Development and validation of an operational numerical model for the simulation of the aerial drop of firefighting products

The aerial drop of firefighting products, whether chemical retardants or just plain water, play an important role in the overall efficiency of operations and resources in terrain within a wide range of situations, especially in emerging fires, inaccessible mountainous areas, or in sensible areas or situations requiring a rapid intervention. However, since on-board systems for computer-assisted drops have not yet been used operationally, the efficiency of aerial means is extremely dependent on pilot skills in dealing with reduced visibility and erratic atmospheric conditions. In this context, the development of numerical modelling tools can be of primary importance towards the optimisation of firefighting operations.

The main objective of the current investigation was the development and validation of the operational Aerial Dropping Model - ADM. This numerical tool allows a near real time simulation of the aerial dropping of firefighting products for a wide range of viscosities (from unthickened products to highly thickened long-term retardants), while covering the most important stages of the process.

For the particulate phase, the volume of product released per time is calculated for the three types of aerial delivery systems available in the market: conventional, constant flow, and pressurized (MAFFS). After the outflow of the liquid from the aircraft tank, ADM calculates the jet column bending and fracture that is related to the continuous stripping of droplets from the exposed surface of the jet by Rayleigh-Taylor and Kelvin-Helmholtz instabilities. The sizes of the child droplets resulting from this primary breakup stage are computed through the jet stability theory (in a similarity with fuel spray modelling for the automotive industry), according to which the droplets sizes are related to the wavelengths of the most unstable waves. Droplets are then subjected to secondary breakup by bag or shear breakup regimes that are identified by the model through the dimensionless numbers Weber and Ohnesorge. The spatiotemporal evolution of secondary breakup is calculated from experimental correlations. Droplets trajectories during breakup are described by a Lagrangian dispersion scheme. The effect of deformation on the motion of the free-falling firefighting droplets is introduced through a dynamical drag model that accounts for the effect of non-sphericity on drag. Prior to reaching the ground, a canopy interception module applies the concept of film thickness (from rainfall interception studies) in order to allow an approximate estimate of the fraction of volume retained by vegetation.

For the simulation of the gas-phase the vegetative canopy model coupled to a modified surface-layer model is used. This approach allows considering the effects on the wind field of the atmospheric stability and the presence of trees, which are characterised by their Leaf Area Index (LAI). For simplicity, the code does not include the effect of thermally induced air motions on the product's behaviour. Therefore, it is specially indicated for ‘indirect attacks', in which the drop is made at some distance from the fire front.

ADM performance was investigated against measured data of product ground concentration obtained during 18 drops conducted in Marseille (France) and Marana (US) with an S2 Tracker aircraft. These measurements of product concentration at ground followed the “cup-and-grid” method, according to which a grid of cups is used and the weight of product in each one is registered after total deposition. The delivery system type, flight parameters, meteorological conditions and product characteristics were varied in order to evaluate the model performance within a wide range of input conditions. The validation procedure consisted on the intercomparison of the ground patterns shape, plus a statistical analysis of computed data in comparison to measurements, in terms of the length and area of each isoconcentration contour (i.e., coverage level).

In general, ADM allowed a good representation of the spatial distribution of product for the different coverage levels. The statistical validation of the results showed that the model accuracy is actually within the statistical uncertainty of the cup-and-grid sampling method. Line lengths per coverage level are within a 10% error in general, with an average normalised mean squared error (NMSE) of 0.01 and a Pearson correlation coefficient above 0.9 in both Marseille and Marana drop trials. The accuracy of the simulated areas per level decreases to an average NMSE of 0.02 and 0.04, for the two drop trials respectively, although the good correlation remains. In all cases, nearly 90% of the results were within a factor of two of observations. Also, the geometric mean was between 1.1 (for area) and 1.2 (for line length), indicating that the mean bias is clearly within the ±30% variation from the mean established by the model acceptance criteria. In all situations, all the statistical metrics fulfilled the requirements of the referred criteria. The accuracy of the simulations shows no strong relation with the corresponding viscosity, although better results are obtained in the range from 700 to 1100 cP.

ADM provides a new insight on the importance of aerodynamic breakup mechanisms on the generation and behaviour of droplets of firefighting liquid, while maintaining the run-time on a feasible level given the limits imposed by the intended operational application. Due to its characteristics and performance, ADM can potentially be used in formation, training and demonstration activities with pilots, aerial resource coordinators, civil protection personnel or general firefighters, or in the testing of the effectiveness of firefighting chemicals, complementing the data obtained from real scale drop tests and laboratorial experiments. The user control over the input parameters allows the effect on ground pattern to be assessed for a wide range of dropping scenarios, avoiding the natural variability and irreproducibility of field conditions, and a better understanding of the multiple interrelated phenomena involved.

Submitted to oral presentation in the following topic: “Model Studies and Development”