Numerical modelling of the aerial drop of firefighting agents by fixed-wing aircraft. Part I: model development

The efficiency of the aerial drop of firefighting agents (water and retardants) is extremely dependent on pilot skills in dealingwith complex atmospheric conditions, mostly because on-board systems for computer-assisted drops have not yet been used operationally. Hence, numerical modelling tools can be of primary importance for the optimisation of firefighting operations and in the testing of new chemical products. The current work addresses the development of the operational Aerial Drop Model. This numerical tool allows a near real-time simulation of aerial drops with fixed-wing aircraft, while covering the fundamental stages of the process. It copes with awide range of product viscosities, fromwater to highly thickened long-term retardants. The Aerial Drop Model simulates the continuous stripping of droplets from the liquid jet by the action of Rayleigh–Taylor and Kelvin–Helmholtz instabilities applying the linear stability theory. The subsequent secondary breakup and deformation of the formed droplets due to aerodynamic forces is based on experimental correlations defined in terms of the dimensionless Weber number. Droplet trajectories are computed by applying a Lagrangian approach, in which a dynamical drag module accounts for the effect of deformation. This operational tool provides an improved understanding of the behaviour and effectiveness of aerially delivered firefighting liquids. Additional keywords: drop effectiveness, droplet flow, forest fires. Introduction and background The World Health Organization (WHO 2007) has identified forest fires as one of the threats to public health security in the 21st century, and climate change has been positively linked to an increase in the frequency and severity of forest fires (Westerling et al. 2006; IPCC 2007). Aerial application of firefighting products plays an important role in protecting human lives and patrimony fromwildfires, and its importance is likely to increase as wildfire severity increases. In fact, aircraft use against wildfires has increased since the 1960s, especially in the United States, Australia and several European countries, in particular Greece and France. If integrated into an effective global strategy, aircraft can play an important role in wildfire management, especially in situations requiring rapid intervention, such as emerging fires, inaccessible mountainous areas, or other highrisk situations. The efficiency of the aerial drop of firefighting liquids is determined by the application of the product in the correct spot and in the quantity most adequate for retarding or extinguishing the fire front, and permitting the subsequent attack by ground resources. However, as the factors that determine drop efficiency are numerous, without the use of operational decision-support systems (DSS), this is potentially an operation with unpredictable results, highly dependent on the skills of the pilot. The use of modelling tools that can aid the pilot’s decision on the best way to conduct the drop can be of primary importance during firefighting or training operations. Despite the development of powerful numerical codes for fluid dynamics modelling, associated with the rapid growth of hardware performance, it is still difficult to determine the ground distribution of the applied liquid, even though the parameters affecting drop performance and ground distribution are known (Giménez et al. 2004). The complexity inherent in the numerical simulation of this process results mostly from the panoply of dynamic phenomena that contribute to the breakup of the bulk liquid, i.e. the dynamical transition into droplets of varying dimensions, and also in the following drift and deposition of the formed droplets. These factors will ultimately determine the coating of the fuel by the product and the characteristics of the ground pattern, including the position of the pattern in relation to the target, the length and area of each coverage level and the volume of drifted agent. Under this scope, the objective of the current work was the development (Part I) and validation (Part II, Amorim 2011) of the operational Aerial Drop Model (ADM), which is intended for the simulation of the spatiotemporal behaviour of firefighting liquid agents (water and retardants) in the atmosphere and the resulting coverage pattern of the ground surface. ADM was designed to cover the main stages involved, namely: (1) the outflow of the liquid from the aircraft tank; (2) the two-stage liquid breakup; (3) the droplet shape distortion and gravitational settling; and (4) the ground deposition of the spray cloud. Whereas Part I, the current document, is dedicated to the development of the model, Part II (Amorim 2011) describes the comparison of modelling results with a set of real-scale drop tests, in which a wide range of operational conditions were analysed, including different delivery system types, flight parameters, meteorological conditions and product characteristics. CSIRO PUBLISHING International Journal of Wildland Fire 2011, 20, 384–393 www.publish.csiro.au/journals/ijwf IAWF 2011 10.1071/WF09122 1049-8001/11/030384 Literature review on the numerical modelling of the aerial drop of firefighting liquids During an aerial drop, the liquid undergoes a complex sequence of dynamic mechanisms, as shown by Andersen et al. (1974a, 1974b, 1976). The first stage starts with the release of the firefighting agent from the tank. Depending on the tank’s volume, the number of compartments opened simultaneously and the type of delivery system, the time for total efflux of conventional non-pressurised systems can typically take between 0.5 and 2 s for a dropped volume of ,5000L, whereas in constant-flow systems, it can easily increase to 5 s or more. The geometrical characteristics of the tank and the doors’ opening rate shape the emerging fluid in the first milliseconds of the drop. As a result of the relative velocity between the emerging liquid and the atmosphere it enters (which at this stage is typically in the range from 50 to 70m s ), the jet column of bulk liquid bends and deforms through thinning and lateral spreading. The increase of the frontal cross section of the jet column is, therefore, a result of the balance of aerodynamic drag, liquid inertia, gravity, surface tension, and viscous forces. Simultaneously, the bulk product undergoes a sequence of complex breakup mechanisms, which start with the continuous stripping of droplets from the liquid surface due to Rayleigh– Taylor and Kelvin–Helmholtz instabilities. This process produces a cascade of fluid structures that form a spray region with the characteristic cloud shape shown in the different stages of Fig. 1. The aerodynamic breakup of liquid jets is, in fact, a twostage process composed of the primary breakup of the jet into large droplets (or globs) and the subsequent secondary breakup of these fluid structures with the formation of the spray cloud. After being formed, droplets are entrained in the wake flow that develops behind the liquid column, as found in other studies on the primary breakup of liquid jets (e.g. Linne et al. 2005). In this process, the smaller droplets resulting from the atomisation of the column in the first instants of the drop are also affected by the aircraft wake (generated by the fuselage and propellers). But as the droplet inertia is the determinant factor on the effect of the aircraft wake over the trajectory of the cloud, this effect is more relevant for pressurised aerial delivery systems than for conventional or constant-flow ones. Droplet dynamics within the gaseous flow is then governed by the interaction between the droplets (influenced by their size and shape) and the airflow, which results in a drag-induced deceleration. Finally, the gravitational settling of the liquid culminates with the penetration and coating of the canopy and the ground deposition of the remaining material not retained by the leaves and branches. The breakup (or atomisation) is, in fact, the most important process controlling the behaviour of the product in the atmosphere, because it determines the size, velocity and location of the formed droplets. This will ultimately control the ground pattern of the product and the overall effectiveness of the drop. Hence, it is ofmajor importance to pursue an accurate numerical description of the breakup stage, even in operational fastrunning models. However, few attempts have succeeded in predicting, either experimentally or numerically, the complex process firefighting products (especially retardants) undergo when exposed to aerodynamic breakup, and the consequences on size distribution of droplets and final ground deposition. The first and most detailed study on the breakup of firefighting liquids was undertaken by the Shock Hydrodynamics Division, from the Whittaker Corporation (California, US), under contract to the Intermountain Forest and Range Experiment Station of the US Forest Service (USDA-FS). These works, published in the mid-70s by Andersen et al. (1974a, 1974b, 1976), represent an important step forward on the understanding of the relation between the rheological characteristics of the products and aerial delivery performance. From this extensive work, significant relevance should be attributed to the 0.5 s