Research PaperModelling and simulation of fruit drop tests by discrete element method
Introduction
In general, modelling and simulation can be applied to improve and optimise post-harvest handling and transportation equipment design. Whilst many other software applications exist, and have been shown to be useful the Discrete Element Method (DEM) is part of a class of methods, including different the Contact Dynamics (CD) method, Molecular Dynamics (MD) method, and the Granular Element Method (GEM) that utilise physics and numerical techniques for simulation (Kafashan et al., 2019). The use of the DEM is being increasingly used in various engineering fields for simulating complex physical systems, but according to the number of papers published, mainly in particle-based systems. Many applications where realistic particle shape models have been implemented in the DEM simulations are still in development phases and many simulations neglect the complexity of the shapes of particles by using single-spheres in their DEM models (Van Zeebroeck et al., 2006b, Van Zeebroeck et al., 2006a; Hogue et al., 2008; Kobylka & Molenda, 2013; Ghodki & Goswami, 2017; An et al., 2018; Sun et al., 2018; Wiacek et al., 2020).
In horticultural products, the first 3D-DEM model was used for simulation of apple in handling and transport by Van Zeebroeck et al., 2006b, Van Zeebroeck et al., 2006a, although they only made use of simple sphere to model the apples and this had a few shortcomings. For example, it could not represent real particles and their response unless the real particle was uniformly sphere-like. Indeed, modelling to predict the physical behaviour of various foods during handling is possible but there are difficulties involved and there is no exception with DEM. The application of an accurate DEM model is a challenge and lies within the area of defining a realistic particle shape model. Different studies have shown that the contact behaviour of a multi-sphere particle dropped onto a flat surface is different from that of a spherical particle with the same material properties (Kruggel-Emden et al., 2008) and the effect of particle shape has been explored (He et al., 2018; Markauskas et al., 2015; Wiacek et al., 2012; Hohner et al., 2014) using different approaches. Due to necessity in DEM of detecting contacts, calculating contact forces and defining geometry of shapes is more difficult in DEM than to mesh-based methods (Kafashan et al., 2019) such as Finite Element Method (FEM), Finite Difference Method (FDM) and other computational methods (Kafashan et al., 2005; Leung & Berzins, 2003; Sadrnia et al., 2007; Trobec & Kosec, 2015). In addition, calculation of the contact force between irregularly shaped particles in the DEM simulations exists as a challenge with no general methodology. Despite the fact a perfect spherical particle can be easily modelled in DEM, in various states a more realistic model is crucial. Furthermore, with ever improving computer technology, interest of implementing simulations and using realistic particle shapes is increasing exponentially (Cleary & Sawley, 2002; Kafashan et al., 2005, 2007, 2019; Klomp et al., 2021; Mead & Cleary, 2015; Sadrnia et al., 2007; Suhr & Six, 2020).
Overall, particulate materials in nature and industry typically consist of a wide range of differently formed objects. Frequently, the particle shapes are irregular or asymmetric and a single sphere is a weak representation of the real particle shape. Therefore, a multi-sphere (MS) method has been proposed by Favier et al. (1999) for DEM simulations, that allows for representing non-spherical particles of axi-symmetrical shapes by clumping together multiple spheres. The method is similar to the clustering method (Jensen et al., 1999; Ning et al., 1997) used to reproduce agglomerate-type particles.
Despite the computational effort required increasing with the number of spheres used to describe irregularly-shaped particles, over last few decades the MS method has been widely applied (Chung & Ooi, 2006; Haeri, 2017; He et al., 2018; Li et al., 2015; Markauskas et al., 2010; Parafiniuk et al., 2014; Wiacek et al., 2012). Although different methods have been introduced (Dong et al., 2015; Elias, 2013; Fraige et al., 2008; Gan et al., 2016; Gan & Yu, 2020; He et al., 2012; Jin et al., 2011; Kafashan et al., 2005, 2007; Kodam et al., 2010; Muth et al., 2007; Wang & Ji, 2021; You et al., 2017) for modelling non-spherical particles, the MS method is still extensively utilised because it is user-friendly, easy to implement, cost-competitive and is less time-consuming in its initial preparation for running any simulation (Cabiscol et al., 2018; Chen et al., 2018; Haeri, 2017; Pasha et al., 2017; Scheffler et al., 2018; Wang et al., 2017). For instant, a polygon-based contact description method was proposed to improve DEM results (Smeets et al., 2015), however, this only assessed the computational performance of the proposed method by simulating the motion of artificially-made particles with no real comparison used to validate that method. Also, no experimental validation for that method has yet been reported for apple dynamics.
Kafashan et al. introduced the Multi-Ring Model (MRM) to create non-spherical particles for computational simulations (Kafashan et al., 2010, 2011). They only described the methodology, particle orientation, particle arrangement in a bulk assembly and different particle shapes without experimental and simulation (Kafashan et al., 2011). Contrary to the MS method, MRM methodology has the advantage of producing non-array shapes and asymmetric particles. With respect to computational efficiency for detecting contacts and calculating force, the MRM method is well suited. In addition, it represents a realistic particle shape and is very user-friendly. However, the method has not yet been validated. Additionally, finding optimal number of spheres to form a particle model in DEM simulation with least side-effects of is a need. Therefore, the current research is considered as a part of the development of a DEM model to simulate the behaviour of particles for an specific scenario of handling fruit and drop tests application. Although there are numerous studies on different particle shapes and realistic shapes, a detailed review of literature shows that the number of studies combining experimental studies and computational simulations using DEM for realistic particles of biomaterials is limited (Kafashan et al., 2019).
This study aims to model Jonagold apples using the DEM. The focus is on shape modelling. The apples composed of various number of spheres were dropped onto a rigid platform from different heights, and the distances between the ending position and impact point were measured. Since there is a need to model fresh products such as fruit and vegetables to develop optimised handling and transportation machinery, this study focuses on experiments and numerically simulating in 3D drop tests of apples. Different models to represent realistic apple shapes were used and experimental validation of the MRM associated with the particle shape model effects was carried out.
Section snippets
Experiment setup
A container made of clear acrylic plastic with dimensions 450 mm × 450 mm × 500 mm (Fig. 1) was used to study the dynamics of the free-falling apples. The container was placed on a flat table and for visual reference grid/engineering paper was placed on one side wall and on the outside of the base of the container. A pneumatic suction cup powered by a vacuum cleaner was used to grip each apple before it free-fell over the base of container. Since the container was closed, the effect of any air
Different models in the simulation
Simulations of free-falling of apple-shaped particle from different drop heights were performed for four different models of apple. Model 1 consisted of two sets of 10 spheres, Model 2 consisted of three sets of 10 spheres, Model 3 consisted of five sets of 10 spheres and Model 4 consisted of five sets of 20 spheres includes 100 spheres in full.
Figure 6 shows three snapshots of a free-falling single apple from a height of 300 mm at release, after impact and at its final location for four models
Conclusions
Experimental results and DEM simulations of free falling of apples simulated by generated spheres using the MRM approach were conducted. A methodology was developed and applied for different single particle models. Experiments and simulations were performed using scanning, visualisation, measurement techniques and a DEM code. The free fall of objects dropped from three different drop heights was simulated. The apple-shaped particles, generated by using the MRM method, included two, three and
Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgements
The first author would like to express his thanks to Prof. Poschel, Institute for Multiscale Simulation; Dr. Tijskens, Department of Computer Science of UAntwerpen; Prof. Kruggel-Emden and Dr. Darius Markauskas, TU Berlin; Prof. C.J. Coetzee, Stellenbosch University; Dr. Kejun Dong, Western Sydney University and Prof. Eutiquio Gallego, Polytechnic University of Madrid for their modesty in responding, valuable emails and scientific discussions regarding DEM.
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