Simulation of grain drying when air-flow is non-parallel

J. agric. Engng Res. (1982) 27, 21-33

Simulation

of Grain Drying when Air-flow

is Non-parallel

E. A. SMITH*

Much work has been done on simulating the drying process in grain beds where air flows in parallel streamlines. This paper presents a method of simulating drying which can be used on any shape of streamline, that is on any shape of grain heap. Isotraverse lines, which have often been used to give the shape of a drying front, can be used to simplify the calculation. Also it is shown that although isotraverse lines are close to lines of constant moisture content, temperature and humidity, they are not coincident with them.

1.

Introduction

In some driers air travels in parallel streamlines and drying has often been successfully simulated The grain moisture content, temperature and in this situation using computer programs.’ humidity profile through a bed can be calculated using these programs. This detailed information can be used to predict the occurrence of germination damage* and will also be useful in predicting protein damage or mould growth. However, in most on-floor drying systems and in many hot air driers, air travels in streamlines which are not parallel. Most of the work done to simulate drying in this situation has been to develop methods of determining the position of the drying front and the approximate time to dry out the grain3 but very little has been done to calculate the moisture content, temperature or humidity profiles throughout such a heap. In this paper 2 methods of simulating the drying of any shape of grain heap are described. In both methods, drying along a streamline is calculated using a modified version of a computer program4 originally designed for parallel air-flow. The first method is to dry along enough streamlines throughout a grain heap to build up a complete picture of the drying behaviour of the heap. The second method uses the concept of an isotraverse line which is the line joining points of equal traverse time along all streamlines. It has been argued, and to some extent shown,3*5 that these lines give the position of a drying front as it moves through a grain bed, so that isotraverse lines approximate lines of constant moisture content, temperature and humidity. Thus by drying along one streamline, isotraverse lines can be used to show how the rest of the grain heap dries. The second method costs much less to compute than the first since only one drying simulation is required. However, this work confirmed that moisture content, temperature and humidity are not constant on isotraverse lines and that, although in many applications they can be neglected, the errors which occur are large enough to be important when accurate values of moisture content, temperature and humidity are required, as, for example, in predicting germination damage. The isotraverse line method is used to calculate the moisture content profile in an on-floor system5 and this is compared with the experimental result. 2. Drying equations The differential equations used to calculate the state variables using parallel air-flow are:4 from the conservation of moisture

when deep grain beds are dried

GS&pF) *Scottish

Institute

Received

26 February

of Agricultural 1981;

Engineering,

accepted

in revised

Penicuik, form

. ..(l)

Midlothian,

7 October

Scotland

1981

21 0021-8634/82/010021

i- 13 $02.00/O

0

1982 The

British

Society

for

Research

in Agricultural

Engineering

22

SIMULATION

;

c

co CD C” G D F G h

ha H AH K M M, AM AM, P P, r

r.h. R S AS t At T AT u Ul Uz ui U* V W x2 Y 6 P Pa z

NOTATION constant in Eqn (7) constant in Eqn (7) specific heat of wet air, J kg-l “C-l specific heat of dry air, J kg-l “C-l specific heat of dry grain, J kg-l “C-l specific heat of water vapour, J kg-l, “C-l specific heat of water, J kg-l “C-l diffusion coefficient, mz/s total air mass flow rate into grain bed, kg/s dry air mass flux, kg mm2 s-l latent heat of evaporation of water, J/kg bed heat transfer coefficient, J rnd3 s-l ‘C-l air specific humidity, kg/kg dry air H at air outlet-H at air inlet, kg/kg dry air constant in Eqn (8) moisture content, kg/kg dry grain equilibrium moisture content, kg/kg dry grain M on streamline 2 or 3 -M on streamline 1, kg/kg dry grain M at air outlet -M at air inlet, kg/kg dry grain air pressure, Pa atmospheric pressure, Pa radial distance in spherical kernel, m relative humidity, % resistance to air flow, Pa mm2 s distance along a streamline, m step length along a streamline, m time, s small time step, s air temperature, “C Tat air outlet -T at air inlet, “C air volume flux, m/s air volume flux given by Eqn (8), m/s air volume flux given by Eqn (IO), m/s U at air inlet, m/s U at air outlet, m/s volume of dried grain, m3 velocity of drying front, m/s Cartesian co-ordinate system, m grain temperature, “C grain dry bulk density, kg/m3 density of dry air, kg/m3 air flux traverse time, s

OF

GRAIN

DRYING

E.

A.

23

SMITH

from the enthalpy change in the air G (C,+C,H)

g

=

(‘-k,+pc,.+)

(T-Q,

..

and from the enthalpy change in the grain p(C,+MC,)

;

[h+(C,.-CJ

= h,(T-O)+p

4 +y.

. ..(3)

If it is assumed that the kernel is spherical the drying rate of individual grains can be described by ?A4 2 aM 1 ?A4 . ..(4) c?r”+--av=--, D

c?t

with M = M, on the surface of the grain and M uniform initially. In Eqns (2) and (3) heat is transferred between air and grain by convection. It is assumed that radiation and conduction of heat, and energy generated by the viscosity of air are negligible. Because of this, heat flow perpendicular to streamlines is ignored. Also, by neglecting viscosity, velocity gradients across streamlines are ignored. Thus the problem is l-dimensional in space with only changes along a streamline affecting drying, so 8 in the equations can represent elements of arc length along a streamline. If the problem becomes 2-dimensional when, for example, conduction is important, then a a-dimensional co-ordinate system would need to be set up and this would greatly increase the complexity of the problem since extra terms would have to be introduced to represent the curvature of the streamlines and &Swould no longer be adequate to represent distance along a streamline. However, Eqns (l)-(4) are accurate for 1-dimensional drying no matter what the shape of the streamlines, so the same equations can be used for both non-parallel and parallel air-flow. The only difference between the two is that the air velocity changes in magnitude along a streamline in non-parallel flow but is constant in parallel flow. 3. Drying along streamlines 3.1. Calculation of streamlines and volume fluxes To calculate the drying behaviour of a grain heap in which the air-flow is non-parallel it is necessary to calculate the position of some streamlines and the air velocities along them. The air pressure distribution in a grain bed can be represented6 by gradp = -RU,

. ..(5)

where U is the volume of air crossing a square metre per second, i.e. the volume flux of air. It is equal to air velocity multiplied by porosity, it thus satisfies the incompressibility condition for velocity div U = 0. . ..(6) The resistance

to air-flow in Eqn (5) can be related to U by6 aU R= ln( 1 + bu)

. ..(7)

where, for barley a = 27,233.2, b = 13.3858 and, for wheat, a = 22,419*9, b = 12.7953.’ A program for solving Eqns (5)-(7) using the finite element technique has been developed by Marchant.“ Once the isobars are calculated the position of a streamline can be found by starting at a point at the air inlet and deriving the next point from XII,, = Xold+&Y”,W dx = _As @laxand I grad P I

= JJ,,,+~.!J, AY = _AS aPpiaY I wdp I ’

24

SIMULATION

OF GRAIN

DRYING

The values of Igrad p 1, appli3x and ap’piaycan be calculated at any point using the element nodal values of these quantities which are calculated by the finite element program.8 The air volume flux at any point along a streamline is given by Eqn (5). This has been done for the symmetrical section of an on-floor duct system shown in Fig. 1. This was one of the systems studied by Williamson;’ the one he named the C2 system. The duct is wire mesh covered with hessian, it is 0.229 m high, 0,279 m wide and the upper part is a semicircle with radius 0.140 m. The grain bed is 1.829 m deep and 0.914 m wide. The grain is Atle wheat but the resistance which fitted quite well to the curve given by Williamson, relating air flux to pressure, is given by Eqn (7) with a = 27,233.2 and b = 13.3858, which were derived for barley. Streamlines 3

1

Fig. 1.

I

2

I

I

I

Some isobars and streamlines in the on-floor duct system studied by Williamson, with a duct pressure 416 Pa. The streamlines numbered 1, 2 and 3 correspond to those in Table I

of

3.2. Drying Drying can be calculated using the usual finite difference techniques’ to solve Eqns (l)-(4). The air mass flux at successive points along the streamline are obtained by interpolation between values of air volume flux calculated by the finite element program* and Eqn (5) and multiplied by air density. The drying behaviour of the whole grain bed could be calculated by drying along several streamlines. An alternative is to use isotraverse lines. 3.3. Isotraverse lines The time taken for air to travel from where it enters the grain bed up to a point in the bed is called the traverse time at that point. Points throughout the grain heap with the same traverse time form an isotraverse surface. For simplicity, grain heaps in which air travels in only 2

E.

A.

25

SMITH

dimensions are considered, so points with the same traverse time form isotraverse lines. The methods of simulating drying would be equally applicable in 3 dimensions. The true traverse time must be calculated using the actual air velocity along a streamline but to do this requires a knowledge of the grain porosity. To avoid this complication the air volume flux along a streamline can be used to calculate a flux traverse time and this is the value used here. It seems reasonable that isotraverse lines give the shape of the drying front and are lines of constant moisture content, temperature and humidity. Two arguments are next presented which support this view. The first is a very approximate calculation, while the second is a more detailed argument which has some experimental backing. However, after these arguments, a detailed drying simulation shows that this currently held view is only approximately true. That isotraverse lines are approximately lines of constant moisture content, temperature and humidity can be seen by considering a drying system in which the air-flow is not parallel. The air inlet conditions are constant and the drying front lies within the bed so the air outlet conditions are also constant. The air-flow along a streamline controls the drying of the grain within a tube surrounding the streamline. This streamtube has a cross-section small enough that drying conditions across it can be considered constant. The drying time is related to the volume of dried grain in the streamtube by

t=-v,PAMS FAH

but the flux traverse time up to the front at time t is

so that 7/t = pu p

AH z&’

The right-hand side of this equation is constant on all streamtubes, showing that T is proportional to t. Thus after drying for a time t the position of the front is given by a line of constant flux traverse time. However, the position of the drying front is vaguely defined in terms of the volume of dried grain in the streamtube, V, so the moisture content, temperature and humidity on the front referred to by t and r may not be the same in all streamtubes. Thus the argument does not show that isotraverse lines are lines of constant M, T, 6’or H. That they may, in fact, be so can be seen by considering the simplified drying equation developed by Baughman, Hamdy and Barre9 which was found to work quite well.‘OThey argue that if the drying front moves with a velocity W at some point then all4 at

-=

aT

aM

-Was and-= at

-W-.

aT

as

They assume that W is the same for the M and T fronts and has the value w=

_

AT

m

dMsh’

Thus since the velocity of the front on any streamline is proportional to the mass flux there, the flux traverse time is proportional to the drying time so that isotraverse lines are lines of constant M and T. Although this work was done for parallel airflow it will be just as accurate for nonparallel air-flow. Thus, a method of simulating drying which includes the idea that isotraverse lines are lines of constant M and T is found to give quite good results.10

26

SIMULATION

OF GRAIN

DRYlNG

This equality can also be tested by simulating drying along the 3 streamlines marked in Fig. 1 using the method described in section 3.2 and comparing values of M, 0 and r.h. on isotraverse lines. This is done in Table I. The inlet air temperature used in this simulation is 15”C, relative humidity is 64*8x, the initial dry basis moisture content is 0.2820, and pressure in the duct is 416 Pa. The table shows the values of M, 0 and r.h. on several isotraverse lines after 1, 4 and 8 days of drying. Along each streamline 3 regions can be identified. The first is the undried region which on Day 1 goes from z = 5 to z = 13. The second is the region where drying is proceeding rapidly, on Day 4 it stretches from z = 1 to z = 11 and on Day 8 from T = 7 to z = 13. The third region is where the grain has dried down close to the moisture content in equilibrium with the inlet air. The drying is much slower than in the second region. In Day 8 it goes from T = 1 to t = 5. There is not a sharp division between each region. The second rapidly drying, region is the drying front and in it the isotraverse lines are seen to be fairly close to lines of constant M, 19and r.h. The difference in M values on the isotraverse lines in the drying front are about 4 % in the more rapidly drying regions. For 8 the difference is approximately 3 % and for r.h. it is about 4%. Outside the drying front, in the first and third regions, the values of M, 9 and r.h. vary so little throughout the region that they would be approximately constant on any line. For the isotraverse lines in the first and third regions the difference in M is about 0.1% and there is no difference in 6 or r.h. to the accuracy in Table I.

TABLE

1

The moisture content (M), grain temperature (0) and air relative humidity (r.h.) on each of the streamlines in Fig. I. The values are shown as functions of the air flux traverse time (2) on days 1, 4 and 8 of drying

-

-

T

Streamline 1

I

Streamline

_

5

M ____ Day 1 1

I3

r.h.

___

M

I9

r.h. -__

--

Streamline

3

_M

e

r.h.

11 13

0.2082 0.2582 0.2823 0.2824 0.2824 0.2824 0.2824

14.4 12.7 12.0 12.0 12.0 12.0 12.0

68.7 84.0 92.6 92.7 92.7 92.7 92.7

0.2090 0.2588 0.2824 0.2824 0.2824 0.2824 0.2824

14.4 12.6 12.0 12.0 12.0 12.0 12.0

69.0 84.2 92.7 92.7 92.7 92.7 92.7

0.2093 0.2603 0.2819 0.2825 0.2822 0.2823 0.2823

14.3 12.5 12.0 12.0 12.0 12.0 12.0

69.2 85.2 92.5 92.7 92.7 92.7 92.7

Day 4 1 3 5 7 9 11 13

0.1607 0.1702 0.1890 0.2223 0.2646 0.2821 0.2824

15.0 14.8 14.5 13.6 12.4 12.1 12.1

65.1 66.2 69.3 76.4 87.7 92.6 92.7

0.1608 0.1709 0.1906 0.2248 0.2700 0.2824

15.0 14.8 14.4 13.6 12.3 12.1 12.1

65.1 66.3 69.6 77.0 89.3 92.6 92.7

0.1609 0.1721 0.1949 0.2327 0.2737 0.2820 0.2823

15.0 14.8 14.3 13.2 12.2 12.1 12.1

65.1 66.6 70.8 79.6 90.6 92.6 92.7

Day 8 1 3 5 7 9 11 13

0.1550 0.1558 0.1579 0.1625 0.1718 0.1899 0.2224

15.0 15.0 15.0 14.9 14.8 14.4 13.6

64.8 64.9 65.2 65.7 67.0 69.9 76.8

0.1549 0.1559 0.1581 0.1626 0.1720 0.1905 0.2235

15.0 15.0 15.0 14.9 14.8 14.4 13.6

64.8 64.9 65.2 65.7 67.0 70.0 77.1

0.1549 0.1560 0.1587 0.1642 0.1751 0.1958 0.2310

15.0 15.0 15.0 14.9 14.7 14.3 13.4

64.8 64.9 65.2 66.0 67.6 71.4 79.2

3 5 7 9

-

-

0.2a2i

-

-

E. A.

27

SMITH

3.4. Changes in M on isotraverse lines The 4% difference in M along isotraverse lines in the drying front in Table I could be due to errors in the values of volume flux and in the position of isotraverse lines caused by using the method described in section 3.1. This can be examined by drying along 3 streamlines on which the volume flux is defined so that its value and the position of the isotraverse lines are known accurately. The values of volume flux used were U, = (Ui-UJexp(-KS)+U,.

. ..(8)

For all streamlines ZJ, = 0.080 but on streamline 1 Ui = 0.149 and K = 10, on streamline 2 Ui = 0.103 and K = 9 and on streamline 3 Ui = 0.033 and K = 5. These values were chosen so that the volume fluxes on each streamline were similar to those on the streamlines in Table I. Although the volume fluxes in Eqn (8) are not from an on-floor system it should not affect the argument since drying along one streamline is independent of drying along any other streamline, even one in a different grain bed provided the initial and boundary conditions are the same in both beds.

Flux traverse

time

,s

Fig. 2. Drying simulation with volume f2u.x U, and air temperature equal to 20°C. The upper curve is the moisture content profile along streamline I after 4 days of drying. The lower curves are the moisture content on streamline 2 or 3 minus the moisture content on streamline 1 at the same J¶UX traverse time

Fig. 2 shows the moisture content values along streamline 1 after 4 days drying, as a function of flux traverse time. Also shown on Fig. 2 is AM as a function of flux traverse time. AM is M on either streamline 2 or streamline 3 at a particular traverse time subtracted from M on streamline 1 at the same traverse time. The shape of the AM curves is similar to that in Fig. 2 throughout the drying period in that AM rises to a maximum value at some flux traverse time which changes with drying time. The maximum value of AM occurs in the drying front. The variation in the largest value of AM with drying time is shown in Fig. 3. The maximum value of AM for streamline 2 throughout the whole drying period is approximately 0.2 % of M while the equivalent value for streamline 3 is 2% of M. These values of AM are related to the different volume air fluxes on each streamline. The maximum difference in volume flux occurs at the air inlet where the value on streamline 1 is I .45 times larger than the value on streamline 2

28

SIMULATION

0.005

OF

GRAIN

DRYING

-

0 004 -

z

0.003

-

E i ‘ii P 2

\

__---

/ ,/----_=z=_

--__

_-’

-O.OOll;L

I

I

I

I

I

I

2

3

4

5

2 3

d

6

Drying time , days

Fig. 3. Drying simulation with volume flux U, and air temperature equal to 20°C. The most positive or negative value of AM, whichever has the largest magnitude, as a function of drying time (--) when h, is a function of u and (- - -) when h, does not depend on lJ

and 4.52 larger than on streamline 3. The AM are largest in the front and increase as drying proceeds. This means that some process in a front causes the grain to dry more slowly on a streamline with a low volume flux than would be expected from the drying on the same isotraverse line on a streamline with a higher volume flux. Suppose that once a front is set up the values of M, T, 8 and Hare constant on isotraverse lines. If the heat and mass transfer coefficients were independent of volume flux then by Eqn (4) CM/at will be constant on these lines, also by Eqn (2) GaT/&S is constant, by Eqn (1) G aH/ aS is constant and, finally, by Eqn (3) i%I/at is constant. At the end of the next time step M, T, Hand 19will be constant on isotraverse lines because of the following argument. Since aM/i?t and iZlO/& are constant on isotraverse lines at time t, M and 8 will be constant there at time t+ At. Also, because M, T, 8 and H are constant along the air inlet at t+ At, GaTjaS and Gi?H/BS are constant there so that on the next isotraverse line from the inlet at time t + At, T and H are constant as well as M and 0. This applies to all isotraverse lines at time t + At. Thus once M, T, B and H are set up constant along isotraverse lines they will remain that way if the heat and mass transfer coefficients are independent of U. Then, because of the result shown in Fig. 3, either or both of these assumptions are wrong. While it is usually accepted that the mass transfer coefficient is independent of volume flux this is not true for heat transfer. The heat transfer coefficient is h,

=

856,800 [U(T+273)/~1.]~‘~~l~.

. . .(9)

The change of U along each of the streamlines is given by Eqn (8). The effect of this change on h, in Eqn (9) can be removed by replacing U by a typical value of volume flux 0.080; the value at the air exit on each streamline. As a result the maximum values of AM are reduced as shown in Fig. 3. This shows that the effect of volume flux on heat transfer is a major cause of AM. The remaining difference is small and is similar for streamlines 2 and 3 so it may result from inaccuracy in the drying simulation. The example just considered is applicable to on-floor drying systems. An example more relevant to high temperature drying systems is now considered. It is the same as the previous

E. A.

29

SMITH

one except that the air temperature is 40°C and the values of air volume streamlines are twice those in Eqn (8):

flux used on the 3 . ..(lO)

u, = 2 u,. Fig. 4 shows the moisture tions of flux traverse time. the effect of air flux, but AM it has its largest value at the

content on streamline 1 and d M after 90 min drying, both as funcAs in Fig. 2 AM on streamline 3 is greater than AM on 2, showing on streamline 3 has a different shape from that in Fig. 2, in particular air inlet and is negative at the leading edge of the front.

03

7

o-2 -

//- 0.01

- 0.005

.O

s u

- -0 005

0

O-I

0.2

0.3

0.4

0.5

Flux traverse

0.6 lime,

0.7

00

09

_i-o~ol I .o

s

Fig. 4. Drying simulation with volume flux lf2 and air temperature equal to 40°C. The upper curve is the moisture content profile along streamline I after 90 min drying. The lower curves are the moisture content on streamline 3 minus the moisture content on streamline 1 at the same flux traverse time

2 or

The effect of drying time on the largest value of AM is shown in Fig. 5. The values of AM are larger than in Fig. 3 as would be expected from the larger flux difference between streamline 1 and streamline 3. Removing the effect of U on h,, by putting U=O*O80 in Eqn (9), produces the result shown in Fig. 5. Showing, as before, that a major cause of AM is the effect of volume flux in heat transfer. Thus using the isotraverse line method to simulate drying when the air-flow is non-parallel can give errors as large as 10% in moisture content. Where accurate values of M, T, 8 and H are required, for example in calculating germination damage in high temperature driers, drying along several streamlines would be better. This is especially so if there are large differences in volume flux on the same isotraverse line. The large errors, however, only occur in the drying front. In applications where the object is to dry the grain to a uniform moisture content, the error in M in the drying front is not SO important, e.g. the low temperature drying of grain for

30

SIMULATION

OF

GRAIN

DRYING

0 015

8 9

0.01

5

E

z %

0005

0

-0.005

l,,,,,i

0

0.5

I.0

15 Drying

20 time,

2.5

30

h

Fig. 5. Drying simulation with volume flux U, and air temperature equal to 40°C. value of AM, whichever has the largest magnitude, as a function of drying time (--) (- - -) when h, does not depend on U

The most positive or negative when h. is a function of U and

animal feed. The fact that there was at one stage a 10% error in M does not matter so long as the front has passed out of the bed. In this case the simulation of drying using isotraverse lines will be adequate.

4.

Comparison with experiment

Williamson5 performed a drying experiment in the system shown in Fig. 1. The Atle wheat was initially at 0.2820 moisture content dry basis and the duct pressure was 416 Pa. The air inlet temperature and humidity were not recorded but the inlet air was given a temperature rise of about 5°C above ambient in order to dry the grain to a dry basis moisture content between 0.15 and 0.16. Drying continued for 8 days, at which time lines of constant moisture content were measured; these are shown in Fig. 6. To simulate this experiment the temperature of the inlet air was taken as 15°C with a relative humidity of 64.8%. It was assumed that the average ambient temperature was approximately 10°C with a relative humidity of about 85 % which are typical values for Bedfordhire in October. The drying program used was that developed by Ingram with the modification described in section 3.2. The equilibrium moisture contents used were from the equation M,=

l-7544-

0.07949 In (l-

developed by Nellist13 and modified with a diffusion coefficient

s)

- 0.29714 In (T+273),

by Bailey. I4 It was assumed

D=4*2705 x lo-l2

that the grain dried as in Eqn (4)

exp (0.0519 T),

which is smaller than that given by Pabis15 but has been found to give more accurate barley16 when the inlet air temperature is 20°C.

results for

E.

A.

Fig. 6.

SMITH

Experimental values of moisture content proJile (--_) moisture content values on them as calculated

31

after 8 days drying, isotraverse lines (- - -) with on streamline I marked in Fig. 1

In Williamson’s experiment the grain bed shrank from 1.83 m to 1.65 m. This was accounted for in the simulation by reducing the bed depth by one-seventh of this shrinkage at the end of each day and then recalculating the streamlines and volume fluxes. The drying program calculates values of the state variables at constant intervals along a streamline. It is assumed that at the end of each day these intervals reduce by a constant amount to account for shrinkage. The values of the state variables at the end of each interval stay the same during the shrinkage. This should model the change fairly well provided the streamlines do not change position too much or shrink too much each day. Fig. 6 shows the position and moisture content values for several lines of constant moisture content. Although there is general similarity between the experimental and computer results there are some differences. The shape of the lines of constant moisture content is not the same as that of the isotraverse lines calculated assuming uniform resistance to air-flow. Williamson5 also noted this and said it could be explained by assuming that grain shrinkage reduced the resistance in the regions that have dried more so that air will flow in those regions faster than calculated. Since the highest air-flow, and hence the most rapid drying, occurs vertically in this example, resistance will fall more rapidly in this direction. If the simulation were recalculated with a lower resistance in the drier regions the isotraverse lines would be higher up in the middle. The isotraverse lines would then be closer in shape to the experimental moisture content lines, although there would still be differences between the calculated moisture content on the isotraverse lines and the experimental values. Some of these differences could also be explained by incorrect assumptions about the inlet conditions for the simulation. Also the drying program computes inaccurate results because of the simplifying assumptions made to formulate the mathematical model and the inadequate data on grain properties used in the calculation. The experimental work will also be a source of error.

SIMULATION

32 5.

OF

GRAIN

DRYING

Conclusion

The values of the state variables in a grain bed can be calculated when the air-flow is nonparallel using one of the 2 methods described in this paper. The computationally faster method is to dry along one streamline and use isotraverse lines to give the values of moisture content, temperature and relative humidity throughout the rest of the bed. Using this method an error of 10% in the grain moisture content arose in the high temperature drying simulation described in the paper. This error is caused by the dependence of the heat transfer coefficient on the air volume flux. For this simulation the volume flux at the air inlet on one streamline was 4.5 times the value on another. This range in volume flux is quite large so a 10% error will probably be near the maximum value. The largest errors arise only in the drying front, while the errors are negiligible in the undried and dried areas on each side of the front. In applications where the object is to dry the grain to a uniform moisture content, the value of moisture content in the drying front is not important, e.g. the low temperature drying of grain for animal feed. The fact that there was at one stage a 10 % error in moisture content does not matter so long as the front has passed out of the bed. In these cases the simulation of drying using isotraverse lines will be adequate. In high temperature grain drying the drying is often stopped when the front is still in the grain bed. In these cases an error as high as 10 % in moisture content in some parts of the drying front would result from using the isotraverse line method. Drying simulations which also calculate germination damage require not only the final moisture content but also the way in which the moisture content and temperature vary throughout the drying. In this case a 10% error in moisture content and a corresponding error in temperature in the front would permanently affect the estimate of damage even after the front has passed out of the bed. These errors can be avoided by using the second method, of simulating drying when the air-flow is non-parallel, which is to dry along several streamlines throughout the grain bed. There are other problems with accuracy which apply to all types of drying simulation. Accurate values of M, are required as well as an accurate description of the drying of individual grains. Values of grain resistance to air-flow are required for a wider range of conditions than previously considered. During drying, grain shrinkage will alter the resistance and although values have been quoted” for various moisture contents these do not take into account the changes in the porosity of the grain bed during drying. It would also be useful if measurements of resistance were made at the higher air velocities which commonly occur in the restricted entry points of air into grain.

REFERENCES

Ingram, G. W. Deep bed drier simulation with intra-particle moisture diflision. J. agric. Engng Res., 1976 21 (3) 263-272 2 Nellist, M. E. Safe temperaturesfir drying grain. Rep. No. 29, Natn. Inst. agric. Engng, Silsoe 1978

1

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