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In deep bed drying,
• All the samples in the dryer are not fully exposed to the same condition of drying air
• Condition of dry air at any point in mass changes with time and with the depth of sample bed
• Drying in the deep bed can be taken as a sum of several thin layers
• Humidity and temperature of air entering and leaving each layer vary with time depending upon the stage of drying, the moisture removing from the dry layer until equilibrium moisture content is reached
Some examples for deep bed drying
Drying grain (e.g., shelled corn) with the
drying air flowing through more than two to
three layers of kernels
Dehydration of solid food materials
inaoutaa ,,
Fan
grain of mass totalgm
ina, :ratiohumidity
MCgrain in change gW
outa, :ratiohumidity
am
Basic Drying Process
(Mass Conservation)
Total moisture conservation equation
compare: moisture added to air
to
moisture removed from product
Drying time
ggaa Wmtm
kga
ss
kgw
kga
kgw
kgg
kgg
aa
gg
m
Wmt
Heat balance for drying
Q- Air flow rate m3/min
v – specific volume
Ca – specific heat of air kJ/kg
Ta- Temperature of air in plenum 0C
Tg- Temperature of air leaving grain mass 0C
hfg –latent heat of vaporization kJ/kg moisture
DM – Dry matter content kg
M0 – Initial Moisture content (db - decimal)
Me – Final equilibrium moisture content (db-decimal)
)(*)(**)(**60*
( 0 efggaa MMDMhtTTcQ
Time taken by the drying front to reach the top of the bed can be calculated using following equation
Where,
Mi = % Dry basis initial moisture content of the sample
Mx = % Dry basis average moisture content at the end of the drying front advance to the top
ti = Time of advance (hr)
A = Cross sectional area of the dryer through which air passes
G = Mass flow rate of dry air (kg/ hr.m2)
Hs= Humidity of air leaving the dryer
Hi = Humidity of air entering the dryer
Wd = Mass of the dry sample in the bin (kg)
iis
xid tHHAGMMW
100
For the changes in drying air conditions
psychrometric principles can be applied
Hard wheat at 75°F is being dried from 18% to
12% w.b. in a batch grain drier. Drying will be
stopped when the top layer reaches 13%.
Ambient conditions: Tdb = 70°F, RH = 20%
Determine the exit air temperature early in the
drying period?
Determine the exit air RH and temperature at
the end of the drying period?
Example
Twb
emc=13%RHexit
Texit
Part II
At inlet ambient air enters
T db = 70°F RH =20%
During drying air enthalpy doesn’t change
Part I
inlet ambient
T db = 70°F RH =20%
emc = 18%
Texit air = 53.5°F
Twb
emc=18%
Tdb,e
Loewer, et al. (1994 )
Mathematical models are needed to predict temperature and moisture profiles in the deep-bed and inside the grain
The models propose that the system with two control volumes Grain where moisture is at liquid phase
Humid air outside the kernel
To pull the moisture from grain and to enter to the vapor phase sensible and latent heat is needed
Models assume the steady state drying
According to Hukill ( 1947,1954) bulk drying curves can be used to find:
approximate moisture content at any depth in the deep bed drying system at any time after drying has started
Three parameters were used to represent any deep drying systems
Moisture ratio ( MR)
Depth factor ( D)
Time unit ( Y)
Moisture ratio
122
2
YD
D
MR
Where,
MR = ( M – Me ) / ( Mo - Me )
Mo = Moisture content at the start of drying ( d.b. ,decimal )
M = Grain Moisture ( d.b. ,decimal )
Me = Moisture content when the grain as reached equilibrium with air
D = Depth factor
Y = Time unit
Depth factor (D) DM’ is needed to calculate depth factor
DM’ is constant throughout the drying periodDM’ = dry matter per depth factorTg = Temperature of exit airTa = Temperature of inlet airhfg = Btu/ lbcfm = Air flow rate in cubic ft per minuteca = Btu/lb v = ft3 / lb
)(
)(60*'
2/1
eofg
gaa
MMvh
tTTccfmDM
Depth factor zero (D=0)
However,
D=0 contains half of the grains of the other
depth factors
DM’ – is considered as a constant value
throughout the drying period
(volume of grain/depth factor depends on density, it
changes with drying ?? But to simplify the analysis
assume no shrinkage. Select a logical value, ie at M0 )
Time unit ( Y)
Y = t / t1/2
t1/2 = Time required for fully exposed grain to dry from MR=1 to MR = 0.5 ( obtained from a table )
t = Drying time
Values of t1/2 for shelled corn
Temp F
Original
MC
%wb
60
15.55 C
80
26.66 C
100
37.77 C
120
48.88 C
140
60 C
160
71.11 C
180
82.22 C
35 5.6 5.5 4.5 3.3 2.4 1.5 1.2
30 6.0 5.0 3.9 3.0 2.6 2.1 1.7
25 6.3 5.2 4.3 3.2 2.9 2.6 2.4
20 6.6 6.4 5.6 4.4 4.0 3.5 3.4
(t1/2 –Time required for fully exposed corn to dry from MR=1 to MR=0.5 at given
temperatures. The air has a dew point temperature of 50 F
Example1. Air flow rate in a dryer = 16330 cfm
Ta = 83.5 F -Air temp at the plenum
Фa = 35% (RH)
Tg = 64.0 -exit air temp,
Ca- 0.24 BTU/lb F
v = 13.86 ft3/lb specific volume of air
M0 = 33.33% db
Me = 9.28% db -at plenum air conditions
Dia of the dryer -27 ft-Floor area = 573 ft2 - height of grain 8 ft -Given
Drying time 75 h
Find a). Location of the drying zone
b). The thickness of the zone
c). The average moisture content of the grain
T1/2 = 5 h
MR= M - Me / (M0- Me )
M = Me + MR (M0- Me)
MR M
0 - 9.28
0.1 - 11.69
0.2 14.09
. .
1.0 33.33
Y = t/ t1/2
t = Y * 5
Y = 75/5 = 15 Refer to the drying curves pgs 197-98
a) after 75h drying, bottom of the drying zone is 8.5
depth factors (or 2.78 ft) from the bottom
Top of the zone is 21.5 depth factors (or 7.03 ft)
from the bottom
To calculate the height of a depth factor
Use the DM’ equation
b) Drying zone = 7.03- 2.78 ft
= 4.25 ft
DM’ – Dry matter per depth factor
)(
)(60*'
2/1
eofg
gaa
MMvh
tTTccfmDM
0928.03333.01200*86.13
0.5*0.645.8324.0*60*16330'
DM
= 5732 lb dry matter per depth factor
Grain density at M0 (25% (w.b.) = 40.8 lb/ft3
Dry mass per 1 ft3 = 40.8 * 0.75 lb
Volume per Depth factor = 5732/40.8*0.75
= 187.32 ft3
Floor area of the dryer = 573 ft2 - Given
The thickness of a depth factor = Vol of a depth factor/floor area of the dryer
= 187.32 ft3 / 573 ft2
= 0.327 ft
But “0” DF = ½ * 0.327 = 0.163 ft
Mc (d.b.) can be read from the graph
Mc along the 15 Y line for curves or can be calculated from
122
2
YD
D
MRMR = ( M – Me ) / ( Mo - Me )
M av = weighted %/total No of Depth factors= 455.83%/24.5 = 18.61 d.b.Or 15.69 w.b.
DDepth factor
Y Time unit
MR Moisture Ratio
MMC-decimal
0 15 3.05176E-05 0.092807
1 15 6.10333E-05 0.092815
2 15 0.000122059 0.092829
3 15 0.000244088 0.092859
4 15 0.000488058 0.092917
5 15 0.00097564 0.093035
6 15 0.001949377 0.093269
7 15 0.003891169 0.093736
12 15 0.111114125 0.119523
20 15 0.969697866 0.326012
21 15 0.984615847 0.329600
22 15 0.992248297 0.331436
23 15 0.996109068 0.332364
24 15 0.998050742 0.332831
24.5 15 0.998620879 0.332968
Depth factor
D
Depth of
Grain
% MC d.b. Weighted %
0 0.163 9.28 4.64
1-8 2.779 9.28 74.24
9 3.106 9.65 9.65
10 3.433 10.00 10.00
11 3.760 10.69 10.69
12 4.087 11.95 11.95
13 4.414 14.05 14.05
14 4.741 17.30 17.30
15 5.068 21.31 21.31
16 5.395 25.31 25.31
17 5.722 28.52 28.52
18 6.049 30.66 30.66
19 6.376 31.92 31.92
20 6.703 32.6 32.60
21 7.030 32.96 32.96
22-24 8.011 33.33 99.99
455.83
A simple model for drying rice grains in a
deep bed dryer
The deep bed drying can be described as several
thin layers
If height of the bed is Z,
air entering at Z=0 and
air leaving from the bed at Z=L
Uniform temperature distribution across the grain
phase is assumed. But the temperature is changed.
Drying process inside the grain requires a two
phase model. At the second falling rate period,
diffusion of bound water takes place.
Xms= Maximum sorption water content
X0 = Initial moisture content
Xeq = Equilibrium moisture content
D0 = Diffusion coefficient at initial time(m2s-1)
Equilibrium moisture content is calculated using isotherm
)
)(
eqms
eq
obedXX
XXDD
D1 = Constant of Arrhenius type equation (m2s-1)
Ea = Activation energy per unit mass (Jkg-1)
R = Ideal gas constant ( Jkg-1k-1)
T = Time (s)
)exp(10RT
EDD a
D0 = Diffusion coefficient at initial time
Conservation of mass equation state the moisture
loss by the grain phase
X = Grain moisture content ( kg moisture / kg
drain )
Wa = Axial drying air flux per unit of deep bed
cross sectional area ( m s-1)
H = Absolute air humidity ( kg moisture/kg dry
air)
Z
HW
t
Xa
ss
a
Energy conservation for each of the thin layer
Heated air can evaporate water coming from the
grain and increase the temperature from Ts to Tg
Energy balance,
Z
HTTcpTlW
t
Txcpcp
Z
THcpcpW sgvsvaa
swsss
g
vaaa
)]()([)()(
Change of rice temperature in solid and liquid
phase
t
TXcpcpTTha s
wssssgeff
)()()(
cpv = Specific heat of vapor (Jkg-1k-1)
Cpw = Specific heat of water ( Jkg-1k-1)
haeff = Volumetric pseudo convective heat
transfer coefficient (Wm-3k-1)
Tg = Air temperature
Ts = Temperature of solid
ρss = Apparent density of dry grain
ρa = Density of dry air
lv = Vaporization heat of water ( Jkg-1)
Modeling of temperature changes in air phase
Z
HTTcpTlTT
W
ha
Z
HHcpcp sgvsvag
aa
eff
va
)]()([)(
)()(
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