Finite Element Simulation Investigation Of RF Heating Of Black Pepper Based On Particle Accumulation And Motion Process

Most agricultural products are granular materials,including legumes,grains and spices.Due to the harvesting process and storage environment,agricultural products are susceptible to contamination by foodborne pathogens.Although most agricultural products are considered low-moisture foods during storage,the potential for bacterial contamination still exists,as they may survive in a low-moisture environment and endanger people’s health.Traditional pasteurization techniques are not suitable for low-moisture foods due to their low thermal diffusivity.RF heating as an emerging pasteurization technology,its penetration as well as heating properties have been widely studied and applied in agricultural products,such as cereals,black pepper,cumin,chestnuts,peanuts and soybeans.Black pepper is loved for its ability to give a special flavor to food and is one of the more economically consumed spice crops in the world.Bulk black pepper（Piper nigrum）granular material exhibits a unique heating behavior different from pure solid or fluid food materials due to the presence of voids and contact points.The stacking arrangement of different porosity and contact points may lead to different heating rates and uniformity.The research in this paper consists of three main parts:1.the effect of orderly accumulation of equal diameter black pepper particles on RF heating uniformity;2.the effect of disordered accumulation of non-equal diameter black pepper particles on RF heating uniformity;3.the numerical simulation of continuous transport of equal diameter black pepper particles for sterilization process.In this study,black pepper particles with an identical diameter（5 mm）and four different arrangements were selected to compare their heating rate and temperature distribution in radio frequency heating with computer modeling.The four arrangements were simple cubic,body centered cubic,rhombohedral and face centered cubic.Within different arrangements,as the porosity increased from 0.25 to 0.47,the heating time increased from 500 to 780 s for reaching a target temperature of 70℃.For heating rates comparison at the center and corners,rhombohedral model had the highest R²（0.9953,0.9975）and lowest RMSE（1.0709,0.7642）,respectively,among all arrangements.For temperature distribution on the top surface,the highest similarity of heating pattern between simulation and experiment was also found in rhombohedral model with an RMSE of 124.30.Therefore,the optimal prediction results were obtained in an arrangement with the closest porosity to randomly stacked globe particles in experiment.This study verified the importance of porosity and arrangement of particles in RF heating,and expanded the usage of RMSE for modeling accuracy evaluation.The particle size distribution of black pepper particles is complex and not completely isometric,and discrete element simulation can effectively predict the particle size distribution of granular materials.In this study,an RF heating model of disordered piled black pepper particles is constructed to investigate the joint discrete element and finite element simulation method based on individual particle modeling strategy.The accuracy of the model and experiments are verified by comparing the RMSE and R² of temperature distribution and heating rate.The discrete element simulation results show that the models that pass the tests of grid independence and stability of simulation results（RMSE≈0.00）are likely to have higher accuracy and closer RMSE between models.Compared with other simulation results,the particle stacking model shown in this paper is in high agreement with the experimental particle stacking morphology,and therefore the model developed can be used to predict the disordered stacking of black pepper particles by RF heating for further studies.From the temperature distribution diagram of the upper surface of the sample,it can be found that the hot spots of the black pepper sample inside the acrylic container after RF heating are located at the corners and edges of the sample,while the cold spots are at the center of the sample surface.At 550 s,the center temperature of the experimental sample reached69.93℃ and the hot spot temperature reached 81.50℃.At this time,the simulated center temperature of the selected particle stacking models both reached 68.92℃ and the hot spot temperature was close to 81.23℃.The selected particle stacking models were close to the experimental results,further confirming that the tested particle stacking models have high prediction accuracy based on the combined discrete element and finite element simulation method based on a single particle modeling strategy is feasible and has a high accuracy of simulation results.Continuous RF sterilization equipment can achieve efficient continuous industrial sterilization,with greater development prospects.At present,the simulation method for continuous RF processing class of spherical particles still needs to be further explored.In this study,the motion of black pepper particles in a horizontal screw conveyor was simulated by the discrete element simulation software EDEM（?）with the horizontal screw conveyor and the particle stacking shape was subsequently imported into the commercial finite element simulation software COMSOL Multiphysics（?）to simulate the RF heating process of the sample,and to analyze the developed method for RF heating simulation of continuous conveying The feasibility of the developed method for the continuous transport of granular materials was analyzed.The total number of contacts of black pepper particles was found to be able to detect a gradual increase in the number of contacts between 0 and 4 s of the simulated process as the material falls from the inlet into the conveying tube.Between 4 and 60 s,the number of contacts decreases as the pellets are driven up horizontally by the screw blades perpendicular to the transport direction.After the transport stabilization,the contact number fluctuates up and down based on 6025,which indicates that the horizontal screw conveyor in this experiment can transport the particles effectively.It can be found from the particle force that there are several peaks in the particle force during the particle conveying process,which is due to the greater force required to push the particles falling vertically to the interpitch.The overall curve fluctuation is more gentle,which indicates that the horizontal screw conveyor has stable conveying ability.From the visualization of black pepper particles conveying process,it can be found that the particle distribution at the upper left corner of all samples is more dispersed and high,and the particle accumulation at the right side is more significant,and the particle distribution shows high left and low right.The particle accumulation pattern is basically the same for all four time points,and the particle position at the upper left corner is slightly different and the number of particles is very small,and the particles have less influence on the overall warming due to overheating near the upper pole plate,so it may be reasonable to construct a geometric model based on the particle distribution within a single pitch.From the simulated body-averaged temperature warming curve of black pepper samples,it can be found that the total warming time is 11 min and the average sample warming rate is 6.42℃ min^-1.The maximum temperature of the sample was 69.59℃ after the fifth mixing and heating and 70.53℃ after the sixth mixing and heating.the temperature of the sample after multiple mixing（6 times）was in the range of 64.12 to 69.63℃.Therefore,the constructed simulation model of continuous sterilization of equal diameter black pepper particles is feasible and reasonable.