Discrete Element Model of Different Moisture Hygroscopic Fertilizer Particles

Abstract

The discrete element computer simulation method is an effective tool that enables the study of the interaction mechanism between the fertilizer discharge device. However, the lack of accurate fertilizer models for hygroscopic fertilizer particles (HFP) has limited the application and development of the discrete element method in research precision fertilizer discharge device. Taking HFP as the research object, this research aims to establish the discrete element model of different moisture hygroscopic fertilizer particles, and to develop a method for predicting the discrete element parameters of HFP based on moisture content. The Hertz–Mindlin with JKR discrete element model was selected as the contact model for the HFP. The repose angle of HFP was used as the test index to select nine discrete element models for the HFP. Firstly, a mathematical model characterizing the relationship between fertilizer moisture content and the repose angle was established. Subsequently, the Plackett–Burman test identified the surface energy of hygroscopic fertilizer particles (HFP), the restitution coefficient between fertilizer and PC board, and the shear modulus as significant factors influencing the test index. The value range of the above parameters were determined by the steepest ascent test results. The Box–Behnken test obtained the regression model between the significant factors and the test index. The optimal combination of parameters of 2%, 4%, and 6% moisture contents of HFP were predicted based on the regression model and the HFP repose angle. The parameters were optimized using the repose angle error as the target. In order to further verify the accuracy of the HFP discrete element model, a fertilizer discharging simulation test was conducted. The results show that, compared with the actual fertilizer discharge amount, the simulation fertilizer discharge amount error of different moisture HFP was below 8.32%. The collective results indicated this method could reliably and precisely establish the discrete element model of various moisture content HFP. This model can be applied to the analysis of hygroscopic fertilizer discharging processes and the design of precision fertilizer discharge technology devices.

1. Introduction

Fertilization in agricultural fields is a vital strategy for guaranteeing consistent rice yields, and mechanized precision fertilization serves as an essential approach to enhance cost-effectiveness and operational efficiency. However, existing conventional fertilizer discharge devices exhibit low operational efficiency and poor operational quality during the fertilization process of hygroscopic fertilizer particles (HFP), which seriously affects the efficiency and quality of paddy field fertilization. Therefore, the development of high-performance fertilizer discharge devices is crucial for high-quality and efficient paddy field fertilization.

To develop such devices, the interaction mechanism between the equipment and fertilizer particles must be investigated to optimize the structural and operational parameters of fertilizer discharge devices. The discrete element method (DEM) computer simulation model is an effective tool for studying the interaction mechanism between fertilizer discharge components and fertilizer particles [1,2]. This approach can significantly shorten the research and development cycle, reduce experimental costs, and improve device performance [3,4,5].

This method is extensively applied in the design and optimization of fertilizer discharge structures [6,7,8,9]. Yuan Quan chun et al. [10,11,12] adjusted the discrete element parameters for organic fertilizer, soil, and composite fertilizer particles using the repose angle method for granular materials. Han Shujie et al. [13,14] fine-tuned the discrete element parameters for organic fertilizer, soil, and fertilizer particles collectively using the repose angle method for granular materials. Zhu Xinhua [15] and Bai, Jinyin [16] et al. developed a moisture content-repose angle model through the cylinder lifting method and regression fitting. Additionally, they formulated a discrete element model for sheep manure particles with varying moisture content by integrating Plackett–Burman and hill-climbing tests. Zhao Shuhong et al. [17] employed a discrete element model to study powdered organic fertilizers with varying moisture levels, aiming to develop an organic fertilizer feeding apparatus tailored for northeast China. Yan Yinfa [8] et al. utilized the discrete element method to simulate and analyze the dynamics of motion and collisions among four different types of granular fertilizers, namely, nitrogen, phosphorus, potassium and organic fertilizers, in a four-fluted roller feed distributor. Geldart et al. [18] investigated the measurement technique for determining the angles of packing for eight different types of powdered particles. Sun, J. et al. [19] explored the dynamics of granular fertilizers within sheave-wheeled fertilizer dischargers and evaluated the characteristics of such dischargers. Their study involved a combined approach of simulation analysis and bench testing to investigate these features. The above studies illustrate that numerous national and international researchers have employed discrete element analysis methods to investigate the kinematics and dynamics of fertilizer particles. These methods have been applied to design and optimize fertilizer dispensing structures to further enhance their performance. Nevertheless, in practical production, the moisture absorption of fertilizer particles is an inescapable phenomenon, especially under the high-temperature and high-humidity conditions that are widespread in the southern rice-growing regions of China. As a result, the surface adhesion of the particles significantly increases while their mobility notably decreases. Consequently, the fertilizer particles are more likely to adhere to the inner walls of the discharge device, hindering proper discharge [20,21,22]. There remains a gap in the literature regarding the investigation of the kinematics and dynamics of viscous agricultural materials, such as granular fertilizers with varying moisture content post-absorption, utilizing the discrete element method. This knowledge gap highlights the necessity of addressing this issue.

The objective of this paper is to develop a discrete element model for hygroscopic fertilizer particles (HFP) and to investigate a method for representing moisture content using discrete element method (DEM) parameters. Based on the repose angle test, the repose angle error was adopted as the test index. Nine parameters, including the surface energy of fertilizer particles, recovery coefficient, and friction coefficient, were selected as the test factors. The Plackett–Burman, steepest ascent, and Box–Behnken tests were conducted in sequence to calibrate the DEM parameters of HFP. The findings enabled the calibration of the DEM for fertilizer particles after moisture absorption and provided modeling tools for the design of precision fertilizer devices.

2. Materials and Methods

2.1. Hygroscopic Fertilizer Particles Parameter Determinations

2.1.1. Physical Characteristics of Hygroscopic Fertilizer Particles

Stanley compound fertilizer (17-17-17), a typical compound fertilizer in the southern rice-growing regions of China, was used as the experimental material. The moisture content of HFP in the southern rice region ranged from 2% to 6%. The sphericity φ was between 0.887 and 0.899%, the equivalent diameter d_e was 3.27–3.53 mm, and the actual density was 1.622–1.766 g/cm³ [23] (Figure 1).

2.1.2. Preparation of Hygroscopic Fertilizer Particles

An MGC–450R artificial climate chamber (Jingcheng Instrument Co., Ltd, Qingdao, China) was used to obtain HFP in the southern rice-growing region of China. A plastic box measuring 52 cm × 34 cm, filled with a single layer of fertilizer particles, was positioned flat inside the artificial climate chamber for moisture absorption treatment. The temperature and humidity settings were adjusted to 25.00 °C and 80.00%, respectively. The moisture content of the fertilizer particles was measured using Karl Fischer’s moisture titration method.

2.1.3. Angle of Repose of Hygroscopic Fertilizer Particles

A pre-test established that the HFP had characteristics of granular property and cohesiveness. Therefore, in this paper, the repose angle test was used as the basic test for HFP calibration. The repose angle of the HFP was used to determine the characteristics of the fertilizer particles with different moisture. The repose angle error of the HFP was used as the test index to calibrate the HFP simulation parameters. The repose angle was measured using the cylinder lifting method [24]. Figure 2 illustrates the repose angle test system and procedure for HFP, encompassing three complementary sub-figures: Figure 2a depicts the repose angle testing apparatus, comprising a bottomless cylinder (with an inner diameter of 32 mm and a height of 200 mm), an automatic lifting device (TMS-Pro texture instrument, Tengba Instrument Technology Co., Ltd, Shanghai, China), a PC board platform (Bakway, Suzhou, China), and a repose angle image acquisition camera. The camera was used to capture images related to the repose angle formation process.

Before the test, the bottomless cylinder was placed on a PC board platform, and the HFP were loaded into the cylinder. The cylinder was then lifted at a constant speed of 8.3 mm/s. Figure 2b shows the simulation of the repose angle. Fertilizer spilled from beneath the cylinder, accumulating on the PC board to form a stable pile, as illustrated in Figure 2b. Figure 2c illustrates the repose angle measurement method. The repose angle (θ₀) of the HFP was determined through the image-based digital simulation method and the Formula (1) [12,16,25]. Briefly, the boundary contour of the angle of repose was first extracted via image processing, followed by graphical fitting using MATLAB (R2025a) to obtain the boundary line of the angle of repose, and finally the measurement of its value. The extraction and measurement process of the angle of repose are illustrated in Figure 2c. The test was conducted ten times for fertilizers with different moisture contents to obtain the average value. In this paper, to establish a mathematical relationship equation between fertilizer moisture content and angle of repose, the angle of repose of fertilizer particles with moisture contents of 2%, 3%, 4%, 5%, and 6% were measured separately.

$${\theta }_0={\displaystyle \frac{{\theta }_L+{\theta }_R}{2}}$$

(1)

where the θ₀ is the repose angle of HFP, °; θ_L, θ_R represent the angles of repose on the left and right sides of the fertilizer pile, respectively.

2.2. Discrete Elemental Modeling of Hygroscopic Fertilizer Particles

2.2.1. Intrinsic Parameters

Based on previous research, the moisture content of HFP in the rice-growing areas of southern China ranges from 2% to 6% [23]. Following the research method outlined in reference [13,14], HFP with a moisture content of 4% were initially chosen to establish a discrete element mode (DEM). These particles were assigned an equivalent diameter of 3.43 mm and a density of 1.667 g/cm³. The parameters of the PC board (fertilizer discharge device material) were derived from reference [23]. Those above parameters were presented in

Table 1. Intrinsic parameters of fertilizer particles and PC.

Materials	Density g/cm3	Poisson Ratio	Shear Modulus/pa
Fertilizers	1.662~1.766	0.2~0.5	1 × 107~3.6 × 107
PC board	1.18	0.39	9 × 109

.

2.2.2. Contact Model Parameters

Hertz–Mindlin with Johnson–Kendall–Roberts (JKR) is a commonly used model for analyzing cohesive wet particles materials [13,14]. This contact model is built into the EDEM software (Altair EDEM 2022.1). It is a contact model that can reflect the cohesiveness of particles, established based on the Johnson–Kendall–Roberts theory. On the basis of the Hertz–Mindlin contact model, it takes into account the influence of van der Waals forces in the contact area on particle movement. It is suitable for simulating wet-containing particles, and characterizes the adhesion between particles through numerical surface energy, which can better simulate HFP [15,16]. The JKR model is particularly suitable for simulating adhesion and agglomeration of particle materials arising from factors such as electrostatic force between particles, moisture content and other reasons [26,27,28]. Bai Jin and Zhu bao yu et al. productively used this contact model in the simulation of wet brown rice [16] and paddy soil. Due to the highly cohesive nature of HFP after moisture absorbing, the Hertz–Mindlin with JKR model was presently chosen as the contact model for discrete element hygroscopic fertilizer particle modeling. The contact parameters and the range of values of JKR model parameters were determined by integrating data from the Generic EDEM material model database (GEMM database) with intrinsic parameters of fertilizer and PC board, as detailed in

Table 2. Fertilizer particles and PC contact parameters, JKR model parameter range.

Parameters	Values
Static friction coefficient of fertilizer-fertilizer	0.2~1.5
Dynamic friction coefficient of fertilizer-fertilizer	0.4~1
Recover coefficient of fertilizer-fertilizer	0~0.5
surface energy of fertilizer-fertilizer, J/m2	0~2
Static friction coefficient of fertilizer-pc	0.2~0.6
Dynamic friction coefficient of fertilizer-pc	0.2~0.5
Recover coefficient of fertilizer-pc	0.1~0.5

.

2.3. Construction of the Repose Angle-Discrete Element Parameter Model for HFP

2.3.1. Repose Angle EDEM Simulation of HFP

To ensure consistency with the physical test, a 3D model of the cylinder and PC board, created at a 1:1 scale using SolidWorks 3D modeling software (Solidworks2022), was imported into the EDEM simulation system in STEP format. The simulation was saved at intervals of 0.05 s, with a time step set to 20% and a grid radius three times larger than the size of the smallest particle entity. A model consisting of a cylinder filled with 3000 particles of hygroscopic fertilizer particle was utilized. The cylinder ascended at a constant speed of 8.3 mm/s. In order to ensure that the fertilizer pile has completely reached a stationary state, the duration of each simulation was set as 40 s. Upon completion of the simulation, the MATLAB image processing method was used to extract the repose angle of the fertilizers in both the XOZ plane and the YOZ plane [12]; the test results were obtained by averaging the values from three repeated tests.

2.3.2. Simulation Parameter Calibration

The repose angle error of the HFP was used as a test index to calibrate the discrete element simulation parameters. The simulation parameters with significant influence on the repose angle error were screened out by the Plackett–Burman test. The steepest ascent test was then used to approximate the better value range of the significant parameters. Finally, the Box–Behnken test was used to obtain the regression model between the test parameters and the test index. The regression equation was optimized to obtain the best parameter combination, and the combination was verified by simulation tests. The repose angle error is defined as

$$\phi ={\displaystyle \frac{|{\theta }_1-{\theta }_2|}{{\theta }_2}}\times 100\%$$

(2)

where φ is the repose angle error, %; θ₁ and θ₂ is the simulated and measured values of the HFP repose angle, respectively, in °.

2.4. Mathematical Model for Correlating Repose Angle with EDEM Parameters of HFP

The repose angle of HFP with the moisture contents (4%) was chosen as the target variable, the repose angle-DEM parameter model was derived from the Box–Behnken design. This model was solved to determine the optimal combination of DEM parameters. Utilizing the optimal combination of EDEM parameters of HFP (the values of non-significant parameters consistent with those determined in the hill climbing test), the simulation of cylinder lifting was conducted in the EDEM system to measure the repose angle. The repose angle error between the simulated and the physical value was calculated to verify the accuracy of the DEM parameter model for HFP.

3. Results and Discussion

3.1. Modeling the Correlation Between Moisture Content and Repose Angle

Table 3. Table of Box–Behnken significance level parameters.

Moisture Content of HFP/%	Repose Angle/°
2	29.54
3	30.00
4	32.50
5	34.89
6	42.87

presents the results of repose angle measurements for HFP with varying moisture content, obtained using the cylinder lifting test. A third-order polynomial regression was fitted to the relationship between moisture content and repose angle of HFP, yielding the moisture content-repose angle model (see Equation (3) and Figure 3). This fitting approach was selected as it effectively captures the observed trend, with the model achieving a high correlation coefficient of 0.9935. As illustrated in Figure 3, the repose angle of HFP increases with rising moisture content, primarily due to reduced particle mobility and enhanced adhesive forces among HFP particles following hygroscopic absorption.

y = 0.2592x³ − 2.023x² + 6.001x + 23.57

(3)

where x represents moisture content, %; y represents the angle of rest, °.

3.2. Plackett–Burman Test

The Plackett–Burman test allows for the rapid screening of test factors that have a significant impact on an indicator under conditions of a larger number of test factors. In this test, ten simulation parameters were selected. Each parameter was assigned two levels, high and low, which were coded as +1 and −1, respectively, as outlined in

Table 4. Factors and level of Plackett–Burman test.

Element	Parameters	Low-Level (−1)	High-Level (+1)
A	Poisson ratio of fertilizer	0.2	0.5
B	Shear modulus of fertilizer, (MPa)	10	36
C	Static friction coefficient of fertilizer–fertilizer	0.2	1.5
D	Dynamic friction coefficient of fertilizer–fertilizer	0.4	1
E	Recover coefficient of fertilizer–fertilizer	0	0.5
F	JKR surface energy of fertilizer–fertilizer, J/m2	0	2
G	Static friction coefficient of fertilizer–PC	0.2	0.6
H	Dynamic friction coefficient of fertilizer–PC	0.2	0.5
I	Recover coefficient of fertilizer–PC	0.1	0.5

. The test scheme and results were shown in

Table 5. Scheme and result of Plackett–Burman test.

Experimental Number	Experimental Factors									Angle of Rest/°
	A	B	C	D	E	F	G	H	I
1	−1	−1	−1	−1	−1	−1	−1	−1	−1	19.16
2	1	−1	1	1	1	−1	−1	−1	1	21.54
3	−1	1	1	−1	1	1	1	−1	−1	45.75
4	1	−1	−1	−1	1	−1	1	1	−1	21.84
5	1	1	−1	−1	−1	1	−1	1	1	44.68
6	1	1	−1	1	1	1	−1	−1	−1	44.02
7	−1	1	−1	1	1	−1	1	1	1	18.47
8	−1	1	1	1	−1	−1	−1	1	−1	22.00
9	−1	−1	−1	1	−1	1	1	−1	1	90.00
10	1	1	1	−1	−1	−1	1	−1	1	31.73
11	−1	−1	1	−1	1	1	−1	1	1	90.00
12	0	0	0	0	0	0	0	0	0	50.59
13	1	−1	1	1	−1	1	1	1	−1	46.35

. Significance analysis of the test results was performed using Design-Expert. The significance of the effect of each parameter on the test indices is presented in

Table 6. Significance analysis of parameters in the Plackett–Burman test.

Element	Effect	Mean Square	Contribution/%	Significance Rank
A	−12.54	471.59	6.61	4
B	−13.70	563.44	7.90	3
C	1.71	8.73	0.12	8
D	−1.79	9.65	0.14	7
E	−2.05	12.60	0.18	6
F	37.68	4258.71	59.71	1
G	2.12	13.53	0.19	5
H	−1.48	6.54	0.092	9
I	16.22	788.99	11.06	2

.

As shown in Table 6, the contribution of the nine test factors to the test index was ranked from highest to lowest. The order was F, I, B, A, G, E, D, C, H. The significance analysis of the test results, prioritizing parameters, revealed that the surface energy of fertilizer–fertilizer (F), the coefficient of restitution of fertilizer–PC (I), and the shear modulus of fertilizer (B) were particularly influential.

3.3. Steepest Ascent Test

To narrow the parameter range and determine the optimal interval, the three parameters with relatively significant impact were increased by equal gradient based on the Plackett–Burman test results. Furthermore, the average values obtained from the physical tests were utilized as the initial parameters for the HFP. A steepest ascent test was conducted to determine the range of value for the significant parameters.

The specific design of parameter levels and the results of the steepest ascent test are shown in

Table 7. Steepest ascent test design and results.

No.	Shear Modulus of Fertilizer (B)	Surface Energy of Fertilizer-Fertilizer (F)	Recover Coefficient of Fertilizer-PC (I)	Repose Angle/(°)	Repose Angle Error (%)
1	1 × 107	0	0.1	25.77	−20.70
2	1.65 × 107	0.5	0.2	37.76	16.17
3	2.3 × 107	1	0.3	51.60	58.77
4	2.95 × 107	1.5	0.4	42.35	30.32
5	3.6 × 107	2	0.5	43.82	34.84

. The repose angle exhibited an increasing trend with the increase of the parameter. When the parameter gradient increases from No. 1 to No. 2, the repose angle error transitions from negative to positive territory, and the absolute value of the repose angle error for the No. 2 test was the smallest. Hence, it could be inferred that the parameter region adjacent to No. 2 was optimal. Consequently, No. 1 and No. 3 were designated as the negative and positive levels, respectively, to conduct the response surface simulation for repose angle.

3.4. Box–Behnken Test

Following the results of the steepest ascent test, a Box–Behnken test was designed to conduct the response surface simulation test for the repose angle. This allowed for the extraction of the repose angle for each treatment. The parameter labeled No. 2 in the steepest ascent test was set as the 0 level. The parameters labeled No. 1 and No. 3 were set as the −1 level and +1 level, respectively. The remaining parameter values remained consistent with those used in the steepest ascent test [29]. The test factor code table is shown in

Table 8. Factor and codes of the Box–Behnken test.

Codes	Factors
	Shear Modulus of Fertilizer (B)	Surface Energy of Fertilizer-Fertilizer (F)	Recover Coefficient of Fertilizer-PC (I)
−1	1 × 107	0	0.1
0	1.65 × 107	0.5	0.2
1	2.3 × 107	1	0.3

. The Box–Behnken test design was performed using Design-Expert software (Design Expert13) according to the parameter levels in Table 8. The scheme and results are shown in

Table 9. Scheme and result of the Box–Behnken test.

Number	Shear Modulus of Fertilizer (B)	Surface Energy of Fertilizer-Fertilizer (F)	Recover Coefficient of Fertilizer-PC (I)	Angle of Rest/°
1	1.65 × 107	0.5	0.2	38.865
2	2.30 × 107	0	0.2	22.671
3	2.30 × 107	0.5	0.1	37.110
4	1.65 × 107	1	0.3	50.324
5	1.65 × 107	0.5	0.2	38.865
6	1.00 × 107	0	0.2	27.042
7	1.65 × 107	0.5	0.2	38.865
8	2.30 × 107	0.5	0.3	36.818
9	1.00 × 107	0.5	0.1	39.376
10	1.00 × 107	1	0.2	46.242
11	2.30 × 107	1	0.2	49.047
12	1.65 × 107	0.5	0.2	38.865
13	1.65 × 107	1	0.1	47.319
14	1.65 × 107	0.5	0.2	38.865
15	1.65 × 107	0	0.3	22.548
16	1.65 × 107	0	0.1	22.740
17	1.00 × 107	0.5	0.3	40.260

. Multiple regression analysis was performed on the test results using Design-Expert software to obtain the repose angle regression model, which was subjected to analysis of variance. The variance analysis outcomes of the regression model are detailed in

Table 10. Box–Behnken test quadratic polynomial regression model analysis of variance.

Source of Variance	Sum of Squares	Degree of Freedom	Mean Square	F	p
Model	1053.71	9	139.30	114.64	<0.0001 **
B-Shear modulus of fertilizer	6.61	1	6.61	5.44	0.0524
F-Surface energy of fertilizer	1198.81	1	1198.81	986.62	<0.0001 **
I-Static friction coefficient of fertilizer-PC	1.45	1	1.45	1.19	0.3109
BF	12.87	1	12.87	10.60	0.0140 *
BI	0.35	1	0.35	0.28	0.6102
FI	2.56	1	2.56	2.10	0.1903
B2	2.015 × 10−3	1	2.015 × 10−3	1.658 × 10−3	0.9687
F2	29.27	1	29.27	24.09	0.0017 **
I2	1.04	1	1.04	0.85	0.3867
Residual	8.51	7	1.22
Lack of Fit	8.51	3	2.84
Pure Error	0.000	4
Cor Total	1262.22	16
R2 = 0.9933; R2adj = 0.9846; CV = 2.95%; Adeq Precision = 33.203

Note: ** represents extremely significant influence (p < 0.01), * represents significant influence (0.01 < p < 0.05).

.

A diverse regression analysis of the Box–Behnken test parameters was conducted to derive the quadratic polynomial fitting equation for the correlation model between the repose angle (θ₁) and the DEM parameters, given by

θ₁ = 28.26 − 3.425 × 10⁻⁷B + 22.72F + 23.56I + 5.520 × 10⁻⁷BF − 4.523 × 10⁻⁷BI
+ 15.99FI + 5.177 × 10⁻¹⁶B² − 10.55F² − 49.59I²

(4)

As shown in Table 10, the variance analysis of the regression model was highly significant (p < 0.0001). The factors F and F² exhibit a highly significant effect on the repose angle (p < 0.01), while parameters B, I, BF, FI and I² demonstrate a significant effect on the repose angle (0.05 < p < 0.1). The adjusted coefficient is R²adj = 0.9846. Both coefficients are close to 1, with a difference of less than 0.2, indicating a well-fitted regression equation. The model’s reasonableness is confirmed by the adequate precision value (Adequate Precision = 33.203).

3.5. DEM Parameter Prediction and Validation

The minimum value of repose angle error served as the boundary condition, the repose angle of HFP with moisture content of 2%, 4%, and 6% were considered as the target value to solve the regression model. In this way, the DEM parameters of HFP with moisture in 2% and 6% were predicted, included shear modulus (B), fertilizer surface energy (F), and coefficient of restitution of fertilizer–PC-board (I). The optimal combination of fertilizer intrinsic contact parameters was utilized to conduct cylinder lifting simulation. This process resulted in the determination of the optimal EDEM parameter combination for the HFP model under each moisture content condition.

The cylinder lifting simulation of HFP with moisture at 2% and 6% was performed in EDEM software (Altair EDEM 2022.1); the DEM parameters of different HFP were set based on

Table 11. DEM parameters for HFP with different moisture contents.

Moisture Content	Shear Modulus of Fertilizer (B)	Surface Energy of Fertilizer (F) (J/m2)	Recover Coefficient of Fertilizer-PC (I)	Simulated Repose Angle (°)	Physical Repose Angle (°)	Repose Angle Error (%)
2%	15,555,112.15	0.17	0.28	29.664	29.548	0.39%
4%	18,787,070.99	0.28	0.21	32.489	32.499	0.03%
6%	11,417,529.40	0.65	0.26	42.264	42.873	1.42%

. After the simulation finished, the repose angle of HFP with moisture contents at 2% and 6% were obtained according to the method in Section 2.1.3. The simulation result and repose angle error are shown in Table 11 and Figure 4.

As indicated in Table 11, the repose angle error of viscous HFP with 2% and 6% moisture contents were 0.39% and 1.42%, respectively. Moreover, as depicted in Figure 5, the simulated repose angle profiles of every HFP exhibited substantial geometric correspondence to their actual morphological characteristics. This finding validated that this method, which incorporated fertilizer moisture content and repose angle as the critical parameter, accurately predicts the DEM parameters of HFP under each moisture content condition.

3.6. Discussion

The three significant parameters calibrated for HFP in this research were generally consistent with the research patterns of S J Han [13], L. M. Wang [14], etc., including JKR surface energy and coefficient of restitution. There is a certain similarity with the research patterns of X. H. Zhu [15], and J. Bai [16], etc. Among the three significant parameters, JKR surface energy is consistent with that in references [15,16], while the other two parameters are different. By comparing the research object of this paper (HFP) with those of references [15,16] (sheep manure and brown rice), it is speculated that the differences in parameters may be caused by factors such as particle shape and particle size.

Through comparison with previous studies, it is found that when the spherical JKR contact model is used for HFP, the parameters which have a significant impact on the angle of repose in the calibration of DEM parameters include several of the following: JKR surface energy, coefficient of restitution, inter-particle rolling friction coefficient, and inter-particle static friction coefficient. Therefore, in subsequent studies on the calibration of contact parameters of viscous bulk materials based on the discrete element method (DEM), it is necessary to focus on investigating the variation laws of the above four parameters.

In addition, H. Y. Liu [30] established a prediction model between the moisture content (7.8% to 18.5%) of columnar granular organic fertilizer and DEM parameters using the same method as this study, which further verifies the accuracy of the research method adopted herein. X. Deng [31] calibrated cohesive-wet soil with high moisture content (up to 33%) using the Edinburgh Elasto-Plastic Adhesion contact model. F. Elskamp [32] and H. Kim [33] characterized and simulated the shear characteristics and liquid bridge features between wet particles by means of the DEM method, respectively. Both of these studies analyzed the influence law of moisture content on inter-particle interactions in wet granular materials from a microscopic perspective, whereas this research, together with references [13,14,15,30], mainly focuses on the analysis of morphological characteristics of wet particle groups from a macroscopic perspective.

Based on a comprehensive comparison of the above analysis, this study only selected one brand of granular compound fertilizer as a representative of viscous granular materials in the composting process to study the contact parameters: the moisture content of HFP at 6–12%, which has certain limitations. Future experiments will include comparative studies on different types of granular fertilizers such as slow-release fertilizers and controlled-release fertilizers to further improve the law model of contact parameters of viscous granular materials in granular fertilizers. Meanwhile, multiple modeling methods can be employed to analyze the influence of moisture on the mechanical behavior of wet particles from macroscopic and microscopic perspectives, respectively.

4. HFP Discharge Process Simulation and Verification

To validate the precision of the DEM model of HFP, an HFP discharge process discrete element simulation was performed by using a self-cleaning fertilizer device with a cam top plate, followed by a bench validation test. These tests aimed to compare and analyze the fertilizer discharge error in a single loop discharge simulation; the single-revolution fertilizer discharge amount of the fertilizer device was taken as the evaluation index.

4.1. HFP Discharge Process EDEM-RecurDyn Joint Simulation

The structure of the cam top plate self-cleaning fertilizer discharge device is shown in Figure 5. A collaborative effort between EDEM and the multi-body dynamics software RecurDyn was undertaken to construct a simulation model for the cam top plate self-cleaning fertilizer device. This model aimed to accurately simulate the fertilizer discharge process of the cam top plate self-cleaning fertilizer device.

The components of the cam top plate self-cleaning fertilizer device were imported into the RecurDyn multi-body dynamics software (RecurDyn2025) system in a 1:1 ratio using the step format. The material for each component of the fertilizer device was designated as PC board, and the rotational speed of the fertilizer device was configured to be 20 rad/min. The simulation model of the cam top plate self-cleaning fertilizer device was created by integrating the EDEM system (Altair EDEM 2022.1) with the RecurDyn system (RecurDyn2025). A dynamic box was positioned directly beneath the fertilizer discharger to serve as a fertilizer collection container. The geometric model of the simulation is illustrated in Figure 6. The optimal DEM parameters of the HFP model with moisture contents of 2%, 4%, and 6% from Table 11 were incorporated into the simulation model. Following the fertilizer discharge simulation, the total simulation time was configured to be 10 s. In the EDEM post-processing module, the fertilizer discharge volume of single loop under the stable fertilizer discharge state was tested. The fertilizer discharge simulation of each moisture content HFP was repeated three times.

4.2. Bench Experiment of HFP Discharge Process

The component of the bench experiment of the HFP discharge process is shown in Figure 7. A motor power was transmitted to the fertilizer discharge wheel via a six-square shaft and double-cross universal coupling. The rotational velocity of the fertilizer discharger was set as the same value as the simulation process. The fertilizer collection barrel and weighing sensor were positioned directly beneath the fertilizer outlet of the fertilizer discharger. The weighing sensor was used to promptly capture and measure the quantity of discharged fertilizer.

4.3. Results and Analysis

The results of the fertilizer discharge simulation and bench validation tests are presented in Figure 8 and

Table 12. Results of the fertilizer discharge simulation and bench validation tests.

Moisture	Stimulated Single Loop Fertilizer Discharging Volume (g)	Actual Single Loop Fertilizer Discharging Volume (g)	Relative Error (%)
2%	48.58	52.99	8.32%
4%	46.74	50.64	7.70%
6%	39.07	41.86	6.67%

. The relative errors between the simulated fertilizer discharge volumes of HFP (with moisture contents of 2%, 4%, and 6%) and the actual single-loop discharge volume are 8.32%, 7.70%, and 6.67%, respectively. The simulated fertilizer discharge volume decreased as moisture content increased, mirroring the trend observed in the actual single-loop discharge volume. The reduced discharge volume during the process was attributed to increased moisture content, which enhanced the viscosity and reduced the mobility of HFP.

The aforementioned analysis indicates that the moisture content–DEM parameter correlation model can directly and precisely predict the model parameters of HFP with varying moisture contents. This model can also be applied to construct a discrete element model (DEM) of HFP based on their moisture content. The DEM accurately captures the viscous properties of HFP. Additionally, it can simulate the interaction between HFP and fertilizer devices.

This study provides research methodologies and theoretical models for predicting DEM parameters of HFP, as well as for designing and developing precision fertilizer discharge technology devices.

5. Conclusions

Through simulation and regression analysis of experimental results, a characterization method for the moisture content of hygroscopic fertilizer particle materials was proposed, and a mathematical model between discrete element simulation parameters such as surface energy and moisture content was developed, and the following conclusions were obtained:

(1)

A polynomial regression model of repose angle versus moisture content (Equation (1)) in the HFP moisture content range of 0–6% was established based on physical tests by the cylinder lifting method, and the model correlation coefficient value indicates its high accuracy.

(2)

The significant parameters (shear modulus of fertilizer, surface energy, and fertilizer-PC recovery coefficient) and their optimal intervals for DEM of HFP were determined. A repose angle–DEM parameter model (Equation (2)) was also established. Using this model along with the moisture content–repose angle regression equation (Equation (1)), the DEM parameters of HFP with 2% and 6% moisture content were predicted. The repose angle errors of viscous HFP at these moisture contents were 0.39% and 1.42%, respectively, demonstrating the model’s accuracy in predicting HFP discrete element parameters across different moisture contents.

(3)

Fertilizer discharge simulations and bench validation tests were conducted using the cam top plate self-cleaning fertilizer discharge device. The relative errors between the simulated single-loop discharge volumes of HFP and the actual volumes were 8.32%, 7.70%, and 6.67%, respectively. These results confirm that the moisture content–DEM parameter correlation model can directly and precisely predict HFP model parameters across varying moisture contents. This study provides research methodologies and theoretical models for predicting DEM parameters of HFP, as well as for designing and developing precision fertilizer discharge technology devices.

(4)

This study has limitations as it only examined contact parameters using one brand of granular compound fertilizer as a representative of viscous granular materials. Future research should include comparative studies on other granular fertilizer types (e.g., slow-release and controlled-release fertilizers) to further refine the contact parameter law model for viscous granular materials in granular fertilizers.