The outstanding thermal damage effect of thermobaric explosive (TBX) is enhanced in closed or semiclosed spaces, which may pose a serious threat to the security of people sheltered in tunnels or other protective engineering. In order to investigate the thermal environment inside a tunnel after thermobaric explosion, we developed a damage evaluation method for the thermal radiation of explosion fireballs in tunnels; secondly, the air temperature distribution inside a tunnel shortly after explosion was theoretically analyzed; finally, the dynamic thermal environment after the explosion and the influences of TBXs mass and initial ground temperature on it in cases of open and blocked tunnels were numerically simulated with the FLUENT software. The results show that the fireball thermal radiation damage occurs mainly in the vicinity of the explosion source. The air temperature inside a tunnel shortly after the explosion decreases continuously with increasing distance from the explosion source and finally reaches the initial air temperature. The decay rate of air temperature inside a tunnel is slower in the blocked case, which increases the probability of causing a secondary fire disaster. The increase of explosive mass and the initial ground temperature favor the high-temperature performance of TBX, especially for the blocked tunnel.
Thermobaric explosive (TBX), a new subcomponent of volumetric explosives presents a number of advantages with respect to traditional high explosives, including longer duration, higher impulse shock wave, and diversified damage effects [
Due to its outstanding features, the damage effects of TBX have been the focus of much research in recent years. Many studies have been conducted on the overpressure field and pressure damage effects [
Mohamed et al. [
Combined with certain fireball models and thermal damage criterion, the damage range of thermal radiation can be evaluated. Guo et al. [
The above studies were conducted in the open field and cannot well reflect the thermal damage effects of TBX because of the shorter duration of fireballs. In terms of closed or semiclosed environment explosion, there are several studies. Using an enclosed explosion container to simulate the limited space, Yan et al. [
However, few studies have been done on the thermal radiation evaluation method of thermobaric explosion in closed or semiclosed spaces, and even fewer works are available on the dynamic thermal environment after the explosion in such spaces, due to the difficulty in conducting effective measurements in such poor test conditions and with limited testing methods. In this paper, we first establish a damage evaluation method for the thermal radiation of thermobaric explosion fireball in a tunnel and then theoretically deduce the air temperature distribution inside a tunnel shortly after the explosion. Taking this distribution as an initial condition, we analyze the dynamic thermal environment after the explosion and the influences of TBXs mass and initial ground temperature on it by simulating the temporal and spatial variation of air temperature in a tunnel with the FLUENT software. The purpose of this paper is to investigate the thermal environment inside a tunnel after thermobaric explosion and provide prerequisites for thermoprotection design of protective engineering.
In order to evaluate the thermal radiation damage effects of a thermobaric explosion fireball, it is first necessary to determine the heat flux or heat dose received by the targets surface. However, it is often difficult to achieve an accurate experimental measurement of these two parameters. To solve this problem, various types of thermal radiation models for fireballs, suitable for different fuels or explosives, have been proposed, including the Dorofeev model [
In the Baker model, the heat flux and heat dose received by the targets surface can be, respectively, expressed according to the following two equations [
The heat dose damage criterion is chosen in this paper to evaluate the thermal radiation damage effects of a thermobaric explosion fireball due to its applicability to a variety of transient combustion or explosion processes [
Thermal radiation damage range for the thermobaric explosion in a tunnel.
Damage effects | Damage threshold values (kJ/m2) [ |
Damage range (m) |
---|---|---|
Igniting wood | 1030 | 30.14 |
Death | 592 | 39.77 |
Serious injury | 392 | 48.88 |
Third-degree burn | 375 | 49.97 |
Second-degree burn | 250 | 61.21 |
Slight injury | 172 | 73.80 |
First-degree burn | 125 | 86.56 |
Cutaneous pain | 65 | 120.05 |
For the thermobaric explosion in an open space, the thermal radiation damage range can be calculated by
However, when the TBX explodes inside a tunnel, the flame will be constrained by the surrounding rocks, which is obviously a different process from the fireball generated by an open space explosion. In order to apply Baker model, which is suitable for open space explosions only, to the confined space explosion, the concept of the tunnel equivalent heat dose The explosion process is instantaneous, and the heat damage is caused by the fireball radiation. The effects of heat conduction, heat convection, and the heat radiation absorbed by air and by the surrounding rocks are ignored. The tunnel is straight with a uniform section, surrounded by smooth and adiabatic rocks.
The relationship between the tunnel equivalent heat dose and the open space heat dose can be expressed as
Substituting (
Letting
When the explosive shock wave propagates in a straight tunnel, it will gradually form a stable plane shock wave after undergoing several reflections [
Schematic illustration of the plane shock wave propagation.
The following assumptions have been made in order to simplify the model: Heat transfer and friction loss during the shock wave propagation are ignored, and the process is considered adiabatic. The gas state in the whole process satisfies the ideal gas equation. All the explosion energy of TBX has been released before the formation of the plane shock wave, ignoring the chemical reaction process. Moreover, the explosion energy is constant for a certain amount and type of thermobaric charge. The amount of the gas compressed by the shock wave is concentrated in a very thin layer of thickness The flow velocity distribution in the thin layer is uniform and equal to the wave front velocity The pressure distribution in the thin layer is uniform and equal to the wave front pressure
According to the momentum theorem, the gas in the thin layer must satisfy the following relation:
Using the relations
For a very strong shock wave,
According to assumption (1), the energy released by the TBX explosion is fully converted into work, increasing the internal energy and kinetic energy of the thin layer gas. The internal energy can be expressed as
The kinetic energy can be expressed as
The explosion of thermobaric charges is a process which can be divided into an anaerobic stage and aerobic stage (or postcombustion stage). The energy released in the anaerobic stage is known as explosion heat
According to the assumption (3),
Therefore, (
Combined with the basic relation of a strong shock wave, which is
According to assumption (2), we have
Substituting (
To validate the accuracy and reliability of the model proposed in this paper, the air temperature distributions calculated with the above formula are compared with Yan et al.’s experimental data [
Comparison between theoretical calculations and experimental results for the temperature distribution.
Figure
The temperature distribution was calculated for a specific RDX-based TBX, which consists of 20% RDX, 43% ammonium perchlorate (AP), 25% Al, and 12% hydroxyl-terminated polybutadiene (HTPB) in mass fraction, exploding at the tunnel entrance [
Calculated air temperature distribution in the tunnel.
The air temperature inside the tunnel decreases with the increasing distance, eventually reaching the original air temperature of the tunnel. In addition, the air temperature decreases rapidly in the range 0~100 m and then gradually becomes nearly constant, similarly to the attenuation of shock wave overpressure over an increasing distance.
A 2D tunnel model, which represents the longitudinal section along the central axis of the tunnel, was established in this paper as shown in Figure
Schematic illustration of the numerical model.
The continuity equation can be expressed as
The momentum conservation equation can be expressed as
The energy conservation equation can be expressed as
The air in tunnel is considered as still in the moment after explosion, and the ventilation system is stopped. The flow of high-temperature air is a low Reynolds number turbulent flow driven by the temperature difference. In order to characterize the airflow properly, the
It is worth mentioning that the low Reynolds number turbulent flow simulated by the RNG
The above-mentioned equations are subject to the boundary conditions indicated by Figure
The far-field boundaries were set as no-slip solid walls with a constant temperature equivalent to the initial temperature of the surrounding rocks.
The two interfaces between separate blocks were considered as interior surfaces and set as temperature-coupled walls.
There are two kinds of boundary conditions for the tunnel entrance: one is the pressure outlet boundary, which was applied to the open tunnel case; the other is the wall boundary with third temperature boundary condition, which was applied to simulate the case in which the tunnel is blocked by fallen rocks. For the pressure outlet boundary, the return air temperature was set to 298 K, ignoring the outdoor air temperature changes under the influence of the explosion. As for the wall boundary, the convective heat transfer coefficient was taken as 14.5 W/m2·K [
The temperature distribution shortly after the explosion was assigned to the air field as the initial condition in the numerical model by a User Defined Function (UDF), which is a C language file that can dynamically connected to the FLUENT solver to improve its simulating performance. It is worth noting that the calculated temperature is relatively high in the vicinity of the explosion source. We therefore made a correction by setting the fireball temperature (3153.3 K) as the air temperature at the explosion source and connecting to the theoretical curve in 3000 K by linear attenuation. Considering the radiation heat transfer between the high-temperature air and the surrounding objects, the Discrete Transfer Radiation Model (DTRM) was selected.
The surrounding rock was considered to be homogeneous and isotropic, and its initial temperature was set to 293 K.
The physical properties of the surrounding rock are shown in Table
Physical properties of surrounding rocks.
Density |
Constant-pressure specific heat |
Heat conductivity coefficient |
---|---|---|
2500 | 840 | 2.04 |
For the high-temperature air, the main physical parameters of the high-temperature air in the tunnel vary significantly with temperature, according to the following empirical piecewise polynomial functions [ Density Constant-pressure specific heat Heat conductivity coefficient Radiation absorption coefficient
In addition, the air viscosity can be calculated by the following equation [
A quadrilateral mesh was applied to the model and appropriately refined at the fluid-solid coupling region, amounting to 44000 mesh. The governing equations were discretized using the finite volume method and solved by the SIMPLE algorithm combining the conditions mentioned above. All the presented numerical results were calculated by using the FLUENT software with a time step of 0.1 s. The convergence was reached when residuals were smaller than 10−6 for energy and 10−3 for other variables.
Figure
Temporal and spatial variation of temperature in the open tunnel.
6 s
24 s
60 s
In order to achieve a more accurate understanding of the temporal and spatial distribution of the air temperature inside the tunnel, Figure
Spatial distribution of temperature in the open tunnel at different times.
The temporal and spatial variations of temperature in the blocked tunnel case are illustrated in Figure
Temporal and spatial variation of temperature in the blocked tunnel.
16 s
84 s
300 s
Figure
Spatial distribution of temperature in the blocked tunnel at different times.
In order to study the influence of TBX mass on the dynamic thermal environment changes, three TBXs of the same type with different mass (1 kg, 10 kg, and 100 kg, resp.) were chosen as the research subjects. Keeping other parameters at the same value as in the previous paragraphs, the maximum temperature attenuation curves for different explosive masses were obtained in both the open and blocked tunnel cases, and they are shown in Figure
Maximum temperature attenuation curves of different TBX mass.
Open tunnel
Blocked tunnel
In order to study the influence of initial temperature conditions on the dynamic thermal environment changes, the different annual average ground temperatures of four typical Chinese cities with totally different climatic conditions were chosen as the initial temperature of the surrounding rocks, as shown in Table
Annual average ground temperature of typical cities [
City | Annual average ground temperature (K) |
---|---|
Shenyang | 283.47 |
Beijing | 287.11 |
Wuhan | 291.94 |
Guangzhou | 296.76 |
Setting the TBX mass as 100 kg and keeping other parameters consistent with the previous text, the maximum temperature attenuation curves for different initial ground temperatures were obtained in both the open and blocked tunnel cases and they are shown in Figure
Maximum temperature attenuation curves of different initial ground temperature.
In order to investigate the extent to which the initial temperature conditions affect the thermal environment changes in different tunnel cases, the cooling time can be taken as an index and an influence rate parameter can be defined as
Figure
Cooling time changes against initial ground temperature.
To learn about the thermal environment inside a tunnel after thermobaric explosion in detail, a damage evaluation method for thermal radiation of explosion fireball in a tunnel was established based on the Baker fireball model and the heat dose damage criterion; the air temperature distribution inside a tunnel shortly after the explosion was studied by theoretical derivation; taking the calculated distribution as an initial condition, the dynamic thermal environment after the explosion was analyzed in two different cases (open tunnel or blocked tunnel) and in different conditions (TBX mass or initial ground temperature) was numerically analyzed. Based on the above investigations, the following conclusions may be drawn: The fireball thermal radiation damage ranges for 100 kg of RDX-based TBX in a tunnel were determined based on the damage evaluation method. The thermal radiation lethal range, serious injury range, and slight injury range are 39.77 m, 48.88 m, and 73.80 m, respectively. The thermal radiation damage occurs mainly in the vicinity of the explosion source. The air temperature inside a tunnel shortly after explosion decreases continuously with the increase of distance from the explosion source and finally reaches the initial air temperature. In the calculation condition of this paper, the air temperature decreases rapidly in the range 0~100 m and then gradually becomes nearly constant. In the open tunnel case, the high-temperature region gradually concentrates on the top and moves towards the depth of the tunnel. Conversely, in the blocked tunnel case, the high-temperature region concentrates near the explosion source without a clear displacement and with a shorter duration of thermal stratification, stretching gradually over time. The decay rate of air temperature inside a tunnel is slower in the blocked case, which increases the probability of causing a secondary fire disaster. Increasing the explosive mass significantly increases the high-temperature duration and decreases the decay rate. The cooling time of different TBXs masses in the blocked tunnel is 1.56, 1.63, and 1.72 times as long as the open tunnel, showing that a larger amount of explosive makes TBX more powerful in the blocked tunnel. In both the open and closed tunnel cases, a higher initial ground temperature results in a slower attenuation, and the temperature differences between different conditions are larger and larger over time. The cooling time increases exponentially with increasing change rate of initial ground temperature, and the influence rate of the blocked tunnel case is larger than that of the open tunnel case at all times, showing that the increase of the initial ground temperature favors the high-temperature performance of TBX, especially for the blocked tunnel.
The authors confirm that this paper’s content has no conflicts of interest.