Simulating the dynamics of spray droplets in the atmosphere using ballistic and random-walk models combined
This paper presents a simulation model based on earlier work that combines both ballistic and random-walk models to describe the three-dimensional dynamics of spray droplets released in a specified direction from ground-based appliances in various weather conditions. The velocity of spray droplets i...
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Published in | Journal of wind engineering and industrial aerodynamics Vol. 67; pp. 923 - 933 |
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Main Authors | , , , |
Format | Journal Article |
Language | English |
Published |
Amsterdam
Elsevier Ltd
01.04.1997
Elsevier Science |
Subjects | |
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Abstract | This paper presents a simulation model based on earlier work that combines both ballistic and random-walk models to describe the three-dimensional dynamics of spray droplets released in a specified direction from ground-based appliances in various weather conditions. The velocity of spray droplets is considered as a weighted sum of their ballistic and random-walk velocities scaled by a factor (1−β) and β, respectively, where β is defined as the ratio of the sedimentation velocity and the relative velocity between the spray droplets and the ambient wind speed. The contribution of the random-walk model to the initial velocity is seen to be negligible at first, but increases progressively, though not proportionally, as β increases. As soon as the spray droplets attain their sedimentation velocities,
β = 1, the random-walk velocity component predominates and β plays no further part in the calculations. The predicted effects close to the sprayer of the drop size, wind velocity and direction, evaporation on the transport process have been evaluated and combined to provide an analysis of spray drift. |
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AbstractList | The trajectories of agrochemical spray droplets are controlled by the prevailing atmospheric conditions, including the frictional forces due to wind motion and external body forces like gravity. A three-dimensional model is developed to calculate the dynamics of spray droplets, which accounts for the combined effects of turbulence and momentum loss by considering the velocities of the spray droplets as a weighted sum of their ballistic and random-walk velocities. The ballistic velocities are calculated using Newton's second law of motion, and the random-walk velocities are obtained using the Markov process. The effects of air entrainment and evaporation are also considered. All governing equations are elucidated, and results are presented from a preliminary model evaluation using two weather conditions. This paper presents a simulation model based on earlier work that combines both ballistic and random-walk models to describe the three-dimensional dynamics of spray droplets released in a specified direction from ground-based appliances in various weather conditions. The velocity of spray droplets is considered as a weighted sum of their ballistic and random-walk velocities scaled by a factor (1−β) and β, respectively, where β is defined as the ratio of the sedimentation velocity and the relative velocity between the spray droplets and the ambient wind speed. The contribution of the random-walk model to the initial velocity is seen to be negligible at first, but increases progressively, though not proportionally, as β increases. As soon as the spray droplets attain their sedimentation velocities, β = 1, the random-walk velocity component predominates and β plays no further part in the calculations. The predicted effects close to the sprayer of the drop size, wind velocity and direction, evaporation on the transport process have been evaluated and combined to provide an analysis of spray drift. This paper presents a simulation model based on earlier work that combines both ballistic and random-walk models to describe the three-dimensional dynamics of spray droplets released in a specified direction from ground-based appliances in various weather conditions. The velocity of spray droplets is considered as a weighted sum of their ballistic and random-walk velocities scaled by a factor (1- beta ) and beta , respectively, where beta is defined as the ratio of the sedimentation velocity and the relative velocity between the spray droplets and the ambient wind speed. The contribution of the random-walk model to the initial velocity is seen to be negligible at first, but increases progressively, though not proportionally, as beta increases. As soon as the spray droplets attain their sedimentation velocities, beta identical with 1, the random-walk velocity component predominates and beta plays no further part in the calculations. The predicted effects close to the sprayer of the drop size, wind velocity and direction, evaporation on the transport process have been evaluated and combined to provide an analysis of spray drift. |
Author | Salt, D.W. Ford, M.G. Lee, B.E. Mokeba, M.L. |
Author_xml | – sequence: 1 givenname: M.L. surname: Mokeba fullname: Mokeba, M.L. – sequence: 2 givenname: D.W. surname: Salt fullname: Salt, D.W. – sequence: 3 givenname: B.E. surname: Lee fullname: Lee, B.E. email: blee@civl.port.ac.uk – sequence: 4 givenname: M.G. surname: Ford fullname: Ford, M.G. |
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Cites_doi | 10.1016/0021-8634(83)90134-8 10.1016/0021-8634(77)90097-X 10.13031/2013.36835 10.1002/aic.690120416 10.1016/0021-8634(89)90046-2 10.1007/BF02186086 |
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Keywords | Spray drift Wind Simulation Dynamics Ground-based appliances Spray droplets Computational fluid dynamics Ground based measurement Spraying Aerodynamics Velocity distribution Evaporation Ballistic transport Droplet Three dimensional model Random walk model Mixed model Numerical simulation Trajectory |
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References | Miller, Hadfield (BIB2) 1988; 42 Schaefer, Allsopp (BIB3) 1983; vol. 3 Briffa, Dombrowski (BIB9) 1966; 12 Ranz, Marshall (BIB10) 1952; 48 Lafara (BIB11) 1973 Thompson, Ley (BIB4) 1983; 28 Panofsky, Tennekes, Lenshow, Wyngaard (BIB7) 1977; 11 Williamson, Threadgill (BIB5) 1974; 17 Bache, Johnson (BIB6) 1992 Marchant (BIB1) 1977; 22 Panofsky, Dutton (BIB8) 1984 Schaefer (10.1016/S0167-6105(97)00129-3_BIB3) 1983; vol. 3 Panofsky (10.1016/S0167-6105(97)00129-3_BIB7) 1977; 11 Bache (10.1016/S0167-6105(97)00129-3_BIB6) 1992 Briffa (10.1016/S0167-6105(97)00129-3_BIB9) 1966; 12 Miller (10.1016/S0167-6105(97)00129-3_BIB2) 1988; 42 Thompson (10.1016/S0167-6105(97)00129-3_BIB4) 1983; 28 Panofsky (10.1016/S0167-6105(97)00129-3_BIB8) 1984 Williamson (10.1016/S0167-6105(97)00129-3_BIB5) 1974; 17 Marchant (10.1016/S0167-6105(97)00129-3_BIB1) 1977; 22 Ranz (10.1016/S0167-6105(97)00129-3_BIB10) 1952; 48 Lafara (10.1016/S0167-6105(97)00129-3_BIB11) 1973 |
References_xml | – volume: 42 start-page: 135 year: 1988 end-page: 147 ident: BIB2 article-title: A simulation of the spray drift from hydraulic nozzles publication-title: J. Agric. Eng. Res. contributor: fullname: Hadfield – start-page: 397 year: 1984 ident: BIB8 article-title: Atmospheric Turbulence contributor: fullname: Dutton – volume: vol. 3 start-page: 1057 year: 1983 end-page: 1065 ident: BIB3 article-title: Spray droplet behaviour above and within a canopy publication-title: Proc. 10th Int. Congr. on Plant Protection contributor: fullname: Allsopp – volume: 11 start-page: 355 year: 1977 end-page: 361 ident: BIB7 article-title: The characteristics of turbulent velocity components in the surface layer under convective conditions publication-title: Boundary-layer Meteorol. contributor: fullname: Wyngaard – volume: 48 start-page: 173 year: 1952 end-page: 180 ident: BIB10 article-title: Evaporation from drops publication-title: Chem. Eng. Prog. contributor: fullname: Marshall – start-page: 239 year: 1992 ident: BIB6 article-title: Microclimate and Spray Dispersion contributor: fullname: Johnson – volume: 12 start-page: 708 year: 1966 end-page: 717 ident: BIB9 article-title: Entrainment of air into a liquid spray publication-title: Am. Inst. Chem. Eng. contributor: fullname: Dombrowski – volume: 22 start-page: 93 year: 1977 end-page: 96 ident: BIB1 article-title: Calculation of spray droplet trajectory in a moving airstream publication-title: J. Agric. Eng. Res. contributor: fullname: Marchant – start-page: 326 year: 1973 ident: BIB11 article-title: Computer methods for Science and Engineering contributor: fullname: Lafara – volume: 28 start-page: 419 year: 1983 end-page: 435 ident: BIB4 article-title: Estimating spray drift using random-walk model of evaporating drops publication-title: J. Agric. Eng. Res. contributor: fullname: Ley – volume: 17 start-page: 254 year: 1974 end-page: 261 ident: BIB5 article-title: A simulation for the dynamics of evaporating spray droplets in agricultural spraying publication-title: Trans. Am. Soc. Agric. Eng. contributor: fullname: Threadgill – volume: 28 start-page: 419 year: 1983 ident: 10.1016/S0167-6105(97)00129-3_BIB4 article-title: Estimating spray drift using random-walk model of evaporating drops publication-title: J. Agric. Eng. Res. doi: 10.1016/0021-8634(83)90134-8 contributor: fullname: Thompson – volume: 22 start-page: 93 year: 1977 ident: 10.1016/S0167-6105(97)00129-3_BIB1 article-title: Calculation of spray droplet trajectory in a moving airstream publication-title: J. Agric. Eng. Res. doi: 10.1016/0021-8634(77)90097-X contributor: fullname: Marchant – volume: 17 start-page: 254 year: 1974 ident: 10.1016/S0167-6105(97)00129-3_BIB5 article-title: A simulation for the dynamics of evaporating spray droplets in agricultural spraying publication-title: Trans. Am. Soc. Agric. Eng. doi: 10.13031/2013.36835 contributor: fullname: Williamson – volume: 12 start-page: 708 issue: 4 year: 1966 ident: 10.1016/S0167-6105(97)00129-3_BIB9 article-title: Entrainment of air into a liquid spray publication-title: Am. Inst. Chem. Eng. doi: 10.1002/aic.690120416 contributor: fullname: Briffa – volume: 42 start-page: 135 year: 1988 ident: 10.1016/S0167-6105(97)00129-3_BIB2 article-title: A simulation of the spray drift from hydraulic nozzles publication-title: J. Agric. Eng. Res. doi: 10.1016/0021-8634(89)90046-2 contributor: fullname: Miller – volume: vol. 3 start-page: 1057 year: 1983 ident: 10.1016/S0167-6105(97)00129-3_BIB3 article-title: Spray droplet behaviour above and within a canopy contributor: fullname: Schaefer – start-page: 239 year: 1992 ident: 10.1016/S0167-6105(97)00129-3_BIB6 article-title: Microclimate and Spray Dispersion contributor: fullname: Bache – volume: 48 start-page: 173 year: 1952 ident: 10.1016/S0167-6105(97)00129-3_BIB10 article-title: Evaporation from drops publication-title: Chem. Eng. Prog. contributor: fullname: Ranz – volume: 11 start-page: 355 year: 1977 ident: 10.1016/S0167-6105(97)00129-3_BIB7 article-title: The characteristics of turbulent velocity components in the surface layer under convective conditions publication-title: Boundary-layer Meteorol. doi: 10.1007/BF02186086 contributor: fullname: Panofsky – start-page: 397 year: 1984 ident: 10.1016/S0167-6105(97)00129-3_BIB8 article-title: Atmospheric Turbulence contributor: fullname: Panofsky – start-page: 326 year: 1973 ident: 10.1016/S0167-6105(97)00129-3_BIB11 article-title: Computer methods for Science and Engineering contributor: fullname: Lafara |
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Snippet | This paper presents a simulation model based on earlier work that combines both ballistic and random-walk models to describe the three-dimensional dynamics of... The trajectories of agrochemical spray droplets are controlled by the prevailing atmospheric conditions, including the frictional forces due to wind motion and... |
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SubjectTerms | Applied sciences Buildings. Public works Climatology and bioclimatics for buildings Computation methods. Tables. Charts Computer simulation Domestic appliances Dynamics Exact sciences and technology Ground-based appliances Mathematical models Simulation Spray drift Spray droplets Structural analysis. Stresses Wind |
Title | Simulating the dynamics of spray droplets in the atmosphere using ballistic and random-walk models combined |
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