The fire flame is simulated by a turbulent diffusion combustion model, which considers mass transfer, momentum transfer, species transfer, and energy transfer: 1∂ρ‾∂t+∂ρ‾ũi∂xi=0,2∂ρ‾ũj∂t+∂ρ‾ũiũj∂xi=-∂p‾∂xj+∂∂xi(μ̃+μt)S̃ij+ρ‾g, 3∂ρ‾Ỹk∂t+∂ρ‾ũiỸk∂xi=∂∂xiρ‾Dk+νsgsSct∂Ỹk∂xi+ω˙k′′′‾,4∂ρ‾h̃∂t+∂ρ‾ũih̃∂xi=∂∂xiρ‾Dth+νsgsPrt∂h̃∂xi+q˙c‾, where overbars denote density-based variables and tildes denote Favre-based variables. ρ‾ is the density, ũ is the velocity, p‾ is the pressure, μ̃ is the dynamic viscosity, μt is the turbulent viscosity, S̃ij is the shear stress, g is the gravitational force, Ỹk is the mass fraction of species k, Dk is the mass diffusion coefficient, Sct is the turbulent Schmidt number, νsgs is the sub-grid scale viscosity, ω˙k′′′‾ is the chemical reaction rate, h̃ is the enthalpy, Dth is the thermal diffusion coefficient, Prt is the turbulent Prandtl number. The Lewis number is assumed to be unity.

The sub-grid scale turbulent kinetic energy ksgs is modelled by a one-eddy equation: 5∂(ρ‾ksgs)∂t+∇⋅(ρ‾ũksgs)=∇⋅(μ+μt)∇ksgs+P-ρ‾εsgs where μt is the turbulent viscosity, and calculated by μt=ρ‾ckΔksgs.

The flame fuel is assumed to be methane vapor, which flows into the domain through the fuel inlet surface. The combustion occurs immediately once the methane vapor mixes with air under the assumption of eddy dissipation process, which is a widely used model for diffusion flame. Chemical reaction is modelled by one-step global reaction of methane: R1CH4+O2=CO2+2H2O. The heat of combustion of the methane is about 5×107Jkg-1, which controls heat release rate of the fuel. Detailed reaction mechanism can be considered for more advanced combustion simulation, but is beyond the purpose of this work. This one-step global reaction is widely used in fire modelling due to its simplicity and efficiency, but it cannot predict complex flame dynamics, such as ignition and extinction process.

Figure 1 shows the physical model considered in this work, and the computational domain sizes are 150 m in length, 80 m in wide and 100 m in height. The fire source (methane vapor inlet) is 40 m away from the Inlet surface, which is the wind inlet. The Outlet surface is the exit for the flow. The top surface is set as slip boundary for the velocity and zero gradient for other variables. A Rayleigh damping layer is adopted at the upper 10 % of the domain to eliminate the oscillating wave caused by density variations. To minimize the effect of top boundary on the flame plume development near the ground, the length and height are chosen to make sure the plume mainly exits the domain through the outlet surface. The back and front surface (not labelled) are set as slip for velocity and zero gradient for other variables. Friction at the bottom surface is modelled by a universal law available in OpenFOAM. The fire source is 2 m wide. To capture temperature and velocity variation near the flame, mesh is refined in this region. The mesh consists of four level grids, as shown in Fig. 2. The first level is adopted for the whole domain, the second level is used between (30, 26, 0) and (70, 54, 32), the third level is used between (34, 34, 0) and (60, 46, 12), and the fourth level is used between (38, 37, 0) and (48, 43, 5). This refined mesh leads to a mesh size of 0.125 m in x direction, 0.125 m in y direction and 0.03 m in z direction. The total number of mesh is about 3.79 million.

As for the inlet, two kinds of velocity are considered, a uniform fixed velocity and a turbulent velocity. The uniform fixed velocity uses a power-law profile of U0⋅(z/10)0.12, and U0 is the reference velocity, which is set as 2 or 5 ms-1 in the simulations. This uniform velocity does not induce any turbulence at the inlet, and is sometimes used for the fire modelling in the ABL. The turbulent velocity is generated by the divergence-free spectral representation (DFSR) method, whose validity for turbulent ABL has been discussed in its original paper (Melaku and Bitsuamlak, 2021) and is not discussed in this work. Inputs for for this turbulent generation method include mean velocity, turbulent intensities and length scales. The mean velocity profile is same to the uniform case. The turbulent intensities and length scales uses expressions suggested by wind engineering (Yue et al., 2025). In this work, turbulent intensity profile and length scale profile are not varied. We collected the mean velocity profiles and turbulent fluctuations at a location before the fire source. The mean streamwise velocity is shown in Fig. 3 ad velocity fluctuations are shown in Fig. 4. Because averaging time is short (240 s, which is discussed later), these profiles have oscillations. From Fig. 3, the mean velocity of the turbulent condition is close to that of the uniform case, but with small deviations from the mean uniform velocity profile due to turbulence. From Fig. 4, velocity fluctuations of the 2 ms-1 case are less than 0.03 m2s-2, and are less than 0.24 for the 5 ms-1 case because we used similar turbulent intensities for both cases.

The Euler method is adopted for the time discretization, and the time step is variable with the maximum Courant number smaller than 0.8. A central differencing scheme with flux limiter is used for the momentum convection term, and total variation diminishing scheme with limiter is applied for the energy and species convection terms, and the species are additionally bounded between 0 and 1. The PIMPLE method (PISO and SIMPLE combined) is used for the pressure-velocity coupling with 3 outer correctors and 2 correctors. Pre-conditioned gradient solver is used for the density and the GAMG (geometric-algebraic multi-grid) with Gauss–Seidel smoother is adopted for pressure equation, while Preconditioned Bi-Conjugate Gradient Stabilized (PBiCGStab) solvers are used for the velocity, energy and species equations. The detailed model parameters can be seen in the file (Sun, 2025).

The simulation process is spin-up for the first 200 s without fuel vapor and combustion. After 200 s, the fuel vapor starts to enter the domain through its inlet and burns immediately when encountering air. Time averaging is activated from 250 s to avoid the effect of initial combustion on the statistic. Total averaging time lasts 240 s, which corresponds to about 3 and 8 flow-through time for wind velocities of 2 ms-1, 5 ms-1 respectively. This time window is small for obtaining mean values for the background wind turbulent statistics, but this size is enough for the fire plume turbulent statistics due to its more intermittent flow. Time averaged results for the fire plume are found to be not changing when further increasing time averaging window, which are shown in Fig. A1.

Figure 5 compares mean velocity magnitudes for uniform and turbulent cases at the Y=40m plane (left column) and X=50m plane (right column) for U0=2ms-1. The velocity distributions at both planes are similar for two cases, but they differ in magnitudes. At the Y middle plane, the maximum velocity occurs near X=43m or both cases, but the magnitude is slightly higher for uniform case. At the X=50m plane, velocity is bimodal due to counter-rotating vortex pairs, and the uniform case also predicts larger velocity.

Figure 6 compares mean temperature at the Y=40m plane (left column) and X=50m plane (right column) for U0=2ms-1 Temperature distributions are also same for both cases, and the maximum mean temperature can reach about 1650 K. Similar to the velocity fields, temperatures are higher for uniform cases for both the middle Y plane and X plane.

For this weak wind case, the plume inclination is almost the same for the uniform and turbulent case. Temperature is slightly lower and become less symmetric at the X=50m plane for the turbulent case, and this is maybe caused by strengthened spanwise velocity fluctuations due to turbulence.

Figure 7 compares mean velocity magnitudes for uniform and turbulent cases at the Y=40m lane (left column) and X=50m lane (right column) for U0=5ms-1. The velocity distributions are similar for two cases at the middle Y plane, but different at the X plane. Due to stronger wind force, plume velocities are much closer to the ground compared to those of 2 ms-1 cases. At the Y middle plane, the maximum velocity induced by the fire heat is much higher for the uniform case. However, for the turbulent case, the velocity is slightly smaller and seems more scattered. At the X=50m plane, velocity is also higher for the uniform case, with a larger velocity gradient in the core of the plume pairs.

Figure 8 compares mean temperature at the Y=40m lane (left column) and X=50m plane (right column) for U0=5ms-1. Temperature distributions are also inclined larger as the velocity fields. The maximum temperature for both cases can reach about 1942 K and occurs at the surface of the fuel vapor. For both cases, the flame cores (temperature larger than 700 K) are almost attached to the ground surface compared to those of the 2 ms-1 case. This is because the wind inertial force is dominant over the buoyant force. Temperature distributions before X=45m are almost the same for the two cases. At downstream, temperature is more scattered for the turbulent condition. At the X=50m plane, we can clearly see that the temperature is much higher for the uniform case, with larger values occurring near the bottom of the plume pairs.

Figures 9 and 10 shows the mean velocity and temperature profiles along height at different X locations for U0=2ms-1. At X=43-70m, it can be clearly seen the velocity profiles of two cases are almost identical except that velocity of the turbulent case is slightly higher at some heights at X=45-60. Maximum velocities of two cases are also close to each other. The dashed red lines seem smoother than the solid black lines, and this means the turbulent inflow does not necessarily lead to more fluctuated flow for this fire plume.

Comparison of temperature profiles shows some differences compared to those of the velocities (Fig. 10). Temperature of the turbulent case is smaller at X=45m, but larger at X≧50m. At X>50m, the mean temperature of turbulent case is larger than that of the uniform case. The differences become gradually smaller at further downwards and the fire plume for the turbulent case is slightly higher

Figure 11 and 12 show the mean velocity and temperature profiles along height at different x locations for U0=5ms-1. Velocity profiles of two cases are very close to each other and almost identical at X=43m. Compared to the 2 ms-1 condition, a sharp increase of velocity can be observed near the ground surface, which is a consequence of larger inertial under 5 ms-1 condition. At further downstream, the velocity profiles of turbulent case are smoother and larger near the ground surface. Temperature profiles are also close to each other for two cases before X=45m. Maximum temperatures of turbulent case are larger at downstream, and the maximum difference is located at X=50m. Temperature profiles of uniform case have narrower gaussian shapes at X≧50m. This indicates that the uniform inflow method will decrease the vertical transport of momentum and heat flux.

To further reveal the effect of approaching turbulence on the temperature variations, Fig. 13 compares root mean square (rms) of temperature fluctuations near the fire flame under different inlet conditions. For both velocities, rms of temperature is more inclined to downstream, similar to the mean temperature and velocity fields. However, there is a significant difference between two velocities. Under 2 ms-1 condition, the distributions of rms of temperature are almost same and show a shoe-like pattern for uniform or turbulent inflow, with the latter case predicts smaller values. Flame is attached to the surface for both cases. Under 5 ms-1 condition, patterns of the rms of the temperature are completely different for the uniform and turbulent cases. For uniform case, the pattern has a narrower region of large rms compared to that of 2 ms-1 condition. For turbulent case, the pattern is completely different, with the high rms regions become wider and higher. This is maybe caused by the relatively large velocity fluctuations (as in Fig. 4) for this case, which breaks the steady flame structure that would exist in the uniform case and induce larger streamwise, spanwise and vertical momentum flux.

To show the effect of inlet turbulence on the fire plume turbulent fluctuations, Fig. 14 compares the streamwise, spanwise and vertical velocity fluctuations under uniform and turbulent cases for U0=2ms-1. Maximum values of three components are about 3.52, 1.95, and 9.38m2s-2, with the vertical component has the largest value. Clearly, the turbulent fluctuations at this plane are dominated by the vertical and streamwise components. Three components have very similar structure for uniform and turbulent case, indicating that wind turbulence does not have significant influence on the fire plume turbulent structure, and it is mainly controlled by the buoyant force and mean wind force. However, their distributions are completely different for 5 ms-1 condition, as shown in Fig. 15. For this inlet velocity condition, three components of velocity fluctuations are different between the uniform and turbulent cases. For the streamwise component, it is larger for turbulent case, with the maximum value reaches 2.09 m2s-2, while it is only about 1.16 m2s-2 for the uniform case. Moreover, it encompasses a larger region in turbulent case. For the spanwise component, the difference between the uniform and turbulent case is generally similar to that of the streamwise component. An additional large spanwise fluctuations are observed near the ground at X=47m for the turbulent case, which means more spanwise momentum flux transport. For the vertical component, the maximum value is about 4.43 m2s-2 and the turbulent case has a wider distribution.

Figure 16 and 17 show the normalized turbulent kinetic energy (TKE) profiles along height at different X locations for U0=2 and 5 ms-1 respectively. The turbulent kinetic energy is calculated as k=(uu‾+vv‾+ww‾)/2. For the 2 ms-1 condition, the TKE of the turbulent case is smaller at X=43 and 45 m. At further downstream, the TKE is always larger for the turbulent case. The TKE become larger at higher locations at further downstream, consistent with the plume rise. For the 5 ms-1 condition, the TKE profiles show some different features. Firstly, the fire induced large TKE values are limited to a smaller range below Z=2m before X=45m, which is a consequence of stronger wind force. Secondly, the TKE of the turbulent case is always larger than that of the uniform case. This is partially because the approaching flow for this inlet velocity condition has a larger velocity fluctuation along the heights (as shown in Fig. 4). At downstream, the uniform and turbulent cases predict similar TKE profile pattern but the turbulent case has larger maximum values, which are almost as twice as that of the uniform case. Thirdly, significant differences of TKE maximums between X=43 and 45 m for the uniform and turbulent cases can be observed near the ground, with the turbulent case having larger values. This large turbulent kinetic energy can considerably alter the flow structure in this region and leads to different mixing and air entrainment here, which eventually cause the different temperature fluctuations (Fig. 13).