Development and validation of a fully analytical model for designing pressure-compensating flow devices for drip irrigation and other applications*

Design of pressure-compensating (PC) devices can be a time-consuming, expensive process. PC devices often use a flexible diaphragm whose deformation under increasing pressure proportionally raises the flow resistance, resulting in a constant flow rate. This 'Fluid-Structure Interaction' (FSI) is governed by coupled, nonlinear differential equations, which raises the computational cost of the simulating PC action. The most common alternative to this is to run time-consuming iterative design experiments. To enable rapid design-space exploration, we propose a novel 1D analytical model to simulate the entire flow-pressure response of a PC device, focusing initially on drip emitters. Each emitter feature is treated as a flow resistance depending on device geometry, material properties, pressure, and flow rate. Resistances are evaluated in series using suitable analytical expressions, before being wrapped into an iterative scheme to resolve the inherent nonlinearity of the problem. This approach's main benefit is to avoid the overhead of fully simulating the FSI by instead modeling multiple, simple features inside the emitter. We demonstrate the utility of the model by designing a new PC emitter capable of regulating flow from 40-50% lower pressures than comparable commercial products. This allows for reduced energy consumption, lowering the overall operating costs of drip irrigation.