Study of the Distribution Characteristics of the Airflow Field in Tree Canopies Based on the CFD Model

Abstract

Air-assisted sprayers are the mainstream orchard plant protection machinery in China. During the usage of sprayers, the pesticide droplets carried by strong air jets from sprayers enter into the target canopy. Therefore, the distribution of airflow field in the canopy has significant influence on the spatial movement of the droplets and the adhesion and penetration of the droplets inside the canopy. To enhance the working performance of sprayers, it is imperative to study their use in tree canopies. Based on computational fluid dynamics (CFD), the k-ε turbulence model, and the SIMPLE algorithm, a 3D simulated model of the spatial distribution of the airflow field in and around the tree canopy was established based on the porous model in this paper. The model was used to simulate and calculate the air field distribution of an air-assisted orchard sprayer under different operating parameters. The results showed that the optimal operation effect was achieved when the driving speed and the air speed of the fan outlet were 1 m/s and 20 m/s, respectively, while the air speed in the canopy was not less than 2 m/s. The 36 points measured in the canopy were compared with the simulated results through field experiments. It showed that average relative error between the measured and simulated values was 13.85%, and the overall goodness-of-fit was 0.97656. The model accurately simulated the airflow distribution in the canopy and provided a basis for optimizing the operating parameters of the air-assisted sprayers in orchards.

1. Introduction

In the operation process of the air-assisted orchard sprayer, the auxiliary airflow generated by the fan envelops the movement of fog droplets and transports them to the target area or to various parts beyond the target area [1,2]. The influence of the tree canopy on the airflow cannot be ignored [3], and the interaction between the airflow and the plant canopy will produce complex airflow patterns. It affects the spatial movement of fog droplets and their deposition distribution in the canopy. Since the spatial distribution law of the airflow field is not clear, it affects the accurate control of the operation parameters meaning the sprayer does not have accurate control, causing the loss of pesticide droplets. Therefore, it is necessary to improve the deposition and deposition coverage of pesticide droplets within the canopy of trees, and study the interactions between the operating parameters of the sprayer and the auxiliary airflow and the tree canopy [4,5].

The deposition distribution state of pesticide droplets in the canopy of fruit trees under air-assisted spraying conditions is a key technical index to measure the performance of wind-fed sprayers in orchards. Matching the spatial distribution characteristics of a wind-fed airflow field and the characteristic parameters of a fruit tree canopy is the focus and difficulty of research on wind-fed spraying technology in orchards [6]

A number of scholars have carried out field experiments and simulation studies on the airflow field distribution of air-assisted orchard sprayers [7,8,9,10]. Lü et al. [11] studied the airflow field distribution of an air-assisted orchard sprayer by setting a reasonable guide-plate angle to make the wind field distribution consistent with the fruit tree canopy, so as to achieve the purpose of imitated spray. The research results of Fu et al. [12] showed that the change of inlet airflow velocity had no significant influence on the airflow velocity field distribution characteristics of the sprayer. However, this model ignored the influence of the canopy on air field distribution. Therefore, the simulation test model needs to be further optimized.

To improve the authenticity of simulation results, some researchers introduced the tree canopy model into the CFD simulation domain. Endalew et al. [13,14,15] defined the fruit tree model as a porous medium upon model establishment, and integrated the characteristic factors of the fruit tree into the CFD model, including all branches, to form a three-dimensional model [16,17]. Porous fields were added around the branches to simulate small branches and leaves.

In summary, the research results showed that the CFD models can visually identify the characteristics of the airflow field, the error between the measured and simulated values was small, and the model is highly reliable. In order to explore the effect of the canopy structure on the distribution characteristics of the airflow field, in this paper, the porous model was applied to treat fruit tree canopies based on ANSYS Fluent2020R2 combined with the N–S equation, standard turbulence model, slip grid technology, and SIMPLE algorithm. A CFD simulation model was established for the distribution of the flow field in the canopy of fruit trees during the application of the air-assisted sprayer in the orchard. This paper intends to provide technical support for visual characterization of the interaction law between the canopy and airflow field and improve the uniformity and accuracy of pesticide droplet deposition coverage.

2. Materials and Methods

2.1. Air-Assisted Orchard Sprayer

The 3WQF-1000 trailer air-assisted orchard sprayer developed by the Institute of Agricultural Facilities and Equipment of Jiangsu Academy of Agricultural Sciences and LOVOL was selected in this paper. The sprayer has the characteristics of advanced technical performance, such as a uniform and symmetrical wind field, adjustable wind volume and fog volume, and the matching of the fog flow field and tree crown profile. The dimensions of the 3WQF-1000 traction air-assisted orchard sprayer are shown in Figure 1. The height of the fan axis from the ground is 0.97 m. The width of the air outlet arc surface is 0.15 m, and the radius of the arc surface is 0.55 m of the fan shell. The height of the bottom of the fan enclosure (the horizontal position of the lower guide plate) is 0.55 m from the ground.

2.2. Simulation Model

2.2.1. Master Equations and Turbulence Models

The Navier–Stokes (N–S) equation was used as the governing equation of fluid movement in the airflow field of the air-assisted orchard sprayer [18,19,20,21]. The additional conditions of the governing equations were introduced into the N–S equation by means of RANS. As a result, the turbulence model was closed and all unknowns could be solved with enough equations. The standard $k-\epsilon$ turbulence model was selected to solve the main control equation in a closed CFD simulation of airflow inside tree canopies discharged from air-assisted sprayers [22,23]. Two turbulent quantities, $k$ and $\epsilon$, were used to simplify the Reynolds stress. The standard $k-\epsilon$ model is the most widely used turbulence model, which can provide relatively good airflow prediction accuracy [24]. The governing equation is as follows.

Turbulent kinetic energy equation:

$$\frac{\partial \left(\rho k{u}_i\right)}{\partial x_i}=\frac{\partial }{\partial x_j}\left(\left(\mu +\frac{{\mu }_t}{{\delta }_k}\right)\frac{{\partial }_k}{\partial x_j}\right)+G_k-\rho \epsilon$$

(1)

Equation of dissipation rate of turbulent kinetic energy:

$$\frac{\partial \left(\rho \epsilon u_i\right)}{\partial x_i}=\frac{\partial }{\partial x_j}\left(\left(\mu +\frac{{\mu }_t}{{\delta }_{\epsilon }}\right)\frac{{\partial }_{\epsilon }}{\partial x_j}\right)+C_1{}_{\epsilon }\frac{\epsilon }{k}{G}_k-C_2{}_{\epsilon }\frac{{\epsilon }^2}{k}\rho$$

(2)

where $u_i$ is velocity, $\mathrm{m}\cdot {\mathrm{s}}^{-1}$; ${\mu }_t$ is turbulent viscosity coefficient, $\mathrm{Pa}\cdot \mathrm{s}$; $x_i$ and $x_j$ are the distances in the direction of x and y, respectively; $G_k$ is the generation term of turbulent kinetic energy $k$ due to the average velocity gradient; $C_1{}_{\epsilon }$ and $C_2{}_{\epsilon }$ are empirical constants, which are 1.42 and 1.68, respectively; ${\delta }_k$ and ${\delta }_{\epsilon }$ are the inverses of the effective turbulence numbers of $k$ and $\epsilon$.

2.2.2. Porous Model of Fruit Tree Canopy

Canopy resistance causes the momentum loss of auxiliary airflow, so it is vital to consider the influence of the tree canopy on wind field when conducting air field tests. The porous model simplifies the computation process and effectively improves the simulation efficiency. In this research, the structure of fruit trees is divided into two parts: the canopy and the trunk. By measuring the characteristic parameters of fruit trees, the canopy was reconstructed by SolidWorks software. The modeling of the tree crown model refers to the appearance characteristics of peach trees. By measurement, the height of the whole tree H and the trunk h were 3 m and 0.6 m, respectively. The crown width d was 2.2 m. The simplified model of a fruit tree is shown in Figure 2. In the numerical simulation, it was assumed that the fruit tree structure in the orchard is fully grown and the canopy is pruned to a regular size and shape.

There is a specific pressure loss coefficient Cir within the tree canopy. Moreover, a decompression loss coefficient between the canopy and the air, based on the percentage of volume, is shown in Figure 3. An appropriate coefficient can be set to simulate the attenuation of airflow movement in the tree canopy, and the source terms of the momentum and turbulence of the tree canopy can be defined [25]. This method not only avoids the complicated process of geometric modeling and meshing of the actual tree canopy structure, but also can model it with different shapes and sizes. In addition, it does not require the preprocessing of repeated mesh generation in the flow field.

Momentum loss and turbulence induced by tree canopy were calculated using the following equation:

$$\Delta p=-C_{ir}\frac{1}{2}\rho v|v|\Delta m$$

(3)

$$S_k=C_d{L}_{AD}{\beta }_p{|v|}^3-C_d{L}_{AD}{\beta }_d|v|k$$

(4)

$$S_w=C_d{L}_{AD}\left({\alpha }_p-1\right){\beta }_p\frac{w}{k}{|v|}^3-C_d{L}_{AD}\left({\alpha }_d-1\right){\beta }_d\frac{w}{k}|v|k$$

(5)

where $\Delta p$ is canopy pressure loss, $\mathrm{Pa}$; $C_{ir}$ is pressure loss coefficient, ${\mathrm{m}}^{-1}$; $v$ is air speed, $\mathrm{m}\cdot {\mathrm{s}}^{-1}$; $\Delta m$ is thickness of porous medium, $\mathrm{m}$; $k$ is turbulent kinetic energy, ${\mathrm{m}}^2\cdot {\mathrm{s}}^{-}{}^2$; $w$ is specific dissipation rate, ${\mathrm{s}}^{-1}$; $S_k$ is the source term of turbulent kinetic energy; $S_w$ is the source term of the turbulent dissipation rate; $C_d$ is canopy resistance coefficient; $L_{AD}$ is leaf area density, ${\mathrm{m}}^{-1}$; ${\beta }_p$ is the proportional coefficient of kinetic energy loss from fluid to turbulent kinetic energy loss due to crop resistance, which was set to 1; ${\beta }_d$ is energy loss coefficient of interaction with crops, which was set to 4; ${\alpha }_p$ and ${\alpha }_d$ are adjustment coefficients, which were 1.5 and 1.5.

As the air flows through the canopy, some of its momentum is absorbed. In the process of studying the resistance characteristics of the fruit tree canopy, the following conclusions were drawn: under normal air speed or when it reached a specific value, the flow resistance was dominated by inertial resistance, while the effect of viscous resistance was almost negligible [26]. Therefore, the following assumptions were made in this study: the porous medium was set as isotropic. Only the inertial resistance loss term was considered in the flow process of the porous medium, and the influence of the viscous resistance loss was ignored. Since viscous resistance was not considered, the pressure loss in the canopy can be expressed as:

$$C_{ir}=2C_d{L}_{AD}$$

(6)

The resistance coefficient $C_d$ of the plant canopy is about 0.25 [27]. In this paper, the leaf area density of a peach tree was measured by a CI-110 digital image analyzer of the plant canopy. The measured leaf area density of peach trees was 1.75–2.3 ${\mathrm{m}}^{-1}$, and the average was 2 ${\mathrm{m}}^{-1}$. The corresponding pressure loss coefficient $C_{ir}$ was 1, as calculated by Equation (6).

2.3. Computational Domains and Boundary Conditions

The influence of the geometry of the spray machine on the airflow pattern was negligible [28]. Considering the symmetry of the sprayer operation, the calculation domain of the geometric model was defined as a one-sided tree environment in the numerical simulation to avoid excessive computational cost.

In this research, the sliding grid model was adopted to simulate the movement of the sprayer, and the length, width, and height of the calculation domain of the outflow field were set as 14 m, 16 m, and 12 m (Figure 4). The air outlet of the fan was simplified into an arc surface with a width of 0.25 m. The top and bottom end of the air outlet were provided with a guide plate, respectively. The upper guide-plate was set to 25°, and the lower guide-plate was set to 5°.

Since the subdomain of the trunk does not require a solution, boolean difference operation was used to remove it from the calculation area in the pre-processing process, and only the outer boundary of the trunk was kept and set as the wall. The arc surface where the air outlet of the sprayer was located was set as the inlet. The ground was set as the non-slip wall, and the other boundaries were set as the pressure outlet. The pressure at all boundaries of the atmospheric domain was 0. According to previous studies on turbulence intensity [29,30], 30% turbulence intensity was selected.

2.4. Calculation Method and Parameter Setting

In this paper, the governing equation was discretized to solve the transient flow field based on the finite volume method. The SIMPLE algorithm, suitable for steady state and unsteady state simulation, was used for pressure–velocity coupling. The second order upwind discrete scheme was chosen to discretize the momentum, turbulent kinetic energy, and turbulent kinetic energy dissipation rate in the space domain, which could achieve high accuracy for solving unstructured tetrahedral meshes. A pressure-based solver was used to solve incompressible fluids. The convergence criterion of the energy equation was 1.0 ×${10}^{-6}$, and the convergence criterion of the residuals of all variables was 1.0 ×${10}^{-4}$. Air was regarded as an incompressible ideal gas, and the time step was set to 0.1 s.

The quality of meshing in the calculation area directly affects the accuracy and efficiency of the numerical solution. The unstructured grid saves computation time and the size of the grid is easier to control. In this paper, an unstructured mesh, suitable for complex entities in ANSYS Meshing, was selected to divide the computational area. In the atmospheric domain, the grid size was 0.05 m. The grid of the outlet area of the orchard air supply sprayer was encrypted, and the grid size was 0.01 m. After division, the total number of calculated meshes was about 950,000.

The skewness was used to check the quality of tetrahedral mesh in the computational domain. Statistics show that the maximum skewness of the grid was 0.88, and the average value was 0.21, which conform to the requirement that the maximum and the average skewness of the grid should be less than 0.95 and 0.33, respectively. Therefore, the values can be used for numerical simulation.

2.5. Mesh Independence Verification

The correlation between the calculated results and the mesh number was verified to determine the reasonable mesh number. The calculation results are shown in

Table 1. Mesh-independent verification.

Number of Grid Nodes	The Height Above the Ground
	1 m	2 m
127,824	3.2643 a	1.9258 a
156,862	3.1784 b	1.9024 b
174,626	3.0566 c	1.8862 c
193,347	3.0513 c	1.8834 c
201,687	3.0586 c	1.8879 c
223,616	3.0988 c	1.8881 c

Note: Different lowercase in the same column indicate significant differences (p < 0.05).

. The instantaneous velocity of 1 m and 2 m from the ground at two points on the axis of the tree crown was analyzed when the air speed at the outlet of the fan was 17.8 m/s. Increasing the number of grid nodes had no significant effect on the air speed of the measuring points; it is considered that the calculation results were independent of the meshes.

It can be concluded that when the total number of grid nodes was 127,824 and 156,862, there was a significant difference in canopy velocity. However, there was no significant difference in air speed when the number of grid nodes continued to increase. As a result, a grid division scheme with a total number of grid nodes of 174,626 was selected.

3. Results

For the air field distribution in the canopy, it is necessary to consider not only the airflow of the sprayer, but also the influence of the traveling speed of the air-assisted sprayer. In this paper, the air speed outlet of the fan was set to 15 m/s, 20 m/s, and 25 m/s, and the sprayer speed was set to 0.5 m/s, 1 m/s, and 1.5 m/s.

The characteristic section of the airflow in the canopy was selected as the vertical plane parallel to the axis of the fan, which were planes P1, P2, and P3, respectively. The distance from the axis d of the fan was 1 m, 1.5 m, and 2 m, respectively.

3.1. The Influence of Traveling Speed on the Distribution of Airflow Field

3.1.1. Contours of Airflow Distribution

Figure 5 shows the distribution cloud of the airflow field in the canopy of fruit trees at different driving speeds when the air speed at the fan outlet was 20 m/s.

When the spray machine was stationary, the airflow was symmetrically distributed in the tree canopy. Due to the guiding and limiting effect of the flow guide plate, the airflow velocity in the canopy was relatively large and concentrated near the upper and lower parts of the canopy. When the longitudinal airflow passed through the central region of the canopy, only part of the airflow entered into the inner part of the fruit tree canopy due to the canopy resistance. The airflow decayed from bottom to top, and developed in a cylindrical shape. On account of the distance from the fan outlet to the top of the tree canopy, the airflow velocity was small and divergent. The airflow attenuated more significantly when the lateral airflow passed through the inner area of the canopy. The longitudinal and transverse airflows generated by the fan finally formed the cloud diagram, as shown in Figure 5a.

The air-assisted sprayer moved forward from left to right, and the canopy structure produced friction, adsorption, and decomposition on the airflow. The higher the driving speed, the more significantly the airflow decayed when it reached the central and rear part of the crown (plan P2 and P3). The main reason was that with the increase of forward velocity, the displacement air volume of the canopy per unit time was reduced, which led to the weakening of wind field penetration. Meanwhile, the air delivered by fan and the atmospheric airflow had a relative movement, resulting in the tilted airstream in the canopy in the opposite direction to the sprayer. The inclining angle of the airflow increased with the increase of driving speed, and finally formed the velocity cloud diagram shown in Figure 5b–d.

3.1.2. Airflow Velocity in Canopy

Figure 6 shows the variation of the maximum airflow velocity in the canopy at different driving speeds when the air-assisted sprayer passed through the crown. When the air-assisted sprayer was still, the air in the canopy (plan P1, P2, and P3) with height no more than 3 m was relatively stable, and the airflow velocity in the canopy was greater than 2 m/s. When the driving speed increased to 0.5 m/s, the airflow velocity in the canopy was near 2 m/s within the height of 5 m (planes P1, P2, and P3). When the driving speed was 1 m/s, the airflow velocity in the front and middle of the crown (plane P1 and P2) was more than 2 m/s at the height of 3.6 m, while the airflow velocity in the rear part of the canopy (plane P3) was affected by the canopy resistance and reduced to 2 m/s at the height of 3 m. When the driving speed continued to increase to 1.5 m/s, the airflow velocity in the canopy was greater than 2 m/s at the height of 3 m in the front and middle of the crown (plane P1 and P2). At the rear of the crown (plane P3), it was less than 2 m/s at the height of 2 m. At this moment, the air in the canopy fluidity was poor.

In conclusion, the greater the driving speed of the air-assisted sprayer, the more obvious the velocity attenuation of the air in the vertical direction. Therefore, appropriately increasing the driving speed can reduce the flow of air outside the canopy and effectively improve the utilization rate of air volume inside the canopy. The distribution of airflow in the canopy was optimal when the driving speed was 1 m/s.

3.2. Influence of Outlet Fan Speed on Air Field Distribution

Increasing the air speed of the fan can effectively improve the flow and penetration of airflow in the canopy, so as to increase the proportion of pesticide droplets deposited by airflow. However, it is easy to cause the pesticide droplets to drift away and reduce the spray effect if the airflow velocity is too high. Therefore, the air speed at the outlet of the fan is an important factor affecting the spray effect.

3.2.1. Contours of Airflow Distribution

Figure 7 shows the distribution contours of the airflow field in the crown at different air speeds of the fan outlet when the traveling speed of the sprayer was 1 m/s. The penetration of airflow in the horizontal canopy was obviously enhanced by increasing the air speed at the outlet of the fan. Therefore, it can be appropriately increased to achieve the complete penetration of airflow through the canopy.

3.2.2. Airflow Velocity in Canopy

Figure 8 shows the airflow velocity distribution in the canopy at different fan outlet velocities. When the air speed at the outlet of the fan was 15 m/s, the airflow at the front of the canopy (plan P1) was greater than 2 m/s at the height of 3 m, and this was not enough to overcome the canopy resistance. Similarly, in the middle and back of the canopy (planes P2 and P3), it rapidly decayed to lower than 2 m/s at the height of 1.5 m. With the increase in height, the airflow gradually disappeared. When the air speed at the outlet of the fan increased to 20 and 25 m/s, it was greater than 2 m/s within the height of 3 m (planes P1, P2, and P3). However, when the air speed of the fan was 25 m/s, the airflow velocity was greater than 2 m/s above the canopy (at height of 3–5.5 m), which increased the potential risk of the pesticide droplet loss.

In conclusion, the airflow distribution in the canopy was stable when the air speed of the fan outlet was 20 m/s, which provided a good air field condition for carrying pesticide droplets to disturb the blades and improve the deposition rate of droplets.

3.3. The Field Test

To verify the reliability of computer numerical simulation results, field experiments were carried out in a peach orchard of Jiangsu Academy of Agricultural Sciences, Nanjing, China. The change of air speed directly affects the distribution of airflow velocity field in the canopy. In this experiment, the tractor power (PTO) was set as 720 r/min, the orchard air-assisted sprayer kept a traveling speed at 1 m/s, and the airflow velocity at the fan outlet was about 19.8 m/s.

3.3.1. Test Design

The axis of the air-assisted sprayer was about 2 m from the center of the tree trunk. The horizontal planes L1, L2, L3, and L4 were 1.1 m, 1.6 m, 2.1 m, and 2.6 m above the ground, respectively. The canopy was divided into four layers from bottom to top. The vertical planes at 1.5 m, 2 m, and 2.5 m away from the axis of the blower were P1, P2, and P3, respectively. Three points were uniformly selected at the intersection line of each horizontal plane and vertical plane with an interval of 0.5 m. A total of 36 points were selected in this experiment, as shown in Figure 9. Each group of tests was repeated three times, and the average value was taken to reduce the test error.

3.3.2. Comparative Analysis on Experimental and Simulation Results

The test results of air velocity in the canopy were analyzed and compared with the numerical simulation results. Figure 10 shows the distribution of the test and simulation values of 36 test points.

As can be seen from Figure 10, the variation trend of the test value at each test point was similar to that of the simulated value. Furthermore, the farther the horizontal distance and vertical distance from the axis of the fan, the lower the air speed. At the same time, the simulated value was slightly larger than the measured value in the higher air-speed range. During the operation of the sprayer, the air velocity was large, and when the external airflow movement direction had a certain angle, the airflow was offset, weakened, or superimposed. In the low air-speed range, the measured value was greater than the simulated value, which is mainly due to the fact that the air was gradually weakened in the canopy during the field experiment, and the distribution of the canopy flow field was dominated by the external air. While the external airflow was unstable, its weakening effect on the airflow in the canopy was more obvious in the field experiment.

When the air speed was low in the canopy, the measured value was greater than the simulated value. In the field experiment, the airflow delivered by the fan gradually weakened in the canopy, and the external airflow dominated, at a speed of 1 m/s. This resulted in the increase of the measured value under the superposition of the airflow from the fan and the external field airflow.

The relative error statistics of each test point in the canopy are shown in

Table 2. Relative error statistics of airflow velocity simulated in the canopy.

Surface	P1	P2	P3	Mean Relative Error
L1	15.11	8.38	22.66	15.38
L2	15.05	8.37	6.29	9.90
L3	10.42	5.85	18.18	11.48
L4	22.78	17.44	15.72	18.65
Mean relative error	15.84	10.01	15.71	13.85

.

The average relative error between the simulated and measured values of airflow velocity distribution within the canopy was 13.85%, with 83% of the error values less than 20%.

In the simulation, it was assumed that the tree canopy shape was regular and the canopy resistance was isotropic. However, there are differences in the internal porosity of fruit tree canopies used in actual field experiments, and the attenuation effect of branches and leaves in the canopy on airflow is also different. In addition, the large airflow field would also cause the instantaneous airflow instability inside the canopy, leading to the existence of errors.

A linear fit regression analysis was performed on the experimental and simulated values, and the results are shown in Figure 11. The fitted linear equation was $\mathrm{y}=1.1502\mathrm{x}-0.12317$, and the overall goodness of fit ${\mathrm{R}}^2=0.97656$. It was proven that the simulation model of the wind field was reliable.

4. Discussion

Field trials of air-assisted spraying not only consume a large amount of time and effort, but also require costly instruments to accurately measure airflow. The repeatability of the tests is also poor due to natural air speed and other environmental and climatic factors. Previous studies have shown that fruit trees are subjected to 8–15 pest and disease controls during the annual growth cycle [31,32]. However, the pesticide utilization rate was only about 30% [33], consuming vast resources and manpower. Therefore, based on the computer numerical simulation, the distribution pattern of the air-assisted airflow field within the canopy of fruit trees was studied to improve the stability and repeatability of the operation. The study serves as a guideline for adjusting operational parameters.

Admittedly, it takes a lot of time to calculate the number, shape, and position of leaves in fruit tree canopies. Loch et al. [34] used laser scanners to sample data from leaf surfaces and built leaf models based on mathematical methods of surface fitting to real leaf-sampled data. Cui et al. [35] proposed a digital method for predicting the airflow distribution in the cotton canopy, using computational fluid dynamics (CFD) and machine learning (ML) methods. However, building a canopy model composed of a large number of leaves has very high computational requirements, and it is difficult for existing computer processors to meet these requirements.

Mercer [36] replaced fruit trees with a porous model consisting of spheres and cylinders. The simulation accuracy was somewhat reduced due to the inhomogeneity of airflow within the crop canopy, errors in leaf area density measurements, and complex interactions between the airflow and the target canopy [37]. However, the study fully demonstrated the validity and feasibility of using the porous model to deal with the numerical simulation of the airflow field under the participation of the fruit crop canopy.

The CFD model developed by Tsay et al. [38] omitted the geometric features of the sprayer and used an impulse function to simulate the actual movement of the sprayer during the application operation. Without a good mesh structure and accurate velocity interpolation at the fan outlet, the impulse function could not satisfy the quality continuity of the mesh, and the accuracy of the simulation results would be compromised.

5. Conclusions

To study the spatial distribution law of an airflow field inside the fruit tree crown, a simulation based on the CFD model was established. The canopy was simplified as a porous medium model, and the obstructing effect of the canopy on airflow was simulated by defining the pressure loss coefficient of the fruit tree canopy. When the driving speed was 1 m/s and the air speed of the fan outlet was 20 m/s, the distribution of airflow in the canopy was optimal, providing a reasonable air field condition for carrying pesticide droplets to disturb the leaves and improving the droplet deposition rate. The validation results showed that the average relative error between the simulated and measured values was 13.85%. The linear regression equation was $\mathrm{y}=1.1502\mathrm{x}-0.12317$, and the adjusted ${\mathrm{R}}^2=0.97656$, showing that the experimental values fit well with the simulated values and proved the accuracy of the numerical simulation results.