Hybrid centrifugal spreading model to study the fertiliser spatial distribution and its assessment using the transverse coefficient of variation

Studying centrifugal spreading by carrying out field or in-door experiments using fertiliser collection trays is tedious and labour intensive. This is particularly true when several implementation methods need to be compared, numerous replications are required or fertiliser sample characterisation is required. To circumvent cumbersome experiments, an alternative approach consists in performing in silico studies. In order to reach this objective, a hybrid centrifugal spreading model is designed by combining theoretical fertiliser motion equations with statistical information. The use of experimental measurements to characterise fertiliser properties, outlet velocity, angular mass flow distribution and spread pattern deposition, ensure a realistic calibration of the model. Based on this model, static spread patterns and transverse distributions are computed for a virtual twin-disc spreader. The number of fertiliser granules used to compute a spread pattern is deduced from the target application rate while the granule properties and their motion parameters are randomly selected from pre-established statistical distributions. This Monte Carlo process reproduces the random variability of fertiliser spread pattern depositions. Using this model, simulations demonstrate the mean and standard deviation of CV value decrease with the application rate. The CV mean value also decreases with the collection tray surface, while the standard deviation decreases with the collection tray length. Mathematical relationships are deduced from simulation results to express the mean and standard deviation of the CV as functions of the application rate and collection tray surface or length. The simulation model is also used to compare spreader test methods and study the influence of some fertiliser particles properties on the transverse distribution.