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Computers and Electronics in Agriculture 56 (2007) 161–173

Predicting drift from field spraying by means of a 3Dcomputational fluid dynamics model

K. Baetens a,∗, D. Nuyttens b, P. Verboven a, M. De Schampheleire c,B. Nicolaı a, H. Ramon a

a BIOSYST-MeBioS, Catholic University of Leuven, de Croylaan 42, 3001 Leuven, Belgiumb Institute for Agricultural and Fisheries Research (ILVO), Scientific Institute of the Flemish Community, Unit Technology and

Food-Agricultural Engineering, Burg. Van Gansberghelaan 115, 9820 Merelbeke, Belgiumc Department of Crop Protection, University Ghent, Coupure Links 653, 9000 Ghent, Belgium

Received 14 April 2006; received in revised form 25 January 2007; accepted 26 January 2007

Abstract

In order to investigateand understand driftfrom fieldsprayers,a steady statecomputational fluiddynamics (CFD)model was devel-

oped. The model was developed in 3D in order to increase the understanding of the causes of drift: a deviation in the wind direction

cannot be captured by a 2D approach, the wake behind a wind screen is not symmetrical, the effects of a changed nozzle orientation

may not be symmetrical. The model’s accuracy was validated with field experiments carried out according to the international stan-

dard ISO 22866. A fieldsprayer with a spray boom width of 27m and 54nozzles (Hardi ISO F110-03 at 3 bar) was driving at 2.22m/s

over a flatpasture.During theexperiments the wind directionwas perpendicular to thetractor track.The model explained the variation

in drift replicates during each single field experiment through varying boom height (0.3–0.7m), wind velocity (1.3–2.5 m/s), wind

deviation (−18

◦

to+18

◦

) from thedirection perpendicular to the tractor track andinjection velocityof thedroplets (17–27m/s).Boommovements hadthe highest impact on the variations in drift values (deviations in drift deposits of 25%), followed by variation in wind

velocity (deviations in drift deposits of 3%) and injection velocity of the droplets (deviations in drift deposits of 2.5%). Wind devia-

tion from the direction perpendicular to the tractor track had a reducing effect on the drift values (deviations in drift deposits of 2%).

Small variations in driving speed hadlittle influence on drift values. Near drift (<5m) is predicted well by the model but the increased

complexity compromised the predictions at greater distances. The model will be further developed in order to improve far drift pre-

diction. Dynamic simulations will be performed and the model for turbulent dispersion will be optimized. The model did not require

calibration.

© 2007 Elsevier B.V. All rights reserved.

Keywords: Spray drift; Field sprayer; Computer simulation; Model; Sensitivity analysis; Crop protection

1. Introduction

Drift or the unintentional deposit of pesticides next to the application field duringsprayingmay cause many problems,

including damage to neighboring crops, ecosystems, water ways and human health. Especially in Flanders which is

known to have an intensive agriculture and relatively small fields that are scattered and close to living area, the need

∗ Corresponding author. Tel.: +32 16 320588; fax: +32 16 322955.

E-mail address: [email protected] (K. Baetens).

0168-1699/$ – see front matter © 2007 Elsevier B.V. All rights reserved.

doi:10.1016/j.compag.2007.01.009

mailto:[email protected]

http://localhost/var/www/apps/conversion/tmp/scratch_4/dx.doi.org/10.1016/j.compag.2007.01.009

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mailto:[email protected]

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162 K. Baetens et al. / Computers and Electronics in Agriculture 56 (2007) 161–173

for a good understanding of drift from field sprayers is a high priority. A review about the current knowledge of drift

has been presented by Gil and Sinfort (2005).

There are a number of good field drift models available (Holterman et al., 1997; Mokeba et al., 1997; Zhu et

al., 1994; Miller and Hadfield, 1989; Thompson and Ley, 1983). However, none of the above models investigate the

variability found in drift values during field experiments. The variability of drift can be quite high during one exper-

iment (Nuyttens et al., 2006b). This variability can be significant in order to make a realistic drift risk assessment.

Some of the earlier developed models are only 2D, whereas the arrangement of the nozzles and the air entrain-ment requires a 3D approach. Therefore these models only start modelling the droplet tracks at a rather undefined

position under the nozzle (Zhu et al., 1994; Miller and Hadfield, 1989). The 2D/3D model of Holterman et al.

(1997) accounts for 3D nozzle flow and air entrainment. However, the droplet flow model is not fully coupled to

the wind flow model, resulting in a pragmatic approach to the entrainment problem. A practical pesticide appli-

cation tool for farmers was developed by Zhu et al. (1995), but this tool is based on a 2D model verified against

results obtained by droplets of a uniform diameter and validated in a wind tunnel, so not including the effect of vari-

ability in environmental parameters nor including the effect of a non-uniform droplet size distribution produced by

nozzles.

The presented work aims to contribute to the interpretation of the already developed models by developing a 3D fully

mechanistic model constructed in CFX 5.7 (Ansys CFX, Canonsburg, PA). A 3D approach was chosen because not all

flow problems have a symmetrical solution. A deviation in the wind direction cannot be captured by a 2D approach: thewake behind a wind screen is not symmetrical and the effects of a changed nozzle orientation may not be symmetrical.

The Reynolds averaged Navier–Stokes equations with a k –ε model for turbulence accounting for the flow field model

were fully coupled to a Lagrangian particle tracking model. A Lagrangian approach was chosen due to its particular

advantage of straightforwardly accounting for droplet trajectory crossing (Chen and Pereira, 1996). The drift model

was validated by means of field experiments. During field experiments it is impossible to keep wind velocity, wind

direction, boom height and tractor speed constant. Moreover, it is difficult to obtain realistic input data for injection

velocity of droplets. Therefore an investigation on the influence of the temporal variation of these parameters during

experiments was performed.

2. Materials and methods

2.1. Field experiments

The model was developed to simulate field experiments performed in the summer of 2005 in Merelbeke, Belgium

(ILVO, Nuyttens et al., 2006b). Theseexperiments were all carried out accordingto the internationalstandard ISO 22866

(2005) f or field drift measurements. In these experiments a trailed field sprayer (Hardi Commander Twin Force) with a

boomwidth of27 m was spraying a 100 m distance with a nominal speed of2.22m/s overa pasture.No air assistance was

used. The wind direction was approximately perpendicular to the driving direction of the tractor. The sprayed liquid con-

sisted of water mixed with Brilliant Sulfo Flavine (BSF), a fluorescent tracer. The nozzle distance and boom height were

0.5 m. The nozzle type used was a Hardi ISO 110 03 standard flat fan nozzle at 300 kPa (1.2l/min) resulting in an appli-

cation volume of 180 l/ha. The nozzles were placed in such a way that the longest axis of the cross section of the spraymadean angle of8◦ with the longitudinal axis of the boom sprayer. Samples of filter paper (0.25 m×0.25m) wereputat

0.5, 1, 2, 3, 5, 10, 15 and 20 m from the directly sprayed zone in order to investigate drift at various distances down wind

from the outer nozzle of the boom. This sample row was replicated three times during each run with a distance of 10 m

between each replicate. Drift (vol.%) in each sampling point was calculated by dividing the mass deposit at the sampling

points by themeasuredmass deposit in thedirectlysprayed zone. Duringeach experiment thewind velocityand direction

at 1.5 and 3.25 m height were measured by means of ultrasonic anemometers together with air temperature and relative

humidity.

Three experiments (in three replicates) at different meteorological conditions were performed and used for model

validation. ‘Experiment 1’ had a ‘reference’ (at 1.5 m height) wind velocity of 2.0 m/s, ‘Experiment 2’ 3.1 m/s and

‘Experiment 3’ 3.9 m/s. Table 1 details the meteorological circumstances of each experiment. The drift deposit results

of the experiments are in the same range as found by Holterman et al. (1997).

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K. Baetens et al. / Computers and Electronics in Agriculture 56 (2007) 161–173 163

Table 1

Meteorological values during each experiment

Experiment 1 Experiment 2 Experiment 3

Wind deviation (◦) −18.08 −18.50 3.13

Deviation range (◦) 1.38 20.00 12.63

Relative humidity (%) 79.99 61.79 68.06

Temperature (◦C) 16.19 22.03 13.61Velocity at 1.5 m (m/s) 2.00 3.12 3.94

Velocity at 3.25 m (m/s) 2.47 3.67 4.62

Maximum velocity at 1.5 m (m/s) 2.22 3.80 3.94

Minimum velocity at 1.5 m (m/s) 1.30 2.64 3.10

A negative deviation means the tractor is driving down wind.

2.2. Model formulation

The model uses a 3D CFD (computational fluid dynamics) approach to predict drift. The CFD code used in this work

is ANSYS CFX 5.7 (Ansys, Inc., Canonsburg, PA, USA). The domain width was set to 60 m (20 m of sampling length

and 27 m of boom width and some space for the wind profile to settle). The length was set to 100 m (representing thedriving distance covered by the tractor). The 3D model domain (see Fig. 1) consisted of a base plane (called ‘pasture

plane’) of 60 m× 100 m representing the pasture. The height of the domain has to be sufficient to model the boundary

layer. This height was determined to be 6 m by means of numerical experiments and verification against the methods

and results of Blocken et al. (2007).

2.3. Droplet spray model

For discrete droplets travelling in a continuous fluid medium, the acting forces on the droplet that affect the droplet

acceleration are due to the difference in velocity between the droplet and the fluid and due to the displacement of the

fluid particle. Neglecting all the other forces except the drag and buoyancy forces, the following equation of motion

for the droplet was used:

mddvdi

dt =

1

8πρd 2cd|vi − vdi|(vi − vdi) +

1

6πd 3(ρd − ρ)gi (1)

where md is the droplet mass (kg), d the droplet diameter (m), suffix i represents the direction (i = x , y or z), νi

the continuous fluid velocity including a turbulent component that implements the turbulent dispersion (m/s), νdi the

discrete droplet velocity (m/s), cd the drag coefficient, ρd the discrete droplet density (kg/m3), ρ the air density (kg/m3),

gi the gravitational acceleration (m/s2), and t is the time (s).

The drag coefficient (cd) in Eq. (1) was calculated using the Ishii–Zuber drag model (Ishii and Zuber, 1979). It is

an empirical correlation based on the shape and state of the particles. At sufficiently small Reynold numbers droplets

behave as solid spherical particles, the drag coefficient for this regime will be referred by as cd,sphere. At larger Reynolds

Fig. 1. Scheme of the rectangular domain used as the drift modeling area. The black arrows represent the cross wind. The white arrow represents

the driving direction. The position of the nozzles (27 in total) is indicated by the white line on the bottom of the model.

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numbers droplets become first ellipsoidal in shape (drag coefficient will be referred by as cd,ellipse) to finally become

spherical cap shaped (drag coefficient will be referred by as cd,cap). The drag coefficient for spherical fluid droplets is

based on the Schiller Naumann drag coefficient (Schiller and Naumann, 1933) using a Reynolds mixture number for

incorporating the density of the droplets:

cd,sphere =24

Rem

(1 + 0.15Re0.687m )

where Rem is a mixture Reynolds number based on a mixture viscosity, defined by

Rem =ρ|vi − vdi|d

µm

and µm is the mixture viscosity (kg/(m s)) defined by

µm

µc= (1 − rd)−2.5µ∗

µc is the viscosity of the continuous phase (kg/(m s)), r d the discrete phase volume fraction and µ* is defined by

µ∗ =µd + 0.4µc

µd + µc

with µd is the viscosity of the discrete phase (kg/(m s)).

The drag coefficient for densely distributed ellipse shaped particles is defined as

cd,ellipse = E(rd) · cd∞

E (r d) defined by

E(rd) =1 + 17.67f (rd)6/7

18.67f (rd)

and

f (rd) =µc

µm

· (1 − rd)1/2

cd∞ defined by

cd∞ = 23 E0

1/2

where E 0 or the Eotvos number is known as the dimensionless group through which the drag coefficient of ellipse

shaped droplets is determined. It is defined by

E0 =g · ρ · d 2p

σ

with g is the gravitational acceleration (m/s2), ρ the density difference of the two phases (kg/m3) and σ is the surface

tension coefficient (N/m).

The drag coefficient for densely distributed cap shaped particles is defined as

cd,cap = (1 − rd)2cd∞

with cd∞ =8/3.

The CFX code pulls through an automatic regime selection by the following procedure:

cd = cd,sphere if cd,sphere ≥ cd,ellipse

cd = min(cd,ellipse, cd,cap) if cd,sphere < cd,ellipse

Most drift models use the model of Schiller and Naumann (1933) to calculate the drag coefficient. The benefit of

this model is that the effect of the density of the droplets and the shape of the droplets on the droplet track is integrated

in the calculation of the droplet track.

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The particle displacement ( x i) is calculated using forward Euler integration of the particle velocity over time step,

δt :

xni = xo

i + vdiδt

where the superscripts o and n refer to the old and new values, respectively. The particle velocity at the beginning

of the time step is assumed to prevail over the entire step. At the end of each time step, the new particle velocity is

calculated from Eq. (1). As the velocity fluctuations of the air flow are not available within the k –ε model it is the task of a turbulent dispersion model to regenerate accurate velocity fluctuation. The model for turbulent dispersion used in

this study was developed by Gosman and Ioannides (1981).

The source/sink termS u inEq. (2) representsthe integrated effectsof momentumexchange withthe continuous phase.

These Eulerian variables are calculated from the Lagrangian droplet variables by volume averaging the contributions

from all individual droplets within the cell volume. The coupling term is given as

S u = −1

V cell

nd d

dt (mdvdi) = −

1

V cell

ndmd

dvdi

dt (2)

where nd is the number of droplets in the cell and V cell is the cell volume (m3). The first term on the right-hand side

of Eq. (2) results from the interaction forces between the two phases without any phase change. A more in depthmathematical description can be found in Delele et al. (2005).

2.4. Atmospheric airflow model

Since the air flow of interest takes part of a bigger flow field (the atmosphere), it is of high importance that proper

boundary conditions are set in order to simulate a continuum between modelled field area and the atmosphere.

The wind flow is modelled by introducing a logarithmic wind profile above the crop at the upwind side of the

pasture. The logarithmic wind profile is given by the following equation:

u(z) =u∗

κln

z + d r

d r

where u( z) (m/s) is the wind velocity at a height z (m), u* the friction velocity (m/s). κ the von Karman constant (0.41)and d r the roughness length (m). The roughness length of this profile is fitted to the experimental wind velocity profile

of the experiment (see Fig. 2 f or an example). The deviation of the cross wind direction was measured and taken into

account in the model. Due to the small height of the pasture grass, the wind profile inside the crop canopy has not been

modelled. Relative humidity and temperature were assumed to be constant throughout the simulations. The tractor was

driving in a crosswind at 2.22 m/s. This is simulated by introducing a moving coordinate system in which the ‘pasture

plane’ was set to be a moving wall with a velocity of 2.22 m/s in the opposite direction of the driving direction. At the

inlet planes an apparent wind of 2.22 m/s in the same direction was added.

The kinetic energy and dissipation parameters are implemented at the inlet boundaries according to the theory of

atmospheric boundary layers (Blocken et al., 2007):

k =

u2∗

C0.5

, ε =

u3∗

κ(z + d r)

with k is the kinetic energy (m2 /s2). C is an internal model constant (0.09) and ε is the eddy dissipation velocity

(m3 /s2).

The airflow above the field was solved by means of the Reynolds averaged Navier–Stokes equations with the k –ε

model of turbulence (Wilcox, 2000) and source terms. The pasture was assigned a roughness length of 0.01 m, the

value for grass lands (Tieleman, 2003).

2.5. Nozzle characteristics

The droplet diameter distribution of the ISO 110-03 nozzle (at 300 kPa) was obtained from experiments with a Phase

Doppler Particle Analyser (Aerometrics Inc.) in a conditioned room (Nuyttens et al., 2006a). The droplet diameter

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Fig. 2. Logarithmic wind profile at the inlet planes of the model (solid line). The dots represent the experimental values of the wind speed at 1.5 m

(2 m/s) and at 3.25 m (2.47 m/s). The obtained roughness length (d r) was 0.056 m.

distribution was fitted by a Rosin Rammler model (Fig. 3) with a spreading factor γ of 3.2441 and a diameter d e at

which the cumulative mass fraction becomes 1/ e. The value of d e was 310m. The liquid sheet break-up length of

the nozzle was 0.023 m (Bayvel and Orzechowski, 1993). The randomized horizontal injection position of the droplets

was attained by distributing the droplets at random over the ellipse area of the spray cross section at a distance from

the nozzle equal to the break-up length. The vertical injection velocity of the droplets was assumed constant and equal

to 20 m/s for all droplets (Sidahmed et al., 2005). Sidahmed et al. (2005) measured a droplet velocity in the range of

14–22 m/s with an average of 17 m/s at 0.04 m from the orifice of a flat fan nozzle ISO F 110-03 at 200 kPa. Droplet

velocity was found to depend on droplet diameter. For this work (working pressure of 300 kPa), the average velocity

was augmented with a factor of (3/2)1/2 based on Bernouilli’s law. A constant velocity injection value of 20 m/s wastherefore used, as was the case in the models of Zhu et al. (1995) and Holterman et al. (1997). The other injection

velocity components were determined from the fan angle (110◦), its shape and the droplet’s starting position in the

ellipse.

2.6. Numerical procedure

The model was solved numerically using the finite volume method. The simulations were performed on a P4 2.6 GHz

PC with 1 Gb RAM requiring an average of 65,000 CPU seconds for each simulation. Unstructured tetrahedral volume

Fig. 3. Rosin Rammler distribution fitted to experimental data of the droplet size distribution of an ISO F110-03 nozzle working under a pressure

of 300 kPa, a spreading factor (γ ) of 3.2441 and a reference diameter (d e) of 310m.

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Fig. 4. Predicted drift values (vol.%) obtained at different distances from the field by modeling 1000 dpn (droplets per nozzle), 10,000 dpn and

20,000dpn.

elements were used with prismatic elements on the ground surface. Eight lakh elements were required for mesh

independent results. The drift values from a reference simulation with 27 nozzles and injecting respectively 1000,

10,000 and 20,000 droplets per nozzle are presented in Fig. 4. The drift values for a model using 1000, 10,000 and

20,000 droplets per nozzle were almost identical, with increasing relative differences with distance. A trade-off between

computational effort and accuracy was achieved at 10,000 droplets per nozzle.

Drift values from a reference simulation using 14, 27 and 54 nozzles are compared in Fig. 5. From Fig. 5 it becomes

clear that droplets from the outer nozzle sprays still contribute to drift. Indeed, the drift profile changes when modelling

the complete boom (54 nozzles) and when modelling only half a boom (27 nozzles). The far distance (>5 m) drift profile

is most affected, though considering the logarithmic scale of the graph minimal. The changes in the nearby drift profile

are small. A trade-off in favour of the use of computational effort was made and simulations were performed with 27

nozzles.

Fig. 5. Predicted drift values (vol.%) obtained at different distances from the field by modelling 14 nozzles, 27 nozzles and 54 nozzles.

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2.7. Parameter sensitivity study

The influence of the variation of boom height, tractor speed, injection velocity of the droplets and wind speed on

drift values was studied. While the model is formulated in steady state, only the effect of the vertical boom height was

investigated without dynamic boom movement. Langenakens et al. (1999) measured a maximum deviation of 0.39 m

for a boom moving at 2.22 m/s. Simulations were therefore performed with three different boom heights, namely 0.3,

0.5 and 0.7 m. Driving speeds were changed from 1.94 m/s (or 7 km/h) to 2.22 m/s (or 8 km/h) to 2.5 m/s (or 9 km/h),according to the round off error of the tractor speed indicator. During the performance of one experiment, the wind

velocity at a height of 1.5 m was changing. For example, in Experiment 1, the minimally and maximally measured

wind velocity values were 1.3 and 2.2 m/s with an average value of 2.0 m/s. These three values are used to study the

effect of a changing wind velocity during one experiment. The tractor was not driving perfectly crosswind, a deviation

from this direction was measured during the experiment. This deviation was implemented in the model. The resulting

variation in drift obtained by the model was compared to the variation observed in each experiment. As explained

earlier, Sidahmed et al. (2005) measured a droplet velocity in the range of 14–22 m/s 0.04 m from the orifice of a flat

fan nozzle ISO F 110-03 at 200 kPa. Hence, after augmenting these outer values with a factor of (3/2)1/2, simulations

with droplet velocities of 17, 20 and 27 m/s were studied.

Eventually, the obtained drift curves were evaluated by calculating the surface under the drift curve. Using this

method the ‘total drift’ of a simulation over a distance from 0 to 20 m was determined. The same method was used todetermine short distance drift (0–5 m) and far distance drift (5–20 m).

3. Results

In Fig.6 the predicted trajectories of individual droplets during field spraying are presented. The gray scale represents

the diameters of the droplets. The conical and dense sprays can be recognized underneath the nozzles. Due to the cross

wind, smaller droplets tend to drift across the field boundary. The smaller the droplet, the further they drift. It is also

important to notice that all nozzles contribute to the far distance drift (>5 m), while the near distance drift (<5 m) is

mainly due to larger drops from the nozzles closest to the field boundary.

In Fig. 7 the model predictions are compared to the measured drift profiles for each experiment. The difference

between experiments is mainly caused by variations in wind velocity. The predicted near distance drift (<5 m) corre-sponds well with the experimental values. At far distance, the model always predicts significantly lower values than

in the experiment. In average terms, the total measured nearby (<5 m) drift increased from 9.1% over 14.4% to 19.2%

for an increase in wind velocity from 2.0 to 3.1 to 3.9 m/s, respectively. The corresponding far distance (>5 m) drift

increased from 1.35% over 4.32% to 12.2%. The model predictions for these conditions were 8.03%, 11.8% and 16.1%

Fig. 6. Visualisation of the model output. The black line represents the theoretical boundary of the field. Model parameters: boom height of 0.5 m,

27 nozzles (ISO F110-03 at 3 bar), driving speed of 2.22 m/s (or 8 km/h).

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Fig. 7. Validation of ‘Experiment 1’ (a), ‘Experiment 2’ (b) and ‘Experiment 3’ (c). Bars are representing minimum and maximum values of the

replicates of each experiment. See Table 1 f or the meteorological details during each experiment.

for the near distance and 0.5%, 1.54% and 2.8% for the far distance drift. There is an underestimation of drift by the

model for all the experiments, this underestimation is bigger at far distances. In the experiment, higher wind velocities

at 1.5 m imply more drift. This trend is reproduced by the model.

4. Discussion

The main discrepancy between the model and the experimental values exist in the far distance region, i.e. for driftfurther than 5 m from the field. Other field drift models predict drift up till maximum 6 m (Holterman et al., 1997; Miller

and Hadfield, 1989; Mokeba et al., 1997). The model of Zhu et al. (1995) predicts drift up till 200 m. However, this

model was never validated against field experimentsand describesthe situation only forone single droplet. A first reason

for the discrepancy between experimental and model results is due to the model’s simplification for computational

reasons. The model uses 10,000 drops per nozzle and 27 out of a total of 54 nozzles on the boom. Figs. 4 and 5 show

that increasing the number of nozzles in the simulation contributes to the increase of far distance drift predictions. The

number of modelled nozzles has little effect on short distance drift.

Secondly, the simulation employed a simplified model of turbulent dispersion in an Eulerian–Lagrangian approach

(Gosman and Ioannides, 1981), which has computational advances and has been widely used in the analysis of Klose

et al. (2001) comparing different isotropic dispersion approaches to turbulent dispersion, the choice of model did not

affect overall model performance for polydisperse systems. The drawback of all these approaches is that temporal

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Fig. 8. Sensitivity analysis of predicted drift values of ‘Experiment 1’. The input parameters are 2 m/s for wind velocity at 1.5 m with a variation

from 1.3 to 2.27 m/s for (a). The wind deviation in all graphs but (b) is 18◦. In (b) there is a variation from −18◦ to 18◦. The tractor is driving at

8 km/h with variation from 7 to 9 km/h in (c). The standard boom height is 50 cm with a variation from 30 to 70 cm for (d), and the injection velocity

of the droplets is 20 m/s with variation between 17 and 27 m/s in (e).

and directional correlations are not brought into account. To overcome this limitation, other formulations are required

including a different type of turbulence model (Reynolds stress models) for the continuous phase (Chen and Pereira,

1996). This would lead to a larger computational complexity and will be subject of future investigation.

The remaining discrepancy between model and experiment is believed to be mainly due to experimental variability

and uncertainty of the model input parameters. The experimental variability is large as shown in Fig. 7 by the error

bars. A sensitivity analysis was performed by means of model simulations to determine whether the observed model

discrepancy can be explained. The effect of the different factors is given in Fig. 8a–e. The resulting total uncertaintyon the model prediction is given in Fig. 9 f or the three experiments.

Wind velocity variations and wind direction are influenced by the surrounding topography (Raupach and Finnigan,

1997). Little is known about the quantitative influence of the topography on wind velocity profiles. The outer velocity

values at 1.5 m measured during Experiment 1 are tested for their effect on drift deposition using the model (Fig. 8a).

When the wind speed is reduced from 2 to 1.3 m/s the effect is quite considerable (in total 2.7% less drift with a lower

windspeed). An increase from 2 to 2.2 m/s has little or no effect on the drift values (an increase of 0.05% with higher

wind speed). The same range of variability is found by the model of Holterman et al. (1997). Experimental field results,

however, have a dynamic variability as well.

The influence of wind deviation is very little documented. In Experiment 1 the wind deviation was 18◦ upwind,

with less than 2◦ variation in wind direction during the experiment. Fig. 8b shows that the highest drift values occur

when the tractor is driving perfectly perpendicular to the wind direction. This is as expected because the cross wind

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Fig. 9. Comparison of modeled and experimental drift ranges at different distances. Dark bars represent the minimum and maximum values of the

experiments. Light bars represent modeled drift values with a boom height of 0.3 m (lower bars) and 0.5 m (highest bars). Figure (a) represents

‘Experiment 1’, (b) ‘Experiment 2’ and (c) ‘Experiment 3’. See Table 1 f or the meteorological details during each experiment.

drag forces become relatively less important when there is a deviation from the perpendicular wind direction. Fig. 8c

shows that small variations in driving speed have little or no influence on the variation in drift. This was also found by

Teske et al. (2001). It is reported in Holterman et al. (1997) that higher tractor speeds lead to higher drift depositions.

This trend cannot be seen in this study due to the small tractor velocity range that was investigated.

Fig. 8d shows that boom height has by far the most influence on drift values. A boom height of 0.3 m decreases

total drift by 8.4%, compared to a boom height of 0.5 m. A boom height of 0.7 m increases total drift by 17.02%.

These results are supported by the study of Herbst and Wolf (2001), who found for tractor mounted sprayers a rangeof 10–22% for coefficient of variation of spray deposit distribution.

Sidahmed et al. (1999) f ound by experimental investigation as well as theoretical considerations that smaller droplets

have a smaller injection velocity. Smaller droplets are more prone to drift. Fig. 8e shows that a lower injection velocity

results in a smaller amount of predicted short distance drift. Compared with an injection velocity of 20 m/s, there is

1% more short distance predicted drift with an injection velocity of 17 m/s. With an injection velocity of 27 m/s there

is 1.5% less short distance drift. Far distance drift remains more or less constant with different injection velocities

(1.44%, 1.20% and 1.16% short distance drift for injection velocities of 17, 20 and 27 m/s, respectively).

Fig. 9 shows that accumulated variation due to the above factors results in a model uncertainty comparable to that

of the experiment. Although, bringing into account this variation the model versus experimental discrepancy at far

distance is not fully captured. For this aspect, improved models for turbulence and near-nozzle characteristics are

necessary.

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Finally, inherent dynamic variation during experiments could only be explained fully by simulating field spraying

in a transient mode. Some experimental data on spatial and temporal variability in drift experiments have been made

available by Van De Zande et al. (2006). Future studies should incorporate such dynamic behavior.

5. Conclusions

A steadystate 3D CFDmodel for drift from field spraying was able to predict short distance drift. Reliable predictionswere obtained at distances up to 5 m from the field boundary for the experimental conditions studied. The prediction

for far distance drift suffers from the limitations of the turbulence model that was used and the simplified descriptors of

the nozzle characteristics. Both items require considerable further model development before advances can be made.

The effect of small variations of some of the machine and environmental input variables on the model predictions

was significant. The resulting model uncertainty was due to measurement uncertainty as well as natural variability.

Boom height was according to this study the most sensitive parameter, followed by wind direction and wind velocity.

Tractor speed and injection velocity had little influence on the drift values. To fully account for the temporal fluctuations

of boom height, wind direction, wind velocity, injection velocity and tractor speed, dynamic simulations are required.

Acknowledgement

The authors wish to thank the IWT-Vlaanderen (Projects IWT-20424 and IWT-040708) for financial support.

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