Article pubs.acs.org/IECR
Experimental Study of Wet Cohesive Particles Discharging from a Rectangular Hopper Anshu Anand,† Jennifer S. Curtis,*,† Carl R. Wassgren,‡ Bruno C. Hancock,§ and William R. Ketterhagen§ †
Chemical Engineering Department, University of Florida, Gainesville, Florida 32611, United States School of Mechanical Engineering, Purdue University, West Lafayette, Indiana 47907, United States § Pfizer Global Research and Development, Groton, Connecticut 06340, United States ‡
S Supporting Information *
ABSTRACT: The present work investigates discharge phenomenon for wet cohesive particles from a rectangular hopper. Three specific characteristic of the hopper flow are investigated: discharge rate, angle of repose of the material, and size of clumps formed during the discharge. These characteristics are compared to predictions from previously published Discrete Element Method (DEM) simulations. The primary objective of this work is simulation validation. The current experimental results agree well with previous simulation results. Generally, as cohesion increases, the discharge rate decreases, the angle of repose increases, and the size of the clumps increases.
1. INTRODUCTION The prediction of granular flow and its mixing and segregation behavior becomes especially problematic for cohesive particles, even in relatively simple systems.1−3 Hoppers are important devices that are widely used during the processing and handling of granular materials. Accurate prediction of discharge rate from hoppers is critical in many industrial processes. Discrete Element Method (DEM) computer simulations can be used to understand and predict such hopper flow phenomena, with and without particle cohesivity, as shown in the works of Anand et al.4,5 The primary objective of this work is simulation validation. In this work, three different and important characteristics of hopper flow are investigated experimentally: discharge rate, angle of repose of material left in the hopper, and maximum size of clumps formed during cohesive discharge. For example, the angle of repose is studied because it is important in characterizing avalanching.6 The measured flow characteristics are compared to the DEM simulation predictions.4,5 These simple experiments are vital for direct validation of the DEM computational models, which incorporate particle cohesivity due to liquid bridging; they also make it possible to obtain a better estimate of some of the parameters used in the DEM simulations, with the help of these experiments. For example, the particle−particle friction coefficient for the cast-iron shots can be estimated from the angle of repose of the material remaining in the hopper after discharge.
cast iron shots with an average size of 0.235 cm. In order to introduce cohesion into the system, two types of liquids are used with different surface tensions: water, with a surface tension value of 73 dyn/cm, and silicone oil, with a lower surface tension of 20.8. The resulting four cohesive systems (glass−water, glass−oil, iron−water, and iron−oil) that are investigated experimentally are listed in Table 1. Cohesionless Table 1. Types of Experimental Cohesive Systems Bond number 0.3 1 1 3.5
cast iron shots and glass beads (no liquid) are also used in the experiments. Cast iron shots with silicone oil represent the least cohesive system, whereas glass beads with water represent the most cohesive system. Cast iron shots with water and glass beads with silicone oil have identical Bond numbers, which suggests that they should show similar cohesive properties. The hoppers are shown in Figure 1 and are made of clear acrylic to facilitate visualization of the flow. The hoppers have dimensions of 12.5 cm × 12.5 cm × 100 cm. There is a 12.5 cm × 2.5 cm rectangular orifice at the bottom of the hopper, equipped with a gate, as shown in Figure 2D (presented later in this work). The hoppers have half angles of 90° (flat-bottomed) and 55°, with respect to vertical. A Ohaus Champ-square
2. EXPERIMENTAL SECTION This section discusses the details of the experimental component of the work. The granular media and hoppers used in the experiments are described. Then, the procedure for carrying out the experiments and the method used to collect the data are presented. 2.1. Materials. Two types of granular media are used in the experiments: glass beads with an average size of 0.22 cm and © 2015 American Chemical Society
system cast iron shots with silicone oil cast iron shots with water glass beads with silicone oil glass beads with water
Special Issue: Scott Fogler Festschrift Received: Revised: Accepted: Published: 4545
November 9, 2014 March 9, 2015 March 11, 2015 March 11, 2015 DOI: 10.1021/ie504440q Ind. Eng. Chem. Res. 2015, 54, 4545−4551
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Industrial & Engineering Chemistry Research
Figure 1. Schematic of the experimental hopper: (A) assembly, (B) cross-section of the 55° hopper, (C) cross-section of the 90° hopper, and (D) gate and orifice of the hopper.
balance was used with Collectv6.1 software to dynamically
the material left in the hopper, and the clump size in the cohesive discharge. To measure the discharge rate, the balance is connected to the computer using the Ohaus proprietary cable, and Collectv6.1 software is used to collect the weight
capture the weight of the material remaining in the hopper. 2.2. Procedure. Three different characteristics of hopper flow were investigated: the discharge rate, the angle of repose of 4546
DOI: 10.1021/ie504440q Ind. Eng. Chem. Res. 2015, 54, 4545−4551
Article
Industrial & Engineering Chemistry Research
Figure 2. Snapshots for calculating angle of repose: (A) experiments and (B) simulation.
readings on the balance every 0.4 s. At the start of each discharge rate experiment, the hopper is cleaned and placed on the Ohaus balance. For the case of cohesion, the appropriate liquid is mixed with the granular media of interest in a separate container. These wet particles are then immediately poured
into the hopper, assuming that the liquid is uniformly distributed and a negligible amount liquid remains in the separate container. The hopper slide gate is opened, and the particles that exit the hopper are collected in a container that is not placed on the balance. At any point in time, the balance 4547
DOI: 10.1021/ie504440q Ind. Eng. Chem. Res. 2015, 54, 4545−4551
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Industrial & Engineering Chemistry Research
particles. A set of three images for a particular Bond number is analyzed in this way to give the average number of particles in the largest clumps formed at any given Bond number. To calculate the size of clumps from the simulation, the visualization of the flow can be directly used in a similar manner to calculate the number of particles in a clump.
reads the amount of material remaining in the hopper. By plotting the data of mass remaining in the hopper versus time, and calculating the slope of this curve, the hopper discharge rate can be determined. The plot of mass remaining in the hopper versus time shows negligible fluctuation, and the correlation coefficient (R2) for the linear region was ∼1 for all conditions. A set of three experimental runs are made for each system. The sources of error in calculating the discharge rate are due to the nonuniformity of liquid distribution in the system, the sensitivity or the stabilization time of the Ohaus balance in recording the data, and in determining the region of constant discharge rate, following the initial transient just after opening the hopper gate. To calculate the angle of repose of the material left in the hopper, a snapshot of the cross section of the hopper is taken after the discharge is complete, as shown in Figure 2A for cohesionless glass beads. A set of two snapshots from each system is analyzed to obtain the average angle of repose. To calculate the angle of repose from the simulations, a similar snapshot is taken from the visualization of the flow, as shown in Figure 2B. For highly cohesive systems, there is some variability in determining the free surface of the particles. The free surface of the particles was averaged as a straight line by visual approximation to calculate the angle of repose. For all conditions except B0 = 3.5, the free surface was fairly regular and, in this case, visual approximation of the free surface results in, at most, a 2° variation in the angle of repose. The free surface for B0 = 3.5 was less regular and, in this case, visual approximation of the free surface results in, at most, a 4° variation in the angle of repose. To determine the size of the clumps, a high-speed camera (with a speed of 400 fps) is used to capture the particles coming out of the hopper. Individual frames are extracted from the video of the flow. Generally, a distribution of clump sizes is observed for any given Bond number. The largest-sized individual clumps, which are generally formed near the end of discharge, are visually identified and isolated. These raw images are then analyzed for the number of pixels within the largest clump. By knowing the number of pixels occupied by a single particle, the total number of particles in the clump can be estimated. Figure 3 shows one such clump formed in the cast iron shots with water system. The number of pixels occupied by the central large clump is 1498. One particle occupies the space of ∼100 pixels, suggesting that the clump is composed of ∼15
3. DEM SIMULATIONS The Discrete Element Method (DEM) simulation has emerged as one of the most important recent tools in probing granular flows. All details of the DEM simulations and the force models employed in this work, which incorporate particle cohesivity due to liquid bridging, can be found in the work of Anand et al.4,5 Every simulation parameter used in this study is available in the Supporting Information. The DEM model is applied to the case of hopper flow in which a quasi-three-dimensional (quasi-3D) plane flow hopper with periodic boundary conditions on the front and back wall is employed. The hopper is defined by the following geometric variables as shown in Figure 4: the hopper width (W), hopper
Figure 4. Schematic of the quasi-three-dimensional (quasi-3D) computational domain that models a thin slice of a large, rectangular cross-sectioned hopper.
outlet width (W0), hopper depth (Zdepth), the hopper angle as measured from the vertical (θ), and the initial fill height (H). The hopper has a rectangular cross-section with the lateral walls modeled as planar surfaces. The use of periodic boundary conditions greatly increases the computational efficiency and, hence, only a thin slice of the hopper needs to be simulated to predict the behavior of a fully 3-D system. It is desirable to use the smallest computational domain that still produces the same results as a system without periodic boundaries. The predictions are independent of Zdepth/d for values greater than 2.1, as noted by Anand et al.5
Figure 3. Example of a snapshot from a high-speed camera used for the calculation of clump size. 4548
DOI: 10.1021/ie504440q Ind. Eng. Chem. Res. 2015, 54, 4545−4551
Article
Industrial & Engineering Chemistry Research In order to study the effect of cohesion on the hopper discharge, identical hopper parameters are used as in the cohesionless case. The particles in the simulations are glass or cast iron spheres and have a particle density of 2.5 g/cm3 and 7.85 g/cm3, respectively. Previous experimental work done by Scheel et al. showed that mechanical stiffness is rather insensitive to liquid content.7 Hence, the baseline liquid content is fixed at 2 vol %. This ensures a pendular regime, where liquid bridges are independent of each other. The liquid for the baseline case studied is water. In this work, the Bond number (ratio of cohesive force to gravitational force) is varied by changing the surface tension of the liquid, but the viscosity and contact angles of the liquid with different surfaces are assumed to be identical to that of pure water. The contact model in the DEM simulations for calculating forces in the normal direction is the soft sphere model of Walton and Braun,8 while forces in the tangential direction employ the model developed by Cundall and Strack.9 The liquid bridge force model for calculating the cohesive force due to liquid bridging uses the regression expressions developed based on the work of Mikami et al.10 and Soulie et al.11 Rolling resistance is included and a small rolling resistance value is used to take into account surface asperities and/or a slightly nonspherical shape, which act to inhibit rolling in real materials. However, the discharge rate results are insensitive to this parameter.
Figure 5. Illustration of clump sizes from simulation: (A) B0 = 0.3, corresponding to silicone oil with cast iron; (B) B0 = 1, corresponding to water with cast iron/silicone oil with glass; and (C) B0 = 3.5, corresponding to water with glass.
4. RESULTS The three measured characteristics of the hopper flow discharge rate, angle of repose of the material left in the hopper,
4.1. Discharge Rate. Discharge rate experiments were performed in both the 90° (flat-bottomed) hopper and the 55° hopper. The results for the 90° hopper are summarized in Table 2; results for the 55° hopper are available in the Supporting Information. A set of three experimental runs was carried out for each system, and the 95% confidence intervals from the experiments are listed in the table. The experiments show that, with increasing cohesion, the discharge rate decreases, and this decrease is
