Computers and Electronics in Agriculture xxx (2017) xxx–xxx

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Computers and Electronics in Agriculture

journal homepage: www.elsevier.com/locate/compag

Original papers

CFD simulation of airflow inside tree canopies discharged

from air-assisted sprayers
Se-Woon Hong a, Lingying Zhao a,⇑, Heping Zhu b
a
Department of Food, Agricultural and Biological Engineering, The Ohio State University, 59 Woody Hayes Drive, Columbus, OH 43210, USA
b
USDA-ARS Application Technology Research Unit, 1680 Madison Avenue, Wooster, OH 44691, USA

a r t i c l e i n f o a b s t r a c t

Article history: Effective pesticide application is not only essential for specialty crop industries but also very important
Received 9 December 2016 for addressing increasing concerns about environmental contamination caused by pesticide spray drift.
Received in revised form 31 March 2017 Numerical analysis using computational fluid dynamics (CFD) can contribute to better understanding
Accepted 11 July 2017
of the transport of spray droplets carried by strong air jets from sprayers. In this research, an integrated
Available online xxxx
CFD model was developed to predict air velocity distributions inside and around tree canopies blown by
an air-assisted pesticide sprayer. The sprayer motion was simulated by the sliding mesh technique, and
Keywords:
the tree canopies were defined in the computational domain as virtual porous media without their geo-
Air-assisted sprayer
Airflow
metric modeling. Validation of the CFD model was accomplished in three steps by comparing the CFD
Computational fluid dynamics results with previous measurements. Air velocities and airflow pressures downwind from the sprayer
Porous modeling agreed well with the measurements when the sprayer was both stationary and in motion. The model
Tree structure was also able to predict accurately the peak air velocity and airflow pressure inside the canopies with
average RMS errors of 1.68 m s
1 and 0.89 kg m
2, and relative errors of 29.2% and 20.2%, respectively.
Although discrepancy existed between the field experiment measurement and CFD simulation this study
can conclude that the simulation will give a reasonable prediction of air distributions discharged from
air-assisted sprayers. The validated CFD model was applied to predict air distribution inside canopies
with various canopy dimensions and densities. The complex airflow patterns obtained by the CFD model
offered advantages of analyzing effects of various factors on sprayer performance.
Ó 2017 Elsevier B.V. All rights reserved.

1. Introduction these sprayers are complex and three-dimensional interactions

between the strong air jets and target crops. Insufficient knowl-
In specialty crop industries, high-quality crops must be pro- edge about these airflow patterns leads to poor prediction of dro-
duced to satisfy consumers’ demands. Application of pesticides is plet movements and misapplication of chemicals. In order to
essential for mass production of high-quality crops. The excessive improve the efficacy of air-assisted spraying and reduce off-
use of pesticide and off-target spray deposition has raised concerns target drift, it is essential to understand sprayer-induced airflow
about dietary risks from pesticides and contamination of soil, sur- patterns in and around the target canopy as well as at locations
face water, and ground water. Improving safety and environmental far from the target.
friendliness of pesticide application is necessary for sustainability The airflow patterns produced by air jets have been studied by
in high-value crop industries (Zhu et al., 2006b). experiments and modeling. Early studies stressed that field exper-
In most pesticide spray applications with air-assisted sprayers, iments are limited because wind cannot be controlled during a sin-
air-jet streams carry spray droplets released from arrays of nozzles. gle spray event (Zhu et al., 1995). Measurements were taken to
Air jets play key roles in transporting spray droplets deeply into investigate the amount of drift rather than understand the aerody-
canopies by blowing droplets to and beyond the target (Endalew namics of moving droplets (Tsay et al., 2002). In recent years,
et al., 2010a). The strong air jets increase deposition by reducing numerical analysis using computational fluid dynamics (CFD) has
flight time and reducing the influence of weather conditions on contributed to better understanding of transport of spray droplets.
droplets (Weiner and Parkin, 1993). The airflow patterns from The three-dimensional airflow patterns from sprayers are deter-
mined by spraying injection, wind, and plant structure (Farooq
and Salyani, 2004; Delele et al., 2005; Baetens et al., 2007;
⇑ Corresponding author.
Endalew et al., 2010b). Computer simulations have benefited the
E-mail address: zhao.119@osu.edu (L. Zhao).

http://dx.doi.org/10.1016/j.compag.2017.07.011
0168-1699/Ó 2017 Elsevier B.V. All rights reserved.

Please cite this article in press as: Hong, S.-W., et al. CFD simulation of airflow inside tree canopies discharged from air-assisted sprayers. Comput. Electron.
Agric. (2017), http://dx.doi.org/10.1016/j.compag.2017.07.011
2 S.-W. Hong et al. / Computers and Electronics in Agriculture xxx (2017) xxx–xxx

prediction of long distance droplet drift while full-scale experi- target canopies of up to 3.2 m in height at 1.5 m distance from
ments are usually expensive and difficult to perform because of the sprayer. The heights of the four nozzle manifolds were 0.85,
variability in meteorological conditions (Endalew et al., 2010a). 1.35, 1.85, and 2.35 m above the ground. The manifolds were cast
In previous CFD studies, the geometrical features of sprayers with five nozzle ports, each at a radial angle of 15° to improve
and tractors were not included in the CFD model due to their com- spray penetration into dense nursery crops by dividing a conven-
plicated shapes. In the case that the tractor or sprayer was moving tional large air jet into five small jets (Zhu et al., 2006a). The inside
during spraying, a pulse function was used to replace actual move- diameter of the injection nozzle was 36 mm.
ment of the tractor or sprayer (Delele et al., 2005; Endalew et al.,
2010b). A pulse function might not satisfy a mass continuity for 2.2. Development of an integrated CFD model
air jets without well-structured meshes at the injector and accu-
rate interpolation over the meshes. Furthermore, plants were not CFD models were developed with a commercial CFD program
effectively modeled in most previous CFD works. Endalew et al. Fluent 15.0 (ANSYS, Inc., PA, U.S.). The geometry and computa-
(2010a, 2010b) included the effect of trees into their CFD models. tional domain were generated with the ICEM CFD 14.5 (ANSYS,
The geometric properties of full-scale pear trees, including all the Inc., PA, U.S.). The CFD model using the sliding mesh technique
branches, were modeled as a 3D object. Porous sub-domains were for sprayer motion and virtual porous media for tree canopies
also added around the branches to simulate very thin branches, was validated by previous experimental data for a variable-rate
flowers, and leaves. In several other studies, plants were modeled air-assisted sprayer system. Validation was carried out in terms
as a porous media with cuboidal or spherical geometries (Mercer, of air jet velocities from the sprayer in an open field and air veloc-
2009). While the former studies took advantage of more computa- ities in and around tree canopies (Gu et al., 2011, 2012, 2014).
tional time and cost to offer a realistic representation of tree cano-
pies, the latter might oversimplify the canopy for the sake of 2.2.1. Governing equations and models
economy in the numerical calculations. Neither study achieved In this study, the fluid phase was solved by the Reynolds-
both realism and economy. averaged Navier-Stokes (RANS) equations. The Reynolds stresses
An accurate CFD representation of air-blast sprayers requires were simplified by two turbulence quantities, k and x. The SST
modeling the complex airflow patterns resulting from the interac- k-x model was used for the turbulence modeling. The SST k-x
tion of the spray air jet and various types of plant canopies. The model has been increasingly used in the numerical simulation of
objective of this research was to develop an integrated CFD model flow around bluff bodies (Yang et al., 2009). The SST k-x model
to simulate spray jet performance of a moving air-assisted sprayer has also provided more accurate and reliable predictions for a wide
inside tree canopies. The developed CFD model will be applied to class of flow compared with widely-used k-e models (Fluent,
predict air velocity distribution through canopies of specialty crops 2014). Delele et al. (2004) found the SST k-x model gave relatively
with various dimensions, densities, and shapes. Eventually, the better accuracy for airflow prediction from a stationary air-assisted
realistic and economic model will be helpful in understanding sprayer compared with the k-e models.
the effect of tree canopy structure on spray jet performance. A sprayer in motion was modeled by the sliding mesh technique
that described flow situations involving interaction between sta-
tionary and moving parts. The stationary and moving parts repre-
2. Materials and method sented the fluid phase and the sprayer, respectively, in this study.
Two parts were in contact, and the contact surfaces between the
2.1. An air-assisted sprayer two parts, the interface boundary, was continuously changing
according to the location of the moving part. While the sprayer
A variable-rate air-assisted sprayer system was developed to part moved relatively to the stationary fluid phase, the non-
control the spray discharges from 20 nozzles independently conformal interface algorithm (Fluent, 2014) computed fluxes
according to canopy density and distribution (Chen et al., 2012, across the interface boundaries satisfying a mass continuity
2013). Spray fluid is discharged from four specially-designed through the interface.
five-port-nozzle manifolds on both sides of the sprayer as shown The pressure based solver was used to solve incompressible
in Fig. 1. The sprayer was designed for its spray pattern to cover flows, and the SIMPLE algorithm was used for steady and unsteady
simulations to calculate pressure-velocity coupling. The pressure
was discretized by the Second-order scheme. Momentum and tur-
bulent quantities were discretized by the Second-order Upwind
scheme. The convergence criteria of residuals for all variables were
set as 1.0  10
4.

2.2.2. Canopy architecture

Tree canopies were modeled as a porous media as most similar
studies have done (Mercer, 2009). The trees were simulated using a
sphere for leaves and branches and a cylinder for the stem. The
classical modeling approach has strived to generate unstructured
meshes consisting of such rounded geometries or, sometimes, real-
istic tree branches. However, it may be questioned whether it is
worth the time and effort to make so-called ‘perfect’ meshes for
irregular tree structures. Alternatively, this study modeled the tree
canopies by setting porosity at structured cells where imaginary
trees are assumed to be located, as shown in Fig. 2. This method
avoids any complex processes for geometric modeling and mesh-
ing of actual trees but enables modeling of a number of trees or
Fig. 1. An intelligent sprayer with four five-nozzle manifolds on both side of the changing the shape of trees without repeating pre-processing for
sprayer (Chen et al., 2013). mesh generation.

Please cite this article in press as: Hong, S.-W., et al. CFD simulation of airflow inside tree canopies discharged from air-assisted sprayers. Comput. Electron.
Agric. (2017), http://dx.doi.org/10.1016/j.compag.2017.07.011
 S.-W. Hong et al. / Computers and Electronics in Agriculture xxx (2017) xxx–xxx 3

injected from the sprayer nozzles could be delivered to the atmo-

sphere domain. The other part of the boundary of the atmosphere
domain was set as Pressure-Inlet. The side boundaries of the atmo-
sphere domain were set as Pressure-Outlet. The pressure at all
boundaries of the atmosphere domain was set as zero. The ground
was set as a no-slip wall. The circular boundaries of the sprayer
domain were set as Velocity-Inlet with a flow velocity of
70 m s
1 as measured by Gu et al. (2011). The sprayer domain
was set to move at 0.8889 m s
1 (3.2 km h
1) in the sprayer travel
direction (W). Experiments by Gu et al. (2012) showed that sprayer
travel speeds did not significantly influence leeward air velocities.
Fig. 2. Demonstration of virtual porous media and its pressure loss coefficient Selection of a faster travel speed will require smaller time step
distribution. The lines represent an imaginary tree outline profile.
sizes for CFD simulation resulting in an increase in computational
costs.
Cells located within the imaginary canopy had a selected pres- The sprayer domain had 11 thousand tetrahedron cells, and the
sure loss coefficient while cells straddling the boundary between atmosphere domain had 7.5 million hexahedron cells. Cells in the
the imaginary canopy and the air had a reduced pressure loss coef- atmosphere domain were created in a structured grid, which has
ficient based on the percent volume inside the tree boundary. Fig. 2 been known to be highly space efficient and has the advantage of
demonstrates how the pressure loss coefficient is distributed in better convergence compared with unstructured grids (Fluent,
and around a tree canopy. User-defined functions (UDFs) were 2014). For the atmosphere domain, the size of cells was constant
developed and used to determine such virtual porous media, set 0.02 m in the sprayer traveling direction (W). The mesh size was
proper pressure loss coefficients into cells, and define source terms gradually increased from 0.018 m near the nozzles to 0.5 m in
of momentum and turbulence quantities for tree canopies. the vertical direction (H), and from 0.02 m near the nozzles to
The momentum loss due to tree canopies was modeled by Eq. 0.5 m in the spraying direction (L). The mesh was designed denser
(1). The pressure loss coefficient is inversely proportional to the near the nozzles, especially within the distance of 3.2 m (L) from
porosity of canopies, but the relationship between the pressure the nozzles and the height of 3 m (H) above the ground, compared
loss coefficient and the tree porosity has not been determined. with the rest of domains. Additional mesh adaption, which split a
hexahedron cell into eight hexahedron cells, was conducted for
1
rp ¼
C ir qjv jv Dm ð1Þ cells that were in contact with the sprayer domain. Therefore,
2 the mesh size near the nozzles was actually 0.01 m (W) 
0.009 m (H)  0.01 m (L).
where rp is the pressure loss by tree canopy (Pa), C ir is the pressure
loss coefficient (m
1), q is the air density (kg m
3), v is the air
2.2.4. CFD model validation
velocity (m s
1), and Dm is the thickness of porous media (m).
Experiments were conducted to investigate the air velocity
The tree canopy may increase or decrease the turbulence quan-
from the nozzles and its downwind distribution and reported by
tities in the air flow. The effects were achieved by introducing the
Gu et al. (2011, 2012, 2014). Gu et al. (2011) measured air injection
additional terms (Eqs. (2) and (3)) for turbulence source or sink
velocities from nozzles and found 70 m s
1 to be practical in most
(Yang et al., 2012).
spray application events. A value of 70 m s
1 was used throughout
Sk ¼ C d LAD bp jv j3
C d LAD bd jv jk ð2Þ this simulation study. Gu et al. (2012) measured air velocities and
airflow pressures in an open field at seven distances (0.025, 0.25,
x x 0.5, 1.0, 1.5, 2.0, and 3.0 m) from the nozzles of the stationary
Sx ¼ C d LAD ðap
1Þbp jv j3
C d LAD ðad
1Þbd jv jk ð3Þ sprayer and moving sprayer (four travel speeds between 3.2 and
k k
8.0 km h
1). The sprayer travel speeds did not significantly influ-
where Sk and Sx are the source terms for turbulence kinetic energy, ence the leeward air velocities. Gu et al. (2014) measured air veloc-
k, (m2 s
2) and specific dissipation rate, x, (s
1), C d is the drag coef- ity distribution inside three tree canopies of different sizes, shapes,
ficient of tree canopy, LAD is the leaf area density (m
1), bp is the and foliage densities from the moving sprayer. The leaf area
fraction of mean flow kinetic energy being converted to wake- indexes (LAI) of three trees were measured, and air velocities and
generated energy by canopy drag, bd is the magnitude of energy airflow were measured at 13–29 locations in each canopy.
losses from interactions with obstacles, and ap and ad are the model The developed CFD model was validated in three steps using the
constants. experimental data from the above studies. First, the model was
tested in a steady state condition without tree canopies. The
2.2.3. Computational domain and boundary conditions sprayer was located stationary at the middle of its travel path,
The sprayer in an open field was modeled, but the geometry of i.e. at the center point in the direction of sprayer driving (W). Air
the tractor was not included in the simulation to avoid excessive velocities at the distance of 0.025, 0.25, 0.5, 1, 1.5, 2, and 3 m
computation costs. Delele et al. (2004) showed that the effect of downwind from the nozzles were obtained at four manifold
detailed geometry of the sprayer on airflow patterns could be neg- heights, i.e. 0.85, 1.35, 1.85, and 2.35 m, as shown in Fig. 4 and
ligible. The computational domain consisted of two domains, compared with the measurement made by Gu et al. (2012).
atmosphere domain for the stationary part and sprayer domain Second, the model was tested in an unsteady state condition
for the moving part as shown in Fig. 3. The atmosphere domain without tree canopies. The simulation ran for 910 time steps, each
was cuboidal with a size of 10.4 m (W)  10 m (H)  26 m (L). of which had a constant step size of 0.0125 s. While the sprayer
The boundary surface where the sprayer was located was curved traveled along the direction of W for 11.375 s, peak air velocities
along the arrangement of spray nozzles. The sprayer domain had and airflow pressures were obtained at the distance of 0.5, 1, 1.5,
20 small cylindrical volumes with a length of 4 mm and a diameter 2, and 3 m downwind and at four manifold heights, as shown in
of 36 mm, which corresponded to the inner diameter of spray noz- Fig. 4, and compared with the measurement made by Gu et al.
zles. The atmosphere domain and the sprayer domain were in con- (2012). The airflow pressure suggested by Gu et al. (2012) was cal-
tact, and the overlapped faces were set as interfaces, so the flow culated by Eq. (4).

Please cite this article in press as: Hong, S.-W., et al. CFD simulation of airflow inside tree canopies discharged from air-assisted sprayers. Comput. Electron.
Agric. (2017), http://dx.doi.org/10.1016/j.compag.2017.07.011
4 S.-W. Hong et al. / Computers and Electronics in Agriculture xxx (2017) xxx–xxx

Fig. 3. Computational domains consisting of atmosphere part and moving sprayer part, and interface boundaries between two domains.

Fig. 4. Schematic of measuring points for air velocity downwind distribution (validation step 1 and 2).


Pf ¼ qVT ð4Þ

where Pf is the airflow pressure (kg m
2), q is the air density

(kg m
3), V is the mean air velocity (m s
1) during the effective time
period, T (s), in which air velocity increased by the effect of the
sprayer in motion.
The airflow pressure indicated the moving mass of air entering
the tree canopy per unit area perpendicular to the flow direction
and was calculated by the mean air velocity and the time for the
effective air velocities. Gu et al. (2012) determined the effective
time period in their measurement as the time period during which
the air velocities were greater than 0.5 m s
1. In this simulation,
the effective time period was determined by detecting sudden rise
or fall of the air velocities reaping a benefit from the simulation
approach. Fig. 5. Schematic top view of trees for CFD modeling.

Lastly, the model was tested under an unsteady state condition

same as the second step but with three tree canopies. Tree cano-
pies were designed in the same manner as the experiment con- sink equation for vegetative shelter (Wilson, 1985). C d values for
ducted by Gu et al. (2014). The dimensions and locations of three Tsuga Canadensis (Tree 1) and Acer rubrum (Tree 3) were measured
trees are given in Fig. 5 and Table 1. Parameters were determined to be 0.14 and 0.59, respectively, by Mayhead (1973) and Kane and
to be bp = 1, bd = 4, ap = 1.5, and ad = 1.5 as proposed by Yang et al. Smiley (2006). C d value for Ficus benjamina (Tree 2) was not found
(2012), while the leaf area density (LAD ) were 17.5, 2.34, and in literature but assumed the same as Tree 3 because the leaf shape
1.13 m
1 for Tree 1, Tree 2, and Tree 3, respectively, as measured of Tree 2 was more similar to Tree 3 than Tree 1. The pressure loss
by Gu et al. (2014). The pressure loss coefficients for tree canopies coefficients for three tree canopies were estimated as 4.89, 2.77,
were estimated by 2LAD C d , which was derived from the momentum and 1.33, respectively. The pressure loss coefficient for stems was

Please cite this article in press as: Hong, S.-W., et al. CFD simulation of airflow inside tree canopies discharged from air-assisted sprayers. Comput. Electron.
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 S.-W. Hong et al. / Computers and Electronics in Agriculture xxx (2017) xxx–xxx 5

Table 1 coefficient for leaved trees ranged from 0.8 to 6.9 for a normal den-
Physical characteristics of three target trees. sity canopy and from 1.2 to 13.4 for a high-density canopy. Table 2
Tree 1 Tree 2 Tree 3 summarizes three model simulation cases and the associated
Species Tsuga Ficus Acer dimensions and canopy densities representing a range of typical
canadensis benjamina rubrum specialty trees in orchards considering the coverage of the target
Tree diameter (m) 1.5 1.0 2.5 sprayer. The tree canopies were modeled into the existing compu-
Tree height (m) 1.65 2.35 3.0 tational domain by the virtual porous method.
Stem diameter (m) 0.4 0.1 0.1
Stem height (m) 0.5 0.75 1.0
For the first case, three canopy depths (1.5, 2.0, and 2.5 m) with
Pressure loss coefficient (m
1) 4.89 2.77 1.33 a fixed height of 2.85 m and three canopy heights (1.85, 2.35, and
2.85 m) with a fixed depth of 1.5 m were selected. All cases had a
canopy width of 1.5 m in the direction of sprayer travel, a stem
height of 0.85 m, a stem diameter of 0.4 m, and pressure loss coef-
set as an extremely large value (999) assuming that airflow rarely ficient of 3.0. In the second example, a tree with the same dimen-
penetrated through the stems. sion as Tree 3 shown in Table 1 was modeled to evaluate air
Air velocities were obtained at 13 points for Tree 1 and Tree 2, penetration in the tree canopy according to eight pressure loss
and 29 points for Tree 3 inside the tree canopies as shown in Fig. 6. coefficients (0.1, 0.5, 1.0, 1.5, 2.0, 3.0, 5.0, and 10.0).
The sampled data were grouped into six sections: front depth (FD), In the third case, the tree was modeled in two ways as shown in
middle depth (MD), and back depth (BD) according to the distance Fig. 7. One had a spherical shape with a canopy diameter of 2.0 m, a
from the sprayer, lower height (LH), middle height (MH), and top tree height of 2.5 m, a stem height of 0.75 m, and a stem diameter
height (TH) according to the height from the ground. The air veloc- of 0.2 m. The other had tree branches and sub-porous domains
ities and airflow pressures at the six sections were compared with around the branches while the entire dimension was similar to
the measurements made by Gu et al. (2014) using the root- that of the spherical shape as shown in Fig. 7. The diameters of
mean-square (RMS) error, ERMS , and the average relative error, branches and sub-porous domains were determined as 0.1 m and
Er;av g , calculated by the Eqs. (5) and (6). 0.3 m, respectively. The tree branches were generated by the
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Honda branch model (Honda, 1971) with adding random factors
P 2
n ð£m
£s Þ
to the branching angle and the branch length by MATLAB
ERMS ¼ ð5Þ (R2016a, the MathWorks, Inc.) scripts. The pressure loss coefficient
n
was set as 3.0 for canopies and a large value (999) for stems and
!
X£m
£s  branches.
Er;av g ¼   =n ð6Þ
 £ 
n m
3. Results and discussion
£m and £s are the measured and simulated values, respectively,
and n is the number of data compared. 3.1. Airflow patterns resulted from an air-assisted sprayer

2.3. Applications of the CFD model for predicting airflow patterns of The most significant additions to the CFD model development
typical trees compared with other works were the sprayer travel and the easy
design of tree canopies. Fig. 8 presents the time-varying air velocity
The validated CFD model was implemented to predict airflows distribution downwind induced by a sprayer in motion. When tree
and air penetration through typical specialty crop trees with (1) canopies existed, the injected air directly reached only the tree
various canopy dimensions, (2) various canopy densities, and (3) located right in front of the sprayer because the travel speed was
the detailed representation of tree branches. The specialty trees considerably lower than that of air injection from nozzles. The
have different sizes according to their species and growing stage. spray air jets were quickly slowed down by canopies, and airflow
Tree height can reach 4.5 m for blueberries and 9 m for standard behind the trees was slightly biased and looked like being trailed
apple trees while dwarf trees are about 30–60% of the size of stan- by the sprayer. The spray air jets obviously traveled further dis-
dard trees (Hoover and Marini, 2013; UK, 2013). By investigating tances without tree canopies. The accuracy of the simulated air-
various tree species, Gromke (2012) suggested the pressure loss flow patterns was evaluated in the below validation chapters.

3.2. Model validation

All simulation cases were converged well, showing residuals

below 10
4 within 3000 iterations for steady state calculations

Table 2
Example cases for CFD model applications.

Case statements Case variables Control variables

(1) Tree Canopy depths: Tree height: 2.85 m,
dimension 1.5, 2.0, 2.5 m C ir : 3.0 m
1
Tree heights: Canopy depth: 1.5 m,
1.85, 2.35, 2.85 m C ir : 3.0 m
1
(2) Canopy C ir : 0.1, 0.5, 1.0, 1.5, Tree height: 3.0 m,
density 2.0, 3.0, 5.0, 10.0 m
1 Canopy diameter: 2.5 m
(3) Tree Spherical-shaped Tree height: 2.5 m,
simplification tree/Branched tree C ir : 3.0 m
1
Fig. 6. Schematic of measuring points for air velocity distribution inside the tree Canopy diameter: 2.0 m
canopies (validation step 3).

Please cite this article in press as: Hong, S.-W., et al. CFD simulation of airflow inside tree canopies discharged from air-assisted sprayers. Comput. Electron.
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6 S.-W. Hong et al. / Computers and Electronics in Agriculture xxx (2017) xxx–xxx

Fig. 7. Virtual porous models for a spherical tree and a branched tree made in ANSYS Fluent. The branches were modeled by the Honda’s algorithm (Honda, 1971) in MATLAB.
X, Y, and Z are the direction of air jets, height, and travel of the sprayer, respectively.

Fig. 8. Air velocity distributions at 5.0, 7.5, and 10.0 s induced by the sprayer in motion with and without trees.

and 30 iterations per each time step for unsteady state calcula- The adjusted CFD simulation still over-predicted the air veloci-
tions. The CFD model and its validation were accomplished in three ties in the distance where air velocities were lower than 10 m s
1.
steps. As shown in air velocity distributions of Fig.10a, downwind air
velocities of 10 m s
1 were shown at the distance of approximately
3.2.1. Step 1: Air velocity distribution resulted from stationary sprayer 1 m from the sprayer. While the air velocities within 1 m distance
For the stationary sprayer, the measured and simulated air from the sprayer showed a good agreement between the measure-
velocities downwind from the nozzles were shown in Fig. 9a. At ments and the CFD simulation, those beyond 1 m distance were
first, injection air velocities were all set as 70 m s
1 as measured over-predicted by the CFD simulation. The main reason was the
by Gu et al. (2011). Most of the calculated air velocities agreed well momentum decrease in the simulations was smaller than in the
with the measurement, but air velocities at the height of the fourth field experiments. This might result from the limited computa-
manifold (H4) were over-predicted resulting in the overall R2 value tional domain size and less ground effect in the simulation. The
of 0.8619. This was because the injection air velocities at the high- ground roughness was neglected during the simulations, but the
est manifold were set too high. As pointed out by Gu et al. (2012), drag effect from the ground will decrease the downwind air veloc-
the air velocity was lowest at the highest manifold where the hose ity if considered. Larger computational domains may also decrease
length from the air blower to the nozzles was longest. Thus, the the downwind air velocity by avoiding the air being confined in a
injection air velocities were adjusted considering any unbalanced small closed domain. Another possible reason might be field mea-
air supply due to the different hose lengths. Comparing the mea- surement errors. Since the measurement was taken in open terrain,
sured and calculated air velocities at a distance of 0.025 m from there was also a possibility of wind interfering in the measured air
the nozzles, the injection air velocities at the highest and the low- velocities or distorting the main airflow stream, especially a few
est manifold were reduced by 40% and 10%, respectively, and set as meters away from the nozzles where the air velocities decreased
42 m s
1 and 63 m s
1 in the CFD simulation. sufficiently.

Please cite this article in press as: Hong, S.-W., et al. CFD simulation of airflow inside tree canopies discharged from air-assisted sprayers. Comput. Electron.
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 S.-W. Hong et al. / Computers and Electronics in Agriculture xxx (2017) xxx–xxx 7

(a) Injecon air velocity = 70 m s-1 (b) Adjusted injecon air velocies

Fig. 9. Comparison of downwind air velocities (m s
1) from the stationary sprayer between the CFD simulation and field measurement (with standard deviations on vertical
bars) when injection air velocity of all manifolds was (a) assumed to be 70 m s
1 and (b) adjusted according to the height. H1, H2, H3, and H4 indicate 0.85 m, 1.35 m, 1.85 m,
and 2.35 m above the ground, respectively.

Fig. 10. Downwind air velocity (m s
1) distributions: (a) obtained by measurements of Gu et al. (2012) and (b) calculated by CFD simulations.

The adjusted air injections improved the overall R2 value to 3.2.2. Step 2: Air velocity distribution resulted from moving sprayer
0.9397 showing better agreement with the measured air veloci- Fig. 11 presents the comparison of peak air velocities and air-
ties (Fig. 9b). The RMS error and average relative error were flow pressures downwind derived by the sprayer in motion. When
4.6 m s
1 and 35.2%, respectively. Most large relative errors were the sprayer was moving, peak air velocities calculated at each sam-
found further than 1 m distance from the sprayer where air veloc- pling point were slightly different from the measurements. The lar-
ity was low, showing the average relative error of 50.2%, while gest gap was found at a distance of 0.5 m from nozzles, followed by
the average relative error was 23.9% within 1 m distance from a distance of 1.0 m. While the measured air velocities at the dis-
the sprayer. Despite the inaccuracy at further distances, the CFD tance of 0.5 m ranged from 6 m s
1 to 15 m s
1, the CFD results
simulation was considered as a useful approach because the air ranged from 14 m s
1 to 22 m s
1. As shown in Fig. 10b, air veloc-
jet discharged from the sprayer would reach tree canopies at ities varied greatly near the nozzles because of the strong air jet.
the distance of 0.6 m from the sprayer if the trees were placed Slight movement of the sampling position may cause a few meters
as shown in Fig. 5, which was discussed in Section 3.2.3: Step 3 per second increase or decrease in air velocity. Moreover, the
of the validation. sprayer in motion might cause a greater variance of air velocity

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8 S.-W. Hong et al. / Computers and Electronics in Agriculture xxx (2017) xxx–xxx

(a) Peak air velocity (m s-1) (b) Airflow pressure (kg m -2)
Fig. 11. Comparison of (a) peak air velocity and (b) airflow pressure at distances of 0.5, 1.0, 1.5, 2.0, and 2.5 m from the sprayer in motion between simulation and
measurements (with standard deviations on vertical bars).

compared with the stationary sprayer because the peak air velocity
is highly influenced by time-varying vortex and air flows. In this
regard, the airflow pressure is a good indicator to quantify the
cumulative effect of airflow. The reason was that the calculation
included the effective time and the average air velocity due to
the effect of the sprayer motion on sampling positions during the
effective time period.
As shown in Fig. 11b, the airflow pressure showed a good agree-
ment between CFD simulations and measurements. RMS errors of
peak air velocities and airflow pressures were 3.96 m s
1
(2.18 m s
1 except D = 0.5 m) and 1.93 kg m
2, respectively. The
average relative errors were 28.5% (17.6% except D = 0.5 m) and
22.1%, respectively. The accuracy of the simulation results was
quite reasonable compared with other CFD studies, one of which
(a) Peak air velocity (m s-1)
(Delele et al., 2005) showed the average relative error of 32.7%
for peak air velocities at distances of 1.75 m and 3.5 m from a
sprayer in motion.
The airflow pressure increased as the distance from the sprayer
increased. While the airflow pressures calculated at the distances
of 0.5 and 1.0 m from the sprayer were agreed well with the mea-
surements, the CFD simulations tended to over-predict the airflow
pressure at 1.5 m distance and under-predict at further distances.
The reason for larger airflow pressure measurement at such dis-
tances might result from the possibility of wind. The wind was rel-
atively calm during the experiment, but its velocity was not
measured. If the wind blew gently or momentarily during the
experiments, it would increase the effective time since effective
time was calculated as a period during which the measured air
velocity was higher than 0.5 m s
1. Considering uncontrollable
variables that might have occurred, it could be concluded that
(b) Airflow pressure (kg m-2)
the CFD simulations predicted the airflow pressure downwind Fig. 12. Comparison of (a) peak air velocity and (b) airflow pressure inside three
from the sprayer in motion well. tree canopies (T1: Tree 1, T2: Tree 2, T3: Tree 3) between simulation (‘S’) and
measurements (‘M’) with standard deviations on vertical bars. FD, MD, BD, TH, MH,
and LH indicate Front depth, Middle depth, Back depth, Top height, Middle height,
3.2.3. Step 3: Air velocity distribution in tree canopies
and Lower height, respectively.
Air velocities inside tree canopies were analyzed for the peak air
velocity and airflow pressure at six sections of the tree canopy.
Fig. 12(a) shows the measured and calculated peak air velocities ities also followed a trend similar to the measured ones but were
inside the canopies. The measured air velocities quickly decreased over-predicted at TH location for the shortest tree, Tree 1, and at
with depth, as did the calculated ones. However, the air velocity at LH for taller trees, Tree 2 and Tree 3. However, the CFD calculations
BD location was not decreased as much as the measurement lay within standard deviations of the measured mean peak air
showed for Tree 1 and Tree 2. velocity, showing a reasonable agreement. Fig. 12(b) presents the
Vertical distributions of air velocities in tree canopies were airflow pressures in the same manner. The spatial distribution of
more influenced by the relative locations of nozzles and the tree the airflow pressure was similar to that of the peak air velocity.
height. The measured air velocity with respect to the height was Three tree cases showed the same pattern that the measured air-
highest at MH location for Tree 1 and Tree 2, while it was highest flow pressure decreased with depth. The calculated airflow pres-
at LH location for the tallest tree, Tree 3. The calculated air veloc- sures showed the same trend as the measured ones and mostly

Please cite this article in press as: Hong, S.-W., et al. CFD simulation of airflow inside tree canopies discharged from air-assisted sprayers. Comput. Electron.
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 S.-W. Hong et al. / Computers and Electronics in Agriculture xxx (2017) xxx–xxx 9

were within standard deviations of the measured mean airflow study. Air velocity inside the canopy decreased quickly with depth,
pressure except for Tree 3 at BD and LH. e.g. in the Tree 1 case, air velocity decreased from 9.4 m s
1 at FD to
Three trees had different dimensions and canopy densities. The 1.1 m s
1 at BD while penetrating the depth of 1.5 m. Shifting a
air velocity and airflow pressure inside the canopies were highly sampling location to 10 cm apart can lead to air velocity changes
influenced by two factors but could not be determined by only of ±0.55 m s
1 based on an arithmetical calculation.
one of them. The air penetration into the canopies was a complex
process that involved combined effects of canopy dimension and 3.3. Effect of tree structures on air jet penetration
density. For example, Tree 1 had the densest canopy but did not
show the lowest air velocity and airflow pressure at all locations. 3.3.1. Effect of tree dimensions
Similarly, the largest tree, Tree 3, did not have the lowest values The mean peak air velocity and airflow pressure in the tree
at all locations compared with other trees. CFD simulation had canopy were decreased as the canopy depth increased and the tree
the advantage of predicting airflows through porous media in that height increased as shown in Table 3. This meant the capability of
sense. Notwithstanding a few disagreements at location BD and LH, air jet penetration into the canopy decreased in the airflow direc-
the calculated peak air velocity and airflow pressure inside the tion. There was one exception to this trend, which was the airflow
canopies were clearly different between three tree canopies, which pressure at FD. Table 3 showed the canopy with the greater depths
agreed well with the measurements. In both measurements and resulted in lower peak air velocity but higher airflow pressure at
simulations, Tree 2 showed the highest values at all locations. FD. This was because the canopy with a depth of 2.5 m increased
The canopy of Tree 2 was comparatively small and less dense the air resistance but promoted retention of the air within the
resulting in less aerodynamic resistance and more air penetration. canopy to a greater extent, compared with those with smaller
The lowest values, i.e. the highest aerodynamic resistance and the depths.
lowest air penetration, were obtained by Tree 1 at MD, BD, and LH, Meanwhile, once the air penetrated into the canopy, it rapidly
and by Tree 3 at FD and TH. At MD location, Tree 1 and Tree 3 slowed down before MD and passed through the canopy at almost
showed a similar level of air penetration in both measurements steady speeds. Thus, the mean peak air velocity at BD was the same
and simulations. or slightly lower than those at MD in all cases except when the
Average RMS errors of peak air velocities and airflow pressures canopy height was 1.85 m. The canopy with a height of 1.85 m
were 1.68 m s
1 and 0.89 kg m
2, respectively, which corre- was located below the highest nozzle, 2.35 m, and the air jets pass-
sponded to the average relative errors of 29.2% and 20.2%. The ing by fast over the canopy supplemented the air movement on the
errors were slightly larger compared with the similar CFD study back side of the canopy. Therefore, the mean peak air velocity at BD
by Endalew et al. (2010b), which showed the maximum RMS error was slightly increased compared with those at MD. On the other
of 1.68 m s
1 and relative error of 11.04% for simulated peak air hand, the airflow pressure was increased along with depth loca-
velocities around a fully branch-modeled pear tree. However, the tions when the canopy depth was smaller than 2.0 m while it
CFD results of this study were considered reasonable taking into was decreased when the canopy depth was 2.5 m. This indicated
account that tree canopies were more simplified than those of air penetrating the canopy was mostly retained in the middle of
Endalew et al. (2010b) in order to reduce computational loads. In the canopy when the canopy depth was smaller than 2.0 m. How-
addition, Endalew et al. (2010b) only measured the air velocities ever, for the canopy with greater depth, the air could not effec-
before and behind the tree rather than inside the canopy. tively penetrate into the canopy and was retained in the front
Looking into the errors by depth and height also presented a depth of the canopy.
distinctive result. The average RMS errors of peak air velocities at It is still challenging to find what tree depth and height the
FD, MD, and BD, (1.48 m s
1, 2.69 m s
1, and 1.61 m s
1 for Tree sprayer can cover because the appropriate levels of air velocity
1, Tree 2, and Tree 3, respectively) were greater than average and airflow pressure that should be satisfied at the back of trees
RMS errors of TH, MH, and LH (0.98 m s
1, 1.79 m s
1, and 1.40 were not investigated. However, given such information, CFD sim-
m s
1 for Tree 1, Tree 2, and Tree 3, respectively.) This meant the ulation can contribute to optimizing the sprayer with respect to
CFD simulations might contain more errors in predicting the peak tree dimension.
air velocity at different depths compared with different heights.
While the air jets from the sprayer reached the three heights, i.e. 3.3.2. Effect of canopy density
TH, MH, and LH, at the almost same time, the air jets reached the CFD results obtained for eight pressure loss coefficients were
FD at the first time and proceeded to MD and BD eventually. Inac- summarized in Table 4, which clearly showed the peak air velocity
curate predictions at a certain depth will cause cumulative errors inside the trees was much decreased as the pressure loss coeffi-
at subsequent depths. cient of the trees was increased. As expected by the Eq. (1), an
The CFD computations predicted peak air velocities and airflow air stream passing through the canopy lost more momentum and
pressures inside a tree canopy well. However, excellent agreement slowed down quickly as the pressure loss coefficient increased.
between the measurements and the CFD simulations was not The airflow pressures calculated from CFD simulations also
obtained over all locations in the canopy. The disagreement was decreased in all locations as the pressure loss coefficient increased.
due to the discrepancy between the actual tree canopies and the For greater values of the pressure loss coefficient, both the peak air
assumption in this study, in terms of the canopy shape and unifor- velocity and the airflow pressure were gradually decreased show-
mity. Deviations were found at several locations inside the canopy. ing less sensitivity to the further increase of canopy density.
Tree 1 had the largest relative error of 227% (mean peak air veloc- Table 4 also showed air penetration into the canopy declined as
ity) at BD, and Tree 3 showed 83% (airflow pressure) at BD. This the pressure loss coefficient increased. For the pressure loss coeffi-
might result from the nonhomogeneous distribution of leaves cient of 0.1, the peak air velocities at MD and BD were decreased by
and branches in experimental tree canopies. It is obvious that more 17% and 21%, respectively, compared with that at FD. However,
dense or more sparse leaves near anemometers resulted in lower they were greatly decreased by 81% and 87% when the pressure
or higher air velocity readings than expected for homogeneous loss coefficient increased to 10.0. The airflow pressure also
canopies. Another possible reason might be the irregular shape of decreased with depth for pressure loss coefficients greater than
tree canopies. The exact sampling locations could be different 1.5, and the pressure loss coefficient of 10.0 resulted in the
between the measurement and the CFD simulation because the decrease of 86% and 95% at MD and BD, respectively. However,
shape of actual tree canopies was not spherical as assumed in this for smaller pressure loss coefficients, the airflow pressures at MD

Please cite this article in press as: Hong, S.-W., et al. CFD simulation of airflow inside tree canopies discharged from air-assisted sprayers. Comput. Electron.
Agric. (2017), http://dx.doi.org/10.1016/j.compag.2017.07.011
10 S.-W. Hong et al. / Computers and Electronics in Agriculture xxx (2017) xxx–xxx

Table 3
Mean peak air velocity and airflow pressure at three depth sections according to canopy depth.

Canopy height Canopy depth Mean peak air velocity (m s
1) Airflow pressure (kg m
2)
FD MD BD FD MD BD
2.85 m 2.5 m 10.0 3.1 2.9 6.4 5.9 5.5
2.85 m 2.0 m 12.5 3.8 3.6 5.4 6.2 6.0
2.85 m 1.5 m 12.8 5.1 4.7 5.0 7.0 7.1
2.35 m 1.5 m 15.1 5.9 5.1 6.6 7.8 7.4
1.85 m 1.5 m 17.7 6.0 7.3 8.0 8.2 9.2

Table 4
Mean peak air velocity and airflow pressure at three depth sections according to eight pressure loss coefficients of tree canopy.

Pressure loss coefficient Mean peak air velocity (m s
1) Airflow pressure (kg m
2)
FD MD BD FD MD BD
0.1 10.8 9.0 8.6 5.9 6.9 8.0
0.5 10.5 8.3 6.7 5.4 6.2 6.5
1.0 10.4 6.4 4.5 4.9 5.1 4.8
1.5 9.7 5.3 3.1 4.6 4.5 3.7
2.0 9.0 4.3 2.2 4.4 3.9 2.6
3.0 8.1 3.1 1.3 4.1 2.9 1.2
5.0 6.9 1.8 0.9 3.7 1.5 0.4
10.0 5.1 1.0 0.7 2.8 0.4 0.1

and BD were even greater than those at FD. Even though air veloc- and the resulting air velocity at the back section of the canopy
ities at MD and BD were lower than those at FD, the effective time were influenced by canopy simulation methods. This study could
periods at MD and BD were greater than those at FD. This meant not judge which way was right due to a lack of validation studies.
the air jet was retained within the canopy for a longer time at However, results from the branched tree seemed to be close to real
MD and BD compared with FD. These results emphasized the air airflow patterns for tree canopies while the spherical simplification
velocity by spray air jets could not be maintained at the same level might represent the average state of air trapping effect caused by
throughout the canopy depth, but the cumulative effect of spray air irregularly shaped trees.
jets might be uniform within the canopy when the appropriate The benefit of the virtual porous modeling was the ease with
conditions of canopy density and spray air jet velocity were met. which the trees were represented into the computational domain.
The results from eight pressure loss coefficients can be com- If a three-dimensional geometry of a tree and its branches was
pared with those from the previous validation for Tree 3. Assuming obtained by measurement, an actual feature of the tree could be
that lower RMS deviations between measurements and simula- easily modeled and tested for spraying performance providing a
tions reflected greater accuracy, Tree 3 indeed had a better fit at CFD approach with more realism.
a pressure loss coefficient of 2.0 rather than our presumed value
of 1.33, showing smaller RMS deviations of 1.20 m s
1 and 0.58
kg m
2 for the peak air velocity and airflow pressure, respectively. 4. Conclusions
Estimating the pressure loss coefficient using the LAD and Cd for
various tree species is still ambiguous because few studies have An integrated CFD model was developed in this study to simu-
been conducted on it. The accurate pressure loss coefficient of tree late air velocity distributions inside and around tree canopies dis-
canopies can be measured experimentally (Bitog et al., 2011), and charged from an air-assisted sprayer. The CFD model calculated
doing so would enhance the accuracy of CFD predictions on the complex airflow patterns induced by the strong air jets from the
spray effect in tree canopies. However, if the experiment is not sprayer, integrating the motion of the sprayer by the sliding mesh
available, the pressure loss coefficient can also be indirectly esti- technique and the effect of tree canopies on air momentum and
mated through repetitive CFD simulations by searching the value turbulence quantities by UDFs. The tree canopies were modeled
at which the model performs the best as described in this study. by virtual porous media replacing any geometric modeling and
meshing of actual trees. This enabled inclusion of tree canopies
into a computational domain as a form of simplified shape as well
3.3.3. Effect of canopy simulation as a branched tree as a complex branched shape, without any changes or modifica-
Fig. 13 displays the air velocity vector and contour plots around tions in meshes and domains.
the branched tree. The air jets, created by the sprayer, obviously Validation of the CFD model was accomplished in three steps by
slowed down at branches and penetrated through the space comparing the calculated results with previous measurement
between the branches. Therefore, air velocity distribution in the works. Air velocities downwind from the sprayer agreed with the
canopy was uneven unlike the case of the spherical canopy and measurements when the sprayer was both stationary and in
greatly dependent on the location of branches. motion. The model was also able to accurately predict the peak
Table 5 presents mean peak air velocities and airflow pressures air velocity and airflow pressure inside three tree canopies with
for the spherical tree and the branched tree. Two trees showed a the average RMS error of 1.68 m s
1 and 0.89 kg m
2, respectively,
similar level of air trapping effects at FD and MD locations. The and the average relative error of 29.2% and 20.2%, respectively.
mean peak air velocity and airflow pressure for the branched tree However, perfect agreement between the measured and calculated
were 0.1 m s
1 and 1.2 kg m
2 lower than those of the spherical results was not obtained due to the discrepancy between the field
tree. However, at BD, the branched tree showed 2.8 m s
1 and experiment and CFD simulation. Nonetheless, the findings from
4.8 kg m
2 higher mean peak air velocity and airflow pressure this study concluded the CFD simulation could still give a reason-
compared with the spherical tree. This meant that air penetration able prediction of air distributions from air-assisted sprayers

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 S.-W. Hong et al. / Computers and Electronics in Agriculture xxx (2017) xxx–xxx 11

Fig. 13. Air velocity vector and contour plots around the branched tree model at the height of 0.85, 1.6, and 2.2 m above the ground. The stems and branches are displayed as
lines to make them easier to understand.

Table 5
Comparison of mean peak air velocity and airflow pressure at three depth sections between spherical and branched trees. FD, MD, and BD indicate Front depth, Middle depth, and
Back depth, respectively.

Tree model Mean peak air velocity (m s
1) Airflow pressure (kg m
2)
FD MD BD FD MD BD
Spherical tree 14.8 4.5 4.9 9.0 8.1 7.1
Branched tree 14.1 4.8 7.7 7.3 7.5 12.0

because the study showed good overall agreement between CFD the Ohio Supercomputer Center (OSC, Columbus, Ohio) under
simulation and measurements. Grant No. PAS0228.
The simulation results showed that the air penetration into tree
canopies was highly influenced by the size of tree canopy and the
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Please cite this article in press as: Hong, S.-W., et al. CFD simulation of airflow inside tree canopies discharged from air-assisted sprayers. Comput. Electron.
Agric. (2017), http://dx.doi.org/10.1016/j.compag.2017.07.011