Calibration and validation of DEM parameters of food waste with high total solid content (≥20%) using physical experiments and EDEM simulations

Since discrete element method (DEM) parameters are important for the calculation accuracy of EDEM simulations, the DEM parameters of food waste with high total solid content (≥20%) are calibrated and validated by experiments and simulations in this paper. The physical properties of food waste are obtained by physical experiments, and then the optimal values of DEM model parameters recommended for food waste can be obtained from the GEMM database. Finally, the repose angle and the average torque obtained by EDEM simulations are compared with the experimental results to validate the calibrated DEM parameters of food waste. The average relative error of the repose angle between the experimental values and the simulation values is 3.23%, and the average relative error of the average torque value is 5.29%. That means the DEM parameters of food waste calibrated in this paper are correct and can be applied for simulating the mixing performance of food waste with high total solid content (≥20%).


Introduction
At present, the technology of anaerobic digestion of food waste to produce biogas has been quite mature.Biogas is mainly composed of methane, carbon dioxide, and other gases, which is a clean and pollutionfree energy source [1].As one of the raw materials for biogas production, food waste has significant advantages such as large output, low cost, and renewable.Therefore, many scholars have been attracted to studying the anaerobic digestion technology of food waste.In the process of anaerobic digestion of food waste, the mixing performance of food waste is one of the key factors determining the efficiency of hydrolysis and acidification [2].However, most of the studies on the hydrolysis and acidification efficiency of food waste are conducted by experiments, and few scholars carry out research by discrete element method (DEM) simulation.Compared with the experiment, the DEM simulation experiment saves time and effort and also saves a lot of resources.
It is reasonable to use DEM to simulate its motion characteristics.Bao et al. [3] numerically simulated the mixing of soil particles was simulated by DEM and obtained the optimum combination of stirrer parameters.Li et al. [4] established concrete slump and J-ring models by using DEM and calibrated the DEM model and JKR model of concrete to study the flow characteristics of concrete.Food waste with high total solid content ( 20%) has physical properties similar to soil and concrete, so it is appropriate to study it by DEM.
In the DEM, the parameter calibration of the material is the focus of the simulation, which directly determines the accuracy of the simulation results.Therefore, the parameter calibration of food waste with high solid content is studied in this paper.The accurate discrete element calibration parameters obtained in this paper will provide a scientific theoretical basis and data support for scholars.The simplified geometric model of the reactor is shown in Figure 1, which retains the reaction cylinder and stirring paddle of the reactor and will be used in EDEM simulation.Among them, the bottom of the reaction cylinder is a semi-cylindrical groove with an inner diameter of 280 mm, and the upper dimension is a cuboid with a size of 280 mm*400 mm*190 mm.The total volume of the cylinder body is 33 L. The axis of the mixing paddle is placed with the axis of the bottom semi-cylindrical groove, and the mixing paddle can rotate around its axis.The working principle of the reactor mixing is that the motor drives the stirring paddle to rotate, the stirring paddle applies force to the food waste particles and inoculum particles in the reaction cylinder, and the particles in the reaction cylinder diffuse and convective motion to realize the uniform mixing of the particles, to achieve the purpose of efficient reaction.[5] is a bonding force contact model, which can calculate the effect of the bonding force on the motion of the particles when they are in contact and is mainly used for discrete element simulation of particles or wet particles with van der Waals forces.This model applies to water-bearing particles, wet particles, or particles that bond due to static electricity, such as cement, soil, and laundry detergent.At present, the theoretical research of the JKR model has matured, and the physical significance of contact parameters has been clarified.In this paper, the Hertz-Mindlin model with JKR bonding force is used as the contact model of food waste particles after crushing.

Modeling of food waste particles.
In the DEM, if the actual shape of the particle is reconstructed by the simulated particle, the simulation results we get can almost restore reality [6].The food waste samples used in the experiment were from a canteen of the Guangxi University of Science and Technology.The food waste samples mainly include rice, rice noodles, vegetables, pork, and chicken, among which rice accounts for about 60%, vegetables for about 28%, meat for about 10%, and others for about 2%.Before the hydrolysis and acidification of food waste, the upper layer oil of food waste should be manually removed, because oil has an inhibitory effect on anaerobic digestion.Then, the food waste is pretreated to speed up the conversion rate of organic matter in the food waste.Mechanical crushing is one of the effective pretreatment methods.Food waste is 2-10 mm in diameter after mechanical crushing pretreatment.As shown in Figure 2, spherical particles with a diameter of 5 mm were selected to simulate rice particles, combined particles with a diameter of 6 mm were selected to simulate vegetable particles, and combined particles with a diameter of 9 mm were selected to simulate meat particles.In addition, inoculated bacteria particles were simulated with 5 mm spherical particles.The essence of inoculants is the food waste after hydrolysis and acidification, so inoculants and food waste have similar physical properties.The more realistic particle shapes need to be filled with small particles, the higher the computing performance requirements of the computer are.At the same time, the time required for simulation computation will increase significantly.The simulated particles in this paper are established under the premise that the simulation results are accurate enough and the calculation is efficient.

Discrete element method input parameters.
One of the key points of DEM is model parameter calibration, which directly affects the accuracy of simulation results.In this paper, food waste with a total solid content of 20.34% was taken as the research object (the total solid content of food waste was directly measured according to the APHA standard method (2005)).The physical properties of food waste were determined through experimental measurements and references.By integrating the physical properties and repose angle parameters of food waste particles measured in experiments into the GEMM database, the optimal DEM parameters recommendation value of food waste particles was obtained.
The composition of food waste is complex.After mechanical crushing pretreatment, food waste changes from blocks to particles with small diameters, which makes it difficult to measure the physical properties of various substances in food waste; on the other hand, the cumulative measurement error of multiple physical parameters worsens the simulation results.To make the food waste particles suitable for the study of discrete element method simulation, the food waste is regarded as a kind of material with uniform mixing.Food waste density was measured by immersion [7].Poisson's ratio and elastic modulus of food waste particles and steel are determined in [8,9].The average repose angle of food waste was 22.55° as measured by the repose angle acquisition experiment [10].The DEM parameters of food waste are obtained by inputting the physical properties of food waste and the average repose angle into the GEMM database.Among them, the static friction coefficient, collision recovery coefficient, and rolling friction coefficient between particles are 0.8, 0.45, and 0.139 respectively.The static friction coefficient, collision recovery coefficient, and rolling friction coefficient between the particle and wall are 0.7, 0.4, and 0.08 respectively.The surface energy between particles is 0.895.The surface energy between the particle and the wall is 0.8.

Results & discussion
To verify the accuracy of the model parameters, EDEM 2021 software was used to repeat the simulation experiment to obtain the repose angle ten times.The time step selected in this study is 20% of Rayleigh time, and the relative error between simulation and experimental results is shown in Figure 3.The overall relative error and coefficient of variation are 3.23% and 3.71%, respectively.This proves that the DEM parameters provided in this paper have good accuracy and can be used to study the mixing performance of food waste particles.The state of food waste accumulation obtained by the simulation and the state of food waste accumulation measured in the laboratory are shown in Figure 4.The accuracy of the DEM model was evaluated by comparing the average torque values at different speeds in simulation and simulation.The model was verified in a reaction cylinder using a trapezoidal paddle configuration.The simulation and experiment used the same rotational speed, filling degree, inoculated bacteria, and food waste ratio, and the reactor geometry in the simulation was the same as in the experiment.
In the simulation, the number of inoculated bacteria particles first generated in the reaction tank was 66, 700, and inoculated bacteria particles formed a particle layer at the bottom of the tank under the action of gravity.When the movement speed of the bacteria particles to be inoculated was less than 0.0001 m/s, 33, 300 food waste particles were generated.When the movement speed of food waste particles is less than 0.0001 m/s, the particle filling ends.At this time, the filling degree of the reaction cylinder is about 40%.The paddle began to rotate at a constant speed.To observe the mixing of particles in the simulation process, the inoculated bacteria particles are set to pink, and the food waste particles are set to yellow.
In the experiment, 8 L of inoculant was first added to the reaction cylinder, which was tiled at the bottom of the cylinder to form the inoculant layer.Then, 4 L of food waste was slowly added to the cylinder, and the filling degree in the cylinder was 40%.Finally, the stirring paddle was rotated at a uniform speed.During the experiment, the torque of the mixing paddle at every moment was recorded by a torque meter.The variation of average torque with speed obtained through simulation and experiment is shown in Figure 5.Where the red icon represents the simulated average torque value, the blue icon represents the experimentally measured average torque value, and the blue vertical bar represents the error size between the simulated and experimental values.Among them, when the stirring paddle is 45 rpm, the error value of simulation and simulation is the largest, 7.59%.The average error value of the average torque value corresponding to 5-45 rpm is 5.29%.This further validates that the DEM parameters provided in this paper can accurately simulate the experimental measurements in the reaction cylinder equipped with a trapezoidal paddle.

Conclusions
In this paper, the physical properties of food waste and reactors were determined by combining experimental measurements with references.Then the average repose angle of food waste was obtained by the repose angle experiment.Finally, DEM parameters are obtained by inputting physical properties and average repose angle into the GEMM database.The next step is to verify DEM parameters.The repose angle of food waste with a total solid content of 20.34% and the torque value required for mixing were obtained by simulation.Then, the simulation results are compared with the experimental results, and the relative error between them is calculated.The verification results show that the DEM parameters provided in this paper can accurately simulate the movement and stress state of food waste particles in the reaction tank.The results of DEM parameters calibration of food waste provide a theoretical basis and data support for subsequent scholars.This is helpful to guide scholars to study the mixing of food waste through DEM and promote the further development of anaerobic digestion of food waste to produce biogas technology.

Figure 3 .
Figure 3. Relative error between simulation and experimental results.

Figure 4 .
Figure 4. Comparison of simulation and experiment for the repose angle of food waste.

Figure 5 .
Figure 5.Comparison of torque results from simulation calculation and experimental results.