The fuel supply system of a cartridge-type kerosene heater is shown in Figure 1. When the fuel level in the auxiliary tank drops below the level of the fuel tank cap, air enters the tank through the cap and fuel flows from the cartridge-type fuel tank (hereinafter referred to as "cartridge tank") into the auxiliary tank through the saucer. The air inflow into the tank stops when the fuel level in the auxiliary tank rises to the height of the fuel tank cap. This ensures that the fuel level in the auxiliary tank is kept at a constant level. When a kerosene heater is mistakenly refueled with gasoline, it is usually empty before the refueling. The high vapor pressure of the misfueled gasoline causes a volumetric expansion of the cartridge tank vapor phase section. This results in the fuel being pushed out of the cartridge tank, causing the fuel level in the auxiliary tank to rise and the fuel to overflow, which causes the overflowing fuel to ignite and start a fire. Figure 2 shows a simplified diagram of the relationship between the fuel and the auxiliary tanks in the case of misfueling the cartridge tank with gasoline.

After a cartridge tank misfueled with gasoline was loaded into an experimental kerosene heater and the heater was ignited, combustion began. The temperature of both the kerosene heater body and the room increased, and the temperature of the gasoline in the cartridge tank also increased. This increased the vapor pressure of the gasoline (p_f0 →p_f), which resulted in an expansion of the air in the cartridge tank (V₀ →V), thereby reducing the partial pressure of the air. The following equation holds true owing to the equilibrium of the pressures inside and outside the cartridge tank:

V₀ is the volume of the gas-phase section [L] before the heater ignition and V₁ is the volume of the gas-phase section [L] when it is saturated with fuel vapor. Additionally, p_atm is the atmospheric pressure [Pa], p_air is the partial air pressure in the cartridge tank [Pa], p_g is the partial pressure of gasoline vapor in the cartridge tank [Pa], T is the gasoline temperature in the tank [K], ρ is the gasoline density (720 kg/m³), g is the acceleration due to gravity (9.8 m/s²), h is the difference in the height of the fuel surface between the cartridge tank and the auxiliary tank [m], and the subscript 0 indicates the state before the heater ignition. The unscripted variables V, p_air, p_f, and T are the variables after the heater ignition. Because the difference in the height of the fuel level is usually several tens of centimeters and the differential pressure ρgh is negligible with respect to the partial pressure of air and gasoline, Eq. (1) can be approximated as follows:

If the change in temperature at this time is T₀ →T, the partial pressure of the air can be expressed by Boyle-Charles’ law as follows:

From Eqs. (2) and (3), the volume expansion rate V /V₀ due to gasoline misfueling is

Eq. (4) shows that the rate of volumetric expansion V /V₀ of the gas-phase section in the cartridge tank due to the increase in temperature during kerosene heater use is determined only by the vapor pressure p_f of the fuel and temperature T. In other words, if the initial volume V₀ is known, the amount of fuel that is pushed into the auxiliary tank by the expansion of the gas-phase section can be calculated from the temperature-vapor pressure characteristics of the fuel. Based on these assumptions, the gasoline temperature at which fuel overflow occurs can be predicted if the initial fuel volume V'_refuel and the capacity V'_full of the auxiliary tank are measured in advance.

The relationship between the gasoline vapor pressure and temperature can be described expressed by the Clausius-Clapeyron equation[12,13].

where A and B are Clausius-Clapeyron constants.

The preliminary measurements taken prior to the kerosene heater fire experiment confirmed that the auxiliary tank of the kerosene heater had a capacity that slightly exceeded 1.0 L and that the auxiliary tank of the kerosene heater held approximately 0.18 L of kerosene during normal combustion. From these values, the amount of fuel required to generate the overflow from the auxiliary tank was calculated to be approximately 0.84 L. Additionally, the actual maximal measured capacity of the cartridge tank, which was 4.0 L according to the specifications, was found to be slightly higher than 4.4 L. Table 1 shows the data for the measurements.

Experiments on kerosene heater fires, which occur owing to misfueling with gasoline, were conducted based on the fire mechanism resulting from overflowing fuel described in the previous section. A radiant-type heater with a wick was used. As shown in the previous section, the amount of gasoline expansion from the time the tank was loaded into the main unit until the time the fuel overflow occurred was 840 mL. Therefore, the temperature at which the fuel overflow would occur was predicted from the initial ambient temperature at the start of the experiment using Eqs. (4) and (5). The Clausius-Clapeyron constants A and B for the test gasoline were derived from the measured saturated vapor pressures of gasoline at 20.8 and 2973, respectively. The gasoline temperature that would be required to generate fuel overflow was predicted to be at least 20 °C (Table 2).

Because the kerosene heater was ignited in the fire test laboratory (dimensions: 15 m × 15 m × 15 m) at the National Research Institute of Police Science and the gasoline temperature could not be expected to rise due to the spacious laboratory in all fire experiments, 180 mL of kerosene was poured into an empty auxiliary tank (remaining volume in auxiliary tank at normal refueling shown in Table 1) and 830 mL of gasoline was added to reconstruct the condition of fuel on the verge of overflow, and the remaining gasoline was kept in a cartridge tank (Table 3). In the experiment, a cartridge tank filled with gasoline was set on a kerosene heater. Kerosene heaters used for experiments featured an automatic ignition system. As specified in the owner's manual, after turning the wick adjuster knob clockwise until the wick has been raised to its maximum height, the experiment began with pushing the ignition button to bring the glowing igniter into contact with the wick. During the experiment, the kerosene heater was placed on a load cell to measure its weight loss during the fuel overflow fire (Figure 3). The kerosene heater fire experiments were carried out for four patterns of gasoline misfueling volume: 1.0, 1.5, 2.0, and 3.0 L.

During the kerosene heater fire experiment, fires caused by the overflow of fuel occurred, except for the experimental scenario with 1.0 L gasoline misfueled. The fact that fire did not occur in this case was considered to be because the amount of gasoline remaining in the cartridge tank was as little as 170 mL, which did not cause the fuel to overflow, or because the overflow was extremely small and was inadequate to induce fire. Furthermore, through these experiments, it was found that setting the heater’s power using the wick adjuster knob tended to be less likely to cause fuel overflow fires at a high setting and more likely to cause fuel overflow fires at a low setting. This was considered to be because the amount of fuel consumed by combustion was relatively high at a high setting, and the amount of gasoline pushed out of the cartridge tank was consumed by combustion, thereby reducing the probability of fuel overflow. Therefore, the heater's power of all experimental scenarios was set at a low using the wick adjuster knob.

Using the load cell data from the kerosene heater fire experiments described in the previous section, we developed the initial fire source models for the three patterns of gasoline misfueling (1.5 L, 2.0 L, and 3.0 L), in each of which an overflowing fuel fire occurred. Figures 4-6 show for each pattern, the weight loss that occurred during the heater fire experiments after fire caused by fuel overflow occurred and the heat release rate (HRR) calculated assuming the heat of combustion of gasoline to be 44.1 MJ/kg[15]. These figures show that heat release rate peaks around 2 min after fuel overflow fire started, and then gradually decreases for all the patterns.

Part of a house was constructed by professional builders in the fire test laboratory at the National Research Institute of Police Science. The house was constructed in a typical Japanese style, and it comprised two rooms and a corridor with wooden floorboards and pillars, and gypsum board walls and ceilings covered with wallpaper. Figures 7 and 8 show the floor plan and three-dimensional drawing of the experimental house.

A new kerosene heater similar to that shown in Figure 3 was used as the fire source in the house fire experiment. The volume of misfueled gasoline was set to 3.0 L. Because the room temperature at the time of the experiment was 21.7 °C, a fuel overflow temperature of 32.4 °C was required by kerosene heater ignition in the fire test laboratory, as predicted by Eqs. (4) and (5). After 0.18 L of kerosene was poured into the empty auxiliary tank, an additional 0.7 L of gasoline was poured into the auxiliary tank to shorten the time until fuel overflow occurred after the kerosene heater was ignited. The volume of gasoline was set to 0.7 L, slightly smaller than 0.83 L, to avoid fuel overflow while preparing the experiment in the house. Furthermore, in order to be consistent with a real fire case in winter, the experiment was conducted with gasoline in the cartridge tank cooled to 1.1 °C with ice water. The experiment was begun with 2.3 L (3.0 L minus 0.7 L) as the volume of misfueled gasoline in the cartridge tank. After turning the wick adjuster knob clockwise until the wick was raised to its maximum height, the ignition button was pushed to bring the glowing igniter into contact with the wick, and the heater’s power was adjusted to low using the wick adjuster knob.

Gasoline overflow from the auxiliary tank was observed 290 s after the ignition of the kerosene heater. As shown in Figure 9, because flames rose from the kerosene heater 295 s after ignition, this time was designated as the start of the house fire experiment (t = 0 s). Flames reached the ceiling at t = 75 s, and the ignition room flashed over at t = 110 s. The flames spread the corridor and burst out from the opening of the corridor at t = 125 s. The windows began to crack in several places, and new openings were created at t = 158, 185, 220, 228, and 252 s. Flames entered the fire-spreading room through the Fusuma on the corridor side at t = 221 s. Additionally, the fire-spreading room flashed over at t = 255 s, which was immediately followed by the flames bursting out from the opening of the fire-spreading room. Because the intense fire continued owing to the formation of these multiple openings, the fire was extinguished by spraying water at t = 400 s and the fire experiment was then terminated.

A house fire simulation was conducted using FDS Ver. 5.4.3. The dimensions of the computational domain for the simulation were 5.5 m × 7.4 m × 4.0 m, which included the house and its surroundings, as shown in Figure 10. Considering the accuracy and computing time, cubic grids having a side length of 10 cm were used in the simulation. In the FDS input file, the domain was divided into grids of 162,800 cells. Initial opening configurations and all material settings including "Fusuma" and wallpaper in the simulation were set exactly the same as in the full-scale house fire experiment. For the initial calculations, both windows were considered to be closed, and openings were set up in the corridor and in the fire-spreading room, as shown in Figure 11. The boundary between the ignition room and the corridor was initially open. The boundary between the ignition room and the fire-spreading room and that between the corridor and the fire-spreading room were each closed using "Fusuma" (sliding doors). Several pieces of furniture were placed inside the two rooms, the same as in the fire experiment. The ambient temperature at the beginning of the simulation was 21.7 °C, which was the same as the temperature at the start of the fire experiment. The air inflow and outflow at the boundary of the computational domain were set to open-air conditions, except at the bottom. When the kerosene heater was misfueled with 3.0 L of gasoline, the fire origin of the fuel overflow fire was represented using the initial fire source model (Figure 6(b)) on a 50 cm × 30 cm metal surface similar in size to the kerosene heater. During the fire experiment, the window glass broke and collapsed; therefore, in the simulation, new openings were set to create at the same locations and at the same times as in the experiment. The set opening times and locations of the windows are presented in Table 4 and Figure 12.

The simulation results show the following fire behavior, as shown in Figure 13. The start time of the kerosene heater fire was set to t = 0 s. The heater flames spread to the adjacent wooden bookshelf, and flames reached the ceiling at t = 77 s. The flammable gases accumulated in the ignition room burned rapidly, and flashover occurred at t = 103 s. Subsequently, the flames spread to the corridor because of the lack of oxygen in the ignition room at t = 106 s, and they burst out from the opening of the corridor. Flames burst out from the window on the ignition room side owing to glass breakage at t = 159 s. At t = 216 s, the Fusuma, a sliding door on the corridor side, burned away and flames entered the fire-spreading room from the corridor. At t = 222 s, flames burst out from the opening of the fire-spreading room. At t = 253 s, all the windows were broken, and the entire house was engulfed in flames. At approximately t = 485 s, the ignition room burned again. At approximately t = 650 s, the fire size began to gradually decrease. At approximately t = 800 s, the fire spontaneously extinguished, and most of the floorboards had been burned away, except for the areas where furniture had been installed.

A comparison between the house fire experiment and the simulation in terms of fire behavior showed that the behavior of the flames was generally reconstructed. Some time differences could be observed in the scene where the flame contacted the ceiling (Figures 9(c) and 13(a)), the scene where the ignition room flashed over (Figures 9(d) and 13(b)), and the scene where flames burst out from the opening of the fire-spreading room (Figures 9(g) and 13(f)). Notably, the simulation reconstructed the scene in which the flames entered the fire-spreading room from the corridor side through the Fusuma sliding door instead of from the ignition room side (Figures 9(f) and 13(e)), as confirmed by the experimental video taken from the side of the fire-spreading room. Additionally, the simulation offered many advantages, such as the ability to study scenes that were difficult to observe in the fire experiment owing to smoke (Figure 13(c)), and cases in which the experimental fire had to be extinguished for the safety of the fire test laboratory (Figures 13(h)-13(j)). Another advantage of the simulation is that it can be used to carry out similar studies under different conditions. The simulation conducted with the fire source setting changed to 1.5 L of misfueled gasoline (Figure 5(b)) confirmed that the fire would propagate to the house as well, although each of the fire behaviors was delayed by ten to several tens of seconds.

One possible reason that the flames burst out from the two openings in the corridor and the fire-spreading room earlier in the simulation than in the experiment was considered to be the limitation of the FDS, where flammable gases spontaneously ignite without a fire source when they meet with fresh air (oxygen) near the openings.