A revised model of the wheat drying process

J. agric. Engng Res. (1972) 17, 189-194

A Revised Model of the Wheat Drying Process H. B. SPENCER* Details are given of an improved model of the "deep" bed drying of wheat and its field of application. The model is shown to produce results in reasonable agreement with experiment and close enough to justify using the model to produce design data. Comments are made on the modelling technique when using "thin" layer results as a basis for a "deep" bed model.

1. Introduction Reference' gave details of a mathematical simulation of deep bed drying of wheat. The model gave reasonable agreement with experiment for values of bed mean moisture content. Comparisons of exhaust air conditions were in general not so good. Additional factors have now been taken into account and this has led to better agreement being obtained. Details of the factors are given and experimental results compared with those predicted by the revised model.

2. Revised model The revised model has 3 additional factors.

2.1. Variation of latent heat of evaporation with moisture content The relation used is that given in reference! i.e.

H=[l056'5-0'55 (8-520)] [1 +23 EXP (-4Oa)] where H=Latent heat of evaporation Btu/lb 8=Grain temperature absolute) a =Moisture content of grain d.b. (decimal)

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2.2. Bed shrinkage The amount of bed shrinkage, expressed as change in depth (L1d ft) per unit depth (ft) is used to alter the finite element width during drying. The factor L1d/ft was evaluated from the results of reference", which only gives overall bed shrinkages for changes in bed mean moisture contents, therefore the value used was only an approximate correction when applied to each finite element. Analysis of the results of reference" gives :

L1d/ft =0·85L1a where L1a is the change in bed mean moisture content (dry basis) from the initial value expressed as a decimal i.e.

2.3. Variation of grain berry surface moisture content In the previous model, using Becker's" description of the drying rate, as was taken as a constant equal to 0·11 (d.b.). On the hypothesis that as is probably independent of berry shape and dependent only on the nature of the surface-air interface it was decided to use the value of as derived for corn in references , which is temperature and humidity dependent. The drying rate equations for the individual layers were extended to moisture contents < 0·11 using Becker's expressions. As the work of references only covers air conditions to 80 % relative humidity some form of extrapolation of the data was necessary in order to complete the description of the drying process. • N.LA .E. Scottish Stat ion , Penicuik , Midlothian , Scotland

189

190

A REVISED MODEL OF THE WHEAT DRYING PROCESS

A generalized cubic was used to extrapolate into the region 80 %
3.1. 6 in deep beds Three conditions were chosen from the results given in reference". These were: Drying air temperature 1l0°F, 150°F, 190°F Initial moisture content (nominal) 20 %w.b. Air flow rate 3·8 Ib mirr-' ft- 2 The ambient air moisture contents and initial grain temperatures corresponding with the test conditions were used. Figs la, band c show respectively comparisons of the bed mean moisture content, exhaust air dry bulb temperature, and exhaust air relative humidity for each of the drying air temperatures. 130r--------------~

Drying AirTemp • IJO°F } • 150°F Expt. ref6 x 190°F

018

I

120

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Fig. 1. (a), Comparison ofpredicted and experimental bed meanm.c. (w.b.) for a 6 in deep bed; (b), Comparison of predicted and experimental exhaust air dry bulb temperature for a 6 in deep bed

191

H. B. SPENCER

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Drying time (min)

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As can be seen from these figures reasonable agreement between model predictions and experiment is obtained.

3.2. 24 in deep beds The deepest bed experiments so far reported in any detail are those of reference" These were carried out over a wide range of conditions at nominally 2 ft depth and with initial moisture contents of 35 % and 45 % d.b. These sets of experiments therefore offered a means of checking the model predictions at greater depths and higher moisture contents than were previously possible. Three experimental tests were chosen for comparison with model predictions. These represent the extreme ranges of the conditions likely to be encountered in practice. The comparisons are shown in Figs 2,3 and 4. The conditions of each test are given in Table I. TABLE I Experimental test conditions for nominal 2 ft deepbeds

Fig. no.

m.c. (d.b.)

Bed depth (ft)

TDCC)

Go (lb minr? ft- 2)

T. Cc)

Wmi (lbfft3)

2 3 4

0·37 0·33 0·47

2·0 2·0 2·3

32·2 27·2 64-4

1·78 6·21 1·70

16·0 14·0

44'5 45·0 42·6

I

I

-

Wmi is the initial bulk density of the grain. TD is the drying air temperature at inlet to the bed.

G. is the air flow rate.

Figs 2, 3 and 4 show comparisons of model predictions and experiment for bed mean moisture content, surface layer moisture content, exhaust air dry bulb temperature and relative humidity. As can be seen from the figures reasonable agreement with bed mean moisture contents is obtained. However in some cases the comparisons of the other parameters are not so good.

192

A REVISED MODEL OF THE WHEA T DRYING PROCESS 0·40,.-----------------------,

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Fig. 2. (Top) Comparison ofpredicted and experimental bed mean and surface layer m,c. for a 2 ft deep bed; (Bottom) Comparison of predicted and experimental exhaust air dry bulb temperature and r.h. for a 2ft deep bed

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193

H. B. SPENCER 05

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Fig. 4. (Top) Comparison ofpredicted and experiment of bed mean and surface layer m.c. for a 2·3 ft deep bed; (Bottom) Comparison ofpredicted and experimental exhaust air dry bulb temperatures and r.h. for a 2·3 ft deep bed

4. Discussion 4.1. Revised model predictions Predicted exhaust air conditions for the 2 ft deep beds at low air flow rate are not in very good agreement with experiment. Agreement is also not good when the surface layer of the bed starts to dry. A number of factors could be causing lack of agreement. Model predictions indicate that at low flow rates (~I· 7 Ib min' ft-2) the gradient of moisture content at the surface of the bed at the time the surface starts to dry and for an appreciable period thereafter, is about Q·05/in. Experimentally obtained moisture content values quoted for layers near the bed surface are therefore likely to be in error unless based on samples drawn very precisely from these layers. To date no systematic study of the drying rates of thin layers or individual berries has been carried out at high humidities with very moist materials e.g. 0·35 to 0·45 m.c. (d.b.). This data is essential for deep bed analysis as the drying "front" is within the bed for an appreciable time. In this paper extrapolation was required to produce data for relative humidities >80 %.

4.2. Field of application It is felt that the improvements in these comparisons between predicted and experimental data

warranted the use of the model to produce design data, for beds of 3 and 6 in initial depth. The data, considered to have acceptable engineering accuracy, are given in reference' in tabular form

194

A REVISED MODEL OF THE WHEAT DRYING PROCESS

covering a wide range of conditions. Also included are the effects of changes in environmental conditions. The low air flow rate conditions examined in this paper Rj 1·7 lb mirr' £1- 2 required element lengths of 0·5 in in order to obtain convergence. In this case the digital simulation for about 16 h real drying time took 45 min of computer time (ICL-4-75) for the 2ft deep beds. Lower air flow rates and deeper beds could impose burdens on computer facilities. However it is, in practice, unnecessary to employ the model to predict the behaviour of deep beds. For most practical purposes 2 regimes exist in which different techniques are applicable. For convenience these can be called: (1) shallow bed; (2) deep bed. The "shallow bed" regime is characterized by (see Fig. 1): (a) Non-linear bed mean moisture content curve against drying time. (b) Exhaust air conditions which are continually changing throughout the drying time. The "deep bed" regime is characterized by (see Figs 3 and 4): (a) Linear bed mean moisture curve against drying time for a large part of the drying time. (b) Exhaust air conditions which are essentially constant for a large part of the drying time. Design methods covering the deep bed regime have been given in reference", although precise limits have yet to be defined for the range of applicability of this technique. For "shallow beds" design methods based on simple approximations appear unlikely to be successful so resort must be made to experimental or mathematical model predictions. 4.3.

Comments on modelling of deep bed drying

It has been the practice to use the results of thin layer or individual berry drying tests carried out with constant air conditions as the basis for deep bed simulation. However drying in deep beds takes place, at each layer, with air conditions that are far from constant and continuously change from low temperature high humidity to high temperature low humidity. This simulation assumes therefore that the drying rates of individual layers in the deep bed process are independent of the time rates of change of temperature and humidity. It could well be that changes in the drying process are slow enough for this to be a very good approximation but experimental verification would be comforting if only to determine the limits of validity of thin layer results in deep bed modelling. A further point concerning modelling of deep beds is the difficulty of modelling conditions of very low air flow rates. As shown in reference I the gradients (spatial) of the air conditions, temperature and humidity, are inversely proportional to the air flow rate. Low air flow rates give rise to steep gradients which could account for the discrepancies in the predictions of relative humidity. The very steepness of these gradients could give rise to a longitudinal diffusion effect which has not been taken into account. REFERENCES I 2

3

4

5

6

7

8

Spencer, H. B. A mathematical simulation ofgrain drying. J. agric. Engng Res. 1969. 14 (3) 226 Gallaher, G. I. A method of determining the latent heat of agricultural crops. Agricultural Engineering, 1951, p. 54 Clark, R. G.; Lamond, W. J. Drying wheat in 2ft beds. J. agric. Engng Res. 1968. 13 (2) 141 Becker, H. A. A study of diffusion in solids ofarbitrary shape, with application to the drying of the wheat kernel. J. appl. Polym, Sci. 1959. 1 (2) 212 Shu-Tung Chu; Hustrulid, A. Numerical solution of diffusion equations. Trans. Am. Soc. Agric, Engng, 1968. p.705 Woodforde, J.; Lawton, P. J. Drying cereal grain in beds 6 in deep. J. agric. Engng Res. 1965. 10,146 Spencer, H. B. A simple method of estimating drying rates in deep beds ofagricultural produce. N.LA.E. Scottish Station, Departmental Note SSNj37 Spencer, H. B. A revised model of the wheat drying process with design data for beds initially 3 in and 6 in deep. N.I.A.E. Scottish Station, Departmental Note SSN/84