Newsletter - Fire spread prediction

This is the December 2014 newsletter from the Fire spread prediction across fuel types project, with updates for project end users.

New faces

We have had two new team members join the project in recent months. Duncan Sutherland has been appointed as a Postdoctoral Fellow, with a first class honours degree and a PhD in applied mathematics from the University of Sydney. Duncan has carried out research on energy dissipating structures in fluid flows, an area of relevance to modelling bushfires in which turbulent energy is both produced and dissipated. His interests also extend to parallel computing and high Reynolds number flows.

Rahul Wadhwani also joins the team as a PhD student, a degree in chemical engineering with a specialisation in hydrocarbon engineering from the Indian Institute of Technology, Roorkee. Rahul’s PhD studies will concentrate on developing mathematical models of pyrolysis (gasification) of Australian vegetation. The resulting data will form an essential component of our strategy to develop a platform on which to build the next generation of bushfire models. Furthermore, data on the physical and combustion characteristics of embers and firebrands produced by Australian vegetation will be collected. All these data will be used as input parameters to a computer model.

Recent progress

Realistic models of trees

Australian trees typically have complicated shapes which presents several problems when developing a physics-based fire spread model. Previous studies, for example Mell et al. [1], of fires propagating through trees and bushland have considered the combustion of American native species such as the Douglas fir tree. These trees are typically a conical shape, have a dense crown, and a single thick trunk. The overall shape in which a plant grows is referred to as a habit. The habit of fir trees very easy to model well in physics-based fire simulations. Indeed, in the work of Mell et al., the entire tree is treated as a solid conical fuel source.

In direct contrast to the regular shape of fir trees, the Australian native eucalyptus has many different habits depending on the type of the eucalyptus, the environment in which it grows, and even the history of the plant. Plants that have recovered from fires may have a different habit to the original plant. Common habits of the eucalyptus are: a tree with a tall trunk and many slender branches which are steeply and irregularly angled emerging from the trunk; a mallee which has many trunks from a single base, which is a common habit of a tree that has recovered from a fire; and a marlock (typically only Western Australian species) which have a single trunk and many dense leafy branches which spread almost to ground level.

Of particular interest is a tree with many different habits which include steeply-angled slender branches and a sparse crown. This type of tree is challenging to include in a physics-based fire model. Apart from the difficulties representing the shape of the tree, correctly modelling the airflow through the canopy is also important. Many authors (see for example [2]) have studied the flow through forest canopies for various applications and found that a tree canopy disrupts the air flow leading to a turbulent wake behind the tree. Therefore, it is crucial to have a reliable model that accounts for both the habit of the tree and the effect of the canopy on the airflow.

In the example of a fractal-like tree in Y-configuration with four levels of branching from the trunk, each child branch is approximately 80% of the size of the parent branch. Each generation of branches is similar to the previous generation of branches.

Remarkably, models for realistic trees have been developed for computational generated images for use in animations, computer games, and so on. The model tree employed is typically a fractal model. Intuitively, a fractal is a spatial pattern which repeats itself and decreases in size with every repetition. This property is called 'self-similarity'. To illustrate the construction of a fractal tree, consider drawing a trunk, then drawing two branches forming a Y-shape. At the end of each new branch drawing a smaller Y-shape and repeating this process indefinitely. Using this process, each child branch is a scale replica of its parent branch.

A true fractal continuous branching ad infinitum but computationally the fractal must be terminated after a finite number of branches. In a real tree the branches eventually terminate in leaves, so the final level of a fractal tree can be considered to be the leafy canopy. The fractal tree can be used to represent many different habits of trees. By varying the number, the size, and the angles of the branches many different shapes can be obtained.

With current computing technology it is not possible to resolve the finest details of a tree, such as the leaves which may only be 25mm wide, and model a fire front of many kilometers. In a computer simulation of air-flow over a tree, typically only the trunk and the largest branches are explicitly considered. Because a fractal tree is self-similar the effect, on the air-flow, of the smaller branches and the leafy canopy can be estimated by scaling the effect of the largest branches and the trunk. This technique is called 'renormalised simulation' or RNS. Recently an experimental validation of this method was performed and the total drag coefficient of a fractal tree calculated using RNS was found to be within 8% of experimental measurements [3]. 

Initial simulations of the velocity field over a fractal-like have been performed. Currently, we are implementing and testing the RNS formulation. Real world trees are typically not a regular fractal pattern. We are interested to see if RNS can be used to approximate flow over an irregular fractal-like tree. We then plan to extend RNS to include the effect of the combustion of the leaves and finer branches.

References:

1. Mell, William, Alexander Maranghides, Randall McDermott, and Samuel L. Manzello. "Numerical simulation and experiments of burning Douglas fir trees." Combustion and Flame 156, no. 10 (2009): 2023-2041.

2. Belcher, Stephen E., Ian N. Harman, and John J. Finnigan. "The wind in the willows: flows in forest canopies in complex terrain." Annual Review of Fluid Mechanics 44 (2012): 479-504.

3. Modeling turbulent flow over fractal trees using renormalized numerical simulation: Alternate formulations and numerical experiments, Jason Graham and Charles Meneveau  Physics of Fluids (1994-present) 24, 125105 (2012); doi: 10.1063/1.4772074

Please let Graham Thorpe know if you have any questions or project feedback.