# Sprinkler irrigation droplet dynamics. II: Numerical solution and model evaluation

Published on May 1, 2016in Journal of Irrigation and Drainage Engineering-asce1.34
· DOI :10.1061/(ASCE)IR.1943-4774.0001004
D. Zerihun7
Estimated H-index: 7
(UA: University of Arizona),
Charles A. Sanchez24
Estimated H-index: 24
(UA: University of Arizona),
Arthur W. Warrick29
Estimated H-index: 29
(UA: University of Arizona)
Abstract
AbstractA system of equations, with strong physical basis, was derived for sprinkler irrigation droplet dynamics in the companion paper. Numerical solution of these equations and model evaluation is discussed in this paper. With the aim of enhancing computational efficiency and robustness, the droplet dynamics equations were scaled using four characteristic variables: characteristic time, length, velocity, and density. The characteristic time, length, and velocity are derived based on consideration of the motion of a droplet falling freely, starting from rest, through a quiescent ambient air, to an eventual steady-state condition. The characteristic density was set to the density of water at standard conditions. The dimensionless system of equations was then solved numerically with a fourth-fifth order pair Runge-Kutta method capable of local error estimation and time-step size control. The numerical model was first evaluated through successful comparisons with simplified solutions derived based on more l...
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References17
#1John R. DormandH-Index: 1
Differential Equations Classification of Differential Equations Linear Equations Non-Linear Equations Existence and Uniqueness of Solutions Numerical Methods Computer Programming First Ideas and Single-Step Methods Analytical and Numerical Solutions A First Example The Taylor Series Method Runge-Kutta Methods Second and Higher Order Equations Error Considerations Definitions Local Truncation Error for the Taylor Series Method Local Truncation Error for the Runge-Kutta Method Local Truncation and...
#1D. Zerihun (UA: University of Arizona)H-Index: 7
#2Charles A. Sanchez (UA: University of Arizona)H-Index: 24
Last. Arthur W. Warrick (UA: University of Arizona)H-Index: 29
view all 3 authors...
AbstractDroplet dynamics simulations are key to predicting sprinkler irrigation precipitation patterns. This paper includes derivations of equations describing droplet motion through a steady, uniform horizontal airflow (wind). The assumptions on which sprinkler irrigation droplet dynamics is based are stated, and the limitations they entail are highlighted. The motion of droplets is treated as an impulsively started accelerated motion of rigid spheres, originating at the sprinkler nozzle with k...
#1David J. Griffiths (Dund.: University of Dundee)H-Index: 45
#2Desmond J. HighamH-Index: 42
Numerical Methods for Ordinary Differential Equations is a self-contained introduction to a fundamental field of numerical analysis and scientific computation. Written for undergraduate students with a mathematical background, this book focuses on the analysis of numerical methods without losing sight of the practical nature of the subject. It covers the topics traditionally treated in a first course, but also highlights new and emerging themes. Chapters are broken down into 'lecture' size piece...
#1John C. ButcherH-Index: 34
A new edition of this classic work, comprehensively revised to present exciting new developments in this important subject The study of numerical methods for solving ordinary differential equations is constantly developing and regenerating, and this third edition of a popular classic volume, written by one of the world’s leading experts in the field, presents an account of the subject which reflects both its historical and well-established place in computational science and its vital role as a c...
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Last. José-María MonteroH-Index: 16
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#1George Lindfield (Aston University)H-Index: 2
#2John E. T. Penny (Aston University)H-Index: 14
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#1Ido SeginerH-Index: 27
#2Dov NirH-Index: 3
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Single‐sprinkler wind‐distorted distribution patterns are simulated utilizing drop trajectory computations, and compared with measured patterns. It is found that the exact formulation of the drag coefficient of single drops is not critical for applications focusing on water distribution. A drag correction factor, k is introduced to account for the effect of the incidence angle between drag force and orientation of a jet segment. The agreement between measured and computed patterns improves consi...
The effect of changing the trajectory angle of a medium‐sized irrigation sprinkler operating in windy conditions has been studied using a computersimulation model. The model, which has been verified both in still air and under windy conditions, shows that the trajectory angle that maximizes distance of throw is a function of the wind velocity and varies from 29° in still air to less than 5° in winds greater than 8 m/s. The advantage gained from trajectory angles greater than 25° in still air is ...
#1E. D. VoriesH-Index: 2
#2R. D. von BernuthH-Index: 4
Last. R. H. MickelsonH-Index: 1
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The uniformity of irrigation systems is important to efficiency, yield, and economics. Wind strongly affects this uniformity. A method is presented for simulating the operation of a sprinkler system in wind. Equations describing the motion of airborne water droplets are shown. The trajectories of water droplets ejected from a sprinkler were numerically computed. Composite results led to predictions of application patterns. Sprinkler droplet size distribution was used to predict the pattern aroun...
#1William H. Press (Harvard University)H-Index: 1
#2Brian P. Flannery (ExxonMobil)H-Index: 28
Last. William T. Vetterling (Polaroid Corporation)H-Index: 21
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