Numerical Simulation of the Smoke Distribution Characteristics in a T-Shaped Roadway

: This paper numerically analyzes the influence of heat release rate (HRR) and longitudinal ventilation velocity on smoke distribution characteristics in a T-shaped roadway when the fire source was located upstream of the T-junction. The back-layering length, critical ventilation velocity, smoke temperature, and CO concentration in the main and branched roadway were investigated and analyzed. The results showed that the ventilation velocity is the key factor influencing back-layering length, while the effect of HRR on back-layering length is gradually weakened as HRR increases. The critical ventilation velocity in the T-shaped roadway is higher than in a single-tube roadway, and the predicted model of dimensional critical ventilation velocity in a T-shaped bifurcated roadway is proposed. The correlation between average temperature (Z = 1.6 m) (both in the main roadway I and the branched roadway) and ventilation velocity fits the power function, and the variation in average temperature (Z = 1.6 m) according to HRR fits the linear formula. The relation between average concentration of CO (Z = 1.6 m) (both inside the main roadway I and the branched roadway) and longitudinal ventilation velocity follows the power relation, and the variation in average concentration of CO (Z = 1.6 m) according to HRR follows the linear function.


Introduction
The underground roadway of mines is a confined space; once fire occurs in the roadway, the high-temperature smoke generates fire pressure and a throttling effect, which can lead to airflow disorder.And the high-temperature smoke will propagate rapidly in the roadway, which will reduce the escape space and threaten workers' lives and health [1][2][3][4].The T-shaped roadway is commonly used in mines; due to the complex geometric characteristics of the T-shaped structure, the fire dynamics and smoke spread in bifurcated roadways will be more complex than in straight roadways.
The smoke distribution in bifurcated roadways and bifurcated tunnels has been studied extensively by many scholars.Xue [5] researched the effect of the bifurcated angle of inclined roadways on the velocity distribution and smoke temperature by using pyrosim software.Lu et al. [6] studied the influence of ambient temperature, ventilation velocity, and heat release rate on smoke temperature and visibility in T-shaped roadways by the numerical simulation method.Gao et al. [7] conducted a series of small-scale fire experiments, measured the back-layering length and smoke temperature in bifurcated tunnels, and proposed the temperature decay model in the main tunnel and the branched tunnel.
Huang et al. [8,9] experimentally investigated thermal smoke movement in branched tunnels, established the predicted model of the maximum ceiling temperature, and quantified the smoke back-layering length under different heat release rates and various longitudinal ventilation velocities.The empirical model is proposed to predict the smoke back-layering length in branched tunnels.Chen et al. [10] compared the smoke temperature distribution of single-line tunnels with T-shaped tunnels by experimentation and developed the modified double-exponential correlation to describe the longitudinal temperature decay process in the entire spreading region of fire smoke in T-shaped tunnel fires.Tao et al. [11] established a model tunnel to research the impact of fire location, bifurcated shaft exhaust velocity, and longitudinal velocity on ceiling temperature and they proposed the temperature decay model.Some scholars [12][13][14][15][16][17][18][19] conducted a series of experiments to study the critical velocity and the smoke backflow in single-line tunnel fires and proposed the prediction model of the dimensionless back-layering length and the ratio of ventilation velocity to critical velocity.Gannouni et al. [20,21] investigated the effect of obstacles on the back-layering length and the critical velocity in single-line tunnel fires by using Fire Dynamic Simulator (FDS) and developed the model to calculate the back-layering arrival time.Lu et al. [22] researched the longitudinal temperature distribution and maximum ceiling temperature by experimentation and the simulation method and proposed a mathematical model to predict the maximum rise in ceiling temperature and the longitudinal temperature distribution in the bifurcated tunnel.Liu et al. [23] studied the effect of longitudinal fire location on temperature distribution in bifurcated roadways and developed empirical models of the maximum temperature in the main tunnel and temperature decay in the branched tunnel.
By and large, the previous studies on bifurcation structure fires focus on tunnel fires, the decay process of ceiling temperature, the maximum rise in ceiling temperature, and the critical ventilation velocity, which were thoroughly studied in bifurcated tunnel fires.Bifurcated roadway fires have been seldom researched; in particular, the back-layering length, temperature, and CO concentration distribution in the main and branched roadways have rarely been studied.The underground space of roadways is smaller than a tunnel, so the smoke will propagate more fully and smoking control measures and emergency rescue will differ from tunnel fires.
Therefore, in order to investigate the smoke distribution characteristics in bifurcated roadways, the T-shaped roadway was selected as the roadway model; the fire source was located upstream of the T-junction, heat release rate and ventilation velocity were selected as the factors affecting the smoke diffusion, and ANSYS 18. 0 was used to simulate the smoke distribution in the main roadway and branched roadway.The critical velocity and the temperature and CO concentration distribution at breathing zone height in the main roadway and the branched roadway were thoroughly analyzed in this paper in order to provide suggestions for emergency rescue and personnel evacuation during underground roadway fires.

Physical Model
Based on the actual underground roadway, the 3D geometric model of T-shaped roadways was established.The size of the main roadway was 3 m × 3 m × 403 m; the branch roadway was in the center of the main roadway and the size was 3 m × 3 m × 200 m.All cross-sections were rectangular, with a width of 3 m and a height of 3 m.Because the upsteam smoke would have been pushed into both the main roadway and branched roadway, the fire source was set upstream of the T-junction.The distance from the center of the fire source to the velocity inlet was 189 m, the length of the fire source was 2 m, and the flame height was chosen to be 3 m; these were the limitations set by the roadway roof.The cross-section of the geometric model of the T-shaped roadway and coordinate system is shown in Figure 1, and the Z-direction is the height direction of the roadway.

Boundary Conditions and Assumptions
The standard k − ε equation and transport equation were chosen to simulate the turbulent flow of airflow and smoke diffusion [24], and the above equations have been extensively used in the fire simulation by scholars.The airflow inlet of the main roadway was set to be the velocity inlet and the airflow outlet of the main roadway and branched roadway were set to be the pressure outlet, as shown in Figure 1.The fire source was defined as the source term, and it was represented by a volumetric source.Due to the thermal radiation of the fire source, the temperature inside the roadway increases and the gas density in the T-shaped roadway would have been changed.Meanwhile, natural convection of gas in the vertical direction would be caused by gravity.So, the influence of gravity and buoyancy effect on air flow were considered in the simulation.
The following assumptions were adopted in the numerical simulation calculations: fresh airflow and fire smoke were considered incompressible fluids; there was no sliding on the roadway wall and no heat exchange between the wall and the air inside the roadway; obstacles such as mining cars and workers in the roadway were ignored; the effect of gas, dust, and blasting smoke on the airflow and smoke diffusion were not considered; the combustion process of the fire was not considered; the fire source was set as an energy source with a fixed rate of heat release [25]; the smoke generated by the fire was presented by CO; and the amount of CO generated by the fire was calculated according to Equation (1) [26]: where  represents the amount of CO generated by the fire (m 3 /s),  represents the heat release rate (kW), and  represents the constant of CO generation rate (m 3 /kJ) (3.22 × 10 −6 m 3 /kJ) [27].

Parameters
In the simulation, the ambient temperature was 25 °C, the gravitational acceleration was 9.81 m/s 2 , and the ambient pressure was 101,325 Pa.The longitudinal ventilation velocities were 1 m/s~3 m/s in the main roadway, the heat release rates were 300 kw, 600

Boundary Conditions and Assumptions
The standard k − ε equation and transport equation were chosen to simulate the turbulent flow of airflow and smoke diffusion [24], and the above equations have been extensively used in the fire simulation by scholars.The airflow inlet of the main roadway was set to be the velocity inlet and the airflow outlet of the main roadway and branched roadway were set to be the pressure outlet, as shown in Figure 1.The fire source was defined as the source term, and it was represented by a volumetric source.Due to the thermal radiation of the fire source, the temperature inside the roadway increases and the gas density in the T-shaped roadway would have been changed.Meanwhile, natural convection of gas in the vertical direction would be caused by gravity.So, the influence of gravity and buoyancy effect on air flow were considered in the simulation.
The following assumptions were adopted in the numerical simulation calculations: fresh airflow and fire smoke were considered incompressible fluids; there was no sliding on the roadway wall and no heat exchange between the wall and the air inside the roadway; obstacles such as mining cars and workers in the roadway were ignored; the effect of gas, dust, and blasting smoke on the airflow and smoke diffusion were not considered; the combustion process of the fire was not considered; the fire source was set as an energy source with a fixed rate of heat release [25]; the smoke generated by the fire was presented by CO; and the amount of CO generated by the fire was calculated according to Equation (1) [26]: where F r represents the amount of CO generated by the fire (m 3 /s), Q represents the heat release rate (kW), and γ co represents the constant of CO generation rate (m 3 /kJ) (3.22 × 10 −6 m 3 /kJ) [27].

Parameters
In the simulation, the ambient temperature was 25 • C, the gravitational acceleration was 9.81 m/s 2 , and the ambient pressure was 101,325 Pa.The longitudinal ventilation velocities were 1 m/s~3 m/s in the main roadway, the heat release rates were 300 kw, 600 kw, 900 kw, and 1200 kw, respectively, and the total simulation cases were 35.Then, the influence of heat release rate and ventilation velocity on smoke diffusion and distribution characteristics were analyzed and discussed; the simulation cases are shown in Table 1.

Mesh
In order to validate the independence of mesh, four kinds of cell sizes were chosen to simulate the roadway fire, which are 0.15 m × 0.15 m × 0.15 m, 0.2 m × 0.2 m × 0.2 m, 0.25 m × 0.25 m × 0.25 m, and 0.28 m × 0.28 m × 0.28 m, repectively.Figure 2 shows the horizontal and vertical temperature distribution in the main roadway when the heat release rate is 600 kw and the ventilation velocity is 2 m/s.It can be seen that, when the interval sizes of the grid are 0.15 m and 0.2 m, the difference in lateral temperature distribution and in longitudinal temperature distribution are very small; so, taking into account both the computational accuracy and time cost, a cell size of 0.2 m × 0.2 m × 0.2 m is selected and the total number of cells is 678,375.
kw, 900 kw, and 1200 kw, respectively, and the total simulation cases were 35.Then, the influence of heat release rate and ventilation velocity on smoke diffusion and distribution characteristics were analyzed and discussed; the simulation cases are shown in Table 1.

Mesh
In order to validate the independence of mesh, four kinds of cell sizes were chosen to simulate the roadway fire, which are 0.15 m × 0.15 m × 0.15 m, 0.2 m × 0.2 m × 0.2 m, 0.25 m × 0.25 m × 0.25 m, and 0.28 m × 0.28 m × 0.28 m, repectively.Figure 2 shows the horizontal and vertical temperature distribution in the main roadway when the heat release rate is 600 kw and the ventilation velocity is 2 m/s.It can be seen that, when the interval sizes of the grid are 0.15 m and 0.2 m, the difference in lateral temperature distribution and in longitudinal temperature distribution are very small; so, taking into account both the computational accuracy and time cost, a cell size of 0.2 m × 0.2 m × 0.2 m is selected and the total number of cells is 678,375.

Back-Layering Length and Critical Velocity
Back-layering length is the important parameter in roadway fires.The back-layering flow is the most fatal contamination to workers who are blocked in upstream of the fire source.

Back-Layering Length and Critical Velocity
Back-layering length is the important parameter in roadway fires.The back-layering flow is the most fatal contamination to workers who are blocked in upstream of the fire source.
Figure 3 shows the relationship between back-layering length and longitudinal ventilation velocity under different heat release rates.Figure 3 indicates that the back-layering length decreases constantly as the ventilation velocity increases and presents a linear trend.Moreover, under the same ventilation velocity, the back-layering length increases as the heat release rate increases.However, when the heat release rate is more than 600 kw, the back-layering length increases quite slowly.This indicates that the influence of heat release rate on the back-layering length is gradually weakened as the heat release rate increases.
Figure 3 shows the relationship between back-layering length and longitudinal ventilation velocity under different heat release rates.Figure 3 indicates that the back-layering length decreases constantly as the ventilation velocity increases and presents a linear trend.Moreover, under the same ventilation velocity, the back-layering length increases as the heat release rate increases.However, when the heat release rate is more than 600kw, the back-layering length increases quite slowly.This indicates that the influence of heat release rate on the back-layering length is gradually weakened as the heat release rate increases.
where  represents the dimensionless critical ventilation velocity,  represents the critical ventilation velocity (m/s),  represents the gravity acceleration (m/s 2 ),  represents the hydraulic tunnel height (m),  represents the dimensionless heat release rate,  =      /  / ⁄ ,  represents the heat release rate (kw),  represents the ambient air density (kg/m 3 ),  represents the specific heat capacity (kJ/(kg⋅K)), and  represents the environment temperature (K).
Li et al. [13] also acquired the correlation between dimensionless critical ventilation velocity and dimensionless heat release rate in a single-tube tunnel, which can be expressed in Equation ( 3): where  =      /  / ⁄ and  represents the tunnel height (m).In this paper, the critical ventilation velocity was determined by the X direction velocity vector beneath the ceiling in the main roadway.The critical ventilation velocities are 1.5 m/s, 1.8 m/s, 2 m/s, and 2.1 m/s when the heat release rates (HRR) are 300 kw, 600 kw, 900 kw, and 1200 kw, respectively.The critical ventilation velocity predicted by CFD [Q] 5/2 , Q represents the heat release rate (kw), ρ 0 represents the ambient air density (kg/m 3 ), c p represents the specific heat capacity (kJ/(kg•K)), and T 0 represents the environment temperature (K).Li et al. [13] also acquired the correlation between dimensionless critical ventilation velocity and dimensionless heat release rate in a single-tube tunnel, which can be expressed in Equation (3): where .Q = Q/ρ 0 c p T 0 g 1/2 H 5/2 and H represents the tunnel height (m).In this paper, the critical ventilation velocity was determined by the X direction velocity vector beneath the ceiling in the main roadway.The critical ventilation velocities are 1.5 m/s, 1.8 m/s, 2 m/s, and 2.1 m/s when the heat release rates (HRR) are 300 kw, 600 kw, 900 kw, and 1200 kw, respectively.The critical ventilation velocity predicted by CFD simulation under different HRRs is shown in Figure 4a, and the critical ventilation velocities calculated by equations proposed by Wu [12] and Li [13] are also presented in Figure 4a for comparison.It can be seen that the critical ventilation velocity increases with the increase in heat release rate and the increased value decreases slowly.Also, we can find that the critical ventilation velocity is higher than Wu's and Li's model, which means the critical ventilation velocity in the T-shaped bifurcated roadway is higher than in the single-tube roadway when the fire is located upstream of the T-junction.This is because, when the airflow passes through the T-junction, a portion of ventilation mass flow is pushed into the branched roadway, so the actual ventilation mass flow in the main roadway of the T-shaped bifurcated roadway is lower than in the single-tube roadway.Figure 4b presents the correlation between dimensional critical ventilation velocity and dimensional heat release rate.According to Figure 4b, ; hence, the prediction model of dimensional critical ventilation velocity in the T-shaped bifurcated roadway can be expressed as: It can be found that Equation ( 4) is similar to Equations ( 2) and ( 3) and is more close to Li's model.simulation under different HRRs is shown in Figure 4a, and the critical ventilation velocities calculated by equations proposed by Wu [12] and Li [13] are also presented in Figure 4a for comparison.It can be seen that the critical ventilation velocity increases with the increase in heat release rate and the increased value decreases slowly.Also, we can find that the critical ventilation velocity is higher than Wu's and Li's model, which means the critical ventilation velocity in the T-shaped bifurcated roadway is higher than in the single-tube roadway when the fire is located upstream of the T-junction.This is because, when the airflow passes through the T-junction, a portion of ventilation mass flow is pushed into the branched roadway, so the actual ventilation mass flow in the main roadway of the T-shaped bifurcated roadway is lower than in the single-tube roadway.Figure 4b presents the correlation between dimensional critical ventilation velocity and dimensional heat release rate.According to Figure 4b,  is directly proportional to  / ; hence, the prediction model of dimensional critical ventilation velocity in the T-shaped bifurcated roadway can be expressed as: It can be found that Equation ( 4) is similar to Equations ( 2) and ( 3) and is more close to Li's model.To further validate the accuracy of the numerical model adopted in this paper, the critical ventilation velocities predicted by CFD were compared with data from Li's small-scale tests [13].Li's small-scale experimental tests were conducted in a 12 m long model tunnel.The fire source, which was a 100 mm diameter porous bed burner, was located in the center of the tunnel model.We built the same simulated tunnel model as Li's, and the numerical model was the same as mentioned above (see section 2.2).The fire source was set as a volumetric source with a height of 0.25 m and a diameter of 0.1 m.Table 2 presents the critical ventilation velocity predicted by CFD under different cases in Li's experiment, and the comparison between simulation values of critical ventilation velocity and tested results by Li is shown in Figure 5.According to Table 2 and Figure 5, there is a reasonable agreement between the simulation and the experiment tests.To further validate the accuracy of the numerical model adopted in this paper, the critical ventilation velocities predicted by CFD were compared with data from Li's smallscale tests [13].Li's small-scale experimental tests were conducted in a 12 m long model tunnel.The fire source, which was a 100 mm diameter porous bed burner, was located in the center of the tunnel model.We built the same simulated tunnel model as Li's, and the numerical model was the same as mentioned above (see Section 2.2).The fire source was set as a volumetric source with a height of 0.25 m and a diameter of 0.1 m.Table 2 presents the critical ventilation velocity predicted by CFD under different cases in Li's experiment, and the comparison between simulation values of critical ventilation velocity and tested results by Li is shown in Figure 5.According to Table 2 and Figure 5, there is a reasonable agreement between the simulation and the experiment tests.

Longitudinal Temperature Profile in the Main and Branched Roadway
Inhaling high-temperature smoke is the main factor to cause casualties in fire accidents, so the temperature distribution at breathing zone height (Z = 1.6 m) was analyzed in this paper.The tolerance time in a fire environment is 12 min for a person [28], so the escape temperature that a person can escape from the fire environment successfully is set to be 60 °C.
Figure 6 presents the longitudinal temperature profile at breathing zone height of the main roadway when heat release rates are 300 kw, 600 kw, and 900 kw, respectively.Figure 6a illustrates that, when the longitudinal ventilation velocity is 1 m/s, the maximum temperature is located at the fire source and the value is 101.636°C, and the influence range of the fire source on upstream temperature is 21.4 m, which can be explained by smoke backflow and thermal convection.When the longitudinal ventilation velocities are 1.5 m/s, 2 m/s, 2.5 m/s, and 3 m/s, respectively, the influence range of fire source on upstream temperature is 0 m and the smoke temperature at the fire source increases dramatically from 25 °C to 41.16 °C, 37.13 °C, 34.73 °C, and 33.07 °C, respectively; then, the temperature rises slightly and becomes steady along the longitudinal direction (X direction).The smoke temperatures in the main roadway Ⅰ are all lower than escape temperature when the ventilation velocities are 1 m/s~3 m/s.As shown in Figure 6b, when the longitudinal ventilation velocities are 1 m/s and 1.5 m/s, the values of maximum temperature are 179 °C and 140 °C, respectively, and the influence ranges of fire source on upstream temperature are 24.2 m and 14 m, respectively.When the longitudinal ventilation velocities are 2 m/s, 2.5 m/s, and 3 m/s, respectively, the smoke temperature at the fire source increase dramatically from 25 °C to 37.366 °C, 34.869 °C, and 33.2 °C, respectively; then, the temperature rises slightly and becomes steady along the longitudinal direction (X direction).The smoke temperatures in the main roadway Ⅰ are all

Longitudinal Temperature Profile in the Main and Branched Roadway
Inhaling high-temperature smoke is the main factor to cause casualties in fire accidents, so the temperature distribution at breathing zone height (Z = 1.6 m) was analyzed in this paper.The tolerance time in a fire environment is 12 min for a person [28], so the escape temperature that a person can escape from the fire environment successfully is set to be 60 • C.
Figure 6 presents the longitudinal temperature profile at breathing zone height of the main roadway when heat release rates are 300 kw, 600 kw, and 900 kw, respectively.Figure 6a illustrates that, when the longitudinal ventilation velocity is 1 m/s, the maximum temperature is located at the fire source and the value is 101.Then, the effect of longitudinal ventilation velocity and heat release rate on average temperature at breathing zone height inside the bifurcated roadway is discussed thoroughly.Figure 7 presents the average temperature at Z = 1.6 m inside the main roadway Ⅰ and branched roadway under different ventilation velocities and different heat release rates.Then, the effect of longitudinal ventilation velocity and heat release rate on average temperature at breathing zone height inside the bifurcated roadway is discussed thoroughly.Figure 7 presents the average temperature at Z = 1.6 m inside the main roadway I and branched roadway under different ventilation velocities and different heat release rates.It can be observed from Figure 7 that the average temperatures in the main roadway Ⅰ and branched roadway are lower than 60 °C when the HRR is 300 kw and the ventilation velocities are 1 m/s, 1.5 m/s, 2 m/s, 2.5 m/s, and 3 m/s and when the HRR is 600 kw and the ventilation velocities are 2 m/s, 2.5 m/s, and 3 m/s and when the HRR is 900 kw and the ventilation velocities are 2.5 m/s and 3 m/s.The average temperatures in the branched roadway under different cases are all slightly lower than that in the main roadway Ⅰ.When the heat release rate is 300 kw, the maximum temperature difference between the main roadway Ⅰ and the branched roadway is 3.1 °C and the minimum temperature difference is 0.7 °C.When the heat release rate is 600 kw, the maximum temperature difference is 2.12 °C and the minimum temperature difference is 0.585 °C.When the heat release rate is 900 kw, the maximum temperature difference is 6.47 °C and the minimum temperature difference is 1.43 °C.When the heat release rate is 1200 kw, the maximum temperature difference is 8 °C and the minimum temperature difference is 0.3 °C.
Figure 7 also shows that, under different heat release rates, the average temperatures in the main roadway Ⅰ and branched roadway decrease as the ventilation velocity increases.This occurs because the thermal convection between airflow and smoke is intensified with the increase in ventilation velocity.And the temperature decay fits the power function, as shown in Equation ( 5): where  represents the average temperature at Z = 1.6 m (°C),  represents longitudinal ventilation velocity (m/s), and  and  represent dimensionless coefficient, respectively.
The fitting curves are shown with solid lines and dashed lines in Figure 7.The values of  and  are displayed in Table 3.It can be seen from Figure 7 and Table 3 the values of R-squares are all above 0.98; it can be concluded that the variation in average temperature in the main roadway Ⅰ and branched roadway according to ventilation velocity can be accurately describe by Equation ( 5).It can be observed from Figure 7 that the average temperatures in the main roadway I and branched roadway are lower than 60 • C when the HRR is 300 kw and the ventilation velocities are 1 m/s, 1.5 m/s, 2 m/s, 2.5 m/s, and 3 m/s and when the HRR is 600 kw and the ventilation velocities are 2 m/s, 2.5 m/s, and 3 m/s and when the HRR is 900 kw and the ventilation velocities are 2.5 m/s and 3 m/s.The average temperatures in the branched roadway under different cases are all slightly lower than that in the main roadway I.When the heat release rate is 300 kw, the maximum temperature difference between the main roadway I and the branched roadway is 3.1 • C and the minimum temperature difference is 0.7 • C. When the heat release rate is 600 kw, the maximum temperature difference is 2.12 • C and the minimum temperature difference is 0.585 • C. When the heat release rate is 900 kw, the maximum temperature difference is 6.47 • C and the minimum temperature difference is 1.43 • C. When the heat release rate is 1200 kw, the maximum temperature difference is 8 • C and the minimum temperature difference is 0.3 • C.
Figure 7 also shows that, under different heat release rates, the average temperatures in the main roadway I and branched roadway decrease as the ventilation velocity increases.This occurs because the thermal convection between airflow and smoke is intensified with the increase in ventilation velocity.And the temperature decay fits the power function, as shown in Equation ( 5): where T represents the average temperature at Z = 1.6 m ( • C), υ represents longitudinal ventilation velocity (m/s), and a and b represent dimensionless coefficient, respectively.The fitting curves are shown with solid lines and dashed lines in Figure 7.The values of a and b are displayed in Table 3.It can be seen from Figure 7 and Table 3 the values of R-squares are all above 0.98; it can be concluded that the variation in average temperature in the main roadway I and branched roadway according to ventilation velocity can be accurately describe by Equation (5).
The variation in average temperature with the increasing heat release rate in the bifurcated roadway is shown in Figure 8.It can be observed that the average temperatures in the main roadway I and branched roadway increase constantly as the heat release rate increases, and the predicted data of average temperature can be correlated to HRR with the following equation: where T represents the average temperature at Z = 1.6 m ( • C), Q represents the heat release rate (kw), and c and d represent the dimensionless coefficient, respectively.The variation in average temperature with the increasing heat release rate in the bifurcated roadway is shown in Figure 8.It can be observed that the average temperatures in the main roadway Ⅰ and branched roadway increase constantly as the heat release rate increases, and the predicted data of average temperature can be correlated to HRR with the following equation: where  represents the average temperature at Z = 1.6 m (°C),  represents the heat release rate (kw), and  and  represent the dimensionless coefficient, respectively.The fitting lines are shown with solid lines and dashed lines in Figure 8.The values of  and  are displayed in Table 4.It can be seen from Figure 8 and Table 4 the values of R-squares are all above 0.99, which indicates that the variation in average temperature in the main roadway Ⅰ and branched roadway according to heat release rate can be accurately predicted by Equation ( 6).  4. It can be seen from Figure 8 and Table 4 the values of R-squares are all above 0.99, which indicates that the variation in average temperature in the main roadway I and branched roadway according to heat release rate can be accurately predicted by Equation ( 6).

The Profile of CO Concentration in the Main and Branched Roadway
Figure 9 presents the smoke propagation in the T-shaped roadway when the HRR is 600 kw and longitudinal ventilation velocity is 1.5 m/s.According to Figure 9, it can be seen that a high concentration of CO mainly gathers near the top plate of the fire source and spreads upstream of the fire source at a certain distance.Under the influence of longitudinal ventilation, the CO generated by the fire gradually spreads downstream of the main roadway and inside the branched roadway and then is rapidly diluted.The CO concentration in the main roadway Ⅰ and branched roadway are much lower than near the fire source.Based on previous fire accident analyses, we know that high-temperature smoke contains CO, and casualties were partly caused by inhaling CO, so the distribution of CO concentration at breathing zone height is thoroughly analyzed and discussed in this section.Figure 10 shows the concentration distribution of CO at breathing zone height in the main roadway Ⅰ and branched roadway under different longitudinal ventilation velocities when the HRR is 600 kw.Based on previous fire accident analyses, we know that high-temperature smoke contains CO, and casualties were partly caused by inhaling CO, so the distribution of CO concentration at breathing zone height is thoroughly analyzed and discussed in this section.Figure 10 shows the concentration distribution of CO at breathing zone height in the main roadway I and branched roadway under different longitudinal ventilation velocities when the HRR is 600 kw.
We can see clearly from Figure 10 that the concentration of CO at the height of the breathing zone in the main roadway I and branched roadway gradually decreases and tends to be of uniform distribution as the longitudinal ventilation velocity increases.When the ventilation velocities are 1 m/s and 1.5 m/s, the concentration of CO at the height of the breathing zone in the main roadway I is higher than in the branched roadway.And, when the ventilation velocities are 2 m/s, 2.5 m/s, and 3 m/s, respectively, the concentration of CO in the branched roadway is slightly higher than in the main roadway I.
The CO volume concentration in the safe evacuation passage is less than 500 ppm in the fire environment [28], so 500 ppm is chosen to be the critical concentration to escape safely for a person.The average concentration of CO at the breathing zone height inside the main roadway I and branched roadway is shown in Figure 11.
According to Figure 11, it can be seen that the average concentrations of CO in the main roadway I and branched roadway are all lower than 500 PPM.When the HRR is 900 kw, the maximum concentration difference between the main roadway I and branched roadway is 84.444PPM and the minimum concentration difference is 5.676 PPM.When the HRR is 600 kw, the maximum concentration difference is 19.72 PPM and the minimum concentration difference is 4.776 PPM.When the HRR is 300 kw, the maximum concentration difference is 54.094 PPM and the minimum concentration difference is 2.686 PPM.In addition, the concentration differences of CO between the main roadway I and the branched roadway decrease as the ventilation velocity increases.And we also can find that the average concentrations of CO inside the main roadway I and branched roadway decrease constantly with the increase in longitudinal ventilation velocity, which fits the power function.The fitting curves are shown in Figure 11 and the fitting functions are shown in Table 5.The values of R-squares are all above 0.95 according to Figure 10 Table 5; the equations describing the variation in average concentration of CO are shown in Table 5.We can see clearly from Figure 10 that the concentration of CO at the height of the breathing zone in the main roadway Ⅰ and branched roadway gradually decreases and tends to be of uniform distribution as the longitudinal ventilation velocity increases.When the ventilation velocities are 1 m/s and 1.5 m/s, the concentration of CO at the height of the breathing zone in the main roadway Ⅰ is higher than in the branched roadway.And, when the ventilation velocities are 2 m/s, 2.5 m/s, and 3 m/s, respectively, the concentration of CO in the branched roadway is slightly higher than in the main roadway Ⅰ.
The CO volume concentration in the safe evacuation passage is less than 500 ppm in the fire environment [28], so 500 ppm is chosen to be the critical concentration to escape safely for a person.The average concentration of CO at the breathing zone height inside the main roadway Ⅰ and branched roadway is shown in Figure 11.According to Figure 11, it can be seen that the average concentrations of CO in the main roadway Ⅰ and branched roadway are all lower than 500 PPM.When the HRR is 900 kw, the maximum concentration difference between the main roadway Ⅰ and branched roadway is 84.444PPM and the minimum concentration difference is 5.676 PPM.When the HRR is 600 kw, the maximum concentration difference is 19.72 PPM and the minimum concentration difference is 4.776 PPM.When the HRR is 300 kw, the  The effect of HRR on average concentration of CO inside the main roadway I and the branched roadway are discussed then.Figure 12 shows the variation in the average concentration of CO according to the heat release rate.It can be seen that, as the heat release rate increases, the average concentration of CO inside the main roadway I and branched roadway increase linearly.And it can be described by the linear function; the fitting lines are shown in Figure 12 and the equations are presented in Table 6.branched roadway increase linearly.And it can be described by the linear function; the fitting lines are shown in Figure 12 and the equations are presented in Table 6.Table 6 illustrates that the value of R-squares is 0.89406 when the ventilation velocity is 1 m/s and the type of roadway is branched roadway.However, the values of R-squares are all above 0.94 in other cases.It can be explained that, when the ventilation velocity is 1 m/s, the volume of fresh airflow pushed into the branched roadway is much lower than in the main roadway Ⅰ, so the mixing of smoke and fresh airflow is uneven, which leads to the disordered distribution of smoke in the branched roadway.Therefore, it can be concluded that the average concentration of CO inside the main roadway Ⅰ and branched roadway can be predicted better by this kind of equation.

FireFigure 1 .
Figure 1.The physical model of the T-shaped roadway in cross-section.

Figure 1 .
Figure 1.The physical model of the T-shaped roadway in cross-section.

Figure 2 .
Figure 2. Validation of numerical method by grid independence.(a) The vertical temperature distribution at X = 30 m in the main roadway.(b) The longitudinal temperature distribution at Z = 2.9 m in the main roadway.

Figure 2 .
Figure 2. Validation of numerical method by grid independence.(a) The vertical temperature distribution at X = 30 m in the main roadway.(b) The longitudinal temperature distribution at Z = 2.9 m in the main roadway.

Figure 3 .
Figure 3. Relationship between back-layering length and longitudinal ventilation velocity.Critical ventilation velocity is also a key parameter for ensuring the safety and proper emergency evacuation of workers in roadway fires.The critical ventilation velocity in single-tube tunnel fires has been researched thoroughly.Wu and Bakar [12] established a mathematical model for dimensionless critical ventilation velocity and dimensionless heat release rate in a single-tube tunnel, as shown in Equation (2):  =   = 0.40 0.20 ⁄  / ,  ≤ 0.20 0.40,  > 0.20(2)

Figure 3 .
Figure 3. Relationship between back-layering length and longitudinal ventilation velocity.Critical ventilation velocity is also a key parameter for ensuring the safety and proper emergency evacuation of workers in roadway fires.The critical ventilation velocity in single-tube tunnel fires has been researched thoroughly.Wu and Bakar [12] established a mathematical model for dimensionless critical ventilation velocity and dimensionless heat release rate in a single-tube tunnel, as shown in Equation (2):

c
represents the dimensionless critical ventilation velocity, v c represents the critical ventilation velocity (m/s), g represents the gravity acceleration (m/s 2 ), H represents the hydraulic tunnel height (m), .Q represents the dimensionless heat release rate, .

Figure 4 .
Figure 4.The relationship between critical ventilation velocity and heat release rate in the T-shaped bifurcated roadway.(a) Comparison between simulation and previous model; (b) the correlation between dimensional critical ventilation velocity and dimensional heat release rate.

Figure 4 .
Figure 4.The relationship between critical ventilation velocity and heat release rate in the T-shaped bifurcated roadway.(a) Comparison between simulation and previous model; (b) the correlation between dimensional critical ventilation velocity and dimensional heat release rate.

Figure 5 .
Figure 5.Comparison of critical ventilation velocity predicted with data from Li's experiments [13].

Figure 5 .
Figure 5.Comparison of critical ventilation velocity predicted with data from Li's experiments [13].

Figure 6 .
Figure 6.The temperature profile (Z = 1.6 m) in the main roadway under different ventilation velocities and different heat release rates: (a) 300 kw; (b) 600 kw; (c) 900 kw.

Figure 6 .
Figure 6.The temperature profile (Z = 1.6 m) in the main roadway under different ventilation velocities and different heat release rates: (a) 300 kw; (b) 600 kw; (c) 900 kw.

FireFigure 7 .
Figure 7.The average temperature (Z = 1.6 m) inside the main roadway Ⅰ and branched roadway under different ventilation velocities and different heat release rates.

Figure 7 .
Figure 7.The average temperature (Z = 1.6 m) inside the main roadway I and branched roadway under different ventilation velocities and different heat release rates.

Figure 8 .
Figure 8.The variation in average temperature according to heat release rate.

Figure 8 .
Figure 8.The variation in average temperature according to heat release rate.The fitting lines are shown with solid lines and dashed lines in Figure 8.The values of c and d are displayed in Table4.It can be seen from Figure8and Table4the values of R-squares are all above 0.99, which indicates that the variation in average temperature in the main roadway I and branched roadway according to heat release rate can be accurately predicted by Equation (6).

Figure 9
Figure9the smoke propagation in the T-shaped roadway when the HRR is 600 kw and longitudinal ventilation velocity is 1.5 m/s.According to Figure9, it can be seen that a high concentration of CO mainly gathers near the top plate of the fire source and spreads upstream of the fire source at a certain distance.Under the influence of longitudinal ventilation, the CO generated by the fire gradually spreads downstream of the main roadway and inside the branched roadway and then is rapidly diluted.The CO concentration in the main roadway I and branched roadway are much lower than near the fire source.

Figure 9 .
Figure 9.The volume concentration of CO in the T-shaped roadway (600 kw and 1.5 m/s).

Figure 9 .
Figure 9.The volume concentration of CO in the T-shaped roadway (600 kw and 1.5 m/s).

Fire 2024, 7 , 16 Figure 10 .
Figure 10.The concentration distribution of CO at breathing zone height in the T-shaped roadway (600 kw).

Figure 10 .
Figure 10.The concentration distribution of CO at breathing zone height in the T-shaped roadway (600 kw).

Figure 11 .
Figure 11.The average concentration of CO (Z = 1.6 m) inside the main roadway I and branched roadway.

Figure 12 .
Figure 12.The variation in the average concentration of CO (Z = 1.6 m) according to heat release rate.

Table 1 .
The parameters and simulation cases.

Table 1 .
The parameters and simulation cases.

Dimensions of Tunnels Heat Release Rate/kw Ambient Temperature/
• C v c /m•s −1

Table 3 .
The values of coefficients a and b.

Table 4 .
The values of coefficients c and d.

Table 5 .
The correlation equations between the average concentration of CO and longitudinal ventilation velocity.is the average concentration of CO at the breathing zone height (PPM). C