A Lagrangian model for spray behaviour within vine canopies

Abstract

This work concerns the numerical prediction of pesticide deposits on vine by air assisted sprayers. This numerical model consists in two different parts: the air flow characteristics were obtained through a Navier–Stokes solver in which additional terms have been introduced in order to account for the modification of the flow by the vine foliage. The theoretical form of these terms was derived through an averaging procedure. As a result, the canopy effect was modelled by introducing momentum and turbulence source terms in the Navier–Stokes equations. The constants were identified thanks to experimental data obtained by direct measurements of the air flow speeds through an artificial canopy. The second part of the model consists in simulating the droplet cloud by means of a lagrangian stochastic model. The average motion of the droplets was computed through the use of lagrangian coordinates and the turbulence effect on the droplets was interpreted in term of statistical properties of the droplet cloud. The tractor displacements were accounted for through unsteady boundary conditions. Once the size and the droplets cloud locations have been determined, the deposit was predicted for a vine row of one meter length using an efficiency coefficient obtained from simulations. Thanks to this approach we were able to quantify the effect of air turbulence on droplet deposition.