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Model development for shelled corn drying in a plug flow fluidized bed dryer
Accepted Manuscript Model development for shelled corn drying in a plug flow fluidized bed dryer Majid Khanali, Asgar Khakpour Giglou, Shahin Rafiee PII:
S1881-8366(17)30001-0
DOI:
10.1016/j.eaef.2017.09.002
Reference:
EAEF 159
To appear in:
Engineering in Agriculture, Environment and Food
Received Date: 3 January 2017 Revised Date:
14 June 2017
Accepted Date: 10 September 2017
Please cite this article as: Khanali M, Giglou AK, Rafiee S, Model development for shelled corn drying in a plug flow fluidized bed dryer, Engineering in Agriculture, Environment and Food (2017), doi: 10.1016/ j.eaef.2017.09.002. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
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Title: Model development for shelled corn drying in a plug flow fluidized bed dryer
Majid Khanali*, Asgar Khakpour Giglou, Shahin Rafiee
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Authors:
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REFERENCE NO. EAEF 159
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Corresponding authors:
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Department of Agricultural Machinery Engineering, Faculty of Agricultural Engineering and Technology, College of Agriculture and Natural Resources, University of Tehran, Karaj, Iran.
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Majid Khanali Department of Agricultural Machinery Engineering, Faculty of Agricultural Engineering and Technology, University of Tehran, Karaj, Iran. Tel: +98-26-32801011, Fax: +98-26-32808138; Email address: [email protected]
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Model development for shelled corn drying in a plug flow fluidized bed dryer
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Abstract In the present study, a differential model of the plug flow fluidized bed dryer for shelled corn was presented. The model was developed by using the mass balance of moisture content inside a control volume of the bed based on the axial dispersion phenomenon and an appropriate drying rate equation. The differential equation resulted from the model was solved numerically by finite difference method. To validate the model, several experiments for shelled corn drying in a plug flow fluidized bed dryer under steady state conditions were performed at three inlet dry solid mass flow rates (245, 420 and 565 g/min), six drying air temperatures (50, 60, 70, 80, 90 and 100 °C) and two weir heights (0.025 and 0.05 m). The model was capable to predict correctly the moisture content of the grains at any locations along the dryer length. Based on the simulation results, the solid moisture content decreased discontinuously at the solid inlet boundary of the bed and then decreased continuously along the dryer length. The simulation results were also analyzed to investigate the effects of inlet gas temperature, weir height and inlet dry solid mass flow rate on the solid moisture content. The solid moisture content decreased by increasing inlet gas temperature and weir height, whereas it increased by increasing the inlet dry solid mass flow rate.
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Keywords Axial dispersion. Drying. Fluidized bed. Modeling. Shelled corn
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Specific surface area of expanded bed (m2/m3) Particle diameter (m) Dispersion coefficient (m2/s) Relative error (%) Mass flow rate of dry solid (kg/s) (g/min) Bed height (m) Weir height (m) Mass transfer coefficient (m/s) Bed length (m) Drying rate per unit bed volume (kg H2O/m3s) Solid moisture content (dry basis) (kg water/kg dry solid) Mean relative deviation (%) Number of measurements Atmospheric pressure (Pa) Saturated vapor pressure (Pa) Reynolds number (dimensionless) (Re = U d ρ ⁄μ ) Equilibrium relative humidity (dimensionless) Solid holdup (kg) Schmidt number (dimensionless) (Sc = % ⁄& ) Sherwood number (dimensionless) (Sh = Kd ⁄&) Drying gas temperature (°C) Axial solid flow velocity (m/s) Superficial fluidization velocity (m/s) Minimum fluidization velocity (m/s) Bed width (m) Bed length coordinate (m) Equilibrium absolute humidity (kg H2O/kg dry air) Absolute humidity of inlet drying air (kg H2O/kg dry air)
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List of symbols a d D E F h h K L m M MRD n P P Re RH S Sc Sh T u U U ) w x Y YGreek Letters α ε μ ν ρ2 ρ ρ Subscripts exp in out pre
Moisture diffusivity in drying air (m2/s) Porosity of stagnant bed (dimensionless) Viscosity (kg/ms) Kinematic viscosity of drying air (m2/s) (% = μ1 ⁄ρ ) Bulk density (kg/m3) Density of drying air (kg/m3) True density (kg/m3)
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Experimental Input Output Predicted
Highlights Plug flow Fluidized bed drying of shelled corn was investigated experimentally. The axial profile of solid moisture content was modeled reasonably well by a differential model.
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The axial dispersion phenomenon and an analytical drying rate equation were considered in the model. Solid moisture content profile showed a discontinuity at the solid inlet port of the dryer and then decreased continuously across the dryer length. 1 Introduction
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Shelled corn (Zea mays L.) is one of the major grains that is usually harvested at considerably high moisture content in the range of 0.4 to 0.5 d.b. (dry basis, kilograms of water per kilogram of dry solid) and has to be dried to a moisture content of around 0.14 d.b for long-term preservation (Brooker et al., 1992). Drying is the most widely practical unit operation in many fields such as agricultural, food, chemical, pharmaceutical and mineral industries. Drying is a complex, time-variant and nonlinear phenomenon. Accurate modeling of the drying process is an important factor for simulation and optimization of the process, design of the drying system and controlling the operation (Mujumdar, 2006). Fluidized bed dryers (FBDs) have been applied extensively for drying of particulate or granular materials in the chemical, food, biomaterials, ceramic, pharmaceutical, agriculture, polymer and waste management industries. Numerous designs of FBDs are available, among which, batch type, continuous well-mixed, plug flow, vibrated, mechanically agitated, centrifugal and spouted types are the more commonly used fluidized bed dryers. Fluidized bed drying operation have several advantages such as high drying rates, good thermal e ciency, low capital and maintenance costs, easy material transport and ease of control (Khanali et al., 2014; Mujumdar, 2006; Mujumdar and Devahastin, 2003; Sivakumar et al., 2016; Topuz et al., 2004). This study is concerned with the mathematical modeling of drying process of shelled corn in a plug flow fluidized bed dryer. This type of dryer features a long narrow bed with length to width ratios of 5:1 to 30:1; the fluidized solid particles flow continuously as a plug through the bed from the inlet to the exit. This plug flow ensures approximately equal residence time for all particles which results in the uniformity of the outlet product moisture content. In this dryer, drying times typically range from 1 min to 2 h and the bed height is relatively low in order to minimize axial mixing of the flowing particles (Baker and Lababidi, 2010). A schematic sketch of the plug flow fluidized bed dryer and the flows of drying air and solid particles are shown in Fig. 1.
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Fig. 1 A schematic diagram of the flows of drying air and solids in a plug flow fluidized bed dryer
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There are two basic modeling methods for plug flow fluidized bed drying process, differential and tanks-in-series. In the differential model, the bed is divided into control volume elements and the mass, energy and momentum balances for both solid and gas phases in each element are developed (Khanali et al., 2013; Nilson and Wimmerstedt, 1987; Pakowski and Mujumdar, 2006; Ramli and Daud, 2007; Sopornonnarit et al., 1996). In some cases, the water diffusion in solid particles is considered based on Fick’s second law (Izadifar and Mowla, 2003). In the tanks-in-series model, the bed is divided into several continuous well-mixed fluidized bed dryer vessels in series. The drying process is analyzed considering the governing equations simulating behavior of each dryer vessel combined with axial dispersion phenomenon (Baker et al., 2006; Baker and Lababidi, 2010; Bizmark et al., 2010; Fyhr et al., 1999; Wanjari et al., 2006). The objective of the present study was to develop a differential model of the plug flow fluidized bed drying process under steady state conditions and to validate it with experimental data of the shelled corn drying in a pilot scale plug flow fluidized bed dryer. Despite the importance of corn drying in Iran and considerable amount of research works on modeling of fluidized bed drying of agricultural materials, there is no study about modeling and investigation of plug flow fluidized bed drying of shelled corn. The model developed in this study builds upon the earlier work by Khanali et al. (2013) in which a mathematical modeling and experimental investigation of the plug flow fluidized bed drying of rough rice was conducted. In the present study, an analytical drying rate equation of solid particles was taken into account instead of the experimental one considered in the work by Khanali et al. (2013) and the axial profile of shelled corn moisture content along the dryer length was derived theoretically and experimentally. The results of simulation were also analyzed to investigate the effects of inlet gas temperature, weir heights and inlet dry solid mass flow rate on axial profile of solid moisture content. 2 Material and methods 2.1 Drying experiments
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The single cross 704 variety of shelled corn used in this study was prepared from Moghan region of Iran. The shelled corn kernels were cleaned to remove broken particles, straw and stones, then the kernels were wetted, mixed and stored 3-5 °C in plastic bags for five days prior to the drying experiments to reach the uniform water concentration. The experiments were performed in a pilot scale plug flow fluidized bed dryer that is shown in Fig. 2. The shelled corn was fed from the hopper to the dryer through a screw conveyor. The drying air was supplied by a centrifugal fan, heated by a controllable electrical heater and entered to the drying chamber after passing through the air distributor plate. The length of the dryer was 100 cm and its width was 8 cm. A detailed illustration about the dryer and its performance used in this study can be found from the work by Khanali et al. (2013). It must be mentioned that the appropriate air distributor plate used specifically for shelled corn was 1 mm thick perforated steel plate and consisted of 4 mm holes on a 5 mm triangular pitch, giving an open area of about 15%. To measure the particles moisture content, sampling was performed at three points along the dryer length at 0.1, 0.5, and 0.9 m from the solid inlet port. The moisture content was determined off-line by drying the grains at temperature of 105 °C for 48 h in a hot air oven. To measure solid holdup within the bed at each drying experiment, the flow of solid particles was stopped suddenly and simultaneously the materials at the outlet of the dryer were collected
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until the entire solid holdup came out of the bed. The weight of the collected sample was the solid holdup within the bed. The drying experiments were conducted under steady state conditions as indicated in Table 1. Stable conditions in terms of outlet solid mass flow rate as well as humidity and temperature of the outlet gas were considered as the steady state conditions. The necessary time to reach the steady state conditions was considered two times the average residence time of the particles in the dryer. It should be noted that the study of the process at the start of the dryer was not in the scope of this study. Each experiment was started when the bed is empty by setting the superficial fluidization velocity, inlet gas temperature and inlet dry solid mass flow rate at the desired levels. The drying experiments were conducted at inlet dry solid mass flow rates of 245, 420 and 565 g/min, drying air temperatures of 50, 60, 70, 80, 90 and 100 °C, weir heights of 0.025 and 0.05 m and superficial fluidization velocity of 3 m/s. The values of solid inlet moisture content in all experiments were in the range of 0.29 to 0.315 d.b.
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Fig. 2 Schematic diagram of the pilot scale plug flow fluidized bed dryer Table 1 Operating conditions for each drying experiment Run F (g/min) h (m) U T (°C) 1 50 245 0.025 2 50 245 0.05 3 50 420 0.025 4 50 420 0.05 5 50 565 0.025 6 50 565 0.05 7 60 245 0.025 8 60 245 0.05 9 60 420 0.025 10 60 420 0.05 11 60 565 0.025 12 60 565 0.05
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Y - (kg/kg) 0.0304 0.0299 0.0316 0.0321 0.0280 0.0287 0.0086 0.0091 0.0013 0.0010 0.0024 0.0103
S (kg) 0.685 1.104 0.761 1.121 0.706 1.275 0.614 1.036 0.626 0.995 0.664 1.267
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2.2 Modeling of drying process
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0.567 1.041 0.575 1.083 0.584 1.181 0.524 0.937 0.598 1.032 0.634 1.079 0.530 0.907 0.599 1.077 0.609 1.011 0.499 0.814 0.541 0.880 0.610 1.037
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Heat and mass balance equations in solids that determine respectively the temperature and moisture content are the basic equations in modeling the drying process. Drying rate of solid material is affected by its temperature. However the temperature of the solid particles in fluidized bed drying method quite rapidly reaches the drying air temperature (Baker et al., 2006; Baker and Lababidi, 2010; Bizmark et al., 2010; Janas et al., 2010; Wanjari et al., 2006). In the case of rough rice drying in a plug flow fluidized bed dryer, the solid temperature increased rapidly within a short distance from the solid inlet port, approached a temperature nearly the same as the drying air temperature, and remained nearly constant until the dryer exit (Khanali et al., 2013). For this reason, the drying process in this study was considered as isothermal process, thus, only the mass balance for the moisture of shelled corn is considered. Mass balance of solid moisture content is written on a control volume (hwdx) placed on an arbitrary position along the bed length as shown in Fig. 3.
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Fig. 3 Schematic differential model of the dryer bed and mass transfer between air and solid particles in the control volume In practice, the ideal plug flow of solid materials through the bed in fluidized bed dryers is rarely met. Because of the motion of gas-bubbles and the particles back-mixing in the bed, particles are mixed horizontally and the result is more spreading of residence time. In the present study, the deviation from ideal plug flow is modeled by considering axial dispersion. Mass balance (referring to the evaporating medium, i.e., the moisture content) in steady state condition is developed by considering both input and output flows of moisture by two major mechanisms, bulk flow and dispersed flow. Although the rate of moisture transfer between drying air and solid particles due to evaporation is considered. The basic mass balance equation in the particles at steady state conditions considering the control volume shown in Fig. 3 is (Levenspiel, 1999): Moisture input rate by bulk flow – moisture output rate by bulk flow + moisture input (1) rate by dispersed flow – moisture output rate by dispersed flow – rate of moisture evaporation from the particles = 0 The values for each term of Eq. (1) in kilograms of water per unit time are given subsequently. The moisture input rate by bulk flow along the dryer length coordinate at x is: (2) hwuρ2 3 M Where h is bed height, w is the bed width, u is the axial solid flow velocity, ρ2 3 is the bed density and M is the particles moisture content. The moisture output rate from the control volume at x + dx by bulk flow can then be expressed as a Taylor series expansion where, neglecting higher-order terms, 36 (3) hwuρ 5M + dx9 78
In words, Equation 3 simply states that moisture transfer rate at x + dx is equal to the value of 36 this component at x plus the amount by which it changes with respect to x ( ) times dx. 78 The degree of axial mixing is quantified by the dispersion coefficient (D) and by an analogy to the Fick’s law of diffusion. The moisture input rate by axial dispersion at x can be calculated as follows (Levenspiel, 1999): 36 (4) −Dhwρ2 3 38 The moisture output rate by axial dispersion at x + dx by applying Taylor series expansion and neglecting higher-order terms is obtained as: 36 3 36 (5) −Dhwρ 5 + 5 9 dx9
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At the solid inlet port, the solid particles transported from the hopper to dryer by the screw conveyor are mixed with partially dried particles inside the dryer. Therefore the equality of the solid inlet moisture content and the sum of carried moisture content by both bulk flow and dispersed flow is considered as the boundary condition at the solid inlet port as: C 36 M- = M− for x = 0 (9) D 38 At the solid exit port, considering the continuous flow of particles over the exit weir, the boundary condition is: 36 (10) =0 for x = L 38
Based on Levenspiel (1999) and Fogler (1987) and considering the flow patterns of the particles at the solid inlet and exit ports, the considered boundary conditions can be classified as closedclosed type. 2.3 Required equations
The drying rate per unit volume of the bed (m) is calculated as follows (Brooker et al., 1992): m = Kaρ (Y − Y - ) (11) The following formula is used to calculate the air absolute humidity in equilibrium with the particle surface (Brooker et al., 1992): JKA LMN Y = 0.622 (12)
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Where RHS , the equilibrium relative humidity of air in contact with shelled corn is related to the solid moisture content and drying air temperature according to the following equation (Samapundo et al., 2007): RH = 1 − exp (−3.11 × 10RY T MZ.[Z\ ) (13) The mass transfer coefficient between the particles and the drying air is calculated according to (Kunii and Levenspiel, 2013): ]3
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Sh = ^ = 2 + 0.6 Re> Sc a (14) _ The bed density (ρ2 3 ) is a function of bed voidage and true density of the solid particles. In order not to disturb the main text, a detailed analysis of the bed voidage calculation based on the two-phase theory of fluidization can be found in Khanali et al. (2013). The axial solid flow velocity was calculated using the following equation: b u= (15)
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The rate of moisture leaving the major control volume due to the moisture evaporation from the particles into the gas is: (6) hwmdx By substituting Eqs. (2-6) into the mass balance expression, i.e., Eq. (1), it follows that: 36 36 36 (7) hwuρ M − hwuρ 5M + dx9 + 5−Dhwρ 9 − ;−Dhwρ 5 +
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The dispersion coefficient was obtained with the following equation (Nilsson and Wimmerstedt, 1988): Z.ef g . Z(cRchijk )l . ZmY no pqr Rqst uvwr.>a (16) d= `x qst a
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Property P
Where h is the bed height (m), y is the superficial fluidization velocity (m/s), yz{ is the minimum fluidization velocity (m/s) and |1 is the gas density (kg/m3). To solve the model, some physical properties of the air-vapor mixture and the shelled corn are required. These properties were measured experimentally or extracted from the literature as summarized in Table 2.
Table 2 Physical properties of air and shelled corn applied in this study Equation
P = 100 ∗ exp 527.0214 − 6887⁄pT + 273.16u − 5.31lnppT + 273.16u ⁄273.16u9 (T in °C) Z.ƒZ
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μ = 1.691 × 10RY + 4.984 × 10Rƒ T − 3.187 × 10RZZ T
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The accuracy of the developed model in prediction of solid moisture content were evaluated on the basis of the relative error (E) and the mean relative deviation (MRD) as follow (Zare et al., 2006): ‡6 R6 ‡ (17) E = ^ˆA A‰^ × 100 6^ˆA Z
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MRD = Š ∑-Œ•Z ;
Where subscripts “pre” and “exp” denote the predicted and the experimental data, respectively. 3 Results and discussion
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Reference (Naghavi et al., 2010) (Janas et al., 2010) (Khanali et al., 2013) (Khanali et al., 2013) (Mohsenin, 1986) Measured Measured Measured Measured
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3.1 Axial profile of solid moisture content By substituting the drying rate per unit volume of the bed (m) based on Eqs. (11-14) into Eq. (8), the result is a second-order nonlinear differential equation in which solid moisture content (M) is the dependent variable, location along the dryer length (x) is the independent variable, and Eqs. (9-10) are its boundary conditions. The resulted differential equation was solved numerically for solid moisture content by using the finite difference method. Based on the solution of the discrete set of equations at finite points along the dryer length, a computer program was developed and implemented in MATLAB (version 8.5) environment to simulate the drying process.
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Based on the experimental observations, a uniform and stable fluidization of the shelled corn kernels across the entire bed cross section during drying process was achieved. The acceptable fluidization state can be attributed to the uniform solids feeding, uniform gas distribution across the bed and perfect solids mixing. As a result, the outlet solids with uniform moisture content was achieved. The simulated profile of solid moisture content along the dryer length as well as the measured values of moisture content of the solid samples taken out of the dryer for typical Runs 1, 6, 12, 18, 22, 28, 32 and 36 are shown in Fig. 4. It is clear that the model predicts the profiles of solid moisture content reasonably well. As shown, the solid moisture content decreases nonlinearly with increasing distance from the solid inlet port. Approximately, similar axial profiles of solid moisture content for plug flow fluidized bed drying of different materials have been reported in the literature (Baker et al., 2006; Baker and Lababidi, 2010; Bizmark et al., 2010; Fyhr et al., 1999; Izadifar and Mowla, 2003; Khanali et al., 2013; Nilson and Wimmerstedt, 1987; Ramli and Daud, 2007; Wanjari et al., 2006). It should be noted that the simulated moisture content showed a discontinuity at the solid inlet port of the dryer. For example, the moisture content of the shelled corn for Runs 1, 18 and 36 were 0.302, 0.305 and 0.308 (d.b.) at the solid inlet port, which respectively decreased into 0.294, 0.287 and 0.268 (d.b.), right after the kernels fed into the bed. This behavior is a combined result of the axially dispersed flow of solid particles inside the bed and the perfect plug flow of the feed particles at the solid inlet port. On the other hand, the simulated discontinuity satisfies the considered inlet boundary condition resembles the dispersed flow imposed on the plug flow of feed stream. It is important to point out that this discontinuity in the plug flow fluidized bed drying process has been only modeled by Khanali et al. (2013). The experimental results of some studies in the field of plug flow fluidized bed drying process showed the rapid decrease of solid moisture content inside the bed within a short distance from the solid inlet port (Bizmark et al., 2010; Izadifar and Mowla, 2003). These studies experimentally confirmed this discontinuity, but it was not described properly via modeling. The ability of the present study to show the discontinuous decrease of inlet solid moisture content at the solid inlet port can be regarded as its unique characteristic. 0.35 0.35 Input Run 1 Input Run 6
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Fig. 4 The typical simulated profile and experimental values of solid moisture content versus dryer length 3.2 Model accuracy
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Values of the relative error and the mean relative deviation of the model in predicting the outlet solid moisture content and the solid moisture content at various locations along the dryer length are given in Table 3. The values of the model relative error for all experiments in predicting solid moisture content at the outlet port and the points located along the bed at 0.1, 0.5 and 0.9 m from the solid inlet port are lower than 7.78%, 4.85%, 6.24% and 5.17%, respectively. The values of mean relative deviation at the outlet and the points along the bed at 0.1, 0.5 and 0.9 m length from the solid inlet port are 3.25%, 2.25%, 2.33% and 2.11%, respectively. As can be seen from Table 3, the relative error values less than 10% are considered acceptable in modeling of the drying process (Brooker et al., 1992; Naghavi et al., 2010; Zare et al., 2006). Therefore, it can be concluded that the present model predicts the axial profile of solid moisture content with a high accuracy.
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Table 3 Model accuracy in predicting solid moisture content along the dryer length Relative error (E, %) Run M1 a M2 M3 Mout 1 0.43 0.52 0.37 5.47 2 1.58 1.37 2.84 0.04 5.25 3 4.02 4.24 1.82 4 0.61 3.63 5.20 5.99 5.72 5 0.61 0.53 0.95 6 1.78 0.49 2.24 4.05 7 4.10 3.82 2.10 3.63 8 2.68 0.48 2.95 3.18 2.59 9 2.59 1.70 0.17 10 1.41 1.46 0.70 0.14 11 2.82 1.46 0.48 2.82 12 1.19 1.26 0.12 3.07 13 0.19 1.85 5.17 7.78 14 0.18 0.06 2.31 3.15 15 3.54 1.95 2.90 4.27 16 2.52 3.16 1.13 0.27 17 2.58 0.40 1.05 2.58 18 0.51 3.19 2.46 0.13 19 3.00 2.49 4.04 7.01 20 3.66 3.02 1.59 0.96 5.10 21 1.67 0.90 1.40 22 0.55 0.77 2.28 2.20 0.47 23 2.33 1.56 2.42 24 1.59 6.24 1.13 1.16 25 2.12 0.88 0.61 0.51 26 3.87 2.29 2.38 1.87 27 4.85 1.53 2.17 1.14 0.71 28 0.89 0.21 1.21 29 3.00 3.72 1.33 0.28 30 0.40 2.17 0.82 0.50 31 0.52 0.26 1.90 1.66 32 0.88 2.71 0.72 1.44 33 1.41 1.25 0.52 0.80 34 0.96 2.26 0.16 0.45 35 1.23 1.69 2.05 1.23 36 1.45 1.32 2.15 0.39 MRD (%) 2.25 2.33 2.11 3.25 a Subscripts 1, 2 and 3 refer to the sampling points at 0.1, 0.5 and 0.9 m from the solid inlet port, respectively.
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3.3 Effect of inlet dry solid mass flow rate on solid moisture content
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Fig. 5 shows the typical simulated axial profiles of shelled corn moisture content at inlet dry solid mass flow rates of 245, 420 and 565 g/min, inlet gas temperature of 80°C and weir height of 0.05 m. At constant inlet gas temperature and weir height as shown in Fig. 5, the shelled corn moisture content increased at any given point along the dryer length with increasing inlet dry solid mass flow rate. The higher moisture content along the dryer length resulted from the increased inlet dry solid mass flow rate is due to the decreased residence time of the corn kernels inside the dryer which in turn led to the lower drying. The non-linear dependency of solid moisture content profile on the inlet dry solid mass flow rate can also be seen in Fig. 5. In this context, the changes of solid moisture content due to the various values of inlet solid mass flow rate at the inlet boundary are different from those at outlet boundary, which are expression of the non-linearity of the system. Similar non-linear behavior was stated for fluidized bed drying of the rough rice (Khanali et al., 2013) and a fast-drying hygroscopic material (Baker et al., 2006).
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3.4 Effect of inlet gas temperature on solid moisture content Fig. 6 shows the typical simulated axial profiles of shelled corn moisture content at inlet gas temperatures of 50, 70, 90 and 100°C, inlet dry solid mass flow rate of 245 g/min and weir height of 0.05 m. At a given inlet dry solid mass flow rate and weir height, the drying rate increased with inlet gas temperature. On the other hand, at any position along the dryer length, the moisture content of the shelled corn decreased with increasing drying gas temperature. This effect is related to the increase of intra-particle moisture transport as the particles temperature increases with increasing inlet gas temperature (Kannan et al., 1995). Similar results were also presented in several studies regarding to the modeling of plug flow fluidized bed drying process (Baker et al., 2006; Bizmark et al., 2010; Khanali et al., 2013; Wanjari et al., 2006). The lower decrease of shelled corn moisture content at the solid inlet port compared to that at the exit port as a result of increased inlet gas temperature is an indication of the non-linearity of the drying process.
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Fig. 6 Effect of inlet gas temperature on solid moisture content (hweir = 0.05 m, F = 245 g/min) 3.5 Effect of weir height on solid moisture content
Fig. 7 shows the simulation results of shelled corn moisture content at weir heights of 0.025 and 0.05 m, inlet gas temperature of 100°C and inlet dry solid mass flow rate of 565 g/min. As shown, at constant inlet gas temperature and inlet dry solid mass flow rate, the solid moisture content at any point along the dryer decreased with increasing weir height. It can be demonstrated that at the fixed solid feed rate, increasing the weir height increased the solid holdup within the bed, thus the residence time of the solid particles in the dryer and the extent of their drying are increased. The nonlinearity of the drying process of shelled corn is clearly shown in this figure. The similar results were also obtained both experimentally and theoretically by Khanali et al. (2013).
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Fig. 7 Effect of weir height on solid moisture content (Tg = 100 °C, F = 565 g/min) 4 Conclusions
In this study, a differential model of the plug flow fluidized bed dryer was developed and validated experimentally by drying shelled corn in a plug flow fluidized bed dryer. The axial profile of solid moisture content was modeled by developing the mass balance of moisture content in the solid particles along with the application of the axial dispersion phenomenon and
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an analytical drying rate equation. The comparison between experimental and estimated values of the shelled corn moisture content showed that the proposed model can predict the drying characteristics with a good degree of accuracy. As a result of axial dispersion, the simulated solid moisture content profile showed a discontinuity at the solid inlet boundary of the bed and then decreased continuously across the dryer length. It was found that the solid moisture content decreased by increasing both the inlet gas temperature and the weir height, whereas increasing the inlet dry solid mass flow rate led to the increased solid moisture content.
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Acknowledgement The authors will like to thank University of Tehran for funding the project numbered 03-6324030. References
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Baker, C., Khan, A., Ali, Y., Damyar, K., 2006. Simulation of plug flow fluidized bed dryers. Chemical Engineering and Processing: Process Intensification 45(8), 641-651. Baker, C., Lababidi, H., 2010. An improved model of plug-flow fluidized bed dryers with an emphasis on energy conservation. Drying Technology 28(5), 730-741. Bizmark, N., Mostoufi, N., Sotudeh-Gharebagh, R., Ehsani, H., 2010. Sequential modeling of fluidized bed paddy dryer. Journal of food engineering 101(3), 303-308. Brooker, D.B., Bakker-Arkema, F.W., Hall, C.W., 1992. Drying and storage of grains and oilseeds. Springer Science & Business Media. Fogler, H.S., 1987. Elements of chemical reaction engineering. Prentice-Hall of India, New Delhi. Fyhr, C., Kemp, I.C., Wimmerstedt, R., 1999. Mathematical modelling of fluidised bed dryers with horizontal dispersion. Chemical Engineering and Processing: Process Intensification 38(2), 89-94. Izadifar, M., Mowla, D., 2003. Simulation of a cross-flow continuous fluidized bed dryer for paddy rice. Journal of Food Engineering 58(4), 325-329. Janas, S., Boutry, S., Malumba, P., Vander Elst, L., Béra, F., 2010. Modelling dehydration and quality degradation of maize during fluidized-bed drying. Journal of food engineering 100(3), 527-534. Kannan, C.S., Thomas, P., Varma, Y., 1995. Drying of solids in fluidized beds. Industrial & engineering chemistry research 34(9), 3068-3077. Khanali, M., Rafiee, S., Jafari, A., 2014. Numerical simulation and experimental investigation of plug-flow fluidized bed drying under dynamic conditions. Journal of Food Engineering 137, 64-75. Khanali, M., Rafiee, S., Jafari, A., Hashemabadi, S.H., 2013. Experimental investigation and modeling of plug-flow fluidized bed drying under steady-state conditions. Drying Technology 31(4), 414-432. Kunii, D., Levenspiel, O., 2013. Fluidization engineering. Elsevier. Topuz, A., Gur, M., Gul, M.Z., 2004. An experimental and numerical study of fluidized bed drying of hazelnuts. Applied Thermal Engineering, 24(10), 535-1547. Levenspiel, O., 1999. Chemical reaction engineering. John Wiley & Sons, New York. Mohsenin, N.N., 1986. Physical properties of plant and animal materials. Gordon and Breach Science Publishers, New York. Mujumdar, A.S., 2006. Handbook of industrial drying. Crc Press. Mujumdar, A.S., Devahastin, S., 2003. Applications for fluidized bed drying, Handbook of fluidization and fluid-particle systems. Marcel Dekker Inc., New York, pp. 469-484.
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Naghavi, Z., Moheb, A., Ziaei-Rad, S., 2010. Numerical simulation of rough rice drying in a deep-bed dryer using non-equilibrium model. Energy Conversion and Management 51(2), 258264. Nilson, L., Wimmerstedt, R., 1987. Drying in longitudinal-flow vibrating fluid-beds: Pilot plant experiments and model simulations. Drying Technology 5(3), 337-361. Nilsson, L., Wimmerstedt, R., 1988. Residence time distribution and particle dispersion in a longitudinal-flow fluidized bed. Chemical engineering science 43(5), 1153-1160. Pakowski, Z., Mujumdar, A.S., 2006. Basic Process Calculations and Simulations in Drying, Handbook of industrial drying. Taylor and Francis Group, London, pp. 79-106. Ramli, W., Daud, W., 2007. A cross-flow model for continuous plug flow fluidized-bed crossflow dryers. Drying Technology 25(7-8), 1229-1235. Samapundo, S., Devlieghere, F., De Meulenaer, B., Atukwase, A., Lamboni, Y., Debevere, J.M., 2007. Sorption isotherms and isosteric heats of sorption of whole yellow dent corn. Journal of Food Engineering 79(1), 168-175. Sivakumar, R., Saravanan, R., Perumal, A.E., Iniyan, S., 2016. Fluidized bed drying of some agro products–A review. Renewable and Sustainable Energy Reviews 61, 280-301. Sopornonnarit, S., Prachayawarakorn, S., Sripawaatakul, O., 1996. Development of cross-flow fluidized bed paddy dryer. Drying Technology 14(10), 2397-2410. Wanjari, A., Thorat, B., Baker, C., Mujumdar, A., 2006. Design and modeling of plug flow fluid bed dryers. Drying technology 24(2), 147-157. Zare, D., Minaei, S., Zadeh, M.M., Khoshtaghaza, M., 2006. Computer simulation of rough rice drying in a batch dryer. Energy Conversion and Management 47(18), 3241-3254.
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DOI:
10.1016/j.eaef.2017.09.002
Reference:
EAEF 159
To appear in:
Engineering in Agriculture, Environment and Food
Received Date: 3 January 2017 Revised Date:
14 June 2017
Accepted Date: 10 September 2017
Please cite this article as: Khanali M, Giglou AK, Rafiee S, Model development for shelled corn drying in a plug flow fluidized bed dryer, Engineering in Agriculture, Environment and Food (2017), doi: 10.1016/ j.eaef.2017.09.002. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
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Title: Model development for shelled corn drying in a plug flow fluidized bed dryer
Majid Khanali*, Asgar Khakpour Giglou, Shahin Rafiee
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REFERENCE NO. EAEF 159
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Corresponding authors:
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Department of Agricultural Machinery Engineering, Faculty of Agricultural Engineering and Technology, College of Agriculture and Natural Resources, University of Tehran, Karaj, Iran.
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Majid Khanali Department of Agricultural Machinery Engineering, Faculty of Agricultural Engineering and Technology, University of Tehran, Karaj, Iran. Tel: +98-26-32801011, Fax: +98-26-32808138; Email address: [email protected]
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Model development for shelled corn drying in a plug flow fluidized bed dryer
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Abstract In the present study, a differential model of the plug flow fluidized bed dryer for shelled corn was presented. The model was developed by using the mass balance of moisture content inside a control volume of the bed based on the axial dispersion phenomenon and an appropriate drying rate equation. The differential equation resulted from the model was solved numerically by finite difference method. To validate the model, several experiments for shelled corn drying in a plug flow fluidized bed dryer under steady state conditions were performed at three inlet dry solid mass flow rates (245, 420 and 565 g/min), six drying air temperatures (50, 60, 70, 80, 90 and 100 °C) and two weir heights (0.025 and 0.05 m). The model was capable to predict correctly the moisture content of the grains at any locations along the dryer length. Based on the simulation results, the solid moisture content decreased discontinuously at the solid inlet boundary of the bed and then decreased continuously along the dryer length. The simulation results were also analyzed to investigate the effects of inlet gas temperature, weir height and inlet dry solid mass flow rate on the solid moisture content. The solid moisture content decreased by increasing inlet gas temperature and weir height, whereas it increased by increasing the inlet dry solid mass flow rate.
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Keywords Axial dispersion. Drying. Fluidized bed. Modeling. Shelled corn
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Specific surface area of expanded bed (m2/m3) Particle diameter (m) Dispersion coefficient (m2/s) Relative error (%) Mass flow rate of dry solid (kg/s) (g/min) Bed height (m) Weir height (m) Mass transfer coefficient (m/s) Bed length (m) Drying rate per unit bed volume (kg H2O/m3s) Solid moisture content (dry basis) (kg water/kg dry solid) Mean relative deviation (%) Number of measurements Atmospheric pressure (Pa) Saturated vapor pressure (Pa) Reynolds number (dimensionless) (Re = U d ρ ⁄μ ) Equilibrium relative humidity (dimensionless) Solid holdup (kg) Schmidt number (dimensionless) (Sc = % ⁄& ) Sherwood number (dimensionless) (Sh = Kd ⁄&) Drying gas temperature (°C) Axial solid flow velocity (m/s) Superficial fluidization velocity (m/s) Minimum fluidization velocity (m/s) Bed width (m) Bed length coordinate (m) Equilibrium absolute humidity (kg H2O/kg dry air) Absolute humidity of inlet drying air (kg H2O/kg dry air)
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List of symbols a d D E F h h K L m M MRD n P P Re RH S Sc Sh T u U U ) w x Y YGreek Letters α ε μ ν ρ2 ρ ρ Subscripts exp in out pre
Moisture diffusivity in drying air (m2/s) Porosity of stagnant bed (dimensionless) Viscosity (kg/ms) Kinematic viscosity of drying air (m2/s) (% = μ1 ⁄ρ ) Bulk density (kg/m3) Density of drying air (kg/m3) True density (kg/m3)
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Experimental Input Output Predicted
Highlights Plug flow Fluidized bed drying of shelled corn was investigated experimentally. The axial profile of solid moisture content was modeled reasonably well by a differential model.
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The axial dispersion phenomenon and an analytical drying rate equation were considered in the model. Solid moisture content profile showed a discontinuity at the solid inlet port of the dryer and then decreased continuously across the dryer length. 1 Introduction
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Shelled corn (Zea mays L.) is one of the major grains that is usually harvested at considerably high moisture content in the range of 0.4 to 0.5 d.b. (dry basis, kilograms of water per kilogram of dry solid) and has to be dried to a moisture content of around 0.14 d.b for long-term preservation (Brooker et al., 1992). Drying is the most widely practical unit operation in many fields such as agricultural, food, chemical, pharmaceutical and mineral industries. Drying is a complex, time-variant and nonlinear phenomenon. Accurate modeling of the drying process is an important factor for simulation and optimization of the process, design of the drying system and controlling the operation (Mujumdar, 2006). Fluidized bed dryers (FBDs) have been applied extensively for drying of particulate or granular materials in the chemical, food, biomaterials, ceramic, pharmaceutical, agriculture, polymer and waste management industries. Numerous designs of FBDs are available, among which, batch type, continuous well-mixed, plug flow, vibrated, mechanically agitated, centrifugal and spouted types are the more commonly used fluidized bed dryers. Fluidized bed drying operation have several advantages such as high drying rates, good thermal e ciency, low capital and maintenance costs, easy material transport and ease of control (Khanali et al., 2014; Mujumdar, 2006; Mujumdar and Devahastin, 2003; Sivakumar et al., 2016; Topuz et al., 2004). This study is concerned with the mathematical modeling of drying process of shelled corn in a plug flow fluidized bed dryer. This type of dryer features a long narrow bed with length to width ratios of 5:1 to 30:1; the fluidized solid particles flow continuously as a plug through the bed from the inlet to the exit. This plug flow ensures approximately equal residence time for all particles which results in the uniformity of the outlet product moisture content. In this dryer, drying times typically range from 1 min to 2 h and the bed height is relatively low in order to minimize axial mixing of the flowing particles (Baker and Lababidi, 2010). A schematic sketch of the plug flow fluidized bed dryer and the flows of drying air and solid particles are shown in Fig. 1.
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Fig. 1 A schematic diagram of the flows of drying air and solids in a plug flow fluidized bed dryer
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There are two basic modeling methods for plug flow fluidized bed drying process, differential and tanks-in-series. In the differential model, the bed is divided into control volume elements and the mass, energy and momentum balances for both solid and gas phases in each element are developed (Khanali et al., 2013; Nilson and Wimmerstedt, 1987; Pakowski and Mujumdar, 2006; Ramli and Daud, 2007; Sopornonnarit et al., 1996). In some cases, the water diffusion in solid particles is considered based on Fick’s second law (Izadifar and Mowla, 2003). In the tanks-in-series model, the bed is divided into several continuous well-mixed fluidized bed dryer vessels in series. The drying process is analyzed considering the governing equations simulating behavior of each dryer vessel combined with axial dispersion phenomenon (Baker et al., 2006; Baker and Lababidi, 2010; Bizmark et al., 2010; Fyhr et al., 1999; Wanjari et al., 2006). The objective of the present study was to develop a differential model of the plug flow fluidized bed drying process under steady state conditions and to validate it with experimental data of the shelled corn drying in a pilot scale plug flow fluidized bed dryer. Despite the importance of corn drying in Iran and considerable amount of research works on modeling of fluidized bed drying of agricultural materials, there is no study about modeling and investigation of plug flow fluidized bed drying of shelled corn. The model developed in this study builds upon the earlier work by Khanali et al. (2013) in which a mathematical modeling and experimental investigation of the plug flow fluidized bed drying of rough rice was conducted. In the present study, an analytical drying rate equation of solid particles was taken into account instead of the experimental one considered in the work by Khanali et al. (2013) and the axial profile of shelled corn moisture content along the dryer length was derived theoretically and experimentally. The results of simulation were also analyzed to investigate the effects of inlet gas temperature, weir heights and inlet dry solid mass flow rate on axial profile of solid moisture content. 2 Material and methods 2.1 Drying experiments
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The single cross 704 variety of shelled corn used in this study was prepared from Moghan region of Iran. The shelled corn kernels were cleaned to remove broken particles, straw and stones, then the kernels were wetted, mixed and stored 3-5 °C in plastic bags for five days prior to the drying experiments to reach the uniform water concentration. The experiments were performed in a pilot scale plug flow fluidized bed dryer that is shown in Fig. 2. The shelled corn was fed from the hopper to the dryer through a screw conveyor. The drying air was supplied by a centrifugal fan, heated by a controllable electrical heater and entered to the drying chamber after passing through the air distributor plate. The length of the dryer was 100 cm and its width was 8 cm. A detailed illustration about the dryer and its performance used in this study can be found from the work by Khanali et al. (2013). It must be mentioned that the appropriate air distributor plate used specifically for shelled corn was 1 mm thick perforated steel plate and consisted of 4 mm holes on a 5 mm triangular pitch, giving an open area of about 15%. To measure the particles moisture content, sampling was performed at three points along the dryer length at 0.1, 0.5, and 0.9 m from the solid inlet port. The moisture content was determined off-line by drying the grains at temperature of 105 °C for 48 h in a hot air oven. To measure solid holdup within the bed at each drying experiment, the flow of solid particles was stopped suddenly and simultaneously the materials at the outlet of the dryer were collected
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until the entire solid holdup came out of the bed. The weight of the collected sample was the solid holdup within the bed. The drying experiments were conducted under steady state conditions as indicated in Table 1. Stable conditions in terms of outlet solid mass flow rate as well as humidity and temperature of the outlet gas were considered as the steady state conditions. The necessary time to reach the steady state conditions was considered two times the average residence time of the particles in the dryer. It should be noted that the study of the process at the start of the dryer was not in the scope of this study. Each experiment was started when the bed is empty by setting the superficial fluidization velocity, inlet gas temperature and inlet dry solid mass flow rate at the desired levels. The drying experiments were conducted at inlet dry solid mass flow rates of 245, 420 and 565 g/min, drying air temperatures of 50, 60, 70, 80, 90 and 100 °C, weir heights of 0.025 and 0.05 m and superficial fluidization velocity of 3 m/s. The values of solid inlet moisture content in all experiments were in the range of 0.29 to 0.315 d.b.
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Fig. 2 Schematic diagram of the pilot scale plug flow fluidized bed dryer Table 1 Operating conditions for each drying experiment Run F (g/min) h (m) U T (°C) 1 50 245 0.025 2 50 245 0.05 3 50 420 0.025 4 50 420 0.05 5 50 565 0.025 6 50 565 0.05 7 60 245 0.025 8 60 245 0.05 9 60 420 0.025 10 60 420 0.05 11 60 565 0.025 12 60 565 0.05
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Y - (kg/kg) 0.0304 0.0299 0.0316 0.0321 0.0280 0.0287 0.0086 0.0091 0.0013 0.0010 0.0024 0.0103
S (kg) 0.685 1.104 0.761 1.121 0.706 1.275 0.614 1.036 0.626 0.995 0.664 1.267
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3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
0.0243 0.0301 0.0280 0.0098 0.0078 0.0010 0.0010 0.0019 0.0132 0.0045 0.0032 0.0013 0.0014 0.0019 0.0020 0.0034 0.0010 0.0012 0.0015 0.0018 0.0023 0.0030 0.0029 0.0033
0.567 1.041 0.575 1.083 0.584 1.181 0.524 0.937 0.598 1.032 0.634 1.079 0.530 0.907 0.599 1.077 0.609 1.011 0.499 0.814 0.541 0.880 0.610 1.037
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Heat and mass balance equations in solids that determine respectively the temperature and moisture content are the basic equations in modeling the drying process. Drying rate of solid material is affected by its temperature. However the temperature of the solid particles in fluidized bed drying method quite rapidly reaches the drying air temperature (Baker et al., 2006; Baker and Lababidi, 2010; Bizmark et al., 2010; Janas et al., 2010; Wanjari et al., 2006). In the case of rough rice drying in a plug flow fluidized bed dryer, the solid temperature increased rapidly within a short distance from the solid inlet port, approached a temperature nearly the same as the drying air temperature, and remained nearly constant until the dryer exit (Khanali et al., 2013). For this reason, the drying process in this study was considered as isothermal process, thus, only the mass balance for the moisture of shelled corn is considered. Mass balance of solid moisture content is written on a control volume (hwdx) placed on an arbitrary position along the bed length as shown in Fig. 3.
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Fig. 3 Schematic differential model of the dryer bed and mass transfer between air and solid particles in the control volume In practice, the ideal plug flow of solid materials through the bed in fluidized bed dryers is rarely met. Because of the motion of gas-bubbles and the particles back-mixing in the bed, particles are mixed horizontally and the result is more spreading of residence time. In the present study, the deviation from ideal plug flow is modeled by considering axial dispersion. Mass balance (referring to the evaporating medium, i.e., the moisture content) in steady state condition is developed by considering both input and output flows of moisture by two major mechanisms, bulk flow and dispersed flow. Although the rate of moisture transfer between drying air and solid particles due to evaporation is considered. The basic mass balance equation in the particles at steady state conditions considering the control volume shown in Fig. 3 is (Levenspiel, 1999): Moisture input rate by bulk flow – moisture output rate by bulk flow + moisture input (1) rate by dispersed flow – moisture output rate by dispersed flow – rate of moisture evaporation from the particles = 0 The values for each term of Eq. (1) in kilograms of water per unit time are given subsequently. The moisture input rate by bulk flow along the dryer length coordinate at x is: (2) hwuρ2 3 M Where h is bed height, w is the bed width, u is the axial solid flow velocity, ρ2 3 is the bed density and M is the particles moisture content. The moisture output rate from the control volume at x + dx by bulk flow can then be expressed as a Taylor series expansion where, neglecting higher-order terms, 36 (3) hwuρ 5M + dx9 78
In words, Equation 3 simply states that moisture transfer rate at x + dx is equal to the value of 36 this component at x plus the amount by which it changes with respect to x ( ) times dx. 78 The degree of axial mixing is quantified by the dispersion coefficient (D) and by an analogy to the Fick’s law of diffusion. The moisture input rate by axial dispersion at x can be calculated as follows (Levenspiel, 1999): 36 (4) −Dhwρ2 3 38 The moisture output rate by axial dispersion at x + dx by applying Taylor series expansion and neglecting higher-order terms is obtained as: 36 3 36 (5) −Dhwρ 5 + 5 9 dx9
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At the solid inlet port, the solid particles transported from the hopper to dryer by the screw conveyor are mixed with partially dried particles inside the dryer. Therefore the equality of the solid inlet moisture content and the sum of carried moisture content by both bulk flow and dispersed flow is considered as the boundary condition at the solid inlet port as: C 36 M- = M− for x = 0 (9) D 38 At the solid exit port, considering the continuous flow of particles over the exit weir, the boundary condition is: 36 (10) =0 for x = L 38
Based on Levenspiel (1999) and Fogler (1987) and considering the flow patterns of the particles at the solid inlet and exit ports, the considered boundary conditions can be classified as closedclosed type. 2.3 Required equations
The drying rate per unit volume of the bed (m) is calculated as follows (Brooker et al., 1992): m = Kaρ (Y − Y - ) (11) The following formula is used to calculate the air absolute humidity in equilibrium with the particle surface (Brooker et al., 1992): JKA LMN Y = 0.622 (12)
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Where RHS , the equilibrium relative humidity of air in contact with shelled corn is related to the solid moisture content and drying air temperature according to the following equation (Samapundo et al., 2007): RH = 1 − exp (−3.11 × 10RY T MZ.[Z\ ) (13) The mass transfer coefficient between the particles and the drying air is calculated according to (Kunii and Levenspiel, 2013): ]3
`
`
Sh = ^ = 2 + 0.6 Re> Sc a (14) _ The bed density (ρ2 3 ) is a function of bed voidage and true density of the solid particles. In order not to disturb the main text, a detailed analysis of the bed voidage calculation based on the two-phase theory of fluidization can be found in Khanali et al. (2013). The axial solid flow velocity was calculated using the following equation: b u= (15)
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The rate of moisture leaving the major control volume due to the moisture evaporation from the particles into the gas is: (6) hwmdx By substituting Eqs. (2-6) into the mass balance expression, i.e., Eq. (1), it follows that: 36 36 36 (7) hwuρ M − hwuρ 5M + dx9 + 5−Dhwρ 9 − ;−Dhwρ 5 +
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The dispersion coefficient was obtained with the following equation (Nilsson and Wimmerstedt, 1988): Z.ef g . Z(cRchijk )l . ZmY no pqr Rqst uvwr.>a (16) d= `x qst a
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Property P
Where h is the bed height (m), y is the superficial fluidization velocity (m/s), yz{ is the minimum fluidization velocity (m/s) and |1 is the gas density (kg/m3). To solve the model, some physical properties of the air-vapor mixture and the shelled corn are required. These properties were measured experimentally or extracted from the literature as summarized in Table 2.
Table 2 Physical properties of air and shelled corn applied in this study Equation
P = 100 ∗ exp 527.0214 − 6887⁄pT + 273.16u − 5.31lnppT + 273.16u ⁄273.16u9 (T in °C) Z.ƒZ
& = pT ⁄273.15u
(T in °C)
μ = 1.691 × 10RY + 4.984 × 10Rƒ T − 3.187 × 10RZZ T
a
677 m2/m3
d ρ ρ2 ε†
7.9×10-3 1185 kg/m3 740 kg/m3 0.37
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ρ = 353.05⁄pT + 273.16u (T in °C)
\
(T in °C)
The accuracy of the developed model in prediction of solid moisture content were evaluated on the basis of the relative error (E) and the mean relative deviation (MRD) as follow (Zare et al., 2006): ‡6 R6 ‡ (17) E = ^ˆA A‰^ × 100 6^ˆA Z
-
6^ˆA R6A‰^ 6^ˆA
…
< Ž
.Y
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MRD = Š ∑-Œ•Z ;
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Reference (Naghavi et al., 2010) (Janas et al., 2010) (Khanali et al., 2013) (Khanali et al., 2013) (Mohsenin, 1986) Measured Measured Measured Measured
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3.1 Axial profile of solid moisture content By substituting the drying rate per unit volume of the bed (m) based on Eqs. (11-14) into Eq. (8), the result is a second-order nonlinear differential equation in which solid moisture content (M) is the dependent variable, location along the dryer length (x) is the independent variable, and Eqs. (9-10) are its boundary conditions. The resulted differential equation was solved numerically for solid moisture content by using the finite difference method. Based on the solution of the discrete set of equations at finite points along the dryer length, a computer program was developed and implemented in MATLAB (version 8.5) environment to simulate the drying process.
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Based on the experimental observations, a uniform and stable fluidization of the shelled corn kernels across the entire bed cross section during drying process was achieved. The acceptable fluidization state can be attributed to the uniform solids feeding, uniform gas distribution across the bed and perfect solids mixing. As a result, the outlet solids with uniform moisture content was achieved. The simulated profile of solid moisture content along the dryer length as well as the measured values of moisture content of the solid samples taken out of the dryer for typical Runs 1, 6, 12, 18, 22, 28, 32 and 36 are shown in Fig. 4. It is clear that the model predicts the profiles of solid moisture content reasonably well. As shown, the solid moisture content decreases nonlinearly with increasing distance from the solid inlet port. Approximately, similar axial profiles of solid moisture content for plug flow fluidized bed drying of different materials have been reported in the literature (Baker et al., 2006; Baker and Lababidi, 2010; Bizmark et al., 2010; Fyhr et al., 1999; Izadifar and Mowla, 2003; Khanali et al., 2013; Nilson and Wimmerstedt, 1987; Ramli and Daud, 2007; Wanjari et al., 2006). It should be noted that the simulated moisture content showed a discontinuity at the solid inlet port of the dryer. For example, the moisture content of the shelled corn for Runs 1, 18 and 36 were 0.302, 0.305 and 0.308 (d.b.) at the solid inlet port, which respectively decreased into 0.294, 0.287 and 0.268 (d.b.), right after the kernels fed into the bed. This behavior is a combined result of the axially dispersed flow of solid particles inside the bed and the perfect plug flow of the feed particles at the solid inlet port. On the other hand, the simulated discontinuity satisfies the considered inlet boundary condition resembles the dispersed flow imposed on the plug flow of feed stream. It is important to point out that this discontinuity in the plug flow fluidized bed drying process has been only modeled by Khanali et al. (2013). The experimental results of some studies in the field of plug flow fluidized bed drying process showed the rapid decrease of solid moisture content inside the bed within a short distance from the solid inlet port (Bizmark et al., 2010; Izadifar and Mowla, 2003). These studies experimentally confirmed this discontinuity, but it was not described properly via modeling. The ability of the present study to show the discontinuous decrease of inlet solid moisture content at the solid inlet port can be regarded as its unique characteristic. 0.35 0.35 Input Run 1 Input Run 6
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Values of the relative error and the mean relative deviation of the model in predicting the outlet solid moisture content and the solid moisture content at various locations along the dryer length are given in Table 3. The values of the model relative error for all experiments in predicting solid moisture content at the outlet port and the points located along the bed at 0.1, 0.5 and 0.9 m from the solid inlet port are lower than 7.78%, 4.85%, 6.24% and 5.17%, respectively. The values of mean relative deviation at the outlet and the points along the bed at 0.1, 0.5 and 0.9 m length from the solid inlet port are 3.25%, 2.25%, 2.33% and 2.11%, respectively. As can be seen from Table 3, the relative error values less than 10% are considered acceptable in modeling of the drying process (Brooker et al., 1992; Naghavi et al., 2010; Zare et al., 2006). Therefore, it can be concluded that the present model predicts the axial profile of solid moisture content with a high accuracy.
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Table 3 Model accuracy in predicting solid moisture content along the dryer length Relative error (E, %) Run M1 a M2 M3 Mout 1 0.43 0.52 0.37 5.47 2 1.58 1.37 2.84 0.04 5.25 3 4.02 4.24 1.82 4 0.61 3.63 5.20 5.99 5.72 5 0.61 0.53 0.95 6 1.78 0.49 2.24 4.05 7 4.10 3.82 2.10 3.63 8 2.68 0.48 2.95 3.18 2.59 9 2.59 1.70 0.17 10 1.41 1.46 0.70 0.14 11 2.82 1.46 0.48 2.82 12 1.19 1.26 0.12 3.07 13 0.19 1.85 5.17 7.78 14 0.18 0.06 2.31 3.15 15 3.54 1.95 2.90 4.27 16 2.52 3.16 1.13 0.27 17 2.58 0.40 1.05 2.58 18 0.51 3.19 2.46 0.13 19 3.00 2.49 4.04 7.01 20 3.66 3.02 1.59 0.96 5.10 21 1.67 0.90 1.40 22 0.55 0.77 2.28 2.20 0.47 23 2.33 1.56 2.42 24 1.59 6.24 1.13 1.16 25 2.12 0.88 0.61 0.51 26 3.87 2.29 2.38 1.87 27 4.85 1.53 2.17 1.14 0.71 28 0.89 0.21 1.21 29 3.00 3.72 1.33 0.28 30 0.40 2.17 0.82 0.50 31 0.52 0.26 1.90 1.66 32 0.88 2.71 0.72 1.44 33 1.41 1.25 0.52 0.80 34 0.96 2.26 0.16 0.45 35 1.23 1.69 2.05 1.23 36 1.45 1.32 2.15 0.39 MRD (%) 2.25 2.33 2.11 3.25 a Subscripts 1, 2 and 3 refer to the sampling points at 0.1, 0.5 and 0.9 m from the solid inlet port, respectively.
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3.3 Effect of inlet dry solid mass flow rate on solid moisture content
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Fig. 5 shows the typical simulated axial profiles of shelled corn moisture content at inlet dry solid mass flow rates of 245, 420 and 565 g/min, inlet gas temperature of 80°C and weir height of 0.05 m. At constant inlet gas temperature and weir height as shown in Fig. 5, the shelled corn moisture content increased at any given point along the dryer length with increasing inlet dry solid mass flow rate. The higher moisture content along the dryer length resulted from the increased inlet dry solid mass flow rate is due to the decreased residence time of the corn kernels inside the dryer which in turn led to the lower drying. The non-linear dependency of solid moisture content profile on the inlet dry solid mass flow rate can also be seen in Fig. 5. In this context, the changes of solid moisture content due to the various values of inlet solid mass flow rate at the inlet boundary are different from those at outlet boundary, which are expression of the non-linearity of the system. Similar non-linear behavior was stated for fluidized bed drying of the rough rice (Khanali et al., 2013) and a fast-drying hygroscopic material (Baker et al., 2006).
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3.4 Effect of inlet gas temperature on solid moisture content Fig. 6 shows the typical simulated axial profiles of shelled corn moisture content at inlet gas temperatures of 50, 70, 90 and 100°C, inlet dry solid mass flow rate of 245 g/min and weir height of 0.05 m. At a given inlet dry solid mass flow rate and weir height, the drying rate increased with inlet gas temperature. On the other hand, at any position along the dryer length, the moisture content of the shelled corn decreased with increasing drying gas temperature. This effect is related to the increase of intra-particle moisture transport as the particles temperature increases with increasing inlet gas temperature (Kannan et al., 1995). Similar results were also presented in several studies regarding to the modeling of plug flow fluidized bed drying process (Baker et al., 2006; Bizmark et al., 2010; Khanali et al., 2013; Wanjari et al., 2006). The lower decrease of shelled corn moisture content at the solid inlet port compared to that at the exit port as a result of increased inlet gas temperature is an indication of the non-linearity of the drying process.
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Fig. 6 Effect of inlet gas temperature on solid moisture content (hweir = 0.05 m, F = 245 g/min) 3.5 Effect of weir height on solid moisture content
Fig. 7 shows the simulation results of shelled corn moisture content at weir heights of 0.025 and 0.05 m, inlet gas temperature of 100°C and inlet dry solid mass flow rate of 565 g/min. As shown, at constant inlet gas temperature and inlet dry solid mass flow rate, the solid moisture content at any point along the dryer decreased with increasing weir height. It can be demonstrated that at the fixed solid feed rate, increasing the weir height increased the solid holdup within the bed, thus the residence time of the solid particles in the dryer and the extent of their drying are increased. The nonlinearity of the drying process of shelled corn is clearly shown in this figure. The similar results were also obtained both experimentally and theoretically by Khanali et al. (2013).
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In this study, a differential model of the plug flow fluidized bed dryer was developed and validated experimentally by drying shelled corn in a plug flow fluidized bed dryer. The axial profile of solid moisture content was modeled by developing the mass balance of moisture content in the solid particles along with the application of the axial dispersion phenomenon and
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an analytical drying rate equation. The comparison between experimental and estimated values of the shelled corn moisture content showed that the proposed model can predict the drying characteristics with a good degree of accuracy. As a result of axial dispersion, the simulated solid moisture content profile showed a discontinuity at the solid inlet boundary of the bed and then decreased continuously across the dryer length. It was found that the solid moisture content decreased by increasing both the inlet gas temperature and the weir height, whereas increasing the inlet dry solid mass flow rate led to the increased solid moisture content.
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Acknowledgement The authors will like to thank University of Tehran for funding the project numbered 03-6324030. References
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Baker, C., Khan, A., Ali, Y., Damyar, K., 2006. Simulation of plug flow fluidized bed dryers. Chemical Engineering and Processing: Process Intensification 45(8), 641-651. Baker, C., Lababidi, H., 2010. An improved model of plug-flow fluidized bed dryers with an emphasis on energy conservation. Drying Technology 28(5), 730-741. Bizmark, N., Mostoufi, N., Sotudeh-Gharebagh, R., Ehsani, H., 2010. Sequential modeling of fluidized bed paddy dryer. Journal of food engineering 101(3), 303-308. Brooker, D.B., Bakker-Arkema, F.W., Hall, C.W., 1992. Drying and storage of grains and oilseeds. Springer Science & Business Media. Fogler, H.S., 1987. Elements of chemical reaction engineering. Prentice-Hall of India, New Delhi. Fyhr, C., Kemp, I.C., Wimmerstedt, R., 1999. Mathematical modelling of fluidised bed dryers with horizontal dispersion. Chemical Engineering and Processing: Process Intensification 38(2), 89-94. Izadifar, M., Mowla, D., 2003. Simulation of a cross-flow continuous fluidized bed dryer for paddy rice. Journal of Food Engineering 58(4), 325-329. Janas, S., Boutry, S., Malumba, P., Vander Elst, L., Béra, F., 2010. Modelling dehydration and quality degradation of maize during fluidized-bed drying. Journal of food engineering 100(3), 527-534. Kannan, C.S., Thomas, P., Varma, Y., 1995. Drying of solids in fluidized beds. Industrial & engineering chemistry research 34(9), 3068-3077. Khanali, M., Rafiee, S., Jafari, A., 2014. Numerical simulation and experimental investigation of plug-flow fluidized bed drying under dynamic conditions. Journal of Food Engineering 137, 64-75. Khanali, M., Rafiee, S., Jafari, A., Hashemabadi, S.H., 2013. Experimental investigation and modeling of plug-flow fluidized bed drying under steady-state conditions. Drying Technology 31(4), 414-432. Kunii, D., Levenspiel, O., 2013. Fluidization engineering. Elsevier. Topuz, A., Gur, M., Gul, M.Z., 2004. An experimental and numerical study of fluidized bed drying of hazelnuts. Applied Thermal Engineering, 24(10), 535-1547. Levenspiel, O., 1999. Chemical reaction engineering. John Wiley & Sons, New York. Mohsenin, N.N., 1986. Physical properties of plant and animal materials. Gordon and Breach Science Publishers, New York. Mujumdar, A.S., 2006. Handbook of industrial drying. Crc Press. Mujumdar, A.S., Devahastin, S., 2003. Applications for fluidized bed drying, Handbook of fluidization and fluid-particle systems. Marcel Dekker Inc., New York, pp. 469-484.
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Naghavi, Z., Moheb, A., Ziaei-Rad, S., 2010. Numerical simulation of rough rice drying in a deep-bed dryer using non-equilibrium model. Energy Conversion and Management 51(2), 258264. Nilson, L., Wimmerstedt, R., 1987. Drying in longitudinal-flow vibrating fluid-beds: Pilot plant experiments and model simulations. Drying Technology 5(3), 337-361. Nilsson, L., Wimmerstedt, R., 1988. Residence time distribution and particle dispersion in a longitudinal-flow fluidized bed. Chemical engineering science 43(5), 1153-1160. Pakowski, Z., Mujumdar, A.S., 2006. Basic Process Calculations and Simulations in Drying, Handbook of industrial drying. Taylor and Francis Group, London, pp. 79-106. Ramli, W., Daud, W., 2007. A cross-flow model for continuous plug flow fluidized-bed crossflow dryers. Drying Technology 25(7-8), 1229-1235. Samapundo, S., Devlieghere, F., De Meulenaer, B., Atukwase, A., Lamboni, Y., Debevere, J.M., 2007. Sorption isotherms and isosteric heats of sorption of whole yellow dent corn. Journal of Food Engineering 79(1), 168-175. Sivakumar, R., Saravanan, R., Perumal, A.E., Iniyan, S., 2016. Fluidized bed drying of some agro products–A review. Renewable and Sustainable Energy Reviews 61, 280-301. Sopornonnarit, S., Prachayawarakorn, S., Sripawaatakul, O., 1996. Development of cross-flow fluidized bed paddy dryer. Drying Technology 14(10), 2397-2410. Wanjari, A., Thorat, B., Baker, C., Mujumdar, A., 2006. Design and modeling of plug flow fluid bed dryers. Drying technology 24(2), 147-157. Zare, D., Minaei, S., Zadeh, M.M., Khoshtaghaza, M., 2006. Computer simulation of rough rice drying in a batch dryer. Energy Conversion and Management 47(18), 3241-3254.
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