Article pubs.acs.org/IECR
Effect of the Friction, Elastic, and Restitution Coefficients on the Fluid Dynamics Behavior of a Rotary Dryer Operating with Fertilizer Beatriz C. Silvério,† Kássia G. Santos,‡ Claudio R. Duarte,§ and Marcos A. S. Barrozo*,§ †
Chemical Institute, Federal University of Goiás, GoiâniaGO 74001-970, Brazil Chemical Engineering School, Federal University of Triângulo Mineiro, UberabaMG 38025-180, Brazil § Chemical Engineering School, Federal University of Uberlândia, Block 1K, Campus Santa Mônica, UberlândiaMG 38408-100, Brazil ‡
ABSTRACT: Some fluid-dynamics aspects of a rotary dryer, operating with granular single superphosphate, were investigated experimentally and by coupled discrete element model−computational fluid dynamics (DEM−CFD) simulations. The experimental data of flight holdup and dynamic angle of repose in the upper half flights, at different angular positions, were successfully used to identify the best set of parameters for the spring−dashpot model used in DEM simulations. The smallest deviations from the experimental data were obtained in the simulation whose parameters values were elastic constant k = 400 N/m, friction coefficient μf = 0.2, and restitution coefficient η = 0.2. The results have shown that the coupled DEM−CFD approach with the selected parameters has been suitable to predict the fluid dynamics behavior of the rotary dryer operating with granular single superphosphate. flights, sliding and rolling, then falling as a rain of particles, is very hard to analyze.8 Another important aspect is the knowledge about the load of solids in the flights. If the flights are underfilled, the dryer will be operating below capacity and therefore inefficiently. On the other hand, excessive overload of the drum will result in a proportion of the material transported by kiln action, and the contact with the hot air is limited.9 Thus, the prediction of the flight holdup is highly desirable for the design of this equipment. With the rapid advances in computational resources today, studies involving numerical simulation have become popular in the field of gas−solid flows10−12 and can help shed light on the fluid dynamic of particles in rotary dryers. Modeling techniques can be categorized by the choice of either a continuum Eulerian or discrete Lagrangian approach for the fluid and solid phases. A Lagrangian approach to particle modeling, together with the use of increasingly powerful computer processors, has many advantages.13 The first computational Lagrangian approach for particles, called the discrete element model (DEM), was introduced by Cundall and Strack.14 The basic idea behind the DEM is that the trajectory of each particle inside the system is calculated, considering all the forces acting on it and integrating Newton’s second law of motion and the kinematic equations for position and orientation.14 Granular flows have been reproduced successfully by DEM simulations of many processes, including packing bed;15 fluidized bed;16 spouted bed;13 and granulator,17 among others.
1. INTRODUCTION 1
In the production of granulated fertilizers, the raw materials (water, ammonia, sulfuric acid, among others) are dosed in the granulator, the goal of which is to make the product to the chemical specifications and increase the size of the particles until it reaches the desired standard.2 After the granulator process, there is a drying operation performed in a rotary dryer.3 Rotary dryers are also used in a wide range of industries because of their flexibility over other types of dryers to handle a wider range of materials. The design of industrial drying units has become a critical issue. In many cases, the design and operation of rotary dryers come about because of empiricism, based on the “experience” of engineers. It is also worth mentioning that rotary dryers are a significant capital investment item for many industrial plants.4 The directly heated rotary dryer basically consists of a long cylindrical drum rotating slowly around its own axis. The drum is slightly inclined to the horizontal and its inside is equipped with lifting flights, arranged in parallel along the length of the drum. With the rotation of the dryer, the particulate materials are caught by the flights and conveyed to a distance around the periphery before dislodging and falling back as a rain of particles through a hot air stream.5 Most of the drying occurs during this period, when the solids are in close contact with the hot air. Therefore, a good design of flight is essential to promote the gas−solid contact that is required for a efficient drying.6 The performance of rotary dryers is based in three transport phenomena, namely, solids transportation, heat, and mass transfer. The ability to estimate each of these transport mechanisms is essential for proper design and operation of these dryers.7 The fluid dynamics of particles in a rotary dryer is quite complex. The combination of particles being lifted by the © 2014 American Chemical Society
Received: Revised: Accepted: Published: 8920
December 13, 2013 April 21, 2014 May 7, 2014 May 7, 2014 dx.doi.org/10.1021/ie404220h | Ind. Eng. Chem. Res. 2014, 53, 8920−8926
Industrial & Engineering Chemistry Research
Article
Table 1. Parameters of DEM Simulation authors
equipment
material
dp (mm)
Neuwirth et al.19 Remy et al.20 Chaudhuri et al.21 Anand et al.22 Geng et al.23 Fries et al.17 Jiang et al.24 Ketterhagen et al.25 Li et al.15 Liu et al.26 Li et al.27 Zhong et al.28 Sahni et al.29 Ren et al.30 Remy et al.20 Li et al.31
fluidized bed shaker calcinator hopper rotary dryer fluidized bed rotating drum hopper fluidized bed spouted bed hopper spouted bed
polymer glass sphere cooper iron sphere aluminum cylinder alumina glass sphere glass sphere poppy seeds glass sphere glass sphere
6 2−4 2 2.35 2 2 1.5−3 0.5−2.24 1.2 4.04 10 1.5−3.0
corn beater
ρ (kg/m3)
6.6, 6.4 2−10 2
1800 2200 8900 7850 2700 1500 2600 2500 1000 2526 2460 1020 1600 1385 2200 2508
The literature presents some models used in the DEM approach to predict the contact forces. Di Renzo18 tested the accuracy of three different contact force models, comparing the results, microscopically, to nearly exact analytical solutions, and, macroscopically, to experimental results. The results showed that the spring−dashpot model presented good results for the prediction of contact forces. The term “spring” refers to the contribution of the response to the elastic forces while the term “dashpot” refers to the dissipation due to plastic deformation. Thus, only the frictional and elastic collisions are considered, accounted by the following parameters: normal (Kn) and tangential (Kt) elastic coefficient (or spring); the coefficient of friction (μf) and restitution coefficient (η). Table 1 presents some parameters related to the contact forces models used for DEM simulations, that are reported in the literature. This table also shows the time step used in each simulation, as well as the number of particles. It can be noted that the values of these parameters reported in the literature differ considerably, once that each DEM simulation was conducted with different equipment and materials, leading to different results for particle−particle and particle−wall collisions. Thus, there is a need to study the influence and interaction of parameters related to the contact forces used in the DEM simulation of granular single superphosphate in a rotary dryer and to find a better set of parameters that best characterize the system. For this, the experimental verification also becomes essential. In the present work, some fluid-dynamics aspects of a rotary dryer, operating with granular single superphosphate, were investigated experimentally and by discrete element model− computational fluid dynamics (DEM-CFD) simulations. The experimental results of dynamic angle of repose in the flights and flight holdup were used to select the best set of parameters for the spring−dashpot model used in DEM simulations.
η
no. particles 5900 14000−20000 8000 6790
0.83, 0.85 0.6 0.8
25·10 15000 35500 9240 44.8
0.02 0.8 0.9 0.94 0.98 0.87
62000 4·104 to 105 23956 and 26 482 14000 and 20 000 1000
0.9 0.7 0.59 0.6 0.93
4
μf
k (N/m)
time step (s)
0.25, 0.32 0.5 3·10−6
6000 250−308
0.2 0.2, 0.3 0.1 0.3 0.1, 0.15 0.1 0.1 0.15, 0.13 0.3 0.7 0.34
250−308 200 800 800 6000
109 680
0.5
10−5 10−6 5·10−5
1.14·10−6 10−6 2·10−6 1·10−6
