**3. Results and Discussion**

Scenarios No. Fire Heat Release Rates (kW) Tunnel Turning Radius <sup>R</sup> *3.1. Variations in Maximum Temperature*

is in direct contact with the flame.

(m) 1–4 0.76 3.5, 4.35, 8, ∞ 5–8 1.01 9–12 1.62 13–16 2.03 Figure 3 depicts an instantaneous flame image observed in the experiment with different heat release rates. The phenomenon of flame plume impingement on the tunnel ceiling is observed even at smaller heat release rates. For instance, for . *Q* = 0.76 kW and 1.01 kW, the flame tip is close to the ceiling, and the thermocouple above the fire source is in direct contact with the flame.

17–20 2.43 21–24 3.05 25–28 4.06 3. Results and Discussion 3.1. Variations in Maximum Temperature Figure 4 plots the measured value of maximum temperature rise versus the turning radius, from which the influence of different turning radiuses can be recognized. The dotted lines represent the average temperature of different turning radiuses for the given heat release rate. It has been disclosed that the measured maximum temperature for different tunnel turning radiuses is nearly identical, which also indicates that the tunnel turning radius has little impact on the variation in maximum temperature.

Figure 3 depicts an instantaneous flame image observed in the experiment with different heat release rates. The phenomenon of flame plume impingement on the tunnel ceiling is observed even at smaller heat release rates. For instance, for Q 0.76 kW and 1.01 kW, the flame tip is close to the ceiling, and the thermocouple above the fire source

Fire 2022, 5, x FOR PEER REVIEW 5 of 13

Figure 3. Instantaneous flame image with different HRRs: (a) Q = 0.76 kW; (b) Q = 1.01 kW; (c) Q = 1.62 kW; (d) Q = 2.43 kW; (e) Q = 4.06 kW. **Figure 3.** Instantaneous flame image with different HRRs: (**a**) . *Q* = 0.76 kW; (**b**) . *Q* = 1.01 kW; (**c**) . *Q* = 1.62 kW; (**d**) . *Q* = 2.43 kW; (**e**) . *Q* = 4.06 kW. release rate. It has been disclosed that the measured maximum temperature for different tunnel turning radiuses is nearly identical, which also indicates that the tunnel turning radius has little impact on the variation in maximum temperature.

Figure 4 plots the measured value of maximum temperature rise versus the turning radius, from which the influence of different turning radiuses can be recognized. The dotted lines represent the average temperature of different turning radiuses for the given heat release rate. It has been disclosed that the measured maximum temperature for different tunnel turning radiuses is nearly identical, which also indicates that the tunnel turning The phenomenon of fire plume impingement in the tunnel can be clearly observed for all scenarios in the experiment. The flame height is almost equivalent to the source-ceiling height, i.e., the ceiling jet is driven by a strong plume. The temperature directly above the fire source mainly relates to the temperature of the impinged plume, which is one of the reasons why the tunnel turning radius has little effect. The phenomenon of fire plume impingement in the tunnel can be clearly observed for all scenarios in the experiment. The flame height is almost equivalent to the sourceceiling height, i.e., the ceiling jet is driven by a strong plume. The temperature directly above the fire source mainly relates to the temperature of the impinged plume, which is one of the reasons why the tunnel turning radius has little effect.

300 **Figure 4.** *Cont*.

200

R

(c) (d)

2 4 6 8

200

R

2 4 6 8

300

Figure 4. Measured value of maximum temperature rise (T<sup>m</sup> ) against the tunnel turning radius: (a) Q = 0.76 kW; (b) Q = 1.01 kW; (c) Q = 1.62 kW; (d) Q = 2.03 kW; (e) Q = 2.43 kW; (f) Q = 3.05 kW; (g) Q = 4.06 kW. **Figure 4.** Measured value of maximum temperature rise (∆*Tm*) against the tunnel turning radius: (**a**) . *Q* = 0.76 kW; (**b**) . *Q* = 1.01 kW; (**c**) . *Q* = 1.62 kW; (**d**) . *Q* = 2.03 kW; (**e**) . *Q* = 2.43 kW; (**f**) . *Q* = 3.05 kW; (**g**) . *Q* = 4.06 kW.

The measured maximum temperature of all the experimental scenarios is compared with the predicted model proposed by Li et al. [9]. Figure 5 plots the measured value of maximum temperature as a function of 2/3 5/3 Q Hef , along with Equation (5). It seems that the measured temperature in this work is significantly higher than the prediction based on Equation (5). This deviation is because Equation (5) is based on the theory of a "weak plume", whereas the ceiling jet condition in this work is more in accordance with the "strong plume driven" condition. As a result, the measured data cannot be accurately de-The measured maximum temperature of all the experimental scenarios is compared with the predicted model proposed by Li et al. [9]. Figure 5 plots the measured value of maximum temperature as a function of . *Q* 2/3 *H* 5/3 *e f* , along with Equation (5). It seems that the measured temperature in this work is significantly higher than the prediction based on Equation (5). This deviation is because Equation (5) is based on the theory of a "weak plume", whereas the ceiling jet condition in this work is more in accordance with the "strong plume driven" condition. As a result, the measured data cannot be accurately described by previously given correlation.

scribed by previously given correlation. A predicted correlation of the temperature rise along the fire plume was proposed by McCaffrey and is given as [26]:

$$2g\frac{\Delta T}{T\_{\infty}} = \left(\frac{\kappa}{\mathcal{C}}\right)^2 \cdot \left(\frac{z}{\dot{Q}^{2/5}}\right)^{2\eta - 1} \tag{7}$$

where *z* is the distance from the fire source in the vertical direction (m), ∆*T* is the temperature rise at the height of *z* (K), and *κ*, *C*, and *η* are constants whose values are shown in Table 2.

Figure 5. Prediction of maximum temperature rise (T<sup>m</sup> ) based on Equation (5). **Figure 5.** Prediction of maximum temperature rise (∆*Tm*) based on Equation (5).

A predicted correlation of the temperature rise along the fire plume was proposed **Table 2.** Empirical constants in Equation (7).

in Table 2.


where z is the distance from the fire source in the vertical direction (m), T is the tem-

perature rise at the height of z (K), and κ, C, and η are constants whose values are shown The fire plume temperature at the same height as the ceiling is given as:

$$
\Delta T\_{\mathcal{W}} \propto \Delta T = \frac{T\_{\infty}}{2g} \left(\frac{\kappa}{\mathcal{C}}\right)^2 \cdot \left(\frac{z}{\dot{Q}^{2/5}}\right)^{2\eta - 1}.\tag{8}
$$

Zone κ C η Equation (8) can be given in a dimensionless form as:

m

$$\frac{\Delta T\_m}{T\_\infty} \propto \left(\frac{H\_{\varepsilon f}/D\_h}{\dot{Q}\_s^{\ast 2/5}}\right)^a. \tag{9}$$

$$\dot{Q}\_s^\* = \frac{\dot{Q}}{\rho\_\infty T\_\infty c\_p \sqrt{g} D\_h^{5/2}},\tag{10}$$

(8)

(10)

2 g C Q , Equation (8) can be given in a dimensionless form as: where: *D<sup>h</sup>* is the hydraulic diameter of the burner outlet (m), α is constant, and . *Q* ∗ *s* is the heat release rate in dimensionless form using *D<sup>h</sup>* as a characteristic length.

\*2/5 ( ) <sup>m</sup> ef h T H D T Q (9) Figure 6 plots the measured maximum temperature rise versus the heat release rate in dimensionless form based on Equation (9), in which a good agreement between Equation (9) and experimental data is shown. The correlation in Figure 6 can be given as:

s

$$\frac{\Delta T\_m}{T\_{\infty}} = 4.79 (\frac{H\_{\varepsilon f}/D\_h}{\dot{Q}\_s^{\ast 2/5}})^{-1} \\ 1.8 \le \frac{H\_{\varepsilon f}/D\_h}{\dot{Q}\_s^{\ast 2/5}} \le 3.7 \tag{11}$$

p h T c g D , where: Dh is the hydraulic diameter of the burner outlet (m), α is constant, and \* Q<sup>s</sup> is the heat release rate in dimensionless form using Dh as a characteristic length. Figure 6 plots the measured maximum temperature rise versus the heat release rate The tunnel ceiling dimensionless maximum temperature rise is related to −1 power of the distance between the fire surface and the ceiling in the vertical direction *He f* , indicating that the intermittent flame zone impinges on the ceiling, which is consistent with the phenomenon observed in our experiments.

in dimensionless form based on Equation (9), in which a good agreement between Equation (9) and experimental data is shown. The correlation in Figure 6 can be given as:

1

10

ΔTm

/T∞

Figure 6. Predicted correlation of maximum temperature for the scenario of strong plume-driven ceiling jet. **Figure 6.** Predicted correlation of maximum temperature for the scenario of strong plume-driven ceiling jet. 3.2. The Longitudinal Attenuation of Temperature

1 \*2/5 \*2/5 4.79( ) 1.8 3.7 <sup>m</sup> ef h ef h s s

T Q Q 

<sup>R</sup>= ∞

Fire 2022, 5, x FOR PEER REVIEW 8 of 13

T H D H D

R = 8.00 m R = 4.35 m R = 3.50 m

> 

> > 1

1

T Q Q 

T H D H D

\*2/5 \*2/5 4.79( ) 1.8 3.7 <sup>m</sup> ef h ef h s s

 

,

,

(11)

(11)

### The tunnel ceiling dimensionless maximum temperature rise is related to −1 power *3.2. The Longitudinal Attenuation of Temperature* The longitudinal attenuation of the temperature below ceilings is depicted in Figure

the phenomenon observed in our experiments.

of the distance between the fire surface and the ceiling in the vertical direction Hef , indicating that the intermittent flame zone impinges on the ceiling, which is consistent with the phenomenon observed in our experiments. 3.2. The Longitudinal Attenuation of Temperature The longitudinal attenuation of the temperature below ceilings is depicted in Figure 7 for a straight tunnel (R = ∞) with various heat release rates, where d denotes the longitudinal distance between the fire source and the temperature measuring point. For a given The longitudinal attenuation of the temperature below ceilings is depicted in Figure 7 for a straight tunnel (*R* = ∞) with various heat release rates, where *d* denotes the longitudinal distance between the fire source and the temperature measuring point. For a given measuring position, the measured temperature rise (∆*T<sup>d</sup>* ) increases with the heat release rate. As the distance from the fire source increases, the temperature decreases gradually. The temperature attenuation in both the upstream and downstream direction were found to be nearly identical. Therefore, only the temperature attenuation in the downstream direction is discussed. 7 for a straight tunnel (R = ∞) with various heat release rates, where d denotes the longitudinal distance between the fire source and the temperature measuring point. For a given measuring position, the measured temperature rise (T<sup>d</sup> ) increases with the heat release rate. As the distance from the fire source increases, the temperature decreases gradually. The temperature attenuation in both the upstream and downstream direction were found to be nearly identical. Therefore, only the temperature attenuation in the downstream direction is discussed. -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5

200

0 100 Figure 7. Longitudinal attenuation of the temperature of the longitudinal direction in a straight tunnel (R = ∞). **Figure 7.** Longitudinal attenuation of the temperature of the longitudinal direction in a straight tunnel (*R* = ∞).

upstream downstream

d (m) Figure 7. Longitudinal attenuation of the temperature of the longitudinal direction in a straight tunnel (R = ∞). Figure 8 depicts the longitudinal attenuation of the temperature below ceilings with different turning radiuses. The temperature decay rate between a straight tunnel and a curved tunnel is similar for a given heat release rate, which indicates that the turning radius has little influence on smoke spread under natural ventilation.

Figure 8 depicts the longitudinal attenuation of the temperature below ceilings with different turning radiuses. The temperature decay rate between a straight tunnel and a curved tunnel is similar for a given heat release rate, which indicates that the turning ra-

dius has little influence on smoke spread under natural ventilation.

**Figure 8.** Longitudinal attenuation of temperature below the tunnel ceiling with different turning radiuses: (**a**) ∆*Tm*) against the tunnel turning radius: (**a**) . *Q* = 0.76 kW; (**b**) . *Q* = 1.01 kW; (**c**) . *Q* = 1.62 kW; (**d**) . *Q* = 2.03 kW; (**e**) . *Q* = 2.43 kW; (**f**) . *Q* = 3.05 kW; (**g**) . *Q* = 4.06 kW.

Figure 9 shows the temperature attenuation of all the experimental scenarios based on Equation (6). The scattering of the experimental data can be clearly observed. It may be suspected that the measurement points from which the maximum temperature is measured cannot serve as the reference point (∆*T*0) for the condition of strong plume impingement since it is not within the region of "one-dimensional flow". Figure 9 shows the temperature attenuation of all the experimental scenarios based on Equation (6). The scattering of the experimental data can be clearly observed. It may be suspected that the measurement points from which the maximum temperature is measured cannot serve as the reference point (T<sup>0</sup> ) for the condition of strong plume impingement since it is not within the region of "one-dimensional flow".

Figure 8. Longitudinal attenuation of temperature below the tunnel ceiling with different turning

= 1.62 kW; (d) Q

= 2.03 kW; (e) Q

= 2.43

= 1.01 kW; (c) Q

Fire 2022, 5, x FOR PEER REVIEW 10 of 13

= 4.06 kW.

= 0.76 kW; (b) Q

= 3.05 kW; (g) Q

radiuses: (a) Q

kW; (f) Q

Figure 9. Plotting of temperature attenuation based on Equation (6). **Figure 9.** Plotting of temperature attenuation based on Equation (6).

To establish the relationship between the maximum temperature and longitudinal temperature attenuation, Heskestad and Hamada's [27] correlation is introduced, which was originally used for the temperature attenuation under an unconfined ceiling. It is given as: To establish the relationship between the maximum temperature and longitudinal temperature attenuation, Heskestad and Hamada's [27] correlation is introduced, which was originally used for the temperature attenuation under an unconfined ceiling. It is given as:

$$\frac{\Delta T\_r}{\Delta T\_m} = 1.92 \left( \frac{r}{b} \right)^{-1} - e^{\left[1.61 \left(1 - \frac{r}{b} \right) \right]} \qquad 1 < \frac{r}{b} < 40 \tag{12}$$

$$b = 0.42 \left[ \left( \rho\_{\infty} c\_p \right)^{4/5} T\_{\infty}^{3/5} g^{2/5} \right]^{-1/2} \frac{T\_m^{1/2} \dot{Q}\_c^{2/5}}{\Delta T\_m^{3/5}},\tag{13}$$

4/5 3/5 2/5 1/2 3/5 0.42[( ) ] m c p m T Q b c T g T , (13) where *r* represents the distance between the fire source and the measuring point in the horizontal direction (m), *b* represents the characteristic length of the fire plume (m), and . *Qc* is the heat release rate of convection (kW).

where r represents the distance between the fire source and the measuring point in the horizontal direction (m), b represents the characteristic length of the fire plume (m), and Qc is the heat release rate of convection (kW). Figure 10 plots the longitudinal attenuation of temperature in dimensionless form based on Equation (12). The longitudinal attenuation of temperature in the longitudinal direction of all scenarios collapsed well. Fire 2022, 5, x FOR PEER REVIEW 11 of 13

Figure 10 plots the longitudinal attenuation of temperature in dimensionless form

Figure 10. Prediction correlation of longitudinal attenuation of temperature below a ceiling for a scenario with a strong plume-driven ceiling jet. are proposed based on Heskestad and Hamada's model, which is capable of predicting **Figure 10.** Prediction correlation of longitudinal attenuation of temperature below a ceiling for a scenario with a strong plume-driven ceiling jet.

Equation (12) has also been plotted in Figure 10, where a significant difference can be

A layer of fresh air will be formed that flows to the fire source during tunnel fires under natural ventilation [28]. Studies concerning induced air spread are of interest and

4/3 (1 0.1 ) 0< 55 <sup>d</sup>

The distribution characteristics of temperature below a curved tunnel ceiling induced by fire is studied through a small-scale tunnel model. The maximum temperature and longitudinal attenuation of temperature are analyzed. The following are some of the con-

(1) The tunnel turning radius has limited influence on the maximum temperature and the longitudinal attenuation of the temperature below the ceiling in a strong plume impingement scenario. The temperature distribution profiles induced by a strong plume in a curved tunnel have similar tendencies to those observed in a straight tunnel (Figures

(2) The maximum temperature below the ceiling under strong plume impingement cannot be well-predicted by previously proposed equations based on weak plume assumptions. This is because the thermocouple is in direct contact with the flame and the measured temperature is related to the axial temperature of the fire plume at the ceiling

(3) Improved correlation for predicting the temperature attenuation along the tunnel

,

(14)

T d r T b b 

ation below an unconfined plate. For fire-induced smoke flow spreading in the tunnel, a region of one-dimensional spreading is formed where the mechanism of smoke spread is distinctly different from that under an unconfined ceiling. According to the fitting results of the experimental data, Equation (14) is more appropriate for predicting the temperature decay in a strong plume-driven tunnel fire. The improved correlation may be more applicable to a large vehicle fire in naturally ventilated tunnels, where the flames can easily

m

impinge on the tunnel ceiling.

will be further studied.

clusions that may be drawn:

height (Figures 5 and 6).

4. Conclusions

4 and 8).

Equation (12) has also been plotted in Figure 10, where a significant difference can be found between Equation (12) and the experimental data. The reason for such a discrepancy may be attributed to the fact that Equation (12) is proposed for temperature attenuation below an unconfined plate. For fire-induced smoke flow spreading in the tunnel, a region of one-dimensional spreading is formed where the mechanism of smoke spread is distinctly different from that under an unconfined ceiling. According to the fitting results of the experimental data, Equation (14) is more appropriate for predicting the temperature decay in a strong plume-driven tunnel fire. The improved correlation may be more applicable to a large vehicle fire in naturally ventilated tunnels, where the flames can easily impinge on the tunnel ceiling.

A layer of fresh air will be formed that flows to the fire source during tunnel fires under natural ventilation [28]. Studies concerning induced air spread are of interest and will be further studied.

$$\frac{\Delta T\_d}{\Delta T\_m} = (1 + 0.1 \frac{d}{b})^{-4/3} 0 < \frac{r}{b} < 55. \tag{14}$$
