Explosion damage effects of aviation kerosene storage tank under strong ignition

Abstract

In order to study the blast damage effects of aviation kerosene storage tanks, the out-field explosion experiments of 8 m3 fixed-roof tanks were carried out. The fragments, shock wave and fireball thermal radiation of the tank in the presence of bottom oil, half oil and full oil, as well as empty tank, were investigated under internal explosion by various TNT charge contents (1.8 kg, 3.5 kg and 6.2 kg). The results showed that the tank roof was the only fragment produced, and the damage forms could be divided into three types. The increase of TNT charge content and oil volume enlarged the deformation of the tank, while the hole ratio presented a trend of increase first and then decrease. The Hr, max and Vmax values positively increased as increasing the TNT charge content and oil volume (from empty to half oil), but decreased in full oil. The Pmax values had a progressive increase with the increment of TNT charge content, but not the case with the increase in oil volumes. The development of fireball was divided into three stages: tank roof 'towed' flame, jet flow flame tumbling and rising, and jet flow flame extinguishing. The Dmax and Hf, max values both increased as increasing TNT charge content and oil volumes. The oscillation phenomenon of fireball temperature was observed in the cooling process. The average temperature of fireball surface was positively correlated with TNT charge content, and negatively correlated with oil volumes.

Headnote

ABSTRACT

In order to study the blast damage effects of aviation kerosene storage tanks, the out-field explosion experiments of 8 m3 fixed-roof tanks were carried out. The fragments, shock wave and fireball thermal radiation of the tank in the presence of bottom oil, half oil and full oil, as well as empty tank, were investigated under internal explosion by various TNT charge contents (1.8 kg, 3.5 kg and 6.2 kg). The results showed that the tank roof was the only fragment produced, and the damage forms could be divided into three types. The increase of TNT charge content and oil volume enlarged the deformation of the tank, while the hole ratio presented a trend of increase first and then decrease. The Hr, max and Vmax values positively increased as increasing the TNT charge content and oil volume (from empty to half oil), but decreased in full oil. The Pmax values had a progressive increase with the increment of TNT charge content, but not the case with the increase in oil volumes. The development of fireball was divided into three stages: tank roof 'towed' flame, jet flow flame tumbling and rising, and jet flow flame extinguishing. The Dmax and Hf, max values both increased as increasing TNT charge content and oil volumes. The oscillation phenomenon of fireball temperature was observed in the cooling process. The average temperature of fireball surface was positively correlated with TNT charge content, and negatively correlated with oil volumes.

Keywords:

Aviation kerosene

Storage tank

Internal explosion

Shock wave

Fireball

1. Introduction

Aviation kerosene is the main energy fuel of civil/military aircraft, including many kinds of aerospace vehicles, and it plays an important role in aerospace transportation [1,2]. The reserve of aviation kerosene and its raw materials is an effective force for countries and regions to cope with regional armed conflicts, and it can greatly promote the development of aerospace science and technology, which make an important guarantee for human safety and happiness [3,4]. The storage of aviation kerosene mainly relies on storage tanks, and its transportation is mainly by tank trucks. However, aviation kerosene is easy to flow and volatilize, and tends to be inflammable and explosive as well. Once storage tank is damaged by natural or human factors, fire and explosion are inevitable. More seriously, it could even trigger a domino chain reaction and result in large-scale combustion and explosion accidents, which might bring a large number of casualties, property losses and severe social impacts [5,6]. For example, the Ras Lanuf tank farm in Libya was attacked by the Islamic State in 2016, which destroyed five storage tanks and 3 million tons of oil. A tank truck exploded and caused 20 deaths and 175 injuries in Wenling (China, June 2020), in which the property loss was as high as $14.65 million. It can be seen that the storage tank explosion accidents had brought huge loss of lives and property. Therefore, it is an urgent need to understand the explosion development process, which would be of significant importance in investigating the accident causes and preventing the explosion occurrence.

The compressed/liquefied gas or liquids are usually stored in tanks. The research objects could be single or multiple gases (such as H2-air, H2eCH4-air mixture) and flammable liquid vapor/droplets (such as gasoline/kerosene vapor, C2H5OH) [7e11]. Cheng [12] studied the explosion and flame propagation behaviors and flame temperature of the H2-air by using the improved two-colour pyrometric technique. Qi [13] observed the flame behaviors of gasoline vapor in a pipeline with an open end. There were three peak pressures at each measuring point, and the mushrooming cloud formed at the open end. Cai [14] pointed out that the flame propagation of vapor explosion can be divided into three stages. The external field pressure showed an exponential attenuation as the distance increased. Grabarczyk [15] experimented the explosion overpressure of various liquid fuels and found that the explosion mechanism gradually transformed from thermodynamics-driven to radiant heat losses-driven by increasing the fuel content. Wang [16,17] studied the shock wave and thermal radiation damage effects of natural gas vapor cloud explosions (VCEs), and pointed out that the 100% fatality of shock wave and thermal radiation is in the 160 m and 266.3 m range, respectively.

The strength of the tank is the guarantee of safety storage and transportation of most petrochemical products. Lots of scholars have studied the dynamic behaviors and failure modes of storage tanks under the explosion shock wave impact or fire thermal radiation. Birk [18] proposed the calculation model of the boiling liquid expanding vapor explosion to evaluate factors such as overpressure and thermal radiation. Leite [19] studied the flame behaviors of oil tanks with various diameters and expounded the relationship between oil tanks with different geometric sizes. Li [20] revealed the damage probability of atmospheric tanks under fire and explosion danger. Liu [21] investigated that the shock wave impact resulted in the plastic deformation of the cylinder, and the generated crack led to the fracture of the cylinder. Duffey [22] used high explosives to impact the long cylindrical vessel, and obtained the functions between the final circumferential strain or radial displacement. Atkinson [23] proposed failure modes and ignition of various types of liquid storage tank during VCEs, and presented methods for assessing the degree of external and internal damage. Zhang [24] used TNT equivalent method to simulate the explosion of petroleum vapor cloud. The initial internal energy generated by the shock wave led to the deformation and structural damage of the tank, while the liquid absorbed part of the impact energy which could weaken the shock wave effects. Clubley [25] studied the effects of long-term explosion load on the response of aluminum cylindrical shell structures with different liquid levels. Li [26,27] extended the study on estimating the internal and external pressure and impulse from vented gas explosion in large cylindrical tanks, and presented the methods for large-scale vented gas explosion overpressure peak prediction. Ding [28] simulated the tank roof damage effects of 3000 m3 vertical vault storage tank. They found that the failure pressures of the tank roof were equal in empty, half and full tank, and the damage pressure of the tank shell and bottom increased with the liquid level. Djelosevic [29] used differential equations of motion, statistical distributions and inertial model to establish a new method for explosion fragments of cylindrical tanks. Lu [30,31] simulated the influence of liquid level heights on steel storage tank in case of explosion impact. They found the peak pressure generated by the liquid was of a similar order of magnitude to the explosion shock wave. The expansion and damage would arise from the combination of the shock wave and the sloshing liquid. The effect of external explosion shock wave on water storage tank was simulated by Mittal [32]. The stress and water sloshing heights increased as the scaled distance decreased and the height-diameter ratio increased. Hu [33] simulated the distribution of explosion load inside the storage tank. It is found that the maximum explosion load increased with the increase of tank capacity, height-diameter ratio and combustible gas content. However, the explosion load reduced as the liquid levels increased. In the previous researches, more attention was paid to the explosion characteristics of combustible gas or the dynamic response of tank surface, and the researches on damage effects of large-scale tanks were mainly based on numerical simulation. There were few field test studies on the distribution of pressure outside the tank under internal explosion, as well as the development of fireball. In this paper, by taking aviation kerosene as the oil medium, the damage effects of fixed-roof tank, distribution law of external-field shock wave and evolution of fireball were studied through field test. The research results are helpful in understanding explosion development and damage effect of storage tank under strong impact load, which is of significance for fully optimizing the layout of storage tank construction, investigating the tank explosion accident causes and reducing the explosion hazards in the future.

2. Experimental details

2.1. Materials

As shown in Fig. 1, aviation kerosene was selected as the oil medium in the test. It is a kind of complex mixture whose flash point and density are 45C and 805 kg/m3 , respectively. It contains 80 components as tested by GC-MS (Beijing ZKGX Research Institute of Chemical Technology, China). 28 substances (over 1%) account for 79.24% such as 3-methylhexane, nonane and undecane, and the remaining 52 substances (below 1%) account for 20.76%. The detailed components of aviation kerosene are listed in Appendix A, and the physical-chemical properties are listed in Appendix B. The TNT charge was used as the ignition source

2.2. Tank scale model

As shown in Fig. 2, according to the Standard HG 21502.1e92 [34], a fixed-roof oil tank (nominal volume was 1000 m3 ) was taken as the model, and the small fixed-roof tank (8 m3 ) was obtained by the reduction ratio of 1:5. The diameter and height of the tank are 2300 mm and 2130 mm, respectively. Considering the stability during processing and transportation, the thickness of the tank is still 6 mm. The roof is flat. The wall and the roof are weakly connected, while the bilateral full welding is adopted between the wall and the base to ensure the strength and sealing of the tank [35]. An oil filler (DN 50) is attached on the tank wall. A breathing valve (DN 30) is installed at the tank roof. A round hole with a diameter of 300 mm is also made in the center of the tank roof. An aluminum casing is installed in this hole and could be disassembled freely as required. The internal diameter of the casing is 295 mm, the length is 1250 mm and the thickness is 2 mm. The TNT charge could be placed in the casing. The first role of the casing is to insulate the kerosene vapor which could ensure the safety when operating the TNT charge. The second role is to ensure that the TNT charge could be placed in the same position (i.e. the same detonation location) when the oil volume is different. When the TNT charge is placed, a flange and circular clamp are used to seal the casing to prevent the excessive explosion venting after TNT detonation.

2.3. Test conditions

The tested tank was placed in the center of a waste oil container (12 m12 m) which was used to prevent kerosene forming uncontrolled flowing fire (seen in Fig. 3). In the 90direction, ten freefield pressure sensors (6233A, KISTLER, Switzerland) were set, and the distance between the sensors and the center of the tank were 6 m, 7 m, 8 m, 9 m, 10 m, 12 m, 15 m, 20 m, 25 m and 30 m, respectively. The natural frequency and rise time of the sensor are >300 kHz and <1 ms, respectively. The range and resolution of the sensor are 170 kPa and 0.05 kPa, respectively. 1# high-speed (FASTCAM SAZ, Photron, Japan) camera, 100 m from the center of the tank, was used to record the destruction process. Similarly, another ten free-field pressure sensors and 2# high-speed camera (MEMRECAM ACS-3, NAC, Japan) were placed at the same distance in the 180direction. The frame rate of high-speed camera is 6000 fps, and the screen resolution is 10241024 pixels. The data acquisition system (TraNET 408s, Elsys AG, Switzerland) was integrated at a distance of 70 m in the 160direction. The sampling frequency was set to 1 MHz. In the 200direction, the infrared camera (FAST M200, Telops, Canada) 200 m away was used to capture the fireball temperature. The frame rate of infrared camera is 312 Hz, and the screen resolution is 640512 pixels. It can detect a minimum temperature difference of 17 mK

The damage effects of the cylindrical tank under internal explosion were experimented when the tank was filled with bottom oil, half oil and full oil, as well as the empty tank. There were 11 test groups and the specific test items are shown in Table 1. The proportion of bottom oil is 3% of the theoretical capacity of the tank. The proportion of half and full oil are 50% and 80% of the safe capacity of the tank, respectively. Different TNT charge contents (1.8 kg, 3.5 kg and 6.2 kg) were selected as the ignition source

3. Results and discussion

3.1. Deformation and damage of storage tank

11 kinds of tank explosion tests were carried out. As shown in Fig. 4, the process is described by taking half oil (1.8 kg TNT) as an example. The tank underwent two typical stages after being ignited. In the first stage, a jet flow flame slightly larger than the tank diameter was formed at the tank roof after explosion. The tank roof was 'buried' in the flame, and the jet flow flame 'towed' by tank roof continued to rise in the initial stage. The flame at the tank roof separated from the jet flow flame at 0.67 s and rose at a speed different from that of the jet flow flame. Then the flame at the tank roof extinguished owing to the fuel burned out, while the tank roof continued to rise. The jet flow flame top developed into a 'mushroom cloud' shaped fireball. At this time, the combustion of kerosene was insufficient and the carbon black generated because the air around the fireball could not be timely supplemented. In the second stage, 'mushroom cloud' shaped fireball extinguished while the remaining smoke continued to rise. Meanwhile, the pool fire was formed in the oil container.

Under the explosion of TNT charge, the weak connection between the tank roof and wall would be destroyed first. The tank roofs were blown off in all experimental items and fell within a range of about 100 m around the remaining tank. According to the damage situation of the tank wall (bulges, holes and cracks, Fig. 5(a)), the damage forms were simply divided into three types (as shown in Figs. 5(b)e5(d)). In other words, Type I had a few bulges, holes and deformation in the tank wall (7 items, 1.8 kg and 3.5 kg TNT charges), Type II had cracks in the tank wall (3 items, 6.2 kg TNT charge), and Type III was complete disintegrated (1 item, 6.2 kg TNT charge without aluminum casing).

Due to the existence of aluminum casing, the casing fragments driven by explosion energy penetrated or impacted the tank wall which resulted in many holes and bulges. The holes and bulges were concentrated around the middle line of the tank wall. When the tank was empty, there would be a varying number of holes in the tank base while there were no such holes in the tank containing kerosene. There were no holes or bulges in the tank wall when the tank was without aluminum casing or in full oil. Meanwhile, the whole tank showed a little expansion and deformation.

The proportion of deformation and damage in the middle part of the tank wall are given in Table 2. The circumference of the middle part became larger with the increase of TNT charge content and oil volumes while the holes proportion showed a trend of increasing first and then decreasing. The maximum values are 40.03% and 8.77%, respectively. This was because that the larger the TNT charge content was, the larger the shock wave formed, and the more explosion products were generated. Hence, the tank was damaged more seriously in the same case. The explosion shock wave compressed kerosene in the tank, which made the tank subject to the combined influence of the shock wave and liquid expansion so the deformation increased [31]. For aluminum casing fragments, kerosene, as an inert medium, could attenuate the kinetic energy and prevent the high-speed impact on the tank wall.

Fig. 6 shows the maximum height (Hr, max) and velocity (Vmax) of tank roofs during the rise process. When the oil volumes were equal, Hr, max and Vmax both showed an increasing trend with the increase of TNT charge content. Hr, max and Vmax were positively increased as the oil volume increased from empty to half oil, but decreased in full oil. The maximum Hr, max and Vmax values were 200.08 m and 171.64 m/s, respectively, which was in the half oil6.2 kg item (Group 10). The roofs fell within 100 m of the remaining tank because of the wind in the field. Therefore, within a range of 100 m when the storage tank explodes, it is considered a hazardous area for fragments. The spacing between storage tanks should be fully considered during the construction.

The total energy generated by the explosion of TNT charge and kerosene vapor was divided into three parts [36,37], that is (1) the energy for the deformation and expansion of tank wall including the rise of tank roof; (2) the energy for the dispersion and ignition of kerosene liquid; (3) the energy for the generation and sustaining of shock wave. There was a weakly connected structure between tank roof and wall, which could be destroyed firstly. The tank roof obtained the initial kinetic energy in the explosion process, and the greater the TNT charge content was, the larger the initial kinetic energy it obtained. In bottom and half oil items, part of kerosene was transformed into cloud and mist owing to the explosion impact, which would prolong the duration of the explosion impact on the tank roof. And the other part of kerosene formed jet flow which played a certain driving role on the tank roof [38]. However, in full oil item, the TNT charge was placed under the oil-air interface. The formation of 'water plume' would consume much more energy [24], so the energy allocated to the tank roof was reduced.

3.2. Distribution law of free field pressure

The pressure-time curves of empty tank explosion for different measuring points are given in Fig. 7. In the test with aluminum casing, the casing quickly melted and formed liquid droplets after TNT exploded, which impacted the tank wall at high speed and left holes (described in subsection 3.1). At this time, the shock wave reached the nearby measuring point through the hole, and the first peak pressure (Pfir) formed. The peak pressure is absolute pressure which means the absolute value exceeding atmospheric pressure. Then the tank roof was destroyed, and the subsequent shock wave reached the same measuring point, which could form the second peak pressure (Psec). As the distance increased, the shock wave attenuated rapidly, and the far measuring point had almost only one peak pressure. The largest pressure value (Pfir or Psec) at the measuring point was defined as the maximum peak pressure (Pmax).

Shock wave damage criteria mainly includes overpressure criteria, impulse criteria and overpressure-impulse criteria [39]. In this paper, the damage radius of explosion shock wave was defined based on the damage to personnel caused by overpressure criteria (as shown in Table 3).

Fig. 8 presents the Pmax values of the empty tank at the different measuring points under various TNT charge content. Firstly, the Pmax values with aluminum casing were compared. When the distance of measuring point was equal, the Pmax values of Group 1 to Group 3 were as follows: 1.8 kg < 3.5 kg < 6.2 kg. The Pmax values of Group 3 were obviously larger than those of Group 1 and Group 2, and the Pmax values of Group 1 and Group 2 were similar. Pmax decreased gradually as increasing the distance of the measuring points, and the personal safety overpressure radius of Group 1e3 was 8 m, 9 m and 20 m, respectively. Then the difference of Pmax values with/without aluminum casing was compared. When R ¼ 6 m, there was a difference of 14.3 kPa between Pmax of Group 3 in the 90and 180directions, and that of Group 4 was 32.0 kPa. Pmax of Group 3 was bigger than or equal to those of Group 4 except for the value in the 90direction when R ¼ 6 m. The personal safety overpressure radius in Group 4 was 15 m.

The differences in the above phenomena were attributable to the different damage types of storage tanks. The whole tank wall of Group 1 and Group 2 was relatively complete, where only some holes appearred (Type I). The pressure was basically bounded inside the tank, and then released from the top. Group 3 was Type II. Two long cracks appeared on the tank wall, which were located in the 0and 270direction, respectively. The cracks in the 0direction were larger, so the initial shock wave mainly ejected from these cracks. Group 4 was Type III. The tank was torn in the 0direction, and the pressure was mainly discharged in the range of 2700e90. As a result, the impact in the 90direction was much higher than that in the 180direction.

The economic losses caused by the explosion accidents when the oil tank was filled with oil would be greater, and problems such as insufficient energy supply would also occur [6]. Therefore, the damage effects of tank with different oil volumes were investigated, and the results are given in Fig. 9. Pmax dropped as the TNT charge content decreased when the oil volumes were equal. As the TNT charge content was equal, Pmax of bottom oil, half oil and full oil showed the following rules: (1) when TNT charge was 1.8 kg, Pmax of bottom oil and half oil showed little difference, slightly higher than that of full oil; (2) when TNT charge was 3.5 kg or 6.2 kg, Pmax of bottom oil was basically consistent to that of half oil in the 90direction, while slightly larger in the 180direction. In the 90direction, the maximum Pmax is over 60 kPa, while it is over 50 kPa in the 180direction. The personal safety overpressure radius of bottom oil was 8 m (1.8 kg), 10 m (3.5 kg) and 20 m (6.2 kg), respectively. In half oil, the overpressure at the first measuring point (12 m, 1.8 kg and 3.5 kg TNT) was less than 19.6 kPa, and the personal safety overpressure radius (6.2 kg TNT) was 20 m. The shock wave overpressure was less than 10 kPa in full oil. The more oil volumes in the storage tank, the smaller the damage area caused by shock wave. It is meaningful to consider the oil volumes in storage tank during daily use.

When the tank contains kerosene, there would be kerosene vapor above the liquid surface. The equivalent TNT method has been widely used to convert the explosion equivalent of vapor or gas [24,40,41]. The total mass of fuel involving in the VCEs can be estimated by using the TNT equivalent method (i.e. Eq. (1)). The energy generated by VCEs can be equivalent to the energy generated by the TNT charge explosion. The empirical formula is as follows where, WTNT is the TNT equivalent of kerosene vapor per unit volume, kg/m3 ; a is the vapor equivalent coefficient, 0.04 [16,17]; Qf is the combustion heat of kerosene per unit mass, 4.3104 kJ/kg; QTNT is the explosion heat of TNT charge per unit mass, 4.5103 kJ/ kg; Wf is the mass of kerosene vapor per unit volume involved in the explosion reaction, kg/m3 ; rf is the density of kerosene vapor, 6.47 kg/m3 [42]. h is the volume fraction of kerosene vapor.

In this test, the concentration of kerosene vapor measured inside the tank ranged from 20% to 30% LEL, and the middle value (25%) was taken for the convenience of calculation. The LEL is 1.72% [43]. Taking the middle value, the volume fraction of kerosene vapor (h) is 0.43%. Thus, the WTNT value is 0.01063 kg/m3 . Therefore, the WTNT value of bottom oil, half oil and full oil is 0.091 kg, 0.057 kg and 0.033 kg, respectively.

Through explosion similarity law analysis and dimensional analysis of explosion shock wave, the functional relation of explosion overpressure can be obtained as follows

The above equation is expanded using Taylor's formula and the higher order infinite minor term is ignored [44,45]. The details can be found in Ref. [45].

where, P is the shock wave overpressure, kPa. x0, x1, x2, x3, /,xn are constants. R/W1/3 is the scaled distance (replaced by R), m/kg1/3. R is the distance between measuring point and ignition center, m. W is the equivalent TNT mass, kg. The fitting curves shown in Fig. 10 were obtained by fitting the Pmax values of the tank with oil. The shock wave fitting formulas in the 90and 180directions are as follows, and the goodness is 0.9408 and 0.9444, respectively. In addition, the R values in this work ranges from 0 to 33 m/kg1

3.3. Evolution of explosion fireball

The TNT charge was all located in the center of the tank. However, the relative positions of ignition were different due to the different oil volumes. The empty tanks contained no oil or vapor so that the TNT charges exploded in the air atmosphere. The ignition position of bottom oil could be considered in the center of kerosene vapor. The TNT charges of half oil and full oil were ignited at the oilair vapor interface and under the oil surface (inside the oil), respectively.

Fig. 11 shows the explosion processes with different oil volumes

The process was filmed by the high-speed camera simultaneously from 90to 180directions. From Fig. 11(a), after the ignition of TNT charge, the fireball was ejected from the top of the casing. The melted droplets from the casing broke through the tank wall and the flame came out. The fireball at the top got bigger as time went by, and began to move upward. The weak connection between the tank roof and wall was destroyed, and a good deal of flame spread outward. The transverse flame began to shrink as the tank roof rose, then the diameter of fireball decreased. Finally, the flame extinguished after rising to a certain height. Figs. 11(b)e11(d) indicated that the explosion process of oil-bearing tank was obviously different from that of empty tank. The flame width at the tank roof was obviously larger than that of the empty tank. This was because kerosene liquid was dispersed by the explosion shock wave and gas products. The broken oil droplets quickly mixed with the air to form aerosols and were quickly combusted. As the flame spread laterally, part of the kerosene liquid fell due to gravity, and the subsequent flame enveloped the tank, which created a 'conical' flame. Then the flame began to rise, and gathered in a huge fireball above the tank. As the oil inside the tank was continuously dispersed, the later flame developed into a jet flow flame.

Table 4 summarizes the maximum diameter (Dmax) and height of fireball (Hf, max), and Dmax means the maximum diameter when the fireball is on the ground surface in early stage. The aluminum casing would restrict the horizontal development of fireball and promoted the vertical development of fireball. Therefore, an empty tank without aluminum casing had a larger fireball diameter and a smaller fireball height. When the TNT charge content was equal, Dmax gradually increased as increasing the oil volumes. The maximum Dmax value is 19.33 ± 0.92 m for half-6.2 kg item. Compared with Dmax of empty tank (1.8 kg), Dmax of bottom oil, half oil and full oil increased by 23.98%, 35.26% and 68.27%, respectively. Dmax also showed an increase trend with larger TNT charge content for the equal oil volume. For empty, bottom and half oil tanks (1.8 kg TNT), Dmax of fireball with 6.2 kg TNT charge increased by 49.08% (empty), 64.73% (bottom) and 101.56% (half), respectively. Hf, max increased with the increase of TNT charge content and oil volumes. The maximum Hf, max value is 172.02±7.83 m for half6.2 kg item. For empty, bottom and half oil tanks (1.8 kg), Hf, max increased by 35.80% (empty), 110.37% (bottom oil) and 189.60% (half oil), respectively, when the tank was ignited by 6.2 kg TNT charge. For empty tank (1.8 kg), Hf, max of bottom oil, half oil, full oil increased 276.59%, 922.38%, 1777.62%, respectively.

Part of the total energy from TNT charge and kerosene vapor explosion was consumed to spread the kerosene liquid. The first two stages were influenced by explosion shock wave and gas products. They impacted the kerosene with a high speed and formed a reflection in the bottom oil and half oil tank. When the tank was full oil, the kerosene above the ignition point moved rapidly upward, and the kerosene below also formed a reflection, which made the jet fire column form in the axial direction after the kerosene gushed from the tank [46]. In the radial direction, the oil liquid spread rapidly in the horizontal direction. The larger the TNT charge content was, the more explosion gas products would be generated, and the larger the shock wave pressure was (Fig. 9). Therefore, the jet flow and dispersion phenomenon of kerosene liquid was much more violent under the same condition, which could make a larger jet flow velocity, flame height and diameter [47,48]. The jet flow and dispersion effects were more obvious with larger oil volumes because the oil-air surface was close to the ignition point, and the flame height and diameter were also larger in the same case.

The development of fireball temperature field with different oil volumes is illustrated in Fig. 12. At the beginning of the explosion, a small elliptic bright flame was formed on the tank roof and the flame temperature was over 1000C. This stage was mainly caused by TNT charge and kerosene vapor. As the time passed, the temperature at the bottom of the flame decreased to about 900C due to the dispersion of kerosene, while the flame temperature at the top continued to increase. The bright area in the fireball became larger because of the combustion of kerosene. And the fireball gradually developed into a banded flame area due to jet flow (seen in Figs. 12(b)e12(d)). The dispersion and jet flow effects were more obvious due to the increase of oil volume in Fig. 12(d). A phenomenon of 'expansion-contraction into bands-secondary expansion-contraction extinction' in the flame development occurred. The flame maintained a high temperature during the secondary expansion process.

Fig. 13 shows the variation of fireball temperature under typical experimental items. Owing to the TNT charge, for the empty tank, the trend of temperature rising process was similar to that of shock wave. Lots of kerosene would disperse and combust in the oilbearing tanks. In this stage, a large amount of air mixed with fuel. The abundant energy released from the kerosene combustion could keep the fireball in a relatively high temperature, which made the fireball temperature show an oscillation attenuation during the cooling process. After that, the fireball entered the free diffusion and rising stage, and the energy spread around. Finally, the fireball temperature gradually dropped.

The temperature parameters of fireball are listed in Table 5. Tmax represented the highest temperature of the fireball, Tave represented the average surface temperature of the fireball when it reached the highest temperature, and Dt represented the duration of the fireball surface temperature over 1000C. Due to the oscillation phenomenon of the fireball temperature (Fig. 13), sever high temperature intervals (i.e., Dt1 and Dt2, Dt ¼ Dt1þDt2) appeared in some test items. Tmax had no obvious linear relationship with the TNT charge content, as well as the oil volumes, while Tave increased as increasing the TNT charge content and decreased as increasing the oil volumes. The dispersion of kerosene would coat the fireball of TNT explosion. The fireball temperature decreased as the oil volumes increased. The duration of flame temperature (Dt, over 1000C) showed an increase trend as increasing the TNT content and oil volumes. For the oil-bearing items, two high temperature intervals appeared in bottom oil (3.5 kg), half oil (3.5 kg) and full oil (1.8 kg), while only one high temperature interval appeared in the rest. The jet flow height was increased due to the large TNT charge content in bottom oil (3.5 kg) and half oil (3.5 kg) while the abundant kerosene volumes in full oil (1.8 kg). All these reasons caused the flame to have a secondary expansion phenomenon, therefore, two high temperature intervals appeared in this test items. For bottom oil (6.2 kg) and half oil (6.2 kg) items, there were cracks on the tank wall (Type II). The kerosene ejected from the cracks, so that it only presented a whole high temperature interval.

The thermal radiation intensity of fireball reflects the explosion degree and is an important index for evaluating the explosion risk of liquid fuel. Personnel and surrounding objects would suffer from different degrees of damage when exposed to the thermal radiation of fireball with a certain intensity. As shown in Table 6, the heat flux is used as a criterion for judgment on personnel injury to discuss the thermal radiation hazards in the tank explosion process [49,50]. The heat flux of the universal fireball model could be calculated by Baker's empirical formula [49]

where, q is the heat flux, kW/m2 ; G is a transmission coefficient, 9.58108 ; D is the fireball diameter, m; L is the distance from the fireball surface, m; F is also a transmission coefficient, 161.7; T is the fireball temperature, K

The bottom oil-6.2 kg TNT item was taken as the example to calculate the heat flux, where D was 14.48 m and Tave was 1499.84 K. As shown in Fig. 14, the q-L curve was obtained based on Eq. (5), and the heat flux damage radius diagram was drawn at the same time. The q values decreased rapidly with the increase of target distance. The radius that would cause personal death was 7.00 m, and the personal safety radius was 19.79 m. Similarly, the personal death and safety radius values of typical items could be obtained, as shown in Table 7. The maximum possible death radius in the test was 8.97 m and the maximum safety radius was 25.40 m. As increasing the TNT charge content, the possible death radius increased. The tank with kerosene had the advantage over the empty tank in thermal radiation damage. However, the linear relationship between death radius and oil volumes were not strong. The oil volume must be considered during daily use to reduce the thermal radiation damage.

4. Conclusions

In this paper, an 8 m3 tank was manufactured by taking a 1000 m3 tank as the model according to the 1:5 shrinkage ratio. Meanwhile, aviation kerosene was used as the medium to study the damage effects of 8 m3 fixed-roof tanks under the impact of TNT charges. The tests were carried out in 11 groups, including different TNT charge content (1.8 kg, 3.5 kg, 6.2 kg) and different oil volumes (empty, bottom oil, half oil, full oil). The influences of the above variables were discussed. The tank damage types were defined, the explosion pressure field was constructed and the influence area of fireball thermal radiation was analyzed. The main conclusions are drawn as follows.

(1) The tank explosion process was mainly divided into tank roof 'towed' flame, jet flow flame tumbling and rising, jet flow flame extinguishing and pool fire stages. According to the bulges, holes and cracks on the tank wall, the tank was divided into three damage types (Type I, Type II and Type III). All the items included seven groups in Type I (Group 1, 2, 5, 6, 8, 9, 11), three groups in Type II (Group 3, 7, 10) and only one group in Type III (Group 4). The deformation in the middle of the tank wall, Hr, max and Vmax, showed a linear relationship with TNT charge content. And the maximum deformation was 40.03% and 8.77%, respectively. However, as the oil volumes increased, the hole ratio, Hr, max and Vmax presented an increase first and then decrease trend. The maximum values of Hr, max and Vmax were 200.08 m and 171.64 m/s, respectively.

(2) Pmax increased with the increase of TNT charge content, and decreased with the increase of the distance of the measuring point. The linear dependence of Pmax on oil volumes was not strong. Overall speaking, the Pmax values of bottom oil and half oil were similar, and Pmax of full oil was slightly smaller. The maximum values of Pmax were over 60 kPa and 50 kPa in the 90and 180directions. The damage type affected the release direction and magnitude of shock wave. In all groups, the minimum and maximum personal safety overpressure radius were 8 m and 20 m, respectively. The shock wave attenuation formulas in the 90and 180directions were obtained, and the overpressure value (P) is positively correlated with the reciprocal of the scaled distance (R) as shown in Eqs. (4) and (5).

(3) Dmax and Hf, max of fireball showed a positively correlated relationship with the TNT charge content and oil volumes. The fireball without an aluminum casing had larger Dmax value and smaller Hf, max value in comparison to those with the casing. The maximum values of Dmax and Hf, max were 19.33 ± 0.92 m and 172.02 ± 7.83 m, respectively. The temperature rising stage presented a sharp increase phenomenon, while the cooling process showed an oscillation attenuation phenomenon. Tave expressed a positive correlation with the TNT charge content and a negative correlation with the oil volumes, while Tmax showed no obvious relationship with these factors. The maximum values of Tmax and Tave were 1567.97C and 1197.56C, respectively. The duration of high temperature flame was positively correlated with the TNT charge content and oil volumes. In all of the test items, the maximum possible death radius and safety radius was 8.97 m and 25.40 m, respectively.

In the construction and storage process of aviation kerosene storage tanks, it is necessary to comprehensively consider the spacing between tanks and the oil volumes in the tank to reduce the explosion hazards.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

The work was supported by National Natural Science Foundation of China Innovation Group (Grant No. 12221002) and Beijing Natural Science Foundation (Grant No. L212018)

Appendix A. Supplementary data

Supplementary data to this article can be found online at https://doi.org/10.1016/j.dt.2023.12.009.

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ARTICLE INFO

Article history:

Received 24 October 2023

Received in revised form

10 December 2023

Accepted 17 December 2023

Available online 22 December 2023

Peer review under responsibility of China Ordnance Society

Footnote

* Corresponding author.

E-mail address: [email protected] (C. Wang).

References

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