Introduction

Resources in underground space are being produced and used more frequently as a result of the rapid expansion of the economy. In China, the government has initiated numerous infrastructure projects such as mining tunnels, traffic tunnels, hydraulic tunnels, and municipal tunnels1,2. Tunnel construction often involves prolonged semi-enclosed excavation conditions. When excavation reaches a certain depth, forced ventilation using fans becomes necessary to ensure adequate fresh air supply at the work site and to expel toxic gases3,4. During tunnel construction, the accumulation of materials and equipment like timber, tape, gasoline, and electrical devices can pose significant fire hazards. For instance, in 2023, a fire erupted in the Second Subsea Tunnel construction area in Jiaozhou Bay; in 2022, a fire in the Housi Tunnel construction led to 9 fatalities; and in 2019, a fire in the Liangbaosi coal mine excavation tunnel trapped 11 workers. Fires in tunnels generate high-temperature smoke and flames that can injure personnel and damage infrastructure and equipment. If the intensity and temperature of a fire are too high, then thermal radiation and convection can cause the fire to spread rapidly, leading to explosions and irreversible structural damage5. Therefore, researchers have focused a great deal of attention on the maximum temperature, which is a key indicator of the destructiveness and hazard of a fire. Tunnel fires typically result in significant casualties, severe economic losses, and considerable negative social impact. Therefore, this paper investigates the maximum fire temperature in roadway heading under forced ventilation conditions. The chapters of this paper are constructed as below. In Sect. 2, a 1:10 scale model was constructed for fire experiments, and FDS was employed to supplement the experimental conditions. In Sect. 3, the maximum temperature prediction models when the fire source is located at the end of the excavation tunnel and in the center of the excavation tunnel are obtained, and the influence of the air duct outlet position on the maximum temperature is analyzed. The main conclusions are shown in Sect. 4.

Experimental and simulation methods

Literature survey

Related research on tunnel fires can be categorized into two main types based on the structural form of the tunnels: open tunnels and confined structure tunnels.

Research on the maximum temperature in open tunnels

Early studies focused on open single tunnels, examining various factors such as tunnel shape, fire source ___location, inclination angle, and ventilation volume under different conditions.

Alpert6 conducted experiments to investigate the maximum temperature of fire plumes at the ceiling of a room. He found that the maximum temperature was significantly influenced by the heat release rate and the roof height, which he expressed through the following equation:

$$\Delta {T_{\hbox{max} }}=K\frac{{{Q^{2/3}}}}{{{H^{5/3}}}}$$
(1)

Where ΔTmax represents the maximum excess ceiling temperature, K; Q denotes the heat release rate, kW; H signifies the ceiling height, m; and K denotes the coefficient.

Li7 used scale model experiments to study the maximum temperatures in tunnels with different structural forms, specifically rectangular and semi-circular arched tunnels. Li introduced the concept of dimensionless wind speed to quantify the impact of wind speed on fire plumes, and they proposed an equation to predict the maximum temperature:

$${\text{\varvec{\Delta}}}{T_{\hbox{max} }}=\left\{ {\begin{array}{*{20}{c}} {\frac{Q}{{Vb_{{{f_0}}}^{{1/3}}H_{{ef}}^{{5/3}}}},{\text{ }}V^{\prime}>0.19} \\ {17.5\frac{{{Q^{2/3}}}}{{H_{{ef}}^{{5/3}}}},{\text{ }}V^{\prime} \leqslant 0.19} \end{array}} \right.$$
(2)

where

$$V^{\prime}=\frac{V}{{{w^ * }}},\quad {w^ * }={\left( {\frac{{{Q_c}g}}{{{b_{{f_0}}}{\rho _0}{c_p}{T_0}}}} \right)^{1/3}}$$
(3)

Where V represents the ventilation velocity, m/s; bf0 indicates the radius of the fire source, m; Hef denotes the effective tunnel height, m; V’ signifies the dimensionless ventilation velocity; w* represents the characteristic plume velocity m/s; Qc denotes the convective heat release rate, kW; ρ0 shows the ambient density, kg/m3; cp denotes the thermal capacity of air, kJ/kg K; and T0 represents the ambient temperature, K.

Furthermore, Kurioka8 employed the ratio of heat release rate to the Froude number to assess the impact on flame behavior. They examined the fire characteristics in the near-field of several tunnel fire source types under longitudinal ventilation settings using both scale model and full scale tunnel experiments. The study determined the maximum temperature results, as expressed in Eq. (4)

$$\begin{array}{*{20}{c}} {\frac{{{\text{\varvec{\Delta}}}{T_{\hbox{max} }}}}{{{T_0}}}=\gamma {{\left( {\frac{{{Q^{ * 2/3}}}}{{{\text{F}}{{\text{r}}^{1/3}}}}} \right)}^\varepsilon }} \\ {{Q^{ * 2/3}}/{\text{F}}{{\text{r}}^{1/3}}<1.35,\quad \gamma =1.77,\quad \varepsilon =6/5} \\ {{Q^{ * 2/3}}/{\text{F}}{{\text{r}}^{1/3}}>1.35,\quad \gamma =2.54,\quad \varepsilon =0} \end{array}$$
(4)

where

$${Q^ * }=\frac{Q}{{{\rho _0}{c_p}{T_0}{g^{1/2}}H_{{ef}}^{{5/2}}}},\quad {\text{Fr}}=\frac{{{V^2}}}{{g{H_{ef}}}}$$
(5)

Where Q* denotes the dimensionless heat release rate; g indicates the gravitational acceleration, m/s2; Fr signifies the Froude number; γ and ε denotes the coefficient.

Some scholars9,10,11,12 conducted further research on the maximum temperature model under special circumstances in single tunnels, enhancing the understanding of maximum temperatures in such environments. This research was also expanded to include bifurcated and intersecting structural tunnels. The research scenarios are now more realistic due to their13,14,15,16 in-depth investigations of the fire maximum temperatures in these complex tunnel structures.

Research on the maximum temperature in confined space tunnels

When a tunnel fire occurs, installing sealing structures within the tunnel can restrict airflow and effectively control the fire’s progression. Some scholars17,18,19 conducted experiments and discovered that the flame extinguishes when the tunnel’s closure ratio reaches 80%.

Some studies20,21,22,23, investigated fire behavior and maximum temperatures for scenarios where one end of the tunnel is completely sealed and the other end is open. During tunnel construction with one end sealed, the space remains confined, hindering natural airflow. To ventilate the closed end, local ventilation fans are typically utilized, directing air through wind tubes. Li24 simulated the airflow field and distribution of harmful gases after a fire-induced rupture of a forced ventilation tube, identifying the “second vortex” phenomenon as a crucial factor affecting harmful gas distribution. The study compared cases with intact and damaged wind tubes during a fire in a forced ventilation tunnel. The results indicated that a damaged wind tube enhanced the fire’s development and increased the risk to trapped personnel. Han25 studied the fire behavior and temperature attenuation in a single-ended closed tunnel with a suspended ceiling air extraction system. Zhao26 conducted simulations on airflow, smoke temperature, and harmful gas distribution in a single-end closed tunnel under various fire source locations and forced ventilation volumes, demonstrating that maximum temperatures initially decrease and then increase as the distance between the fire source and the closed end grows.

Research status summary

Several problems have been identified in recent studies on the maximum temperature of fires in tunnels after a study of the literature on the subject of fires in various tunnel structures.

(1) Research on excavation tunnel fires is insufficient. Due to closed-end, excavation tunnels require the use of fans for forced ventilation, resulting in airflow that is confined. Structural differences imply that research results from studies involving tunnels are not completely applicable to this case.

(2) There is no precise model for predicting the maximum temperature in scenarios involving multiple influencing conditions in excavation tunnels. The positioning of wind tunnel outlets and the volume of forced ventilation are given as range values, lacking clarity in spatial characteristics and fire occurrence traits.

(3) The effect mechanism of forced ventilation flow fields on the peak temperature is unclear due to a lack of research on the elements influencing the maximum temperature in tunneling highways.

To address these issues, this article reports various ventilation scenarios with multiple wind tube outlet positions and air volumes in long-distance single excavation tunnels. It focuses on researching the maximum temperatures of fires with different intensities at the closed end and middle positions of the tunnel. This approach aims to improve the accuracy and feasibility of maximum temperature predictions under complex tunneling conditions, thereby aiding in effective decision-making during emergencies.

Experimental scene design

A T-shaped excavation tunnel was designed for experimental purposes based on the research focus. The main excavation tunnel extends 90 m, with one end featuring a closed structure advancing. A return airway is located on the side, allowing polluted air from the main tunnel to be expelled. The tunnel has a rectangular shape, measuring 5 m in width, 4 m in height, and encompassing a cross-sectional area of 20 square meters. Based on the applicable provisions27, the minimum wind speed in the excavation tunnel needs to be at least 0.25 m/s. Calculations indicate that the air volume delivered to the excavation site via the wind tube needs to be not less than 300 cubic meters per minute. The local ventilation system uses a fan to push air through a duct, which has a diameter of 0.8 m, to the work site at the tunnel’s end. Moreover, the installed local ventilation fans and ducts need to be suspended or elevated, with the height above the ground exceeding 0.3 m. As a result, the air duct is suspended 0.2 m from the ceiling and 0.2 m from one side of the wall. To ensure effective forced ventilation with pressure input, the air duct outlet is required to be within the effective jet range of the duct from the tunnel’s closed end. This setup ensures that fresh air can effectively remove dust and hazardous gases from the excavation site, preventing stagnant air zones.

Using the effective range calculation Equation28 for compressed air ducts, and taking the coefficient at its minimum value, the optimal distance between the air duct outlet and the excavation face was calculated to be less than 17.9 m.

$${L_s} \leqslant \left( {4\sim 5} \right)\sqrt S$$
(6)

Where Ls represents the effective range of jet air volume, m while S denotes the tunnel section, m2.

Experimental platform design

In this study, a scaled experimental platform with a 1:10 ratio was constructed to simulate the ventilation scenario of an excavation tunnel. The Froude criterion was employed to ensure that the parameters used in the scaled model accurately reflect those of the actual tunnel. Table 1 details the scaling law that correlates the parameters of the scale model (denoted with subscript M) to those of the full-scale model (denoted with subscript F).

Table 1 List of parameter size correlation expressions under the Froude criterion.
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Main structure design of the experimental platform

The primary structure of the single-section tunnel is constructed from galvanized steel plates with a thickness of 2 mm. Each section of the model measures 1 m in length, 0.5 m in width, and 0.4 m in height. Three detection holes, each with a diameter of 3 cm and spaced 33 cm apart, are located at the top to accommodate sensors. These holes are sealed after sensor installation to ensure the experimental model remains airtight. To meet experimental requirements, 8 mm calcium silicate fiberboard fireproof boards are installed inside each tunnel section. These boards minimize heat loss through the tunnel walls, thereby simulating real-world conditions more accurately and reducing experimental errors. K-type armored thermocouples are used to monitor the flue gas temperature, with a measurement range of -30 ℃ to 1300 ℃ and an accuracy of ± 0.75% of the measured temperature. Each thermocouple is numbered based on its sensor detection hole ___location and positioned 0.02 m from the top. The layout and numbering are illustrated in Fig. 1. An aluminum telescopic tube with a diameter of 8 cm serves as the air duct, while an XYC14811 fan provides the compressed air. The fan is connected to an external variable frequency control system, which allows adjustment of the fan’s air volume by varying the frequency, with a maximum frequency of 50 Hz.

Fig. 1
figure 1

The general layout of excavation tunnels experimental models.

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Fire source design and heat release rate calculation

Ethanol combustion produces only water and carbon dioxide and is highly flammable. Ethanol is considered to burn completely with 100% combustion efficiency and a heat value of 30,100 kJ/kg. In the experiment, a 95% ethanol concentration was used as fuel, and the heat value calculation took 95% of the pure ethanol combustion heat value. Four circular iron plates with diameters of 12 cm, 15 cm, 18 cm, and 22 cm were used to hold the fuel as ignition sources. The ___location of the fire source, which could be either at the end of the excavation tunnel or 3.5 m from the end, was a variable in the study. A bracket connected the fuel pan to an electronic scale, allowing direct recording of fuel mass changes throughout the experiment. The electronic scale had an accuracy of 0.1 g.

For instance, in Experiment No.1, the weight of the fuel pan was measured every 15 s using an electronic scale. It is evident from Fig. 2 that during the whole combustion process, the change rate of fuel mass is linearly correlated, and the average rate of fuel loss is -1.03 g/s, the heat release rate of the fire source was calculated using the Eq. (7). The method was applied to other experimental groups. The results are summarized in Table 2.

$$\begin{gathered} Q=\eta \cdot \dot {m} \cdot \Delta H \hfill \\ \dot {m}=\frac{{\Delta m}}{{\Delta t}} \hfill \\ \end{gathered}$$
(7)
Fig. 2
figure 2

Data processing of mass loss rate in experiment No.1.

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where η denotes the fuel combustion efficiency, %; \(\dot {m}\) signifies the fuel loss rate, g/s; and ΔH denotes the calorific value of fuel combustion, kJ/kg.

Experimental condition design and data acquisition

Based on the conversion principles outlined in Tables 1 and 24 experimental sets were designed for the platform. The specific working conditions and associated parameters are detailed in Table 2. All physical characteristics were calculated from the average values during a stable combustion condition in the subsequent study on the maximum temperature of excavation tunnel fires.

By comparing the fuel loss rate in Experiment No.1 with the data from thermocouple T-01 in Fig. 3, the fuel loss rate remained in a relatively stable range between 60 s and 350 s. Moreover, the temperature data measured by the thermocouple tend to be stable between 220 s and 300 s, which indicates that the fire source reached stable combustion. For thermocouple T-01 in Experiment No.1, the average temperature recorded from 220 s to 330 s is considered the maximum measurement temperature at that ___location. The data from other thermocouples were processed using the same method.

Fig. 3
figure 3

Experiment No.1 quasi-stable state interval.

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Table 2 Design of experimental platform operating conditions.
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Simulation methods

Numerical simulation techniques were used to improve the experimental results because the experimental platform was limited in its ability to create certain conditions and it was challenging to see wind and temperature field distributions directly. By combining experimental data, simulation outcomes, and flow field characteristics, the factors affecting maximum temperature were analyzed. A thorough full-scale modeling was carried out using the excavation model shown in Fig. 1.

FDS model construction

When FDS is used to simulate the fire process of excavation roadway under forced ventilation conditions, the following equations are mainly solved:

Mass conservation equation:

$$\frac{{\partial \rho }}{{\partial t}}+\nabla \cdot \left( {\rho u} \right)=0$$
(8)

Where u indicates the velocity vector, m/s while ρ represents the gas density, kg/m3.

Compositional conservation equation:

$$\frac{{\partial \rho }}{{\partial t}}\left( {\rho {Y_i}} \right)+\nabla \cdot \rho {Y_i}u=\nabla \cdot {\left( {\rho D} \right)_i}\nabla {Y_i}+{\dot {m}^m}$$
(9)

Where i is the i substance; Yi is the mass fraction of the i substance; D is the diffusion coefficient, m2/s; and \(\dot{m}^{m}\) is the production rate per unit volume of substance i, kg/(sm3).

Momentum conservation equation:

$$\rho \left( {\frac{{\partial u}}{{\partial t}}+\left( {u \cdot \nabla } \right)u} \right)+\nabla p=\rho g+f+\nabla \cdot \tau$$
(10)

Where τ is the viscous pressure vector, kg/(s2m); g is the acceleration of gravity, m/s2; and f is the external force vector, kg/(s2m). p is the pressure, N/m2.

Energy conservation equation:

$$\frac{\partial }{{\partial t}}\left( {\rho h} \right)+\nabla \rho hg - \frac{{Dp}}{{Dt}}=\dot {q}^{\prime\prime\prime} - \nabla {q_{\text{r}}}+\nabla \cdot k\nabla T+\nabla \cdot \sum {{h_i}{{\left( {\rho D} \right)}_i}\nabla {Y_i}}$$
(11)

Where qr is the radiant heat flux, kW/m2; h is the enthalpy, kJ; k is the thermal conductivity, W/(mK); and\(\dot {q}^{\prime\prime\prime}\) is the heat release rate per unit volume, kW/m3.

By default, the large eddy model (LES) is used to solve the turbulent motion in FDS. When the scale of the solution is fine enough, the direct numerical simulation model (DNS) can also be used for calculation, but the calculation time is longer. In this study, the LES model is used as the turbulence calculation model.

Turbulence model:

$$\frac{{\partial \left( {\rho \phi } \right)}}{{\partial t}}+\frac{{\partial \left( {\rho u\phi } \right)}}{{\partial x}}=\frac{\partial }{{\partial x}}\left( {{\Gamma _\phi }\frac{{\partial \phi }}{{\partial x}} - \rho \overline {{u^{\prime}\phi ^{\prime}}} } \right)+{S_\phi }$$
(12)

Where ϕ is the Universal variable, representing u, T, and other solving variables; Γϕ is generalized diffusion; \(\overline {{u^{\prime}\phi ^{\prime}}}\) is turbulence stress; Sϕ is the generalized source term.

The fire source mainly uses radiation heat transfer to transfer heat in the air, while the flue gas will have contact heat conduction with the tunnel wall in the process of contact with the migration and diffusion of wind flow.

Radiation heat transfer model:

$$\vec{s} \cdot \nabla I_{\lambda } (x,\vec{s}) = - \left[ {\kappa _{p} (x,\lambda ) + \sigma _{p} (x,\lambda )} \right]I_{{b,p}} (x,\vec{s}) + \frac{{\sigma _{p} (x,\lambda )}}{{4\pi }}\int {_{{4\pi }} } \Phi \left( {\vec{s},\vec{s}^{\prime}} \right)I_{\lambda } \left( {x,\vec{s}^{\prime}} \right)ds^{\prime}$$
(13)

.

Where κp and σp are the particle absorption and scattering coefficient; Ib, p is the emission term of the particles; \(\vec {s}\) is intensity direction vector; Φ(\(\vec {s}\),\(\vec {s}^{\prime}\))is a scattering phase function that gives the scattered intensity fraction from direction \(\vec {s}^{\prime}\) to \(\vec {s}\).

Wall contact conduction:

$${\rho _{\text{w}}}{c_{\text{w}}}\frac{{\partial {T_{\text{w}}}}}{{\partial t}}=\frac{\partial }{{\partial x}}\left( {{k_{\text{w}}}\frac{{\partial {T_{\text{w}}}}}{{\partial x}}} \right)$$
(14)

Where ρw, cw, Tw, and kw are respectively the density of the wall, the specific heat capacity of the wall material, the wall temperature, and the thermal conductivity of the wall material.

Simulation parameter setting and working condition design

In the experiment, the pressure fan is in the atmospheric environment, so the temperature at the inlet of the air duct is treated as the first type of boundary condition in the simulation. Further, the entrance temperature and the temperature of the simulated environment are set to 20 °C, which is the ambient temperature during the experiment. The ignition fuel is set to ethanol, to ensure that the flow field distribution reaches a stable state during a fire, the fire source was programmed to ignite 60 s into the simulation. In the FDS experiment, 54 different simulated working conditions were designed. The pressure air volume of the duct, the distance between the duct and the head, the heat release rate of the fire source, and other parameters were set according to Table 3.

Table 3 Simulated conditions design.
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Grid sensitivity analysis

It is inefficient and wasteful to use processing power to further reduce the grid size in the FDS numerical simulation process beyond the accuracy requirements. Therefore, balancing grid size with computational accuracy is essential. This study focuses on the maximum temperature and its influencing factors. Previous research29 indicates that the accuracy of simulation results is sufficient when the characteristic diameter of the fire source is 4–16 times the grid size. Using Eq. (15) and a minimum heat release rate of 3 MW for the simulated conditions, the diameter of the fire source (D*) was calculated to be 1.49 m. According to the calculation result, select four grid sizes—0.4 m, 0.3 m, 0.2 m, and 0.1 m—were selected to analyze grid sensitivity.

In Fig. 4, the above four different sizes of grids are adopted, and experiment No.25 is taken as an example to determine the appropriate size of grids through the temperature simulation results above the fire source. It can be observed that the smaller the mesh size, the higher the temperature result, indicating that the finer the mesh will be more accurate the temperature results. The simulation results of larger grids are relatively less accurate, but can also give the overall trend of parameter change. When the mesh size is 0.2 m, the maximum temperature results obtained are not much different from those obtained by the 0.1 m mesh, indicating that the finer mesh does not produce better results for the simulation results. As a result, a grid size of 0.2 m was adopted for the simulation study.

Fig. 4
figure 4

Grid Sensitivity analysis of temperature.

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$${D^*}={\left( {\frac{Q}{{{\rho _0}{c_p}{T_0}{g^{1/2}}}}} \right)^{2/5}}$$
(15)

where D* is the characteristic diameter of the fire source, m.

Simulation validity verification

The experimental setup was confirmed using FDS simulation to ensure a comprehensive comparison between the experimental conditions and the simulation. The following findings were obtained by comparing the maximum temperatures at different locations (as shown in Fig. 5). In contrast to the simulation results, the experimental data demonstrated that the maximum temperature appeared closer to the excavation face when the fire source was positioned in the center of the excavation tunnel. The maximum temperature was slightly higher in the experiment. This discrepancy is attributed to the experimental platform not being tightly sealed at the joints, resulting in lower wind speeds at the fire source ___location compared to the FDS simulation. Therefore, the smoke plume gas shifted less towards the outlet, and the inadequate fresh air volume weakened the cooling effect on the smoke flow, leading to a higher maximum temperature in the experimental setup.

Fig. 5
figure 5

Maximum temperatures obtained from experiments and FDS simulations.

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Despite these differences, a comparison of the temperature data and decay patterns between the experiment and the FDS simulation ultimately showed a good correlation, indicating consistent temperature trends and validating the simulation results.

Result analysis

Analysis of maximum temperature simulation results

The variation in numerical simulation results in maximum temperature with distance is shown in Fig. 6 (a) and (b), and its local fine areas are enlarged as (c) and (d). Several key observations can be made from the graphs:

Fig. 6
figure 6

The variation of maximum temperature with distance in numerical simulation.

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(1). Distance (DL) from air duct outlet to excavation face as a Variable:

Fire source at tunnel end (No.25 to No.51): Some of the results in Fig. 6 (c) are taken as examples shows that the maximum temperature at DL = 5 m is generally higher than at DL = 10 m and DL = 15 m. This effect becomes more significant with increased forced ventilation volume and heat release rate.

Fire source in the middle of the tunnel (No.52 to No.78): Through Fig. 6 (d) found that changes in DL have almost no effect on the maximum temperature. This is because the jet gas from different air duct outlet positions collides with the wall and reverses. When it reaches the fire source position in the middle of the tunnel, the flow field development is almost consistent, thus not impacting the maximum temperature.

(2). Fire Source Location as a Variable:

The maximum temperature is higher when the fire source is located in the middle of the excavation tunnel, consistent with Zhao’s simulation results26. When the fire source is at the tunnel end, the cold air jet from the air duct collides and fuses directly with the fire plume, resulting in a cooling effect that reduces the maximum temperature.

(3). Location of maximum temperature:

For groups No.25 to No.51, the temperature graphs show that the temperature first decreases and then increases at the tunnel end. The fire source is not exactly above the maximum temperature. Combined with the results of the wind speed vector diagram of the longitudinal section at z = 1.5 m and z = 3.5 m in Fig. 7. The air duct is suspended at a higher position, and the high-speed conical jet gas sprayed through the air duct collides with the excavation end wall, forming a backward suction phenomenon. This causes the maximum temperature to appear slightly away from the excavation end rather than directly above the fire source.

Fig. 7
figure 7

Wind speed vector diagram of longitudinal section at z = 1.5 m (a) and z = 3.5 m (b).

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Establishment of the maximum temperature model for excavation tunnel fire

Maximum temperature model for excavation tunnel end fire based on dimensional analysis

This section derives the relationship between the maximum temperature of a single-ended closed tunnel fire with forced ventilation and various influencing factors through dimensional analysis. Several studies13,18 have demonstrated that the maximum temperature is closely related to factors such as heat release rate (Q), tunnel effective height (Hef), air density (ρ0), air heat capacity (cp), ambient temperature (T0), gravity acceleration (g), and wind speed (V). In previous studies, wind speed referred to the average wind speed in the upstream space of the fire source. However, in this study, the forced ventilation method only determines the wind speed at the air duct outlet. As the jet develops and the fire source’s thermal buoyancy influences the flow, the overall flow field becomes turbulent, which can be seen in the wind flow field streamline diagrams in Figs. 7 and 8. Because of this turbulence, it is difficult to simulate and experiment with the wind speed close to the fire source. Moreover, it is evident from the maximum temperature graphs for each experimental group (Fig. 6) that the distance between the air duct and the tunnel’s closed section also impacts the maximum temperature.

Fig. 8
figure 8

Wind speed vector diagram of longitudinal section at y = 0.5 m (a) and y = 2.5 m (b).

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Owing to these reasons, the influence of wind speed on the maximum temperature is expressed as a combination of two factors: the forced ventilation volume (q) and the distance (DL) from the air duct to the tunnel end. The combined expression of maximum temperature and influencing factors is:

$$\Delta {T_{\hbox{max} }}=f\left( {Q,{H_{ef}},{\rho _0},{c_p},{T_0},g,{D_L},q} \right)$$
(16)

where DL is the distance from the duct outlet to the end face, m; q is the forced ventilation volume, m3/s.

Performing dimensional analysis on Eq. (16) leads to the following equation:

$$\frac{{\Delta {T_{\hbox{max} }}}}{{{T_0}}}=f\left( {\frac{Q}{{{\rho _0}{g^{\frac{3}{2}}}{H_{ef}}^{{\frac{7}{2}}}}},\frac{{{c_p}{T_0}}}{{{H_{ef}}g}},\frac{{{D_L}}}{{{H_{ef}}}},\frac{q}{{{H_{ef}}^{{\frac{5}{2}}}{g^{\frac{1}{2}}}}}} \right)$$
(17)

After simplification, we have:

$$\frac{{\Delta {T_{\hbox{max} }}}}{{{T_0}}}=f\left( {\frac{Q}{{{\rho _0}{c_p}{T_0}{g^{\frac{1}{2}}}{H_{ef}}^{{\frac{5}{2}}}}},\frac{{{D_L}}}{{{H_{ef}}}},\frac{q}{{{H_{ef}}^{{\frac{5}{2}}}{g^{\frac{1}{2}}}}}} \right)$$
(18)

The final relationship between dimensionless temperature T* and dimensionless heat release rate Q*, dimensionless duct-to-end distance DL*, and dimensionless ventilation volume q* is:

$${T^*}=f\left( {{Q^*},D_{L}^{*},{q^*}} \right)$$
(19)

where

$${T^*}=\frac{{\Delta {T_{\hbox{max} }}}}{{{T_0}}},{Q^*}=\frac{Q}{{{\rho _0}{c_p}{T_0}{g^{\frac{1}{2}}}{H_{ef}}^{{\frac{5}{2}}}}},D_{L}^{*}=\frac{{{D_L}}}{{{H_{ef}}}},{q^*}=\frac{q}{{{H_{ef}}^{{\frac{5}{2}}}{g^{\frac{1}{2}}}}}$$
(20)

Previous research has established a proportional relationship between T* and Q*. In Fig. 9, corresponding graphs are plotted, and the linear relationship is fitted with the function: T* = aQ* + b

$${T^*}=8.028{Q^*}+0.976$$
(21)
Fig. 9
figure 9

Fitting relationship between Q* and T*.

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The air volume and temperature data collected in the experiment are processed by proportional conversion and dimensionless processing, and the simulation data is also processed by dimensionless processing. Following the preceding data processing process, Fig. 9 ~ Fig. 10 are obtained. The data points with significant deviation from the fitting line in Fig. 9 are mostly temperature data where the air duct is far from the excavation face. When combined with the conclusions obtained in Fig. 6, the distance from the air duct outlet to the excavation end face and the air duct output volume is inversely proportional to the maximum temperature, with a more significant impact when the fire source heat release rate is high. Therefore, T* is represented by Q*/q*DL*. To avoid unstable results due to rounding errors in the calculation process, the calculated value of q*DL* is adopted with exponential processing. Figure 11 verifies the relationship between the dimensionless T* and dimensionless Q*/q*DL*, and it can be seen that there is a linear correlation between the two. Therefore, the dimensionless Q*/q*DL* is used to represent T*. The non-dimensional equation for the maximum temperature under forced ventilation, with the fire source located at the heading face of the tunnel, is ultimately derived as:

$${T^*}=\frac{{0.077{Q^*}}}{{\exp \left( {{q^*}D_{L}^{*}} \right)}} - 0.063$$
(22)
Fig. 10
figure 10

The Maximum Temperature results comparison of the Kurioka Prediction Model.

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Fig. 11
figure 11

Dimensionless temperature fitting relationship.

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Maximum temperature model correction of a fire in the middle of the tunnel

With the fire source located near the middle of the tunnel face, the model described in this work closely fits studies on the peak temperatures seen in breakthrough tunnel fires compared to the results of earlier research. To validate the results, the maximum temperature data obtained from the simulations were compared with classical models provided by Li7 and Kurioka8.

According to Li’s proposed prediction model (Eq. (2)), the maximum temperature data results were predicted and analyzed as shown in Fig. 12. There is a significant deviation between the maximum temperature simulation results and Li’s predictions. This deviation mainly originates from factors. Firstly, in Li’s study, the prediction formula was applied separately to calculate the maximum temperature for horseshoe-shaped and rectangular tunnels. The maximum temperature prediction results for horseshoe-shaped tunnels were closer to the actual values, while those for rectangular tunnels showed greater discrepancies. Secondly, the current study focuses on rectangular tunnels with air ducts, which differs from Li’s model in terms of air entry method and tunnel structure. These differences contributed to the significant deviation between the data results in this study and the temperature prediction expression provided by Li.

Fig. 12
figure 12

The Maximum Temperature results comparison of Li Prediction Models.

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Moreover, as illustrated in Fig. 10, the results of the experiments and simulations conducted for this work were contrasted with Kurioka’s prediction model Eq. (4). This comparison further illustrates the accuracy and limitations of different prediction models in estimating the maximum temperature in tunnel fires.

The maximum temperature simulated in this study is generally higher than the results predicted by existing models. The heat release rate interval values in Kurioka’s study are comparatively lower than those in this study after proportional conversion, according to an analysis of the causes of the temperature deviation of Eq. (4). Moreover, the wind speed conditions in the literature are much higher than those in this study. These two factors result in the Kurioka model generally predicting a lower maximum temperature before the inflection point compared to the results in this paper. Furthermore, the upper-temperature limit in the literature experiment is 800 K, whereas temperatures in some large tunnel fires can exceed this limit, indicating that the Kurioka model has limitations in predicting cases with temperatures exceeding 800 K.

The Kurioka-based model (Fig. 10) shows that the ratio of the dimensionless heat release rate to the Froude number well represents the relationship between experimental and simulated data of the highest fire temperature in the middle of the tunnel, showing a good correlation between the two. By adjusting and correcting the correlation coefficients, the Kurioka prediction model can provide accurate and reliable maximum temperature predictions for this study. The formula after coefficient correction is shown in Eq. (23):

$$T*=2.28{\left( {\frac{{{Q^{*2/3}}}}{{{\text{F}}{{\text{r}}^{1/3}}}}} \right)^{3/5}}$$
(23)

Analysis of the impact of wind tunnel distance on temperature

Upon analyzing the temperature of the fire source located at the end of the excavation tunnel (Fig. 6), it was found that the maximum temperature simulation results for DL = 5 m were generally higher than those for DL = 10 m and DL = 15 m. To analyze the causes of this phenomenon, the wind speed vector diagram and temperature contours of No.28, No.29, and No.30 at the end of the excavation tunnel were analyzed, where x, y, and z represent the length, width, and height of the tunnel respectively. In the longitudinal section, the locations of the fire source and the air duct are indicated, with cases where the air duct and fire source are not within the section represented by dashed lines.

Figure 8 depicts the wind speed vector diagram of the longitudinal section at y = 0.5 m and y = 2.5 m.

Figure 8 (a) reveals that during the combustion of the tunnel end fire source, the surrounding air is heated, causing it to expand upwards, collide with the top wall, and spread outwards. This affects the air duct jet stream, causing its streamline to shift downwards. When the air duct outlet is farther from the excavation end face, the kinetic energy of the jet stream reaching the end face weakens, and the thermal expansion effect of the fire source becomes more pronounced in driving the air. Through the velocity streamline trajectory in the longitudinal cross-section, it can be seen that the vortex motion formed above the fire source by No.30 is more obvious compared to the other two groups, and the impact area is larger.

In Fig. 8 (b), the phenomenon of hot air obstructing the jet flow, leading to the formation of vortices, can be observed on the longitudinal cross-section at y = 2.5 m. Part of the flue gas is entrained by the jet and released immediately together with the jet gas at the vortex, while another part of the flue gas returns to the fire source, where it is heated and released from the upper section of the vortex area. In the No.28, the vortices near the fire source are more pronounced, which hinders the exhaust of smoke. In contrast, the smoke exhaust is more efficient in the No.29 and No.30.

Figure 7 draws the wind speed vector diagram of the longitudinal section at z = 1.5 m and z = 3.5 m.

The outlet of the No.28 air duct is closest to the end, it can be seen from the wind speed vector diagram of the longitudinal section at z = 1.5 m, the velocity of the jet gas reaching the end wall is the highest. Under the influence of the fire source, it collides with the tunnel end wall and forms a circulation around the fire source. In the velocity streamline diagram at z = 3.5 m, a significant circulation is formed at the excavation end in the longitudinal cross-section. High-temperature flue gas is difficult to discharge and accumulates near the fire source, and the jet air does not fully exchange heat with the fire plume, resulting in a relatively high maximum temperature.

For the wind speed vector diagram of the longitudinal section at z = 1.5 m for No.29 and No.30, the jet air offset induced by thermal buoyancy generates a high-speed airflow region near the duct side wall, which aligns with the findings presented in Fig. 8 (a). The inflow of a significant amount of jet air enhances the collision between the upward fire plume, generated by the cold air and the fire source, promoting more effective smoke discharge and influencing the temperature distribution.

For the wind speed vector diagram of the longitudinal section at z = 3.5 m for No. 28 and No. 29, the flue gas near the fire source is primarily driven by thermal buoyancy, facilitating smooth discharge. Adjacent to the air duct outlet, the high-velocity air jet entrains with the buoyant flue gas stream, forming a localized recirculation vortex, which hinders the discharge of some flue gas.

Figure 13 shows the temperature contours of the longitudinal section at z = 1.5 m and z = 3.5 m.

Fig. 13
figure 13

Temperature contours of longitudinal section at z = 1.5 m (a) and z = 3.5 m (b).

Full size image

It was observed that the core temperature zone in No.28 is more inclined towards the jet return zone compared to the other two groups. No.28 also has a larger area in the high-temperature zone above 500 °C.In Fig. 13 (b), near the roof of the excavation tunnel, the high-temperature area of No.28 is larger than the other two groups. This correlates with the velocity flow field study at z = 3.5 m, where the concentration of high-temperature smoke is caused by airflow circulation. This clarifies the reason that when the distance from the air ducts is taken into account as a single variable, the maximum temperature at DL = 5 m is the highest.

It was observed that the center of the temperature layer ring in No.29 deviates the most from the side away from the air duct, indicating that this group of fire sources is most effectively cooled by jet air. Moreover, the temperature of No.29 was significantly lower than the other two groups, confirming that the air duct outlet layout affects the maximum temperature with the same heat release rate as the fire source.

In the No.30 temperature contour, the temperature deviation from the center position is minimal, and the layered ring is more regular, indicating that the impact of jet air on the end fire source is limited. Furthermore, the temperature range of 275–375 °C in Fig. 13(b) represents the largest area, which is consistent with the conclusion that the swirling flow near the outlet of the air duct impedes the discharge of a portion of the flue gas, as shown in Fig. 7(b).

The following conclusions can be drawn from the analysis of the characteristics of the wind flow field and temperature field with different duct distances: The experimental temperature at DL = 5 m is relatively higher due to the formation of a circulating flow of jet air under the coupling effect of the thermal expansion of the fire source. This circulation prevents the effective discharge of high-temperature smoke, leading to higher maximum temperatures. With the increase in the distance between the outlet of the air duct and the closed-end face (DL = 10 m), the jet gas is shifted downward due to the influence of the fire source. The fresh air mixes with the high-temperature flue gas at the fire source, and the flue gas is discharged smoothly. In addition, owing to the cooling effect of the jet gas, the maximum temperature is lower than the experimental group with DL = 5 m. When the outlet of the air duct is positioned farther away (DL = 15 m), the influence range of the vortex formed near the outlet expands, leading to a decrease in exhaust efficiency. Even though the forced ventilation duct outlets are positioned within a reasonable planning range, the air duct outlet positions need to be moved forward on time as the tunnel excavation section progresses.

Conclusion

The 1:10 experimental model developed in this study successfully simulates a tunnel fire under forced ventilation conditions. Numerous conditions and scenarios were thoroughly investigated using numerical simulation techniques and experimental methodologies. The main achievements are summarized as follows:

  1. (1)

    When the fire source is at the end of the excavation tunnel, the wind speed at the fire source is disordered due to the special structure of the roadway. The forced ventilation volume and the distance from the air duct to the tunnel end as key factors influencing the maximum temperature, replacing the turbulent wind speed parameter. The relationship between the maximum fire temperature and the heat release rate of fire source, the ventilation volume and the ___location of the air duct outlet is determined by dimensionless analysis. When the fire source is situated in the center of the excavation tunnel, the data results were compared with Li and Kurioka’s maximum temperature prediction models in the through tunnel. The Kurioka’s model parameters are modified to make it more widely used. Both the dimensionless model and the Kurioka’s correction model have good prediction performance for the experimental data and simulation data in this paper.

  2. (2)

    The position of the air duct outlet significantly affects the maximum temperature in a closed-end fire scenario. When the air duct is positioned too close to the end face (DL = 5 m), the jet air flows around the fire source, reducing its cooling effect on the flue gas. When the air duct outlet is farther from the end face (DL = 15 m), the buoyancy of the fire source smoke obstructs the jet air, reducing the efficiency of smoke discharge. There exists an optimal interval for air duct placement in a forced ventilation tunnel fire, ensuring a balance between effective cooling and smoke removal.