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CONVECTIVE DRYING OF THIN AND DEEP BEDS OF GRAIN a

D. Ž. MILOJEVIĆ & M. S. STEFANOVIĆ

a

a

Boris Kidrich Institute of Nuclear Sciences—Vin⋅a Institute for Thermal Engineering and Energy Research , Belgrade, Yugoslavia Published online: 31 Oct 2007.

To cite this article: D. Ž. MILOJEVIĆ & M. S. STEFANOVIĆ (1982) CONVECTIVE DRYING OF THIN AND DEEP BEDS OF GRAIN, Chemical Engineering Communications, 13:4-6, 261-269, DOI: 10.1080/00986448208910912 To link to this article: http://dx.doi.org/10.1080/00986448208910912

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Chem. Eng. Commun. Vol. 13, pp. 261-269 0098-6445/82/ 1304-026$06.50/0

QGordon and Breach, Science Publishers, Inc., 1982 Printed in the U.S.A.

CONVECTIVE DRYING OF THIN AND DEEP BEDS OF GRAIN

Downloaded by ["Queen's University Libraries, Kingston"] at 22:03 31 December 2014

D.Z. MILOJEVIC AND M.S. STEFANOVIC Boris Kidrich Institute of Nuclear Sciences-VinPa Institute for Thermal Engineering and Energy Research Belgrade. Yugoslavia (Received July 20. 198l;infinal form September 8, 1981) The object of this paper is the experimental and thwretical investigation of heat and mass transfer during drying of packed beds of grain. A deep bed of grain was regarded as a series of thin beds. Analytical expressions for the thin bed drying rate were obtained by defining the air parameters at the grain surface in the falling rate period of drying and using the results of drying experiments. The paper also contains a simulation model for drying decp beds of grain. consisting of four partial differential equations based on energy and mass balances in a bed element. The system of equations was solved using finite difference techniques and a digital computer. A comparison between numerical solutions and experimental results is illustrated.

INTRODUCTION The calculation and optimization of grain dryers by means of electronic computers require a mathematical description of the drying process. However, the number of parameters influencing the drying kinetics of these materials is great and a great number of experiments are necessary in order to obtain generalized drying curves. On the basis of the assumption' that the deep bed of grain can be regarded as a series of thin beds, it is possible to predict the drying behaviour of deep beds by means of layer by layer calculations. In order to apply this method it is necessary to describe the thin layer drying curves mathematically and to develop a mathematical model for deep bed drying based on energy and mass balances in the differential bed element. It has to be noted that several models for layer by layer calculations have already been proposed and solved numeric ally,'^*^' but the problems of the derivation of the equation for thin layer drying rate still exists.

THIN LAYER DRYING For the thin layer drying analysis in this work the following were considered to be of significance. 1. The drying rate of small grains falls during the entire drying time. The internal resistances to moisture transfer are greater than the external ones, but the external resistances are not negligible, at least not during the initial period of drying;

2. As there is no theory, predicting the drying behaviour of small grains, empirical equations for the thin layer drying rate, based on experimental data, are used;

3. In order to reduce the number of necessary drying experiments it is convenient to consider internal and external moisture transfer separately;


4. The external moisture transfer can be considered as a known process, thus providing necessary boundary conditions for the internal moisture transfer; 5. For calculation of external heat and mass transfer, well known correlations of Barker: and Treyba15 can be used. The geometrical grain and bed characteristics (porosity, specific surface area, bulk density, equivalent diameter of grain) must be determined beforehand. The mathematical description of the thin layer drying in this work is based on the approach proposed by A.V. Luikow: but it was observed that the drying coefficient K in the drying rate equation:

is not constant, even for a single drying curve. Moisture diffusivity Dm is not constant in a wide range of moisture contents as it was assumed by L ~ i k o v Drying .~ coefficient depends both on internal and external resistances to moisture transfer. Hence, a great number of drying experiments are necessary for the mathematical description of the thin layer drying process in the form of Eq. ( I ) . In this work an attempt was made to consider the external and internal moisture transfer separately, the former being a known process so that the expression for the thin layer drying rate can be written as:

In the falling rate period of drying a moisture content profile U(x) (see Fig. I) exists inside a porous body. Surface moisture content can be expected to be equal to the equilibrium moisture content corresponding to the air parameters at the body surface and it can be evaluated using desorption isotherms:

The values of 4, and u, continuously fall with time and the drying rate diminishes. The boundary layer thickness in packed beds of grain is small due to sudden changes in the cross-section of the channels and in the direction of the flow. Hence, liquid capillary transfer inside the grain is much slower than convective vapour transfer from the grain surface, thus causing a receding evaporation front.' A surface part of the grain kernel is almost completely dried, while the moisture content of a central part is nearly equal to the initial moisture content. The evaporation front is the narrow zone in which high moisture content gradients exist (see Fig. 1). In this zone the local moisture content U(x) varies from the initial value u, to the value close to u,. As the thickness of the evaporation front is small compared with grain dimensions, its


CONVECTIVE DRYING

X

FIGURE I

Moisture content profile inside a porousbody with r e d i n g evaporation front.

mean depth of recession 9 can be assumed to be equal to the distance between the grain surface and the locality where the moisture content is equal to the average moisture content of the whole grain kernel. Moisture transfer flux can be expressed as:

Assuming that the moisture content profile in the dried zone (see Fig. 1) is linear and that moisture diffusivity in this zone is nearly constant, Eq. (4) can be rewritten as:

The expression for the thin layer drying rate takes the following approximate form: -

du Dm =S ,- ( u - u,) dr 9

or in terms of the internal moisture transfer coefficient:

According to Eqs. (6) and (7) the internal moisture transfer coefficient K, is a function of the grain size and shape, moisture diffusivity in the dried zone (i.e. surface moisture content and temperature), as well as of the position of the evaporation front.


Corn, wheat and other small grains, which have relatively low initial moisture contents, exhibit no appreciable temperature gradients within kernels3 and average grain temperature O may be used for the evaluation of the influence of the dried zone temperature on the internal moisture transfer coefficient. According to Fig. 1 ratio u/uo is a measure of the evaporation front recession. Hence, the empirical expression for the internal moisture transfer coefficient can be3of the form:

Using Eq. (7) the values of the coefficient KY were determined from the differentiated thin layer drying curves and for corn the following empirical expression9n temperatures ranging from 25-95OC was obtained:

Surface moisture content of corn is given by the empirical equilibrium moisture content equation based on experimental data:'

where:

-

C(,, 0.039702 + 1.25858 + 160.6 and

n

- 2.667.

(1 1)

It has to be noted that some other materials, like small pieces of vegetables, exhibit higher internal temperature gradients during the initial drying period. For these materials it is more adequate to use surface temperature for correlations of the form (8) and (10).

DEEP BED DRYING MODEL

The layer by layer calculations in this work were based on the deep bed drying model This model consists of four first order partial differential developed by Brwker et equations obtained from energy and mass balances written on an arbitrary located differential bed element:


CONVECTIVE DRYING

265

The partial vapour pressure at the grain surface necessary for solving Eq. (15) is calculated using Eq. (2) and (7):

where the relation between p, and u, for shelled corn is given by the desorption isotherms Eq. (10). The initial and boundary conditions which are usually applied to the system of Eqs. (1 2) to (1 5) are:

NUMERICAL SOLUTION AND COMPARISON WITH EXPERIMENTS Since an analytical solution of the system of equations describing a drying process of deep bed of grain is impossible, a finite difference computer program was used. A convenient selection of a computational procedure provides a relatively fast execution of the program. The solution includes the average moisture contents, the water removed by the dryer and the energy consumption per 1 kg water removed at specified time intervals, as well as the air and grain temperatures, humidity ratios, relative humidities and moisture contents at selected depths of a bed. A comparison between experimental and calculated thin layer drying curves of shelled corn is shown in Fig. 2, together with the curve calcaulated using thin layer equation of Thompson et a/.' The drying curve calculated in this work shows a very good agreement with experiment. A comparison of calculated and experimental deep bed drying curve of corn is illustrated in Fig. 3. confirming the validity of the thin layer drying equation and the deep bed model. As an additional illustration of the numerical solutions Fig. 4 shows the changes of air and grain temperature, absolute humidity and moisture content profiles during drying 200 mm deep bed of corn. From Fig. 4 very high gradients of all parameters as well as condensation effects at the initial period of drying can be observed. For the case of wheat the model predictions were compared with 20 experimental


-

-

-

FIGURE 2. Comparison of experimental and calculated thin layer drying curve of wrn (r. H. 0.01 kg/kg: u. 0.7 m/s: 8, 22'C: u. 0.45 kg/kg: h. 15 mm).

-

I

0. I

-

-

I

I

I

-

-

-

-

-

6WC.

I

FIGURE 3. Comparison of experimental and calculated deep bed drying curve of corn r. Ha 0.0077 kg/kg; u, 0.85 m/s; 8, 1 5 T ; u, 0.526 kg/kg; h, 80 mm).

-

9S°C;

' i (min)

ZOO

100

-


CONVECTIVE DRYING

- - - -

- -

267

FIGURE 4. Air temperature and humidity, grain temperature and moisture content profiles during drying 200 mm deep bed of corn (1. 70°C, H. 0.01 kg/kg; u. 0.5 m/s; 8, 20°C; u, 0.45 kg/kg; h. 0.2 m; I-r 6 min; 2-r 12 min; 3-7 18 min, 4-7 24 min; 5-7 30 min.)

-

-

-

-

-

drying curves,' showing a similar agreement as in Fig. 3. For other materials (corn, pea beans, potato and carrot small cubes etc.) only 6-7 thin layer drying experiments were necessary. This reduced number of experiments is due to the fact that the deep bed model had been checked before-hand, and only the thin layer drying equation was in question.

CONCLUSIONS The analysis of drying of thin beds of grain presented here is based on the attempt to separate the influences of important parameters on internal and external moisutre transfer. Since convective moisture transfer can be considered as a known process, the number of drying experiments necessary for obtaining a thin layer drying equation is significantly reduced, as the influence of only two parameters, the temperature and the moisutre content of grain, is to be examined. The mathematical model used for the simulation of drying deep beds of grain is based on fundamental laws of heat and mass transfer. However, the model employs an empirical thin layer equation which is always limited to the experimentally examined range of important parameters.

D.Z. MILOJEVIC AND MS. STEFANOVIC

268

NOMENCLATURE specific heat, J/(kgK) moisture diffusivity, m2/s dry mass flow rate, kg/(m2s) Downloaded by ["Queen's University Libraries, Kingston"] at 22:03 31 December 2014

bed height, m absolute air humidity, kg/kg drying coefficient, s-' internal moisture transfer coefficient, s-' partial pressure of water vapour, N/m2 mass flux, kg/(m2s) latent heat of vaporization. J/kg specific surface of a bed, m2/m3 air temperature, "C local value of moisture content, kg/kg dry basis mean moisture content, kg/kg dry basis Greek Symbols a

@ 6 11

convective heat transfer coefficient, W/(m2K) convective mass transfer coefficient, kg/(m2S N/m2) relative air humidity depth of the receding evaporation front, m

0

dry mass density of a porous solid, kg/m3 grain temperature, "C

T

time, s

a e 0

air

P

completely dried solid surface

Pa

s u

w

equilibrium initial value

water vapor water liquid

CONVECTIVE DRYING

269


REFERENCES I. Boycc. D.S.. Grain moisture and temperature changes with position and time during through drying. I . Agric. Eng. Res. 10,333 (1965). 2. Brmkcr. D.B.. Bakker-Arkema. F.W. and Hall, C.W.. Drying Cereal Grains. AVI Publ. Co., Westport. 1974. 3. Milojevid, D., An Analysis of Heat and Mass Transfer During Drying Stagnant Beds of CapillaryPorous Particles. MS. thesis. Univ. of Belgrade. 1979 (in Serbocroatian). 4. Barker, J.J.. Heat transfer in packed beds. Ind. Eng. Chem. 57.43 (1965). 5. Treybal. R.E., Mass Transfer Operations. McGraw-Hill. New York, 1955. 6. Luikov A.V.. Theory of Drying (in Russian). Energiya. Moscow, 1968. 7. Brakel. J.van. Heertjes. P.M.. On the period of constant drying rate. Proc. of the First Intern. Symp. on Drying, p. 70. Montreal. 1978. 8. Thompson. T.L.. Pearl. R.M. and Foster G.H., Mathematical simulation of corn drying-a new model. Trans. ASAE, 11,582 (1968).