Numerical Simulation of Flow and Flame Dynamics of a Pool Fire Under Combined Effects of Wind and Slope

Abstract

Wind has a significant effect on pool fire behavior, which is relevant to many fire conditions, such as wildfires, building fires, and oil transportation fires. Although fire behavior and morphology changes have received considerable attention and been widely researched, there are few works concerning the flow and flam dynamics of pool fire. A large eddy simulation model is adopted to investigate the flow and flame dynamics of a rectangular pool fire considering the combined effects of wind and slope. The results show that, with a wind speed of 0.5 m/s, a flame develops immediately downstream of the fire source and sustains two flanks of plume. Further downstream, the plume starts to rise due to buoyant force. Temperature, velocity, and vorticity distributions show significantly different shapes at different streamwise locations. Near the fire source, the flame is confined to a small region around the fire source. The air circulation downstream shows a cylindrical spiring pattern. When the wind speed increases, the temperature and velocity become more parallel to the surface and their maximum values increase. On the contrary, the temperature fluctuations and turbulent kinetic energy decrease with the wind speed, and they are more frequent near the flame tails.

1. Introduction

Pool fire in the presence of wind presents a complex and significant challenge in terms of fire safety, environmental impact assessment, and combustion research [1]. It is common in forest fires [2], building fires, and chemical engineering [3,4,5]. When subjected to wind, the fire’s behavior changes markedly, with wind-driven effects influencing the flame shape, heat transfer, and combustion efficiency [6]. These interactions increase the fire’s unpredictability, leading to enhanced flame tilt, increased thermal radiation [7,8] in downwind directions, and potentially more rapid spreading [9]. Understanding the dynamics of pool fires under wind conditions is crucial in accurately predicting fire hazards in industrial settings, mitigating risks in oil and gas operations, and developing more effective firefighting strategies. Moreover, studying the wind’s impact on pool fires contributes to broader research in atmospheric effects on combustion processes and pollutant dispersion, which has implications for environmental and safety regulations [10,11].

Pool fire characteristics have been investigated by many researchers. Lin et al. [12] performed an experimental study on flame geometry in pool fires in wind conditions, and determined the variations in flame length, flame height, flame tilt, and flame drag with wind speed and heat release rate. They also proposed correlation laws for these variables based on dimensional analysis. Lin et al. also [13] analyzed pool fire behaviors when the pool fire was placed on a slope and found that the slope reduced the area for air entrainment and introduced negative pressure, leading to a greater flame height. Huang et al. [14] investigated the thermal properties of a line fire under cross wind and found that the gas temperature and radiative heat flux decreased as they moved downstream, and they proposed a revised predictive model for radiative heat flux. Several authors have also investigated the effect of slope. Liu et al. [15] examined the flame shape in pool fire for different aspect ratios under slope conditions and found that the flame length, flame height, and flame tilt angle decreased with the aspect ratio; the flame height and flame tilt angle also decreased with the slope angle, but the flame length increased with the slope angle. Correlations for the flame shapes under different aspect ratios and slope angles were developed. Bi et al. investigated the coupling effect of wind and slope on the flame shape of pool fires and concluded that slope and wind had an antagonistic effect on the flame tilt angle, the synergistic effect on the flame height and attachment length, and the synergistic effect on the flame length when the wind speed was larger than 0.25 m/s. Li et al. [16] analyzed the flow characteristics around two pool fires with wind and found that a counter-rotating vortex pair could be generated downstream of the fire sources. There are also many works investigating flame and heat transfer for pool fire on a slope, such as those by Wu et al. [17], Zhang et al. [18], Ju et al. [19], and Ren et al. [20], to name just a few.

From the above literature review, it can be seen that many researchers have performed excellent work on the flame shape and heat flux for pool fires under wind and slope conditions and have developed rich theories and knowledge on flame morphology and heat transfer. However, there are few works focusing on the flow dynamics or flame dynamics of pool fires. To close this gap, this work aims to investigate the flow and flame dynamics of a rectangular pool fire under the effects of wind and slope by using large-eddy simulation based on the OpenFOAM framework.

2. Numerical Models

2.1. Governing Equations

The combustion process can be simulated by the following mass, momentum, species, and enthalpy equations:

$${\displaystyle \frac{\partial \overline{\rho }}{\partial t}}+{\displaystyle \frac{\partial \overline{\rho }{\tilde{u}}_i}{\partial x_i}}=0$$

(1)

$${\displaystyle \frac{\partial \overline{\rho }}{\partial t}}+{\displaystyle \frac{\partial \overline{\rho }{\tilde{u}}_i{\tilde{u}}_j}{\partial x_i}}=-{\displaystyle \frac{\partial \overline{p}}{\partial x_j}}+{\displaystyle \frac{\partial }{\partial x_i}}\left(\left(\tilde{\mu }+{\mu }_t\right){\tilde{S}}_{ij}\right)+\overline{\rho }g$$

(2)

$${\displaystyle \frac{\partial \overline{\rho }{\tilde{Y}}_k}{\partial t}}+{\displaystyle \frac{\partial \overline{\rho }{\tilde{u}}_i{\tilde{Y}}_k}{\partial x_i}}={\displaystyle \frac{\partial }{\partial x_i}}\left(\overline{\rho }\left(D_k+{\displaystyle \frac{{\nu }_{sgs}}{S{c}_t}}\right){\displaystyle \frac{\partial {\tilde{Y}}_k}{\partial x_i}}\right)+\overline{{\dot{{\omega }^{‴}}}_k}$$

(3)

$${\displaystyle \frac{\partial \overline{\rho }\tilde{h}}{\partial t}}+{\displaystyle \frac{\partial \overline{\rho }{\tilde{u}}_i\tilde{h}}{\partial x_i}}={\displaystyle \frac{\partial }{\partial x_i}}\left(\overline{\rho }\left(D_{th}+{\displaystyle \frac{{\nu }_{sgs}}{{\mathrm{Pr}}_t}}\right){\displaystyle \frac{\partial \tilde{h}}{\partial x_i}}\right)-\overline{\nabla \cdot q_R}+\overline{{\dot{q}}_c}$$

(4)

where the bar denotes the density-based variable while the tilde denotes the Favre-based variable. $\overline{\rho }$ is the density, $\tilde{u}$ is the velocity, $\overline{p}$ is the pressure, $\tilde{\mu }$ is the dynamic viscosity, ${\mu }_t$ is the turbulent viscosity, ${\tilde{S}}_{ij}$ is the shear stress, g is the gravitational force, ${\tilde{Y}}_k$ is the mass fraction of specie k, $D_k$ is the mass diffusion coefficient, $S{c}_t$ is the turbulent Schmitt number, ${\nu }_{sgs}$ is the sub-grid scale viscosity, $\overline{{\dot{{\omega }^{‴}}}_k}$ is the chemical reaction rate, $\tilde{h}$ is the enthalpy, $D_{th}$ is the thermal diffusion coefficient, ${\mathrm{Pr}}_t$ is the turbulent Prandtl number, and $\overline{\nabla \cdot q_R}$ is the radiative heat source. The Lewis number is assumed to be unity.

The one-eddy kinetic equation is applied to solve the turbulent kinetic energy transport equation:

$${\displaystyle \frac{\partial \left(\overline{\rho }{k}_{sgs}\right)}{\partial t}}+\nabla \cdot \left(\overline{\rho }\tilde{u}{k}_{sgs}\right)=\nabla \cdot \left(\left(\mu +{\mu }_t\right)\nabla k_{sgs}\right)+P-\overline{\rho }{\epsilon }_{sgs}$$

(5)

where $k_{sks}$ is the sub-grid scale kinetic energy, ${\epsilon }_{sgs}$ is the eddy dissipation rate, P is the production rate, and ${\mu }_t$ is the turbulent viscosity:

$${\mu }_t=\overline{\rho }{c}_k\Delta \sqrt{k_{sks}}$$

(6)

where c_k is the LES constant.

The eddy dissipation model was adopted to obtain the chemical reaction rate, as follows:

$$\overline{{\dot{{\omega }^{‴}}}_F}=\overline{\rho }{C}_{DEM}{\displaystyle \frac{{\epsilon }_{sgs}}{k_{sgs}}}\min \left({\tilde{Y}}_F,{\displaystyle \frac{{\tilde{Y}}_{O_2}}{s}}\right)$$

(7)

where C_DEM is the model constant. The one-step infinite fast reaction mechanism is used for methanol combustion.

The radiation heat transfer is solved by the radiative transfer equation and a gray gas model, as follows:

$${\displaystyle \frac{\partial I}{\partial s}}=\kappa I_b+\kappa I$$

(8)

where $\kappa$ is the absorption coefficient and I is the radiative intensity.

2.2. Numerical Schemes

Figure 1 shows the computational model. A previously validated model [5] is used to model the physical process. The computational domain consists of four types of surface: the fuel surface is an inlet through which methane vapor enters the domain; the top surface and side surface are open boundaries, which allow air entrainment and outflow. The slope surface is set as a non-slip wall. The inclination angle is defined as $\alpha$, which is fixed as $10°$ in this work. The inlet velocity of fuel is set as 0.1 m/s, with its temperature being 298.15 K; methane is used as the fuel. The bottom wall is assigned the non-slip condition, and a typical wall boundary condition is used for the velocity to satisfy the law of walls, which is achieved by the nutkRoughWallFunction in OpenFOAM framework. The out surface is assigned an outflow boundary condition, with a zero-gradient imposed for all variables. For the inlet boundary, a fixed-value boundary condition with a typical power-law velocity profile of $U_{\mathrm{ref}}\cdot {\left(y/6\right)}^{0.16}$ is used, where $U_{\mathrm{ref}}$ is the inlet wind speed (which is varied). The boundary condition key values can be found in

Table 1. Boundary conditions.

Variable	Slope	Fuel	Side	Top	Out	Inlet
CH4	zeroGradient	totalFlowRateAdvectiveDiffusive	inletOutlet	inletOutlet	inletOutlet	inletOutlet
T	zeroGradient	fixedValue	inletOutlet	inletOutlet	inletOutlet	inletOutlet
U	noSlip	fixedValue	slip	pressureInletOutletVelocity	inletOutlet	fixedValue power-law
p	calculated	calculated	calculated	calculated	calculated	calculated
p_rgh	fixedFluxPressure	fixedFluxPressure	fixedFluxPressure	prghTotalHydrostaticPressure	fixedFluxPressure	fixedFluxPressure

. The computational domain size is 3-2-3 m streamwise, vertical, and spanwise, while the length and width of the fuel are 0.2 m and 0.1 m. The computational mesh consists of 1.28 million hexahedral cells and is refined near the fuel inlet and the flame regions, as shown in the right figure. The cell size near the inlet is 3–5 mm, which is large enough to capture variations in temperature. Numerical schemes are shown in

Table 2. Numerical schemes.

Name	Discretization Method	Key Words in OpenFOAM
Time	First-order implicit	Euler
Advection–velocity	Upwind	Gauss linear LUST grad (U)
Advection–scalars	TVD	Gauss limitedLinear01
Diffusion	Gaussian integration	Gauss linear uncorrected
Pressure–velocity coupling	PIMPLE	PIMPLE

.

3. Results and Discussion

3.1. Transient Temperature and Vortex Structure

Figure 2 shows the transient temperature and Q-criterion contours for U_ref = 0.5 m/s. This is a typical representation of the temperature distribution and vortex structure during fire burning. The maximum temperature for this condition is about 1600 K, which is lower than that of the no-wind condition. A high temperature is observed around the fire source, and the flame is significantly inclined in a downstream direction due to the combined effect of the slope and wind. Further downstream, the gas temperature is lower due to the expansion of the hot gas product and mixing with environmental fresh air. Two streaks with a higher temperature exist near the rear edge of the fire source, which can also be seen in the Q-criterion contour. Hairpin vortexes originate from the fire source due to jet and wind interaction and are then enhanced by the Kelvin–Helmholtz instability between the wind and fire flows. Iso-contours of a Q-criterion larger than 20 s⁻¹ are shown with overlaid color by velocity magnitude, of which the maximum is around 4.41 m/s, much larger than the incoming velocity. The fire-induced velocity is more intense downstream and is weak near the fire source. As the fire products are advected downstream, it is also lifted higher due to buoyant force. A larger and higher hairpin vortex can be observed near the outlet, although with weaker vorticity (a smaller Q-criterion value).

To further demonstrate the flow and flame characteristics, Figure 3 presents the CH₄, temperature, velocity magnitude, and x component of vorticity (denoted as vorticity x hereafter) along spanwise cross-sections at two streamwise locations. X = 0.9 m is near the rear edge of the fire source, and X = 1.5 m is downstream of the fire source.

Vorticity x represents the flow rotation along the streamwise direction and can reveal the flame and air interaction at the spanwise plane. At X = 0.9 m, methane flows into the domain at a low velocity (0.1 m/s) and thus cannot penetrate to higher locations. Part of the methane, especially around the periphery of the fuel vapor, will mix with air and then start to burn, which can be proven by the second figure in the left column. The temperature is only high outside of the fuel vapor due to the lack of oxygen in the interior part of the fuel vapor. Under the effect of buoyant force, high temperature gases (mainly water vapor and carbon dioxide) start to accelerate and move downstream and upward. However, the large velocity here (the maximum is 1.9 m/s) is not solely caused by the buoyant force at this location but is also partially pushed by the air flowing from upstream. During fuel combustion, air entrains at two flanks in the fuel region. With Y = 0.9 m, for example, there is one positive vorticity x region and there are two negative vorticity regions. The positive vorticity x region corresponds to the air supply to the fuel region from the adjacent environment when the fuel is burned and blown away. The former is stronger than the fuel vapor inflow because the fire flow leaves at a higher rate. The upper negative vorticity x is induced by the same factor except that the air supply occurs at the top side. The lower negative vorticity x is caused by the velocity gradient near the bottom surface, where the air supply also dominates.

At X = 1.5 m, all the variables show significantly different distributions compared to 0.9 m. For the methane concentration, it looks like an upside-down triangle, with larger values at higher locations and lower values at two flanks. The methane here is advected from the fire source by the environmental and fire-induced winds and is consumed gradually until being burned out. Temperature shows a bird-like shape, with two large plumes at two sides, which is a consequence of the strong air entrainment in these places. The high temperature in the center region is contributed by two factors: one is local methane combustion, and the other is the convection of flame products from upstream. The velocity contour shows a similar distribution to temperature for the same reason above. It occupies a larger region outside and above the flame region due to the lag effect of velocity to the temperature of the buoyant flame. Vorticity x shows a stratified pattern on two sides of the flame. On the right side, three positive vorticity x regions and two negative vorticity x regions can be observed. The largest positive vorticity and bottom negative vorticity are caused by the air entrainment to the flame region near the slope, while the top positive vorticity and negative vorticity are due to air entrainment to the mid-height flame region. Figure 4 presents the detailed velocity vectors with background temperature distributions. It should be noted that there are tangential velocity vectors, which also have streamwise velocity components, and the flow direction is mainly downwards. It is evident that the two wings of the plume are extracted and stretched out from the center flame region by the air circulation. In the meantime, the high-temperature products in the center region will flow downstream and upwards, which will also induce air entrainment towards the center line. This air circulation will also carry the plume from the lower region to the center line, causing the negative vorticity between the top positive vortex and the largest positive vortex. It must be emphasized that the air entrainment and flame updraft are different at different locations.

The unique pattern of the temperature distribution is different from that under windless and flat surface conditions, where the flame width would generally decrease with height. This is a consequence of the combined effects of wind and slope, which cause strong flame inclination towards the surface and the advection of fuel downstream. The air circulation on two sides of the flame is three-dimensional and more like a cylindrical spiral and becomes more intense downstream, leading to narrower fuel and flame widths near the surface.

3.2. Effect of Wind Velocity on the Mean Fields

Wind speed has a significant effect on the temperature and velocity distributions. Figure 5 shows comparisons of time-averaged temperature distributions at the streamwise middle cross-section under different wind speeds, which are 0.5 m/s, 1 m/s, 2 m/s, and 3 m/s. The most distinct effect is that the flame is more elongated and inclined towards the surface under high velocities. When U_ref = 0.5 m/s, the flame is almost parallel to the surface at immediate locations behind the fire source but starts to rise upward further downstream, which means that the buoyant force and inertial force are comparable under this velocity. When the velocity increases to 1 m/s, the inertial force is stronger and the downstream flame is pushed closer to the surface. The temperature is higher near the flame attachment point. The flame tail is almost parallel to the slope for higher velocities (2 m/s and 3 m/s). Due to this, the unburned fuel in this region will experience a higher heating rate from convective heat transfer and radiative heat transfer.

Figure 6 shows the time-averaged temperature fluctuations $\sqrt{\overline{T^{\prime }{T}^{\prime }}}$ at the streamwise middle cross-section under different wind speeds. It can be seen that the temperature fluctuations have different distributions to the temperature. Contrary to the temperature, temperature fluctuations decrease with the wind speed. For U_ref = 0.5 m/s, the maximum fluctuation is about 523 K, which is about 33% of the temperature. The fluctuation is largest around the location where the flame rises and decreases with height. When the wind speed increases, not only does the temperature fluctuation value become smaller but the region with obvious fluctuations also become smaller. Similarly to the temperature, the fluctuation shape tends to become parallel to the slope under higher velocity. For all the velocity cases, the temperature fluctuations mainly occur near the flame tip, as in Figure 5. For the flame near the fire source, fluctuation is not obvious. This is mainly because the high temperature is quickly advected by the wind. It should be noted that turbulent fluctuations are not imposed on the incoming wind, and this affects the flame dynamics, which we will leave for future investigations.

Figure 7 gives the time-averaged velocity magnitude at the streamwise middle cross-section under different wind speeds. Legends are provided for all the velocities to better show the value range. When U_ref = 0.5 m/s, the maximum velocity is about 2.15 m/s and occurs near the rising point (where the velocity inclines). This happens because the updraft velocity is larger than the wind speed and can rise to higher locations due to buoyant force. Regarding the unburned fuel beneath this region, it is most likely heated by the flame radiation, and the convective heat transfer is lower due to the lower velocity and temperature near the surface. The maximum velocity increases to 2.62 m/s, 3.72 m/s, and 4.82 m/s for wind speeds of 1 m/s, 2 m/s, and 3 m/s, respectively. Similarly to the flame temperature, the fire-induced velocity pattern also becomes longer and closer to the surface under higher velocities. In all cases, the fire-induced velocity is almost parallel close to the surface near the fire source and is greater than the wind speed. Under a higher wind speed, there is both a high temperature and high velocity close to the surface, leading to significantly larger convection heat transfer and radiative heat transfer. This further leads to faster heating, evaporation, and combustion of fuels under the fire-induced wind.

Figure 8 shows the turbulent kinetic energy (TKE) for four wind speeds. Its variation with wind speed is similar to the temperature functions. This is expected, since velocity change is most likely happening around the locations where the temperature changes significantly. The TKE also decreases with the wind speed, from 1.2 m²/s² to 0.9 m²/s², 0.34 m²/s², and 0.028 m²/s². This means that the TKE is smaller for the fire-induced wind, as no turbulent fluctuations are considered for the incoming flow. The TKE is mainly caused by the buoyant-force-induced velocity change. When the buoyant force is dominated (as in 0.5 m/s), the updraft and horizontal flow are both intense in the presence of strong air circulation. When the inertial force is dominated (as in 3 m/s), the upward flow of the high-temperature gas will immediately be blown downwards, suppressing the spanwise air entrainment in the vertical direction. If incoming turbulence is considered, then the TKE field may be different, and this requires further systematic investigation.

4. Conclusions

The flow and flame dynamics of a pool fire on a slope under wind conditions were investigated by a large-eddy simulation method. The fireFOAM solver was used to solve the governing equations. The eddy dissipation model was used to model turbulence–chemistry interaction, and the gray gas model was used for radiation heat transfer. The angle of the slope was fixed, and the effect of wind speed on the temperature and velocity fields was analyzed. The following conclusions were obtained:

• Under a wind speed of 0.5 m/s, a flame develops immediately downstream of the fire source and sustains two flanks of plume. Further downstream, the plume starts to rise due to buoyant force. A hairpin vortex is observed along the plume structure and is advected downstream with a smaller intensity and higher location.
• The temperature, velocity, and vorticity distributions show significantly different shapes at different streamwise locations. Near the fire source, the flame is confined to a small region around the fire source. Downstream, unburned methane advected from upstream looks like an upside-down triangle. The temperature shows a similar shape in the center region, but with two large plume wings, which is caused by the strong air circulation from the environment to the center region. The air circulation flows inside when moving downstream in a cylindrical spiring pattern.
• When the wind speed increases, the temperature and velocity become more parallel to the surface and their maximum values increase. On the contrary, the temperature fluctuations and turbulent kinetic energy decrease with the wind speed, and they are more frequent near the flame tails.