Drying Technology: An International Journal Diffusion ...

This article was downloaded by: [McGill University Library] On: 08 January 2015, At: 15:47 Publisher: Taylor & Francis Informa Ltd Registered in England and Wales Registered Number: 1072954 Registered office: Mortimer House, 37-41 Mortimer Street, London W1T 3JH, UK

Drying Technology: An International Journal Publication details, including instructions for authors and subscription information: http://www.tandfonline.com/loi/ldrt20

Diffusion-Controlled Batch Drying of Particles in a Novel Rotating Jet Annular Spouted Bed a

a

S. Devahastin , A.S. Mujumdar & G.S.V. Raghavan

b

a

Department of Chemical Engineering , McGill University , Montreal, Quebec, H3A 2B2, Canada b

Department of Agricultural & Biosystems Engineering , Macdonald Campus of McGill University , Ste Anne de Bellevue, Quebec, H9X 3V9, Canada Published online: 16 May 2007.

To cite this article: S. Devahastin , A.S. Mujumdar & G.S.V. Raghavan (1998) Diffusion-Controlled Batch Drying of Particles in a Novel Rotating Jet Annular Spouted Bed, Drying Technology: An International Journal, 16:3-5, 525-543, DOI: 10.1080/07373939808917422 To link to this article: http://dx.doi.org/10.1080/07373939808917422

PLEASE SCROLL DOWN FOR ARTICLE Taylor & Francis makes every effort to ensure the accuracy of all the information (the “Content”) contained in the publications on our platform. However, Taylor & Francis, our agents, and our licensors make no representations or warranties whatsoever as to the accuracy, completeness, or suitability for any purpose of the Content. Any opinions and views expressed in this publication are the opinions and views of the authors, and are not the views of or endorsed by Taylor & Francis. The accuracy of the Content should not be relied upon and should be independently verified with primary sources of information. Taylor and Francis shall not be liable for any losses, actions, claims, proceedings, demands, costs, expenses, damages, and other liabilities whatsoever or howsoever caused arising directly or indirectly in connection with, in relation to or arising out of the use of the Content. This article may be used for research, teaching, and private study purposes. Any substantial or systematic reproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in any form to anyone is expressly forbidden. Terms & Conditions of access and use can be found at http:// www.tandfonline.com/page/terms-and-conditions

DRYING TECHNOLOGY. lb(3-5). 525-543 (1998)

Downloaded by [McGill University Library] at 15:47 08 January 2015

Diffusion-Controlled Batch Drying of Particles in a Novel Rotating Jet Annular Spouted Bed S. Devahastin', A S . ~ujumdar',G.S.V.Raghavan' 'Department of Chemical Engineering, McGill University Montreal, Quebec, Canada H3A 2B2 2 ~ e p a ~ m eofn Agricultural t & Biosystems Engineering, Macdonald Campus of McGill University, Ste. Anne de Bellewe, Quebec, Canada H9X 3V9

Key words and phrases : Effective water diffusivity; energy savings; falling rate period; finite element method; variable air flow drying; wheat.

ABSTRACT

Results are presented for batch drying of rewetted wheat (used as model particles) in a newly developed annular spouted bed in which the drying air jet rotates slowly thus spouting bed intermittently. For particles drying in the falling rate period intermittent spouting is shown to result in significant energy savings with small increase in the drying t i e . A finite element simulation is employed to evaluate the effective moisture ditksivity of the test material which is nonspherical in geometry. Further, advantages of variable spouting and heating of the spouting air are demonstrated by a parametric study of the simulation model.

INTRODUCTION Drying of large particles often occurs mainly in the falling rate period which is controlled by internal heat and mass transfer rates. Drying under such conditions can be modelled adequately by the simple diffusion equations for both heat and mass transfer.

Copyright 0 1998 by Marcel Dekkcr. Inc


526

DEVAHASTIN. MUJUMDAR. AND RAGHAVAN

Further, increase in the external transfer rates has only marginal and indirect influence on enhancement of the overall drying rate. Using re-wetted wheat kernels as test material this investigation demonstrates the feasibility and associated advantages of a novel spouted bed dryer which reduces the net energy and drying air consumption while enhancing the produn quality The basic concept involves intermittent spouting of a bed of particles to be dried. In order to obtain a uniform drying performance the spouting jet rotates slowly in an annular vessel resulting in no dead zones of particles. The spouting is thus locally intermittent. In practice, the spouting air may be heated intermittently as well giving additional opportunities for energy savings. This gas-particle contanor, first proposed by Mujumdar [I], is termed rotating jet annular spouted bed (RJASB) and shown in Figure I. This paper presents experirnental data on the drying kinetics of wheat kernels and compares the results with a two-dimensional diffusion model for heat and mass transfer in a single, nonspherical wheat particle assuming perfect mixing of particles in the bed and isotropic material properties. Unlike prior related works [2,3] a finite element technique was employed to account for the true nonspherical shape of the wheat kernel. Effective liquid water diffusivity was computed by fitting the model results to the experirnental batch drying data. It is found that the diffusivity value so computed differ from those obtained assuming the particle to be perfectly spherical. Earlier, Jumah et.al [4] presented results of batch drying kinetics for corn dried in a slightly different design incorporating the basic concept of intermittent spouting and showed clearly the advantages of such a dryer in terms of energy consumption. It should be noted that, for simplicity, throughout this work the word "diffusion coefficient" implies "effective diffusion coefficient". EXPERIMENTAL SET-UP, MATERIALS AND METHODS A schematic diagram of the experimental set-up and the associated instlumentation is shown in Figure 1. The RJASB consists of a slowly rotating inlet air distributor plate equipped with a nozzle under the bed supporting screen. The spouted bed consists of a cast acrylic vessel 45 cm in diameter and 60 cm in height. A galvanized steel cylinder, 20 cm diameter and 55 cm height is mounted centrally in the vessel to avoid formation of a dead zone in the central region of the bed. Inlet air temperature as well as grain temperatures at various locations within the bed were measured using copper-constantan type T thermocouples. Please refer to [5] for a detailed description of the overall experimental set-up and procedure. Rewetted wheat was used as a test material for the batch drying kinetics study. Dimensions and physical properties (average values) of the wheat kernel are given in Table 1. All the properties shown are the values evaluated at the initial conditions. A pre-weighed amount of wheat was rewetted by adding a pre-determined amount of tap water to achieve the required initial moisture content for the drying tests. The


DIFFUSION-CONTROLLED BATCH DRYING

FIGURE I . Schematic diagram of the overall experimental apparatus. I, air distributor ; 2, distributor cover plate ;3, central cylinder ;4, vessel ; 5, screen ;6, motor + gear box ; 7, motor controller ; 8, pulley ;9, ball bearing ; 10, V-belt ; 1I, thermocouples ; 12, scanning thermocouple thermometer

TABLE 1 Physical Properties of Rewetted Wheat Used in Drying Experiments

Property

Value

Property

Vdue

L (mm)

5.863 3.056

P. (kFh3)

1233.6 719.1


528

DEVAHASTIN, MUJUMDAR. AND RAGHAVAN

contents were mixed thoroughly while adding the water in a conical mixer. The grain sample was then placed in a sealed plastic container and kept in cold storage at 4 "C (with periodic mixing) for a minimum of 72 hours to ensure reproducible moisture adsorption and uniform distribution of moisture within the kernels. Before the start of each experiment, the rewetted wheat was removed from the storage and kept at the ambient temperature for 24 hours to achieve thermal equilibration at ambient conditions. Moisture content determination was performed following the ASAE standard [6]. As indicated by various investigators [2,3] wheat drying with an initial moisture content of less than 0.5 kgkg (d.b.) o x u n exclusively in the falling rate period; the main amhibutor to the Mliation of the drying curves is the inlet air temperature. Thus, in this experimental work, emphasis was placed on investigation of the effect of the inlet air temperature on the drying kinetics. The spouting air temperature varied from 63-80 T,the upper limit was suggested by the safe maximum allowable temperature for wheat drying [7] while the lower limit was determined by the flow system behavior, the other parameters were fixed as follows : H = 15 cm; N = 5 rpm; U, = 0.64 mls; D. = 3 cm. The dependent variables measured were : the sample average moisture content

(F) ; bed temperature (TJ which were average values from measurements at various locations in the bed. Earlier, the RJASB was shown to provide good mixing behavior [S]. A TWO-DIMENSIONAL LIQUID DIFFUSION MODEL

Assuming perfect mixing, one can model drying in the RJASB by simply modelling the heat and mass transfer processes in a single wheat kernel. The following key assumptions were made to develop a diffusion model for wheat kernel : 1. Wheat kernel is uniform in s i i , homogenwus and isotropic. 2. Moisture transfer within the wheat particle is wntmlled by liquid diffusion only. 3. Conduction of hcat and moisture b e e n bed particla, heat losses and effects of particle shrinkage an: negligible. With the aforementioned assumptions, the governing equations for heat and mass transfer within the wheat kernel are as follows [XI :

in which an Arrhenius type dependence on temperam is assumed for the Liquid diffusivity. Thus,


529


Initial And Boundary Conditions Assuming uniform moisture content and temperature of the kernel, the initial condition (at any location) is : At I = 0 , X = X , and T = E (4) Two different types of boundary conditions were employed depending on whether the spouting air flowrate is fued or variable. I. Constwu air mnrsJowmre drying : a) Boundary conditions for moisture : At the kernel surface :

Aty = 0 :

b) Boundary wnditions for temperature : At the kernel surface :

Aty = 0 :

where n is the outward drawn normal vector at the surface. 11. Variable air marsfiwrme drying

Since for drying in the falling rate period the rates of internal heat and mass transfer within the particle determine the werall drying iate it is possible not to supply the external

530

DEVAHASTIN. MUIUMDAR, AND RAGHAVAN

hedmass transfer at high intensity with only little penalty in terms of slight increase in drying time. ?his leads to an idea of reducing air mass flowrdte as the drying proceeds. In fact, Devahastin 151 has performed the hydrodynamic experiments in RJASB and showed a significant decrease in a minimum spouting air flow requirement at later srages of the drying P.In this mode of drying, the heat and mass transfer surface boundary conditions are


also governed by equations (5) and (8) with the expression for air mass flowrdte, m,, derived as follows. Fmm the definition of Reynolds number based on the nozzle minimum spouting velocity :

If the ratio of the operating air mass flowme to the minimum spouting air mass flowrate is to be maintained at any ahihary value n for the whole drying process, thus;

where Re-,

nozzle minimum spouting velocity for the RIASB is given by [ S ] :

Lang et.al. [9] have found that the bulk volume d u d a g e is linearly relaled to instanmwus grain moisture redudon. The mulls thus obtained can be applied here to find an instantaneous value of the bed height as :

where A m , shinkage ccefficient, is dependent on the inlef air humidity and temperanue as given by [9]:

The pardcle cenninal velocity, U,,is obtained from [lo] :


The values of panicle equivalent diameter, D , ,

531

and density, p,, vary with kernel


moistwe mntent according to the following expressions [I 1,121 :

To calculate the vafiation of the Archimedes number with particle moisture wntent the variation of panicle effective diameter is also needed in addition to the variation in kernel density. 7he effective particle diameter is calculated by multiplying the particle equivalent diameter, D,, , with the value of particle sphericity,

6 , which is assumed to be

wnslant in this work. Another parameter in the expression for nozzle minimum s p o u ~ g velocity is the circumferential velocity of the air nozzle, V,, which can be calculated according to the following expression :

where R and N are the radial distance of the nozzle from the axis of rotation and rotational speed (rpm) of the spout, respectively.

FINlTE ELEMENT FORMULATlON After spacewise discretization of Eqs. (1) and (2), subject to mvective boundag wnditions the following semidixrete matrix system is obtained :


DEVAHASTIN, MUJUMDAR, AND RAGHAVAN

In the preceding equations, nel is the mral number of elements; the superposed dot denotes differentiation with respect to time; the superscript e designates an element; C,, G, K, and K, are submatrim; F, and F, are subvecton. The coefficients in the submatrices and subvecton are calculated according to the following equations:

Dixretization of the time derivative in Equation (20) is achieved by the backward Euler scheme :

Based on the p d u r e described above, a computer code was written in

FORTRAN 77 and simulations for batch drying of rewelled wheat were camed oul over a range of parameters. The mulls are w m p d with experimenral data for wheat drying in the novel RJASB unit.

RESULTS AND DJSCUSSION Since the panicles in the rotating jet annular spouted bed have been shown to be well mixed [51 it can be assumed lhat the surface of the wheat is subjected to uniform

DIFFUSION-CONTROLLEDBATCH DRYING

533


convective heat and mass transfer and the temperature as well as humidity of the drying air is taken to be uniform at every location on the kernel surface. According to the derivation of the boundary conditions for a grain panicle in the spouted bed [81 T, and Y, are the temperature and humidity of the inlet hot air. The wnvective gas-tqmticle heat m s f e r coefficient was calculated using the following correlation [13]:

The above empirical correlation is for a conventional spouted bed. However, in the RJASB only the shaded area shown in Figure 1 is actually spouted at any inslance. Devahastin [5] derived the following correlation for the value of the locally spouted bed column diameter. This is an appropriate value for the definition of the air supenicial velocity which was then used in the calculation of the Reynolds number in Equation (32) :

It should be noted that since Equation (32) was developed by assuming the particle to be spherical, the d i e t e r substituted must be an equivalent spherical diameter in order to obtain the Nusselt number. The effective panicle diameter is then uEed to calculate the value of heat transfer coefficient. 1. Experimental Validation of the Numerid Model

The numerical model war first compared with the computed results assuming wheat as a onedimensional spherical body with the experimental data for wheat drying in the rorating jet annular spouted bed apparatus. The relevant experimental parameters used for model validation are Listed in Table 2. The hansprl and equilibrium properties for soft wheat are listed in Table 3. The thermodynamic and transport properties for the air-water system are listed in Table 4. First, a simple spherical geometry was chosen to approximate the wheat kernel. For an inlet air temperature of 63 "C and an air mass flow rate of 0.087kg/s, grid dependence tests showed that the maximum difference between the predicted average moisture contint during the drying prooess was less than 0.17 % between numerical runs using 20 elements with a time step of 20 recond and 80 elements with a time step of 5 seconds, while the maximum difference was less than 0.05% when using 40 elements with a time step of 10

DEVAHASTIN. MUJUMDAR, A N D RAGHAVAN


TABLE 2 Exmimental Parameters Used for Model Validation

TABLE 4 Tlmmodynamic and Transport Roperties of Air-Vapor Systems [17,18] P. = lmupl27,0214-(688l/T,)-5321n(T, 127116)l el

= LW926x 1V - 4 . 0 4 0 3 ~l O ~ T + 6 J l 5 9 xI O T - 4 . 0 9 7 ~10-'T'

k. =22.25x 10.'-1889x10-'T-17WxI04T'-8570~

10-"T'


DIFFUSIONEONTROLLED BATCH DRYING

0

60

120

180

240

300

lime (min)

FIGURE 2. Comparison of the numerical predictions assuming spherical g m m q with the experimental results. N = 5 rpm. D. = 3 cm, H = I5 cm, U,=0.64 d s , Xa a 0 3 0 k g k g

m n d and 80 elements with a time of 5 seam&. h s i d e r i n g both accuiacy and computing time 40 elements with a time step of 10 m n d s were u t i W for all onedimensional mmputations. F i g u e 2 presents a m m p a r i m of the drying curves b e t w m the model predictions and the expetimental results for an inlet air flow rate of 0.087 kgls and the inlet air temperahues of 63 "C and 79 'C. It is seen hom this figure that there is an ucellent W m e n t beoveen the numerical predictions and the experimental results despite the numerous simplifyng assumptions. 2. A New Two-Dimensional Efktive Dillusion Cocflicicnt

Though an excellent agreement between the numerical predictions and the experimental results it is shictly not appropriate to simply model wheat which is nonspherical in nature as a simple onedimensional spherical body. Gong et.al.[lg] showed that there exists a deviation in ~ I Y U I results ~ obtained by using the correlation for effective diffusion mefficient developed by muming spherical g m m c q in their hvdmensional liquid diffusion model. Based on both the experimental and numerical results, a two-dimensional effective diffusion coefficient was developed assuming an Arrhenius type relationship for temperature dependency as :


DEVAHASTIN. MUJUMDAR. AND RAGHAVAN

FIGURE 3. Comparison between Faatz's and simulated results. N = 4 tpm. U, = 0.45 mls, D. = 3 cm, H = IS cm, Ti = 58 "C, X. ~ 0 . 3 k0 g k g

A moisture-independent nature of the diffusion coefficient is also reported by o t h e ~ investigators who studied wheat drying process (2.31. Figure 3 shows a comparison between the experimental results of Faatz [20] who dried wheat in a rotating jet spouted bed of different design and simulated results using the present model. It can be seen that there is good agreement between these two sets of data. The small discrepancy between the predicted and observed temperatures is attributed to the uncertain measurement of the particle surface temperature and the simplifying assumptions made in the development of the model e.g., neglecting heat losses. The same phenomenon is also reported by lumah etal. [El who dried yellow dent corn in a rotating jet spouted bed. 3. Variable Air Mass Flowrate Drying

The simulated variation in air flow requirements as a function of time for two different inlet air lemperanures calculated using Equation (12) is shown in Figure 4. The value of the constant air flowrate shown by the dotted line is the value of the air flow requirement at the starting of the drying process. The temperatures selected are the safe maximum values [7] for drying of wheat for commercial uses (60 OC) and for animal feed (80 'C). The values of air mass flowrate were kept at twice the value of the minimum spouting air flow requiremenls (n = 2 in Equation (12)) at all times during the dtying


DIFFUSION-CONTROLLEDBATCH DRYING

Time (min)

FIGURE 4. Simulated variation of air flow requirements. N = 5 rpm, D.

0

50

= 3 cm,

100 150 200 250 300

Time (min)

FIGURE 5 . Simulated variation o f kernel average moisture content. N = 5 rpm, D n = 3 c m , ~ = l S c m , X~ 0 . 3 0 k g / k g

DEVAHASTIN. MUJUMDAR, AND RAGHAVAN


0

50 100 150 200 250 300

Time (min) FIGURE 6. Simulated variation of kernel surface temperature. N = 5 rpm. D . = 3 c m , ~ = l S c m , X oa0.30kjyIg

processes. It can be seen from this figure ha higher the inld air tempemure faster the reduction in air flow requirement. This is due lo the fact that for higher air temperalure the particle bulk s h r i d q e is faster. Thus the values of bed height and hence minimum spouting air flow requirement decreare. Figure 5 presents the simulated variation in kemel avenge moisture wntent with time for two different d y n g air temperatures. It is clearly seen lhat there is no apprsiable diffemce in the drying curves behueen the constant and variable flow cases. The calculations based on the results shown in Figures 4 and 5 show the saving of air consumption up la 10 % (in addition lo approximately 30% saving offered by an intermittent spouting action alone) if the final moisture wntent is chosen lo be at 12 % (d.b.) which is the value recommended for safe smnge of wheat kernels Also shown in Figure 6 is the simulated varialion of the kernel surface tempefahlre as a function of time. It can be seen that the surface tempmature is slightly higher in the case of wnstant air flow than in the case of variable air flow. This is due lo the higher value of heat transfer coefficient at higher air flowrate. This, again, suppom the idea of using a variable air mass flowrate as the drying pmaeds in order lo obtain better dried product quality.

m.

CONCLUSION In this work, a two-dimensional liquid diffusion model was proposed to simulate the heat and mass transfer processes in the falling rate period drying of solid particulates in



539

a novel rotating jet annular spouted bed. Rewetted wheat was selected as the test material. A correlation for the two-dimensional effective liquid water diffusivity was developed based on the experimental and model results. The result obtained was verified and found to be in good agreement with the experimental results. The simulation of the variable air mass flowrate batch drying was performed using the model developed. The results showed a saving of air consumption up to 10% without any significant increase in drying time. Moreover, additional benefits can be obtained in terms of energy savings as well as better product quality due to less mechanical damage. NOMENCLATURE

n o d e cross-sectional are& m1 particle surface area, m' breath, m specific heat, J kg.'K" specific heat of solid, J k g . k 1 diffusion coefficient, m'i' column diameter, m equivalent cylindrical column diameter, m locally spouted bed column diameter, m n o d e diameter, m diffusion coefficient at reference temperature, m'd' effective particle diameter, D, x 4 , m equivalent spherical diameter, m

AH,,

geometric particle diameter, (L x B x z)'", m characteristic particle diameter, m activation energy, kJ gravitational constant, 9.81 m s.' bed height, m wnvective heat transfer coefficient. W m-'~.' heat of desorption-vaporization of water, kJ kg-'

k k, L M.

thermal conductivity, W m ? ~ . ' thermal conductivity of solid, W m ' k ' length, m molar mass of water, kg mol-'

m,

mass flow rate of dry air, kg s"

m, N

mass of dry solid in bed, kg spout rotational speed, revolution per minute


DEVAHASTIN. MUIUMDAR, AND RACHAVAN

shape function outward normal of boundary vapor pressure of pure water, Pa universal gas constant, 8.314 J m o ~ ' K " relative humidity, decimal fraction R/M. = 462 J k g . k l dry grain mass, 0.000045 kg for wheat temperature, "C absolute temperature, K ambient temperature, "C time, s time step, s air superficial velocity, m