Design Innovation Papers

Shape and Form Optimization of On-Line Pressure-Compensating Drip Emitters to Achieve Lower Activation Pressure

[+] Author and Article Information
Pulkit Shamshery

Global Engineering and Research Laboratory,
Massachusetts Institute of Technology,
Cambridge, MA 02139
e-mail: ps544@mit.edu

Amos G. Winter, V

Mechanical Engineering Global Engineering and
Research Laboratory,
Massachusetts Institute of Technology,
Cambridge, MA 02139
e-mail: awinter@mit.edu

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received June 5, 2017; final manuscript received October 3, 2017; published online December 21, 2017. Assoc. Editor: Yu-Tai Lee.

J. Mech. Des 140(3), 035001 (Dec 21, 2017) (7 pages) Paper No: MD-17-1386; doi: 10.1115/1.4038211 History: Received June 05, 2017; Revised October 03, 2017

This study presents the design and validation of on-line pressure-compensating (PC) drip irrigation emitters with a substantially lower minimum compensating inlet pressure (MCIP) than commercially available products. A reduced MCIP, or activation pressure, results in a drip irrigation system that can operate at a reduced pumping pressure, has lower power and energy requirements, requires a lower initial capital cost, and facilitates solar-powered irrigation systems. The technology presented herein can help spread drip irrigation to remote regions and contribute to reducing poverty, particularly in developing countries. The activation pressures of drip emitters at three flow rates were minimized using a genetic algorithm (GA)-based optimization method coupled with a recently published fluid–structure interaction analytical model of on-line PC drip emitter performance. The optimization took into account manufacturing constraints and the need to economically retrofit existing machines to manufacture new emitters. Optimized PC drip emitter designs with flow rates of 3.3, 4.2, and 8.2 lph were validated using precision machined prototype emitters. The activation pressure for all was ≤0.2 bar, which is as low as 16.7% that of commercial products. A limited production run of injection molded 8.2 lph dripper prototypes demonstrated they could be made with conventional manufacturing techniques. These drippers had an activation pressure of 0.15 bar. A cost analysis showed that low MCIP drip emitters can reduce the cost of solar-powered drip irrigation systems by up to 40%.

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Fig. 1

Schematic of a conventional PC on-line emitter. (a) Isometric view of a characteristic, commercial online PC drip emitter. (b) View along the A-A plane pointing out the main topological features and listing the design variables taken into account in the coupled fluid–structure interaction analytical model (described in the text). (c) View along the A-A plane showing the flow path of water in the emitter for low inlet pressures. When the inlet pressure is low, the fluid flow path is not constrained and water can flow into the inlet, through the orifice, over the lands, and out the outlet. The fluid flow path is denoted by the dashed line with triangular arrow heads, driven by an input pressure of Pinlet. The main resistance to fluid flow is through the orifice, characterized by a loss coefficient κo. The flow of fluid through the emitter sets up a pressure differential across the membrane, as seen by the gray vertical arrows pointing at the membrane, Ploading. (d) View along the A-A plane showing the flow path of water in the emitter for high inlet pressures. As the inlet pressure increases, the compliant membrane deflects down to the lands resulting in an upward force being exerted on the membrane by the lands, shown by the large black arrows. Once the membrane contacts the lands, the fluid flow has to divert around the lands and flow through the channel and out through the outlet. The main resistances to fluid flow are now both the orifice and the channel, characterized by a loss coefficient κc. (e) View along the B-B plane showing the shearing of the membrane into the channel (vertical dashed lines on the membrane) as Pinlet increases from state d, which decreases the effective channel area and increases κc.

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Fig. 2

Optimization method. Design variables (x1x8), constraints (g1g8) and parameters (p1p4) are input into the analytical coupled fluid–structure interaction model presented in Ref. [16]. The model iterates between the individual structure and fluid analytical expressions until they converge, yielding a prediction of the flow rate versus pressure behavior of the dripper. This result is then evaluated with the objective function in Eq. (1). A GA is used to vary and test multiple sets of design variables to minimize the objective function.

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Fig. 3

Flow rate versus inlet pressure for emitters designed using the optimization process presented in this study. The three dripper designs with geometries presented in Table 1 are represented, optimized for 8 lph (a), 6 lph (b), and 5 lph (c) (horizontal dotted lines), with corresponding measured nominal flow rates of 8.2 lph, 4.2 lph, and 3.3 lph (horizontal gray lines), respectively. All emitters have an activation pressure of ≤0.2 bar. Two emitters for each specified flow rate were precision machined and tested. The gray band shows the ±10% allowed variation from nominal per industry standards. The black boxes with error bars denote the average and standard error of the 8 experimental data points collected per pressure reading. The dashed line represents the theoretical model prediction, which shows an accurate activation pressure.

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Fig. 4

Manufacturing error sensitivity for an 8 lph dripper produced by Jain Irrigation. This plot is adapted from Ref. [16], showing the variation in expected flow rate (gray band) over the same pressure range investigated in this study, due to tolerances of ±0.01 mm on Dch and ±0.05 mm on Wch. The gray line is the nominal flow rate specified by Jain, with the circles showing results from their data sheet. Experimental data were collected at MIT using the process described in Ref. [16].

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Fig. 5

Flow rate versus inlet pressure for the optimized emitter (MIT) compared to commercially available 8 lph emitters. The optimized emitter (MIT) is depicted as the bold line with circular markers and has an activation pressure that is 21.4% that of Netafim's [25] (bold black line) and 16.7% that of Toro's [24] (bold line with plus markers) and Jain's [23] (dashed line with cross markers). The results for the MIT emitter are averaged data from ten injection molded emitters; the coefficient of variation at every tested pressure point is less than 0.08. The data for the commercial emitters were obtained from their respective specification sheets. The vertical dotted lines denote activation pressures. The horizontal dotted lines denote ±10% variation from the MIT dripper's nominal flow rate of 8.2 lph, which corresponds to allowable industry standards.

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Fig. 6

Capital cost analysis for a representative solar-powered, off-grid drip irrigation system in global markets (rated in $USD). Capital cost analysis of the drip irrigation system required for a representative 1 acre banana farm operating at (a) 1.55 bar (assuming 0.15 bar dripper activation pressure) and (b) 2.4 bar (assuming 1 bar dripper activation pressure) in both Indian and global (tier 1) markets. The estimated capital cost includes the smallest available solar pump required to move water from the source through a system of lateral pipes and drip emitters, sized for 1 day of autonomous off-grid use, a filter system to reduce emitter clogging, pipes to convey water from the source to the drip emitters, valves and joints, and 8 lph drip emitters to produce a controlled flow of water near the plant roots.



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