Calibration and Experimentation of Discrete Elemental Model Parameters for Wheat Seeds with Different Filled Particle Radii

Abstract

A Gas–solid two-phase flow coupling simulation is widely used to study the working process of pneumatic seed dischargers. Due to the demand for deterministic particle orbit numerical calculation models, seeds are mostly modeled using the particle aggregation method, where the seed model is formed through particle aggregation bonding without overlapping. The smaller the radius and the more filled ball particles used in this method, the closer they resemble the real morphology of the seed. However, this results in the over-consumption of simulation computational resources and simulation time growth. In this study, we used wheat seeds as the research object, studied the effect of seed models with different filled ball radii on the kinetic response characteristics between the particles, and searched for the optimal number of filled ball particles for the seed model. With the help of three-dimensional scanning and inverse fitting methods to obtain the seed profile, we used different radii (0.2 mm, 0.24 mm, 0.28 mm, 0.32 mm, 0.36 mm, and 0.4 mm) to fill the ball particles, and formed a wheat particle bonding model for a gas–solid coupling simulation. We used a combination of real tests and simulation measurements of bottomless cylinder-lifting and slip-stacking. The interspecies static and dynamic friction factors in seed models with different radii of filled spherical particles were first calibrated using the angle of repose as an index. Then, the parameters were verified using bottomless cylinder lifting and slip stacking tests, which used the coefficient of variation for the simulation test’s angle of repose as an index. Our results show that the smaller the radius of the filled ball, the closer the simulation results were to the real value. Validation was conducted using a gas–solid coupling simulation of an air-blown wheat seed discharger, with the seed filling rate as an index. Our results showed that the simulation length and simulation accuracy were optimal when the radius of the filling particle was 0.32 mm.

1. Introduction

In the field of agricultural engineering, agricultural material particles are the working medium of agricultural mechanized equipment, and their contact relationship and dynamic response characteristics are associated with agricultural equipment’s working efficiency and operational performance. Thus, research on the motion and dynamic response characteristics of agricultural material particles has received extensive attention from related scholars [1]. With the rapid development of computer technology, simulation analysis has become a common method for studying object dynamics [2]. The finite element and discrete element methods, as two common numerical analysis methods, are applicable to different physical problems, as shown in

Table 1. Comparison of commonly used simulation analysis methods.

Method	Discrete Element Method	Finite Element Method
Define	Numerical methods for analyzing the motion of discrete bodies.	Numerical methods for analyzing the motion of a continuous body.
Principle	Divide the object into many small units, each with its own mass and force.	Divide the solution domain into many small interconnected subdomains, each of which is called a finite element.
Applicable Scenarios	Suitable for managing discrete objects, such as particles, blocks, etc., that can simulate object collision, breakage, and other processes.	Suitable for handling continuous objects, such as elastomers, fluids, etc., and simulating the deformation and vibration of objects.

.

In this study, the discrete element method was chosen for analysis. The discrete element method was used to obtain particles’ macroscopic motion laws by calculating the motion properties of each discrete medium. Zhou and Jin [3,4] successfully simulated particle accumulation using this method. In the early stages of particle material characterization, most researchers chose to use simple spherical particles instead of granular materials in discrete element modeling simulations [5,6]. To simulate scavenging and classification, obtaining an accurate particle model is an important prerequisite. Simple spherical particles cannot realistically simulate the collision and tumble characteristics of irregularly shaped particles such as ore, corn, wheat, etc. Rotheburg et al. [7] proposed the ellipsoidal disk model theory, and Lin et al. [8] proposed the ellipsoidal model. Favier [9] and Salot [10] aggregated or bonded discs or spheres together to form a cluster or agglomerate. Abbaspour–Fard [11] and Kruggel–Edwards et al. [12] proposed a multi-sphere method (MSM) for the particle modeling of agricultural materials with smooth surfaces. With improvements in discrete unit theory and the need for particle modeling accuracy, image analysis technology [13,14] and reverse modeling technology were combined and applied to analyze the appearance and morphology of particles or solids and perform discrete element modeling. Liu and Yuan et al. [15,16] used the reverse engineering theory to obtain point cloud data on rice using 3D laser scanning technology. They imported the data into reverse engineering software (Geomagic Studio) for data processing, obtained the seed contour model and its spatial coordinate information, and finally established a 3D discrete element model of rice seed.

In the gas–solid two-phase flow coupling simulation, EDEM adopts a surface mesh to describe the boundary surface, establishing point-to-point coupling with the boundary surface elements of the CFD fluid mesh. It also adopts a sampling point to represent the particle volume, but the particle volume must be smaller than the control microelement volume (the volume of the grid in the flow field) [17]. Currently, this problem can be solved by simplifying the flow field and seed models and modeling aggregation bonds with no overlap. Since the divisions performed in flow field simplification cause the flow field mesh to be larger than the particle volume, the flow field accuracy is greater. Therefore, most researchers choose the particle bonding method for seed modeling. According to a three-dimensional model compression simulation based on particle bonding models in EDEM2018 software, hundreds of small particles are bonded by the seed particle model using particle replacement and grid fast filling methods. Considering only the similarities between the model and real material, the smaller the radius of the filled particles, the higher the number of particles with a higher matching accuracy between the discrete element model and the real material. However, the larger the number of filled particles, the larger the computational effort and the longer the computational time [18,19,20]. Thus far, there have been no reports on the effect of filled particle size on the simulation accuracy of EDEM.

In this study, we used wheat as the research object, reconstructed the wheat model through 3D laser scanning technology, established six kinds of 3D models of the same wheat seed with different filling ball radii using particle fast filling in the discrete unit method, and calibrated the main parameters of the wheat model with different filling ball numbers using cylinder lifting and slip stacking tests. By comparing the real test with simulation data, we analyzed the influence of different filling ball radii on simulation accuracy and determined the optimal filling ball radius for the wheat model using a gas–solid two-phase flow coupling simulation analysis. These particle modeling methods provide new insights into the simulation accuracy of EDEM.

2. Materials and Methods

2.1. Test Methodology

The angle of repose is a macroscopic parameter that characterizes the flow and friction properties of granular materials. It relates to the contact materials’ physical properties and the materials themselves [21,22]. This study focuses on degrees of error in the angle of repose of wheat seed model simulations at different filled ball sizes.

Firstly, the angles of repose in wheat populations under the two test methods were determined by real tests, followed by a wheat seed model with different filler particle sizes. The inter-seed static friction coefficient and rolling friction coefficient were used as the test factors for the simulation test. The target values were obtained from real measured angles of repose under the two test methods. Binary regression equations for the two main contact parameters were established using the response surface method to solve the two variables, inter-seed static friction coefficient and rolling friction coefficient, for wheat seed simulation under different filler particle radii. The influence of different filled particle radii on the stability of simulated angles of repose was analyzed according to the calibration results of the two main contact parameters.

2.2. Angle of Repose Measurement Test

The test material was selected from Jimai 22 seeds, with a thousand-grain weight of 42.4 g. The material of both test devices was a plexiglass plate. Figure 1 shows the test device, which consisted of a test bench for measuring material properties, a bottomless plexiglass cylinder, a population sliding stacking device, etc. During the cylinder-lifting test, as shown in Figure 1a, the bottomless plexiglass cylinder was dropped onto the plexiglass plate. A certain number of wheat seeds were poured into the cylinder, and the cylinder was lifted at a uniform speed of 0.5 m/s by a motor. Seeds naturally slid down the cylinder and piled up. The angle between the sloping surface of the seed stockpile and the horizontal plane represented the elevation test’s angle of repose. As shown in Figure 1b, the slide stacking test device consisted of a draw plate and shell. The length, width, and height of the shell were 110 mm, 60 mm, and 400 mm, respectively. The test involved inserting seeds into the device. After the population was stabilized, the outward withdrawal of the extraction plate caused the seeds to slide along the leakage hole to scatter and were piled up. The angle between the inclined plane and the horizontal plane is the seed population’s angle of repose. Figure 1 shows the two tests form the angle of repose.

2.3. Simulation Model

2.3.1. Determining the Number of Wheat-Filled Balls

When creating particle models in the discrete element software EDEM, the higher the reduction degree of the particle model, the higher the number of basic spherical particle units required for modeling, the longer the simulation time, and the lower the efficiency. However, if the number of filler spheres in modeling is too small, model errors will increase, causing greater errors in interspecies contact parameter settings during simulation and analysis.

To calculate the number of fills, the following formula was used:

$$v\cdot V_s=N\cdot V_t$$

(1)

$$V_t=\frac{4}{3}\pi \cdot R^2$$

(2)

where v is the filling volume fraction; vs. is the actual volume of the seed model; N is the number of filled particle spheres; V_t is the volume of filled particle spheres; and R is the radius of filled particle spheres.

The selected wheat seed volume vs. was 14.235 mm³, and the best filling effect was achieved when the filling volume fraction was α = 0.56. Therefore, the number of filling spheres corresponded to different filling sphere radii.

2.3.2. Wheat Seed Particle Model Construction

Adopting reverse engineering theory, a 3D laser scanner was used to obtain 3D point cloud data from the seeds. Wheat seeds were fixed to a reference object on a work table using fixed pins, and placed in a suitable position in front of the lens. A blue light photographic scanning method was adopted to photograph each side of wheat seeds from multiple viewpoints. Point cloud data files were imported into reverse engineering software and subjected to a series of processing steps, such as deleting noise points, alignment, merging, encapsulation, accurate surface, format conversion, and so on [23,24]. These steps reconstructed a three-dimensional solid model of wheat, and a three-dimensional raster scanning process was used to obtain three-dimensional point cloud data. Representative wheat seeds of general size without defects were selected. Figure 2a shows the scanned model of wheat seeds obtained through a 3D raster scanning process.

The geometry of the 3D wheat seed model was exported from Solidworks2018 software in .stl format and imported into EDEM software. The seed model was placed into the file horizontally, and the view was adjusted to make the ball particles fully fill each region during the generation process. The particle factory was defined at the upper end of the mold interior, and the dynamically generated ball particles were moved with a certain initial velocity. We used the Hertz–Mindlin particle bonding model to provide better mobility for the filled ball particles. We also set a smaller collision recovery coefficient and dynamic and static friction coefficients to increase the density of the void. Gravity acceleration was set to be larger. After the ball particles filled the model, all the ball particles were exported to the EDEM post-processing interface as a .csv data file with the center coordinates of the ball particles. The generated large particles were replaced with small particles using the API file, and the position of the replacement was oriented by the center coordinates of the large particles. The replaced particles were loaded with a strong bonding force to bond the particles together. Figure 2b shows the complete coupled simulation model of wheat seeds.

After EDEM simulation filling, the simulation time was zeroed, the dec file in .xml format was exported, and the coordinates of the centers of processed spherical particles were inserted into the dec file. The dec file was imported into the newly created particle item of the EDEM file, and EDEM software automatically generated wheat grain models that could be used as templates for the particles. As shown in Figure 2c, the particle bonding model was r = 0.2mm.

3. Simulation Calibration Pre-Test

3.1. Simulation Calibration Pre-Test Program

Several particle parameters in EDEM software can be used to accurately determine parameters and ranges that significantly affect simulation parameters. For example, the wheat model with a filled ball radius of r = 0.18 mm was used to arrange the simulation test and conduct the Plackett–Burman and steepest climb tests. MATLAB2018 was used to process the angle of repose for the wheat particle heap formed by the simulation test (Figure 3). The average tangent value of the angle of repose on both sides was also calculated.

3.2. Determination Test for the Simulation Significance Parameter

Design Expert software was used to conduct the Plackett–Burman test. Eight real and three virtual parameters in EDEM software were selected. Each parameter was set according to two high and low levels expressed in the form of coding, +1 and −1, as shown in

Table 2. List of Plackett–Burman test parameters.

Notation	Parameter	Low Level (−1)	High Level (+1)
X1	Wheat Poisson’s ratio	0.4	0.5
X2	Wheat shear modulus	5 × 107	5 × 109
X3	Wheat–wheat collision recovery factor	0.4	0.5
X4	Wheat–organic plate collision recovery coefficient	0.5	0.6
X5	Wheat–wheat rolling friction coefficient	0.07	0.08
X6	Wheat–wheat static friction coefficient	0.5	0.6
X7	Wheat–organic plate rolling friction coefficient	0.04	0.06
X8	Wheat–organic plate static friction coefficient	0.5	0.6
X9 X10 X11	virtual parameter	-	-

.

The Plackett–Burman experimental design and test results are shown in

Table 3. Plackett–Burman experimental design and results.

Serial Number	X1	X2	X3	X4	X5	X6	X7	X8	X9	X10	X11	Angle of Repose Tangent
1	1	1	−1	1	1	1	−1	−1	−1	1	−1	0.3905
2	−1	1	1	−1	1	1	1	−1	−1	−1	1	0.5016
3	1	−1	1	1	−1	1	1	1	−1	−1	−1	0.3029
4	−1	1	−1	1	1	−1	1	1	1	−1	−1	0.2017
5	−1	−1	1	−1	1	1	−1	1	1	1	−1	0.3934
6	−1	−1	−1	1	−1	1	1	−1	1-	1	1	0.3386
7	1	−1	−1	−1	1	−1	1	1	−1	1	1	0.1313
8	1	1	−1	−1	−1	1	−1	1	1	−1	1	0.2239
9	1	1	1	−1	−1	−1	1	−1	1	1	−1	0.1283
10	−1	1	1	1	−1	−1	−1	1	−1	1	1	0.0618
11	1	−1	1	1	1	−1	−1	−1	1	−1	1	0.1687
12	−1	−1	−1	−1	−1	−1	−1	−1	−1	−1	−1	0.1223

. As shown in

Table 4. Statistical analysis of Plackett–Burman test parameters.

Parameter	Mean Square	F	p-Value	Significance
X1	0.0062	10.28	0.0491	-
X2	0.0002	0.3509	0.5953	-
X3	0.0018	3.02	0.1807	-
X4	0.0001	0.1836	0.6972	-
X5	0.0309	50.90	0.0057	**
X6	0.1489	244.94	0.0006	**
X7	0.0050	8.15	0.0649	-
X8	0.0094	15.38	0.0295	*

Note: ** indicates highly significant, * indicates generally significant.

, an analysis of variance (ANOVA) was performed in Design Expert to analyze the effects of each parameter. The magnitude of each parameter’s effect on the test index’s angle of repose was determined by the magnitude of the variables’ p-value significance in the ANOVA table. As shown in Table 4, the wheat–wheat static friction coefficient, wheat–wheat rolling friction coefficient, wheat–organic plate static friction coefficient, and wheat Poisson’s ratio significantly affect the angle of repose for particle stacking, with p-values of 0.0006, 0.0057, 0.0295, and 0.049, respectively. By contrast, the effects of the other factors are minor. To improve the efficiency and accuracy of the subsequent simulation test, the significance test level was set to 0.01. Generally, significant factors were excluded and two factors, the wheat–wheat static friction coefficient and wheat–wheat rolling friction coefficient, were calibrated as the focus of the simulation test.

3.3. Significance Parameter Range Determination Test

To reach the optimal region for each significant factor as quickly as possible, the steepest climb was applied to the cylinder-lifting simulation test based on the Plackett–Burman test. The significance parameters were incrementally increased according to the selected step size, with factors’ values determining the step change. Parameter values gradually increased from small to large according to parameter range values. After reaching a minimum value, the relative error for the angle of repose obtained from the test and simulation gradually increased.

Table 5. Steepest climbing test design and results.

Serial Number	Wheat–Wheat Static Friction Coefficient	Wheat–Wheat Rolling Friction Coefficient	Angle of Repose Tangent	Relative Error/%
1	0.01	0.002	0.072	76.2
2	0.03	0.005	0.293	10.1
3	0.05	0.008	0.311	3.7
4	0.07	0.011	0.394	25.2
5	0.09	0.014	0.418	35.4
6	0.11	0.017	0.436	38.1

shows the steep climb test design and results. This result shows that the angle of repose increases gradually with the increase in wheat–wheat rolling friction coefficient and wheat–wheat static friction coefficient. Furthermore, the relative error between the angle of repose of the wheat grain pile in the real test and the simulation first decreases, then increases. This relative error is minimized at level no. 3, showing that the optimum value interval is near level no. 3. Therefore, the range near level no. 3 was selected for the design of the subsequent response surface.

4. Simulation Calibration Test

4.1. Simulation Parameter Settings

After pre-test simulations, the simulation calibration parameters were identified as wheat–wheat static friction coefficients and wheat–wheat rolling friction coefficients. The rest of the parameters were obtained from reference [25], as shown in

Table 6. Parameters required for discrete element simulation.

Parameter	Numerical Value
Wheat Poisson’s ratio	0.42
Wheat shear modulus/Pa	5 × 108
Wheat seed density/(g-cm)−3	1.35
Plexiglass Poisson’s ratio	0.39
Plexiglass shear modulus	3.19 × 108
Plexiglass density/(g-cm)−3	1.02
Wheat–wheat collision recovery coefficient	0.42
Coefficient of recovery for wheat collision with plexiglass	0.51
Coefficient of static friction between wheat and plexiglass	0.55
Coefficient of rolling friction between wheat and plexiglass	0.05

.

4.2. Simulation Calibration Test Program

According to the test requirements for measuring two kinds of rest angles for wheat seeds, two geometrical models were established at a ratio of 1:1 (Figure 4). A wheat model with a filled ball radius of r = 0.28 mm was used as an example for simulation tests. A generalized rotating center combination test design method was chosen to calibrate the parameters of the inter-particle static friction coefficients and rolling friction coefficients in the simulation process of wheat seeds.

Based on the pre-test simulation results, ranges of 0.03–0.07 and 0.005–0.01 for inter-seed static friction coefficients and inter-seed rolling friction coefficients, respectively, were determined for a wheat model with a filled ball radius of r = 0.28 mm. The simulation test factor coding table for wheat–wheat static friction coefficient A and wheat–wheat rolling friction factor B is shown in

Table 7. Factor coding for the simulation tests.

Encoding	Consideration
	Coefficient of Static Friction between Wheat A	Coefficient of Rolling Friction between Wheat B
1.414	0.07828	0.011035
1	0.07	0.01
0	0.05	0.0075
−1	0.03	0.005
−1.414	0.02172	0.003965

.

4.3. Simulation Calibration Target Value Acquisition

The angle of repose images acquired under two real test methods were analyzed using MATLAB’s image-processing software (Figure 5). Image denoising, grayscaling, and binarization processing were performed. The edge of the angle of repose curve was also identified by edge detection. The least squares method of straight-line fitting to the boundary points and the slope of the fitted straight line, representing the tangent value of the angle of repose, were also measured. The results of the 10 measurements are shown in

Table 8. Angle of repose measurements under the two test methods.

Experiment	Lift Test Angle of Repose Tangent	Angle of Repose Tangent of the Drawplate Test
1	0.35969	0.63162
2	0.37113	0.64944
3	0.32196	0.60841
4	0.32119	0.62062
5	0.33241	0.63492
6	0.32504	0.56767
7	0.3049	0.56909
8	0.31307	0.55256
9	0.30709	0.56548
10	0.30604	0.55845
average value	0.326	0.5958

. The mean values of the angle of repose tangent values under the two test methods are 0.326 and 0.5958, respectively.

4.4. Calibration Results and Analysis of Different Model Simulations

Design Expert software was used to conduct a generalized rotating center combination test design. The static friction coefficient and rolling friction factor between wheat particles were selected as the test factors, and the angles of repose for the two measurements were considered evaluation indexes. Thirteen simulation test groups were designed according to the test requirements. After completing the simulation, models with different numbers of filled balls were simulated according to the aforementioned real test process. Post-simulation pictures were exported. To obtain the simulated angle of repose of wheat, MATLAB image processing technology was used to extract simulation pictures and obtain the tangent values of different filled models’ angle of repose (

Table 9. Simulation test program design and results.

Serial Number	Wheat–Wheat Static Friction Coefficient A	Wheat–Wheat Rolling Friction Coefficient B	Lift Test Angle of Repose Tangent Y1	Sliding Scattering Method Angle of Repose Tangent Y2
1	−1	−1	0.285	0.471
2	1	−1	0.329	0.527
3	−1	1	0.328	0.479
4	1	1	0.425	0.697
5	−1.414	0	0.273	0.489
6	1.414	0	0.405	0.712
7	0	−1.414	0.291	0.449
8	0	1.414	0.377	0.569
9	0	0	0.306	0.539
10	0	0	0.299	0.564
11	0	0	0.303	0.588
12	0	0	0.307	0.569
13	0	0	0.311	0.569

).

The analysis of variance (ANOVA) for the simulation test results using Design Expert 8.0.6 software (e.g.,

Table 10. Analysis of variance.

Variance Source	Y1				Y2
	Sum of Squares	Freedom	F	P	Sum of Squares	Freedom	F	P
Model	0.0265	7	35.78	0.0006	0.0745	7	35.78	0.0006
A-A	0.0087	1	83.55	0.0003	0.0249	1	83.55	0.0003
B-B	0.0037	1	24.19	0.0044	0.0072	1	24.19	0.0044
AB	0.0007	1	22.05	0.0054	0.0066	1	22.05	0.0054
A2	0.0023	1	4.94	0.0769	0.0015	1	4.94	0.0769
B2	0.0017	1	22.77	0.0050	0.0068	1	22.77	0.0050
A2B	0.0000	1	0.0289	0.8717	8.600E−06	1	0.0289	0.8717
AB2	0.0003	1	0.7189	0.4352	0.0002	1	0.7189	0.4352
Residual	0.0001	5			0.0015	5
Lack of Fit	0.0001	1	0.8200	0.4164	0.0003	1	0.8200	0.4164
Pure Error	0.0001	4			0.0012	4
Cor Total	0.0266	12			0.0760	12

) revealed that both test models were highly significant (p < 0.01), indicating the test’s validity. The regression equation for coded values of factors with a good fit and practical analytical significance was derived after eliminating insignificant factors:

$$Y_1=0.3052+0.041A+0.0326B+0.0133AB+0.0182A^2+0.0157B^2$$

(3)

$$Y_2=0.5658+0.0737A+0.0435B+0.0405AB+0.0145A^2-0.0312B^2$$

(4)

Design Expert 8.0.6 software optimized the regression model using constrained objectives and an optimization module so that the simulation results matched the angle of repose of wheat seeds obtained from the experiment as closely as possible.

objective function $\left\{\begin{array}{c}{Y}_1=0.326\\ Y_2=0.5958\end{array}\right.$

constraint function $\left\{\begin{array}{c}-1.414\le A\le 1.414\\ -1.414\le B\le 1.414\end{array}\right.$

The resulting optimization result was a wheat–wheat static friction factor of 0.0549 and a wheat–wheat rolling friction coefficient of 0.00812. At this time, the angle of repose simulation results met the target indicators. In accordance with the above approach, the other four discrete elemental models of wheat with different filled particle sphere radii were calibrated for the wheat–wheat static friction factor and rolling friction factor. The calibration results are shown in

Table 11. Discrete elemental model results calibrated for physical property parameters by different filled particle radii.

Filled Particle Radius/mm	Wheat–Wheat Static Friction Coefficient	Wheat–Wheat Rolling Friction Coefficient
0.2	0.0405	0.00866
0.24	0.0486	0.00835
0.28	0.0549	0.00812
0.32	0.0568	0.00731
0.36	0.0587	0.00715
0.4	0.0598	0.00674

.

5. Effect of the Number of Model-Filled Particles on Simulation Accuracy

5.1. Seed Stacking Angle of Repose Test

To verify the accuracy of the contact parameters obtained from the calibration test and analyze the influence of different filled particle numbers on simulation accuracy, cylinder lifting and slip stacking tests were used to verify the seed model. Each test was repeated 10 times, all of which used the tangent value of the angle of repose as an index. The simulation pictures were processed by image-processing technology, and the angle of repose was obtained by boundary extraction and fitting.

Table 12. Comparative analysis of simulation results for different filling models and actual test results.

Parameter	Filled Particle Ball Radius/mm
	0.4	0.36	0.32	0.28	0.24	0.2
Y1	0.312	0.341	0.354	0.362	0.397	0.398
Relative error/%	3.95	3.19	2.33	2.41	2.26	2.19
Y2	0.542	0.553	0.564	0.587	0.594	0.599
Relative error/%	4.13	3.74	2.48	2.37	2.24	2.14

shows the tangent value and results.

Our results show that as the radius of the filled particle ball decreased and the number of filled balls increased, the error between the simulated angle of repose and the real test was smaller. The relative error of the angle of repose was larger at r = 0.4 mm. Furthermore, the relative error of the angle of repose decreased significantly when r = 0.32 mm, which was closer to subsequent models with other filling radii.

5.2. Simulation Test of Wheat Gas–Solid Two-Phase Flow Coupling

To further verify the effect of different filled particle numbers on simulation accuracy, a gas–solid two-phase flow coupling simulation test was conducted (Figure 6). The seed dispenser selected for the test used positive pressure airflow to press the seeds into the holes and complete seed filling so that its seed filling link could be analyzed. Due to the small size of wheat seeds, the number of seeds in the seed dispenser chamber was relatively dense, and the influence of particles on the airflow field must be considered in the simulation and analysis process. Therefore, the Eulerian two-way coupling model was used. Using three-dimensional software to establish the airflow field model of the seed dispenser and mesh division, the flow field grid volume was larger than the cohesive particle volume. Using the slip grid method, the shell’s internal chamber grid area defaulted to static, and the planes in contact with each part were used as interfaces to complete the data exchange between the dynamic and static areas. To establish the link between the real and simulation tests, the leakage rate was adopted as an index between the tests.

Considering the position of the type hole in the seed-filling area as the initial point, and the completely detached population as the termination point, we can delineate the seed-filling rate and judgment area. A camera is used to shoot during the seed discharger process, and leakage is judged as leaving the judgment area with no seed in the type hole [26]. The ratio of the number of leakage holes to the total number of holes is the leakage rate, which is calculated by the following formula:

$$z=\frac{Z_1}{Z}\times 100\%$$

(5)

where z is the leakage rate percentage; Z₁ is the number of holes missed; Z is the total number of holes recorded.

The real test waits for the seed discharger to work and stabilize before starting to record. However, due to limited computational resources, the simulation time is shorter. Two consecutive holes have seeds as a triggering condition. Therefore, the number of effective holes, leakage rate, and number of leakage holes are calculated in the same way as the real test.

Jimai 22 varieties were selected as test samples, and the seed discharger was independently driven by an ECMA-C10401ES servo motor with a torque of 0.3 N-m and speed of 3000 r/min. These parameters were accurately controlled to meet the test’s high rotational speed requirements. The seed discharge disk speed was 800 r/min, with six holes, and three tests. Each test detection was no less than 1000 holes. The average value of the seed discharger’s leakage rate was 8.24%.

In the process of simulation and analysis, one must consider the effect of particles on the airflow field. Therefore, the Eulerian two-way coupling model and traction model selection of free flow models (Free-stream) were used. Plant spacing between wheat seeds was set to 0.03 m. The seed filling pipe through wind pressure was 5 kPa, and the seed particle generation rate was set to 100 per second. The particle plant simulation time step was set to 2 × 10⁻⁶, the airflow field simulation time step was set to 2 × 10⁻⁵, and the total simulation time was 2 s. The test results are shown in

Table 13. Effect of different filled particle sphere radii on gas–solid coupling simulation tests.

Parameter	Filled Particle Ball Radius/mm
	0.2	0.24	0.28	0.32	0.36	0.4
Number of statistical holes	200	200	200	200	200	200
Number of leakage type holes	16	16	18	19	21	24
Leakage rate/%	8.0	8.0	9.0	9.5	10.5	12.0
Relative error/%	2.52	4.64	9.28	6.54	24.37	48.50
Simulation time/h	126	116	101	84	62	35

.

Our test results show that as the radius of the filled particle ball decreased, the leakage rate index was closer to the real test results, proving that decreasing the radius of the filled particle ball and increasing the number of filled particles can make the seed shape closer to reality. However, it greatly increases simulation time. Increased radii of filled particle balls greatly reduce simulation time as well as simulation accuracy. Therefore, when r = 0.32 mm, the leakage rate of the simulation test was 9.5% and the relative error rate was 6.54%. Therefore, simulation accuracy and simulation time improved under this filled particle ball radius.

6. Conclusions

(1)

Adopting the particle polymerization and bonding method, six wheat seed models with different radii of filled particles were created. The regression equations of the angle of repose in the cylinder lifting and slip stacking tests, and the main contact parameters between wheat seeds were established using the response surface method. The coefficients of static friction and rolling friction between wheat seed models with different radii of filled particles were also calibrated, respectively.

(2)

The calibration results were validated using cylinder lifting and slip stacking test progressions, respectively. Our results show that the simulation data’s stability decreases as the radius of the filled particle ball increases and the number of filled particles decreases.

(3)

The simulation test of wheat gas–solid two-phase flow coupling helped analyze the influence of wheat seed models with different filled particle ball radii on the simulation accuracy. The real and simulation tests were compared with those of the leakage rate as an index. Our results showed that increasing the filled particle ball radius decreased simulation time and, consequently, simulation accuracy. However, when the radius of the filled particle ball was r = 0.32mm, the simulation time was lower and the simulation accuracy was higher, with a relative error rate of 6.54%.