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Filling of a grain silo. Part 1: Investigation of fine material distribution in a small scale centre-filled silo
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Available online at www.sciencedirect.com
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Research Paper
Filling of a grain silo. Part 1: Investigation of fine material distribution in a small scale centre-filled silo A. Nourmohamadi-Moghadami a, D. Zare a,*, C.B. Singh b, R.L. Stroshine c a
Department of Biosystems Engineering, Shiraz University, Shiraz, Iran School of Engineering, University of South Australia, Mawson Lake, 5095, Australia c Agricultural and Biological Engineering Department, 225 South University Street, Purdue University, West Lafayette, IN, 47907-2093, USA b
article info
When a silo is being filled with the granular material containing a range of particle sizes,
Article history:
larger particles tend to flow towards the silo wall while the smaller particles accumulate
Received 10 March 2019
near the centre of the silo. Shelled corn was used in this study. This work encompasses the
Received in revised form
first part, where the distribution of broken corn and foreign material (BCFM) was investi-
27 July 2019
gated in a small scale silo filled from a central filling point (CFP). Factors that were varied
Accepted 1 January 2020
included initial BCFM, volume flow rate of material and fill pipe diameter. A new approach
Published online xxx
was developed to ensure accurate sampling in the radial and vertical direction in the silo. The results indicated that the distribution of fine material became more uniform at lower
Keywords:
grain depths and for increasing initial BCFM, volume flow rate and fill pipe diameter. The
Central filling
accumulation of fine material at the centre of the silo increased with increase in the dis-
Fine distribution
tance from the bottom of the silo. In addition, a nonlinear model was developed to predict
Material flow
BCFM distribution in CFP method. Based on statistical parameters, namely, coefficient of
Grain silo
determination (R2), Chi-square (c2), RMSE (root mean square error) and MRDM (mean relative deviation modulus), the model fit the experimental data reasonably well. © 2020 IAgrE. Published by Elsevier Ltd. All rights reserved.
1.
Introduction
When a silo is being filled with granular material containing a range of particle sizes, the fine material consists of broken grain kernels and some trash and small foreign material particles which accumulate under the filling point (Stephens & Foster, 1976). Larger particles that have more mass, a longer trajectory and less surface friction than small particles
tend to flow towards the silo wall while the smaller particles accumulate near the centre of the grain mass. In other words, smaller particles remain in the cavities between the kernels whereas the majority of the larger particles migrate towards the bin wall. The inclined surface of a stationary particle bed acts like a sieve through which the smaller particles fall (Savage, 1993; Savage & Lun, 1988; Schulze, 2008). This effect is called sifting (Schulze, 2008). As a result of this effect, the
* Corresponding author. Department of Biosystems Engineering, Shiraz University, Visiting Prof. Mechanical Eng., Dept., University of South Australia, Mawson Lakes Campus, SA 5095, Australia. Fax: þ98 71 32286187. E-mail addresses: [email protected], [email protected] (D. Zare). https://doi.org/10.1016/j.biosystemseng.2020.01.003 1537-5110/© 2020 IAgrE. Published by Elsevier Ltd. All rights reserved. Please cite this article as: Nourmohamadi-Moghadami, A et al., Filling of a grain silo. Part 1: Investigation of fine material distribution in a small scale centre-filled silo, Biosystems Engineering, https://doi.org/10.1016/j.biosystemseng.2020.01.003
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Nomenclature A BCI BCL BCL.i Dg DF Lg NUFR NUFR,j NUFS m n Q R R2 T Tg vr W Wg Wr,i Z c2 s
fex;i fpr;i fex;a
cross section area of apparatus in 2D heap initial percent BCFM local percent BCFM ith local percent BCFM geometric mean diameter (mm) fill pipe diameter (mm) length (mm) non-uniformity factor for a ring (at a certain height in silo) non-uniformity factor for ith ring non-uniformity factor for a silo number of constants in fine distribution model number of observations volume flow rate scaled distance from the centre of the silo (dimensionless) coefficient of determination gap thickness between sidewalls in 2D heap thickness (mm) rise velocity apparatus width in 2D heap width (mm) ith relative weight scaled distance from the bottom of the silo (dimensionless) Chi-square the deviation of BCL at different sampling position along the radial direction (BCL,i) from BCI ith experimental data ith predicted data average of experimental data
inter-seed relative humidity in zones with low air flow, allowing the development of insects, mite species and other infestations (Noyes et al., 2002). In the second part of this research (Nourmohamadi-Moghadami, Zare, Stroshine, & Kamfiroozi, 2020) a new filling method, variable filling point (VFP), was developed and tested as a means of reducing the non-uniform distribution of fine material during filling of a small scale silo. For optimal performance of industrial processes such as aeration of stored products in silos, filling of silos, and handling of granular materials, it is necessary to evaluate the effect of properties of the product and the characteristics of the handling system on the distribution of the fine materials. During conventional filling of a silo, a conical pile is formed so that falling materials flow radially in all directions (Fig. 1a) down the sides of the heap creating a layer of moving material on the surface of the pile. Because particle motion is stopped or bounded by the walls, this type of flow is called bounded heap flow (Fan, Jacob, Freireich, & Lueptow, 2017). Fan et al. (2012) and Fan, Umbanhowar, Ottino, and Lueptow (2013) used a quasi-two-dimensional apparatus to study bounded heap flow (Fig. 1). Bounded heap flow is one of several types of free surface flow which occur in silos during filling. As indicated in Fig. 1b, the filling process includes three stages. In stage I, the falling materials form a rather irregularly shaped heap at the bottom of the
Abbreviations 2D two dimensional 3D three dimensional ANOVA analysis of variance BCFM broken corn and foreign material CFP central filling point MRDM mean relative deviation modulus GMD geometric mean diameter PRE prediction residual error RMSE root mean square error VFP variable filling point
smaller particles form a vertical cylindrical zone of high concentration at the silo centre (Noyes, Navarro, & Armitage, 2002). In corn silos, concentration of fine material under the filling spout is inevitable and this can cause serious problems. The localised concentration of fine material causes non-uniform airflow through the grain mass during the aeration process. This decreases the specific airflow through the grain in the centre of the grain mass compared to the periphery (Bartosik & Maier, 2006; Garg, 2005; Lawrence & Maier, 2011). This leads to higher temperatures and higher
Fig. 1 e (a) Sketch showing a top view of a 3D heap. The arrows indicate flow of the test material. The dashed box is a top view of the quasi-2D heap used here. (b) Sketch showing a side view of a quasi-2D heap rising at a rise velocity of vr ¼ Q/A, where Q is the volume flow rate and A ¼ TW (T and W are, respectively, the gap thickness between the sidewalls of the apparatus and the apparatus width). The three stages of heap flow are: (I) initiation (II) lateral growth and (III) steady filling (redrawn from Fan et al., 2012). (c) A side view of a 2D heap showing velocity profiles of the flowing material (redrawn from Fan et al., 2013).
Please cite this article as: Nourmohamadi-Moghadami, A et al., Filling of a grain silo. Part 1: Investigation of fine material distribution in a small scale centre-filled silo, Biosystems Engineering, https://doi.org/10.1016/j.biosystemseng.2020.01.003
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container. A little while afterwards, the surface of the heap forms an angle with the bottom of the container and its base grows laterally until it reaches the bounding walls (stage II). In stage III, the heap rises steadily at a constant velocity (vr). Figure 1c shows that in this stage the local flow rate decreases linearly with distance from the centre in the downstream direction, resulting in a gradient of streamwise velocity in the streamwise direction (because as flowing materials approach the endwall, the velocity decreases) (Fan et al., 2013). Based on the above discussion, it can be concluded that the velocity of materials through the flowing layer can affect the fine material distribution. Jayas, Sokhansanj, Moysey, and Barber (1987) investigated the distribution of foreign material (chaff and fines) in a bin filled with Tobin canola using two filling methods, a central spout and a conical spreader. They observed that a grain spreader concentrated more fines near the centre and resulted in only slightly more uniform distribution of fines than the use of a spout. The authors also proposed a quadratic equation to describe the distribution of chaff and fines. Because of difficulties in controlling experimental conditions, they did not consider the effects of other parameters on fine material distribution such as initial fine material content, feed rate and, for the central spout method, the inlet diameter. Shinohara, Golman, and Nakata (2001) and Shinohara and Golman (2002) studied the effects of parameters such as feed rate, initial concentration of the components and number of components on the segregation of multi-sized particle mixtures during the filling of a two-dimensional hopper. The results showed that the degree of segregation was significant at low feed rates and for low concentrations of the smallest component. Schulze (2008) stated that as the flow rate increases the flowing layer becomes thicker. Thus, smaller particles move farther down the pile before they percolate to lower layers. For such conditions, more fine material reaches the bounding wall. Combarros, Feise, Strege, and Kwade (2016) investigated the magnitude of segregation of sand particles in a pilot scale silo during filling and discharge. Segregation after filling was studied at different points over the width and the height of the silo. They observed that finer particles are found in the centre and at the bottom of the silo. They also found that the concentration of coarse particles was a quadratic function of the silo width and increased linearly with the silo height. Engblom, Saxen, Zevenhoven, Nylander, and Enstad (2012) studied experimentally the segregation of binary and ternary mixtures as well as commercial construction materials. They presented a model to describe the concentration of fine particles during filling which showed good agreement with experimental data. The variables that affected the distribution of particles during filling were mass fraction of fines, particle size ratio (coarse/fine), particle solid density ratio (coarse/fine), free fall distance, silo diameter and inlet diameter. A survey of the literature indicates there has not been a comprehensive study of the effects of parameters such as initial fine material content, volume flow rate and inlet diameter on fine material distribution in granular agricultural products in the radial and vertical directions in a 3D silo. To conduct such studies, it is preferable to first provide a pilot environment. Therefore, in this study an experimental silo
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was constructed to accurately measure BCFM along radial and vertical directions. The main objectives of present study were: a) to study fine changes as affected by major parameters: initial fine material content, flow (feed) rate and fill pipe (inlet) diameter b) to model changes in the fine material distribution for the different conditions.
2.
Material and methods
2.1.
Description of the experimental facilities
The components of the system include a main container with a volume of 1.2 m3, an elevator, a trapezoidal container and an experimental silo (Fig. 2). The elevator was used to move material from the main container to the trapezoidal container. Volume flow rate of the material discharging from the trapezoidal container was controlled by a fluted roller mechanism. This made the changes in flow rate of material independent of the changes in fill pipe diameter. To avoid segregation, no pile should be formed in the trapezoidal container. For this purpose, flow rate of the material was considered the same at the inlet and outlet of the trapezoidal container. But for more confidence, a horizontal agitator was also situated in the trapezoidal container. When samples are taken the insertion of a probe into the bulk grain disturbs the area where the sample is taken. This can affect the percentage of fine material in the sample, especially in small scale silos. To ensure accurate sampling in the radial and vertical direction, a special experimental silo was constructed (Fig. 3). The silo consisted of seven rings which were installed one on top of the other. A chassis supported the rings and kept them separated from each other by a vertical distance of 15 mm. The height and diameter of each ring were 0.14 and 1 m, respectively.
Fig. 2 e Experimental set up (a) main container, (b) elevator, (c) trapezoidal container, (d) agitator, (e) fluted roller mechanism, (f) fill pipe, (g) pilot scale silo consist of seven rings.
Please cite this article as: Nourmohamadi-Moghadami, A et al., Filling of a grain silo. Part 1: Investigation of fine material distribution in a small scale centre-filled silo, Biosystems Engineering, https://doi.org/10.1016/j.biosystemseng.2020.01.003
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an inclined bottom in such a way that some of the material remained on a circular stand which was placed at the centre of the container. The angle of repose was calculated from the radius of the circular stand and the height of the cone of material formed on the stand. Digital calipers with accuracy of ±0.01 mm were used to measure geometric mean diameter (GMD) of 100 whole kernels. The GMD was obtained to be 7.8 ± 0.88 mm using following equation (Mohsenin, 1986): 13 Dg ¼ Lg Wg Tg =
Fig. 3 e Schematic of the experimental silo.
2.2.
Experimental procedure
Shelled corn of variety 704 was provided from a private grain producer in Shiraz, Fars province, Iran. In accordance with the ASABE Standard (ASABE, 2008) for whole kernel moisture measurement, the initial moisture content of corn (with sample size of 15 g) was measured using a forced convection oven (heating at 103 C for 72 h). It was found to be 14 ± 0.5% w.b. In this study, fine material content is defined as BCFM (broken corn and foreign material) which is the amount of material from the sample that passed through a 4.8 mm (12/64 in.) diameter round-hole sieve as a result of hand sieving (USDA, 2013). The effects of initial percentage BCFM (BCI), volume flow rate (Q), and fill pipe diameter (DF) in both the radial and vertical directions were investigated. The tests were conducted with three levels of BCI which were 5, 7.5 and 10%, three levels of Q were 0.5, 1, 1.5 L s1, and three levels of DF which were 84, 105 and 120 mm (some preliminary tests were carried out to evaluate the possibility of conducting the experiments at the selected levels). The experiments were replicated three times. Therefore, there were 81 runs in the experiments. Prior to experiments, corn kernels were mixed with the desired percentage of fine material. Considering parameters that could influence the distribution of the fines, the bulk density and angle of repose were measured in triplicate for the three levels of BCI (Table 1). Bulk densities of the corn kernels and fine material were measured following procedures described in Stroshine (2004). The angle of repose was measured by removing one side of a wooden container with
(1)
Before the silo was filled, a strip of scotch tape was placed over the gap between the upper and lower rings on the inner side to prevent material from exiting. After the silo was filled, six separator sheets (Fig. 3) were inserted between adjacent rings starting from the bottom and moving upwards through each successive gap until the gap beneath the top ring was reached. This kept pressure on the lower layers due to the weight of the column of material and divided the column of material into seven parts. In order to ensure that the same amount of material was in each sample, sampling had to be carried out on a flat surface formed by the material. For this reason, the upper ring and the separator sheet beneath it were removed without being sampled. This eliminated the cone shaped top surface of the material. In all experiments, it was observed that the stages initiation and lateral growth occurred into the ring at the bottom of the silo. Therefore, to avoid any influence from the variations that can occur during these stages, samples were not taken from the lower ring of the silo. A Y-shaped guide (Figs. 4 and 5b) consisting of ten small rings was used to locate the sampling points in a specific pattern. Sampling cylinders were inserted into the material in the test silo through these small rings. The height and diameter of each sampling cylinder were 0.14 and 0.09 m, respectively. Figure 5a shows the position of sampling points in the test silo. The position of each sampling point could be specified using a scaled distance from the centre (the distance from the centre divided by the radius of the silo), R and a scaled distance from the bottom of the experimental silo (the distance from the bottom divided by the height of the silo), Z. It should be noted that, although the sampling was performed in triplicate, at a given Z, the value of BCL at sampling points A, B and C (Fig. 5b) is the average of the BCL of three samples which are the same distance from the centre. For example, the value of BCL at point A is the average
Table 1 e Physical properties of the initial grain masses at three levels of initial BCFM. Initial BCFM (BCI) Bulk density (kg m3) Angle of repose (o)
0%
5%
7.5%
10%
718 ± 1.6 22.5
732 ± 1.8 24.5
741 ± 1.8 26.2
751 ± 1.9 28
Fig. 4 e Y-shaped guide and sample cylinders used to remove samples from the grain mass.
Please cite this article as: Nourmohamadi-Moghadami, A et al., Filling of a grain silo. Part 1: Investigation of fine material distribution in a small scale centre-filled silo, Biosystems Engineering, https://doi.org/10.1016/j.biosystemseng.2020.01.003
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each sampling cylinder was removed using a vacuum cleaner and weighed using a GF-600 digital balance (A&D Company, Japan) which had a resolution ±0.01 g. Next its BCL was determined. This procedure was also repeated for the other rings from top to bottom. This new procedure was initiated to determine BCL in radial and vertical directions in the pilot scale silo. By applying this procedure, sampling was completed without disturbing the sampling area.
2.3.
Data analysis
The data obtained from CFP experiments were analysed by means of ANOVA using the statistical analysis software SPSS (SPSS Inc., Chicago, IL, USA). The experiments were conducted using a completely randomised factorial design with five treatment factors and three replications and the statistical analysis used a significance level of 5%. Nonlinear regression was used to analyse the experimental data and to develop a model of the fine material distribution in the pilot scale silo. The ability of the different models to predict the fine material distribution was evaluated by using several statistical parameters that quantified the difference between the data from the experiment and the corresponding prediction of the model. These parameters were coefficient of determination (R2), chi-square, (c2), root mean square error (RMSE) and the mean relative deviation modulus (MRDM). Eq. (2) e Eq. (5) give the formulas for calculating these parameters. A trial and error procedure was used to identify the most appropriate model, which was the one that gave the highest value of R2 and lowest values of c2, RMSE and MRDM. 2 Pn fex;i fpr;i R2 ¼ 1 Pni¼1 2 i¼1 fex;i fex;a Pn c2 ¼
i¼1
RMSE ¼
2
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 1Xn f fpr;i n i¼1 ex;i
MRDM ¼
2.4.
fex;i fpr;i nm
(2)
100Xn fex;i fpr;i i¼1 n fex;i
(3)
(4)
(5)
Non-uniformity factor
In the investigation of the fine material distribution in the radial direction at a certain height from the bottom of the silo (for a certain ring), a non-uniformity factor (NUF), as used by Shinohara et al. (2001) was defined, as shown below, in terms of the coefficient of variation: NUFR ¼ Fig. 5 e (a) A sketch showing the sampling positions, where (b) and (c) are top views of the locations where samples were removed.
s BCI
(6)
and s2 ¼ 0
of samples taken from three points which are on the circle A . Using this procedure, the flow of material into the silo was considered in different radial directions. The material inside
4 2 1X BCL;i BCI 3 i¼1
(7)
where s is the deviation of BCL at different sampling positions along the radial direction (BCL,i) compared to the initial
Please cite this article as: Nourmohamadi-Moghadami, A et al., Filling of a grain silo. Part 1: Investigation of fine material distribution in a small scale centre-filled silo, Biosystems Engineering, https://doi.org/10.1016/j.biosystemseng.2020.01.003
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percent BCFM in the shelled corn used for the test BCI. Also, for the silo, which consisted of five separate rings as explained previously, the overall non-uniformity factor is given by: NUFS ¼
3.
5 1X NUFR;j 5 j¼1
(8)
Results and discussion
Section 3.1 presents the results of the ANOVA for assessing the significance of the variations related to the main parameters. Section 3.2 describes the results of the experiments including the variations in percentages of fine material in the radial and vertical directions and the effects of initial percent BCFM, volume flow rate, and fill pipe diameter. The model of the distribution of fine material is described in section 3.3.
3.1.
Data analysis
Table 2 summarises the results of the ANOVA that assessed the significance of the variations related to the main parameters of vertical (Z) and radial (R) position, initial percent BCFM (BCI), volume flow rate (Q) and fill pipe diameter (DF). The effects of all parameters (and also all interactions) were significant at the 5% probability level. Therefore, it can be concluded that BCL is a function of BCI, Q, DF, R and Z. Furthermore, a matrix of Pearson correlation coefficients between variables, as well as the corresponding p-values are given in Table 3 in order to determine the significance of the relationship between variables. As can be seen in the Table, no significant relationship was found between input variables (main parameters) while, there was a significant relationship between all the input variables and output variable (BCL). The Pearson coefficients indicated that the association between input variables BCI, Q, R and Z and output variable BCL is stronger than that between DF and BCL. Another finding was that there was a positive association between Z and BCL while a negative association was found between BCL and other rest parameters (BCI, Q, R and DF).
3.2.
Effect of main parameters
3.2.1.
Distribution of fines along a radial direction
Figure 6a is a hypothetical diagram showing a 3D view of a sector from the layer of grain flowing on the inclined surface
of the heap (Fig. 6b) inside the test silo. The movement of grain in the layer is similar to the flow in a gradually expanding channel. As R increases the thickness of the flowing layer decreases and the velocity decreases along the surface of the heap. This decrease in thickness does not show up in the 2D analysis of the flowing layer (see Fig. 1c). Figure 7 is a graph showing the values of BCL along the radius of the silo (points O to A in Fig. 5b) for ring 1 (Z ¼ 0.21) through ring 5 (Z ¼ 0.79). The local percentage BCFM (BCL) along the flowing layer decreases nonlinearly and the curve drawn through the values at the sampled locations is concave downward (the Pearson coefficient value reported in Table 3 indicates a negative association between R and BCL). The same results were reported by Jayas et al. (1987) and Shinohara et al. (2001). This decrease is probably a result of the sifting effect. There is a high concentration of fines at the heap centre and as the flowing material diverges along a radial direction, fines are spread farther from each other. Also, due to the sifting effect, more fines remain in the sections closer to the centre of the silo. So, the rate of change in BCL between sections 1 and 2 is less than that between sections 2 and 3 and also between sections 3 and 4. The experiments revealed that, in a central filling process, the initial BCFM can be approximated by calculating the weighted mean of the local BCFM measured along the radius of the silo. Figure 5b is a sketch of a top view of the test bin that shows the sampling locations (hollow dots represent the centre of the sampling cylinders) using the sampler and sampling guide. The sampling points that are farther from the centre of the silo contribute more weight than other sampling points (for example in Fig. 5b, point A has the greatest weight and point O has the least weight). As can be determined from examining Fig. 5, the weight at sampling points O, C, B and A (Fig. 5b) is proportional to the area of zones (O00 , C00 , B00 and A00 (Fig. 5c), respectively) corresponding to these points. As mentioned before, when granular materials are poured on to a heap, they flow radially in all directions down the heap. As a result, by increasing the distance from the centre of the silo fines are spread in wider area. Therefore, from the mass balance point of view, the angular displacement of fines as well as annular zone of each sampling location must also be taken into account in distribution of fine. Considering above explanations, the initial BCFM at a given height can be approximated by following equation: P4 BCI ¼
Table 2 e The results of an ANOVA used for assessing the significance of each of the main parameters. Source of variation BCI Q DF Z R Error Total
Degree of freedom
Sum of Squares
Mean Square
F value
2 2 2 4 3 1078 1620
7462.2 447.2 50.2 1051.5 18,486.3 16.9 209,167.5
3731.086 223.609 25.107 262.869 6162.094 0.016
238,353.8* 14,285.2* 1603.9* 16,793.3* 393,662.7*
*Significant at P < 0.05.
Wr;i BCL;i P4 i¼1 Wr;i
i¼1
(9)
where Wr,1, Wr,2, Wr,3 and Wr,4 are the relative weights at points O, C, B and A (the area of zones O00 , C00 , B00 and A00 ), respectively. For example, in Fig. 7 the weighted mean of BCL for ring 1 is: ((0.06 19.7%) þ (0.49 17.7%) þ (0.98 11.8%) þ (1.60 2.3%))/3.14 ¼ 8% which is approximately equal to the value of initial BCFM, 7.5%. It can be concluded that, in a centre filled silo the weighted mean of the local percent BCFM could be used to obtain a good estimate of the initial percent BCFM in the sample. This also shows the validity of the tests. In other words, to accurately estimate the value of initial BCFM or other computations such as estimating the mass of
Please cite this article as: Nourmohamadi-Moghadami, A et al., Filling of a grain silo. Part 1: Investigation of fine material distribution in a small scale centre-filled silo, Biosystems Engineering, https://doi.org/10.1016/j.biosystemseng.2020.01.003
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Table 3 e The Pearson correlation coefficient between variable as well as the corresponding p-values. Q Q DF Z R BCI BCL a
Pearson Correlation Sig. (2-tailed) Pearson Correlation Sig. (2-tailed) Pearson Correlation Sig. (2-tailed) Pearson Correlation Sig. (2-tailed) Pearson Correlation Sig. (2-tailed) Pearson Correlation Sig. (2-tailed)
1 0.000 1 0.000 1 0.000 1 0.000 1 0.120a 0.000
DF 0.000 1 1 0.000 1 0.000 1 0.000 1 0.037 0.135
Z 0.000 1 0.000 1 1 0.000 1 0.000 1 0.185a 0.000
R
BCI
BCL
0.000 1 0.000 1 0.000 1 1
0.000 1 0.000 1 0.000 1 0.000 1 1
0.120a 0.000 0.037 0.135 0.185a 0.000 0.740a 0.000 0.494a 0.000 1
0.000 1 0.740a 0.000
0.494a 0.000
Correlation is significant at the 0.01 level (2-tailed).
product stored in the silos, sampling points should not be randomly selected. As shown in Fig. 7 there is an area of convergence (dashed blue circle) through which all lines drawn through the points pass. This area appeared in the region between R ¼ 0.56 and R ¼ 0.84 (R ¼ 0.7 ± 0.14) in all experiments. In the present study this range is referred to as the convergence range. In practice, sampling should be done within this range. The lines drawn through the initial BCFM (BCI) values always lie within the convergence range. It also means that the value of BCI can always be found within this range. This can be justified as follows. The value of BCI was always between the weighted means of the BCL values for sampling points Fig. 7 e Distributions of local BCFM (BCL) along the radial direction at different heights (for BCI ¼ 7.5%, Q ¼ 0.5 L s¡1 and DF ¼ 84 mm).
located in the circle M (encompassing circles C0 and B0 and point O) and the value of BCL for the sampling point (point A) in shaded zone (Fig. 5b). Recall that in the previous example,
Fig. 6 e (a) A 3D view of a sector from the flowing layer, (b) a side view of half of the test bin showing the flowing layer. The arrows indicate the relative magnitudes of the velocities of the material flowing in the layer.
Fig. 8 e The trends in the local BCFM (BCL) at different distances from the centre of the silo (R) as a function of grain depth in the silo (Z) (for BCI ¼ 7.5%, Q ¼ 0.5 L s¡1 and DF ¼ 105 mm).
Please cite this article as: Nourmohamadi-Moghadami, A et al., Filling of a grain silo. Part 1: Investigation of fine material distribution in a small scale centre-filled silo, Biosystems Engineering, https://doi.org/10.1016/j.biosystemseng.2020.01.003
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Table 4 e Comparison of non-uniformity factor (NUF) when using CFP methods to fill the test silo. Other factors were varied as listed in order to achieve a wide range of experimental conditions. No.
BCI (%)
Q (L s1)
DF (mm)
1
5
0.5
84
2
5
0.5
105
3
5
0.5
120
4
7.5
0.5
105
5
7.5
1
105
6
7.5
1.5
105
7
5
1.5
84
a b
Z 0.79 0.64 0.50 0.35 0.21 0.79 0.64 0.50 0.35 0.21 0.79 0.64 0.50 0.35 0.21 0.79 0.64 0.50 0.35 0.21 0.79 0.64 0.50 0.35 0.21 0.79 0.64 0.50 0.35 0.21 0.79 0.64 0.50 0.35 0.21
NUFR (%) 162.8 144.0 124.1 101.8 78 159.6 142.0 123.6 98.2 74.3 145.4 135.4 116.8 92.1 61.8 100.4 91.5 80.8 67.2 53.8 94.2 85.9 74.8 61.2 46.7 78.2 67.9 55.1 40.47 26.00 111.92 98.91 83.01 65.90 44.10
No.
BCI (%)
Q (L s1)
DF (mm)
Z
NUFR (%)
NUFS (%)
8
7.5
1.5
84
9
10
1.5
84
110.4
10
7.5
1
84
78.8
11
7.5
1
120
72.
12
10
0.5
120
53.6
13
10
1
120
80.7
14
10
1.5
120
82.3 71.9 57.6 42.6 28.2 63.1 56.0 47.7 38.5 30.2 100.4 91.5 80.8 67.2 53.8 86.6 74.2 59.7 45.9 31.0 84.6 79.7 70.5 51.7 31.9 67.4 56.5 44.7 34.6 24.2 50.4 45.1 38.7 29.3 21.2
56.5
119.5
0.79 0.64 0.50 0.35 0.21 0.79 0.64 0.50 0.35 0.21 0.79 0.64 0.50 0.35 0.21 0.79 0.64 0.50 0.35 0.21 0.79 0.64 0.50 0.35 0.21 0.79 0.64 0.50 0.35 0.21 0.79 0.64 0.50 0.35 0.21
NUFS (%) 122.2
a
47.1
78.8
59.5
63.7
45.3
37.0b
Highest value of NUFS in CFP experiments. Lowest value of NUFS in CFP experiments.
BCI was 7.5% which was between the weighted mean of BCL for sampling points in circle M, 14% and the value for the sampling point located in the shaded zone, 2.3%. Note that, the area of shaded zone (Fig. 5b|) is equal to the circle M. Thus, circle M is a boundary circle passing through the midpoint (R ¼ 0.7) of the convergence range. According to Fig. 5b the radius of the circle M (r0 ) can be found by equating the area bounded by circle M and the silo wall (shaded area) to the area of circle M (r0 ¼ (r00 √2)/2 z 0.7 r00 ). In general, it can be concluded that to accurately estimate the value of initial BCFM or other computations such as the mass of product stored in centre filled silos, sampling should be done within convergence range. It should be noted that more experiments are needed in full sized silos to prove this hypothesis.
typical case, BCI ¼ 7.5%, Q ¼ 0.5 L s1 and DF ¼ 105 mm while the same trends were found for other test cases). The Pearson coefficient value reported in Table 3 indicates a positive association between Z and BCL. The trend is different at R ¼ 0.84 where BCL decreased with increasing Z. According to the data given in Table 4, NUFR increased with increasing height (Z). It means that as the grain level in the silo increased, a smaller amount of fine was transferred to the periphery of the bin. This can be explained by the fact that as the silo is filled and the heap rises (Z increases), the distance the material falls decreases and the velocity of the material in the flowing layer decreases. Accordingly, as Engblom et al., 2012 stated, as Z increases, less fine material reaches the outer wall resulting in less uniformity in percentage fines in the radial direction.
3.2.2.
3.2.3.
Effect of height
As can be clearly observed in Fig. 7, when Z decreased there was less variation in BCL between the centre and outer wall of the bin. Figure 8 reveals that at R ¼ 0, 0.28 and 0.56, BCL increased linearly as Z increased (the figure is related to a
Effects of initial BCFM
Figure 9 shows the trends (for a typical case, Z ¼ 0.35, Q ¼ 1 L s1 and DF ¼ 105 mm) in BCL (the same trends were found for other test cases) from R ¼ 0 to R ¼ 0.84 at three levels of BCI. It is obvious BCL increases linearly with increasing BCI
Please cite this article as: Nourmohamadi-Moghadami, A et al., Filling of a grain silo. Part 1: Investigation of fine material distribution in a small scale centre-filled silo, Biosystems Engineering, https://doi.org/10.1016/j.biosystemseng.2020.01.003
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Fig. 9 e The trends in the local BCFM (BCL) at various distances from the centre (R) as influenced by different levels of initial BCFM (for Z ¼ 0.35, Q ¼ 1 L s¡1 and DF ¼ 105 mm).
Fig. 10 e The trends in the local BCFM (BCL) as influenced by different volume flow rates (for BCI ¼ 10%, DF ¼ 120 mm and Z ¼ 0.5).
(the Pearson coefficient value reported in Table 3 indicates a positive association between BCI and BCL). However, the NUFS decreased as BCI increased (. This can be explained by observing that at higher BCI, fine material in the flowing layer percolates to the lower layers along the surface of the heap and therefore more fine material is transferred to the silo outer wall. In other words, when the amount of fine material is high, there is less sifting. There is a second factor that could also help to explain this phenomenon. Material containing a higher percentage of fine materials can form a steeper heap (because the angle of repose is greater) and this leads to faster flow of the material in the flowing layer. Therefore, more fine material reaches the silo wall. It is concluded that the sifting effect in a central filling process is more pronounced with lower BCI than with higher BCI. This agrees with the results of
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Fig. 11 e Distribution profile of local BCFM (BCL) along radial direction in silo as influenced by different volume flow rates (for BCI ¼ 5%, DF ¼ 84 mm and Z ¼ 0.79).
Fig. 12 e The trends in the local BCFM (BCL) at different distances from the centre (R) as influenced by different fill pipe diameters (for BCI ¼ 10%, Q ¼ 1.5 L s¡1 and Z ¼ 0.64).
the studies conducted by Schulze (2008), Shinohara et al. (2001) and Jain, Metzger, and Glasser (2013). As a result, the distribution of fine material in centre-filled silos with higher BCI is more uniform than in silos with lower BCI. However, it should be noted that, notwithstanding the above results, high amounts of fines are undesirable in stored grain.
3.2.4.
Effect of volume flow rate
The effect of volume flow rate on local percentage BCFM (BCL) at the four radial positions is shown in Fig. 10 (the figure is related to a typical case BCI ¼ 10%, DF ¼ 120 mm and Z ¼ 0.5 while the same trends were found for other test cases). At R ¼ 0, 0.28 and 0.56, BCL decreased with increasing volume
Please cite this article as: Nourmohamadi-Moghadami, A et al., Filling of a grain silo. Part 1: Investigation of fine material distribution in a small scale centre-filled silo, Biosystems Engineering, https://doi.org/10.1016/j.biosystemseng.2020.01.003
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Fig. 13 e Distribution of local BCFM (BCL) for different fill pipe diameters (for BCI ¼ 7.5%, Q ¼ 0.5 L s¡1 and Z ¼ 0.79).
flow rate but at the periphery of the silo (R ¼ 0.84) BCL increased with increasing volume flow rate (the Pearson coefficient value reported in Table 3 indicates a negative association between Q and BCL). This means that, at a higher volume flow rate, more fine material is transferred to the periphery. As can be observed in Fig. 11 (the figure is related to a typical case, BCI ¼ 5%, DF ¼ 84 mm and Z ¼ 0.79 while the same trends were found for other test cases), as volume flow rate increases the BCL distribution becomes more uniform. Accordingly, NUFS decreases with increasing volume flow rate. Fan et al., 2017 stated that fine particles gain momentum when colliding with coarser particles (similar to what happens when a tennis ball collides with a basketball). As a result, they
Fig. 15 e Prediction of fine (BCL) distribution in silo after filling, (a) surface plot (b) contour plot.
bounce further down the heap than coarser particles. This effect becomes more prominent at higher volume flow rates where the flow layer is thicker (Fan et al., 2012; Koeppe, Enz, & Kakalios, 1998; Schulze, 2008). Before the fines come to rest in the static bed of the heap, they move farther down the heap in the flowing layer.
3.2.5.
Fig. 14 e Effect of fill pipe diameter on fine (BCL) distribution.
Effect of fill pipe diameter
Tests were conducted using fill pipes with diameters of 84 mm, 105 mm, and 120 mm. As shown in Fig. 12 (the figure is related to a typical case, BCI ¼ 10%, Q ¼ 1.5 L s1 and Z ¼ 0.64 while the same trends were found for other rest cases) at R ¼ 0, 0.28 and 0.56, BCL decreased with increasing fill pipe diameter but at the periphery of the silo (R ¼ 0.84) BCL increased with increasing diameter (the Pearson coefficient value reported in Table 3 indicates a negative association between DF and BCL). The plots shown in Fig. 13 (the figure is related to a typical case, BCI ¼ 7.5%, Q ¼ 0.5 L s1 and Z ¼ 0.79 while the same trends were found for other test cases) demonstrate that fine material distribution is more uniform at larger fill pipe diameters. In other words, the NUFS decreased with increasing pipe diameter. As illustrated in Fig. 14 larger fill pipe makes
Please cite this article as: Nourmohamadi-Moghadami, A et al., Filling of a grain silo. Part 1: Investigation of fine material distribution in a small scale centre-filled silo, Biosystems Engineering, https://doi.org/10.1016/j.biosystemseng.2020.01.003
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Table 5 e Constants of the distribution model for CFP experiments. Constant a1
a2
a3
a4
a5
a6
a7
a8
Value 1.042 1.531 0.013 9.413 22.148 14.013 16.321 20.558
the heap more chamfered at the top (larger area onto which the materials fall) and shortens its height (sloping sides are shorter) which reduces the distance along the surface of the heap where sifting can occur. Another way to explain this is that granular materials flow more easily in a larger pipe and therefore there is less energy loss than in smaller pipes. When the material has more energy, it can more easily reach the silo wall which produces a slightly more even fine material distribution. According to Fig. 12 and the values of NUF in Table 4, the change in BCL when DF increased from 84 to 105 mm was less than when DF increased from 105 to 120 mm. Within this range in pipe diameters, the uniformity of the fine material distribution increased more rapidly as the fill pipe diameter increased. An examination of Table 4 indicates that the best (most uniform) distribution of fines occurred in row 14 where NUFS
was a minimum value (36.9%). Also, the maximum value of NUFS was found to be 122.2% in row 1. The surface plot (Fig. 15a) and contour plot (Fig. 15b) show how BCL changes with individual or simultaneous changes of R and Z. It is apparent that there was a considerable accumulation of fines at the centre of the silo and that this increases when Z (grain depth) increases. There was a much lower concentration of fine material around the periphery of the silo, especially at greater grain depths (greater values of Z). This means that the maximum non-uniformity in fine material distribution occurs near the top of the silo (greater Z values).
3.3.
Modelling of distribution of fines
Considering all the parameters discussed in section 3.2, the following model was proposed for the purpose of describing the effects of treatments namely, BCI, Q, DF, Z and R on the fine material distribution: BCL ¼ a1 BCI þ a2 Q þ a3 DF þ a4 R þ a5 Z þ a6 expðRÞ þ a7 ZR þ a8 (10) where constants a1 to a8 are given in Table 5. This model was the most appropriate with the values of 0.94, 1.14, 1.06, 11.39 for R2, c2, RMSE and MRDM, respectively. BCL is a nonlinear function of R and a linear function of Z, BCI, Q and DF. Although including more and complex terms increases the model complexity, when BCL was assumed to include an exponential function of R and an implicit function of Z and R (ZR), the quality of the model improved significantly. Figure 16a illustrates the promising ability of the model for the prediction of BCL. Figure 16b shows the distribution of prediction residual error (PRE) for the model. It demonstrates that the values of PRE were randomly scattered and there was no obvious trend (sensitivity).
4.
Fig. 16 e (a) Comparison between prediction of the developed model and experimental data (BCL) and (b) distribution of PREs of the developed model for prediction of BCL in silo.
11
Conclusions
This study investigated the distribution of fine material during filling of a small scale silo as influenced by the parameters initial percentage BCFM, volume flow rate and fill pipe diameter. A new approach was developed for measuring the fine material in the radial and vertical directions within the silo. Using this approach, sampling could be done without disturbing the area where sampling was done. The experiments revealed that in a central filling process the initial BCFM can be approximated by calculating the weighted mean of the local BCFM measured along the radius of the silo. A convergence range was observed on plots of fine material distribution in which the value of initial percentage BCFM was always found within that range. The results indicated that the distribution of fine material became more uniform at lower grain depths and for increasing initial BCFM, volume flow rate and fill pipe diameter. There was a considerable accumulation of fine material at the centre of the silo. The percentage increases with increase in grain depth (greater Z). Also, a low concentration of fine material occurred around the periphery of the silo, especially for greater grain depths when the test silo was nearly full. That means that maximum non-uniformity of fine material
Please cite this article as: Nourmohamadi-Moghadami, A et al., Filling of a grain silo. Part 1: Investigation of fine material distribution in a small scale centre-filled silo, Biosystems Engineering, https://doi.org/10.1016/j.biosystemseng.2020.01.003
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distribution occurs near the top surface of the silo (higher values of Z). The distribution of fine material was modelled by developing an equation that took into account the effects of the important parameters in central filling point (CFP) experiments. Based on statistical parameters R2, c2, RMSE and MRDM, the model fit the experimental data reasonably well. The results of this study can lead to a deeper understanding of factors that affect the distribution of fine material in silos.
5. Recommendations for future studies and developments According to the results of this study, the higher values of volume flow rate lead to a more uniform fine material distribution. However, it is not known how much the volume flow rate can be increased because at higher flow rates there is a risk of breaking the grain kernels during the filling process. Other useful techniques such as DEM and machine vision can be employed to investigate the distribution of fines in full scale bins and silos. In addition, the effects of other important parameters on distribution of fines during filling of a silo should be studied, such as moisture content, angle of repose, and internal friction. Due to irregular shapes and a wide range of different sizes of fine material, the study of some physical properties such as mean size and shape indices is almost impossible for this material. However, the study of the effects of such physical properties of whole kernel on fine material distribution is recommended. When a mixture of different-sized particles pours into a silo, three different configurations have been observed. These configurations are: stratification, segregation and mixing (Fan et al., 2012). These have been observed in quasi-twodimensional bounded heap. This leads to the question of whether similar processes occur in 3D bounded heap flow and how they can impact the distribution of the fines during filling a silo. These questions call for additional studies to improve our understanding of fine material distribution in grain silos.
Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
references
ASABE. (2008). ASAE S352.2. Moisture measurement- Unground grain and seeds. St. Joseph, MI, USA: ASABE. Bartosik, R. E., & Maier, D. E. (2006). Effect of airflow distribution on the performance of NA/LT in-bin drying of corn. Transactions of the ASABE, 49(4), 1095e1104. Combarros, M. G., Feise, H. J., Strege, S., & Kwade, A. (2016). Segregation in heaps and silos: Comparison between
experiment, simulation and continuum model. Powder Technology, 293, 26e36. Engblom, N., Saxen, H., Zevenhoven, R., Nylander, H., & Enstad, G. G. (2012). Segregation of powder mixtures at filling and complete discharge of silos. Powder Technology, 215e216, 104e116. Fan, Y., Boukerkour, Y., Blanc, T., Umbanhowar, P. B., Ottino, J. M., & Lueptow, R. M. (2012). Stratification, segregation, and mixing granular materials in quasi-two-dimensional bounded heaps. Physical Review E, 86, 051305. Fan, Y., Jacob, K. V., Freireich, B., & Lueptow, R. M. (2017). Segregation of granular materials in bounded heap flow: A review. Powder Technology, 312, 67e88. Fan, Y., Umbanhowar, P. B., Ottino, J. M., & Lueptow, R. M. (2013). Kinematics of monodisperse and bidisperse granular flows in quasi-two-dimensional bounded heaps. Proceedings of the Royal Society A, 469, 20130235. Garg, D. (2005). Modeling non-uniform airflow and its application for partial chilled aeration using PHAST-FEM. MS thesis. West Lafayette, Indiana: Purdue University. Jain, A., Metzger, M. J., & Glasser, B. J. (2013). Effect of particle size distribution on segregation in vibrated systems. Powder Technology, 237, 543e553. Jayas, D. S., Sokhansanj, S., Moysey, E. B., & Barber, E. M. (1987). Distribution of foreign material in canola bins using a spreader or spout. Canadian Agricultural Engineering, 29, 183e188. Koeppe, J. P., Enz, M., & Kakalios, J. (1998). Phase diagram for avalanche stratification of granular media. Physical Review E, 58, R4104eR4107. Lawrence, J., & Maier, D. E. (2011). Three-dimensional airflow distributions in peaked, leveled and cored grain mass configurations. Biosystems Engineering, 110(3), 321e329. Mohsenin, N. N. (1986). Physical properties of plant and animal materials. New York: Gordon and Breach Science Publisher. Nourmohamadi-Moghadami, A., Zare, D., Stroshine, R., & Kamfiroozi, S. (2020). Filling of a grain silo. Part 2: A new filling method for uniform distribution of fines in a small scale silo. Biosystems Engineering. https://doi.org/10.1016/ j.biosystemseng.2020.01.001 (in press). Noyes, R., Navarro, S., & Armitage, D. (2002). Supplemental aeration systems. In S. Navarro, & R. Noyes (Eds.), The mechanics and physics of modern grain aeration management (pp. 413e488). Boca Raton: CRC Press. Savage, S. B. (1993). Mechanics of granular flows. In K. Hutter (Ed.), In Continuum mechanics in environmental sciences and geophysics (pp. 467e522). Wien-New York: Springer. Savage, S. B., & Lun, C. K. K. (1988). Particle size segregation in inclined chute flow of dry cohesionless granular solids. Journal of Fluid Mechanics, 189, 311e335. Schulze, D. (2008). Powders and bulk solids - behaviour, characterization, storage and flow. Verlag Berlin Heidelberg: Springer (chapter 13). Shinohara, K., & Golman, B. (2002). Segregation indices of multisized particle mixtures during the filling of a two-dimensional hopper. Advanced Powder Technology, 13(1), 93e107. Shinohara, K., Golman, B., & Nakata, T. (2001). Size segregation of multicomponent particles during the filling of a hopper. Advanced Powder Technology, 10(1), 333e343. Stephens, L. E., & Foster, G. H. (1976). Grain bulk properties as affected by mechanical grain spreaders. Transactions of the ASAE, 19(2), 354e358. Stroshine, R. (2004). Physical properties of agricultural materials and food products. Indiana: West Lafayette (Chapter 2). USDA. (2013). Grain inspection, packers and stockyards, grain inspection handbook, book II. Washington, D.C: USDA.
Please cite this article as: Nourmohamadi-Moghadami, A et al., Filling of a grain silo. Part 1: Investigation of fine material distribution in a small scale centre-filled silo, Biosystems Engineering, https://doi.org/10.1016/j.biosystemseng.2020.01.003
Available online at www.sciencedirect.com
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Research Paper
Filling of a grain silo. Part 1: Investigation of fine material distribution in a small scale centre-filled silo A. Nourmohamadi-Moghadami a, D. Zare a,*, C.B. Singh b, R.L. Stroshine c a
Department of Biosystems Engineering, Shiraz University, Shiraz, Iran School of Engineering, University of South Australia, Mawson Lake, 5095, Australia c Agricultural and Biological Engineering Department, 225 South University Street, Purdue University, West Lafayette, IN, 47907-2093, USA b
article info
When a silo is being filled with the granular material containing a range of particle sizes,
Article history:
larger particles tend to flow towards the silo wall while the smaller particles accumulate
Received 10 March 2019
near the centre of the silo. Shelled corn was used in this study. This work encompasses the
Received in revised form
first part, where the distribution of broken corn and foreign material (BCFM) was investi-
27 July 2019
gated in a small scale silo filled from a central filling point (CFP). Factors that were varied
Accepted 1 January 2020
included initial BCFM, volume flow rate of material and fill pipe diameter. A new approach
Published online xxx
was developed to ensure accurate sampling in the radial and vertical direction in the silo. The results indicated that the distribution of fine material became more uniform at lower
Keywords:
grain depths and for increasing initial BCFM, volume flow rate and fill pipe diameter. The
Central filling
accumulation of fine material at the centre of the silo increased with increase in the dis-
Fine distribution
tance from the bottom of the silo. In addition, a nonlinear model was developed to predict
Material flow
BCFM distribution in CFP method. Based on statistical parameters, namely, coefficient of
Grain silo
determination (R2), Chi-square (c2), RMSE (root mean square error) and MRDM (mean relative deviation modulus), the model fit the experimental data reasonably well. © 2020 IAgrE. Published by Elsevier Ltd. All rights reserved.
1.
Introduction
When a silo is being filled with granular material containing a range of particle sizes, the fine material consists of broken grain kernels and some trash and small foreign material particles which accumulate under the filling point (Stephens & Foster, 1976). Larger particles that have more mass, a longer trajectory and less surface friction than small particles
tend to flow towards the silo wall while the smaller particles accumulate near the centre of the grain mass. In other words, smaller particles remain in the cavities between the kernels whereas the majority of the larger particles migrate towards the bin wall. The inclined surface of a stationary particle bed acts like a sieve through which the smaller particles fall (Savage, 1993; Savage & Lun, 1988; Schulze, 2008). This effect is called sifting (Schulze, 2008). As a result of this effect, the
* Corresponding author. Department of Biosystems Engineering, Shiraz University, Visiting Prof. Mechanical Eng., Dept., University of South Australia, Mawson Lakes Campus, SA 5095, Australia. Fax: þ98 71 32286187. E-mail addresses: [email protected], [email protected] (D. Zare). https://doi.org/10.1016/j.biosystemseng.2020.01.003 1537-5110/© 2020 IAgrE. Published by Elsevier Ltd. All rights reserved. Please cite this article as: Nourmohamadi-Moghadami, A et al., Filling of a grain silo. Part 1: Investigation of fine material distribution in a small scale centre-filled silo, Biosystems Engineering, https://doi.org/10.1016/j.biosystemseng.2020.01.003
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Nomenclature A BCI BCL BCL.i Dg DF Lg NUFR NUFR,j NUFS m n Q R R2 T Tg vr W Wg Wr,i Z c2 s
fex;i fpr;i fex;a
cross section area of apparatus in 2D heap initial percent BCFM local percent BCFM ith local percent BCFM geometric mean diameter (mm) fill pipe diameter (mm) length (mm) non-uniformity factor for a ring (at a certain height in silo) non-uniformity factor for ith ring non-uniformity factor for a silo number of constants in fine distribution model number of observations volume flow rate scaled distance from the centre of the silo (dimensionless) coefficient of determination gap thickness between sidewalls in 2D heap thickness (mm) rise velocity apparatus width in 2D heap width (mm) ith relative weight scaled distance from the bottom of the silo (dimensionless) Chi-square the deviation of BCL at different sampling position along the radial direction (BCL,i) from BCI ith experimental data ith predicted data average of experimental data
inter-seed relative humidity in zones with low air flow, allowing the development of insects, mite species and other infestations (Noyes et al., 2002). In the second part of this research (Nourmohamadi-Moghadami, Zare, Stroshine, & Kamfiroozi, 2020) a new filling method, variable filling point (VFP), was developed and tested as a means of reducing the non-uniform distribution of fine material during filling of a small scale silo. For optimal performance of industrial processes such as aeration of stored products in silos, filling of silos, and handling of granular materials, it is necessary to evaluate the effect of properties of the product and the characteristics of the handling system on the distribution of the fine materials. During conventional filling of a silo, a conical pile is formed so that falling materials flow radially in all directions (Fig. 1a) down the sides of the heap creating a layer of moving material on the surface of the pile. Because particle motion is stopped or bounded by the walls, this type of flow is called bounded heap flow (Fan, Jacob, Freireich, & Lueptow, 2017). Fan et al. (2012) and Fan, Umbanhowar, Ottino, and Lueptow (2013) used a quasi-two-dimensional apparatus to study bounded heap flow (Fig. 1). Bounded heap flow is one of several types of free surface flow which occur in silos during filling. As indicated in Fig. 1b, the filling process includes three stages. In stage I, the falling materials form a rather irregularly shaped heap at the bottom of the
Abbreviations 2D two dimensional 3D three dimensional ANOVA analysis of variance BCFM broken corn and foreign material CFP central filling point MRDM mean relative deviation modulus GMD geometric mean diameter PRE prediction residual error RMSE root mean square error VFP variable filling point
smaller particles form a vertical cylindrical zone of high concentration at the silo centre (Noyes, Navarro, & Armitage, 2002). In corn silos, concentration of fine material under the filling spout is inevitable and this can cause serious problems. The localised concentration of fine material causes non-uniform airflow through the grain mass during the aeration process. This decreases the specific airflow through the grain in the centre of the grain mass compared to the periphery (Bartosik & Maier, 2006; Garg, 2005; Lawrence & Maier, 2011). This leads to higher temperatures and higher
Fig. 1 e (a) Sketch showing a top view of a 3D heap. The arrows indicate flow of the test material. The dashed box is a top view of the quasi-2D heap used here. (b) Sketch showing a side view of a quasi-2D heap rising at a rise velocity of vr ¼ Q/A, where Q is the volume flow rate and A ¼ TW (T and W are, respectively, the gap thickness between the sidewalls of the apparatus and the apparatus width). The three stages of heap flow are: (I) initiation (II) lateral growth and (III) steady filling (redrawn from Fan et al., 2012). (c) A side view of a 2D heap showing velocity profiles of the flowing material (redrawn from Fan et al., 2013).
Please cite this article as: Nourmohamadi-Moghadami, A et al., Filling of a grain silo. Part 1: Investigation of fine material distribution in a small scale centre-filled silo, Biosystems Engineering, https://doi.org/10.1016/j.biosystemseng.2020.01.003
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container. A little while afterwards, the surface of the heap forms an angle with the bottom of the container and its base grows laterally until it reaches the bounding walls (stage II). In stage III, the heap rises steadily at a constant velocity (vr). Figure 1c shows that in this stage the local flow rate decreases linearly with distance from the centre in the downstream direction, resulting in a gradient of streamwise velocity in the streamwise direction (because as flowing materials approach the endwall, the velocity decreases) (Fan et al., 2013). Based on the above discussion, it can be concluded that the velocity of materials through the flowing layer can affect the fine material distribution. Jayas, Sokhansanj, Moysey, and Barber (1987) investigated the distribution of foreign material (chaff and fines) in a bin filled with Tobin canola using two filling methods, a central spout and a conical spreader. They observed that a grain spreader concentrated more fines near the centre and resulted in only slightly more uniform distribution of fines than the use of a spout. The authors also proposed a quadratic equation to describe the distribution of chaff and fines. Because of difficulties in controlling experimental conditions, they did not consider the effects of other parameters on fine material distribution such as initial fine material content, feed rate and, for the central spout method, the inlet diameter. Shinohara, Golman, and Nakata (2001) and Shinohara and Golman (2002) studied the effects of parameters such as feed rate, initial concentration of the components and number of components on the segregation of multi-sized particle mixtures during the filling of a two-dimensional hopper. The results showed that the degree of segregation was significant at low feed rates and for low concentrations of the smallest component. Schulze (2008) stated that as the flow rate increases the flowing layer becomes thicker. Thus, smaller particles move farther down the pile before they percolate to lower layers. For such conditions, more fine material reaches the bounding wall. Combarros, Feise, Strege, and Kwade (2016) investigated the magnitude of segregation of sand particles in a pilot scale silo during filling and discharge. Segregation after filling was studied at different points over the width and the height of the silo. They observed that finer particles are found in the centre and at the bottom of the silo. They also found that the concentration of coarse particles was a quadratic function of the silo width and increased linearly with the silo height. Engblom, Saxen, Zevenhoven, Nylander, and Enstad (2012) studied experimentally the segregation of binary and ternary mixtures as well as commercial construction materials. They presented a model to describe the concentration of fine particles during filling which showed good agreement with experimental data. The variables that affected the distribution of particles during filling were mass fraction of fines, particle size ratio (coarse/fine), particle solid density ratio (coarse/fine), free fall distance, silo diameter and inlet diameter. A survey of the literature indicates there has not been a comprehensive study of the effects of parameters such as initial fine material content, volume flow rate and inlet diameter on fine material distribution in granular agricultural products in the radial and vertical directions in a 3D silo. To conduct such studies, it is preferable to first provide a pilot environment. Therefore, in this study an experimental silo
3
was constructed to accurately measure BCFM along radial and vertical directions. The main objectives of present study were: a) to study fine changes as affected by major parameters: initial fine material content, flow (feed) rate and fill pipe (inlet) diameter b) to model changes in the fine material distribution for the different conditions.
2.
Material and methods
2.1.
Description of the experimental facilities
The components of the system include a main container with a volume of 1.2 m3, an elevator, a trapezoidal container and an experimental silo (Fig. 2). The elevator was used to move material from the main container to the trapezoidal container. Volume flow rate of the material discharging from the trapezoidal container was controlled by a fluted roller mechanism. This made the changes in flow rate of material independent of the changes in fill pipe diameter. To avoid segregation, no pile should be formed in the trapezoidal container. For this purpose, flow rate of the material was considered the same at the inlet and outlet of the trapezoidal container. But for more confidence, a horizontal agitator was also situated in the trapezoidal container. When samples are taken the insertion of a probe into the bulk grain disturbs the area where the sample is taken. This can affect the percentage of fine material in the sample, especially in small scale silos. To ensure accurate sampling in the radial and vertical direction, a special experimental silo was constructed (Fig. 3). The silo consisted of seven rings which were installed one on top of the other. A chassis supported the rings and kept them separated from each other by a vertical distance of 15 mm. The height and diameter of each ring were 0.14 and 1 m, respectively.
Fig. 2 e Experimental set up (a) main container, (b) elevator, (c) trapezoidal container, (d) agitator, (e) fluted roller mechanism, (f) fill pipe, (g) pilot scale silo consist of seven rings.
Please cite this article as: Nourmohamadi-Moghadami, A et al., Filling of a grain silo. Part 1: Investigation of fine material distribution in a small scale centre-filled silo, Biosystems Engineering, https://doi.org/10.1016/j.biosystemseng.2020.01.003
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an inclined bottom in such a way that some of the material remained on a circular stand which was placed at the centre of the container. The angle of repose was calculated from the radius of the circular stand and the height of the cone of material formed on the stand. Digital calipers with accuracy of ±0.01 mm were used to measure geometric mean diameter (GMD) of 100 whole kernels. The GMD was obtained to be 7.8 ± 0.88 mm using following equation (Mohsenin, 1986): 13 Dg ¼ Lg Wg Tg =
Fig. 3 e Schematic of the experimental silo.
2.2.
Experimental procedure
Shelled corn of variety 704 was provided from a private grain producer in Shiraz, Fars province, Iran. In accordance with the ASABE Standard (ASABE, 2008) for whole kernel moisture measurement, the initial moisture content of corn (with sample size of 15 g) was measured using a forced convection oven (heating at 103 C for 72 h). It was found to be 14 ± 0.5% w.b. In this study, fine material content is defined as BCFM (broken corn and foreign material) which is the amount of material from the sample that passed through a 4.8 mm (12/64 in.) diameter round-hole sieve as a result of hand sieving (USDA, 2013). The effects of initial percentage BCFM (BCI), volume flow rate (Q), and fill pipe diameter (DF) in both the radial and vertical directions were investigated. The tests were conducted with three levels of BCI which were 5, 7.5 and 10%, three levels of Q were 0.5, 1, 1.5 L s1, and three levels of DF which were 84, 105 and 120 mm (some preliminary tests were carried out to evaluate the possibility of conducting the experiments at the selected levels). The experiments were replicated three times. Therefore, there were 81 runs in the experiments. Prior to experiments, corn kernels were mixed with the desired percentage of fine material. Considering parameters that could influence the distribution of the fines, the bulk density and angle of repose were measured in triplicate for the three levels of BCI (Table 1). Bulk densities of the corn kernels and fine material were measured following procedures described in Stroshine (2004). The angle of repose was measured by removing one side of a wooden container with
(1)
Before the silo was filled, a strip of scotch tape was placed over the gap between the upper and lower rings on the inner side to prevent material from exiting. After the silo was filled, six separator sheets (Fig. 3) were inserted between adjacent rings starting from the bottom and moving upwards through each successive gap until the gap beneath the top ring was reached. This kept pressure on the lower layers due to the weight of the column of material and divided the column of material into seven parts. In order to ensure that the same amount of material was in each sample, sampling had to be carried out on a flat surface formed by the material. For this reason, the upper ring and the separator sheet beneath it were removed without being sampled. This eliminated the cone shaped top surface of the material. In all experiments, it was observed that the stages initiation and lateral growth occurred into the ring at the bottom of the silo. Therefore, to avoid any influence from the variations that can occur during these stages, samples were not taken from the lower ring of the silo. A Y-shaped guide (Figs. 4 and 5b) consisting of ten small rings was used to locate the sampling points in a specific pattern. Sampling cylinders were inserted into the material in the test silo through these small rings. The height and diameter of each sampling cylinder were 0.14 and 0.09 m, respectively. Figure 5a shows the position of sampling points in the test silo. The position of each sampling point could be specified using a scaled distance from the centre (the distance from the centre divided by the radius of the silo), R and a scaled distance from the bottom of the experimental silo (the distance from the bottom divided by the height of the silo), Z. It should be noted that, although the sampling was performed in triplicate, at a given Z, the value of BCL at sampling points A, B and C (Fig. 5b) is the average of the BCL of three samples which are the same distance from the centre. For example, the value of BCL at point A is the average
Table 1 e Physical properties of the initial grain masses at three levels of initial BCFM. Initial BCFM (BCI) Bulk density (kg m3) Angle of repose (o)
0%
5%
7.5%
10%
718 ± 1.6 22.5
732 ± 1.8 24.5
741 ± 1.8 26.2
751 ± 1.9 28
Fig. 4 e Y-shaped guide and sample cylinders used to remove samples from the grain mass.
Please cite this article as: Nourmohamadi-Moghadami, A et al., Filling of a grain silo. Part 1: Investigation of fine material distribution in a small scale centre-filled silo, Biosystems Engineering, https://doi.org/10.1016/j.biosystemseng.2020.01.003
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5
each sampling cylinder was removed using a vacuum cleaner and weighed using a GF-600 digital balance (A&D Company, Japan) which had a resolution ±0.01 g. Next its BCL was determined. This procedure was also repeated for the other rings from top to bottom. This new procedure was initiated to determine BCL in radial and vertical directions in the pilot scale silo. By applying this procedure, sampling was completed without disturbing the sampling area.
2.3.
Data analysis
The data obtained from CFP experiments were analysed by means of ANOVA using the statistical analysis software SPSS (SPSS Inc., Chicago, IL, USA). The experiments were conducted using a completely randomised factorial design with five treatment factors and three replications and the statistical analysis used a significance level of 5%. Nonlinear regression was used to analyse the experimental data and to develop a model of the fine material distribution in the pilot scale silo. The ability of the different models to predict the fine material distribution was evaluated by using several statistical parameters that quantified the difference between the data from the experiment and the corresponding prediction of the model. These parameters were coefficient of determination (R2), chi-square, (c2), root mean square error (RMSE) and the mean relative deviation modulus (MRDM). Eq. (2) e Eq. (5) give the formulas for calculating these parameters. A trial and error procedure was used to identify the most appropriate model, which was the one that gave the highest value of R2 and lowest values of c2, RMSE and MRDM. 2 Pn fex;i fpr;i R2 ¼ 1 Pni¼1 2 i¼1 fex;i fex;a Pn c2 ¼
i¼1
RMSE ¼
2
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 1Xn f fpr;i n i¼1 ex;i
MRDM ¼
2.4.
fex;i fpr;i nm
(2)
100Xn fex;i fpr;i i¼1 n fex;i
(3)
(4)
(5)
Non-uniformity factor
In the investigation of the fine material distribution in the radial direction at a certain height from the bottom of the silo (for a certain ring), a non-uniformity factor (NUF), as used by Shinohara et al. (2001) was defined, as shown below, in terms of the coefficient of variation: NUFR ¼ Fig. 5 e (a) A sketch showing the sampling positions, where (b) and (c) are top views of the locations where samples were removed.
s BCI
(6)
and s2 ¼ 0
of samples taken from three points which are on the circle A . Using this procedure, the flow of material into the silo was considered in different radial directions. The material inside
4 2 1X BCL;i BCI 3 i¼1
(7)
where s is the deviation of BCL at different sampling positions along the radial direction (BCL,i) compared to the initial
Please cite this article as: Nourmohamadi-Moghadami, A et al., Filling of a grain silo. Part 1: Investigation of fine material distribution in a small scale centre-filled silo, Biosystems Engineering, https://doi.org/10.1016/j.biosystemseng.2020.01.003
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percent BCFM in the shelled corn used for the test BCI. Also, for the silo, which consisted of five separate rings as explained previously, the overall non-uniformity factor is given by: NUFS ¼
3.
5 1X NUFR;j 5 j¼1
(8)
Results and discussion
Section 3.1 presents the results of the ANOVA for assessing the significance of the variations related to the main parameters. Section 3.2 describes the results of the experiments including the variations in percentages of fine material in the radial and vertical directions and the effects of initial percent BCFM, volume flow rate, and fill pipe diameter. The model of the distribution of fine material is described in section 3.3.
3.1.
Data analysis
Table 2 summarises the results of the ANOVA that assessed the significance of the variations related to the main parameters of vertical (Z) and radial (R) position, initial percent BCFM (BCI), volume flow rate (Q) and fill pipe diameter (DF). The effects of all parameters (and also all interactions) were significant at the 5% probability level. Therefore, it can be concluded that BCL is a function of BCI, Q, DF, R and Z. Furthermore, a matrix of Pearson correlation coefficients between variables, as well as the corresponding p-values are given in Table 3 in order to determine the significance of the relationship between variables. As can be seen in the Table, no significant relationship was found between input variables (main parameters) while, there was a significant relationship between all the input variables and output variable (BCL). The Pearson coefficients indicated that the association between input variables BCI, Q, R and Z and output variable BCL is stronger than that between DF and BCL. Another finding was that there was a positive association between Z and BCL while a negative association was found between BCL and other rest parameters (BCI, Q, R and DF).
3.2.
Effect of main parameters
3.2.1.
Distribution of fines along a radial direction
Figure 6a is a hypothetical diagram showing a 3D view of a sector from the layer of grain flowing on the inclined surface
of the heap (Fig. 6b) inside the test silo. The movement of grain in the layer is similar to the flow in a gradually expanding channel. As R increases the thickness of the flowing layer decreases and the velocity decreases along the surface of the heap. This decrease in thickness does not show up in the 2D analysis of the flowing layer (see Fig. 1c). Figure 7 is a graph showing the values of BCL along the radius of the silo (points O to A in Fig. 5b) for ring 1 (Z ¼ 0.21) through ring 5 (Z ¼ 0.79). The local percentage BCFM (BCL) along the flowing layer decreases nonlinearly and the curve drawn through the values at the sampled locations is concave downward (the Pearson coefficient value reported in Table 3 indicates a negative association between R and BCL). The same results were reported by Jayas et al. (1987) and Shinohara et al. (2001). This decrease is probably a result of the sifting effect. There is a high concentration of fines at the heap centre and as the flowing material diverges along a radial direction, fines are spread farther from each other. Also, due to the sifting effect, more fines remain in the sections closer to the centre of the silo. So, the rate of change in BCL between sections 1 and 2 is less than that between sections 2 and 3 and also between sections 3 and 4. The experiments revealed that, in a central filling process, the initial BCFM can be approximated by calculating the weighted mean of the local BCFM measured along the radius of the silo. Figure 5b is a sketch of a top view of the test bin that shows the sampling locations (hollow dots represent the centre of the sampling cylinders) using the sampler and sampling guide. The sampling points that are farther from the centre of the silo contribute more weight than other sampling points (for example in Fig. 5b, point A has the greatest weight and point O has the least weight). As can be determined from examining Fig. 5, the weight at sampling points O, C, B and A (Fig. 5b) is proportional to the area of zones (O00 , C00 , B00 and A00 (Fig. 5c), respectively) corresponding to these points. As mentioned before, when granular materials are poured on to a heap, they flow radially in all directions down the heap. As a result, by increasing the distance from the centre of the silo fines are spread in wider area. Therefore, from the mass balance point of view, the angular displacement of fines as well as annular zone of each sampling location must also be taken into account in distribution of fine. Considering above explanations, the initial BCFM at a given height can be approximated by following equation: P4 BCI ¼
Table 2 e The results of an ANOVA used for assessing the significance of each of the main parameters. Source of variation BCI Q DF Z R Error Total
Degree of freedom
Sum of Squares
Mean Square
F value
2 2 2 4 3 1078 1620
7462.2 447.2 50.2 1051.5 18,486.3 16.9 209,167.5
3731.086 223.609 25.107 262.869 6162.094 0.016
238,353.8* 14,285.2* 1603.9* 16,793.3* 393,662.7*
*Significant at P < 0.05.
Wr;i BCL;i P4 i¼1 Wr;i
i¼1
(9)
where Wr,1, Wr,2, Wr,3 and Wr,4 are the relative weights at points O, C, B and A (the area of zones O00 , C00 , B00 and A00 ), respectively. For example, in Fig. 7 the weighted mean of BCL for ring 1 is: ((0.06 19.7%) þ (0.49 17.7%) þ (0.98 11.8%) þ (1.60 2.3%))/3.14 ¼ 8% which is approximately equal to the value of initial BCFM, 7.5%. It can be concluded that, in a centre filled silo the weighted mean of the local percent BCFM could be used to obtain a good estimate of the initial percent BCFM in the sample. This also shows the validity of the tests. In other words, to accurately estimate the value of initial BCFM or other computations such as estimating the mass of
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Table 3 e The Pearson correlation coefficient between variable as well as the corresponding p-values. Q Q DF Z R BCI BCL a
Pearson Correlation Sig. (2-tailed) Pearson Correlation Sig. (2-tailed) Pearson Correlation Sig. (2-tailed) Pearson Correlation Sig. (2-tailed) Pearson Correlation Sig. (2-tailed) Pearson Correlation Sig. (2-tailed)
1 0.000 1 0.000 1 0.000 1 0.000 1 0.120a 0.000
DF 0.000 1 1 0.000 1 0.000 1 0.000 1 0.037 0.135
Z 0.000 1 0.000 1 1 0.000 1 0.000 1 0.185a 0.000
R
BCI
BCL
0.000 1 0.000 1 0.000 1 1
0.000 1 0.000 1 0.000 1 0.000 1 1
0.120a 0.000 0.037 0.135 0.185a 0.000 0.740a 0.000 0.494a 0.000 1
0.000 1 0.740a 0.000
0.494a 0.000
Correlation is significant at the 0.01 level (2-tailed).
product stored in the silos, sampling points should not be randomly selected. As shown in Fig. 7 there is an area of convergence (dashed blue circle) through which all lines drawn through the points pass. This area appeared in the region between R ¼ 0.56 and R ¼ 0.84 (R ¼ 0.7 ± 0.14) in all experiments. In the present study this range is referred to as the convergence range. In practice, sampling should be done within this range. The lines drawn through the initial BCFM (BCI) values always lie within the convergence range. It also means that the value of BCI can always be found within this range. This can be justified as follows. The value of BCI was always between the weighted means of the BCL values for sampling points Fig. 7 e Distributions of local BCFM (BCL) along the radial direction at different heights (for BCI ¼ 7.5%, Q ¼ 0.5 L s¡1 and DF ¼ 84 mm).
located in the circle M (encompassing circles C0 and B0 and point O) and the value of BCL for the sampling point (point A) in shaded zone (Fig. 5b). Recall that in the previous example,
Fig. 6 e (a) A 3D view of a sector from the flowing layer, (b) a side view of half of the test bin showing the flowing layer. The arrows indicate the relative magnitudes of the velocities of the material flowing in the layer.
Fig. 8 e The trends in the local BCFM (BCL) at different distances from the centre of the silo (R) as a function of grain depth in the silo (Z) (for BCI ¼ 7.5%, Q ¼ 0.5 L s¡1 and DF ¼ 105 mm).
Please cite this article as: Nourmohamadi-Moghadami, A et al., Filling of a grain silo. Part 1: Investigation of fine material distribution in a small scale centre-filled silo, Biosystems Engineering, https://doi.org/10.1016/j.biosystemseng.2020.01.003
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Table 4 e Comparison of non-uniformity factor (NUF) when using CFP methods to fill the test silo. Other factors were varied as listed in order to achieve a wide range of experimental conditions. No.
BCI (%)
Q (L s1)
DF (mm)
1
5
0.5
84
2
5
0.5
105
3
5
0.5
120
4
7.5
0.5
105
5
7.5
1
105
6
7.5
1.5
105
7
5
1.5
84
a b
Z 0.79 0.64 0.50 0.35 0.21 0.79 0.64 0.50 0.35 0.21 0.79 0.64 0.50 0.35 0.21 0.79 0.64 0.50 0.35 0.21 0.79 0.64 0.50 0.35 0.21 0.79 0.64 0.50 0.35 0.21 0.79 0.64 0.50 0.35 0.21
NUFR (%) 162.8 144.0 124.1 101.8 78 159.6 142.0 123.6 98.2 74.3 145.4 135.4 116.8 92.1 61.8 100.4 91.5 80.8 67.2 53.8 94.2 85.9 74.8 61.2 46.7 78.2 67.9 55.1 40.47 26.00 111.92 98.91 83.01 65.90 44.10
No.
BCI (%)
Q (L s1)
DF (mm)
Z
NUFR (%)
NUFS (%)
8
7.5
1.5
84
9
10
1.5
84
110.4
10
7.5
1
84
78.8
11
7.5
1
120
72.
12
10
0.5
120
53.6
13
10
1
120
80.7
14
10
1.5
120
82.3 71.9 57.6 42.6 28.2 63.1 56.0 47.7 38.5 30.2 100.4 91.5 80.8 67.2 53.8 86.6 74.2 59.7 45.9 31.0 84.6 79.7 70.5 51.7 31.9 67.4 56.5 44.7 34.6 24.2 50.4 45.1 38.7 29.3 21.2
56.5
119.5
0.79 0.64 0.50 0.35 0.21 0.79 0.64 0.50 0.35 0.21 0.79 0.64 0.50 0.35 0.21 0.79 0.64 0.50 0.35 0.21 0.79 0.64 0.50 0.35 0.21 0.79 0.64 0.50 0.35 0.21 0.79 0.64 0.50 0.35 0.21
NUFS (%) 122.2
a
47.1
78.8
59.5
63.7
45.3
37.0b
Highest value of NUFS in CFP experiments. Lowest value of NUFS in CFP experiments.
BCI was 7.5% which was between the weighted mean of BCL for sampling points in circle M, 14% and the value for the sampling point located in the shaded zone, 2.3%. Note that, the area of shaded zone (Fig. 5b|) is equal to the circle M. Thus, circle M is a boundary circle passing through the midpoint (R ¼ 0.7) of the convergence range. According to Fig. 5b the radius of the circle M (r0 ) can be found by equating the area bounded by circle M and the silo wall (shaded area) to the area of circle M (r0 ¼ (r00 √2)/2 z 0.7 r00 ). In general, it can be concluded that to accurately estimate the value of initial BCFM or other computations such as the mass of product stored in centre filled silos, sampling should be done within convergence range. It should be noted that more experiments are needed in full sized silos to prove this hypothesis.
typical case, BCI ¼ 7.5%, Q ¼ 0.5 L s1 and DF ¼ 105 mm while the same trends were found for other test cases). The Pearson coefficient value reported in Table 3 indicates a positive association between Z and BCL. The trend is different at R ¼ 0.84 where BCL decreased with increasing Z. According to the data given in Table 4, NUFR increased with increasing height (Z). It means that as the grain level in the silo increased, a smaller amount of fine was transferred to the periphery of the bin. This can be explained by the fact that as the silo is filled and the heap rises (Z increases), the distance the material falls decreases and the velocity of the material in the flowing layer decreases. Accordingly, as Engblom et al., 2012 stated, as Z increases, less fine material reaches the outer wall resulting in less uniformity in percentage fines in the radial direction.
3.2.2.
3.2.3.
Effect of height
As can be clearly observed in Fig. 7, when Z decreased there was less variation in BCL between the centre and outer wall of the bin. Figure 8 reveals that at R ¼ 0, 0.28 and 0.56, BCL increased linearly as Z increased (the figure is related to a
Effects of initial BCFM
Figure 9 shows the trends (for a typical case, Z ¼ 0.35, Q ¼ 1 L s1 and DF ¼ 105 mm) in BCL (the same trends were found for other test cases) from R ¼ 0 to R ¼ 0.84 at three levels of BCI. It is obvious BCL increases linearly with increasing BCI
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Fig. 9 e The trends in the local BCFM (BCL) at various distances from the centre (R) as influenced by different levels of initial BCFM (for Z ¼ 0.35, Q ¼ 1 L s¡1 and DF ¼ 105 mm).
Fig. 10 e The trends in the local BCFM (BCL) as influenced by different volume flow rates (for BCI ¼ 10%, DF ¼ 120 mm and Z ¼ 0.5).
(the Pearson coefficient value reported in Table 3 indicates a positive association between BCI and BCL). However, the NUFS decreased as BCI increased (. This can be explained by observing that at higher BCI, fine material in the flowing layer percolates to the lower layers along the surface of the heap and therefore more fine material is transferred to the silo outer wall. In other words, when the amount of fine material is high, there is less sifting. There is a second factor that could also help to explain this phenomenon. Material containing a higher percentage of fine materials can form a steeper heap (because the angle of repose is greater) and this leads to faster flow of the material in the flowing layer. Therefore, more fine material reaches the silo wall. It is concluded that the sifting effect in a central filling process is more pronounced with lower BCI than with higher BCI. This agrees with the results of
9
Fig. 11 e Distribution profile of local BCFM (BCL) along radial direction in silo as influenced by different volume flow rates (for BCI ¼ 5%, DF ¼ 84 mm and Z ¼ 0.79).
Fig. 12 e The trends in the local BCFM (BCL) at different distances from the centre (R) as influenced by different fill pipe diameters (for BCI ¼ 10%, Q ¼ 1.5 L s¡1 and Z ¼ 0.64).
the studies conducted by Schulze (2008), Shinohara et al. (2001) and Jain, Metzger, and Glasser (2013). As a result, the distribution of fine material in centre-filled silos with higher BCI is more uniform than in silos with lower BCI. However, it should be noted that, notwithstanding the above results, high amounts of fines are undesirable in stored grain.
3.2.4.
Effect of volume flow rate
The effect of volume flow rate on local percentage BCFM (BCL) at the four radial positions is shown in Fig. 10 (the figure is related to a typical case BCI ¼ 10%, DF ¼ 120 mm and Z ¼ 0.5 while the same trends were found for other test cases). At R ¼ 0, 0.28 and 0.56, BCL decreased with increasing volume
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Fig. 13 e Distribution of local BCFM (BCL) for different fill pipe diameters (for BCI ¼ 7.5%, Q ¼ 0.5 L s¡1 and Z ¼ 0.79).
flow rate but at the periphery of the silo (R ¼ 0.84) BCL increased with increasing volume flow rate (the Pearson coefficient value reported in Table 3 indicates a negative association between Q and BCL). This means that, at a higher volume flow rate, more fine material is transferred to the periphery. As can be observed in Fig. 11 (the figure is related to a typical case, BCI ¼ 5%, DF ¼ 84 mm and Z ¼ 0.79 while the same trends were found for other test cases), as volume flow rate increases the BCL distribution becomes more uniform. Accordingly, NUFS decreases with increasing volume flow rate. Fan et al., 2017 stated that fine particles gain momentum when colliding with coarser particles (similar to what happens when a tennis ball collides with a basketball). As a result, they
Fig. 15 e Prediction of fine (BCL) distribution in silo after filling, (a) surface plot (b) contour plot.
bounce further down the heap than coarser particles. This effect becomes more prominent at higher volume flow rates where the flow layer is thicker (Fan et al., 2012; Koeppe, Enz, & Kakalios, 1998; Schulze, 2008). Before the fines come to rest in the static bed of the heap, they move farther down the heap in the flowing layer.
3.2.5.
Fig. 14 e Effect of fill pipe diameter on fine (BCL) distribution.
Effect of fill pipe diameter
Tests were conducted using fill pipes with diameters of 84 mm, 105 mm, and 120 mm. As shown in Fig. 12 (the figure is related to a typical case, BCI ¼ 10%, Q ¼ 1.5 L s1 and Z ¼ 0.64 while the same trends were found for other rest cases) at R ¼ 0, 0.28 and 0.56, BCL decreased with increasing fill pipe diameter but at the periphery of the silo (R ¼ 0.84) BCL increased with increasing diameter (the Pearson coefficient value reported in Table 3 indicates a negative association between DF and BCL). The plots shown in Fig. 13 (the figure is related to a typical case, BCI ¼ 7.5%, Q ¼ 0.5 L s1 and Z ¼ 0.79 while the same trends were found for other test cases) demonstrate that fine material distribution is more uniform at larger fill pipe diameters. In other words, the NUFS decreased with increasing pipe diameter. As illustrated in Fig. 14 larger fill pipe makes
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Table 5 e Constants of the distribution model for CFP experiments. Constant a1
a2
a3
a4
a5
a6
a7
a8
Value 1.042 1.531 0.013 9.413 22.148 14.013 16.321 20.558
the heap more chamfered at the top (larger area onto which the materials fall) and shortens its height (sloping sides are shorter) which reduces the distance along the surface of the heap where sifting can occur. Another way to explain this is that granular materials flow more easily in a larger pipe and therefore there is less energy loss than in smaller pipes. When the material has more energy, it can more easily reach the silo wall which produces a slightly more even fine material distribution. According to Fig. 12 and the values of NUF in Table 4, the change in BCL when DF increased from 84 to 105 mm was less than when DF increased from 105 to 120 mm. Within this range in pipe diameters, the uniformity of the fine material distribution increased more rapidly as the fill pipe diameter increased. An examination of Table 4 indicates that the best (most uniform) distribution of fines occurred in row 14 where NUFS
was a minimum value (36.9%). Also, the maximum value of NUFS was found to be 122.2% in row 1. The surface plot (Fig. 15a) and contour plot (Fig. 15b) show how BCL changes with individual or simultaneous changes of R and Z. It is apparent that there was a considerable accumulation of fines at the centre of the silo and that this increases when Z (grain depth) increases. There was a much lower concentration of fine material around the periphery of the silo, especially at greater grain depths (greater values of Z). This means that the maximum non-uniformity in fine material distribution occurs near the top of the silo (greater Z values).
3.3.
Modelling of distribution of fines
Considering all the parameters discussed in section 3.2, the following model was proposed for the purpose of describing the effects of treatments namely, BCI, Q, DF, Z and R on the fine material distribution: BCL ¼ a1 BCI þ a2 Q þ a3 DF þ a4 R þ a5 Z þ a6 expðRÞ þ a7 ZR þ a8 (10) where constants a1 to a8 are given in Table 5. This model was the most appropriate with the values of 0.94, 1.14, 1.06, 11.39 for R2, c2, RMSE and MRDM, respectively. BCL is a nonlinear function of R and a linear function of Z, BCI, Q and DF. Although including more and complex terms increases the model complexity, when BCL was assumed to include an exponential function of R and an implicit function of Z and R (ZR), the quality of the model improved significantly. Figure 16a illustrates the promising ability of the model for the prediction of BCL. Figure 16b shows the distribution of prediction residual error (PRE) for the model. It demonstrates that the values of PRE were randomly scattered and there was no obvious trend (sensitivity).
4.
Fig. 16 e (a) Comparison between prediction of the developed model and experimental data (BCL) and (b) distribution of PREs of the developed model for prediction of BCL in silo.
11
Conclusions
This study investigated the distribution of fine material during filling of a small scale silo as influenced by the parameters initial percentage BCFM, volume flow rate and fill pipe diameter. A new approach was developed for measuring the fine material in the radial and vertical directions within the silo. Using this approach, sampling could be done without disturbing the area where sampling was done. The experiments revealed that in a central filling process the initial BCFM can be approximated by calculating the weighted mean of the local BCFM measured along the radius of the silo. A convergence range was observed on plots of fine material distribution in which the value of initial percentage BCFM was always found within that range. The results indicated that the distribution of fine material became more uniform at lower grain depths and for increasing initial BCFM, volume flow rate and fill pipe diameter. There was a considerable accumulation of fine material at the centre of the silo. The percentage increases with increase in grain depth (greater Z). Also, a low concentration of fine material occurred around the periphery of the silo, especially for greater grain depths when the test silo was nearly full. That means that maximum non-uniformity of fine material
Please cite this article as: Nourmohamadi-Moghadami, A et al., Filling of a grain silo. Part 1: Investigation of fine material distribution in a small scale centre-filled silo, Biosystems Engineering, https://doi.org/10.1016/j.biosystemseng.2020.01.003
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distribution occurs near the top surface of the silo (higher values of Z). The distribution of fine material was modelled by developing an equation that took into account the effects of the important parameters in central filling point (CFP) experiments. Based on statistical parameters R2, c2, RMSE and MRDM, the model fit the experimental data reasonably well. The results of this study can lead to a deeper understanding of factors that affect the distribution of fine material in silos.
5. Recommendations for future studies and developments According to the results of this study, the higher values of volume flow rate lead to a more uniform fine material distribution. However, it is not known how much the volume flow rate can be increased because at higher flow rates there is a risk of breaking the grain kernels during the filling process. Other useful techniques such as DEM and machine vision can be employed to investigate the distribution of fines in full scale bins and silos. In addition, the effects of other important parameters on distribution of fines during filling of a silo should be studied, such as moisture content, angle of repose, and internal friction. Due to irregular shapes and a wide range of different sizes of fine material, the study of some physical properties such as mean size and shape indices is almost impossible for this material. However, the study of the effects of such physical properties of whole kernel on fine material distribution is recommended. When a mixture of different-sized particles pours into a silo, three different configurations have been observed. These configurations are: stratification, segregation and mixing (Fan et al., 2012). These have been observed in quasi-twodimensional bounded heap. This leads to the question of whether similar processes occur in 3D bounded heap flow and how they can impact the distribution of the fines during filling a silo. These questions call for additional studies to improve our understanding of fine material distribution in grain silos.
Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
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Please cite this article as: Nourmohamadi-Moghadami, A et al., Filling of a grain silo. Part 1: Investigation of fine material distribution in a small scale centre-filled silo, Biosystems Engineering, https://doi.org/10.1016/j.biosystemseng.2020.01.003