Mass flow measurement of granular materials in aerial application - Part 1: Simulation and modeling

The mass flow of granular particles in an aerial spreader duct was regarded as a sequence of cluster passage events. Ar low flow densities, the total mass per time unit could be estimated by measuring the diameter (length of each individual particle passing a sensor and accumulating the associated m asses. At higher flow densities, the lengths of clusters would be measured rather than the lengths of particles. However; because of overlapping, the cluster lengths cannot simply be accumulated The total length of a cluster is always smaller than the lengths of the individual particles within it. T herefore, a reconstruction method is necessary to estimate the total length of the particles within a cluster from the measured cluster length. This r econstruction algorithm was developed using MarLab (TM) as a simulation too l and was called the "Exponential Estimator" Simulations were conducted for particles with 1) Identical diameters, 2) Uniformly distributed diameters, 3) Gaussian distributed diameters, and 4) Urea-distributed diameters. A si mple universal relationship was discovered between the event ratio (the rat io between the original number of particles in an experiment and the number of measured clusters) and the flow density. This relationship was found to be independent of both the mean diameter of particles and the diameter dis tribution, which is of great importance when mass flows of fertilizer are i nvolved. The flow density cannot be measured directly. However another simp le relationship was found between the flow density and the number of cluste rs in certain length categories, which can be measured on the fly. This rel ationship was found to be independent of the mean diameter of particles, bu t dependent on the diameter distribution. Combination of these two relation ships led to the Exponential Estimate,: It contains only a single material- specific constant for distributed-diameter particles. The simplicity and co mpactness of the discovered relationships indicate the possibility to deriv e the Exponential Estimator from theoretical principles. The simulation too l as developed here could be a valuable instrument for this purpose.