prediction formula of different blockage ratios.**Figure 14.** Maximum temperature rise prediction formula of different blockage ratios.

**0 50 100 150 200 250 300 350**

( ) **5/2**

 

 **--- Li et al.**

 

 

 

 

 

 

 

 

 − *φ=***0**

**Figure 15.** Comparison between the Li's model and the experimental data considered in this study.

under the interconnected tunnel by combining the velocity and HRR of the fire source

an impact on the maximum temperature rise in the interconnected tunnel. The maximum

and the blockage ratio. Depending on who is more impacted by the velocity or blockage ratio, the maximum temperature rise differs. The maximum temperature rise decreases, and the impact of the blockage ratio diminishes when the velocity in the interconnected tunnel decreases. This is because the convective heat transfer near the fire source in-

under various blockage ratios. The following are the key conclusions of this paper:

The model-scale tunnel calculates the maximum temperature increase in the smoke

(1) The velocity of the ramps upstream of the fire source and the adjacent ramp have

(2) The maximum temperature rise in the interconnected tunnel varies with velocity

(3) In an underground interconnected tunnel fire, the maximum temperature rise is

We only studied blockage rates between 0% and 30% in this paper. Additionally, the

influenced by the velocity upstream of the fire source and the adjacent tunnel. As a result, this research provides a novel method for predicting the maximum temperature rise un-

angles between ramp C and ramp D were not considered. More research will be carried

*φ=***10%** *φ=***20%** *φ=***30%**

**2/3 \***

> **1/3 1**

*r*

*Q*

*F*

**5/2 1/3**

 **/**

 *F*

 *r*

temperature rise is jointly impacted by both ramps' ventilation.

der the underground interconnected tunnel that is blocked by vehicles.

*m a*

> ( )

**1**

 

−

**2/3 \***

*T T*

 =

*T Q*

*a*

**0**

**50**

**100**

**150**

**200**

**∆***T***m (K)**

**4. Conclusions**

creases.

out in the next stage.

**250**

**300**

**350**

**Figure 15.** Comparison between the Li's model and the experimental data considered in this study. **Figure 15.** Comparison between the Li's model and the experimental data considered in this study.

**0 150 300 450 600 750 900**

 **Blockage ratio**

 **30% 20 % error bars**

 **0% 10% 20%**

−

 **22.8**

**Figure 14.** Maximum temperature rise prediction formula of different blockage ratios.
