A Hybrid Computational and Analytical Model of Inline Drip Emitters

Abstract

This paper details a hybrid computational and analytical model to predict the performance of inline pressure compensating drip irrigation emitters. Pressure compensating emitters deliver a constant flow rate over a range of applied pressures to accurately meter water to crops. Flow rate is controlled within the emitter via a fixed resistance tortuous path, and a variable flow resistance composed of a flexible membrane that deflects under changes in pressure, restricting the flow path. A pressure resistance parameter was derived using an experimentally validated computational fluid dynamics (CFD) model to describe the flow behavior in tortuous paths. The bending mechanics of the membrane were modeled analytically and refined by deriving a correction factor using finite element analysis (FEA). A matrix formulation that calculates the force applied by a line or a patch load of any shape on a rectangular membrane, along which there is a prescribed deflection, was derived and was found to be accurate to be 1%. The combined hybrid computational–analytical model reduces the computational time of modeling emitters from hours to less than 30 min, dramatically lowering the time required to iterate and select optimal designs. The model was validated experimentally using three commercially available drip emitters and was accurate to within 12% of the experimental results.