Approaching Terminal-Velocity of Large Firebrands for Extreme Fire Events ^†

Abstract

Wildfire spread on a large scale is heavily driven by the transport of firebrands, as it leads to short- and long-range spotting. Detailed knowledge of terminal velocity can help predict firebrand transport and therefore overall wildfire spread modelling. The current work evaluates an approach to estimating terminal velocity based on CFD simulations with a detailed firebrand shape and assesses its impact on orientation. For the selected firebrand and simulation setup, a range of terminal velocities of approximately 5 to 11 m/s is calculated. This is based on 352 RANS simulations for one particular detailed firebrand at 11 different orientations and two turbulence models, with varying inlet velocities and two mesh refinements. DES and LES turbulence models are considered as a next step for a detailed comparison with wind tunnel measurements.

1. Introduction

Firebrands are an important fire spread mechanism in addition to gas radiation and convection, and they play a crucial role in wildfires, where their impact is known as fire spotting and is a leading cause of house loss in the Wildland–Urban Interface (WUI). Firebrand transport has been extensively studied in the past with increasing complexity [1,2,3].

This work focuses on the detailed calculation of terminal velocity on a small scale under controlled environments with varying simulation complexity. The aim is to provide refined terminal velocities of a representative set of firebrands [4] for large-scale simulations [5,6,7,8,9]. Unlike previous work, we focus not only on generic firebrand shapes like discs and cylinders but also on real firebrand shapes collected previously [4].

2. Methods

2.1. Description of Firebrand

The methodology covers 11 different orientations, varying Reynolds numbers, and two mesh settings, using a RANS modelling approach based on velocity-dependent force curves. In its current state, the terminal velocity is evaluated for a single representative firebrand, which is candle bark (see Figure 1). The shape was collected during experiments and later determined by photometry. The selected firebrand has a bounding box of approximately −0.069 m, 0.022 m, −0.0 m to 0.069 m, 0.022 m, 0.052 m, a volume of about 5.143 × 10⁻⁵ m³, and, with a measured mass of 3.717 g, a resulting density of 131.81 kg/m³.

2.2. Description of Orientation

The original scanned geometry was later used to create 10 additional variations by applying random rotations, rolls, and pivots. At this stage, the goal is not to achieve a perfectly statistically distributed set of orientations, but rather to establish an initial setup to study the terminal velocity variations of the selected firebrand. Figure 2 illustrates the generated firebrand variations for all 10 additional orientations.

2.3. Simulation Setup

In the current state, the firebrands are placed in a generic wind tunnel setup (domain size of 3 m, 3 m, 2.5 m) with a block inlet profile, a turbulence intensity of 10%, a mixing length of 0.1 m, at an ambient temperature of 300 K and an ambient density of 1.0 kg/m³. Inlet velocities were varied between 3 m/s and 10 m/s for all 11 orientations. Steady RANS-based simulations were conducted using two different turbulence models (k-epsilon and k-omega-SST) in OpenFOAM (v2506). To avoid any impact of mesh settings across different orientations, an automated meshing approach was chosen to ensure that refinement levels and refinement zones around the firebrand remain consistent regardless of orientation. See Figure 3 (left), which highlights the main refinement zones around the firebrand for two orientations. The simulation setup is automated with the application in mind for high-performance computing systems, enabling multiple complex scenarios to be generated with minimal setup effort. An initial mesh refinement was also investigated. The meshes differ only in the refinement level around the firebrand, resulting in approximately 17.5 million cells for the initial mesh and about 18.3 million cells for the refined mesh.

Further mesh refinement studies are planned, with continued emphasis on generating high-quality automatic meshes for complex shapes.

3. Results and Discussion

With variations in inlet velocity, mesh setup, turbulence model, and orientation, a total of 352 simulations were carried out. As the primary focus is on the terminal velocity, force-velocity relations were created from the resulting simulations. Terminal velocity was then derived separately for each orientation. For the current setup, the impact of the turbulence model is negligible, so no further evaluation is shown here. The two chosen mesh setups are quite similar, so the resulting terminal velocity differences are also not shown here.

Compared to the other settings, there is a strong dependence of the calculated terminal velocity on orientation and inlet velocity. Figure 4 shows the force-velocity curve for the k-omega-SST setup with a 17.5-million-cell mesh.

The results show that the terminal velocity ranges from approximately 5 m/s to 11 m/s, with a mean velocity of about 6.5 m/s, skewed toward lower values. Figure 4 (right) visualizes the flow velocity in a selected slice at position x=0.0 m for orientations 4 and 6, which exhibit very different terminal velocities. It is clear that orientation has a significant impact on the flow field and, consequently, on the resulting forces. Orientation 4 produces a much smaller total frontal area compared to orientation 6.

It is noted that these calculated firebrand terminal velocities are derived for a well-known and fixed scenario. That is, the actual behaviour will vary during firebrand transport in real conditions due to factors such as changing shape and density caused by combustion and ambient conditions. Nevertheless, the current approach provides initial insight into model sensitivities. Furthermore, the orientation of the firebrands is dynamic; a fixed position is not realistic, and rotating orientations are highly probable.

4. Conclusions

The work highlights the impact of orientation on the terminal velocity for a selected candle bark firebrand. The calculated terminal velocity ranges from 5 to 11 m/s for the selected setup.

Further mesh refinement studies are needed, and more detailed LES or hybrid RANS-LES simulations are planned for selected orientations and setups. The next steps will also include validation calculations using wind tunnel measurements of generic disc and cylinder shapes at various fixed orientations. The same approach will be applied to complex firebrand shapes.