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WITHDRAWN: Effect of moisture content on some simulation parameters of wheat and soybean required in DEM
Effect of moisture content on some simulation parameters of wheat and soybean required in DEM Fanyi Liu, Bo Li, Lanhua Yi, Jian Zhang, Jun Chen PII: DOI: Reference:
S0032-5910(16)30050-X doi: 10.1016/j.powtec.2016.02.009 PTEC 11488
To appear in:
Powder Technology
Received date: Revised date: Accepted date:
1 September 2015 28 January 2016 5 February 2016
Please cite this article as: Fanyi Liu, Bo Li, Lanhua Yi, Jian Zhang, Jun Chen, Effect of moisture content on some simulation parameters of wheat and soybean required in DEM, Powder Technology (2016), doi: 10.1016/j.powtec.2016.02.009
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ACCEPTED MANUSCRIPT Effect of moisture content on some simulation parameters of wheat and soybean required in DEM
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College of Mechanical and Electronic Engineering, Northwest A&F University,
Yangling, Shaanxi Province 712100, China. b
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Fanyi Liua, Bo Lia, Lanhua Yib, Jian Zhanga, Jun Chena,*
College of Food Science and Engineering, Northwest A&F University, Yangling,
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Shaanxi Province 712100, China.
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* Corresponding author. Tel./Fax: +86-029-8709 1867.
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E-mail address: [email protected]
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ACCEPTED MANUSCRIPT ABSTRACT The discrete element method (DEM) is widely used nowadays but the determination
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of the simulation parameters required in DEM simulations is still the main challenge
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for effective utilization of this tool. This study focused on some simulation parameters required in DEM for two typical crops: wheat and soybean. The effect of moisture content (wet basis) on these parameters was investigated. Experimental results
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demonstrated that with increasing moisture content from 10.05% to 21.63% for wheat
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and 11.23% to 19.48% for soybean, the size (length, width and thickness) and static friction coefficients of two contact types (particle-wall and particle-particle) increased
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linearly, but the true density and shear modulus decreased. However, both the
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particle-wall and particle-particle coefficient of restitution showed different trends for
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the two crops. For wheat, the two coefficients of restitution went down continuously; while for soybean, the two coefficients of restitution decreased before they began to
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increase. The results of analysis of variables (ANOVA) showed that the effect of moisture content on these parameters was significant (*P < 0.05). Regression equations of all parameters with the moisture content except the coefficient of restitution of soybean were established and verified with relative errors below 10%. At last, the measured parameters of the two crops with the initial moisture content were validated using a silo discharge test. Results showed that the total discharge time and flow patterns of wheat were almost the same in experiments and simulations. However, more than 15% difference for the total discharge time was observed for soybean. With the particle-wall and particle-particle coefficient of rolling friction 2
ACCEPTED MANUSCRIPT increasing to 0.05, the difference can be eliminated. Keywords: Simulation parameters; Moisture content; Discrete element method;
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Wheat; Soybean
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ACCEPTED MANUSCRIPT 1. Introduction Developed by Cundall and Strack in 1979, the discrete element method (DEM) is
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now a promising numerical technique to study the dynamics of crop particles and
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their interaction with equipments. Based on DEM, much research has been performed in handling [1-3], sorting [4,5], cleaning [6], and drying [7,8] processes. These studies not only verified the feasibility of the DEM in simulating the motion of crop particles,
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but also helped to design advanced equipments.
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In DEM simulations, the microscopic parameters are of great importance but difficult to be determined. There are two common ways to obtain them: ―virtual
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calibration‖ and ―direct measurement‖. Most researchers use the ―virtual calibration‖
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method [9,10]. However, the main drawback of calibration method is that an adjusted
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microscopic value is dependent on the numerical code used in the calibration process, thus invalidating some of the values to be used in other codes and applications [11].
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Few researchers use the ―direct measurement‖ method due to the difference between particles and the anisotropy of an individual particle. Although it is difficult to measure these DEM parameters directly by a single particle, the ―direct determination‖ is more precise and has a wider applicability for different codes and applications compared to the calibration method [12]. In our experiments, the ―direct measurement‖ was used at particle level except in the determination of the true density for both crops and particle-particle coefficient of static friction for soybean. Large sample and reduplication were used to reduce the measuring error. On the other hand, the physical and mechanical properties of crop seeds are 4
ACCEPTED MANUSCRIPT influenced by various factors such as cultivars, maturity and moisture content etc. In recent years, the effect of moisture content on physical and mechanical properties of
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sorghum [13], faba bean [14], wheat [15] and barley [16] etc. have been investigated.
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These properties provide essential parameters to design machinery and process equipments [17]. Similarly, the simulation parameters required in DEM are vital in building simulation models. Measurement of these parameters does not only provide
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reference values of wheat and soybean under different moisture content for DEM
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simulation, but also offer measuring methods for other crop seeds. To our knowledge, no systematic report about the effect of moisture content on the simulation parameters
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of wheat and soybean required in DEM has been reported.
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In this paper, some simulation parameters of wheat and soybean used in DEM
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were investigated under four levels of moisture content. The ANOVA was used to judge the significance of the effect of moisture content on these parameters and
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regression equations of all parameters with the moisture content were established and verified except the coefficient of restitution of soybean. Moreover, the measured parameters of the two crops with the initial moisture content were validated by comparing the total discharge time and flow patterns observed in experiments and DEM simulations. 2. Materials and methods 2.1 Sample preparation In this study, the wheat (Xi Nong 223) harvested in 2014 was provided by the Wheat Breeding Center of the Northwest Agriculture and Forestry University; the 5
ACCEPTED MANUSCRIPT soybean (Dong Nong 44) was bought from the market in 2014. The samples with different moisture content were obtained as follows:
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Ⅰ. In order to gain the initial moisture content, the two crops were dried in an
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oven at 105 °C until they reached constant weights (Standard S352.2, DEC97, ASAE, 1999).
Ⅱ. The distilled water was added to obtain the samples with different pre-set
Wi M f M i
100 M
(1)
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Q
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moisture content and the amount of water can be calculated from Eq. (1).
f
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where Q is the amount of distilled water to add (g); Wi , M i are the initial weight
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and moisture content of the sample (g, % w.b.) and M f is the final (pre-set) moisture content (% w.b.).
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Ⅲ. The samples were put into seal bags and stored in a refrigerator at 4 °C for 10 days. During that time the samples were mixed every 8 hours to make the water
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redistribute uniformly.
Ⅳ. Before the tests, the sealed samples were put under ambient environment for 24 hours to warm up to the room temperature. After treatment, the final moisture content of the samples was measured according to ASAE Standard S352.2 as mentioned above. In this study, the final four levels of moisture content (wet basis) were 10.05%, 13.51%, 17.31% and 21.63% for wheat and 11.23%, 14.12%, 16.66% and 19.48% for soybean. 2.2 Measurement of the simulation parameters
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ACCEPTED MANUSCRIPT Five types of simulation parameters were measured in our experiments, including the size, true density, shear modules, coefficient of restitution and static
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friction of two types of contact (particle-particle and particle-wall).
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2.2.1 Size ( L , W , T )
For wheat and soybean, a digital venire caliper (accuracy ~ 0.01 mm) was used to measure the three-dimensional size: length ( L ), width ( W ) and thickness ( T ). At
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each level of moisture content for the two crops, 50 particles were selected randomly
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for measurement. 2.2.2 True density ( )
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The true densities of the both crops under different moisture content were
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measured using the pycnometer method (ASTM D854-10). Methylbenzene was used
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as measure liquid to reduce the error caused by absorption. A certain quality of sample ( m ) was added into a given volume of methylbenzene rapidly. The volume variation
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of methylbenzene ( v ) was read as soon as possible. Therefore, the true density of the sample can be described by m . 5 samples were conducted for each level of v moisture content to obtain the average value. 2.3.3 Young’s modulus ( E ), shear modulus ( G ) and Poisson’s ratio ( ) Young’s modulus reflects the abilities of objects to resist elastic deformation. It is defined as the ratio of stress and strain in a direction. According to the ASAE Standard (S368.4, DEC2000, ASAE, R2012), two parallel plates were used as loading tools in this experiment. Based on Hertz equation, the Young’s modulus can be described as: 7
ACCEPTED MANUSCRIPT 1 1 0.338F 1 2 1 3 1 3 1 1 KU E KL 3 2 R R R U L RL D U
3
2
(2)
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where E is the Young’s modulus (Pa); F is the compression force (N); is Poisson’s ratio (dimensionless); D is the deformation of the test particles (m);
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RU , RU and RL , RL are the maximum and minimum radii of curvature of the convex surface of the sample at the point of contact with the upper and lower plate (m),
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respectively; KU , K L are constants and can be found in the ASAE S368.4 through
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cos . For parallel plate contacts, the cos can be calculated by: RU RU RL RL or cos cos RU RU RL RL
(3)
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According to the assumption of ASAE S368.4, the Poisson’s ratios of the two
G
E 2 1
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crops are 0.42 and 0.40, respectively. Thus, the shear modulus can be calculated by: (4)
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Here, the compression tool (Fig. 1) used was HY-0230 universal tester (HengYi Precise Instrument co., Ltd., Shanghai, China), and the test speed was 0.2 mm/min. At each level of moisture content of the two crops, 25 particles were selected randomly for measurement. Fig. 1.
2.3.4 Coefficient of restitution (1) Particle-wall coefficient of restitution ( ePW ) The method used to measure the particle-wall coefficient of restitution was similar to the free-fall method by Fu et al. [18], as shown in Fig. 2. A particle was 8
ACCEPTED MANUSCRIPT attracted by a vacuum pump at H 0 (Fig. 2a), and then fell freely under gravity with the pump off. Then the particle rebounded to a height of H1 (Fig. 2b) after impacting
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with an acrylic board. The acrylic board was used because of its wide usage in DEM
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validation experiments. The whole process was recorded by an Olympus I-speed3 high speed camera (Olympus (China) co., Ltd., Guangzhou, China) which running at 500 fps (Fig. 3). Assuming that the particle rebound vertically and has no rotational
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speed after collision, the particle-wall coefficient of restitution ePW can be expressed
1
2
(5)
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ePW
H 1 H0
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by:
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In this experiment, 20 particles were selected randomly and measured with 20 replications for each particle under each level of moisture content for the two crops.
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Only the cases when the particles rebounded nearly vertically or rotated minimally
Fig. 2. Fig. 3.
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were selected [19].
(2) The particle-particle coefficient of restitution ( ePP ) The method used to measure the particle-particle coefficient of restitution originated from the double pendulum method by González-Montellano et al. [11], as shown in Fig. 4. During the test, particle 1 was lifted at a height of H 0 by the suction pipe of the vacuum pump on the right (Fig. 4a). After the pump was turned off, particle 1 began to swing and collided with particle 2. Subsequently, the two particles swung respectively. The maximum height of particle 1 and particle 2 were H1 and 9
ACCEPTED MANUSCRIPT H 2 , respectively (Fig. 4b). Therefore, the particle-particle coefficient of restitution can be calculated by: 1
T
1
H0 2
(6)
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ePP
1
H 2 2 H1 2
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The whole process was recorded by the high speed camera at 500 fps (Fig. 5). In present study, 20 groups (40 particles) were selected randomly and measured with 20
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repetitions for each group under four levels of moisture content for the two crops. Only the cases when the particles rotated minimally were selected.
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Fig. 4.
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Fig. 5.
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2.3.5 The coefficient of static friction
(1) The particle-wall coefficient of static friction ( f PW )
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The three-particle sliding friction method proposed by Chung and Ooi [20] was used to measure the particle-wall coefficient of static friction (Fig. 6). During the
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measurement, the lifting board was elevated at a slow speed until the acrylic board began to slide. The whole process was recorded by the high speed camera at 500 fps. The coefficient of static friction between particles and the acrylic board can be described by the tangent of the included angle between the lifting board and the horizontal line. In this study, 20 groups (60 particles) were selected randomly and measured with 5 repetitions for each group under four levels of moisture content for the two crops. Fig. 6.
(2) The particle-particle coefficient of static friction ( f PP ) 10
ACCEPTED MANUSCRIPT The particle-particle coefficient of static friction is hard to measure since the size of the crop seed is usually small and the shape is irregular. Two different methods
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were used to measure this parameter for wheat and soybean, respectively.
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For wheat, a method based on particle scale which similar to the method by Han et al. [21] was employed (Fig. 7) due to the prolate shape of wheat particles. In this test, the particles were glued on a board which was fixed on the lifting board. While
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measuring, a test particle was placed on the ―seedbed‖, subsequently; the lifting board
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was lifted at a constant slow speed. The high speed camera was used to detect the slide of the test particle (500 fps). 20 particles were selected and measured with 5
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repetitions for each particle under each level of moisture content.
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For soybean, the repose angle test by Chung et al. [22] with little modification
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was employed (Fig. 8). To reduce the error caused by the baseboard, boards glued with seeds were used. The diameter and height of the bottomless and topless acrylic
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cylinder was 100×200 mm. After the granular heap formed, a computer image analysis method similar to that by Frączek et al. [23] was used to calculate the repose angle. The particle-particle coefficient of static friction can be approximately described by the tangent of the repose angle. One sample with 5 repetitions were conducted for each level of moisture content to obtain the mean value. Fig. 7. Fig. 8.
2.3 Data analysis For all the test results, the box plot and Grubbs test were used to detect the 11
ACCEPTED MANUSCRIPT outliers which largely departed from sample average and all the outliers were removed. The mean values and standard deviations were determined for all
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parameters. Then all the results were subjected to ANOVA using SPSS 22.0 software
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to study the effect of the moisture content on all the parameters considered in this work. The regression analysis was conducted using Origin 8.1 software. 2.4 Verification of the regression equations
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To verify the regression equations established in this work, samples with
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moisture content of 18.67% for wheat and 12.46% for soybean were prepared using the method described in section 2.1. Accordingly, the physical parameters were
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measured using the methods described in section 2.2. The measured values were
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compared to the fitted ones to obtain the relative errors.
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2.5 Validation of the measured parameters In present study, only the wheat and soybean with the initial moisture content
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(10.05% and 11.23%) were used for validation. This can be explained by the following reasons: (ⅰ) the coefficient of rolling friction was not measured in this work considering the difficulty in measurement, the particle-wall and particle-particle coefficient of rolling friction of wheat and soybean were set as 0.01 which were the default values in EDEM software and commonly used by other researchers for dry crop particles [24-26]; (ⅱ) for crop particles with higher moisture content, the viscidity might be taken into consideration[27]. To validate the physical parameters measured in this study, a lab-scale silo discharge test was conducted. The size of the wedge-shaped acrylic silo is illustrated 12
ACCEPTED MANUSCRIPT in Fig. 9. The discharge processes were recorded using the high speed camera, from which the total discharge time and the flow pattern can be acquired. In order to
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identify the characteristics of the particle flow more accurately, several black-dyed
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wheat and soybean particles were used as ―markers‖ and placed inside the silo at a certain height. During discharging, these markers were moved by the surrounding grains and the flow pattern can be illustrated by the deformation of the line of the
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markers[28].
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Fig. 9. Fig. 10.
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For DEM simulation, a silo with the same dimensions as used in the lab test was
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modeled using the EDEM 2.7 software. The Hertz-Mindlin (no slip) contact model
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was adopted to describe both the particle–wall and particle–particle contacts. According to the shapes of the two crops, a five-particle model and a four-particle
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model were constructed for wheat (Fig. 10(a)) and soybean (Fig. 10(b)), respectively. The size distribution was set as normal for wheat (Mean:1; STD:0.07 ) and soybean (Mean:1; STD:0.06). To avoid generating too small particles, the particles were restrict to the minimum and maximum particle sizes. Specifically, the radius of the spherical elements which made up the five-particle and four-particle models were set as 0.65-1.21 and 0.92-1.07 times as their initial sizes. The time steps used in all simulations were 20% of the Rayleigh time. The cell size employed was 3Rmin, where Rmin is the minimum radius of the spherical elements. In the virtual silo, the ―markers‖ were also reproduced by colouring those particles that occupied the same positions 13
ACCEPTED MANUSCRIPT with the black-dyed particles in lab test. 3. Results and discussion
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3.1 Simulation parameters
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3.1.1 Size
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As described in Table 1, for wheat and soybean, the three-dimensional size (length, width, thickness) changed significantly with the increase of moisture content
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(*P < 0.05).
Fig. 11(a) and Fig. 11(b) show the mean values and standard deviations of the
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size of the two crops under different moisture content. For wheat particles, with
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increasing moisture content from 10.05% to 21.63%, the length increased from 6.60
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mm to 6.79 mm, the width from 3.62 mm to 3.95 mm and the thickness from 3.18 mm to 3.47 mm (Fig. 11a). Similarly, Fig. 11(b) shows that for soybean, with the
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increase of moisture content from 11.23% to 19.48%, the length, width and thickness increased from 7.28 mm to 7.34 mm, from 7.17 mm to 7.34 mm and from 6.69 mm to
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6.89 mm, respectively. The increase of the dimensions was attributed to expansion or swelling as a result of moisture uptake in the intracellular spaces of the seeds [29]. According to the regression analysis of the size of wheat and soybean changed with the moisture content, the variation trends can be represented by the following equations:
LW 0.01833M C 6.41607
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2
0.94
(7)
WW 0.02819M C 3.34709
R
2
0.99
(8)
TW 0.02251M C 2.97076
R
2
0.93
(9)
LS 0.04512M C 6.76882
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2
0.99
(10) 14
ACCEPTED MANUSCRIPT WS 0.02088M C 6.94151
R
2
0.98
(11)
TS 0.02264M C 6.42202
R
2
0.95
(12)
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and
S
represent the length, width, thickness of wheat and soybean,
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with subscripts
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where M C is the moisture content of the particles (% w.b.), the variables L, W, T
respectively.
This linear increase in the three-dimensional size with the moisture content was
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also found in the research of wheat [15], soybean [30] and caper seeds [31] etc.
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Fig. 9.
3.1.2 True density
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From Table 1, we also noted that the influence of moisture content on the true
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density was significant for both crops (*P < 0.05).
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The mean values and standard deviations of the true density for wheat and soybean are given in Fig. 11(a) and Fig. 11(b), respectively. The true density exhibited
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a linear decrease trend with the increase of moisture content for both crops. With increasing moisture content from 10.05% to 21.63%, the true density of wheat ( W ) decreased from 1405.15 kg/m3 to 1306.81 kg/m3; for soybean, this parameter ( S ) went down from 1251.74 kg/m3 to 1201.49 kg/m3 as the moisture content increasing from 11.23% to 19.48%. The decrease of true density was mainly due to the larger increase in kernel volume compared to the increase in kernels mass [32]. The regression equations can be expressed as follows:
W 8.75016M C 1495.36118
R
2
0.99
(13)
S 6.2822M C 1322.48804
R
2
0.98
(14)
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ACCEPTED MANUSCRIPT The linear decrease of the true density was also reported in the work of wheat [15]. For soybean, Kashaninejad et al. [30] reported an increase of the kernel density
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with the moisture content, which was contrary to the findings of Deshpande et al. [33]
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and this study. These differences may result from the different measuring method Kashaninejad et al. adopted. The linear decrease of the true density with moisture content also matched well with the researches of paddy rice [34], green gram [35] and
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lentil [36] etc.
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Table 1
3.1.3 Shear modulus
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The smallest P values in ANOVA of all the properties (Table 1) for wheat
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(7.323E-70) and soybean (5.6038E-28) mean the assumption that the moisture content
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has a significant effect on the shear modulus is the most acceptable. Fig. 12 shows that the shear modulus had an opposite dependence on moisture
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content for both crops. It decreased by 70% as the moisture content rising from 10.05% to 21.63% for wheat. For soybean, this value decreased by 67% with the moisture content increasing from 11.23% to 19.48%. The shear modulus of wheat did not decrease linearly. Actually, it went down gently at first and then decreased faster as the moisture content rising. The decrease of shear modulus was attributed to that the particle structure became softer after absorbing water and its ability to resist deformation became weaker [37]. A second-order polynomial and linear fitting were used to describe the trends of shear modulus for wheat ( GW ) and soybean ( GS ), respectively. The fitting equations 16
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R
2
0.97
(15)
GS 35.01052M C 823.42165
R
2
0.99
(16)
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GW 3.14543M C2 67.77189M C 169.62155
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The decrease of shear modulus with the moisture content observed in this research was similar to that found in rice grains [37], faba beans [38] and apricot pit [39] etc.
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Fig. 10.
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3.1.4 The coefficient of restitution
(1) The particle-wall coefficient of restitution
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The ANOVA of the effect of moisture content on the particle-wall coefficient of
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restitution (Table 1) showed that the moisture content had a greater influence on this
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parameter than the difference between particles for the two crops (*P < 0.05). From Fig. 13(a), we can see the particle-wall coefficient of restitution decreased
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(from 0.57 to 0.43) with the increase of moisture content (from 10.05% to 21.63%) for wheat. This was because the wheat particle became softer after absorbing water. When the particle collided with the acrylic board, it had a greater deformation and more energy was dissipated. Accordingly, the rebound height decreased. Interestingly, for soybean, the effect of moisture content on this parameter had a much different trend. With increasing moisture content (from 11.23% to 14.12%), this parameter decreased (from 0.50 to 0.47). However, when the moisture content increased further, it began to increase (from 0.47 to 0.50). The reason is uncertain, but this may because the character of soybean particles with higher moisture content had changed greatly 17
ACCEPTED MANUSCRIPT and their elastic ability increased and this need to be further investigated. Only the regression equation of wheat ( EWPW ) under different moisture content
as below: 2
0.95
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R
EWPW 0.01146M C 0.68399
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was given because of the low R 2 for soybean. The linear equation can be described
(17)
LoCurto et al. [40] found that the coefficient of restitution of soybean impacting with
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the acrylic board decreased significantly with the moisture content (10.7% to 15.5%,
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d.b.).
Fig. 11.
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(2) The particle-particle coefficient of restitution Table 1 shows that the moisture content had a significant influence on the
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particle-particle coefficient of restitution for the both crops (*P < 0.05). According to Fig. 13(b), the particle-particle coefficient of restitution had a
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similar trend with the particle-wall coefficient of restitution for the both crops. As the moisture content increased, the particle-particle coefficient of restitution of wheat ( EWPP ) went down (from 0.48 to 0.33); but for soybean, it decreased firstly (from 0.45 to 0.41) and then began to increase (from 0.41 to 0.47). The change trends of particle-particle coefficient of restitution were corresponding with those of the particle-wall coefficient of restitution for the two crops, which further increased the credibility of the two measuring methods. Accordingly, the changes could also be explained by the reason of particle-wall coefficient of restitution. Similarly, the regression equation of soybean was not given because of the low 18
ACCEPTED MANUSCRIPT R 2 . For wheat, the relationship between the particle-particle coefficient of restitution
and the moisture content can be described by the following linear equation:
0.99
T
2
(18)
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EWPP 0.01323M C 0.61414
(1) The particle-wall coefficient of static friction
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3.1.5 The coefficient of static friction
The results of ANOVA (Table 1) showed that the moisture content had a
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significant influence on the particle-wall coefficient of static friction (*P < 0.05).
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Fig. 14(a) shows the changes of the particle-wall coefficient of static friction for wheat ( FWPW ) and soybean ( FSPW ). With the increase of moisture content, this
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parameter showed an upward trend for both crops (from 0.34 to 0.48 and from 0.29 to
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0.38 for wheat and soybean, respectively). This may be attributed to the fact that an
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increase in moisture content increased the cohesion between the seeds and the test board, thereby increasing the friction they experienced [41].
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The relationship between the particle-wall coefficient of static friction and the moisture content can be expressed by the following linear equations for the two crops:
FWPW 0.01259M C 0.22083
R
2
0.92
(19)
FSPW 0.01132M C 0.15844
R
2
0.97
(20)
These results were similar to the researches of millet [42], rapeseed [43] and karanja seeds [44] etc which based on sliding tests at particle group level. Fig. 12.
(2) The particle-particle coefficient of static friction From Table 1, we can see that statistically significant changes in the 19
ACCEPTED MANUSCRIPT particle-particle coefficient of static friction were produced as moisture content rising (*P < 0.05).
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Fig. 14(b) shows that the moisture content had a similar effect on the
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particle-wall and particle-particle coefficient of static friction. For wheat and soybean, the values increased from 0.48 to 0.58 and from 0.36 to 0.50, respectively. This can also be explained by the increase of adhesion of the particle surface after absorbing
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water.
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The particle-particle coefficient of static friction under different water content for the two crops can be respectively described by the following linear equations:
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FSPP 0.01719M C 0.15842
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FWPP 0.00851M C 0.39948
R
2
0.98
(21)
R
2
0.96
(22)
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Our findings for the particle-particle coefficient of static friction were smaller than those for wheat [15] and soybean [30], but corresponding with the values
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summarized by Boac et al. [19]. Similar linear increase of this parameter was reported in the researches for lentil seeds [36], sorghum seeds [13] and paddy rice [34] etc. Table 1
3.2 Verification of the regression equations Table 2 gives the relative errors of the measured values and the fitted values calculated from the regression equations. From the table, we can see all the relative errors were below 10%. This means the regression models have a good accuracy. The relative errors of the three-dimensional and true density were quite small (<1%); the model for the shear modulus of wheat had a maximum error of 8.76% and the error 20
ACCEPTED MANUSCRIPT for soybean was 5.38%. For other parameters, the errors ranged from 1.75% to 5.71% for the two crops.
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3.3 Results of silo discharge test
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3.3.1 The total discharge time
Table 3 summarizes the total discharge time measured in experiments and DEM simulations for the two crops. For wheat, the difference of the mean value of the total
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discharge time between the experiments and simulations was relatively small (less
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than 2%). However, this difference for soybean was much larger (more than 15%). This might because the sphericity of the four-particle model was higher than that of
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the real soybean particle and the coefficient of rolling friction used in the simulations
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was small. So the particle-wall and particle-particle coefficient of rolling friction were
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increased to 0.05. As a result, the mean value of the total discharge time for the modified simulations increased to 4.57 s and the relative error between the lab tests
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and simulations decreased to 1.72%. 3.3.2 Flow pattern Fig. 15 compares the flow patterns of the two crops obtained in lab tests and DEM simulations at different time (0 s, 0.5 s, 1 s, 1.5 s) since discharging. The flow patterns of wheat observed experimentally were almost the same with those in simulations. For soybean, the deformation of the line of the markers was similar in the experiments and simulations, but the simulated free-flow surfaces were lower than those of the experiments. It also showed the flow rate in simulation was larger and could be attributed to the same with the less total discharge time for soybean in simulation. For 21
ACCEPTED MANUSCRIPT simulations with the modified coefficient of rolling friction, both the deformation of the line of markers and the free-flow surfaces the lab tests matched well with those in
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DEM simulations.
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4. Conclusions
In present study, the size, true density, shear modulus, particle-wall and particle-particle coefficient of restitution and static friction of wheat and soybean
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required in DEM were measured based on particle-group or single-particle
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experiments under four levels of moisture content.
The ANOVA results showed that the effect of moisture content on all the test
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parameters was significant. The regression equations for all parameters with the
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moisture content were established and verified except the coefficient of restitution of
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soybean.
For wheat and soybean, with the increase of moisture content, the size and
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coefficient of static friction of two contact types increased linearly, while the true density and shear modulus decreased. For wheat, the particle-wall and particle-particle coefficient of restitution had downward trends, from 0.57 to 0.43 and 0.48 to 0.33. However, for soybean, when the moisture content increased from 11.23% to 14.12%, these parameters decreased firstly (from 0.50 to 0.47 and from 0.45 to 0.41) and with the moisture content increased further, they began to increase (from 0.47 to 0.50 and from 0.41 to 0.47). The measured parameters of the two crops with the initial moisture content were validated by comparing the total discharge time and flow pattern in a wedge-shaped 22
ACCEPTED MANUSCRIPT silo discharge test. For wheat, the simulated results were almost the same with the experimentally observed ones. However, more than 15% difference for the total
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discharge time was observed between lab test and DEM simulation. By increasing the
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particle-wall and particle-particle coefficient of rolling friction to 0.05, a well match can be observed in experiment and simulation for both the total discharge time and flow pattern. Though the silo discharge test could be basically modeled using the
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measured parameters in later research.
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measured parameters, more validation tests should be conducted to validate these
Though the physical properties of crops seeds are complicated and influenced by
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many factors, the results of these tests can be used as reference values when modeling
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DEM simulation or initial values in calibration procedure for the two crops.
other crops.
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Meanwhile, the measuring methods can be adopted to determine these properties for
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Acknowledgements
This research was supported by grants from Research Fund for the Doctoral Program of Higher Education of China (20130204110020) and Fundamental Research Funds for the Central Universities (ZD 2013015). Reference [1] R. Balevičius, I. Sielamowicz, Z. Mróz, R. Kačianauskas, Investigation of wall stress and outflow rate in a flat-bottomed bin: A comparison of the DEM model results with the experimental measurements, Powder Technology, 214 (2011) 322-336. [2] B. Ren, W. Zhong, Y. Chen, X. Chen, B. Jin, Z. Yuan, Y. Lu, CFD-DEM simulation of spouting of 23
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[41] S. Balasubramanian, R. Viswanathan, Influence of moisture content on physical properties of minor millets, Journal of food science and technology, 47 (2010) 279-284. [42] E.A. Baryeh, Physical properties of millet, Journal of Food Engineering, 51 (2002) 39-46.
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oleifera L.), Journal of Food Engineering, 69 (2005) 61-66. [44] R.C. Pradhan, S.N. Naik, N. Bhatnagar, S.K. Swain, Moisture-dependent physical properties of
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Karanja (Pongamia pinnata) kernel, Industrial Crops and Products, 28 (2008) 155-161.
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ACCEPTED MANUSCRIPT Table 1 ANOVA of the physical properties of wheat and soybean under different moisture content. Wheat
Soybean Significance
F values
P values
Significance
L
7.185
0.000134
S*
9.429
0.000008
S
W
25.741
4.3957E-14
S
9.429
0.006
S
T
18.629
1.1302E-10
S
2.717
0.046
S
ρ
41.576
1.6604E-7
S
3.381
0.039
S
G
1048.805
7.323E-70
S
0.16
5.6038E-28
S
ePW
74.505
2.6557E-12
S
9.471
0.000037
S
ePP
11.091
0.001
S
8.534
0.00127
S
fPW
33.165
1.3872E-10
S
8.634
0.000179
S
fPP
8.968
0.0133
20.58
3.458E-8
S
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P values
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F values
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Items
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S means that the effect of moisture content on this parameter is significant (P < 0.05).
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ACCEPTED MANUSCRIPT Table 2 Verification of the regression equations with wheat (18.67%, w.b.) and soybean (12.46%, w.b.). Wheat
soybean
Items Fitted values
Error(%)
Measured values
Fitted values
Error(%)
L
6.78
6.76
0.3
7.37
7.33
0.54
W
3.90
3.87
0.77
7.21
7.20
0.14
T
3.38
3.39
0.3
6.71
6.70
0.15
ρ
1326.83
1332
0.4
1246.34
1244.21
0.17
G
311.26
338.52
8.76
367.42
387.19
5.38
ePW
0.45
0.47
4.44
/
/
/
ePP
0.35
0.37
5.71
/
/
/
fPW
0.47
0.46
2.13
0.29
0.30
3.45
fPP
0.57
0.56
1.75
0.38
0.37
2.63
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D TE CE P AC
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T
Measured values
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Comparison of the discharge observed in experiments and simulations for wheat and soybean. Soybean Experiment
Simulation 1a
Simulation 2b
1
3.50
3.51
4.65
3.96
4.56
2
3.54
3.45
4.68
3.94
4.58
3
3.49
3.46
4.61
3.94
4.56
Mean value T
3.51
3.47
4.65
3.95
4.57
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Simulation 1a
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Experiment
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Wheat Repetitions
a: Simulations with given particle-wall and particle-particle coefficient of rolling friction of 0.01;
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b: Simulations with modified particle-wall and particle-particle coefficient of rolling friction of
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0.05.
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ACCEPTED MANUSCRIPT Fig. 1. Compression tool used to measure the Young’s modulus. Fig. 2. Schematic of the apparatus used to measure the particle-wall coefficient of restitution: (a) before
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impact, (b) after impact.
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Fig. 3. Snapshots of the particle-wall coefficient of restitution test: (a) before impact, (b) impact, (c) after impact.
Fig. 4. Double pendulum apparatus used to determine the particle-particle coefficient of restitution: (a)
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before impact, (b) after impact.
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Fig. 5. Snapshots of the particle-particle coefficient of restitution test: (a) before impact, (b) impact, (c) after impact.
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Fig. 6. Schematic of the apparatus used to measure the particle-wall coefficient of static friction.
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Fig. 7. Schematic of the apparatus used to measure the particle-particle coefficient of static friction of
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wheat.
Fig. 8. Schematic of the apparatus used to measure the particle-particle coefficient of static friction of
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soybean.
Fig. 9. Sizes of the wedge-shaped silo. Fig. 10. Shapes and sizes of the DEM particle models for: (a) wheat, (b) soybean. Fig. 11.Mean values and standard deviations of the size and true density with moisture content: (a) wheat, (b) soybean. (■) length, L; (●) width, W; (▲) thickness, T; (◆) density, . Fig. 12. Mean values and standard deviations of the shear modulus with moisture content: (■) wheat; (●) soybean. Fig. 13. Mean values and standard deviations of the coefficient of restitution of the two contact types with moisture content: (■) wheat; (●) soybean. 32
ACCEPTED MANUSCRIPT Fig. 14. Mean values and standard deviations of the coefficient of static friction of the two contact types with moisture content for: (■) wheat; (●) soybean.
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Fig. 15. Comparison of the flow patterns observed in experiments and simulations at different time
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since discharging for wheat and soybean. (a: Simulations with given particle-wall and particle-particle coefficient of rolling friction of 0.01; b: Simulations with modified particle-wall and particle-particle
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coefficient of rolling friction of 0.05.)
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Figure 1
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Figure 2
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Figure 3
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Figure 4
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Figure 5
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Figure 6
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Figure 7
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Figure 8
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Figure 9
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Figure 10
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1270
1410
7.8
1260
6.0
1380
7.6
1250
5.5
1350
5.0
1320
4.5
1290
6.8
1230
6.6
1200 24
10
12
14
16
18
20
22
6.4
T 10
Moisture content, %, w.b.
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44
1220
12
14
1210 1200 1190 1180
16
18
Moisture content, %, w.b.
Figure 11
1230
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7.0
3.0 8
7.2
1260
3.5
1240
7.4
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4.0
Size, mm
6.5
b
-3
1440
20
Density, Kg m
8.0
7.0
Density, Kg m
Size, mm
a
-3
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Shear modulus， Mpa
50
20
10
12
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10 14
16
18
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Moisture content, %, w.b.
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CE P
TE
D
Figure 12
45
20
22
0.56 0.54 0.52 0.50 0.48 0.46 0.44 0.42 0.40 0.38
0.54 0.51 0.48
T
0.58
0.45
IP
b
0.42 0.39
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0.60
0.36 0.33 0.30 0.27
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Particle-wall coefficient of restitution
a
Particle-particle coefficient of restitution
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8 10 12 14 16 18 20 22 24
Moisture content, %, w.b.
Moisture content, %, w.b.
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8 10 12 14 16 18 20 22 24
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Figure 13
46
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0.36 0.32 0.28 0.24
8 10 12 14 16 18 20 22 24
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Moisture content, %, w.b.
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CE P
TE
D
Figure 14
T
0.40
0.56 0.52
IP
0.44
0.60
0.48 0.44
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0.48
Particle-particle coefficient of static friction
b
0.52
0.40 0.36
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Particle-wall coefficient of static friction
a
47
0.32
8 10 12 14 16 18 20 22 24 Moisture content, %, w.b.
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DEM
Test
DEM
Test
DEM
Test
DEM
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Wheata
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Soybeana
Time since
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Soybeanb
0s
0.5 s
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discharging
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Figure 15
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1s
1.5 s
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Graphical abstract
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ACCEPTED MANUSCRIPT Highlights Physical properties of wheat and soybean required in DEM were determined.
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The moisture content had a significant effect on all the test parameters.
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The size and coefficients of static friction increased with moisture content. The true density and shear modulus decreased with moisture content.
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CE P
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Coefficients of restitution of both crops varied differently with moisture content.
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S0032-5910(16)30050-X doi: 10.1016/j.powtec.2016.02.009 PTEC 11488
To appear in:
Powder Technology
Received date: Revised date: Accepted date:
1 September 2015 28 January 2016 5 February 2016
Please cite this article as: Fanyi Liu, Bo Li, Lanhua Yi, Jian Zhang, Jun Chen, Effect of moisture content on some simulation parameters of wheat and soybean required in DEM, Powder Technology (2016), doi: 10.1016/j.powtec.2016.02.009
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ACCEPTED MANUSCRIPT Effect of moisture content on some simulation parameters of wheat and soybean required in DEM
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College of Mechanical and Electronic Engineering, Northwest A&F University,
Yangling, Shaanxi Province 712100, China. b
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a
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Fanyi Liua, Bo Lia, Lanhua Yib, Jian Zhanga, Jun Chena,*
College of Food Science and Engineering, Northwest A&F University, Yangling,
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Shaanxi Province 712100, China.
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* Corresponding author. Tel./Fax: +86-029-8709 1867.
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E-mail address: [email protected]
1
ACCEPTED MANUSCRIPT ABSTRACT The discrete element method (DEM) is widely used nowadays but the determination
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of the simulation parameters required in DEM simulations is still the main challenge
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for effective utilization of this tool. This study focused on some simulation parameters required in DEM for two typical crops: wheat and soybean. The effect of moisture content (wet basis) on these parameters was investigated. Experimental results
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demonstrated that with increasing moisture content from 10.05% to 21.63% for wheat
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and 11.23% to 19.48% for soybean, the size (length, width and thickness) and static friction coefficients of two contact types (particle-wall and particle-particle) increased
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linearly, but the true density and shear modulus decreased. However, both the
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particle-wall and particle-particle coefficient of restitution showed different trends for
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the two crops. For wheat, the two coefficients of restitution went down continuously; while for soybean, the two coefficients of restitution decreased before they began to
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increase. The results of analysis of variables (ANOVA) showed that the effect of moisture content on these parameters was significant (*P < 0.05). Regression equations of all parameters with the moisture content except the coefficient of restitution of soybean were established and verified with relative errors below 10%. At last, the measured parameters of the two crops with the initial moisture content were validated using a silo discharge test. Results showed that the total discharge time and flow patterns of wheat were almost the same in experiments and simulations. However, more than 15% difference for the total discharge time was observed for soybean. With the particle-wall and particle-particle coefficient of rolling friction 2
ACCEPTED MANUSCRIPT increasing to 0.05, the difference can be eliminated. Keywords: Simulation parameters; Moisture content; Discrete element method;
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Wheat; Soybean
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ACCEPTED MANUSCRIPT 1. Introduction Developed by Cundall and Strack in 1979, the discrete element method (DEM) is
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now a promising numerical technique to study the dynamics of crop particles and
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their interaction with equipments. Based on DEM, much research has been performed in handling [1-3], sorting [4,5], cleaning [6], and drying [7,8] processes. These studies not only verified the feasibility of the DEM in simulating the motion of crop particles,
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but also helped to design advanced equipments.
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In DEM simulations, the microscopic parameters are of great importance but difficult to be determined. There are two common ways to obtain them: ―virtual
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calibration‖ and ―direct measurement‖. Most researchers use the ―virtual calibration‖
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method [9,10]. However, the main drawback of calibration method is that an adjusted
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microscopic value is dependent on the numerical code used in the calibration process, thus invalidating some of the values to be used in other codes and applications [11].
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Few researchers use the ―direct measurement‖ method due to the difference between particles and the anisotropy of an individual particle. Although it is difficult to measure these DEM parameters directly by a single particle, the ―direct determination‖ is more precise and has a wider applicability for different codes and applications compared to the calibration method [12]. In our experiments, the ―direct measurement‖ was used at particle level except in the determination of the true density for both crops and particle-particle coefficient of static friction for soybean. Large sample and reduplication were used to reduce the measuring error. On the other hand, the physical and mechanical properties of crop seeds are 4
ACCEPTED MANUSCRIPT influenced by various factors such as cultivars, maturity and moisture content etc. In recent years, the effect of moisture content on physical and mechanical properties of
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sorghum [13], faba bean [14], wheat [15] and barley [16] etc. have been investigated.
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These properties provide essential parameters to design machinery and process equipments [17]. Similarly, the simulation parameters required in DEM are vital in building simulation models. Measurement of these parameters does not only provide
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reference values of wheat and soybean under different moisture content for DEM
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simulation, but also offer measuring methods for other crop seeds. To our knowledge, no systematic report about the effect of moisture content on the simulation parameters
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of wheat and soybean required in DEM has been reported.
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In this paper, some simulation parameters of wheat and soybean used in DEM
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were investigated under four levels of moisture content. The ANOVA was used to judge the significance of the effect of moisture content on these parameters and
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regression equations of all parameters with the moisture content were established and verified except the coefficient of restitution of soybean. Moreover, the measured parameters of the two crops with the initial moisture content were validated by comparing the total discharge time and flow patterns observed in experiments and DEM simulations. 2. Materials and methods 2.1 Sample preparation In this study, the wheat (Xi Nong 223) harvested in 2014 was provided by the Wheat Breeding Center of the Northwest Agriculture and Forestry University; the 5
ACCEPTED MANUSCRIPT soybean (Dong Nong 44) was bought from the market in 2014. The samples with different moisture content were obtained as follows:
IP
T
Ⅰ. In order to gain the initial moisture content, the two crops were dried in an
SC R
oven at 105 °C until they reached constant weights (Standard S352.2, DEC97, ASAE, 1999).
Ⅱ. The distilled water was added to obtain the samples with different pre-set
Wi M f M i
100 M
(1)
MA
Q
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moisture content and the amount of water can be calculated from Eq. (1).
f
D
where Q is the amount of distilled water to add (g); Wi , M i are the initial weight
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and moisture content of the sample (g, % w.b.) and M f is the final (pre-set) moisture content (% w.b.).
CE P
Ⅲ. The samples were put into seal bags and stored in a refrigerator at 4 °C for 10 days. During that time the samples were mixed every 8 hours to make the water
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redistribute uniformly.
Ⅳ. Before the tests, the sealed samples were put under ambient environment for 24 hours to warm up to the room temperature. After treatment, the final moisture content of the samples was measured according to ASAE Standard S352.2 as mentioned above. In this study, the final four levels of moisture content (wet basis) were 10.05%, 13.51%, 17.31% and 21.63% for wheat and 11.23%, 14.12%, 16.66% and 19.48% for soybean. 2.2 Measurement of the simulation parameters
6
ACCEPTED MANUSCRIPT Five types of simulation parameters were measured in our experiments, including the size, true density, shear modules, coefficient of restitution and static
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friction of two types of contact (particle-particle and particle-wall).
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2.2.1 Size ( L , W , T )
For wheat and soybean, a digital venire caliper (accuracy ~ 0.01 mm) was used to measure the three-dimensional size: length ( L ), width ( W ) and thickness ( T ). At
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each level of moisture content for the two crops, 50 particles were selected randomly
MA
for measurement. 2.2.2 True density ( )
D
The true densities of the both crops under different moisture content were
TE
measured using the pycnometer method (ASTM D854-10). Methylbenzene was used
CE P
as measure liquid to reduce the error caused by absorption. A certain quality of sample ( m ) was added into a given volume of methylbenzene rapidly. The volume variation
AC
of methylbenzene ( v ) was read as soon as possible. Therefore, the true density of the sample can be described by m . 5 samples were conducted for each level of v moisture content to obtain the average value. 2.3.3 Young’s modulus ( E ), shear modulus ( G ) and Poisson’s ratio ( ) Young’s modulus reflects the abilities of objects to resist elastic deformation. It is defined as the ratio of stress and strain in a direction. According to the ASAE Standard (S368.4, DEC2000, ASAE, R2012), two parallel plates were used as loading tools in this experiment. Based on Hertz equation, the Young’s modulus can be described as: 7
ACCEPTED MANUSCRIPT 1 1 0.338F 1 2 1 3 1 3 1 1 KU E KL 3 2 R R R U L RL D U
3
2
(2)
IP
T
where E is the Young’s modulus (Pa); F is the compression force (N); is Poisson’s ratio (dimensionless); D is the deformation of the test particles (m);
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RU , RU and RL , RL are the maximum and minimum radii of curvature of the convex surface of the sample at the point of contact with the upper and lower plate (m),
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respectively; KU , K L are constants and can be found in the ASAE S368.4 through
MA
cos . For parallel plate contacts, the cos can be calculated by: RU RU RL RL or cos cos RU RU RL RL
(3)
TE
D
According to the assumption of ASAE S368.4, the Poisson’s ratios of the two
G
E 2 1
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crops are 0.42 and 0.40, respectively. Thus, the shear modulus can be calculated by: (4)
AC
Here, the compression tool (Fig. 1) used was HY-0230 universal tester (HengYi Precise Instrument co., Ltd., Shanghai, China), and the test speed was 0.2 mm/min. At each level of moisture content of the two crops, 25 particles were selected randomly for measurement. Fig. 1.
2.3.4 Coefficient of restitution (1) Particle-wall coefficient of restitution ( ePW ) The method used to measure the particle-wall coefficient of restitution was similar to the free-fall method by Fu et al. [18], as shown in Fig. 2. A particle was 8
ACCEPTED MANUSCRIPT attracted by a vacuum pump at H 0 (Fig. 2a), and then fell freely under gravity with the pump off. Then the particle rebounded to a height of H1 (Fig. 2b) after impacting
IP
T
with an acrylic board. The acrylic board was used because of its wide usage in DEM
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validation experiments. The whole process was recorded by an Olympus I-speed3 high speed camera (Olympus (China) co., Ltd., Guangzhou, China) which running at 500 fps (Fig. 3). Assuming that the particle rebound vertically and has no rotational
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speed after collision, the particle-wall coefficient of restitution ePW can be expressed
1
2
(5)
D
ePW
H 1 H0
MA
by:
TE
In this experiment, 20 particles were selected randomly and measured with 20 replications for each particle under each level of moisture content for the two crops.
CE P
Only the cases when the particles rebounded nearly vertically or rotated minimally
Fig. 2. Fig. 3.
AC
were selected [19].
(2) The particle-particle coefficient of restitution ( ePP ) The method used to measure the particle-particle coefficient of restitution originated from the double pendulum method by González-Montellano et al. [11], as shown in Fig. 4. During the test, particle 1 was lifted at a height of H 0 by the suction pipe of the vacuum pump on the right (Fig. 4a). After the pump was turned off, particle 1 began to swing and collided with particle 2. Subsequently, the two particles swung respectively. The maximum height of particle 1 and particle 2 were H1 and 9
ACCEPTED MANUSCRIPT H 2 , respectively (Fig. 4b). Therefore, the particle-particle coefficient of restitution can be calculated by: 1
T
1
H0 2
(6)
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ePP
1
H 2 2 H1 2
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The whole process was recorded by the high speed camera at 500 fps (Fig. 5). In present study, 20 groups (40 particles) were selected randomly and measured with 20
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repetitions for each group under four levels of moisture content for the two crops. Only the cases when the particles rotated minimally were selected.
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Fig. 4.
D
Fig. 5.
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2.3.5 The coefficient of static friction
(1) The particle-wall coefficient of static friction ( f PW )
CE P
The three-particle sliding friction method proposed by Chung and Ooi [20] was used to measure the particle-wall coefficient of static friction (Fig. 6). During the
AC
measurement, the lifting board was elevated at a slow speed until the acrylic board began to slide. The whole process was recorded by the high speed camera at 500 fps. The coefficient of static friction between particles and the acrylic board can be described by the tangent of the included angle between the lifting board and the horizontal line. In this study, 20 groups (60 particles) were selected randomly and measured with 5 repetitions for each group under four levels of moisture content for the two crops. Fig. 6.
(2) The particle-particle coefficient of static friction ( f PP ) 10
ACCEPTED MANUSCRIPT The particle-particle coefficient of static friction is hard to measure since the size of the crop seed is usually small and the shape is irregular. Two different methods
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T
were used to measure this parameter for wheat and soybean, respectively.
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For wheat, a method based on particle scale which similar to the method by Han et al. [21] was employed (Fig. 7) due to the prolate shape of wheat particles. In this test, the particles were glued on a board which was fixed on the lifting board. While
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measuring, a test particle was placed on the ―seedbed‖, subsequently; the lifting board
MA
was lifted at a constant slow speed. The high speed camera was used to detect the slide of the test particle (500 fps). 20 particles were selected and measured with 5
D
repetitions for each particle under each level of moisture content.
TE
For soybean, the repose angle test by Chung et al. [22] with little modification
CE P
was employed (Fig. 8). To reduce the error caused by the baseboard, boards glued with seeds were used. The diameter and height of the bottomless and topless acrylic
AC
cylinder was 100×200 mm. After the granular heap formed, a computer image analysis method similar to that by Frączek et al. [23] was used to calculate the repose angle. The particle-particle coefficient of static friction can be approximately described by the tangent of the repose angle. One sample with 5 repetitions were conducted for each level of moisture content to obtain the mean value. Fig. 7. Fig. 8.
2.3 Data analysis For all the test results, the box plot and Grubbs test were used to detect the 11
ACCEPTED MANUSCRIPT outliers which largely departed from sample average and all the outliers were removed. The mean values and standard deviations were determined for all
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parameters. Then all the results were subjected to ANOVA using SPSS 22.0 software
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to study the effect of the moisture content on all the parameters considered in this work. The regression analysis was conducted using Origin 8.1 software. 2.4 Verification of the regression equations
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To verify the regression equations established in this work, samples with
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moisture content of 18.67% for wheat and 12.46% for soybean were prepared using the method described in section 2.1. Accordingly, the physical parameters were
D
measured using the methods described in section 2.2. The measured values were
TE
compared to the fitted ones to obtain the relative errors.
CE P
2.5 Validation of the measured parameters In present study, only the wheat and soybean with the initial moisture content
AC
(10.05% and 11.23%) were used for validation. This can be explained by the following reasons: (ⅰ) the coefficient of rolling friction was not measured in this work considering the difficulty in measurement, the particle-wall and particle-particle coefficient of rolling friction of wheat and soybean were set as 0.01 which were the default values in EDEM software and commonly used by other researchers for dry crop particles [24-26]; (ⅱ) for crop particles with higher moisture content, the viscidity might be taken into consideration[27]. To validate the physical parameters measured in this study, a lab-scale silo discharge test was conducted. The size of the wedge-shaped acrylic silo is illustrated 12
ACCEPTED MANUSCRIPT in Fig. 9. The discharge processes were recorded using the high speed camera, from which the total discharge time and the flow pattern can be acquired. In order to
IP
T
identify the characteristics of the particle flow more accurately, several black-dyed
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wheat and soybean particles were used as ―markers‖ and placed inside the silo at a certain height. During discharging, these markers were moved by the surrounding grains and the flow pattern can be illustrated by the deformation of the line of the
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markers[28].
MA
Fig. 9. Fig. 10.
D
For DEM simulation, a silo with the same dimensions as used in the lab test was
TE
modeled using the EDEM 2.7 software. The Hertz-Mindlin (no slip) contact model
CE P
was adopted to describe both the particle–wall and particle–particle contacts. According to the shapes of the two crops, a five-particle model and a four-particle
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model were constructed for wheat (Fig. 10(a)) and soybean (Fig. 10(b)), respectively. The size distribution was set as normal for wheat (Mean:1; STD:0.07 ) and soybean (Mean:1; STD:0.06). To avoid generating too small particles, the particles were restrict to the minimum and maximum particle sizes. Specifically, the radius of the spherical elements which made up the five-particle and four-particle models were set as 0.65-1.21 and 0.92-1.07 times as their initial sizes. The time steps used in all simulations were 20% of the Rayleigh time. The cell size employed was 3Rmin, where Rmin is the minimum radius of the spherical elements. In the virtual silo, the ―markers‖ were also reproduced by colouring those particles that occupied the same positions 13
ACCEPTED MANUSCRIPT with the black-dyed particles in lab test. 3. Results and discussion
T
3.1 Simulation parameters
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3.1.1 Size
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As described in Table 1, for wheat and soybean, the three-dimensional size (length, width, thickness) changed significantly with the increase of moisture content
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(*P < 0.05).
Fig. 11(a) and Fig. 11(b) show the mean values and standard deviations of the
MA
size of the two crops under different moisture content. For wheat particles, with
D
increasing moisture content from 10.05% to 21.63%, the length increased from 6.60
TE
mm to 6.79 mm, the width from 3.62 mm to 3.95 mm and the thickness from 3.18 mm to 3.47 mm (Fig. 11a). Similarly, Fig. 11(b) shows that for soybean, with the
CE P
increase of moisture content from 11.23% to 19.48%, the length, width and thickness increased from 7.28 mm to 7.34 mm, from 7.17 mm to 7.34 mm and from 6.69 mm to
AC
6.89 mm, respectively. The increase of the dimensions was attributed to expansion or swelling as a result of moisture uptake in the intracellular spaces of the seeds [29]. According to the regression analysis of the size of wheat and soybean changed with the moisture content, the variation trends can be represented by the following equations:
LW 0.01833M C 6.41607
R
2
0.94
(7)
WW 0.02819M C 3.34709
R
2
0.99
(8)
TW 0.02251M C 2.97076
R
2
0.93
(9)
LS 0.04512M C 6.76882
R
2
0.99
(10) 14
ACCEPTED MANUSCRIPT WS 0.02088M C 6.94151
R
2
0.98
(11)
TS 0.02264M C 6.42202
R
2
0.95
(12)
W
and
S
represent the length, width, thickness of wheat and soybean,
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with subscripts
IP
T
where M C is the moisture content of the particles (% w.b.), the variables L, W, T
respectively.
This linear increase in the three-dimensional size with the moisture content was
NU
also found in the research of wheat [15], soybean [30] and caper seeds [31] etc.
MA
Fig. 9.
3.1.2 True density
D
From Table 1, we also noted that the influence of moisture content on the true
TE
density was significant for both crops (*P < 0.05).
CE P
The mean values and standard deviations of the true density for wheat and soybean are given in Fig. 11(a) and Fig. 11(b), respectively. The true density exhibited
AC
a linear decrease trend with the increase of moisture content for both crops. With increasing moisture content from 10.05% to 21.63%, the true density of wheat ( W ) decreased from 1405.15 kg/m3 to 1306.81 kg/m3; for soybean, this parameter ( S ) went down from 1251.74 kg/m3 to 1201.49 kg/m3 as the moisture content increasing from 11.23% to 19.48%. The decrease of true density was mainly due to the larger increase in kernel volume compared to the increase in kernels mass [32]. The regression equations can be expressed as follows:
W 8.75016M C 1495.36118
R
2
0.99
(13)
S 6.2822M C 1322.48804
R
2
0.98
(14)
15
ACCEPTED MANUSCRIPT The linear decrease of the true density was also reported in the work of wheat [15]. For soybean, Kashaninejad et al. [30] reported an increase of the kernel density
IP
T
with the moisture content, which was contrary to the findings of Deshpande et al. [33]
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and this study. These differences may result from the different measuring method Kashaninejad et al. adopted. The linear decrease of the true density with moisture content also matched well with the researches of paddy rice [34], green gram [35] and
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lentil [36] etc.
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Table 1
3.1.3 Shear modulus
D
The smallest P values in ANOVA of all the properties (Table 1) for wheat
TE
(7.323E-70) and soybean (5.6038E-28) mean the assumption that the moisture content
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has a significant effect on the shear modulus is the most acceptable. Fig. 12 shows that the shear modulus had an opposite dependence on moisture
AC
content for both crops. It decreased by 70% as the moisture content rising from 10.05% to 21.63% for wheat. For soybean, this value decreased by 67% with the moisture content increasing from 11.23% to 19.48%. The shear modulus of wheat did not decrease linearly. Actually, it went down gently at first and then decreased faster as the moisture content rising. The decrease of shear modulus was attributed to that the particle structure became softer after absorbing water and its ability to resist deformation became weaker [37]. A second-order polynomial and linear fitting were used to describe the trends of shear modulus for wheat ( GW ) and soybean ( GS ), respectively. The fitting equations 16
ACCEPTED MANUSCRIPT are expressed:
R
2
0.97
(15)
GS 35.01052M C 823.42165
R
2
0.99
(16)
IP
T
GW 3.14543M C2 67.77189M C 169.62155
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The decrease of shear modulus with the moisture content observed in this research was similar to that found in rice grains [37], faba beans [38] and apricot pit [39] etc.
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Fig. 10.
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3.1.4 The coefficient of restitution
(1) The particle-wall coefficient of restitution
D
The ANOVA of the effect of moisture content on the particle-wall coefficient of
TE
restitution (Table 1) showed that the moisture content had a greater influence on this
CE P
parameter than the difference between particles for the two crops (*P < 0.05). From Fig. 13(a), we can see the particle-wall coefficient of restitution decreased
AC
(from 0.57 to 0.43) with the increase of moisture content (from 10.05% to 21.63%) for wheat. This was because the wheat particle became softer after absorbing water. When the particle collided with the acrylic board, it had a greater deformation and more energy was dissipated. Accordingly, the rebound height decreased. Interestingly, for soybean, the effect of moisture content on this parameter had a much different trend. With increasing moisture content (from 11.23% to 14.12%), this parameter decreased (from 0.50 to 0.47). However, when the moisture content increased further, it began to increase (from 0.47 to 0.50). The reason is uncertain, but this may because the character of soybean particles with higher moisture content had changed greatly 17
ACCEPTED MANUSCRIPT and their elastic ability increased and this need to be further investigated. Only the regression equation of wheat ( EWPW ) under different moisture content
as below: 2
0.95
SC R
R
EWPW 0.01146M C 0.68399
IP
T
was given because of the low R 2 for soybean. The linear equation can be described
(17)
LoCurto et al. [40] found that the coefficient of restitution of soybean impacting with
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the acrylic board decreased significantly with the moisture content (10.7% to 15.5%,
MA
d.b.).
Fig. 11.
TE
D
(2) The particle-particle coefficient of restitution Table 1 shows that the moisture content had a significant influence on the
CE P
particle-particle coefficient of restitution for the both crops (*P < 0.05). According to Fig. 13(b), the particle-particle coefficient of restitution had a
AC
similar trend with the particle-wall coefficient of restitution for the both crops. As the moisture content increased, the particle-particle coefficient of restitution of wheat ( EWPP ) went down (from 0.48 to 0.33); but for soybean, it decreased firstly (from 0.45 to 0.41) and then began to increase (from 0.41 to 0.47). The change trends of particle-particle coefficient of restitution were corresponding with those of the particle-wall coefficient of restitution for the two crops, which further increased the credibility of the two measuring methods. Accordingly, the changes could also be explained by the reason of particle-wall coefficient of restitution. Similarly, the regression equation of soybean was not given because of the low 18
ACCEPTED MANUSCRIPT R 2 . For wheat, the relationship between the particle-particle coefficient of restitution
and the moisture content can be described by the following linear equation:
0.99
T
2
(18)
IP
R
EWPP 0.01323M C 0.61414
(1) The particle-wall coefficient of static friction
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3.1.5 The coefficient of static friction
The results of ANOVA (Table 1) showed that the moisture content had a
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significant influence on the particle-wall coefficient of static friction (*P < 0.05).
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Fig. 14(a) shows the changes of the particle-wall coefficient of static friction for wheat ( FWPW ) and soybean ( FSPW ). With the increase of moisture content, this
D
parameter showed an upward trend for both crops (from 0.34 to 0.48 and from 0.29 to
TE
0.38 for wheat and soybean, respectively). This may be attributed to the fact that an
CE P
increase in moisture content increased the cohesion between the seeds and the test board, thereby increasing the friction they experienced [41].
AC
The relationship between the particle-wall coefficient of static friction and the moisture content can be expressed by the following linear equations for the two crops:
FWPW 0.01259M C 0.22083
R
2
0.92
(19)
FSPW 0.01132M C 0.15844
R
2
0.97
(20)
These results were similar to the researches of millet [42], rapeseed [43] and karanja seeds [44] etc which based on sliding tests at particle group level. Fig. 12.
(2) The particle-particle coefficient of static friction From Table 1, we can see that statistically significant changes in the 19
ACCEPTED MANUSCRIPT particle-particle coefficient of static friction were produced as moisture content rising (*P < 0.05).
IP
T
Fig. 14(b) shows that the moisture content had a similar effect on the
SC R
particle-wall and particle-particle coefficient of static friction. For wheat and soybean, the values increased from 0.48 to 0.58 and from 0.36 to 0.50, respectively. This can also be explained by the increase of adhesion of the particle surface after absorbing
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water.
MA
The particle-particle coefficient of static friction under different water content for the two crops can be respectively described by the following linear equations:
TE
FSPP 0.01719M C 0.15842
D
FWPP 0.00851M C 0.39948
R
2
0.98
(21)
R
2
0.96
(22)
CE P
Our findings for the particle-particle coefficient of static friction were smaller than those for wheat [15] and soybean [30], but corresponding with the values
AC
summarized by Boac et al. [19]. Similar linear increase of this parameter was reported in the researches for lentil seeds [36], sorghum seeds [13] and paddy rice [34] etc. Table 1
3.2 Verification of the regression equations Table 2 gives the relative errors of the measured values and the fitted values calculated from the regression equations. From the table, we can see all the relative errors were below 10%. This means the regression models have a good accuracy. The relative errors of the three-dimensional and true density were quite small (<1%); the model for the shear modulus of wheat had a maximum error of 8.76% and the error 20
ACCEPTED MANUSCRIPT for soybean was 5.38%. For other parameters, the errors ranged from 1.75% to 5.71% for the two crops.
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T
3.3 Results of silo discharge test
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3.3.1 The total discharge time
Table 3 summarizes the total discharge time measured in experiments and DEM simulations for the two crops. For wheat, the difference of the mean value of the total
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discharge time between the experiments and simulations was relatively small (less
MA
than 2%). However, this difference for soybean was much larger (more than 15%). This might because the sphericity of the four-particle model was higher than that of
D
the real soybean particle and the coefficient of rolling friction used in the simulations
TE
was small. So the particle-wall and particle-particle coefficient of rolling friction were
CE P
increased to 0.05. As a result, the mean value of the total discharge time for the modified simulations increased to 4.57 s and the relative error between the lab tests
AC
and simulations decreased to 1.72%. 3.3.2 Flow pattern Fig. 15 compares the flow patterns of the two crops obtained in lab tests and DEM simulations at different time (0 s, 0.5 s, 1 s, 1.5 s) since discharging. The flow patterns of wheat observed experimentally were almost the same with those in simulations. For soybean, the deformation of the line of the markers was similar in the experiments and simulations, but the simulated free-flow surfaces were lower than those of the experiments. It also showed the flow rate in simulation was larger and could be attributed to the same with the less total discharge time for soybean in simulation. For 21
ACCEPTED MANUSCRIPT simulations with the modified coefficient of rolling friction, both the deformation of the line of markers and the free-flow surfaces the lab tests matched well with those in
IP
T
DEM simulations.
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4. Conclusions
In present study, the size, true density, shear modulus, particle-wall and particle-particle coefficient of restitution and static friction of wheat and soybean
NU
required in DEM were measured based on particle-group or single-particle
MA
experiments under four levels of moisture content.
The ANOVA results showed that the effect of moisture content on all the test
D
parameters was significant. The regression equations for all parameters with the
TE
moisture content were established and verified except the coefficient of restitution of
CE P
soybean.
For wheat and soybean, with the increase of moisture content, the size and
AC
coefficient of static friction of two contact types increased linearly, while the true density and shear modulus decreased. For wheat, the particle-wall and particle-particle coefficient of restitution had downward trends, from 0.57 to 0.43 and 0.48 to 0.33. However, for soybean, when the moisture content increased from 11.23% to 14.12%, these parameters decreased firstly (from 0.50 to 0.47 and from 0.45 to 0.41) and with the moisture content increased further, they began to increase (from 0.47 to 0.50 and from 0.41 to 0.47). The measured parameters of the two crops with the initial moisture content were validated by comparing the total discharge time and flow pattern in a wedge-shaped 22
ACCEPTED MANUSCRIPT silo discharge test. For wheat, the simulated results were almost the same with the experimentally observed ones. However, more than 15% difference for the total
IP
T
discharge time was observed between lab test and DEM simulation. By increasing the
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particle-wall and particle-particle coefficient of rolling friction to 0.05, a well match can be observed in experiment and simulation for both the total discharge time and flow pattern. Though the silo discharge test could be basically modeled using the
MA
measured parameters in later research.
NU
measured parameters, more validation tests should be conducted to validate these
Though the physical properties of crops seeds are complicated and influenced by
D
many factors, the results of these tests can be used as reference values when modeling
TE
DEM simulation or initial values in calibration procedure for the two crops.
other crops.
CE P
Meanwhile, the measuring methods can be adopted to determine these properties for
AC
Acknowledgements
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IP
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SC R
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D
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CE P
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IP
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ACCEPTED MANUSCRIPT Table 1 ANOVA of the physical properties of wheat and soybean under different moisture content. Wheat
Soybean Significance
F values
P values
Significance
L
7.185
0.000134
S*
9.429
0.000008
S
W
25.741
4.3957E-14
S
9.429
0.006
S
T
18.629
1.1302E-10
S
2.717
0.046
S
ρ
41.576
1.6604E-7
S
3.381
0.039
S
G
1048.805
7.323E-70
S
0.16
5.6038E-28
S
ePW
74.505
2.6557E-12
S
9.471
0.000037
S
ePP
11.091
0.001
S
8.534
0.00127
S
fPW
33.165
1.3872E-10
S
8.634
0.000179
S
fPP
8.968
0.0133
20.58
3.458E-8
S
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T
P values
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F values
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Items
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S means that the effect of moisture content on this parameter is significant (P < 0.05).
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ACCEPTED MANUSCRIPT Table 2 Verification of the regression equations with wheat (18.67%, w.b.) and soybean (12.46%, w.b.). Wheat
soybean
Items Fitted values
Error(%)
Measured values
Fitted values
Error(%)
L
6.78
6.76
0.3
7.37
7.33
0.54
W
3.90
3.87
0.77
7.21
7.20
0.14
T
3.38
3.39
0.3
6.71
6.70
0.15
ρ
1326.83
1332
0.4
1246.34
1244.21
0.17
G
311.26
338.52
8.76
367.42
387.19
5.38
ePW
0.45
0.47
4.44
/
/
/
ePP
0.35
0.37
5.71
/
/
/
fPW
0.47
0.46
2.13
0.29
0.30
3.45
fPP
0.57
0.56
1.75
0.38
0.37
2.63
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D TE CE P AC
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T
Measured values
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Comparison of the discharge observed in experiments and simulations for wheat and soybean. Soybean Experiment
Simulation 1a
Simulation 2b
1
3.50
3.51
4.65
3.96
4.56
2
3.54
3.45
4.68
3.94
4.58
3
3.49
3.46
4.61
3.94
4.56
Mean value T
3.51
3.47
4.65
3.95
4.57
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Simulation 1a
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Experiment
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Wheat Repetitions
a: Simulations with given particle-wall and particle-particle coefficient of rolling friction of 0.01;
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b: Simulations with modified particle-wall and particle-particle coefficient of rolling friction of
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0.05.
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ACCEPTED MANUSCRIPT Fig. 1. Compression tool used to measure the Young’s modulus. Fig. 2. Schematic of the apparatus used to measure the particle-wall coefficient of restitution: (a) before
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impact, (b) after impact.
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Fig. 3. Snapshots of the particle-wall coefficient of restitution test: (a) before impact, (b) impact, (c) after impact.
Fig. 4. Double pendulum apparatus used to determine the particle-particle coefficient of restitution: (a)
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before impact, (b) after impact.
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Fig. 5. Snapshots of the particle-particle coefficient of restitution test: (a) before impact, (b) impact, (c) after impact.
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Fig. 6. Schematic of the apparatus used to measure the particle-wall coefficient of static friction.
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Fig. 7. Schematic of the apparatus used to measure the particle-particle coefficient of static friction of
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wheat.
Fig. 8. Schematic of the apparatus used to measure the particle-particle coefficient of static friction of
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soybean.
Fig. 9. Sizes of the wedge-shaped silo. Fig. 10. Shapes and sizes of the DEM particle models for: (a) wheat, (b) soybean. Fig. 11.Mean values and standard deviations of the size and true density with moisture content: (a) wheat, (b) soybean. (■) length, L; (●) width, W; (▲) thickness, T; (◆) density, . Fig. 12. Mean values and standard deviations of the shear modulus with moisture content: (■) wheat; (●) soybean. Fig. 13. Mean values and standard deviations of the coefficient of restitution of the two contact types with moisture content: (■) wheat; (●) soybean. 32
ACCEPTED MANUSCRIPT Fig. 14. Mean values and standard deviations of the coefficient of static friction of the two contact types with moisture content for: (■) wheat; (●) soybean.
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Fig. 15. Comparison of the flow patterns observed in experiments and simulations at different time
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since discharging for wheat and soybean. (a: Simulations with given particle-wall and particle-particle coefficient of rolling friction of 0.01; b: Simulations with modified particle-wall and particle-particle
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coefficient of rolling friction of 0.05.)
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Figure 1
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Figure 2
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Figure 3
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Figure 4
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Figure 5
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Figure 6
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Figure 7
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Figure 8
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Figure 9
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Figure 10
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1270
1410
7.8
1260
6.0
1380
7.6
1250
5.5
1350
5.0
1320
4.5
1290
6.8
1230
6.6
1200 24
10
12
14
16
18
20
22
6.4
T 10
Moisture content, %, w.b.
NU MA D TE CE P
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1220
12
14
1210 1200 1190 1180
16
18
Moisture content, %, w.b.
Figure 11
1230
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7.0
3.0 8
7.2
1260
3.5
1240
7.4
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4.0
Size, mm
6.5
b
-3
1440
20
Density, Kg m
8.0
7.0
Density, Kg m
Size, mm
a
-3
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T IP
40 30
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Shear modulus， Mpa
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20
10
12
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16
18
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Moisture content, %, w.b.
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TE
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Figure 12
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20
22
0.56 0.54 0.52 0.50 0.48 0.46 0.44 0.42 0.40 0.38
0.54 0.51 0.48
T
0.58
0.45
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b
0.42 0.39
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0.60
0.36 0.33 0.30 0.27
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Particle-wall coefficient of restitution
a
Particle-particle coefficient of restitution
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8 10 12 14 16 18 20 22 24
Moisture content, %, w.b.
Moisture content, %, w.b.
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8 10 12 14 16 18 20 22 24
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CE P
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Figure 13
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0.36 0.32 0.28 0.24
8 10 12 14 16 18 20 22 24
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Moisture content, %, w.b.
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CE P
TE
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Figure 14
T
0.40
0.56 0.52
IP
0.44
0.60
0.48 0.44
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0.48
Particle-particle coefficient of static friction
b
0.52
0.40 0.36
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Particle-wall coefficient of static friction
a
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0.32
8 10 12 14 16 18 20 22 24 Moisture content, %, w.b.
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DEM
Test
DEM
Test
DEM
Test
DEM
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Wheata
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Soybeana
Time since
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Soybeanb
0s
0.5 s
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discharging
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Figure 15
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1s
1.5 s
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Graphical abstract
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ACCEPTED MANUSCRIPT Highlights Physical properties of wheat and soybean required in DEM were determined.
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The moisture content had a significant effect on all the test parameters.
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The size and coefficients of static friction increased with moisture content. The true density and shear modulus decreased with moisture content.
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Coefficients of restitution of both crops varied differently with moisture content.
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