Modelling and Simulation of Deep-Bed Grain Dryers

Transcription

1 Diponegoro University From the SelectedWorks of Istadi August, 2001 Modelling and Simulation of Deep-Bed Grain Dryers Johnner P. Sitompul Istadi Istadi, Diponegoro University I Nyoman Widiasa, Diponegoro University Available at:

2 DRYING TECHNOLOGY, 19(2), (2001) MODELING AND SIMULATION OF DEEP-BED GRAIN DRYERS Johnner P. Sitompul, 1; Istadi, 2 and I. N. Widiasa 2 1 Dept. of Chemical Engineering, Institute of Technology Bandung, Jl. Ganesha 10, Bandung, 40132, Indonesia 2 Dept. of Chemical Engineering, Diponegoro University, Jl. Prof. Sudarto, Tembalang, Semarang, 50239, Indonesia ABSTRACT This paper concerns with heterogeneous modeling of deepbed grain dryers based on two-phase model by taking into account coupled heat and mass transfer within grains. This model also consider axial mass and heat dispersion in the fluid phase. The dynamictwo-phase equations are solved numerically by finite difference with alternating direction implicit method algorithm, and then applied to simulate humidity and temperature profile of drying gas across dryers together with moisture content and temperature of grains. The capabilities of these models were compared with experimental data obtained from available literatures, under drying conditions such as temperature and absolute humidity of drying gas and moisture content of grains. The simulation results show that the dynamic of corn drying within the bed is well predicted by the two-phase model. johnner@termo.pauir.itb.ac.id 269 Copyright & 2001 by Marcel Dekker, Inc.

3 270 SITOMPUL,ISTADI,AND WIDIASA Key Words: Alternating direction implicit method; Deepbed dryers; Finite-difference; Grain drying; Heterogeneous modeling; Simulation. INTRODUCTION Drying process plays an important role in a number of industries such as agriculture, medicine, and food. Conventional dryers of grain can be classified in two methods, i.e. batch dryers and continuous dryers. Batch dryers are characterized by the fact that grain is dried with either heated air in certain shallow layers with drying gas or air. In low temperature of drying air, the drying may take place over many hours, days or even weeks. Continuous dryers are usually characterized by the relative directions of flow of grain and air, i.e. cross flow, cocurrent flow, and counter flow (Parry, 1985). Generally, drying of grain requires exposure to an atmosphere of lower relative humidity than the equilibrium value at the grain surface. This can be arranged by flowing a hot gas of low relative humidity around the grain, usually in the bed of grain. One of the most conventional methods of drying is deep bed type. In this type of dryer, grain drying considered as batch process where moisture content, air and grain temperature, and the humidity of the air change simultaneously. Other type, moving bed dryer considered that grain and drying gas flow continuously. Mathematical modeling and computer simulation of grain drying are now widely used in agricultural engineering research. Several models have been proposed to describe the heat and mass transfer processes in the types of convective grain dryer. The basic simulation approach used was to calculate the drying performed on a thin layer of grain and then combine many thin layers to the grain bed and simulate them by consecutively calculating changes that occur during increments of time (Thompson et al., 1968; Courtois, 1997). In view of modeling of deep bed dryer, Thompson (1968) attempted to simulate profile of temperature and moisture of the drying gas across the dryer by one-phase (pseudohomogeneous) model. Gupta (1973) later modified the model of Thompson by considering interphase gradient with no intraphase gradient in grain. Palancz (1985) concerned with study of heat and mass transfer processes between gas phase and solid particles in a deep bed throughflow dryer, however no axial dspersion considered in the bed. The simulated particles have a moderate size, but high heat and mass transfer resistances. A simple cell model approach is used to describe the drying process and the model was solved numerically by orthogonal collocation

4 DEEP-BED GRAIN DRYERS 271 method. The transport resistances of particles are taken into account by embedding a Luikov-type distributed parameter model for each each cell. Abid et al. (1990) studies heat and moisture content profile by coupled transfers of heat and mass inside a corn grain that developed on the basis of the Luikov model. Their model considers the transfer of water by diffusion under the influence of a gradient of the moisture content and by thermodiffusion under the influence of a temperature gradient. The temperature profiles obtained are generally flat, however distribution of the moisture content inside the grain shows large variation with time. Courtois (1997) studies a dynamicmodel of the thin layer corn drying, but no intraphase gradient in the grain. However, the grain is divided into three compartments, which are supposed to be uniform in both temperature and moisture content of each compartment. Recently, Lopez et al. (1998) studies a simulation of deep bed drying of hazelnut. The deep bed of hazelnut was considered to be divided into a number of thin layers. It was found that the model can predict the average moisture content changes with time. Air temperature and relative humidity and hazelnut temperature profile as function of time can also be predicted by the model. MATHEMATICAL MODELING OF DEEP-BED GRAIN DRYER Drying is an operation, which involves simultaneous heat and mass transfer. The physical mechanism of drying in hygroscopic-porous products such as corn grain is quite complicated. It is generally agreed that the moisture within grain moves in the form of a liquid and/or vapor. A number of physical mechanisms have been proposed to describe the transfer of moisture in products. The liquid movement can be due to surface forces (capillary flow), moisture concentration differences (liquid diffusion) and diffusion of moisture on the pore surface (surface diffusion). The vapor movement can be due to moisture concentration differences (vapor diffusion) and temperature differences (thermal diffusion). Also, it can be a water and vapor movement due to the total pressure differences (hydrodynamic flow) (Brooker et al., 1978). In this paper, we proposed two-phase model or heterogeneous model, which considered in the deep bed dryer, by taking into account of the parabolic-hyperbolic type equation for the bed together with parabolictype equation for the spherical grains. The mass and heat flux equations are following the Robin s type, which is easily modified for either, Dirichlet or Neuman s type. The capabilities of these models were compared with experimental data obtained from available literatures (Courtois, 1997),

5 272 SITOMPUL,ISTADI,AND WIDIASA Figure 1. Elemental bed of corn grains. under drying conditions such as temperature and absolute humidity of drying gas and moisture content of grains. The coupled of heat and mass transfers within intraparticle has been developed on the basis of the Luikov s model which was founded on the principles of irreversible thermodynamics (Palancz, 1985). Average transfer coefficient between the bulk gas stream and the grain surface can be correlated in terms of dimensionless groups which characterize the flow conditions. Hence, both heat and mass transfer coefficients are influenced by thermal and flow properties of the air, and the geometry of the system (Marinos-Kouris et al., 1995). The model development of deep bed dryer follows as below. Consider a bed of grain of cross sectional area A and height L. The elemental layer was depicted in FIGURE 1. The conservation equations are written over elemental control volume over unit cross section and of height z. The following assumptions were made in order to simplify the mathematics of grain drying modeling in a deep bed, i.e. no shrinkage during drying; uniform grain kernels are in size and internally homogeneous/isotropicspheres, moisture migration path within each particle is in the radial direction only due to liquid diffusion, dryer walls are essentially adiabatic, the surface moisture content takes a value of dynamic equilibrium moisture content, and no conduction between close.

6 DEEP-BED GRAIN DRYERS 273 Governing equations for the dynamicmodel of mass and heat balance for describing humidity and temperature of the drying gas can be written as a ðcp a þ YCp v ÞT b ¼ D a a þ a 1 e b e l a a 1 e b e b k m ðy zðr a zðr a ðcp a þ YCp v ÞT b ðhðt b T P Þþk m ðy YÞdH v Þ Diffusion in the drying of solids has been well recognized as the most complex phenomena encountered. Drying theories have assigned diffusion to many interrelated transport phenomena that take place during moisture movement, such as molecular diffusion, capillary flow, Knudsen flow, hydrodynamic flow, or surface diffusion. The effective moisture diffusivity combines all these phenomena in a p ¼ 1 r p Cp ¼ l p eff r 2 r D p eff r p þ r r @r zr p e p r p D p eff r In this paper, the spherical coordinate is applied for the grain, and note that d is the thermomigration coefficient and z is phase conversion factor (z ¼ 0 for liquid diffusion only and z ¼ 1 for vapor diffusion only) (Abid et al., 1990). The effective moisture diffusivity is generally considered to be greatly affected by material moisture content and temperature. The temperature dependence of moisture diffusivity has been verified by most researchers in the field and a general agreement for an Arrhenius-type relationship has been reached (Chu et al., 1968). ð2þ ð3þ ð4þ D p eff ¼ð1=110 4 Þð1=60Þ 0:02522 exp 2513 þð0:045t 5:5ÞX T ð5þ

7 274 SITOMPUL,ISTADI,AND WIDIASA Initial and boundary conditions required solving set of partial differential equations can be written as follows: For drying air phase: Yð0; zþ ¼Y o ; T b ð0; zþ ¼T bo Yðt; 0Þ ¼Y i ; T b ðt; 0Þ ¼T ¼ 0; ¼ 0 ðt;lþ For grain phase: Xð0; rþ ¼X o ; T p ð0; rþ @r ¼ 0; P ¼ 0 r p D p ¼ k m ðy YÞ ðt;rþ l p ¼ hðt p T b Þþk m H v ðy YÞ ðt;rpþ ð6þ ð7þ Computation of the equilibrium moisture content of the drying gas having direct contact with the grain surface ðy Þ, the following relations can be used (Palancz, 1985): log p w ¼ 0:622 þ 7:5T p s 0 < T 238 þ T ps < 1008C ð8þ ps Y fp ¼ 0:622 w ð9þ 760 fp w Abid (1990) proposed parameter for corn grain drying: 1 ¼ 1 X 1=0:3 ð10þ s 10 30:22 T P 1:31 Thompson (1968) also proposed parameter for corn grain drying (Zahed et al., 1992): f ¼ 1 exp 8: ð100x Þ 1:8634 ðt b 273:16 þ 49:81Þ ð11þ The coupled governing equations (Equations (1) through equation (4)) were solved numerically by finite difference method with alternating

8 DEEP-BED GRAIN DRYERS 275 direction implicit method algorithm for a cylindrical bed shape together with the boundary conditions (BC s) and initial conditions (IC s). The discretization of differential terms in axial bed and radial grain nodes will be implicit and explicit at alternate time intervals for the solution of the governing equations. Discretization for transient terms are made use of backward difference method, while spatial terms are discretized by central difference one. The steps of numerical solutions are carried out as bellows. At one time interval, the equations are solved by implicit imposed for axial bed direction while the radial variables of the particle in the governing equations are in the explicit form. In the next step, the equations are solved alternately for other implicit direction, and the sequence is therefore repeated. This procedure may be continued until steady state is reached. The source terms, especially convective mass and heat transfer between phases takes the explicit form. The implicit discretization for all governing equations will give linear algebraicequation that have tridiagonal matrix that solved using iteratif tridiagonal matrix routine (Davis, 1984). RESULTS AND DISCUSSION Parameters and respected value for simulation are given in TABLE 1. Simulation results are depicted in FIGURE 2 to FIGURE 5. FIGURE 3 presents temperature profile of the outlet drying gas across the bed. Temperature profile of the outlet drying gas showed an increasing trend as the moisture removal decreased. The model shows low temperature rise Table 1. Data Used for Simulation Parameter Value Parameter Value Y I D p 7.85E-11 T bi 100 l P 4.59E-2 X o 0.58 l a 6.5E-1 T po 20 d 0.08 U z 0.42 e b 0.35 A 850 e p 0.45 Cp a 1012 r a Cp v 2030 r p 1350 Cp p 1122 L 0.16 H v 2.357E6

9 276 SITOMPUL,ISTADI,AND WIDIASA Figure 2. Comparison between simulated and experimental profile for the evolution of the output drying gas humidity. Figure 3. Comparison between calculated and experimental curves for the evolution of the output drying gas temperature. at initial periods of drying process on the deep bed of 0.16 m. This phenomena can be explained as follows, at initial periods, the bed is predominantly occupied by initial wet grain with large enough moisture removed, and that can cause increasing humidity of the outlet drying gas as shown in

10 DEEP-BED GRAIN DRYERS 277 Figure 4. Comparison between calculated and experimental profile for the average grain moisture content. Figure 5. Simulation results of average grain temperature profile. FIGURE 2. After certain time, absolute humidity of the outlet drying gas decrease as time evolved since only little moisture removed from the dried grains. FIGURE 4 shows predictions of average moisture content across the grains as the drying proceeds through the bed. The moisture content of

11 278 SITOMPUL,ISTADI,AND WIDIASA grain is decreasing during removal of the moisture. The moisture removal is large enough in the initials periods of drying and small enough in the end of periods because of moisture diffusivity dependence on grain moisture content and temperature. As shown on FIGURE 4, the removal of moisture up to about 0.14 kg moisture/kg dry grain from initial moisture content 0.58 kg moisture/kg dry grain, takes place at approximately hours under certain variable conditions. FIGURE 5 shows simulated profile of average grain temperature during the course of drying at the bed height of 0.2 m. The average grain temperature gradually increases throughout the drying period, while the temperature of the grain on the exhaust drying gas increases to the wet bulb temperature of the drying air. As the grain temperature of this last layer warms up to the wet bulb temperature, moisture is may be condensed from the air into the grain, thus will be incresng the grain moisture content. The variation of bed layer or position along the bed has been simulated on the figures. Further, simulations of models need parameters that should be optimized to make prediction close to the experimental data, especially at steady state condition of drying gas temperature and humidity. CONCLUSIONS The drying mathematical models were developed and presented in this paper. It was found that the model could predict the average moisture content and temperature of corn grain at different position of axial bed as function of time. Air temperature and absolute humidity at different position of axial bed as function of time can also be predicted by the model. The simulation results show that the dynamicof corn drying within the bed is well predicted by the two-phase model. NOTATION A cross sectional area of bed, m 2 a specific surface per volume of bed, m 2 m -3 cp a specific heat of gas, J kg -1 K -1 cp p specific heat of solid, J kg -1 K -1 cp v specific heat of water vapor, J kg -1 K -1 D a eff effective axial moisture dispersion of the drying gas, m 2 s -1 D P eff effective moisture diffusivity within particle, m 2 s -1 d p particle diameter, m h heat transfer coefficient, J m -2 s -1 K -1

12 DEEP-BED GRAIN DRYERS 279 k m mass transfer coefficient, kg m -2 s -1 L height of grain bed, m r space coordinate in radial direction in a particle, m t time, s T b temperature of the drying gas, K T p temperature of the particle, K U z axial linier gas velocity, m s -1 X grain moisture content, kg moisture / kg dry grain X equilibrium moisture content, kg moisture / kg dry grain Y absolut humidity of the drying gas, kg moisture / kg dry gas Y absolut humidity at equilibrium, kg moisture / kg dry gas z space coordinate along the length of the bed, m saturation vapor pressure of water in the surface of grain, mmhg P w Greek Letters z phase conversion factor relative humidity l a eff effective thermal conductivity of solid phase, J m -1 s -1 K -1 l p eff effective thermal conductivity of drying gas, J m -1 s -1 K -1 r a density of the drying gas, kg m -3 r P density of grain, kg m -3 e b bed porosity e P grain porosity d thermomigration coefficient, K -1 H v vaporization heat of water, J kg -1 ACKNOWLEDGEMENTS The RUT Grant through Indonesia Research Council (DRN) are gratefully acknowledged for this research. The second author also would like to thank the Dept. of Chemical Engineering, Diponegoro University for permission to study on leave in the Dept. of Chemical Engineering Institute of Technology Bandung. REFERENCES 1. Abid, M., R. Gibert, and C. Laguerie, 1990, An Experimental and Theoretical Analysis of The Mechanisms of Heat and Mass Transfer During The Drying of Corn Grains in a Fluidized Bed, Int. Chem. Eng., 30(4), pp

13 280 SITOMPUL,ISTADI,AND WIDIASA 2. Brooker, D.B., F.W. Bakker-Arkema and C.W. Hall, 1978, Drying Cereals Grains, Westport, CN: AVI Publishing Co., Inc. 3. Chu, S.T., and A. Hustrulid, 1968, Numerical Solution of Diffusion Equations, Trans. ASAE, 11, pp Courtois, F., 1997, DynamicModelling of Drying to Improve Processing Quality of Corn, papers/phd/phd. html. 5. Davis, M.E., 1984, Numerical Methods and Modelling for Chemical Engineers, John Wiley & Sons, Inc., New York, pp Gupta, K.L., 1973, Mathematical Simulation of Deep Bed Grain Drying, PhD Thesis, Queen s University, Kingston, Canada. 7. Lopez, A., Pique, M.T., and Romero, A., 1998, Simulation on Deep Bed Drying of Hazelnuts, Drying Technology, 16 (3-5), pp Marinos-Kouris, D., and Z.B. Maroulis, 1995, Transport Properties in The Drying of Solids, pp , in A.S. Mujumdar (Editor) HandBook of Industrial Drying, 2 nd ed., Marcel Dekker, Inc., New York. 9. Palancz, B., 1985, Modelling and Simulation of Heat and Mass Transfer in A Packed Bed of Solid Particles Having High Diffusion Resistance, Comp. and Chem. Eng., 9(6), pp Parry, J.L., 1985, Mathematical Modelling and Computer Simulation of Heat and Mass Transfer in Agricultural Grain Drying: A Review, J. Agric. Eng. Res., 32, pp Thompson, T.L., R.M. Peart, and G.H. Foster, 1968, Mathematical Simulation of Corn Drying - A New Model, Trans. of The ASAE, 11(4), pp Zahed, A.H. and Epstein, N., 1992, Batch and Continuous Spouted Bed Drying of Cereal Grains. The Thermal Equilibrium Model, Can. J. of Chem. Eng., 70, pp

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