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Temperature control of the continuous peanut drying process using microwave technology

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ABSTRACT
BOLDOR, DORIN. Temperature Control of the Continuous Peanut Drying Process Using
Microwave Technology. (Under the direction of Timothy H. Sanders and Kenneth R.
Swartzel.)
The relationship between dielectric properties of peanuts (Arachis hypogaea L.),
thermal and moisture distribution during continuous microwave drying, and automated
control of the drying process was investigated. Dielectric properties (ε', ε'') of ground
samples of peanut pods and kernels were measured for several densities, temperatures, and
moisture contents, in the range of 300 to 3000 MHz. Dielectric mixture equations were used
to correlate the dielectric properties with density. The coefficients of quadratic and linear
dielectric mixture equations are tabulated for 915 and 2450 MHz, for different temperatures
and moisture contents. The values of the dielectric constants (ε') and loss factors (ε'') of bulk
peanut pods and kernels were determined by extrapolation of the first and second-order
polynomials that relate ε' and ε'' with density. An equation that determines the dielectric
properties of bulk peanut pods and kernels as a function of their temperature and moisture
content was determined using multiple linear regression.
Peanut dielectric properties were used in transport phenomena equations previously
developed for batch-type microwave drying. The equations were adapted to account for the
spatial variation of the electric field inside a continuous microwave drying applicator. The
theoretical equations developed, together with experimental methods, were used to determine
the effect of microwave power level, initial moisture content and dielectric properties on the
temperature profiles and the reduction in moisture content of peanuts.
The temperature profiles obtained from solution of these equations matched the
experimental profiles determined using fiber optic temperature probes. The temperature
profiles were determined to be dependent on both moisture content and microwave power
level. Although the maximum temperature in the microwave applicator was a function of
power level only, the rate at which that maximum was attained was a function of dielectric
properties and moisture contents of the peanuts. An absolute theoretical determination of
moisture content reduction during microwave drying was not possible due to the dependence
of dielectric properties on the moisture content. When dielectric properties were assumed
independent of moisture content, the theoretical estimations of moisture losses were always
lower than the losses determined experimentally, although they were in the same range of
values. The surface temperature distribution of the peanut bed measured using infrared
pyrometry was well correlated with internal temperature profiles. Thermal imaging
demonstrated that the temperature of the peanut bed surface at the exit of the microwave
curing chamber was uniformly distributed.
The surface temperature determined as a function of power level was used to create a
feedback control loop of the continuous microwave drying process of farmer stock peanuts of
different varieties and various initial moisture contents. Process parameters were determined
using process reaction curves and a PI (proportional, integral) controller was implemented in
the software routine that controlled the microwave generator power level. The servo scenario
(set point change) was simulated to determine the optimum tuning parameters of the PI
controller. The potential for a combined feedback/feed forward control of the process based
on complete surface temperature distribution measured with an infrared camera placed at the
location of maximum surface temperature was evaluated.
This study quantifies the relationships between the various parameters that influence
the continuous microwave drying process of peanuts. The results of this study may be used as
a foundation for development of optimum process conditions in microwave drying of peanuts
and other agricultural commodities, as well as for development of advanced process control
methods in continuous microwave processing.
TEMPERATURE CONTROL OF THE CONTINUOUS PEANUT DRYING
PROCESS USING MICROWAVE TECHNOLOGY
by
DORIN BOLDOR
A dissertation submitted to the Graduate Faculty of
North Carolina State University
in partial fulfillment of the
requirements for the Degree of
Doctor of Philosophy
FOOD SCIENCE
BIOLOGICAL AND AGRICULTURAL ENGINEERING
Raleigh
2003
APPROVED BY:
UMI Number: 3107746
________________________________________________________
UMI Microform 3107746
Copyright 2004 by ProQuest Information and Learning Company.
All rights reserved. This microform edition is protected against
unauthorized copying under Title 17, United States Code.
____________________________________________________________
ProQuest Information and Learning Company
300 North Zeeb Road
PO Box 1346
Ann Arbor, MI 48106-1346
To my father
ii
BIOGRAPHY
Dorin Boldor was born on February 6th, 1974, in Onesti, Romania. He received a Bachelor of
Science degree in Mechanical Engineering in 1997, from Aurel Vlaicu University of Arad,
Romania. During his undergraduate studies, Dorin Boldor was employed as a computer
operator and computer programmer assistant with the Oil Unit Production and General Petro
Service, in Arad, Romania. He was admitted to graduate school at University of Missouri –
Columbia in 1998 to pursue a master’s program in Biological Engineering. In the summer of
1998 he transferred to North Carolina State University, where he received a dual Master of
Science degree in Food Science and Biological and Agricultural Engineering in May 2000.
Prior to admission to graduate school he played in the Romanian National Basketball League,
for West Petrom Arad. He married Cristina Sabliov in July 2000, and they are expecting a
baby girl in July 2003.
iii
ACKNOWLEDGEMENTS
I would like to extend my sincere gratitude to Dr. Tim Sanders and Dr. Ken Swartzel for
their support and understanding throughout the years we have worked together to complete
this project. Their help and advice was invaluable and I will always remember it.
I would like to thank Drs. Andy Hale, Joel Trussell and Michael Drozd too for serving on
my Advisory Committee and providing excellent suggestions.
I thank Dr. Josip Simunovic, my good friend and mentor, for the time, effort, resources
and humor that supported me for the last 5 years.
I would like to recognize Karl Hedrick, Jack Canady, Gary Cartwright and all the people
that work in the Dairy Plant at North Carolina State University for the help they provided
during the years I spent in graduate school. Special thanks go to Keith Hendrix and the
people working in the USDA-ARS, Market Quality and Handling Research Unit at North
Carolina State University for their invaluable help and suggestions regarding the
experimental part of this study. I am also grateful to Elaine Lowell, Susie Kall, Sue Strong,
Paula Pharr, Beth McGlamery and Lisa Gordon for their support in fighting bureaucracy.
Good times were provided by the Food Engineering crew, Brian Farkas, KP Sandeep,
Stephen Sylvia, Jon Bell, Heather Stewart, Koray Palazoglu, Pablo Coronel, Jeff Resch,
Qixin Zhong, Ediz Batmaz, and Brian Lloyd.
I would like to thank all my friends that were next to me during these last three years in
both good and bad times: Brian, Laura, Hannah, Rachel, Cristina, Artem, Josip, Nada, and
countless others.
iv
A special acknowledgement is made to my parents, Dorin and Aurelia Boldor, who
always believed in me, even though my father did not live to see my greatest
accomplishments. My sister, Nicoleta Belean, and her family Sorin, Radu and Andrada,
together with my aunt Dorina Mesteroiu, and my mother in law Pusa, are the perfect family. I
love you all.
I would like to thank my wife, Cristina Sabliov, and soon-to-be-born baby girl, for their
endless supply of love and support, and for all the joy they bring into my life.
v
TABLE OF CONTENT
LIST OF TABLES………………………………………………………………………
viii
LIST OF FIGURES……………………………………………………………………...
x
INTRODUCTION……………………………………………………………………….
1
Justification of research…………………………………………………………….
1
Objectives…………………………………………………………………………..
5
REFERENCES……………………………………………………………………..
6
Manuscript 1. Dielectric Properties of In-Shell and Shelled Peanuts at Microwave
Frequencies………………………………………………………………
7
ABSTRACT………………………………………………………………………..
8
INTRODUCTION………………………………………………………………….
9
Dielectric properties of heterogeneous mixtures…….……………………….
11
MATERIALS AND METHODS…………………………………………………..
13
RESULTS AND DISCUSSION..………………………………………………….
15
CONCLUSIONS…………………………………………………………………...
18
LIST OF SYMBOLS………………………………………………………………
19
REFERENCES…………………………………………………………………….
20
FIGURE CAPTIONS………………………………………………………………
24
Manuscript 2. Thermal Profiles and Moisture Loss during Continuous Microwave
Drying of Peanuts.……………………………………………………….
30
ABSTRACT…………………….………………………………………………….
31
INTRODUCTION………………………………………………………………….
33
Mathematical development..………………………………………………….
38
MATERIALS AND METHODS…………………………….…………………….
44
vi
RESULTS AND DISCUSSION…………………………………………………...
48
Simulated results……………………………………………………………...
48
Experimental results………………………………………………………….
49
Experimental design 1………………………………………………….…….
50
Experimental design 2………………………………………………………..
52
CONCLUSIONS…………………………………………………………………..
57
LIST OF SYMBOLS………………………………………………………………
59
REFERENCES…………………………………………………………………….
60
FIGURE CAPTIONS………………………………………………………………
70
Manuscript 3. Control of Continuous Microwave Drying Process of Farmer Stock
Peanuts…………………………………………………………………... 107
ABSTRACT……………………………………………………………………….. 108
INTRODUCTION…………………………………………………………………. 109
Theoretical considerations……………………………………………………
110
MATERIALS AND METHODS………………………………………………….. 114
RESULTS AND DISCUSSIONS………………………………………………….
116
CONCLUSIONS…………………………………………………………………... 120
LIST OF SYMBOLS………………………………………………………………
121
REFERENCES…………………………………………………………………….
122
FIGURE CAPTIONS…..………………………………………………………….
126
PROJECT SUMMARY…………………………………………………………………
134
FUTURE RESEARCH………………………………………………………………….
136
vii
LIST OF TABLES
Values for coefficients and r2 of the quadratic and linear regressions at
915 MHz for kernels………………………………………………………
22
Values for coefficients and r2 of the quadratic and linear regressions at
915 MHz for pods…………………………………………………………
22
Values for coefficients and r2 of the quadratic and linear regressions at
2450 MHz for kernels……………………………………………………..
23
Values for coefficients and r2 of the quadratic and linear regressions at
2450 MHz for pods………………………………………………………..
23
Table 2.1.
Locations of the infrared thermocouples ……….………………………...
64
Table 2.2.
Parameters for temperature profiles in Eqn. [2.19] and Figure 2.10 .…….
65
Table 2.3.
Parameters for convective and radiative losses in Eqns. [2.35], [2.36] and
Figure 2.11………………………………………………………………..
65
Table 2.4.
Parameters for moisture losses in Eqn. [26] and Figure 12……………….
65
Table 2.5.
Moisture contents (% db) for Virginia type peanuts in three consecutive
passes……………………………………………………………………...
66
Moisture contents (% db) for Runner type peanuts in three consecutive
passes……………………………………………………………………...
66
Surface temperature distribution for Virginia and Runners type peanuts
at the exit from the drying tunnel at 2 power levels and three initial
moisture contents………………………………………………………….
66
Relationship between surface and internal temperatures for 11% mc
Runner type peanuts………………………………………………………
67
Relationship between surface and internal temperatures for 14% mc
Runner type peanuts………………………………………………………
67
Relationship between surface and internal temperatures for 21% mc
Runner type peanuts………………………………………………………
68
Relationship between surface and internal temperatures for 33% mc
Runner type peanuts………………………………………………………
68
Table 1.1.
Table 1.2.
Table 1.3.
Table 1.4.
Table 2.6.
Table 2.7.
Table 2.8.
Table 2.9.
Table 2.10.
Table 2.11.
viii
LIST OF TABLES (cont)
Table 2.12.
Moisture losses at 6 power levels…………………………………………
69
Table 2.13.
Average surface temperature (°C) and standard deviation (°C) for
Runner type peanuts at 4 initial moisture contents undergoing drying at 6
different power levels……………………………………………………..
69
Infrared thermocouples locations, grouping and relationship between
internal and surface temperature for Runner type peanuts at 33% initial
mc…………………………………………………………………………
124
Table 3.1.
Table 3.2.
Process parameters for Virginia and Runner type peanuts at 3 initial mc... 124
Table 3.3.
Initial tuning parameters for Virginia and Runner type peanuts at 3 initial
mc…………………………………………………………………………
125
Initial and optimum tuning parameters and times to get to the set point
for Runner type peanuts at 33% initial mc...……………………………...
125
Table 3.4.
ix
LIST OF FIGURES
Figure 1.1.
Density dependence of peanut kernels dielectric properties at 18% mc
and 30°C at 915 MHz. a. Dielectric constant (ε'); b. Dielectric loss
(ε'')……………………………………………………………………...
25
Density dependence of peanut pods dielectric properties at 23% mc
and 30°C at 2450 MHz. a. Dielectric constant (ε'); b. Dielectric loss
(ε'')……………………………………………………………………...
26
Dielectric properties of peanut pods at several moisture contents as a
function of frequency at 23°C. a. Dielectric constant (ε'); b. Dielectric
loss (ε'')…………………………………………………………………
27
Temperature and moisture dependence of dielectric properties of
peanut kernels based on the quadratic equations [1.12] and [1.15].
a. Dielectric constant (ε'); b. Dielectric loss (ε'')……………………….
28
Temperature and moisture dependence of dielectric properties of
peanut pods based on the linear equations [1.13] and [1.16].
a. Dielectric constant (ε'); b. Dielectric loss (ε'')……………………….
29
Figure 2.1.
Mechanisms of ionic interaction (Zhong, 2001)……………………….
73
Figure 2.2.
Mechanisms of dipolar interaction (Zhong 2001)……………………...
74
Figure 2.3.
Distribution of the electric field in a transversal section of the TE10
waveguide in the presence of a lossy dielectric at the center of the
waveguide. Wave is propagating into the paper. a – waveguide
height, b – waveguide width, w – height of dielectric load……………
75
Temperature distribution during microwave drying. The time
coordinate can be changed into distance for a belt moving at constant
speed (Metaxa and Meredith, 1983)……………………………………
76
Electric field distribution along a traveling wave applicator. The
distance coordinate is dependent on the time coordinate through the
conveyor belt speed…………………………………………………….
76
Figure 2.6.
Microwave generator (a) and the curing chamber (b)………………….
77
Figure 2.7.
Schematic of the microwave drying system (top) and infrared
thermocouple locations along the waveguide bottom).………………...
77
Transmitted and reflected power at an impedance mismatch (change
of transmission medium, Stuchly and Hamid, 1972)…………………..
78
Figure 1.2.
Figure 1.3.
Figure 1.4.
Figure 1.5.
Figure 2.4.
Figure 2.5.
Figure 2.8.
x
LIST OF FIGURES (cont)
Figure 2.9.
Fiber optic probes in peanuts and their location on the conveyor belt…
78
Figure 2.10.
Estimated temperature profiles for Runner type peanuts at 21% mc
and 6 power levels……………………………………………………...
79
Estimated convective and radiative losses of Runner type peanuts at
21% mc and 2 kW……………………………………………………...
79
Estimated moisture losses for Runner type peanuts at 21% mc and 2
kW……………………………………………………………………...
80
Internal temperature (lines) and bed surface temperature (symbols)
distributions in Runner type peanuts at 18% initial mc for pods in
different locations on the belt. Pod P1 is located closest to the right
wall…………………………………………………………………….
81
Side panels covering cleaning slots on the right side of the drying
chamber………………………………………………………………...
81
Internal temperatures (lines) and surface temperatures (symbols) of
Runner type peanuts at 3 initial mc undergoing drying at 1.2 kW……..
82
Internal temperatures (lines) and surface temperatures (symbols) of
Runner type peanuts at 3 initial mc undergoing drying at 2 kW……….
82
Internal temperatures (lines) and surface temperatures (symbols) of
Virginia type peanuts at 3 initial mc undergoing drying at 1.2 kW……
83
Internal temperatures (lines) and surface temperatures (symbols) of
Virginia type peanuts at 3 initial mc undergoing drying at 2 kW……...
83
Internal and external temperatures of pods (lines) and bed surface
temperatures (symbols) of Runner type peanuts at 3 initial mc
undergoing drying at 1.2 kW…………………………………………..
84
Internal and external temperatures of pods (lines) and bed surface
temperatures (symbols) of Runner type peanuts at 3 initial mc
undergoing drying at 2 kW…………………………………………….
84
Surface temperature distribution at the end of drying of Runner type
peanuts at two power levels (1.2 kW – left column, 2 kW – right
column) and indicated initial mc……………………………………….
85
Figure 2.11.
Figure 2.12.
Figure 2.13.
Figure 2.14.
Figure 2.15.
Figure 2.16.
Figure 2.17.
Figure 2.18.
Figure 2.19.
Figure 2.20.
Figure 2.21.
xi
LIST OF FIGURES (cont)
Figure 2.22.
Figure 2.23.
Figure 2.24.
Figure 2.25.
Figure 2.26.
Figure 2.27.
Figure 2.28.
Figure 2.29.
Figure 2.30.
Figure 2.31.
Figure 2.32.
Surface temperature distribution at the end of drying of Virginia type
peanuts at two power levels (1.2 kW – left column, 2 kW – right
column) and indicated initial mc……………………………………….
86
Internal temperature (lines) and bed surface temperature (symbols)
distributions for Runner type peanuts at 11% initial mc and 6 power
levels……………………………………………………………………
87
Internal temperature (lines) and bed surface temperature (symbols)
distributions for Runner type peanuts at 14% initial mc and 6 power
levels……………………………………………………………………
87
Internal temperature (lines) and bed surface temperature (symbols)
distributions for Runner type peanuts at 21% initial mc and 6 power
levels……………………………………………………………………
88
Internal temperature (lines) and bed surface temperature (symbols)
distributions for Runner type peanuts at 33% initial mc and 6 power
levels……………………………………………………………………
88
Standard deviations for internal temperature (lines) and bed surface
temperature (symbols) distributions for Runner type peanuts at 11%
initial mc and 6 power levels…………………………………………...
89
Standard deviations for internal temperature (lines) and bed surface
temperature (symbols) distributions for Runner type peanuts at 14%
initial mc and 6 power levels…………………………………………...
89
Standard deviations for internal temperature (lines) and bed surface
temperature (symbols) distributions for Runner type peanuts at 21%
initial mc and 6 power levels..………………………………………….
90
Standard deviations for internal temperature (lines) and bed surface
temperature (symbols) distributions for Runner type peanuts at 33%
initial mc and 6 power levels. ………………………………………….
90
Internal temperatures as function of surface temperature at different
distances in the microwave drying tunnel for Runner type peanuts at
11% initial mc….…………………………………………....................
91
First derivative of the internal temperature with respect to distance for
Runner type peanuts at 11% initial mc and 6 power levels……………
92
xii
LIST OF FIGURES (cont)
Figure 2.33.
Figure 2.34.
Figure 2.35.
Figure 2.36.
Figure 2.37.
Figure 2.38.
Figure 2.39.
Figure 2.40.
Figure 2.41.
Figure 2.42.
Figure 2.43.
Figure 2.44.
Figure 2.45.
First derivative of the internal temperature with respect to distance for
Runner type peanuts at 14% initial mc and 6 power levels……………
92
First derivative of the internal temperature with respect to distance for
Runner type peanuts at 21% initial mc and 6 power levels....................
93
First derivative of the internal temperature with respect to distance for
Runner type peanuts at 33% initial mc and 6 power levels……………
93
Internal temperature (lines) and bed surface temperature (symbols)
distributions for Runner type peanuts at 0.3 kW and 4 initial mc……...
94
Internal temperature (lines) and bed surface temperature (symbols)
distributions for Runner type peanuts at 0.6 kW and 4 initial mc……...
94
Internal temperature (lines) and bed surface temperature (symbols)
distributions for Runner type peanuts at 0.9 kW and 4 initial mc……..
95
Internal temperature (lines) and bed surface temperature (symbols)
distributions for Runner type peanuts at 1.2 kW and 4 initial mc……...
95
Internal temperature (lines) and bed surface temperature (symbols)
distributions for Runner type peanuts at 1.5 kW and 4 initial mc……...
96
Internal temperature (lines) and bed surface temperature (symbols)
distributions for Runner type peanuts at 2 kW and 4 initial mc………..
96
Standard deviations for internal temperature (lines) and bed surface
temperature (symbols) distributions for Runner type peanuts at 0.3 kW
and 4 initial mc..………...…………………………………...................
97
Standard deviations for internal temperature (lines) and bed surface
temperature (symbols) distributions for Runner type peanuts at 0.6 kW
and 4 initial mc…………………………...……………….....................
97
Standard deviations for internal temperature (lines) and bed surface
temperature (symbols) distributions for Runner type peanuts at 0.9 kW
and 4 initial mc………….……………………...………………………
98
Standard deviations for internal temperature (lines) and bed surface
temperature (symbols) distributions for Runner type peanuts at 1.2 kW
and 4 initial mc…………………………………………………………
98
xiii
LIST OF FIGURES (cont)
Figure 2.46.
Figure 2.47.
Figure 2.48.
Figure 2.49.
Figure 2.50.
Figure 2.51.
Figure 2.52.
Figure 2.53.
Figure 2.54.
Figure 2.55.
Figure 2.56.
Figure 2.57.
Standard deviations for internal temperature (lines) and bed surface
temperature (symbols) distributions for Runner type peanuts at 1.5 kW
and 4 initial mc…………………………………………………………
99
Standard deviations for internal temperature (lines) and bed surface
temperature (symbols) distributions for Runner type peanuts at 2 kW
and 4 initial mc.………………………………………….......................
99
First derivative of the internal temperature with respect to distance for
Runner type peanuts at 0.3 kW and 4 initial mc……………………….
100
First derivative of the internal temperature with respect to distance for
Runner type peanuts at 0.6 kW and 4 initial mc……………………….
100
First derivative of the internal temperature with respect to distance for
Runner type peanuts at 0.9 kW and 4 initial mc……………………….
101
First derivative of the internal temperature with respect to distance for
Runner type peanuts at 1.2 kW and 4 initial mc……………………….
101
First derivative of the internal temperature with respect to distance for
Runner type peanuts at 1.5 kW and 4 initial mc……………………….
102
First derivative of the internal temperature with respect to distance for
Runner type peanuts at 2 kW and 4 initial mc…………………………
102
Surface temperature distribution at the end of drying of Runner type
peanuts at 11% initial mc and 6 power levels: a) 0.3 kW, b) 0.6 kW, c)
0.9 kW, d) 1.2 kW, e) 1.5 kW, f) 2.0 kW………………………………
103
Surface temperature distribution at the end of drying of Runner type
peanuts at 14% initial mc and 6 power levels: a) 0.3 kW, b) 0.6 kW, c)
0.9 kW, d) 1.2 kW, e) 1.5 kW, f) 2.0 kW………………………………
104
Surface temperature distribution at the end of drying of Runner type
peanuts at 21% initial mc and 6 power levels: a) 0.3 kW, b) 0.6 kW, c)
0.9 kW, d) 1.2 kW, e) 1.5 kW, f) 2.0 kW………………………………
105
Surface temperature distribution at the end of drying of Runner type
peanuts at 33% initial mc and 6 power levels: a) 0.3 kW, b) 0.6 kW, c)
0.9 kW, d) 1.2 kW, e) 1.5 kW, f) 2.0 kW………………………………
106
xiv
LIST OF FIGURES (cont)
Figure 3.1.
Schematic of the microwave drying system (top) and infrared
thermocouple locations along the waveguide (bottom)...……………...
127
Figure 3.2.
Feedback control loop….………………………………………………
127
Figure 3.3.
First derivative of the internal temperature with respect to distance in
the microwave tunnel for Runner type peanuts at 2 kW and 4 initial
mc………………………………………………………………………
128
Step response of the 16 infrared thermocouples for Runner type
peanuts at 52% initial mc………………………………………………
128
Step response of the six groups of infrared thermocouples for Runner
type peanuts at 33% initial mc…………………………………………
129
Step response of the six groups of infrared thermocouples for Runner
type peanuts at 36% initial mc…………………………………………
129
Step response of the six groups of infrared thermocouples for Runner
type peanuts at 52% initial mc…………………………………………
130
Step response of the six groups of infrared thermocouples for Virginia
type peanuts at 22% initial mc…………………………………………
130
Step response of the six groups of infrared thermocouples for Virginia
type peanuts at 26% initial mc…………………………………………
131
Step response of the six groups of infrared thermocouples for Virginia
type peanuts at 44% initial mc…………………………………………
131
Figure 3.11.
Diagram of the Labview simulation program………………………….
132
Figure 3.12.
Simulation result for initial tuning parameters………............................
133
Figure 3.13.
Simulation result for optimum tuning parameters……………………...
133
Figure 3.4.
Figure 3.5.
Figure 3.6.
Figure 3.7.
Figure 3.8.
Figure 3.9.
Figure 3.10.
xv
INTRODUCTION
Justification of research
The annual production of peanuts in the United States of America has a field value of
more than 1 billion dollars/year (USDA-NASS, 1999b). This figure does not include the
existing stocks at farms that exceeds 50 million pounds. The United States is the third largest
producer of peanuts in the world, with the first two countries being China and India (USDANASS, 1999a).
There are many factors that affect the yield and quality of peanut production. Cultural
practices (climatic conditions, crop rotation, land preparation, variety selection, liming,
fertilization and mineral nutrition, irrigation, weeds, insect and disease control during
growing), maturity at harvesting, and harvesting, curing and storage methods all influence
peanut production and quality (Henning et al., 1982). Of these factors, curing (or drying) is
the most energy intensive process.
Drying is a processing step that reduces the moisture content of peanuts from 50% at
digging to a moisture content safe for long term storage (8-10%). Drying is performed in two
steps. First, peanuts are dried in the field in inverted windrows to 20% moisture content. The
second step is artificial drying in wagons from 20% to 10-11% in about 18-24 hours. After
artificial drying, peanuts are moved to storage facilities where they continue to lose some
moisture during the storage period.
1
Artificial drying is an energy intensive process and therefore expensive in terms of
electrical energy consumed by fans and in terms of fuel consumption for heating the air. A
goal of the peanut industry is to reduce energy requirements during drying through use of
different methods. Recently developed "green grading" procedure which allow for mixing of
different lots before curing are conducing to continuous flow drying procedures. The
reduction in handling will be cost efficient and reduce damage to peanuts.
Current methods used to reduce the cost of artificial drying concentrate on improving
energy efficiency of wagon drying methods. This study is focused on application of a new
technology for reduction of energy consumption: the use of microwave energy in a
continuous drying applicator. Microwave energy is more efficiently converted into heat when
compared with conventional convective drying (Metaxa and Meredith, 1983). Very fast
drying rates can be easily achieved which reduces the drying time and thus energy use.
In conventional artificial drying, the driving forces are the temperature and moisture
gradient created by heated air blowing through the deep bed of peanuts. The heated air
creates a drying front that moves upward through the peanut bed as the drying process
progresses (Young et al., 1982). At the pod level, on the outer shell of the pods, heated air
creates a front at which the water is heated, vaporized and removed. As drying progresses,
this drying front moves inward toward the center of the peanut pod. As the front gets closer
to the center of the pod the drying rate decreases as water vapor must diffuse through the
peanut in order to be removed from the pod.
In microwave drying, the oscillating electric field causes polar molecules to rotate
and charged ions to oscillate. This ionic and molecular movement leads to intermolecular
friction causing rapid heating.
2
The heating takes place volumetrically, and water is heated and vaporized within the
whole volume of the peanut pod. The rapidly formed water vapor creates a large pressure
gradient that is the driving force in microwave drying.
The energy transfer between the microwave field and material is a function of the
dielectric properties of the material. Due to the inherent nature of microwaves, in
conventional microwave ovens, the multiple reflections of the oven walls create standing
electric field patterns. These standing waves lead to heating non-uniformities that are
commonly encountered in microwave units and therefore limit the adoption of the technology
to a few applications such as tempering of frozen meats. New microwave system designs
such as traveling wave applicators create a uniform electric field distribution. A material with
uniform dielectric properties running on a conveyor belt at the center of the applicator is
exposed to the constant electric field and is uniformly heated.
This study focused on understanding the fundamentals of heating and drying
mechanisms of peanuts undergoing continuous microwave drying. There has been little
research on continuous microwave drying of peanuts, thus there is a lack of knowledge
pertaining to thermal and moisture distribution in peanuts during continuous microwave
drying. The influence of dielectric properties on the temperature distribution and moisture
reduction in peanuts is not well understood. This study addressed these fundamental issues of
continuous microwave drying, as well as a practical application of methods to control the
microwave drying process.
The study is structured in three major parts. The first part deals with the dielectric
properties of shelled and in-shell peanuts and the dependence of dielectric properties on
moisture content and temperature.
3
The second part covers the theoretical foundation of heat and mass transfer during
continuous microwave drying, as well as the experimental work performed to validate the
mathematical developments. In this second part, the interpretation of the temperature
distributions and moisture reduction data, as related to dielectric properties and initial
moisture content of peanuts, and relationship between the internal temperature and the
surface temperature of peanut bed are also presented. In the third part relationship between
the surface and internal temperature was used to create an effective feedback control
algorithm that maintains the temperature at a desired level.
The information and technology created in the study of theoretical and practical aspects
of continuous microwave drying can be applied to a large number of agricultural
commodities. This information may lead to significant improvements in the drying methods
currently used in processing of agricultural products.
4
Objectives
Research objectives were:
-
to determine the dielectric properties of peanuts at microwave frequencies and the
relationship to temperature and moisture content.
-
to determine the influence of peanut dielectric properties and initial moisture content
on internal and surface temperature distributions and moisture reduction during
continuous microwave drying.
-
to develop the relationship between the internal and surface temperature distribution
in peanut pods during microwave drying and use the relationship to create a feedback
control mechanism that maintains the surface temperature at a desired level.
5
REFERENCES
Henning R.J., Allison A.H. and Tripp L.D. 1982. Cultural Practices. Ch. 5. In Peanut Science
and Technology. H.E. Pattee and C.T. Young (Ed.), American Peanut Research and
Education Society, Inc., Yoakum, TX.
Metaxa, A.C. and Meredith, R.J. 1983. Industrial Microwave Heating. Peter Peregrinus Ltd.,
London, UK.
USDA-NASS (United States Department of Agriculture - National Agricultural Statistics
Service). 1999a. Agricultural Statistics 1999. United States Government Printing Office.
Washington, DC.
USDA-NASS (United States Department of Agriculture - National Agricultural Statistics
Service). 1999b. Statistical Highlights of U.S. Agriculture. United States Government
Printing Office. Washington, DC.
Young, J.H., Person, N.K., Donald, J.O., and Mayfield, W.D. 1982. Harvesting, Curing, and
Energy Utilization. In Peanut science and technology. Edited by Pattee, H.E. and Young,
C.T. Amer. Peanut Res. Educ. Soc., Inc., Yoakum, TX.
6
Manuscript 1. Dielectric Properties of In-Shell and Shelled Peanuts at Microwave
Frequencies
D. Boldor1, T.H. Sanders2*, J. Simunovic1
1
Department of Food Science
North Carolina State University, Raleigh NC 27695-7624
2
USDA - ARS, Market Quality and Handling Research Unit
North Carolina State University, Raleigh, NC 27695-7624
*
Corresponding author:
Tel: 919-515-6213
Fax: 919-515-7124
E-mail: tim_sanders@ncsu.edu
7
ABSTRACT
Dielectric properties (ε', ε'') of ground samples of peanut (Arachis hypogaea L.) pods
and kernels were measured for several densities, temperatures, and moisture contents, in the
range of 300 to 3000 MHz. Dielectric mixture equations were used to correlate the dielectric
properties with density. The coefficients of quadratic and linear dielectric mixture equations
are tabulated for 915 and 2450 MHz, for different temperatures and moisture contents. The
values of the dielectric constants (ε') and loss factors (ε'') of bulk peanut pods and kernels
were determined by extrapolation of the first and second-order polynomials that relate ε' and
ε'' with density. An equation that determines the dielectric properties of bulk peanut pods and
kernels as a function of their temperature and moisture content was determined using
multiple linear regression.
Keywords: Arachis hypogaea L., dielectric properties, peanuts, microwave
8
INTRODUCTION
Dielectric properties (ε', ε'') of materials characterize their interaction (transmittance,
absorbance, and reflection) with electric fields, and implicitly with electromagnetic waves,
including those in the microwave region. Dielectric theory and dielectric properties of
materials have been studied in detail for many years (von Hippel, 1954; Birks, 1967) and a
comprehensive review has been recently published (Neelakanta, 1995). Dielectric properties
also characterize the ability of the material to dissipate electromagnetic energy as heat
(Nelson, 1992) according to:
P = σ E2 = 2 π f ε0 ε'' E2
[1.1]
Microwave drying and roasting are two major agricultural related processing
applications in which the knowledge of the dielectric properties of various agricultural
commodities is important. Many commodities have their dielectric properties compiled in
extensive studies (Nelson, 1973; ASAE, 2000b).
Whitney and Porterfield (1967) measured the dielectric properties of Starr peanuts at
frequencies up to 50 MHz. While some of their results are similar to those reported by other
researchers, their analysis has been criticized for large errors in high moisture peanuts and
methods used in measurement (Nelson, 1973). Also the dielectric properties in the
microwave region (300 – 3000 MHz) may differ significantly from those at lower
frequencies. The purpose of this study was to determine the effect of temperature and
moisture content on the dielectric properties of peanuts in the microwave region of the
electromagnetic spectrum (300 – 3000 MHz).
9
For biological materials (non ferromagnetic) the dielectric properties of interest are the
dielectric constant (ε') and the dielectric loss (ε''), which relate to the complex permittivity ε
through the relationship (Nelson, 1978):
ε = ε' – j ε''
[1.2]
Where ε' and ε'' are relative to the permittivity of free space (vacuum) ε0.
Free air has a similar permittivity to a vacuum (no loss and the same storage ability),
therefore it can be approximated as:
εair = 1 – j 0
[1.3]
Two other properties of interest in microwave processing of biological materials are
conductivity (σ) and loss tangent (tan δ):
σ = ω ε0 ε''
[1.4]
tan δ = ε''/ε'
[1.5]
The permittivity of materials varies with frequency (von Hippel, 1954; Lawrence et al.,
1990; Neelakanta, 1995), and for pure polar materials it can be expressed using Debye’s
equation (von Hippel, 1954):
ε = ε' ∞ +
ε' s −ε' ∞
;
1 + jω τ
ε' = ε' ∞ +
ε' s −ε' ∞
;
1 + ω2 τ 2
ε' ' =
(ε's −ε'∞ )ω τ
1 + ω2 τ 2
[1.6]
For non-pure polar materials an extension of Debye’s equation (Cole-Cole equation) is
used (Nelson, 1973):
ε = ε' ∞ +
ε' s −ε' ∞
;
1 + (j ω τ)1−α
[1.7]
10
The general equations presented so far cannot be used in evaluating the dielectric
constant and dielectric loss of peanuts as they are not pure polar materials, they have multiple
layers (in the case of in-shell peanuts) and they form a heterogeneous mix with the air that
surrounds them.
Dielectric properties of heterogeneous mixtures
In microwave processing, the influence of the dielectric properties depends on the
amount of mass interacting with the electromagnetic field. Therefore, given that the total
volume is constrained by the microwave cavity, the density (mass/unit volume) will have an
effect on dielectric properties. This is especially notable with particulate dielectrics such as
pulverized or granular materials (Nelson, 1983; Nelson, 1992). The influence of bulk density
on dielectric properties has been studied in detail and equations have been developed that can
be applied to heterogeneous mixtures (van Beek, 1967; Tinga and Voss, 1973).
ε2 −1
1
; if v2 < 0.1
ε mix = 1 + v 2 ∑
3
i 1 + A i (ε 2 − 1)
[1.8]
ε1 (ε 2 − 1)
1
; for any v2
ε mix = 1 + v 2 ∑
3
i ε1 + A i (ε 2 − ε1 )
[1.9]
Where for prolate spheroids:
ai
bi
1


2
2


 ai 
ai

−1
+
Ai =
ln  +   − 1  ; Ai ∈ [0, 1]
2
3
b
b
 
2
 ai 
 2  i  i 
  − 1  a i 


  − 1
 bi 
b
 i 

[1.10]
11
An alternative approach for determining the dielectric properties of particulate and
pulverized materials has been developed throughout the years. It is based on the observation
that the dielectric constant and dielectric loss for granular and pulverized samples depend on
density according to the following formulas (Nelson, 1983; Nelson et al., 1991; Nelson,
1992):
ε' = 1 + A1 ρ + A2 ρ2
[1.11]
(ε')1/2 = m1 ρ + 1
[1.12]
(ε')1/3 = m3 ρ + 1
[1.13]
ε'' = B1 ρ + B2 ρ2
[1.14]
(ε'' + e)1/2 = m2 ρ + (e)1/2
[1.15]
e = B12/(4*B2)
[1.16]
where:
These equations are similar with the complex refractive index mixture equation [1.17]
(Kraszewski, 1977; Nelson et al., 1991) and the Landau and Lifshitz, Looyenga equation
[1.18] (van Beek, 1967)
ε mix = v1 ε 1 + v 2 ε 2 ;
1
1
1
ε mix 3 = v1ε 1 3 + v 2 ε 2 3 ;
v1 = 1 − v 2 ;
[1.17]
v1 = 1 − v 2 ;
[1.18]
Equations [1.11] to [1.18] were successfully used to determine the dielectric properties
of pecans (Nelson, 1981; Lawrence et al., 1992), wheat (Nelson, 1984; Lawrence et al.,
1990), rice (You and Nelson, 1988), and fish meal (Kent, 1977). The present study of
dielectric properties of peanuts is based on the theoretical developments presented above.
12
MATERIALS AND METHODS
Field dried peanuts were shipped from USDA – ARS National Peanut Research
Laboratory in Dawson, Georgia in August 2002 to North Carolina State University. They
were separated into 4 different samples. The first sample was stored in a cooler at 8°C, while
the others were dried on an air blower in three stages, to reach a total of four different
moisture contents. The moisture content of each sample was determined according to ASAE
Standards (ASAE, 2000a). Each sample was subsequently divided into two separate samples,
out of which one was shelled in order to determine the dielectric properties of both in-shell
and shelled peanuts. In addition to bulk moisture content of the samples, the moisture content
of each sample undergoing dielectric properties measurements was measured by collecting a
small sample after the dielectric measurement.
The peanut samples were sealed in quarter size plastic bags and left to equilibrate their
moisture content for 24 hours in refrigerator at 4°C. After equilibration the bags were
removed from the refrigerator and left to equilibrate at room temperature for 4 hours (23°C).
In-shell and shelled peanuts were grounded using a Waring Blendor Model 702B
(Waring Product Corp., New York, NY ) and the ground product size separated using a 3.35
mm U.S. Standard Sieve (Dual Manufacturing Co., Chicago, ILL). Ground samples were
placed in 250 ml sealed mason jars at four different densities (Nelson and You, 1989). The
smallest particle density was achieved by pouring the sample as loose as possible. The higher
particle densities were obtained by tapping and pressing the sample in the jar with three
different weights (1870, 4570 and 16935 g). Measurements for all four densities were
performed at 23°C (room temperature), 30, 40 and 50 °C respectively.
13
For temperatures above room temperature, the jars were held in water baths for a few
hours, until an extra jar with temperature sensor at the geometric center filled at the highest
density was determined to be at thermal equilibrium with the water bath.
Dielectric properties were measured with a HP Network Analyzer 8753C (HewlettPackard, Palo Alto, CA) using the open-ended coaxial probe method adapted from Nelson
and Bartley (2000) and Engelder and Buffler (1991), in a 361 point frequency sweep from
300 MHz to 3 GHz. The network analyzer was controlled by Hewlett-Packard 85070B
dielectric kit software (Hewlett-Packard, Palo Alto, CA) and calibrated using the 3-point
method (short-circuit, air and water at 25°C).
The least square method (Milton and Arnold, 1995) was used in Matlab (The
Mathworks, Inc., Natick, MA) to determine the coefficients of regression (A1, A2, B1, B2, m1,
m2, m3, e) and coefficients of determination (r2) for ε' and ε'' as a function of density for all
361 points in the frequency sweep. The method was used for both first-order and secondorder polynomials according to equations [1.11] - [1.16] as described by Nelson (1984).
Dielectric properties of in-shell and shelled peanuts at nominal bulk density for all
moisture contents and temperatures tested were determined afterward using dielectric
mixture equations [1.11] to [1.15] in Microsoft Excel XP (Microsoft Corp., Redmond, WA).
The equations that relate the dielectric properties of peanut pods and kernels to their moisture
content and absolute temperature were obtained by performing multiple linear regression on
the logarithmic transforms of the data:
log (ε') (or log ε'') = c1 log (10) + c2* log(T(K)) + c3 log(mc)
=>
ε' (or ε'') = 10c1 Tc2 mcc3
[1.19]
[1.20]
14
RESULTS AND DISCUSSION
The FCC regulates the use of frequencies of the electromagnetic spectrum in the US,
and the two frequencies reserved for food uses are 915 MHz and 2.45 GHz. Most of the
results presented here are at these two frequencies.
The dielectric properties of ground pods and kernels as a function of density are
displayed in Figures 1.1 and 1.2. The density dependence of the dielectric properties (ε' and
ε'') of ground peanuts is similar to those obtained for other agricultural commodities (Nelson
and You, 1989). As the density increases, the dielectric properties increase for both ground
kernels and ground pods. The dependence was determined using equations [1.11] to [1.17]
with very good results. In general the quadratic equations [1.11] and [1.14] give better
estimates of the dielectric properties (r2 > 0.9) than linear equation [1.12], [1.13] and [1.15]
respectively. The coefficients for quadratic and linear predictive equations ([1.11] to [1.16])
as a function of density for peanuts at various temperatures and moisture contents are
presented in Tables 1.1 through 1.4.
Two notable exceptions occur for the dielectric loss of ground pods (18% mc and 50°C)
and kernels (33% mc and 50°C). While the quadratic equation [1.14] shows a very good
dependence of bulk density (r2 > 0.9), the linear estimations using equation [1.15] becomes
unusable (e<0, therefore e1/2 is a complex number). In general, the dielectric mixture
equations proved to be more accurate for temperatures below 50°C and lower moisture
contents. Similar effect was observed in high moisture dough (>26%) by Kim et al. (1998)
due to increased water mobility resulting in decreased ionic conductivity.
15
Since deviations from the equation [1.14] are noticed even in lower moisture peanuts,
the authors hypothesize that in addition to increased water mobility, oil extraction from
peanuts also has a previously unaccounted effect on the density dependence of dielectric
properties. The extraction of oil is caused by a combination of the grinding process, the
pressure applied to create a high density mixture, and the higher temperatures. Ground
peanuts change from a heterogeneous mixture of solids and air to a mixture of solids, oil, and
air, and the linear dielectric mixture equations [1.11] – [1.16] do not accurately represent the
system. In this case the quadratic equations [1.11] and [1.14] prove to be valuable tools in
estimating the dielectric properties of peanuts at high temperatures and moisture content.
Dielectric properties of Georgia Green peanut kernels as a function of frequency at
23°C and all four moisture contents are presented in Figure 1.3. While the dielectric
properties decrease with frequency, they increase as the moisture content increases up to
33%, and afterward decrease at 39% mc. This effect was previously noticed in potatoes and
explained by Mudgett (1995) by a dilution of dissolved salts by the extra free water. The
dielectric mixture theory equations [1.11] to [1.16] were used subsequently to determine the
dielectric properties of bulk peanuts at different moisture contents and densities (Figures 1.4
and 1.5).
In the lower moisture region (18-23%), both temperature and moisture content seem to
affect the dielectric constant and dielectric loss of peanuts. In the higher moisture region (2333%), the temperature effect becomes insignificant when compared to the effect of moisture
content. Therefore, for dielectric heating of peanuts in the high moisture content, the rate of
heating (Eqn. [1.1]) will be mainly affected by the moisture content, with the temperature
range studied not affecting the dielectric loss of the peanuts.
16
The authors assume that at temperatures above those studied in this paper, the dielectric
loss of peanuts will increase significantly according to the microwave thermal runaway effect
(Rosenthal, 1992).
The multiple linear regression performed on the logarithmic transforms of the data
(equations [1.19] and [1.20]) gives the following relationship of the dielectric properties of
the peanuts with their moisture content and temperature:
Kernels at 915 MHz:
Kernels at 2450 MHz:
Pods at 915 MHz:
Pods at 2450 MHZ:
ε' = 102.6840 * T(K)-0.5262 * mc0.8870
r2 = 0.83
[1.21]
ε''= 105.5882 * T(K)-1.8323 * mc1.3083
r2 = 0.84
[1.22]
ε' = 102.1730 * T(K)-0.3401 * mc0.8562
r2 = 0.85
[1.23]
ε''= 107.8072 * T(K)-2.7511 * mc1.3483
r2 = 0.86
[1.24]
ε' = 100.7776 * T(K)0.2299 * mc1.2642
r2 = 0.93
[1.25]
ε''= 103.1577 * T(K)-0.7181 * mc2.4603
r2 = 0.93
[1.26]
ε' = 100.5638 * T(K)0.2843 * mc1.1614
r2 = 0.94
[1.27]
ε''= 106.4954 * T(K)-2.0955 * mc2.5433
r2 = 0.95
[1.28]
17
CONCLUSIONS
Peanut dielectric properties were determined using methods previously applied to
wheat, corn and other agricultural commodities. Dielectric theory mixture equations were
found to provide good estimates of the dielectric loss and the dielectric constant as a function
density, and they proved to be very useful in determining the dielectric properties of bulk
peanuts in the microwave region of the electromagnetic spectrum. Data for dielectric
properties of peanut pods and kernels was provided for a range of moisture contents and
temperatures at microwave frequencies used in food processing (915 and 2450 MHz). The
dependence on temperature was found to be more significant at lower moisture contents. At
higher moisture contents, the significance of temperature effects on ε' and ε'' was reduced by
the high dependence on moisture content of dielectric properties. The dielectric properties of
peanuts obtained using equations [1.21] to [1.28] are similar to those presented in literature
(Nelson, 1973), with certain variations due to different moisture contents and frequencies
used.
18
LIST OF SYMBOLS
ai, bi – major and minor axis of the prolate spheroids; m
Ai – depolarizing factor
A1, A2 – regression coefficients of dielectric constant quadratic equations
B1, B2 – regression coefficients of dielectric loss quadratic equations
c1, c2, c3 – coefficients of regression equation
e – regression constant
E – electric field; V/m
f – frequency; Hz
j – (-1)1/2
m1, m2, m3 – regression coefficients for linear equations
mc – moisture content dry basis; %
P – power absorbed per unit volume; W/m3
tan δ – loss tangent (tan δ = ε''/ε' = σ/ωε0ε')
T – absolute temperature; K
v1 – volume fraction of the continuous phase (air)
v2 – volume fraction of the dispersed phase (solid)
α – spread of relaxation times; α∈[0,1]
δ − phase of a complex number
ε – relative complex permittivity or relative complex dielectric constant
ε0 – dielectric constant of the vacuum = 8.854 10-12 Far/m
ε1 – relative dielectric constant of the continuous phase (air)
ε2 – relative dielectric constant of the dispersed phase (solids)
εmix – relative dielectric constant of a mixture
ε∞ – relative dielectric constant as ω goes to infinity
ε 1 – mean value permittivity around a spheroid particle
ε' – relative electric constant or storage factor
εs' – relative static dielectric constant (at ω = 0)
ε'' – relative dielectric loss or loss factor
σ – conductivity; siemen/m
τ – relaxation time for a polar molecule; sec
ω – angular frequency;
19
REFERENCES
ASAE Standards. 2000a. Moisture Measurement – Peanuts. ASAE S410.1 DEC97. ASAE,
2950 Niles Road, St. Joseph, MI 49085-9659 USA
ASAE Standards. 2000b. Dielectric Properties of Grain and Seed. ASAE D293.2 DEC99.
ASAE, 2950 Niles Road, St. Joseph, MI 49085-9659 USA
Birks, J.B. 1967. Progress in Dielectrics. CRC Press, Cleveland, OH.
Engelder, D.S., Buffler, C.R. 1991. Measuring Dielectric Properties of Food Products at
Microwave Frequencies. Microwave World, 12(2):2-11
Kent, M. 1977. Complex Permittivity of Fish Meal: A General Discussion of Temperature,
Density and Moisture Dependence. Journal of Microwave Power, 12(4):341-345
Kim, Y.-R., Morgan, M.T., Okos, M.R., Stroshine, R.L. 1998. Measurement and Prediction
of Dielectric Properties of Biscuit Dough at 27 MHz. Journal of Microwave Power and
Electromagnetic Energy, 33(3):184-194
Kraszewski, A. 1977. Prediction of the Dielectric Properties of Two-Phase Mixtures. Journal
of Microwave Power, 12(3):215-222
Lawrence, K.C., Nelson, S.O., Kraszewski, A. 1990. Temperature Dependence of the
Dielectric Properties of Wheat. Transactions of the ASAE, 33(2):535-540
Lawrence, K.C., Nelson, S.O., Kraszewski, A. 1992. Temperature Dependence of the
Dielectric Properties of Pecans. Transactions of the ASAE, 35(1):251-255
Milton, J.S., Arnold, J.C. 1995. Introduction to Probability and Statistics: Principles and
applications for engineering and the computing sciences. 3rd Ed. Irwin McGraw-Hill,
New York, NY.
Mudgett, R.E. 1995. Electrical Properties of Foods. In Engineering Properties of Foods. 2nd
Ed. Edited by Rao, M.A., Rizvi, S.S.H. Marcel Dekker, Inc. New York, NY.
Neelakanta, P.S.1995. Handbook of Electromagnetic Materials: monolithic and composite
versions and their applications. CRC Press LLC,Boca Raton, FL.
Nelson, S.O. 1973. Electrical Properties of Agricultural Products (A Critical Review).
Transactions of the ASAE, 16(2):384-400
Nelson, S.O. 1978. Frequency and Moisture Dependence the Dielectric Properties of HighMoisture Corn. Journal of Microwave Power, 13(2):213-218
20
Nelson, S.O. 1981. Frequency and Moisture Dependence of the Dielectric Properties of
Chopped Pecans. Transactions of the ASAE, 24(6):1573-1576
Nelson, S.O. 1983. Observations on the Density Dependence of Dielectric Properties of
Particulate Materials. Journal of Microwave Power, 18(2):143-152
Nelson, S.O. 1984. Density Dependence of the Dielectric Properties of Wheat and WholeWheat Flour. Journal of Microwave Power, 19(1):55-64
Nelson, S.O., You, T.-S. 1989. Microwave Dielectric Properties of Corn and Wheat Kernels
and Soybeans. Transactions of the ASAE, 32(1):242-249
Nelson, S.O., Kraszewski, A., You, T.-S. 1991. Solid and Particulate Material Permittivity
Relationships. Journal of Microwave Power and Electromagnetic Energy, 26(1):45-51
Nelson, S.O. 1992. Correlating Dielectric Properties of Solid and Particulate Samples
Through Mixture Relationships. Transactions of the ASAE, 35(2):625-629
Nelson, S.O., Bartley, P.G. 2000. Measuring Frequency – and Temperature – Dependent
Dielectric Properties of Food Materials. Presentation at the 2000 ASAE Annual
International Meeting, Paper No. 006096. ASAE, 2950 Niles Road, St. Joseph, MI
49085-9659 USA
Rosenthal, I. 1992. Electromagnetic Radiation in Food Science. Springer-Verlag Berlin.
Tinga, W.R, Voss, A.G. 1973. Generalized approach to multiphase dielectric mixture theory.
Journal of Applied Physics, 44(9):3897-3902
van Beek, L.K.H. 1967. Dielectric Behaviour of Heterogeneous Systems. In Progress in
Dielectrics, edited by Brick, J.B. CRC Press, Cleveland, OH.
von Hippel, A.R. 1954. Dielectric Materials and Application. The Technology Press of
M.I.T., John Wiley & Sons, Inc., New York, NY and Chapman & Hall, Ltd., London,
UK
Whitney, J.D., Porterfield, J.G. 1967. Dielectric Properties of Peanuts. Transactions of the
ASAE, 10(1):38-39,42.
You, T.-S., Nelson, S.O. 1988. Microwave Dielectric Properties of Rice Kernels. Journal of
Microwave Power and Electromagnetic Energy, 23(3):150-159
21
Table 1.1. Values for coefficients and r2 of the quadratic and linear regressions at 915 MHz for kernels
MC (%), ρ (kg/m3)
Temp (°C)
ε' = A2ρ2+A1ρ+1
ε'1/2 = m1ρ+1
ε'1/3 = m3ρ+1
ε'' = B2ρ 2+B1ρ
(ε''+e)1/2 = m2ρ+e1/2
MC (%), ρ (kg/m3)
Temp (°C)
ε' = A2ρ2+A1ρ+1
ε'1/2 = m1ρ+1
ε'1/3 = m3ρ+1
ε'' = B2ρ 2+B1ρ
(ε''+e)1/2 = m2ρ+e1/2
A2
A1
r2
m1
r2
m3
r2
B2
B1
r2
e
m2
r2
A2
A1
r2
m1
r2
m3
r2
B2
B1
r2
e
m2
r2
23
1.135E-5
-9.280E-4
0.960
2.059E-3
0.837
1.151E-3
0.872
3.025E-6
1.730E-4
0.985
2.481E-3
1.740E-3
0.980
18%, (628 kg/m3)
30
40
9.150E-6 8.530E-6
1.029E-3 1.392E-3
0.849
0.756
2.131E-3 2.106E-3
0.788
0.703
1.187E-3 1.173E-3
0.815
0.725
2.243E-6 2.214E-6
5.590E-4 5.540E-4
0.916
0.787
3.484E-2 3.468E-2
1.494E-3 1.475E-3
0.930
0.798
23
1.327E-5
2.725E-3
0.926
3.014E-3
0.900
1.561E-3
0.925
5.191E-6
2.800E-4
0.948
3.770E-3
2.263E-3
0.952
33%, (715.3 kg/m3)
30
40
1.534E-5 4.698E-6
2.481E-5 1.001E-2
0.958
0.952
3.241E-3 3.055E-3
0.957
0.954
1.665E-3 1.589E-3
0.963
0.909
5.712E-6 2.471E-6
4.380E-4 2.685E-3
0.909
0.954
8.387E-3 7.293E-1
2.392E-3 1.568E-3
0.889
0.959
50
1.138E-5
-7.700E-4
0.897
2.091E-3
0.789
1.166E-3
0.822
3.870E-6
-7.500E-4
0.920
3.634E-2
1.421E-3
0.839
50
-5.909E-6
1.724E-2
0.974
2.819E-3
0.278
1.491E-3
-0.235
-2.856E-6
6.615E-3
0.926
-3.830E+0
N/A
N/A
23
1.670E-5
-3.672E-3
0.994
2.354E-3
0.861
1.279E-3
0.904
4.609E-6
-5.840E-4
0.985
1.851E-2
1.782E-3
0.971
23% (654.6 kg/m3)
30
40
1.450E-5
1.911E-5
-4.242E-3 -6.571E-3
0.956
0.988
1.929E-3
2.144E-3
0.798
0.770
1.073E-3
1.173E-3
0.846
0.808
3.638E-6
5.207E-6
-8.920E-4 -1.740E-3
0.892
0.937
5.469E-2
1.453E-1
1.279E-3
1.259E-3
0.845
0.798
50
1.680E-5
-4.868E-3
0.981
2.145E-3
0.814
1.177E-3
0.859
4.819E-6
-1.640E-3
0.962
1.396E-1
1.192E-3
0.799
23
3.961E-6
-1.962E-2
0.936
2.600E-3
0.611
1.360E-3
0.658
1.356E-5
-6.608E-3
0.825
8.054E-1
1.323E-3
0.529
39% (751.3 kg/m3)
30
40
4.292E-6
1.400E-6
1.159E-2 -1.200E-4
0.985
0.983
3.268E-3
2.715E-3
0.928
0.933
1.697E-3
1.433E-3
0.781
0.976
2.436E-6
4.860E-6
3.261E-3 -1.380E-4
0.971
0.949
1.092E+0
9.820E-4
1.560E-3
2.129E-3
0.969
0.937
50
3.193E-6
9.115E-3
0.970
2.749E-3
0.895
1.456E-3
0.744
1.130E-6
2.996E-3
0.973
1.986E+0
1.063E-3
0.972
Table 1.2. Values for coefficients and r2 of the quadratic and linear regressions at 915 MHz for pods
MC (%), ρ (kg/m3)
Temp (°C)
ε' = A2ρ2+A1ρ+1
ε'1/2 = m1ρ+1
ε'1/3 = m3ρ+1
ε'' = B2ρ 2+B1ρ
(ε''+e)1/2 = m2ρ+e1/2
MC (%), ρ (kg/m3)
Temp (°C)
ε' = A2ρ2+A1ρ+1
ε'1/2 = m1ρ+1
ε'1/3 = m3ρ+1
ε'' = B2ρ 2+B1ρ
(ε''+e)1/2 = m2ρ+e1/2
A2
A1
r2
m1
r2
m3
r2
B2
B1
r2
e
m2
r2
23
2.172E-5
-5.026E-3
0.978
1.673E-3
0.647
1.005E-3
0.687
4.603E-6
-2.000E-4
0.963
2.094E-3
1.937E-3
0.949
A2
A1
r2
m1
r2
m3
r2
B2
B1
r2
e
m2
r2
23
2.289E-5
2.235E-3
0.838
3.723E-3
0.836
1.961E-3
0.868
6.894E-6
1.451E-3
0.754
7.638E-2
2.596E-3
0.837
18% (332 kg/m3)
30
40
1.854E-5
1.095E-5
-4.582E-3 -8.000E-6
0.973
0.933
1.753E-3
1.889E-3
0.685
0.816
1.033E-3
1.107E-3
0.735
0.843
3.965E-6
3.043E-6
-5.400E-4 -2.800E-5
0.999
0.981
1.810E-2
6.250E-5
1.475E-3
1.711E-3
0.933
0.978
33% (366.6 kg/m3)
30
40
4.469E-5
4.137E-5
-8.431E-3 -8.261E-3
0.918
0.775
4.110E-3
3.823E-3
0.867
0.746
2.133E-3
2.003E-3
0.921
0.800
1.995E-5
2.082E-5
-4.860E-3 -6.250E-3
0.870
0.696
2.955E-1
4.697E-1
2.644E-3
2.241E-3
0.817
0.609
50
-3.300E-7
7.601E-3
0.984
2.343E-3
0.845
1.354E-3
0.703
-2.371E-6
3.349E-3
0.988
-1.183E+0
N/A
N/A
50
2.412E-5
3.665E-3
0.965
4.082E-3
0.969
2.130E-3
0.975
1.600E-5
-1.970E-3
0.964
6.092E-2
3.174E-3
0.958
23
1.478E-5
-5.250E-4
0.999
2.270E-3
0.893
1.300E-3
0.931
4.200E-6
-7.400E-5
0.993
3.270E-4
1.981E-3
0.991
23
2.942E-5
6.150E-3
0.735
4.654E-3
0.691
2.388E-3
0.710
9.772E-6
3.243E-3
0.783
2.690E-1
3.070E-3
0.770
23% (338.6 kg/m3)
30
40
3.790E-6
1.412E-5
5.782E-3 -2.770E-4
0.989
0.962
2.387E-3
2.247E-3
0.976
0.880
1.367E-3
1.289E-3
0.924
0.922
8.860E-7
4.257E-6
1.638E-3 -3.000E-4
0.902
0.925
7.571E-1
5.308E-3
9.400E-4
1.781E-3
0.892
0.914
39% (384.3 kg/m3)
30
40
4.897E-5
3.889E-5
-1.083E-2 -3.913E-3
0.991
0.998
4.054E-3
4.207E-3
0.848
0.904
2.096E-3
2.724E-3
0.892
0.937
1.824E-5
1.903E-5
-3.860E-3 -3.470E-3
0.988
0.996
2.041E-1
1.582E-1
2.713E-3
2.987E-3
0.880
0.907
50
5.590E-6
4.401E-3
0.887
2.290E-3
0.865
1.316E-3
0.830
1.328E-6
1.230E-3
0.843
2.849E-1
1.151E-3
0.814
50
2.720E-6
1.391E-3
0.972
3.700E-3
0.842
1.722E-3
0.655
2.249E-6
4.774E-3
0.968
2.534E+0
1.499E-3
0.967
22
Table 1.3. Values for coefficients and r2 of the quadratic and linear regressions at 2450 MHz for kernels
MC (%), ρ (kg/m3)
Temp (°C)
ε' = A2ρ2+A1ρ+1
ε'1/2 = m1ρ+1
ε'1/3 = m3ρ+1
ε'' = B2ρ 2+B1ρ
(ε''+e)1/2 = m2ρ+e1/2
MC (%), ρ (kg/m3)
Temp (°C)
ε' = A2ρ2+A1ρ+1
ε'1/2 = m1ρ+1
ε'1/3 = m3ρ+1
ε'' = B2ρ 2+B1ρ
(ε''+e)1/2 = m2ρ+e1/2
A2
A1
r2
m1
r2
m3
r2
B2
B1
r2
e
m2
r2
23
8.384E-6
5.930E-4
0.949
1.939E-3
0.870
1.094E-3
0.899
3.220E-6
-4.960E-4
0.988
1.911E-2
1.403E-3
0.940
18% ( 628 kg/m3)
30
40
6.937E-6
6.663E-6
2.079E-3
2.129E-3
0.843
0.763
2.027E-3
1.991E-3
0.810
0.731
1.137E-3
1.118E-3
0.833
0.751
2.720E-6
3.051E-6
-2.990E-5 -5.570E-4
0.882
0.765
8.098E-5
2.540E-2
1.616E-3
1.264E-3
0.896
0.636
A2
A1
r2
m1
r2
m3
r2
B2
B1
r2
e
m2
r2
23
9.962E-6
3.966E-3
0.920
2.801E-3
0.915
1.470E-3
0.935
4.677E-6
1.840E-4
0.930
1.800E-3
2.144E-3
0.935
33%, (715.3 kg/m3)
30
40
1.312E-5 2.738E-6
2.713E-3 1.037E-2
0.969
0.956
3.019E-3 2.873E-3
0.967
0.938
1.569E-3 1.510E-3
0.973
0.869
5.228E-6 2.019E-6
9.100E-5 2.324E-3
0.943
0.941
3.940E-4 6.687E-1
2.290E-3 1.417E-3
0.933
0.948
50
8.640E-6
5.450E-4
0.899
1.964E-3
0.828
1.106E-3
0.858
4.272E-6
-1.550E-3
0.897
1.406E-1
9.930E-4
0.620
23
1.327E-5
-1.811E-3
0.996
2.227E-3
0.896
1.221E-3
0.936
5.201E-6
-1.475E-3
0.986
1.046E-1
1.412E-3
0.862
23% (654.6 kg/m3)
30
40
1.124E-5
1.491E-5
-2.115E-3 -3.948E-3
0.960
0.989
1.867E-3
2.049E-3
0.853
0.827
1.046E-3
1.132E-3
0.898
0.869
4.109E-6
5.765E-6
-1.519E-3 -2.631E-3
0.914
0.951
1.404E-1
3.001E-1
1.021E-3
9.310E-4
0.745
0.631
50
-6.565E-6
1.671E-2
0.989
2.653E-3
-0.036
1.416E-3
-0.711
-1.995E-6
4.980E-3
0.963
-3.107E+0
N/A
N/A
23
3.352E-5
-1.606E-2
0.935
2.430E-3
0.631
1.288E-3
0.681
1.251E-5
-6.555E-3
0.884
8.590E-1
1.108E-3
0.507
39% (751.3 kg/m3)
30
40
2.596E-6
1.139E-5
1.172E-2
1.118E-3
0.961
0.988
3.093E-3
2.568E-3
0.889
0.953
1.620E-3
1.368E-3
0.734
0.986
2.335E-6
4.265E-6
2.351E-3 -4.590E-4
0.974
0.968
5.920E-1
1.235E-2
1.527E-3
1.798E-3
0.970
0.952
50
1.293E-5
-2.236E-3
0.978
2.097E-3
0.875
1.158E-3
0.919
5.201E-6
-2.334E-3
0.966
2.618E-1
9.070E-4
0.644
50
1.139E-6
9.965E-3
0.981
2.615E-3
0.837
1.396E-3
0.628
1.666E-6
1.717E-3
0.944
4.423E-1
1.291E-3
0.938
Table 1.4. Values for coefficients and r2 of the quadratic and linear regressions at 2450 MHz for pods
MC (%), ρ (kg/m3)
Temp (°C)
ε' = A2ρ2+A1ρ+1
ε'1/2 = m1ρ+1
ε'1/3 = m3ρ+1
ε'' = B2ρ 2+B1ρ
(ε''+e)1/2 = m2ρ+e1/2
MC (%), ρ (kg/m3)
Temp (°C)
ε' = A2ρ2+A1ρ+1
ε'1/2 = m1ρ+1
ε'1/3 = m3ρ+1
ε'' = B2ρ 2+B1ρ
(ε''+e)1/2 = m2ρ+e1/2
A2
A1
r2
m1
r2
m3
r2
B2
B1
r2
e
m2
r2
23
1.502E-5
-2.119E-3
0.935
1.657E-3
0.725
9.980E-4
0.766
2.754E-6
-1.920E-4
0.997
3.357E-3
1.397E-3
0.974
18% (332 kg/m3)
30
40
1.540E-5
7.286E-6
-2.961E-3
1.743E-3
0.964
0.936
1.748E-3
1.857E-3
0.734
0.887
1.031E-3
1.092E-3
0.783
0.909
4.038E-6
3.689E-6
-1.003E-3 -1.054E-3
0.988
0.998
6.229E-2
7.523E-2
1.051E-3
8.390E-4
0.767
0.660
A2
A1
r2
m1
r2
m3
r2
B2
B1
r2
e
m2
r2
23
1.807E-5
3.571E-3
0.834
3.484E-3
0.847
1.856E-3
0.877
6.141E-6
1.025E-3
0.774
4.274E-2
2.451E-3
0.849
33% (366.6 kg/m3)
30
40
3.912E-5
3.268E-5
-7.182E-3
-4.511E-3
0.923
0.770
3.802E-3
3.603E-3
0.869
0.757
1.997E-3
1.908E-3
0.921
0.799
1.618E-5
1.560E-5
-4.037E-3
-4.532E-3
0.888
0.699
2.518E-1
3.293E-1
2.341E-3
2.003E-3
0.824
0.620
50
-6.100E-7
7.230E-3
0.985
2.223E-3
0.832
1.293E-3
0.687
-2.180E-7
1.487E-3
0.963
-2.534E+0
N/A
N/A
23
1.075E-5
1.503E-3
0.999
2.251E-3
0.951
1.293E-3
0.980
4.517E-6
-6.550E-4
0.997
2.376E-2
1.531E-3
0.925
23% (338.6 kg/m3)
30
40
1.386E-6
9.598E-6
6.894E-3
2.071E-3
0.986
0.957
2.350E-3
2.242E-3
0.912
0.932
1.349E-3
1.289E-3
0.807
0.955
1.245E-6
4.818E-6
1.114E-3 -1.178E-3
0.954
0.927
2.492E-1
7.202E-2
1.116E-3
1.158E-3
0.945
0.744
50
1.637E-5
6.545E-3
0.961
3.817E-3
0.968
2.015E-3
0.947
1.035E-5
-6.240E-4
0.960
9.407E-3
2.895E-3
0.970
23
2.687E-5
4.504E-3
0.736
4.237E-3
0.678
2.204E-3
0.461
1.115E-5
3.490E-4
0.765
2.738E-3
3.209E-3
0.709
39% (384.3 kg/m3)
30
40
4.086E-5
3.183E-5
-7.736E-3 -1.537E-3
0.996
0.995
3.816E-3
3.956E-3
0.760
0.817
1.996E-3
2.067E-3
0.807
0.858
1.579E-5
1.445E-5
-3.958E-3 -2.751E-3
0.992
0.999
2.480E-1
1.310E-1
2.254E-3
2.538E-3
0.823
0.869
50
2.271E-6
6.182E-3
0.873
2.295E-3
0.790
1.320E-3
0.679
2.196E-6
1.920E-4
0.899
4.179E-3
1.482E-3
0.864
50
3.000E-7
1.402E-2
0.992
3.486E-3
0.972
1.875E-3
0.898
2.051E-6
3.125E-3
0.976
1.190
1.432E-3
0.975
23
FIGURE CAPTIONS
Figure 1.1
Density dependence of peanut kernels dielectric properties at 18% mc and 30°C at 915 MHz.
a. Dielectric constant (ε'); b. Dielectric loss (ε'').
Figure 1.2
Density dependence of peanut pods dielectric properties at 23% mc and 30°C at 2450 MHz. a.
Dielectric constant (ε'); b. Dielectric loss (ε'')
Figure 1.3
Dielectric properties of peanut pods at several moisture contents as a function of frequency at
23°C. a. Dielectric constant (ε'); b. Dielectric loss (ε'')
Figure 1.4
Temperature and moisture dependence of dielectric properties of peanut kernels based on the
quadratic equations [1.12] and [1.15]. a. Dielectric constant (ε'); b. Dielectric loss (ε'').
Figure 1.5
Temperature and moisture dependence of dielectric properties of peanut pods based on the
linear equations [1.13] and [1.16]. a. Dielectric constant (ε'); b. Dielectric loss (ε'').
24
9
8
7
6
ε'
ε'^ 0.5
ε'^ 0.33
ε
5
4
3
2
1
0
0
200
a)
400
600
800
1000
Density (kg/m3)
2.5
2
1.5
ε
ε''
(ε''+e)^0.5
1
0.5
0
0
b)
200
400
600
800
1000
3
Density (kg/m )
Figure 1.1. Density dependence of peanut kernels dielectric properties at 18% mc and 30°C
at 915 MHz. a. Dielectric constant (ε'); b. Dielectric loss (ε'').
25
7
6
5
4
ε
ε'
ε'^ 0.5
ε'^ 0.33
3
2
1
0
0
100
200
300
400
500
600
700
Density (kg/m3)
a)
1.4
1.2
1
0.8
ε''
(ε''+e)^0.5
0.6
0.4
0.2
0
0
b)
100
200
300
400
500
600
700
Density (kg/m3)
Figure 1.2. Density dependence of peanut pods dielectric properties at 23% mc and 30°C at
2450 MHz. a. Dielectric constant (ε'); b. Dielectric loss (ε'')
26
12
10
33% mc
ε
8
39% mc
23% mc
6
18% mc
4
2
0
0
500
1000
a)
1500
2000
2500
3000
3500
Frequency (MHz)
4.5
4
3.5
3
33% mc
2.5
ε
39% mc
2
23% mc
1.5
18% mc
1
0.5
0
0
b)
500
1000
1500
2000
2500
3000
3500
Frequency (MHz)
Figure 1.3. Dielectric properties of peanut pods at several moisture contents as a function of
frequency at 23°C. a. Dielectric constant (ε'); b. Dielectric loss (ε'')
27
23°C - 915 MHz
30°C - 915 MHz
40°C - 915 MHz
50°C - 915 MHz
23°C - 2450MHz
30°C - 2450 MHz
40°C - 2450 MHz
50°C - 2450 MHz
13
11
9
ε
7
5
3
1
15%
20%
a)
25%
30%
35%
40%
Moisture content (% dry basis)
23°C - 915 MHz
30°C- 915 MHz
40°C - 915 MHz
50°C - 915 MHz
23°C - 2450 MHz
30°C - 2450 MHz
40°C - 2450 MHz
50°C - 2450 MHz
4
3.5
3
2.5
ε
2
1.5
1
0.5
0
15%
b)
20%
25%
30%
35%
40%
Moisture content (% dry basis)
Figure 1.4. Temperature and moisture dependence of dielectric properties of peanut kernels
based on the quadratic equations [1.12] and [1.15].
a. Dielectric constant (ε'); b. Dielectric loss (ε'').
28
23°C - 915 MHz
30°C - 915 MHz
40°C - 915 MHz
50°C - 915 MHz
23°C - 2450 MHz
30°C - 2450 MHz
40°C - 2450 MHz
50°C - 2450 MHz
9
8
7
ε
6
5
4
3
2
1
15%
20%
25%
30%
35%
40%
Moisture content (% dry basis)
a)
23°C - 915 MHz
30°C - 915 MHz
40°C - 915 MHz
50°C - 915 MHz
23°C - 2450 MHz
30°C - 2450 MHz
40°C - 2450 MHz
50°C - 2450 MHz
4
3.5
3
ε
2.5
2
1.5
1
0.5
0
15%
b)
20%
25%
30%
35%
40%
Moisture content (% dry basis)
Figure 1.5. Temperature and moisture dependence of dielectric properties of peanut pods
based on the linear equations [1.13] and [1.16].
a. Dielectric constant (ε'); b. Dielectric loss (ε'').
29
Manuscript 2. Thermal Profiles and Moisture Loss during Continuous Microwave
Drying of Peanuts
D. Boldor1, T.H. Sanders2*, K.R. Swartzel1, B.E. Farkas1, J. Simunovic1
1
Department of Food Science
North Carolina State University, Raleigh NC 27695-7624
2
USDA - ARS, Market Quality and Handling Research Unit
North Carolina State University, Raleigh, NC 27695-7624
*
Corresponding author:
Tel: 919-515-6213
Fax: 919-515-7124
E-mail: tim_sanders@ncsu.edu
30
ABSTRACT
The use of microwave energy in a planar applicator for continuous drying of farmer
stock (in-shell, uncured) peanuts (Arachis hypogaea L.) was investigated. Transport
phenomena equations previously developed for batch-type microwave drying were
successfully adapted to account for the spatial variation of the electric field inside the
applicator. The theoretical equations developed, together with experimental methods, were
used to determine the effect of microwave power level, initial moisture content and dielectric
properties on the temperature profiles and the reduction in moisture content of peanuts. The
temperature profiles obtained from solution of these equations matched the experimental
profiles determined using fiber optic temperature probes inserted into drying peanut pods.
The temperature profiles were determined to be dependent on both moisture content and
microwave power level. Although the maximum temperature in the microwave applicator
was a function of power level only, the rate at which that maximum was attained was a
function of dielectric properties and moisture contents of the peanuts. An absolute theoretical
determination of moisture content reduction during microwave drying was not possible due
to the dependence of dielectric properties on the moisture content. When dielectric properties
were assumed independent of moisture content, the theoretical estimations of moisture losses
were always lower than the losses determined experimentally, although they were in the
same range of values. The surface temperature distribution of the peanut bed measured using
infrared pyrometry was well correlated with internal temperature profiles. Thermal imaging
demonstrated that the temperature of the peanut bed surface at the exit of the microwave
curing chamber was uniformly distributed.
31
This study quantifies the relationships between the various parameters that influence the
continuous microwave drying process of peanuts. The results may be used as a foundation
for development of optimum process conditions in microwave drying of peanuts and other
agricultural commodities.
Keywords: Arachis hypogaea L., peanuts, drying, microwave, continuous, moisture loss,
temperature, distribution, thermal treatment
32
INTRODUCTION
Peanut drying reduces the moisture content of harvested peanuts to a level at which the
quality is maintained (Young et al.,1982). Curing, or drying, is generally performed in two
stages: field curing in inverted windrows to 20-25% moisture content and drying in wagons
or bins to about 10% moisture content (Baldwin et al., 1990). Field curing is a natural
process and the factors that affect it have been studied and described extensively by other
researchers (Young et al., 1982).
Wagon or bin drying is a process in which water is removed from farmer stock peanuts
(field dried peanuts at 20-25% mc) through moisture and temperature gradients created by air
flowing through the mass of peanuts. Moisture movement during air drying of thin-layer
peanut pods was studied and described by Whitaker and Young (1972a). Moisture flux is
determined by the thermal and physical properties of the peanuts and psychometric properties
of the air (Suter et al., 1975; Whitaker and Young, 1972b; Young et al., 1982). In practice,
drying is performed in deep beds, where air is forced upwards through the peanuts. A drying
zone is created in the lower portions of the bed and moves upward through the bed of peanuts
as the process evolves. Requirements for air flow in terms of volume, temperature and
relative humidity, in wagon drying, combined with the drying time (about 18-24 hours),
make drying in wagons an energy intensive process. A large number of studies have been
conducted to determine ways to increase the energy efficiency in air drying of peanuts
(Troeger, 1982; Blankenship and Chew, 1978; Rogers and Brusewitz, 1977; Chai and Young,
1995). Past studies have frequently focused on the use of high temperatures and on methods
of reducing the amount of running time for fans (Baker et al., 1993; Blankenship and Chew,
1979; Butts, 1996).
33
Little research has studied the use of alternative methods for energy input, such as
microwave or radio frequency energy. The microwave region of the electromagnetic
spectrum has long been used in a variety of industrial applications, ranging from
telecommunication to dielectric heating of foods and other materials. Due to the large
number of applications available, the FCC regulates the use of the frequency bands of the
electromagnetic spectrum, and the two microwave frequencies reserved for dielectric heating
in the United States are 915 and 2450 MHz. The mechanism of dielectric heating has been
thoroughly analyzed and described in many studies (von Hippel, 1954; Rosenthal, 1992;
Clark et al., 1997; Schiffmann, 1997).
The heating of a dielectric in the presence of an electromagnetic field is based on
intermolecular friction that arises via ionic conduction and dipolar rotation (White, 1973;
Schiffmann, 1997). Charged ions present in the dielectric material move according to the
direction of the electric field component of the electromagnetic wave. At the same time, polar
molecules try to align themselves in the position of minimum energy, parallel with the
electric field. The rapid oscillation of the electric field in the electromagnetic wave causes the
charged ions to move back and forth at high speed, and the polar molecules to rotate rapidly.
This molecular motion generates heat through friction with the surrounding molecules and
ions (Figures 2.1 and 2.2, Zhong, 2001).
The potential for ionic conduction and dipole rotation of materials is expressed by the
imaginary part of the relative complex permittivity (relative dielectric loss) (Nelson, 1973;
Boldor et al., 2003):
ε∗ = ε' – j ε''
[2.1]
34
The real part of the complex permittivity is represented by the dielectric constant (ε')
and represents the property that characterizes the ability of material to store and transmit
electromagnetic energy. The power dissipated in dielectric heating is proportional to the
frequency, dielectric properties and the electric field distribution according to formula
(Nelson, 1973; Metaxa and Meredith, 1983):
∆P = σ E2 = 2 π f ε0 ε'' E2
[2.2]
Microwave heating has been used in the past to reduce the moisture content of various
fruits and vegetables such as bananas (Maskan, 2000), apples, mushrooms and strawberries
(Funebo and Ohlsson, 1999; Funebo et al., 2000; Erle and Schubert, 2001), carrots
(Prabhanjan et al., 1995; Sanga et al., 2000), corn (Shivhare et al., 1991; Beke et al., 1995;
Beke et al., 1997), potatoes (Bouraoui et al., 1994; Sanga et al., 2000), and broad bean
(Ptasznik et al., 1990). Blanching of endive and spinach (Ponne et al., 1994), corn (Boyes et
al., 1997), and peanuts (Rausch, 2002) as well as studies performed to investigate the shelf
life and roast quality of microwave blanched peanuts (Katz, 2002) are other examples of
utilization of microwave energy in processing of foods and agricultural commodities. Most
of these studies were performed on static samples that were not characteristic of an industrial
environment typified by continuous processing. Except for Rausch (2002) and Katz (2002)
the research indicated above was based on modification of multimode cavity microwave
ovens used in the home. Modifications were performed to allow air flow and temperature and
mass measurement. An inherent problem in the use of multimode cavity ovens is nonuniform heating due to standing wave patterns created by the electric field (Rosenthal, 1992).
Another drawback is that the multimode cavity home oven frequency (2450 MHz)
yields a shorter wavelength than the 915 MHz frequency found in industrial applications.
35
The oscillating electric field for the 2450 MHz system results in less penetration
according to (Stuchly and Hamid, 1972; Metaxa and Meredith, 1983; Griffiths, 1999):
E = E0 e-α z;
[2.3]
Where:
 µ µ' ε' ε 0 
α = 2πf  0

2


0.5
2
 ε' ' 
1+   −1
 ε' 
[2.4]
Theoretical models for temperature and moisture distribution during microwave drying
of materials, including foods was studied in detail (Lu et al., 1999; Khraisheh et al., 1997;
Ramaswamy and Pillet-Will, 1992; Wei et al., 1985; Ni and Datta, 1999; Lyons et al., 1972).
Other empirical methods were developed to model moisture loss during microwave drying
(Khraisheh et al., 1995; Khraisheh et al., 2000). However, most of these models were also
developed for multimode batch-type processing applications and at the higher frequency of
2450 MHz.
Previous studies on continuous microwave processing in a TE10 (transverse electric)
mode traveling wave applicator concentrated on the effect of power level and the belt speed
on blanching, roast quality and storage stability of peanuts (Rausch, 2002; Katz, 2002). A
semi-continuous microwave dehydration process for apple and mushrooms was developed to
compare conventional and microwave assisted drying in a transverse magnetic mode
applicator (Funebo and Ohlsson, 1999).
The TE10 traveling mode applicators for drying are widely used in the wood and paper
industries (Metaxa and Meredith, 1983; Jones, 1975; Jones, 1986). In a TE10 waveguide at
the center of any transversal section perpendicular on the main axis the distribution of the
electric field is relatively uniform (Figure 2.3).
36
Dielectric material placed at the center of the waveguide, running parallel with the
electrical field, will be heated uniformly by the electric field.
The typical temperature profile in microwave drying of materials is shown in Figure 2.4
(Metaxa and Meredith, 1983; Lyons et al., 1972). Three distinct regions can be observed on
the temperature profile. The first one is the initial heat-up region, when the temperature
increases to the wet bulb temperature of the liquid that is being removed. The second one is
the constant temperature drying region, where most of the liquid is being vaporized within
the sample and removed through pressure gradients. The third region occurs after most of the
liquid has been removed and the temperature increases without any liquid being removed.
For all practical purposes, any microwave drying process should stop at the end of the
constant temperature drying region, unless there is a requirement to heat the material after is
dried.
This study focused on the temperature distribution and potential for moisture removal of
farmer stock peanuts (25 to 45% mc dry basis) in a continuous TE10 traveling wave
applicator using microwaves at 915 MHz.
37
Mathematical development
The fundamental theories of heat and mass transfer during conventional microwave
heating were adapted to the continuous process to account for the unique distribution of the
electric field along the waveguide. While in the conventional ovens the electric field creates a
standing pattern, in traveling wave applicators the electric field is constant in the transversal
section of the waveguide (Figure 2.3). Along the longitudinal axis of the waveguide, the
electric field decreases exponentially as a function of distance (Eqn. [2.3], Figure 2.5), and
the conversion between the time and distance coordinates is performed through the conveyor
belt speed according to:
∂z = vz ∂t
[2.5]
The attenuation constant in this case has to be adjusted for the presence of the dielectric
traveling on the conveyor belt in the center of the applicator according to the formula
(Metaxa and Meredith, 1983):
α = 17.37πε' '
w λg
dB/m
a λ' 02
[2.6]
At the working frequency of 915 MHz and for the waveguide dimension of 247.5 x
123.8 mm the attenuation constant becomes:
α = 894 w ε'' ; dB/m
[2.7]
The governing equation for the transport phenomena assuming negligible convective
and radiating losses during microwave drying is (Metaxa and Meredith, 1983; Lu et al.,
1999):
ε
∂M l ∆P
∂T
= α T∇ 2T + v L h
+
∂t
∂t
Cp
ρC p
[2.8]
38
The coupling between heat and mass transfer phenomena described by Eqn. [2.8] makes
analytical solution extremely difficult. However, we can use the unique properties of the
traveling wave applicators and a few assumptions to simplify the equation by dividing the
waveguide into the three regions. The third region, of heating up without drying is not
considered for this study and the microwave drying process is considered to stop at or toward
the end of the second region (Figure 2.4). The influence of the radiative and convective
losses is treated separately.
Region I. Initial heat-up
Assumptions:
-
In the initial heat-up region, the material heats without any significant moisture loss:
∂M l
=0
∂t
-
[2.9]
Microwave heating is volumetric; no temperature gradient within the sample:
∇T = 0
[2.10]
The partial differential Eqn. [2.8] is now a first order differential equation and after
changing the coordinates from time to distance (Eqn. [2.5]) becomes:
dT
∆P
=
dz v z ρC p
[2.11]
To determine the temperature profile of the material undergoing microwave processing
in a traveling wave applicator, knowledge of the power absorbed over a certain region of the
applicator is required. The absorbed power is dependent on the electric field distribution in
that respective region according to Eqn. [2.2]:
∆P = 2 π f ε0 ε'' E2rms (z)
[2.12]
39
Where:
Erms = E0rms e-α z
[2.13]
Total power input to the system is:
Pin= Awg I
[2.14]
I = c ε0 E0rms2
[2.15]
Where:
Substituting Eqn. [2.13], [2.14], and [2.15] into [2.12] the power loss at distance z is:
∆P =
2π f ε' ' Pin − 2α z
e
A wg c
[2.16]
After substitution and separation of variables in Eqn. [2.11]:
dT =
2π f ε' ' Pin − 2α z
e
dz
v zρC p A wg c
[2.17]
Assuming that the density ρ, specific heat Cp and dielectric loss ε'' do not change as a
function of temperature (Boldor et al., 2003; Metaxa and Meredith, 1983), Eqn. [2.17] can be
solved through integration:
Tz
z
2π f ε' ' P
− 2α z
∫T dT = vzρCp A wginc ∫0 e dz
0
[2.18]
After integration:
Tz = T0 +
π f ε' ' Pin
(1 − e − 2α z )
v zρC p A wg αc
[2.19]
In this region of the microwave applicator the temperature will depend mainly on the
input power level and the belt speed. The temperature follows a first order curve and will
increase at a rate depending on the value of the attenuation constant α.
40
Region II. Drying at constant temperature.
For the second region of the microwave drying process, the simplification of the Eqn. [2.8]
was made using the following assumptions:
-
Drying takes place at constant temperature:
∂T
=0
∂t
-
[2.20]
Microwave heating is volumetric therefore:
∇T = 0
-
[2.21]
All moisture that is being removed leaves the system in vapor form:
εv = 1;
Ml = M
[2.22]
Equation 8 then becomes:
dM
∆P
=−
dz
v z ρL h
[2.23]
Substitution of the power dissipated over the region (Eqn. [2.16]) and separation of
variables yields:
dM = −
2π f ε' ' Pin − 2α z
e
dz
v zρL h A wg c
[2.24]
Equation [2.24] can be solved in two different ways. The first one assumes that the
dielectric loss ε'' and density ρ are independent of the moisture content M, and the solution is
found through simple integration:
M
∫ dM = −
M0
z
2π f ε' ' Pin
e − 2α z dz
∫
v zρL h A wg c z1
[2.25]
After integration:
41
Mz = M0 −
π f ε' ' Pin
(e − 2α z1 − e − 2α z )
v zρL h A wg cα
[2.26]
Equation [2.26] can be used to obtain an approximation of the moisture distribution
during drying, but most of the time the dielectric loss ε'' is a linear function of the moisture
content (Boldor et al., 2003; Metaxa and Meredith, 1983):
ε'' = ε0'' + k1 M
[2.27]
In this case, assuming that the density ρ and the attenuation constant α do not change
significantly with the moisture content, Eqn. [2.24] becomes:
2π f Pin
1
dM = −
e − 2α z dz
ε' '
v z ρL h A wg c
[2.28]
Integrating over a constant distance (z2 - z1):
Mf
∫
Mi
z
2π f Pin 2 − 2α z
1
dM = −
e
dz
ε 0 ' '+ k 1 M
v z ρL h A wg c z∫1
[2.29]
After integration (Metaxa and Meredith, 1983):
ln (k 1 M + ε 0 ' ') M f =
M
i
k 1 π f Pin
(e −2α z 2 − e −2α z1 ) = k 2 = constant
v z ρL h A wg αc
[2.30]
And:
k 1M f + ε 0 ' '
= k3
k 1M i + ε 0 ' '
[2.31]
Equation [2.31] provides information on the moisture leveling effect of the microwave
drying. Assuming that at a certain power level and belt speed the moisture content of a
material is reduced from 25% to 15%. Assume a dielectric constant varying with the
moisture content according to:
ε'' = 0.2 + 8 M
[2.32]
42
To find the final moisture content for a 20% initial moisture content, in Eqn. [2.31]:
8x + 0.2
8 * 0.15 + 0.2
= k3 =
8 * 0.2 + 0.2
8 * 0.25 + 0.2
[2.33]
The final moisture content will be:
x = 0.118 = 11.8 %
[2.34]
For a difference in initial moisture contents of 5%, the difference in final moisture
contents is only 3.2%. In reality, most of the time the higher moisture content material will
also have higher dielectric loss, which will determine a higher attenuation constant (Eqn.
[2.7]). The higher attenuation constant will determine a faster arrival at the constant drying
temperature (Eqn. [2.19]), and therefore a longer time in the applicator, further reducing the
differences between the two final moisture contents.
43
MATERIALS AND METHODS
Field dried peanuts (Runner and Virginia type) at moisture contents ranging from 25 to
45% were used in this study. Samples were shipped from USDA-ARS Peanut National
Laboratory in Dawson, Georgia to the Department of Food Science at North Carolina State
University during the months of September - November of 2002.
The microwave curing chamber (Industrial Microwave Systems, Morrisville, NC) was a
traveling wave applicator composed of a conveyor belt running at the geometrical center
along the axis of an aluminum waveguide (vz = 8.4 mm/s). The microwaves were generated
by a 5 kW microwave generator (Industrial Microwave Systems, Morrisville, NC) and
transported to the curing chamber through aluminum waveguides (Figure 2.6). The curing
chamber was outfitted with an electric fan and an electric heater to assist the microwave
drying process. The heater was set to maintain an ambient temperature of 25°C in the
chamber. The microwave generator was controlled through a data acquisition and control
unit (HP34970A, Agilent, Palo Alto, CA) and a software routine written in LabView
(National Instruments Corp., Austin, TX). The data acquisition unit and the software
monitored and recorded the power output, reflected power and power at the exit of the
microwave curing chamber through power diodes (JWF 50D-030+, JFW Industries, Inc.,
Indianapolis, IN).
All temperature measurements during microwave curing were performed using fiber
optic probes and remote infrared temperature measurement (Mullin and Bows, 1993;
Goedeken et al., 1991).
44
The fiber optic probes (FOT-L/ 10M, Fiso Technologies, Inc., Quebec, Canada) were
connected to a multi-channel fiber-optic signal conditioner (Model UMI 4, Fiso
Technologies, Quebec, Canada) remotely controlled by FISOCommander software (FISO
Technologies, Quebec, Canada) installed on a laptop computer (Dell Inspiron 8500, Dell
Computer Corp., Round Rock, TX). The surface temperature of the peanut bed (3 cm thick)
was monitored with infrared thermocouples (model OS36-T, OMEGA Engineering, Inc.,
Stamford, CN) placed at various distances along the waveguide as shown in Table 2.1 and
Figure 2.7. The surface temperatures were monitored and recorded using the same software
routine that was used to control the generator and to record the power levels.
A Thermovision Alert N infrared camera (FLIR Systems AB, Danderyd, Sweden) was
placed at the exit of the microwave curing chamber to monitor the spatial distribution of the
peanut bed surface temperature. The camera was controlled by Thermovision Remote
software (FLIR Systems AB, Danderyd, Sweden) installed on a laptop computer (Samsung
SensPro 520, Samsung, Ridgefield Park, NJ).
Data collection was started simultaneously for all three systems (fiber optic probes,
infrared thermocouples and infrared camera) in order to match the temperature measured
with the fiber optic probes with the surface temperatures of the peanut bed as measured by
the infrared thermocouples and the infrared camera.
Data was collected based on two experimental designs. The first re-used the same
samples (both Runner and Virginia type peanuts) in three consecutive passes at two power
levels (1.2 and 2 kW) to simulate a three stage microwave curing chamber.
45
For one sample of Runner type peanuts with an initial moisture content of 29%, the
fiber optic probes were mounted such that both the internal temperature of the seed and the
temperature at the pod surface were monitored while in the microwave curing chamber. For
the other samples, one Runner type (25% initial mc) and one Virginia type (46% initial mc),
only the internal seed temperatures were monitored with fiber optic probes in the microwave
curing chamber.
The second experimental design used Runner type peanuts to study the effect of six
power levels (0.3, 0.6, 0.9, 1.2, 1.5, and 2 kW) and four initial moisture contents (33, 20, 14,
and 11%) on seed temperatures, heating rates and moisture content. The initial moisture
contents were obtained through conventional drying on air blowers.
The power levels denoted in this paper were set points on the control panel of the
software routine. Due to the non-linearity of the data acquisition and control unit, the
nominal power levels (or the power output) of the generator were always smaller than the set
points. The reflected power was caused by the change of impedance of the waveguide where
the microwaves entered the planar applicator as shown in Figure 2.8 (Stuchly and Hamid,
1972; Griffiths, 1999). Although the impedance mismatch was minimized through the special
design of the waveguide connector, the reflected power was considered lost and was not
considered for calculations.
The internal temperature measurements were performed on 8 to 12 peanut pods in
two replicates. The fiber optic probes were placed in pods in previously drilled holes and
spread to cover the whole width of the conveyor belt (Figure 2.9).
46
For each set of data the temperature profiles along the waveguides were determined by
averaging all the measurements from the two replicates for the fiber optic probes
measurements (internal temperatures) and the infrared thermocouple measurements (surface
temperatures). Bulk moisture content of the samples and single seed moisture contents of the
peanuts that had mounted fiber optic probes on them were determined using the ASAE
standard (ASAE, 2000).
All temperature and moisture content data, with the exception of the infrared images,
was processed using Microsoft Excel 97 (Microsoft Corp, Redmond, WA). The data on the
spatial distribution of temperatures in the temperature images acquired with the infrared
camera was processed with the Thermacam Researcher software package (FLIR Systems
AB, Danderyd, Sweden). The analytical solutions to Eqn. [2.17] and [2.26] were
implemented using Microsoft Excel 97.
47
RESULTS AND DISCUSSION
Simulated results
The temperature profiles obtained from equation [2.19] at 6 different power levels, with
the parameters estimated for peanuts at 22% moisture content (Table 2.2) are shown in
Figure 2.10. The dielectric loss and bulk density were estimated based on measurements at
different moisture contents and temperatures (Boldor et al., 2003). The solutions to equations
[2.17] and [2.24] do not account for the losses that occur due to convection and radiation,
which can be expressed as (Metaxa and Meredith, 1983; Roussy and Pearce, 1995):
qconv = h A (T – Tinf)
[2.35]
qrad= σT εi A (T4 - T04)
[2.36]
An estimation of these loses at a power level of 2 kW with the parameters given in
Table 2.3 is shown in Figure 2.11. These two types of losses manifest themselves throughout
the microwave drying process. A third type of energy loss occurs during the drying stage of
the process (region II) through evaporative cooling. When all these energy losses are
accounted for, the temperature profiles presented in Figure 2.10 would change; in the first
region the temperature would reach the equilibrium faster and below the plateau resulting
from equation [2.19] and on the second region the temperature would decrease due to cooling
effects.
Moisture losses estimated from Eqn. [2.26] are shown in Figure 2.12, based on the
parameters represented in Table 2.4. Equation [2.24] assumes that all moisture is lost in
vapor form, thus losses due to filtrational flow are not considered (Metaxa and Meredith,
1983; Roussy and Pearce, 1995). Therefore, moisture loss estimated by Eqn. [2.26] is likely
higher than reported.
48
Experimental results
An example of temperature distribution as measured with fiber optic probes for 21% mc
Runner type peanuts exposed to microwave power at 1.2 kW is shown in Figure 2.13. The
temperature profiles are fairly close with the exception of probe one, which had a higher
temperature profile than the others. This behavior was consistent with the location the peanut
pods on the right-most side of the conveyor belt throughout all the experimental runs (rightedge effect). These peanuts were very close to the waveguide right wall. The parameter with
the most influence on the maximum temperature was the magnitude of the electric field (Eqn.
[2.19]). The high temperatures recorded for peanuts on the right-most side of the conveyor
belt may be explained through abnormally high electric fields along the right wall of the
waveguide.
Theoretically, a rectangular waveguide creates a uniform electric field in any crosssectional area perpendicular on the direction of propagation or the main axis of the
waveguide (Figure 2.3). But the existing microwave curing chamber was equipped with side
panels on the right side (Figure 2.14) covering openings in the waveguide that are used for
cleaning purposes. These openings form a discontinuity on the inside of the waveguide wall,
thus generating multiple reflections of the electromagnetic waves. This leads to significant
increases in the electric field values along the right wall. This increase in electric field value
leads to higher temperatures as determined by Eqn. [2.19].
49
Experimental design 1.
The internal temperature profiles in the microwave curing chambers for the consecutive
passes of Virginia and Runner type peanuts at power levels of 1.2 and 2 kW are shown in
Figures 2.15 to 2.18. There was not a significant difference in the temperature profiles
between the three consecutive passes (different moisture contents) at the same power level.
This behavior is consistent with the Eqn. [2.19] which states that the equilibrium temperature
is dependent only on the belt speed, power level, and the dielectric loss of the material. With
the assumption that the dielectric loss of the material does not change significantly with
temperature, the contribution of the attenuating factor α to the magnitude of the temperature
change in Eqn. [2.19] can be considered constant.
While the temperature profiles of the ideal system level off (Figure 2.10), the measured
temperatures start decreasing as the peanuts continue their journey in the waveguide. This
temperature reduction was caused by radiative, evaporative and convection cooling, not
accounted for in the ideal system. Radiative cooling is caused by energy loss to the
environment through radiation (Eqn. [2.36]). Convective cooling is caused by the air flow
through the peanut bed that carries away the removed moisture (Eqn. [2.35]), while
evaporative cooling is an event inherent to all processes in which evaporation takes place.
Radiative and convective cooling increase as the temperature increases, therefore peanuts
that heat more also cool faster. Since more water is being evaporated at the higher power
(Eqn. [2.26]) the evaporative cooling will also increase at the higher power level.
Figures 2.19 and 2.20 show the internal and external temperature distributions of the
same pods of the Runner type peanuts. While the internal temperatures follow the same
profiles discussed above, the surface temperatures behave differently.
50
The initial heat-up region and the constant temperature drying region are present for the
surface of the pods. However, the surface temperature is much lower than the internal
temperatures, and it enters the second region much faster. This behavior is mainly caused by
the different dielectric properties of the shells and the fact that the convective cooling has a
faster effect on the surface of the pods.
Another major difference between the internal and surface temperatures as measured
with the fiber optic probes is that on the surface, after the constant temperature drying region,
the temperatures start increasing before settling to a new equilibrium value. There are two
possible explanations for this effect. The first one is that all the free water from the shells was
removed, and the shells will continue absorbing heat and experience an increase in
temperature (entering region III). At the second position of temperature equilibrium water
that was more tightly bound will start being vaporized, and the surface experiences a second
constant temperature drying region. A second and more plausible explanation is that in this
region of the microwave curing chamber the surface temperatures of the pods starts to
increase through conduction and radiation from the surrounding peanuts. While the infrared
sensors measure the surface temperature of the whole peanut bed, the fiber optic probes were
placed in the middle of the bed, where they were more affected by the heat coming from the
surrounding peanut pods. This behavior of the temperature profiles at the pod surface in the
middle of the peanut bed is very intriguing and deserves further investigation.
The reduction in moisture content for each of the three passes is more significant at
higher moisture content and at the higher power level (Table 2.5 and 2.6). Virginia type
peanuts (initially at 45.2% mc) exposed to a microwave energy at 1.2 kW experienced a total
reduction in moisture content of 26.5%, or an average of 8.8% reduction per pass.
51
The same peanuts exposed to microwave energy at 2 kW experienced a reduction of
32.9%, or an average of 11% reduction per pass (Table 2.5). Runner type peanuts with an
initial moisture content of 25% experienced a total reduction in moisture content of 32.3% at
1.2 kW, or an average of 10.8% per pass. At a power level of 2 kW, the moisture content was
reduced by a total of 39%, or an average of 13% per pass (Table 2.6).
Examples of spatial surface temperature distributions at the exit of the microwave
drying chamber, as determined with the infrared camera are shown in Figures 2.21 and 2.22.
The average temperature values and their standard deviations in the regions delineated by the
rectangles in each image are shown in Table 2.7. For both Virginia and Runners type peanuts
the surface temperature increased with increasing power level at the same moisture content.
The differences registered between the Virginia type peanuts and the Runner type peanuts are
mainly caused by the differences in moisture contents between the two varieties used in this
study (45% initial mc for Virginia, and 25% initial mc for Runner type).
Experimental design 2.
The temperature profiles of peanuts during microwave drying at the same initial
moisture contents and six power levels are shown in Figures 2.23 to 2.26. In this
experimental design the temperature profiles approximate the profiles obtained in Figure 2.10
from Eqn. [2.19]. At the same moisture content, assuming a constant belt speed and dielectric
constant, the temperature profile was determined solely by the power level. Radiative,
evaporative and convective cooling was also observed in this experimental design, having a
larger influence on the temperature profiles at the higher power levels.
52
At the higher power levels, the higher temperatures cause larger convective and
radiative cooling (Eqn. [2.35] and [2.36]), as well as more evaporative cooling.
The standard deviations of the measurements are plotted in Figures 2.27 to 2.30. In
general a higher power level also corresponds to a larger standard deviation, which was
expected considering the higher overall temperatures and the right-edge effect previously
discussed.
A plot of internal temperature versus the surface temperatures at the six power levels
tested in specific location along the microwave curing chamber for 11% mc peanuts is shown
in Figure 2.31. The linear relationships between the internal and surface temperatures (Tables
2.8 to 2.11) have extremely good correlations (r2 > 0.95) and are useful for process control
purposes. This linear correlation is much better at the lower moisture contents (r2 > 0.99),
while at the higher moisture contents, the linear regressions are better for sensors that are
placed closer to the peanut feed input. A temperature feedback control mechanism
implemented using these linear relationships could be very efficient in adjusting the power
level to maintain a desired temperature profile inside the microwave curing chamber.
Plots of the first derivative of temperature versus distance (Figures 2.32 to 2.35) show
that the maximum temperature (derivative is zero) is at the same location for the same
moisture content, independent of the power level. The same observation is true for the
maximum of the derivative (the maximum rate of temperature increase). These locations of
the maximum temperature and of the maximum rate of temperature increase are important
for process control purposes. Placement of surface temperature sensors at these locations
would maximize the efficiency a feedback control system.
53
Using the relationships in Tables 2.8 to 2.11, the control system can adjust the power
input to maintain a constant maximum temperature and rate of temperature increase.
The moisture loss at the 6 power levels for different initial moisture contents is
presented in Table 2.12. In general, the higher power levels removed more moisture than the
lower power levels, which is consistent with the analytical solution (Eqn. [2.26]) to Eqn.
[2.24] for the second region of the microwave drying process.
Plots of the temperature profiles at the same power level and the four different initial
moisture contents tested are shown in Figures 2.36 to 2.41. The variability in temperature
profiles in general decreased with the moisture content (Figures 2.42 to 2.47). The maximum
temperatures are the same at all moisture contents and confirm the fact that they depend only
on the power level and the belt speed (Eqn. [2.19]). However, there are two major differences
between the temperature profiles at the same power level, the first one in region I (initial
heat-up region) and the second one in region II (constant temperature drying region).
For the constant temperature drying region, the energy loss caused by radiative,
convective and evaporative cooling is larger for the higher moisture contents at the same
power level. With the assumption that the radiant emissivity of the peanuts is relatively
constant at all moisture contents, radiative cooling can be ruled out as a major factor
influencing the temperature decrease. With the volumetric heating of the microwaves, the
convective cooling at the surface of the peanuts depends only on the temperature and the
surface area exposed to the air flow, which are both constants. These imply that the main
driving force in the cooling process at the same power level is evaporative cooling. The
higher the moisture content, the more water is being evaporated and the larger the cooling
effect.
54
In the initial heat-up region, plots of the first derivative of temperatures with respect to
distance (Figures 2.48 to 2.53) show that the location of the maximum temperatures (where
the derivative is zero) changes with the moisture content. As the moisture content decreases,
the location of the maximum temperature moves further from the entrance to the microwave
drying chamber. Even though the maximum temperature is the same for the different
moisture contents, the time (or distance in the waveguide) to get to that maximum
temperature is longer as the moisture content decreases. The same observation is true for the
location of the maximum rate of temperature increase (where the derivative is at its peak).
This behavior is again consistent with Eqn. [2.19], where the attenuation factor α is
dependent on the dielectric loss ε'', which is mainly dependent on moisture content. The
higher the moisture content, the higher the attenuation factor (Eqn. [2.7]) and the faster the
temperature increase.
This particularity of the heat-up region of the peanut microwave drying process can be
used in designing a feed-forward control mechanism for the peanut curing process. An
infrared camera is employed to measure the surface temperature distribution in the heat-up
region. The location of the maximum temperature and the location of the maximum rate of
temperature change are determined and the moisture content of the peanuts at the exit of the
microwave curing chamber can be estimated. This would determine the number of passes
required to obtain the desired final moisture content.
This feed forward mechanism can be associated with the feedback control system
previously described and with other sensors that monitor other process variables (moisture,
ambient temperature, air humidity etc.) to implement a very effective feed forward/feedback
control system that would account for all the variables in the process.
55
The distribution of the surface temperatures at the exit of the microwave curing
chamber for all moisture contents and power levels used in this experimental design is shown
in Figures 2.54 to 2.57. The average temperature values, with their respective standard
deviations, of the regions delineated by rectangles are listed in Table 2.13. The average
temperature values and their standard deviations increased with increasing power level. The
average temperature values and their standard deviations also increased with a decrease in
moisture content. This effect was more visible at the higher power levels than at the lower
power levels. This means that the drier the peanuts are, the hotter their surface becomes at the
exit of the microwave applicator. While the surface temperatures at the beginning of the
process increase proportionally with the moisture content, toward the end of the process the
proportionality is reversed. A similar effect was observed on both the heat flux and the
convective heat transfer coefficient during immersion frying in oil (Hubbard and Farkas,
2000). While at the beginning of the frying process both the heat flux and the convective heat
transfer coefficients were proportional with the oil temperature, toward the end of the process
the proportionality was reversed. Hubbard and Farkas (2000) explained this behavior through
the different rates of drying that occur at the different oil temperatures and the total amount
of water available for drying. Since the rate of drying in microwave is also different for the
different initial moisture contents, there will be less moisture toward the end of the
microwave drying process that will be converted into heat at the lower initial moisture
contents. The lower the initial moisture content, the smaller the rate of drying and more
moisture will be available toward the end of the process.
56
CONCLUSIONS
The internal and surface temperature distribution was determined for farmer stock
peanuts undergoing drying in a traveling wave microwave applicator. The transport
phenomena equations developed for microwave assisted drying in multimode cavities were
successfully adapted to estimate the temperature profiles and moisture losses during
continuous microwave drying.
The experimental results confirmed the theoretical predictions that the temperature
profiles were determined only by the power level at the same moisture content and only by
the moisture content at the same power level. At the same moisture contents, the maximum
temperatures and maximum rates of temperature increase occurred in the same time at the
same location in the microwave applicator at all power levels tested. The negligible effect of
temperature on the dielectric properties of the farmer stock peanuts confirmed previously
performed measurements (Boldor et al., 2003). At the same power levels, the maximum
temperatures were the same for all moisture contents tested, but the rate at which that
maximum was reached increased with the increasing moisture contents. This result shows the
dependence of the dielectric loss and the attenuation constant α on the moisture content of
the peanuts, an effect that was also previously observed (Boldor et al., 2003).
A very good correlation was determined between the surface temperatures measured
using infrared technology and the internal temperatures measured using fiber optic probes.
These encouraging results open up the possibility of accurate control of the internal
temperatures through a feedback mechanism that uses the surface temperature as the
measured variable and the power level as the control variable.
57
A combination of computer assisted infrared imaging and feedback control mechanisms
can use the results of this study to determine not only the maximum temperature, but also its
location and the location of the maximum rate of temperature increase. Using the equations
presented in this paper, a more advanced feed forward/feedback control system can be
developed that will more accurately control the microwave peanut drying process.
The measured moisture losses during microwave drying were also in line with
theoretical estimations. The leveling effect of microwaves on moisture content was also
confirmed through measurements, and the total moisture reduction in consecutive passes at
the same power level was determined.
58
LIST OF SYMBOLS
a,b - waveguide height and width; m
Awg - cross sectional area of the waveguide; m2
A - surface area of a peanut pod; m2
c - speed of light; 3x108 m/s
Cp - specific heat; J/kg K
E, E0, Erms, E0rms – electric field (general, initial, r.m.s., initial r.m.s.); V/m
f – frequency; Hz
h - convective heat transfer coefficient; W/m2K
I - intensity of the electromagnetic field; W/m2
j – (-1)1/2 – imaginary part of a complex number
Lh - latent heat of vaporization; J/kg
mc – moisture content dry basis; %
M, Ml, M0 - moisture content (general, liquid, initial); % db
Pin - power input into the system; W
∆P – power absorbed per unit volume; W/m3
qconv, qrad - heat losses (convective, radiative); W
t - time; s
T, T0, Tinf – temperature (general, initial, environment); K, °C
z - distance coordinate; m
vz - belt speed; m/s
w - height of dielectric material on belt; m
α – attenuation constant; m-1, dB/m
αT - thermal diffusivity; m2/s
ε0 – dielectric constant of the vacuum = 8.854 10-12 Far/m
ε∗ – relative complex permittivity or relative complex dielectric constant; ε' - relative electric constant or storage factor; ε'', ε0'' - relative dielectric loss or loss factor (general, initial); εi - radiant emissivity; εv - ratio of vapor flow to total moisture flow; λ0, λg - wavelength (free space, waveguide); m
µo, µ' - magnetic permeability (free space, relative); N/A2
ρ - bulk density; kg/m3
σ – conductivity; siemen/m
σT - Stefan - Boltzmann's constant; W/m2K4
ω – angular frequency;
59
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63
Table 2.1. Locations of the infrared thermocouples.
Waveguide entrance
Sensor 1
Sensor 2
Sensor 3
Sensor 4
Sensor 5
Sensor 6
Sensor 7
Sensor 8
Sensor 9
Sensor 10
Sensor 11
Sensor 12
Sensor 13
Sensor 14
Sensor 15
Sensor 16
Waveguide exit
End
Distance to sensor
(inch)
(m)
0
0
18.75
0.476
21.75
0.552
38.75
0.984
41.75
1.060
44.75
1.137
65.75
1.670
68.75
1.746
71.75
1.822
83.75
2.127
86.75
2.203
89.75
2.279
98.75
2.508
101.75
2.584
104.75
2.661
113.75
2.889
116.75
2.965
129
3.277
164.25
4.172
64
Table 2.2. Parameters for temperature profiles in Eqn. [2.19] and Figure 2.10.
T0
α
vz
f
ε''
ρ
Cp
Awg
c
293
1
0.0085
915
0.7
400
2800
0.0268
3.0E+08
K
1/m
m/s
MHz
Kg/m3
J/Kg K
m2
m/s
Table 2.3. Parameters for convective and radiative losses in Eqns. [2.35], [2.36] and Figure
2.11.
h
As
T0
σT
εi
20
0.0015
293
5.67E-08
0.95
W/m2K
m2
K
W/m2K4
Table 2.4. Parameters for moisture losses in Eqn. [2.26] and Figure 2.12.
α
vz
f
ε''
ρ
Awg
c
M0
Lh
Start point
1
0.0085
915
0.7
400
0.026784
3.0E+08
0.22
2100000
1
m-1
m/s
MHz
Kg/m3
m2
m/s
J/Kg
m
65
Table 2.5. Moisture contents (% db) for Virginia type peanuts in three consecutive passes.
Pass 1
Power
level
1.2 kW
2 kW
Before
45.2
47.4
After
42.4
42.9
Pass 2
%
Reduction
6.2
9.5
Before
41.6
46.5
After
38
39.4
Pass 3
%
Reduction
8.6
15.3
Before
37.2
39.2
After
33.2
31.8
%
Reduction
10.8
18.9
Table 2.6. Moisture contents (% db) for Runner type peanuts in three consecutive passes.
Pass 1
Power
level
1.2 kW
2 kW
Before
25.7
24.6
After
22.5
21.5
Pass 2
%
Reduction
12.5
12.6
Before
22.8
20.3
After
20.3
19.1
Pass 3
%
Reduction
11.0
5.9
Before
19.7
16.9
After
17.4
15
%
Reduction
11.7
11.2
Table 2.7. Surface temperature distribution for Virginia and Runners type peanuts at the exit
from the drying tunnel at 2 power levels and three initial moisture contents.
Virginia
Power level
1.2 kW
2 kW
Runners
Initial mc (% db)
Temp (°C)
Std (°C)
45.2
29.8
1.9
41.6
28.2
2.2
37.2
29.8
2.7
25.7
32.2
2.4
22.8
34.3
2.6
19.7
33.2
2.1
Initial mc (% db)
Temp (°C)
Std (°C)
47.4
32.6
3.1
46.5
33
3.2
39.2
34.6
3.2
24.6
39.9
4.2
20.3
38.5
4.1
16.9
39.7
3.7
66
Table 2.8. Relationship between surface and internal temperatures for 11% mc Runner type
peanuts.
Waveguide entrance:
Sensor 1
Sensor 2
Sensor 3
Sensor 4
Sensor 5
Sensor 6
Sensor 7
Sensor 8
Sensor 9
Sensor 10
Sensor 11
Sensor 12
Sensor 13
Sensor 14
Sensor 15
Sensor 16
Location
(m)
0
0.476
0.552
0.984
1.060
1.136
1.670
1.746
1.822
2.127
2.203
2.279
2.508
2.584
2.660
2.889
2.965
Equation
r2
y = 1.35x - 4.67
y = 1.39x - 6.18
y = 1.73x - 13.78
y = 1.78x - 14.22
y = 1.76x - 15.25
y = 1.83x - 17.29
y = 1.80x - 17.10
y = 1.85x - 18.21
y = 1.76x - 15.69
y = 1.60x - 11.96
y = 1.70x - 13.81
y = 1.58x - 10.81
y = 1.62x - 10.77
y = 1.67x - 11.82
y = 1.61x - 10.47
y = 1.53x - 8.17
0.998
0.999
0.999
0.999
0.999
0.999
0.999
0.999
0.999
0.998
0.999
0.997
0.997
0.997
0.995
0.994
Table 2.9. Relationship between surface and internal temperatures for 14% mc Runner type
peanuts.
Waveguide entrance:
Sensor 1
Sensor 2
Sensor 3
Sensor 4
Sensor 5
Sensor 6
Sensor 7
Sensor 8
Sensor 9
Sensor 10
Sensor 11
Sensor 12
Sensor 13
Sensor 14
Sensor 15
Sensor 16
Location
(m)
0
0.476
0.552
0.984
1.060
1.136
1.670
1.746
1.822
2.127
2.203
2.279
2.508
2.584
2.660
2.889
2.965
Equation
r2
y = 1.35x - 2.61
y = 1.39x - 4.01
y = 1.81x - 13.59
y = 1.81x - 13.9
y = 1.80x - 14.02
y = 1.99x - 19.51
y = 1.95x - 19.15
y = 1.99x - 19.76
y = 1.96x - 19.21
y = 1.78x - 14.91
y = 1.84x - 15.66
y = 1.75x - 13.53
y = 1.77x - 13.17
y = 1.83x - 14.46
y = 1.82x - 14.41
y = 1.70x - 11.3
0.995
0.996
0.996
0.997
0.994
0.997
0.997
0.994
0.997
0.996
0.993
0.994
0.995
0.990
0.991
0.993
67
Table 2.10. Relationship between surface and internal temperatures for 21% mc Runner type
peanuts.
Waveguide entrance:
Sensor 1
Sensor 2
Sensor 3
Sensor 4
Sensor 5
Sensor 6
Sensor 7
Sensor 8
Sensor 9
Sensor 10
Sensor 11
Sensor 12
Sensor 13
Sensor 14
Sensor 15
Sensor 16
Location
(m)
0
0.476
0.552
0.984
1.060
1.136
1.670
1.746
1.822
2.127
2.203
2.279
2.508
2.584
2.660
2.889
2.965
Equation
r2
y = 1.44x - 5.81
y = 1.49x - 7.28
y = 1.77x - 13.76
y = 1.80x - 14.70
y = 1.84x - 16.26
y = 1.93x - 18.73
y = 1.91x - 18.76
y = 2.01x - 20.94
y = 1.85x - 16.93
y = 1.75x - 14.64
y = 1.81x - 15.55
y = 1.69x - 12.83
y = 1.76x - 13.64
y = 1.82x - 15.43
y = 1.82x - 15.69
y = 1.74x - 13.23
0.981
0.984
0.988
0.988
0.989
0.988
0.989
0.989
0.989
0.990
0.991
0.988
0.990
0.991
0.991
0.992
Table 2.11. Relationship between surface and internal temperatures for 33% mc Runner type
peanuts.
Waveguide entrance:
Sensor 1
Sensor 2
Sensor 3
Sensor 4
Sensor 5
Sensor 6
Sensor 7
Sensor 8
Sensor 9
Sensor 10
Sensor 11
Sensor 12
Sensor 13
Sensor 14
Sensor 15
Sensor 16
Location
(m)
0
0.476
0.552
0.984
1.060
1.136
1.670
1.746
1.822
2.127
2.203
2.279
2.508
2.584
2.660
2.889
2.965
Equation
r2
y = 1.77x - 12.38
y = 1.81x - 13.52
y = 2.01x - 17.44
y = 2.02x - 17.60
y = 2.02x - 18.09
y = 2.13x - 21.11
y = 2.09x - 20.74
y = 2.15x - 22.02
y = 2.02x - 18.89
y = 1.88x - 15.38
y = 1.94x - 16.41
y = 1.77x - 12.60
y = 1.87x - 14.31
y = 1.90x - 15.32
y = 1.82x - 13.45
y = 1.69x - 9.59
0.993
0.990
0.972
0.971
0.967
0.959
0.958
0.956
0.949
0.953
0.950
0.947
0.941
0.940
0.933
0.933
68
Table 2.12. Moisture losses at 6 power levels.
Power level (kW)
0.3
0.6
0.9
1.2
1.5
2
Before (%)
After (%)
% reduction
33.02
30.66
7.1
33.07
30.46
7.9
34.30
30.30
11.7
33.04
30.15
8.7
32.86
30.04
8.6
32.10
26.96
16
Before (%)
After (%)
% reduction
20.79
20.21
2.8
20.56
19.57
4.8
21.55
18.80
12.8
19.86
18.14
8.6
20.74
18.64
10.1
20.70
17.91
13.5
Before (%)
After (%)
% reduction
15.42
14.21
7.8
14.63
13.68
6.5
14.63
13.74
6.1
14.05
13.48
4.1
14.26
12.82
10.1
14.38
12.28
14.6
Before (%)
After (%)
% reduction
11.01
10.09
8.4
10.52
9.86
6.3
10.48
9.93
5.2
10.40
9.65
7.2
10.96
9.40
14.2
11.01
9.26
15.9
Table 2.13. Average surface temperature (°C) and standard deviation (°C) for Runner type
peanuts at 4 initial moisture contents undergoing drying at 6 different power levels.
Average temperature (°C)
mcin
Power
2 kW
1.5 kW
1.2 kW
0.9 kW
0.6 kW
0.3 kW
33%
21%
14%
11%
34.6
30.5
28.4
27.2
24.8
23.1
35.9
34.3
31.3
28.4
24.9
22.6
38
33.7
31
29.3
25
22.6
40.1
34
31.7
28.7
25.2
22.7
Standard deviation (°C)
mcin
Power
2 kW
1.5 kW
1.2 kW
0.9 kW
0.6 kW
0.3 kW
33%
21%
14%
11%
2.9
1.9
1.5
1.2
0.7
0.5
3.3
2.6
1.9
1.3
0.7
0.4
3.6
2.6
2
1.6
0.9
0.5
3.8
2.9
2.5
1.8
1.1
0.6
69
FIGURE CAPTIONS
Figure 2.1
Mechanisms of ionic interaction (Zhong, 2001).
Figure 2.2
Mechanisms of dipolar interaction (Zhong 2001).
Figure 2.3
Distribution of the electric field in a transversal section of the TE10 waveguide in the presence
of a lossy dielectric at the center of the waveguide. Wave is propagating into the paper.
a – waveguide height, b – waveguide width, w – height of dielectric load.
Figure 2.4
Temperature distribution during microwave drying. The time coordinate can be changed into
distance for a belt moving at constant speed (Metaxa and Meredith, 1983).
Figure 2.5
Electric field distribution along a traveling wave applicator. The distance coordinate is
dependent on the time coordinate through the conveyor belt speed.
Figure 2.6
Microwave generator (a) and the curing chamber (b).
Figure 2.7
Schematic of the microwave drying system (top) and infrared thermocouple locations along
the waveguide (bottom).
Figure 2.8
Transmitted and reflected power at an impedance mismatch (change of transmission medium,
Stuchly and Hamid, 1972).
Figure 2.9
Fiber optic probes in peanuts and their location on the conveyor belt.
Figure 2.10
Estimated temperature profiles for Runner type peanuts at 21% mc and 6 power levels.
Figure 2.11
Estimated convective and radiative losses of Runner type peanuts at 21% mc and 2 kW.
Figure 2.12
Estimated moisture losses for Runner type peanuts at 21% mc and 2 kW.
Figure 2.13
Internal temperature (lines) and bed surface temperature (symbols) distributions in Runner
type peanuts at 18% initial mc for pods in different locations on the belt. Pod P1 is located
closest to the right wall.
Figure 2.14
Side panels covering cleaning slots on the right side of the drying chamber.
Figure 2.15
Internal temperatures (lines) and surface temperatures (symbols) of Runner type peanuts at 3
initial mc undergoing drying at 1.2 kW.
Figure 2.16
Internal temperatures (lines) and surface temperatures (symbols) of Runner type peanuts at 3
initial mc undergoing drying at 2 kW.
Figure 2.17
Internal temperatures (lines) and surface temperatures (symbols) of Virginia type peanuts at 3
initial mc undergoing drying at 1.2 kW.
Figure 2.18
Internal temperatures (lines) and surface temperatures (symbols) of Virginia type peanuts at 3
initial mc undergoing drying at 2 kW.
Figure 2.19
Internal and external temperatures of pods (lines) and bed surface temperatures (symbols) of
Runner type peanuts at 3 initial mc undergoing drying at 1.2 kW.
Figure 2.20
Internal and external temperatures of pods (lines) and bed surface temperatures (symbols) of
Runner type peanuts at 3 initial mc undergoing drying at 2 kW.
70
Figure 2.21
Surface temperature distribution at the end of drying of Runner type peanuts at two power
levels (1.2 kW – left column, 2 kW – right column) and indicated initial mc.
Figure 2.22
Surface temperature distribution at the end of drying of Virginia type peanuts at two power
levels (1.2 kW – left column, 2 kW – right column) and indicated initial mc.
Figure 2.23
Internal temperature (lines) and bed surface temperature (symbols) distributions for Runner
type peanuts at 11% initial mc and 6 power levels.
Figure 2.24
Internal temperature (lines) and bed surface temperature (symbols) distributions for Runner
type peanuts at 14% initial mc and 6 power levels.
Figure 2.25
Internal temperature (lines) and bed surface temperature (symbols) distributions for Runner
type peanuts at 21% initial mc and 6 power levels.
Figure 2.26
Internal temperature (lines) and bed surface temperature (symbols) distributions for Runner
type peanuts at 33% initial mc and 6 power levels.
Figure 2.27
Standard deviations for internal temperature (lines) and bed surface temperature (symbols)
distributions for Runner type peanuts at 11% initial mc and 6 power levels.
Figure 2.28
Standard deviations for internal temperature (lines) and bed surface temperature (symbols)
distributions for Runner type peanuts at 14% initial mc and 6 power levels.
Figure 2.29
Standard deviations for internal temperature (lines) and bed surface temperature (symbols)
distributions for Runner type peanuts at 21% initial mc and 6 power levels.
Figure 2.30
Standard deviations for internal temperature (lines) and bed surface temperature (symbols)
distributions for Runner type peanuts at 33% initial mc and 6 power levels.
Figure 2.31
Internal temperatures as function of surface temperature at different distances in the
microwave drying tunnel for Runner type peanuts at 11% initial mc.
Figure 2.32
First derivative of the internal temperature with respect to distance for Runner type peanuts at
11% initial mc and 6 power levels.
Figure 2.33
First derivative of the internal temperature with respect to distance for Runner type peanuts at
14% initial mc and 6 power levels.
Figure 2.34
First derivative of the internal temperature with respect to distance for Runner type peanuts at
21% initial mc and 6 power levels.
Figure 2.35
First derivative of the internal temperature with respect to distance for Runner type peanuts at
33% initial mc and 6 power levels.
Figure 2.36
Internal temperature (lines) and bed surface temperature (symbols) distributions for Runner
type peanuts at 0.3 kW and 4 initial mc.
Figure 2.37
Internal temperature (lines) and bed surface temperature (symbols) distributions for Runner
type peanuts at 0.6 kW and 4 initial mc.
Figure 2.38
Internal temperature (lines) and bed surface temperature (symbols) distributions for Runner
type peanuts at 0.9 kW and 4 initial mc.
71
Figure 2.39
Internal temperature (lines) and bed surface temperature (symbols) distributions for Runner
type peanuts at 1.2 kW and 4 initial mc.
Figure 2.40
Internal temperature (lines) and bed surface temperature (symbols) distributions for Runner
type peanuts at 1.5 kW and 4 initial mc.
Figure 2.41
Internal temperature (lines) and bed surface temperature (symbols) distributions for Runner
type peanuts at 2 kW and 4 initial mc.
Figure 2.42
Standard deviations for internal temperature (lines) and bed surface temperature (symbols)
distributions for Runner type peanuts at 0.3 kW and 4 initial mc.
Figure 2.43
Standard deviations for internal temperature (lines) and bed surface temperature (symbols)
distributions for Runner type peanuts at 0.6 kW and 4 initial mc.
Figure 2.44
Standard deviations for internal temperature (lines) and bed surface temperature (symbols)
distributions for Runner type peanuts at 0.9 kW and 4 initial mc.
Figure 2.45
Standard deviations for internal temperature (lines) and bed surface temperature (symbols)
distributions for Runner type peanuts at 1.2 kW and 4 initial mc.
Figure 2.46
Standard deviations for internal temperature (lines) and bed surface temperature (symbols)
distributions for Runner type peanuts at 1.5 kW and 4 initial mc.
Figure 2.47
Standard deviations for internal temperature (lines) and bed surface temperature (symbols)
distributions for Runner type peanuts at 2 kW and 4 initial mc.
Figure 2.48
First derivative of the internal temperature with respect to distance for Runner type peanuts at
0.3 kW and 4 initial mc.
Figure 2.49
First derivative of the internal temperature with respect to distance for Runner type peanuts at
0.6 kW and 4 initial mc.
Figure 2.50
First derivative of the internal temperature with respect to distance for Runner type peanuts at
0.9 kW and 4 initial mc.
Figure 2.51
First derivative of the internal temperature with respect to distance for Runner type peanuts at
1.2 kW and 4 initial mc.
Figure 2.52
First derivative of the internal temperature with respect to distance for Runner type peanuts at
1.5 kW and 4 initial mc.
Figure 2.53
First derivative of the internal temperature with respect to distance for Runner type peanuts at
2 kW and 4 initial mc.
Figure 2.54
Surface temperature distribution of Runner type peanuts at the end of drying at 11% initial mc
and 6 power levels: a) 0.3 kW, b) 0.6 kW, c) 0.9 kW, d) 1.2 kW, e) 1.5 kW, f) 2.0 kW.
Figure 2.55
Surface temperature distribution at the end of drying of Runner type peanuts at 14% initial mc
and 6 power levels: a) 0.3 kW, b) 0.6 kW, c) 0.9 kW, d) 1.2 kW, e) 1.5 kW, f) 2.0 kW.
Figure 2.56
Surface temperature distribution at the end of drying of Runner type peanuts at 21% initial mc
and 6 power levels: a) 0.3 kW, b) 0.6 kW, c) 0.9 kW, d) 1.2 kW, e) 1.5 kW, f) 2.0 kW.
Figure 2.57
Surface temperature distribution at the end of drying of Runner type peanuts at 33% initial mc
and 6 power levels: a) 0.3 kW, b) 0.6 kW, c) 0.9 kW, d) 1.2 kW, e) 1.5 kW, f) 2.0 kW.
72
+
+
−
−
−
+
+
−
+
No Field
−
+
Field Direction
+
+
−
−
+
−
+
−
+
−
+
Field Direction
+
−
+
+
+
−
−
−
+
+
−
Figure 2.1. Mechanisms of ionic interaction (Zhong, 2001).
73
+
+
−
−
−
No Field
+
Field Direction
+
+
−
−
−
+
Field Direction
+
+
−
−
−
+
Figure 2.2. Mechanisms of dipolar interaction (Zhong 2001).
74
w
Emax
a
Wave
direction
b
Figure 2.3. Distribution of the electric field in a transversal section of the TE10 waveguide in
the presence of a lossy dielectric at the center of the waveguide. Wave is propagating into the
paper. a – waveguide height, b – waveguide width, w – height of dielectric load.
75
T
Initial
heat-up
Heat-up,
no drying
Drying
Twb
III
II
T0
I
Time
Figure 2.4. Temperature distribution during microwave drying. The time coordinate can be
changed into distance for a belt moving at constant speed (Metaxa and Meredith, 1983).
Initial
heat-up
Heat-up,
no drying
Drying
E
III
II
I
Distance
Figure 2.5. Electric field distribution along a traveling wave applicator. The distance
coordinate is dependent on the time coordinate through the conveyor belt speed.
76
a)
b)
Figure 2.6. Microwave generator (a) and the curing chamber (b).
Infrared
thermocouples
F
Infrared thermocouple groups
E
D
C
B
A
Microwaves
Peanuts
vz
EXIT
Air flow
ENTRANCE
Figure 2.7. Schematic of the microwave drying system (top) and infrared thermocouple
locations along the waveguide (bottom).
77
Waveguide
Pin
Waveguide with dielectric
Prefl
Ptransm
Pz = Ptransm e-2αz
Distance
Figure 2.8. Transmitted and reflected power at an impedance mismatch (change of
transmission medium, Stuchly and Hamid, 1972).
Figure 2.9. Fiber optic probes in peanuts and their location on the conveyor belt.
78
70
Temperature (°C)
60
2 kW
50
1.5 kW
1.2 kW
40
0.9 kW
0.6 kW
30
0.3 kW
20
10
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
Distance (m)
Figure 2.10. Estimated temperature profiles for Runner type peanuts at 21% mc and 6 power
levels.
1.8
1.6
1.4
q (W)
1.2
q conv
1.0
q rad
0.8
q loss t ot al
0.6
0.4
0.2
0.0
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
Distance (m)
Figure 2.11. Estimated convective and radiative losses of Runner type peanuts at 21% mc
and 2 kW.
79
21.1%
21.0%
Moisture content (%)
20.9%
20.8%
2 kW
1.5 kW
20.7%
1.2 kW
0.9 kW
20.6%
0.6 kW
20.5%
0.3 kW
20.4%
20.3%
20.2%
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
Distance (m)
Figure 2.12. Estimated moisture losses for Runner type peanuts at 21% mc and 2 kW.
80
70
65
Temperature (°C)
60
55
P1
50
P4
P6
45
P7
40
P8
35
IR t emp
30
25
20
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
Distance (m)
Figure 2.13. Internal temperature (lines) and bed surface temperature (symbols) distributions
in Runner type peanuts at 18% initial mc for pods in different locations on the belt. Pod P1 is
located closest to the right wall.
Figure 2.14. Side panels covering cleaning slots on the right side of the drying chamber.
81
45
Temperature (°C)
40
25.7% mc
22.8% mc
35
19.7% mc
25.7% mc IR
30
22.8% mc IR
19.7% mc IR
25
20
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
Distance (m)
Figure 2.15. Internal temperatures (lines) and surface temperatures (symbols) of Runner type
peanuts at 3 initial mc undergoing drying at 1.2 kW.
60
55
Temperature (°C)
50
24.6% mc
45
20.3% mc
16.9% mc
40
24.6% mc IR
20.3% mc IR
35
16.9% mc IR
30
25
20
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
Distance (m)
Figure 2.16. Internal temperatures (lines) and surface temperatures (symbols) of Runner type
peanuts at 3 initial mc undergoing drying at 2 kW.
82
50
Temperature (°C)
45
45.2% mc
40
41.7% mc
37.2% mc
35
45.2% mc IR
41.7% mc IR
30
37.2% mc IR
25
20
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
Distance (m)
Figure 2.17. Internal temperatures (lines) and surface temperatures (symbols) of Virginia
type peanuts at 3 initial mc undergoing drying at 1.2 kW.
70
65
Temperature (°C)
60
55
47.4% mc
50
46.5% mc
39.2% mc
45
47.4% mc IR
40
46.5% mc IR
35
39.2% mc IR
30
25
20
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
Distance (m)
Figure 2.18. Internal temperatures (lines) and surface temperatures (symbols) of Virginia
type peanuts at 3 initial mc undergoing drying at 2 kW.
83
45
40
T in 28.5% mc
Temperature (°C)
T out 28.5% mc
T in 25.4% mc
35
T out 25.4% mc
T in 24.3% mc
T out 24.3% mc
30
IR 28.5% mc
IR 25.4% mc
IR 24.3% mc
25
20
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
Distance (m)
Figure 2.19. Internal and external temperatures of pods (lines) and bed surface temperatures
(symbols) of Runner type peanuts at 3 initial mc undergoing drying at 1.2 kW.
65
60
Temperature (°C)
T in 29.6% mc
55
T out 29.6% mc
50
T in 25.3% mc
T out 25.2% mc
45
T in 21.9% mc
40
T out 21.9% mc
35
IR 25.2% mc
IR 29.6% mc
IR 21.9% mc
30
25
20
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
Distance (m)
Figure 2.20. Internal and external temperatures of pods (lines) and bed surface temperatures
(symbols) of Runner type peanuts at 3 initial mc undergoing drying at 2 kW.
84
mc = 25.7%
mc = 24.6%
mc = 22.8%
mc = 19.1%
mc = 19.7%
mc = 16.9%
Figure 2.21. Surface temperature distribution at the end of drying of Runner type peanuts at
two power levels (1.2 kW – left column, 2 kW – right column) and indicated initial mc.
85
mc = 45.2%
mc = 47.4%
mc = 41.6%
mc = 46.5%
mc = 37.2%
mc = 39.2%
Figure 2.22. Surface temperature distribution at the end of drying of Virginia type peanuts at
two power levels (1.2 kW – left column, 2 kW – right column) and indicated initial mc.
86
55
50
0.3 kW
Temperature (°C)
45
0.6 kW
40
0.9 kW
35
1.5 kW
1.2 kW
2 kW
30
0.3 kW IR
0.6 kW IR
25
0.9 kW IR
1.2 kW IR
20
1.5 kW IR
2 kW IR
15
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
Distance (m)
Figure 2.23. Internal temperature (lines) and bed surface temperature (symbols) distributions
for Runner type peanuts at 11% initial mc and 6 power levels.
60
55
0.3 kW
50
Temperature (°C)
0.6 kW
45
0.9 kW
1.2 kW
40
1.5 kW
35
2 kW
0.3 kW IR
30
0.6 kW IR
0.9 kW IR
25
1.2 kW IR
20
1.5 kW IR
2 kW IR
15
0
0.5
1
1.5
2
2.5
3
3.5
Distance (m)
Figure 2.24. Internal temperature (lines) and bed surface temperature (symbols) distributions
for Runner type peanuts at 14% initial mc and 6 power levels.
87
60
Temperature (°C)
55
50
0.3 kW
45
0.9 kW
0.6 kW
1.2 kW
40
1.5 kW
2 kW
35
0.3 kW IR
30
0.6 kW IR
0.9 kW IR
25
1.2 kW IR
20
1.5 kW IR
2 kW IR
15
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
Distance (m)
Figure 2.25. Internal temperature (lines) and bed surface temperature (symbols) distributions
for Runner type peanuts at 21% initial mc and 6 power levels.
65
60
55
0.3 kW
0.6 kW
Temperature (°C)
50
0.9 kW
45
1.2 kW
1.5 kW
40
2 kW
35
0.3 kW IR
0.6 kW IR
30
0.9 kW IR
25
1.2 kW IR
1.5 kW IR
20
2 kW IR
15
0.0
0.5
1.0
1.5
2.0
Distance (m)
2.5
3.0
3.5
Figure 2.26. Internal temperature (lines) and bed surface temperature (symbols) distributions
for Runner type peanuts at 33% initial mc and 6 power levels.
88
4
1/ 2 of Standard deviation (°C)
3.5
0.3 kW
3
0.6 kW
0.9 kW
2.5
1.2 kW
1.5 kW
2
2 kW
0.3 kW IR
1.5
0.6 kW IR
1
0.9 kW IR
0.5
1.5 kW IR
1.2 kW IR
2 kW IR
0
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
Distance (m)
Figure 2.27. Standard deviations for internal temperature (lines) and bed surface temperature
(symbols) distributions for Runner type peanuts at 11% initial mc and 6 power levels.
4.0
1/2 of Standard deviation (°C)
3.5
0.3 kW
0.6 kW
3.0
0.9 kW
2.5
1.2 kW
1.5 kW
2.0
2 kW
0.3 kW IR
1.5
0.6 kW IR
0.9 kW IR
1.0
1.2 kW IR
0.5
1.5 kW IR
2 kW IR
0.0
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
Distance (m)
Figure 2.28. Standard deviations for internal temperature (lines) and bed surface temperature
(symbols) distributions for Runner type peanuts at 14% initial mc and 6 power levels.
89
4.5
1/2 of Standard deviation (°C)
4.0
0.3 kW
3.5
0.6 kW
0.9 kW
3.0
1.2 kW
2.5
1.5 kW
2 kW
2.0
0.3 kW IR
1.5
0.6 kW IR
0.9 kW IR
1.0
1.2 kW IR
0.5
1.5 kW IR
2 kW IR
0.0
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
Distance (m)
Figure 2.29. Standard deviations for internal temperature (lines) and bed surface temperature
(symbols) distributions for Runner type peanuts at 21% initial mc and 6 power levels.
9
1/2 of Standard deviation (°C)
8
0.3 kW
7
0.6 kW
0.9 kW
6
1.2 kW
5
1.5 kW
2 kW
4
0.3 kW IR
3
0.6 kW IR
0.9 kW IR
2
1.2 kW IR
1
1.5 kW IR
2 kW IR
0
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
Distance (m)
Figure 2.30. Standard deviations for internal temperature (lines) and bed surface temperature
(symbols) distributions for Runner type peanuts at 33% initial mc and 6 power levels.
90
55
A t 0.480 m:
Internal temperature (°C)
50
y = 1.3468x - 4.6687
R2 = 0.9981
A t 0.556 m:
y = 1.4942x - 7.4556
R2 = 0.9985
A t 0.986 m:
y = 1.9789x - 16.305
R2 = 0.999
0.556
y = 2.0181x - 16.98
R2 = 0.999
1.061
45
40
A t 1.061 m:
0.480
0.986
Linear (0.480)
35
Linear (0.556)
Linear (0.986)
30
Linear (1.061)
25
20
15
20
25
30
35
Surface Temperature (°C)
Figure 2.31. Internal temperatures as function of surface temperature at different distances in
the microwave drying tunnel for Runner type peanuts at 11% initial mc.
91
60
50
40
dT/dz (°C/m)
0.3 kW
0.6 kW
30
0.9 kW
1.2 kW
20
1.5 kW
2 kW
10
0
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
-10
Distance (m)
Figure 2.32. First derivative of the internal temperature with respect to distance for Runner
type peanuts at 11% initial mc and 6 power levels.
70
60
dT/dz (°C/m)
50
0.3 kW
40
0.6 kW
0.9 kW
30
1.2 kW
1.5 kW
20
2 kW
10
0
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
-10
Distance (m)
Figure 2.33. First derivative of the internal temperature with respect to distance for Runner
type peanuts at 14% initial mc and 6 power levels.
92
70
60
50
dT/dz (°C/m)
40
0.3 kW
0.6 kW
30
0.9 kW
20
1.2 kW
10
2 kW
1.5 kW
0
-10
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
-20
Distance (m)
Figure 2.34. First derivative of the internal temperature with respect to distance for Runner
type peanuts at 21% initial mc and 6 power levels.
100
80
dT/dz (°C/m)
60
0.3 kW
0.6 kW
0.9 kW
40
1.2 kW
1.5 kW
20
2 kW
0
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
-20
Distance (m)
Figure 2.35. First derivative of the internal temperature with respect to distance for Runner
type peanuts at 33% initial mc and 6 power levels.
93
29
Temperature (°C)
27
11% mc
14% mc
25
21% mc
23
33% mc
11% mc IR
21
14% mc IR
21% mc IR
19
33% mc IR
17
15
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
Distance (m)
Figure 2.36. Internal temperature (lines) and bed surface temperature (symbols) distributions
for Runner type peanuts at 0.3 kW and 4 initial mc.
34
Temperature (°C)
32
11% mc
14% mc
30
21% mc
28
33% mc
11% mc IR
26
14% mc IR
21% mc IR
24
33% mc IR
22
20
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
Distance (m)
Figure 2.37. Internal temperature (lines) and bed surface temperature (symbols) distributions
for Runner type peanuts at 0.6 kW and 4 initial mc.
94
45
Temperature (°C)
40
11% mc
14% mc
21% mc
35
33% mc
11% mc IR
30
14% mc IR
21% mc IR
33% mc IR
25
20
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
Distance (m)
Figure 2.38. Internal temperature (lines) and bed surface temperature (symbols) distributions
for Runner type peanuts at 0.9 kW and 4 initial mc.
55
50
11% mc
Temperature (°C)
45
14% mc
21% mc
40
33% mc
11% mc IR
35
14% mc IR
21% mc IR
30
33% mc IR
25
20
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
Distance (m)
Figure 2.39. Internal temperature (lines) and bed surface temperature (symbols) distributions
for Runner type peanuts at 1.2 kW and 4 initial mc.
95
50
45
Temperature (°C)
11% mc
14% mc
40
21% mc
33% mc
35
11% mc IR
14% mc IR
30
21% mc IR
33% mc IR
25
20
0
0.5
1
1.5
2
2.5
3
3.5
Distance (m)
Figure 2.40. Internal temperature (lines) and bed surface temperature (symbols) distributions
for Runner type peanuts at 1.5 kW and 4 initial mc.
65
60
Temperature (°C)
55
11% mc
14% mc
50
21% mc
45
33% mc
11% mc IR
40
14% mc IR
35
21% mc IR
30
33% mc IR
25
20
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
Distance (m)
Figure 2.41. Internal temperature (lines) and bed surface temperature (symbols) distributions
for Runner type peanuts at 2 kW and 4 initial mc.
96
0.7
1/2 of Standard deviation (°C)
0.6
11% mc
0.5
14% mc
21% mc
0.4
33% mc
11% mc IR
0.3
14% mc IR
21% mc IR
0.2
33% mc IR
0.1
0
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
Distance (m)
Figure 2.42. Standard deviations for internal temperature (lines) and bed surface temperature
(symbols) distributions for Runner type peanuts at 0.3 kW and 4 initial mc.
1.6
1/2 of Standard deviation (°C)
1.4
1.2
11% mc
14% mc
1
21% mc
33% mc
0.8
11% mc IR
14% mc IR
0.6
21% mc IR
0.4
33% mc IR
0.2
0
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
Distance (m)
Figure 2.43. Standard deviations for internal temperature (lines) and bed surface temperature
(symbols) distributions for Runner type peanuts at 0.6 kW and 4 initial mc.
97
1/2 of Standard deviation (°C)
2.5
2
11% mc
14% mc
21% mc
1.5
33% mc
11% mc IR
1
14% mc IR
21% mc IR
33% mc IR
0.5
0
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
Distance (m)
Figure 2.44. Standard deviations for internal temperature (lines) and bed surface temperature
(symbols) distributions for Runner type peanuts at 0.9 kW and 4 initial mc.
5
1/2 of Standard deviation (°C)
4.5
4
11% mc
3.5
14% mc
21% mc
3
33% mc
2.5
11% mc IR
2
14% mc IR
1.5
21% mc IR
33% mc IR
1
0.5
0
0
0.5
1
1.5
2
2.5
3
3.5
Distance (m)
Figure 2.45. Standard deviations for internal temperature (lines) and bed surface temperature
(symbols) distributions for Runner type peanuts at 1.2 kW and 4 initial mc.
98
4.5
1/2 of Standard deviation (°C)
4
3.5
11% mc
14% mc
3
21% mc
2.5
33% mc
11% mc IR
2
14% mc IR
1.5
21% mc IR
1
33% mc IR
0.5
0
0
0.5
1
1.5
2
2.5
3
3.5
Distance (m)
Figure 2.46. Standard deviations for internal temperature (lines) and bed surface temperature
(symbols) distributions for Runner type peanuts at 1.5 kW and 4 initial mc.
9
1/2 of Standard deviation (°C)
8
7
11% mc
14% mc
6
21% mc
5
33% mc
11% mc IR
4
14% mc IR
3
21% mc IR
2
33% mc IR
1
0
0
0.5
1
1.5
2
2.5
3
3.5
Distance (m)
Figure 2.47. Standard deviations for internal temperature (lines) and bed surface temperature
(symbols) distributions for Runner type peanuts at 2 kW and 4 initial mc.
99
8
6
dT/dz (°C/m)
4
11% mc
14% mc
2
21% mc
33% mc
0
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
-2
-4
Distance (m)
Figure 2.48. First derivative of the internal temperature with respect to distance for Runner
type peanuts at 0.3 kW and 4 initial mc.
20
15
dT/dz (°C/m)
10
11% mc
14% mc
5
21% mc
33% mc
0
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
-5
-10
Distance (m)
Figure 2.49. First derivative of the internal temperature with respect to distance for Runner
type peanuts at 0.6 kW and 4 initial mc.
100
30
25
dT/dz (°C/m)
20
15
11% mc
14% mc
10
21% mc
33% mc
5
0
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
-5
-10
Distance (m)
Figure 2.50. First derivative of the internal temperature with respect to distance for Runner
type peanuts at 0.9 kW and 4 initial mc.
50
40
dT/dz (°C/m)
30
11% mc
14% mc
20
21% mc
33% mc
10
0
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
-10
Distance (m)
Figure 2.51. First derivative of the internal temperature with respect to distance for Runner
type peanuts at 1.2 kW and 4 initial mc.
101
60
50
dT/dz (°C/m)
40
11% mc
30
14% mc
21% mc
20
33% mc
10
0
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
-10
Distance (m)
Figure 2.52. First derivative of the internal temperature with respect to distance for Runner
type peanuts at 1.5 kW and 4 initial mc.
100
80
dT/dz (°C/m)
60
11% mc
14% mc
40
21% mc
33% mc
20
0
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
-20
Distance (m)
Figure 2.53. First derivative of the internal temperature with respect to distance for Runner
type peanuts at 2 kW and 4 initial mc.
102
a) 0.3 kW
b) 0.6 kW
c) 0.9 kW
d) 1.2 kW
e) 1.5 kW
f) 2.0 kW
Figure 2.54. Surface temperature distribution at the end of drying of Runner type peanuts at
11% initial mc and six power levels: a) 0.3 kW, b) 0.6 kW, c) 0.9 kW, d) 1.2 kW, e) 1.5 kW,
f) 2.0 kW.
103
a) 0.3 kW
b) 0.6 kW
c) 0.9 kW
d) 1.2 kW
e) 1.5 kW
f) 2.0 kW
Figure 2.55. Surface temperature distribution at the end of drying of Runner type peanuts at
14% initial mc and six power levels: a) 0.3 kW, b) 0.6 kW, c) 0.9 kW, d) 1.2 kW, e) 1.5 kW,
f) 2.0 kW.
104
a) 0.3 kW
b) 0.6 kW
c) 0.9 kW
d) 1.2 kW
e) 1.5 kW
f) 2.0 kW
Figure 2.56. Surface temperature distribution at the end of drying of Runner type peanuts at
21% initial mc and six power levels: a) 0.3 kW, b) 0.6 kW, c) 0.9 kW, d) 1.2 kW, e) 1.5 kW,
f) 2.0 kW.
105
a) 0.3 kW
b) 0.6 kW
c) 0.9 kW
d) 1.2 kW
e) 1.5 kW
f) 2.0 kW
Figure 2.57. Surface temperature distribution at the end of drying of Runner type peanuts at
33% initial mc and six power levels: a) 0.3 kW, b) 0.6 kW, c) 0.9 kW, d) 1.2 kW, e) 1.5 kW,
f) 2.0 kW.
106
Manuscript 3. Control of Continuous Microwave Drying Process of Farmer Stock
Peanuts
D. Boldor1, T.H. Sanders2, S.A. Hale3*
1
Department of Food Science
North Carolina State University, Raleigh NC 27695-7624
2
USDA - ARS, Market Quality and Handling Research Unit
North Carolina State University, Raleigh, NC 27695-7624
3
Department of Biological and Agricultural Engineering
North Carolina State University, Raleigh NC 27695-7624
*
Corresponding author:
Tel: 919-515-6760
Fax: 919-515-7760
E-mail: andy_hale@ncsu.edu
107
ABSTRACT
Feedback control of the continuous microwave drying of farmer stock peanuts (Arachis
hypogaea L.) of different varieties and initial moisture contents was investigated using the
peanut's surface temperature as the controlled variable and microwave power level as the
manipulated variable. Process parameters were determined using process reaction curves, and
a PI (proportional, integral) controller was implemented in a software routine that controlled
the microwave generator's power level. The servo scenario (set point change) was simulated
in software to determine the optimum tuning parameters of the PI controller. The potential
for a more advanced control of the process based on complete surface temperature
distribution measured with an infrared camera placed at the location of maximum surface
temperature was evaluated.
Keywords: Arachis hypogaea L., peanuts, drying, control, continuous, microwave,
temperature, distribution.
108
INTRODUCTION
Process control methods are widely used in food industry for quality assurance
purposes. The characteristics and requirements for various food processing operations are
described by Mittal (1996) and McFarlane (1995). For peanut processing, a complex fuzzy
control system for the roasting process, based in part on theoretical modeling (Landman et
al., 1994) was developed by Davidson et al. (1999).
The study reported here focuses on the process control for continuous microwave
drying of peanuts, where the microwave energy delivered to the dryer can be changed as
needed. Microwave energy is increasingly used in food processing operations. The utilization
of microwave energy in heating and drying applications has been addressed in many books
(Decareau, 1985; Metaxa and Meredith, 1983). New microwave cavity designs that eliminate
temperature non-uniformity commonly seen in multimode microwave ovens are being
developed for food processing applications. These designs, such as focusing structures and
traveling wave (or planar) applicators, are currently used for heating of fluids (Coronel et al.,
2003) and drying and blanching of various agricultural commodities (Rausch, 2002; Katz,
2002; Boldor et al. 2003). In the drying process, the most important processing parameter is
product temperature. Due to the inherent nature of microwaves, traditional temperature
sensors, such as thermocouples, cannot be used in the presence of microwave fields.
Ramaswamy et al. (1991) developed a shielded thermocouple to be used for feedback control
of heating in domestic microwave oven. These are useful when implementing model-based
temperature control in microwave-convection heating systems (Sanchez et al., 2000).
109
While shielded thermocouples can be very useful in microwave heating of fluids, they
are rendered useless in continuous drying of agricultural commodities, where continuous
monitoring of internal temperatures of seeds is impossible even when using shielded
thermocouples or fiber optic temperature probes. However, the correlation between the
internal temperatures of peanuts and the surface temperature of the peanut bed (Table 3.1,
Boldor et al., 2003) makes remote temperature measurement of peanut bed surfaces a
feasible method of peanut temperature measurement for process control purposes. Remote
surface temperature measurement are performed using either infrared thermocouples inserted
at critical locations along the microwave waveguide (Figure 3.1, Boldor et al., 2003), or a
properly calibrated infrared imaging system (Goedeken et al., 1991; Schelssinger, 1995).
Theoretical considerations
For process control purposes, the transient behavior of the physical system needs to be
determined. The transient response of a first or second order process with dead time (Eqn.
[3.1] and [3.2]) can be represented in the Laplace domain using the following transfer
functions (Marlin, 2000):
− θs
Y(s) K p e
G p (s) =
=
X(s) τ p s + 1
[3.1]
K p e − θs
Y(s)
G p (s) =
=
X(s) τ 2ps 2 + 2ξτps + 1
[3.2]
110
Process reaction curves are used to determine Kp, θ, and τp. They are determined as
follows:
1. Allow the process to reach steady state.
2. Introduce a single step change in the input variable.
3. Collect input and output response data until the process again reaches steady state.
4. Perform the graphical process reaction curve calculations. The process gain (Kp) is
the ratio of the magnitude change of the output to the magnitude change of the
input. The time constant τp and dead time θ are determined according to:
τp = 1.5 (t2 - t1)
[3.3]
θ = t2 - τp
[3.4]
Where:
t1 - time at which the output reaches 28% of the final steady state value
t2 - time at which the output reaches 63% of the final steady state value.
5. Return to the original input value to make sure that the output returns to original
steady state.
The major advantage of using the process reaction curve in determination of the transfer
function is that the transfer functions of the sensor and the final control element are included
in the model. The disadvantage is that the method is limited to first and second order systems
with dead time.
One of the most widely used process control method is feedback control using a PID
(proportional, integral, derivative) algorithm. In this control method, the response of the
controller is proportional with the difference between the desired value of the controlled
variable (set point SP) and the measured value of the controlled variable (CV).
111
Schematically, a feedback control loop is represented in Figure 3.2 (Marlin, 2000). The
transfer function of the PID controller can be written as:


1
G c (s) = K c 1 +
+ τ d s 

 τis + 1
[3.5]
Once the transfer function of the open loop (the system without the controller) is
determined, the transfer function of the closed loop feedback system can be determined using
the following formula:
G p (s)
Y(s)
=
X(s) 1 + G p (s)G c (s)
[3.6]
For determination of the control parameters Kc, τi, and τd, several methods exists in
literature, out of which the most commonly used ones are Ciancone (Ciancone and Marlin,
1992), Lopez (Lopez et al., 1969), and Ziegler-Nichols (Ziegler and Nichols, 1942). The
parameters determined using these methods are only starting points, afterward the control
loops needs to be fine tuned such that either the integral square of error (ISE) or absolute
value of error (IAE) are minimized (Marlin, 2000):
∞
ISE = ∫ (SP(t) − CV(t) ) dt
2
[3.7]
0
∞
IAE = ∫ SP(t) − CV(t) dt
[3.8]
0
In the continuous microwave drying of peanuts, Boldor et al. (2003) determined not
only the relationship between the temperature of the peanuts and the surface temperature of
the peanut bed, but also the locations of the maximum temperature and of the maximum rate
of temperature increase, as shown in Figure 3.3.
112
The location of the maximum temperature (zero derivative) and of the maximum rate of
temperature increase (maximum derivative) is determined by the moisture content of the
peanuts entering the microwave curing chamber. Therefore, the relationship between the
temperature of the peanut bed surface and the internal temperature of the peanut pods are
most useful when they are evaluated at the locations of maximum temperatures and
maximum rates of temperature increases. These locations are suitable for installation of
surface temperature monitoring equipment such as infrared pyrometers, infrared
thermocouples or thermal imaging equipment.
In this study, for process control purposes the surface temperature of the peanut bed
(CV) was measured with infrared thermocouples; and a feedback control mechanism
adjusted the microwave power level (MV) to maintain the surface temperature at the desired
set point (SP).
Infrared thermocouples measured an average temperature of a fairly large surface area
(a circle of 3 cm diameter). A thermal imager (or infrared camera) would be able to measure
the complete surface temperature distribution, determining both the temperature at a specific
location as well as the location of the maximum temperature. This data could be used to
create a combination of feedback loop (described above) and a feed forward control method
that would determine the number of passes required to obtain desired final moisture content.
113
MATERIALS AND METHODS
Field dried peanuts (Runner and Virginia type) at moisture contents ranging from 22 to
52% (dry basis) were used in this study. Samples were shipped from USDA-ARS Peanut
National Laboratory in Dawson, Georgia to the Department of Food Science at North
Carolina State University during the months of September - November of 2002.
The microwave system included a planar applicator (Industrial Microwave Systems,
Morrisville, NC) that consisted of a conveyor belt running at the geometrical center of an
aluminum waveguide. Microwaves were generated by a 5 kW microwave generator
(Industrial Microwave Systems, Morrisville, NC) and transported to the applicator through
aluminum waveguides. The curing chamber was outfitted with an electrical fan to assist the
microwave drying process. Air flow temperature was maintained at 25°C through an
electrical heater.
Surface temperature sensors were based on infrared technology (Mullin and Bows,
1993, Goedeken et al., 1991). Infrared thermocouples (model OS36-T, OMEGA
Engineering, Inc., Stamford, CN) were placed at various distances along the waveguide as
shown in Table 3.1 and Figure 3.1 (Boldor et al., 2003). The surface temperatures were
monitored and recorded through a data acquisition and control unit (HP34970A, Agilent,
Palo Alto, CA) and a software routine written in LabView (National Instruments Corp.,
Austin, TX). The same data acquisition and control unit and software routine were used to
control the microwave generator and to monitor and record the power output, reflected power
and power at the exit of the microwave curing chamber through power diodes (JWF 50D030+, JFW Industries, Inc., Indianapolis, IN).
114
The process model (Kp, τp, θ) was determined using empirical identification based on
process reaction curves, graphical method II (Marlin, 2000) for each peanut variety, initial
moisture content and group of sensors. The transient response of the process was obtained
through analysis of the step response when the power level was changed from 1.2 to 2 kW.
Due to the slight non-linearity of the HP unit voltage output and the actual current generating
the microwaves, the nominal power levels (or the power output) of the generator were always
slightly smaller than the set points.
For each peanut variety and moisture content, the transient response of the system was
obtained by performing an average of 9 replicates of the process reaction curves. Bulk
moisture contents of the samples were determined using the USDA standard (ASAE, 2000).
All temperature and moisture content data was analyzed using Microsoft Excel (Microsoft
Corp, Redmond, WA).
The feedback control routine was developed in Labview, using a simulation of the first
order process with dead-time. Once the optimum control parameters were determined, the
control routine was added to the master Labview program.
115
RESULTS AND DISCUSSIONS
The process reaction curves determined for all temperature sensors at the locations
listed in Table 3.1 are shown in Figure 3.4. Due to infrared thermocouple positioning in
groups of 2 or 3 (Figure 3.1), the process reaction curves were very similar for sensors placed
in the same group (Figure 3.4). The temperatures recorded by the sensors in the same group
were averaged to reduce the number of controlled variables from 16 to 6 (A, B, C, D, E, and
F respectively). The resulting six process reaction curves for each peanut variety and
moisture content are shown in Figures 3.5 to 3.10. Upon analysis of the process reaction
curves, it was determined that at the last two groups of infrared thermocouples (E and F) the
process did not reach the required steady state and their measurements were dropped from
the analysis. The drying of Virginia type peanuts was a first order process, with time
constants and dead-times increasing as the temperature sensors were placed further from the
entrance of the drying tunnel. In the case of Runner-type peanuts, the process reaction curves
seem to indicate an over-damped second order process (ξ>1), with time constants and deadtime also increasing as the sensors were placed farther away from the entrance of the
microwave unit. For process control purposes, the over-damped second order process can be
treated as a first order process with dead-time (Luyben, 1990). Therefore, the calculations of
process parameters were based on the first-order model with dead-time. The values for the
open loop process parameters for all peanut varieties, initial moisture contents and groups of
sensors are shown in Table 3.2.
116
The gain of the process, Kp, for Virginia type peanuts at all moisture contents decreased
as sensors were placed further away from the microwave entrance, a decrease that is
consistent with the lower temperatures caused by the evaporative, convective and radiating
cooling experienced by peanuts undergoing drying (Boldor et al., 2003). In the case of
Runner type peanuts, the process gain followed a similar dependence on sensor position, with
the exception of peanuts at 33% moisture content. At 33% mc, the process gain increased
initially from group A to group B, decreasing afterward. At this moisture content, the
maximum temperature during drying (Figure 3.3) is located in the same region of the
microwave tunnel as the second group of sensors (group B), giving a higher process gain
when this group of sensors was used.
The time constants of the processes increased as the sensors were placed further away
from the microwave tunnel entrance. While this increase was expected, there was a fairly
significant variation between the time constants of the same groups of sensors for different
initial moisture contents. This variation was probably caused by difference between the fixed
location of the infrared thermocouples and the changing locations of maximum temperatures
with moisture content (Figures 3.1 and 3.3).
These peculiarities of the distribution of maximum surface temperature as a function of
initial moisture content show that an adequate measurement of surface temperature
distribution, would be useful in determining the location of the maximum temperature and
subsequently the moisture content of the peanuts in the microwave drying tunnel. This
information is critical in the determination of the needed number of passes through similar
drying chambers to obtain a desired final moisture content.
117
Although there are some crude mathematical models of temperature and moisture
distribution in continuous microwave drying (Boldor et al., 2003), they cannot be reliably
used to create a feed forward/feedback control mechanism for the continuous microwave
drying. More data representing the kinetics of the microwave drying, together with better
mathematical models of moisture and temperature distribution, are needed to create an
advanced control system for the microwave drying process. The limitations of the data
acquisition system used for this study and the lack of knowledge described previously,
determined the use of a simple feedback control loop to maintain the surface temperature of
the peanut bed at a desired value (SP), which was previously related with the internal
temperature of the peanuts undergoing microwave drying (Boldor et al., 2003).
The dead time of the process was determined to be negligible for Virginia type peanuts
at almost all sensor groups and initial moisture contents. The exception occurred at 26%
initial moisture content peanuts and only at the last groups of sensors. For Runner-type
peanuts, approximating the step response with first-order with dead-time model, the dead
time was negligible for the first group of sensors, while for all other groups of sensors it
increased as the sensors where placed further away from the microwave entrance. The slower
heating was caused by the decaying electric field as energy is being absorbed first by the
peanuts closer to the entrance.
The Ciancone open-loop method (Ciancone and Marlin, 1990) was used to determine
the initial parameters of a feedback controller for the two peanut varieties and the three initial
moisture contents used in this study (Table 3.3). The lack of dead time for the sensors placed
closer to entrance in the microwave applicator (Table 3.2) combined with the low signal-tonoise ratio permitted the use of a PI controller, with no derivative component.
118
The fine tuning of the PI feedback controller was simulated in Labview (Figures 3.11)
using the servo scenario, with the controller acting to track set point changes. The optimum
tuning parameters (Table 3.4) were determined such that the process variable never overshot
the desired level.
The results of the simulation for Runner-type peanuts at 33% initial moisture content
with the temperature from the first group of sensors as controlled variable (servo scenario)
are shown in Figures 3.12 and 3.13. The initial temperature and set point temperatures were
27°C and 34°C respectively, matching the temperatures used in the step response analysis.
The results of the simulation with the initial and optimal tuning parameters are shown in
Figures 3.12 and 3.13 respectively. The process variable arrived at the set point in 33 seconds
for the optimum tuning parameters, about 3.7 times faster than for initial parameters (Figures
3.12 and 3.13, Table 3.4). In general, these optimum parameters worked very well in the
temperature range used for determination of process reaction curves.
119
CONCLUSIONS
Process reaction curves were determined for peanuts undergoing microwave drying in a
continuous applicator, using the surface temperature as the controlled variable and the
microwave power level as the manipulated variable. Process parameters determined using
process reaction curves were used to estimate initial tuning parameters of a PI feedback
control loop to maintain the surface temperature at the desired level. Computer simulation
was successfully implemented to determine the optimum tuning parameters at two different
loop speeds. The results of the simulations performed to determine the process response with
the PI controller predicted good behavior without overshooting of the controlled variable.
Possibilities of overall improvement of the process control procedure using a
combination of feedback/feed forward mechanism were discussed, including the use of an
infrared thermal imager or an array of infrared thermocouples placed at the locations of
maximum temperature and maximum rate of temperature increase.
120
LIST OF SYMBOLS
CV(s), CV(t) - controlled variable (Laplace domain, time domain)
CVm(s) - measured controlled variable (Laplace domain)
E(s) - error (Laplace domain)
Gc(s) - transfer function of the controller (Laplace domain)
GFCE(s) - transfer function of the final control element (Laplace domain)
Gp(s) - transfer function of the process (Laplace domain)
Gs(s) - transfer function of the sensor (Laplace domain)
Kc - proportionality constant
Kp - process gain, the ratio of final steady state value to the initial steady state value
MV(s) - manipulated variable (Laplace domain)
s - Laplace domain variable
SP(s), SP(t) - set point (Laplace domain, time domain)
t1 - time at which the output reaches 28% of the final steady state value
t2 - time at which the output reaches 63% of the final steady state value
X(s) - input function (Laplace domain)
Y(s) - output function (Laplace domain)
θ - dead time of the process
τi - integral time
τd - derivative time
τp - time constant of the process;
ξ - damping coefficient
121
REFERENCES
ASAE Standards. 2000a. Moisture Measurement – Peanuts. ASAE S410.1 DEC97. ASAE,
2950 Niles Road, St. Joseph, MI 49085-9659 USA
Boldor, D, Sanders, T.H., Swartzel, K.R., Farkas, B.E., and Simunovic, J. 2003. Thermal
profiles and moisture loss during continuous microwave drying of peanuts. In Automated
Temperature Control of the Continuous Peanut Drying Process Using Microwave
Technology. Ph.D. Thesis. North Carolina State University. Raleigh, NC
Ciancone, R., and Marlin, T. 1992. Tune controllers to meet plant objectives. Control, 5:5057.
Coronel, P., Simunovic, J., and Sandeep K.P. 2003. Temperature profiles within milk after
heating in a continuous flow tubular microwave system operating at 915 MHz. Accepted
for publication in Journal of Food Science, May 13th, 2003.
Davidson, V.J., Brown, R.B., and Landman, J.J. 1999. Fuzzy control system for peanut
roasting. J Food Eng., 41:141-146.
Decareau. 1985. Microwave in the food processing industry. Academic Press, Inc., New
York, NY.
Goedeken, D.L., Tong, C.H., and Lentz, R.R. 1991. Design and Calibration of a Continuous
Temperature Measurement System in a Microwave Cavity by Infrared Imaging. J. Food
Proc Preservation, 15:331-337.
Katz, T.A. 2002. The effect of microwave energy on roast quality of microwave blanched
peanuts. Masters thesis. North Carolina State University, Raleigh, NC.
Landman, J.J., Davidson, V.J., Brown, R.B., Hayward, G.L., and Otten, L. 1994. Modelling
of a continuous peanut roasting process. In Automatic Control of Food and Biological
Processes. (eds) Bimbenet J.J., Dumoulin, E., Trystram, G. Elsevier B.V. Oxford, UK. p:
207-214.
Lopez, A., Murrill, P., and Smith, C. 1969. Tuning PI and PID digital controllers. Instr. And
Contr. Systems, 42:89-95.
Luyben, W.L. 1990. Process modeling, simulation, and control for chemical engineers. 2nd
ed. McGraw-Hill Publishing Co. New York, NY.
Marlin, T.E. 2000. Process control. Designing processes and control systems for dynamic
performance. 2nd ed. McGraw-Hill Publishing Co., Boston, MA.
McFarlane, I. 1995. Automatic control of food manufacturing processes, 2nd ed. Chapman &
Hall, Glasgow, UK.
122
Metaxa, A.C. and Meredith, R.J. 1983. Industrial Microwave Heating. Peter Peregrinus Ltd.,
London, UK.
Mittal, G. S.1996. Computerized control systems in the food industry. Marcel Dekker Inc.
New York, NY.
Mullin, J., and Bows, J. 1993. Temperature Measurement During Microwave Cooking. Food
Additives and Contaminants, 10(6):663-672.
Ramaswamy, H., van de Voort, F.R., Raghavan, G.S.V., Lightfoot, D., and Timbers, G.
1991. Feedback Temperature Control System for Microwave Ovens Using a Shielded
Thermocouple. J Food Sci., 56(2):550-555
Rausch, T.D. 2002. Effect of microwave energy on blanchability and shelf-life of peanuts.
Masters thesis. North Carolina State University, Raleigh, NC.
Sanchez, I., Banga, J.R., and Alonso, A.A. 2000. Temperature Control in Microwave
Combination Ovens. J Food Eng., 46:21-29.
Schlessinger, M. 1995. Infrared technology fundamentals, 2nd ed. Marcel Dekker, Inc. New
York, NY.
Ziegler, J., and Nichols, N. 1942. Optimum settings for automatic controllers. Trans. ASME,
64:759-768.
123
Table 3.1. Infrared thermocouples locations, grouping and relationship between internal and
surface temperature for Runner type peanuts at 33% initial mc (Boldor et al., 2003).
Group
Sensor
A
Sensor 1
Sensor 2
Sensor 3
Sensor 4
Sensor 5
Sensor 6
Sensor 7
Sensor 8
Sensor 9
Sensor 10
Sensor 11
Sensor 12
Sensor 13
Sensor 14
Sensor 15
Sensor 16
B
C
D
E
F
Location
(inch)
18.75
21.75
38.75
41.75
44.75
65.75
68.75
71.75
83.75
86.75
89.75
98.75
101.75
104.75
113.75
116.75
Location
(m)
0.476
0.552
0.984
1.060
1.136
1.670
1.746
1.822
2.127
2.203
2.279
2.508
2.584
2.660
2.889
2.965
Equation
r2
y = 1.77x - 12.38
y = 1.81x - 13.52
y = 2.01x - 17.44
y = 2.02x - 17.60
y = 2.02x - 18.09
y = 2.13x - 21.11
y = 2.09x - 20.74
y = 2.15x - 22.02
y = 2.02x - 18.89
y = 1.88x - 15.38
y = 1.94x - 16.41
y = 1.77x - 12.60
y = 1.87x - 14.31
y = 1.90x - 15.32
y = 1.82x - 13.45
y = 1.69x - 9.59
0.993
0.990
0.972
0.971
0.967
0.959
0.958
0.956
0.949
0.953
0.950
0.947
0.941
0.940
0.933
0.933
Table 3.2. Process parameters for Virginia and Runner type peanuts at 3 initial mc.
mc%
44
26
22
Group
A
6.292
6.572
6.277
Virginia
Group
Group
B
C
5.642
4.287
6.016
4.537
5.639
4.288
Group
D
4.011
3.631
4.011
τp
44
26
22
0.288
0.325
0.288
0.688
1
0.688
1.4
1.5
1.4
θ
44
26
22
-0.038
0.042
-0.038
-0.087
-0.058
-0.087
-0.083
0.567
-0.083
Kp
mc%
52
36
33
Group
A
4.771
4.718
4.824
Runners
Group
Group
B
C
4.478
3.222
4.580
3.362
5.101
4.096
Group
D
2.821
3.173
3.891
2.325
1.475
2.388
52
36
33
0.45
0.575
0.513
0.865
1.05
1.225
1.6
1.388
3.988
1.613
1.5
1.563
-0.275
1.433
-0.337
52
36
33
0.075
-0.025
0.038
0.612
0.35
0.325
1.117
1.188
1.354
2.013
2.017
2.213
124
Table 3.3. Initial tuning parameters for Virginia and Runner type peanuts at 3 initial mc.
Virginia
Group Group
B
C
0.195
0.257
0.183
0.282
0.195
0.257
Group
D
0.274
0.226
0.274
Kc
44%
26%
22%
Group
A
0.175
0.178
0.175
τi
44%
26%
22%
0.058
0.084
0.058
0.138
0.217
0.138
0.303
1.219
0.303
τd
44%
26%
22%
0
0.009
0
0
0
0
0
0.090
0
Runners
Group Group
B
C
0.219
0.304
0.317
0.262
0.339
0.347
Group
D
0.246
0.203
0.160
Kc
52%
36%
33%
Group
A
0.293
0.233
0.228
0.472
2.042
0.472
τi
52%
36%
33%
0.121
0.127
0.127
1.060
0.665
0.432
1.951
1.823
2.644
2.483
2.384
2.544
0
0.284
0
τd
52%
36%
33%
0.005
0
0
0.114
0.053
0.043
0.211
0.232
0.206
0.399
0.401
0.442
Table 3.4. Initial and optimum tuning parameters and time to get to the set point for Runner
type peanuts at 33% initial mc.
Kc
τi
Time (sec)
Initial
0.228
0.127
121.5
Optimum
1.75
1.02
33
125
FIGURE CAPTIONS
Figure 3.1
Schematic of the microwave drying system (top) and infrared thermocouple locations along
the waveguide (bottom).
Figure 3.2
Feedback control loop.
Figure 3.3
First derivative of the internal temperature with respect to distance in the microwave tunnel
for Runner type peanuts at 2 kW and 4 initial mc.
Figure 3.4
Step response of the 16 infrared thermocouples for Runner type peanuts at 52% initial mc.
Figure 3.5
Step response of the six groups of infrared thermocouples for Runner type peanuts at 33%
initial mc.
Figure 3.6
Step response of the six groups of infrared thermocouples for Runner type peanuts at 36%
initial mc.
Figure 3.7
Step response of the six groups of infrared thermocouples for Runner type peanuts at 52%
initial mc.
Figure 3.8
Step response of the six groups of infrared thermocouples for Virginia type peanuts at 22%
initial mc.
Figure 3.9
Step response of the six groups of infrared thermocouples for Virginia type peanuts at 26%
initial mc.
Figure 3.10
Step response of the six groups of infrared thermocouples for Virginia type peanuts at 44%
initial mc.
Figure 3.11
Diagram of the Labview simulation program
Figure 3.12
Simulation result for initial tuning parameters.
Figure 3.13
Simulation result for optimum tuning parameters.
126
Infrared
thermocouples
F
Infrared thermocouple groups
E
D
C
B
A
Microwaves
Peanuts
vz
EXIT
ENTRANCE
Air flow
Figure 3.1. Schematic of the microwave drying system (top) and infrared thermocouple
locations along the waveguide (bottom).
Final control
element
GFCE(s)
MV(s)
CV(s)
Process
Gp(s)
Sensor
Gs(s)
Control element
Gc(s)
−
E(s)
CVm(s
)
+
SP(s)
Figure 3.2. Feedback control loop.
127
100
80
dT/dz (°C/m)
60
40
20
0
0
0.5
1
1.5
2
2.5
3
3.5
-20
Distance (m)
11% mc
14% mc
21% mc
33% mc
Figure 3.3. First derivative of the internal temperature with respect to distance in the
microwave tunnel for Runner type peanuts at 2 kW and 4 initial mc.
36
7
34
6
32
5
30
4
28
3
26
2
24
1
22
20
-200
-100
0
100
200
0
400
300
Time (sec)
T1
T2
T3
T4
T5
T6
T7
T8
T10
T11
T12
T13
T14
T15
T16
P
T9
Figure 3.4. Step response of the 16 infrared thermocouples for Runner type peanuts at 52%
initial mc.
128
38
8
36
7
34
Temperature (°C)
32
5
30
4
28
3
26
2
24
1
22
20
-200
-100
Power level (kW)
6
0
0
100
200
300
400
Time (sec)
Group A
Group B
Group C
Group D
Group E
Group F
P ower
Figure 3.5. Step response of the six groups of infrared thermocouples for Runner type
peanuts at 33% initial mc.
40
8
38
7
36
Temperature (°C)
32
5
30
4
28
3
26
2
24
1
22
20
-200
-100
Power level (kW)
6
34
0
0
100
200
300
400
Time (sec)
Group A
Group B
Group C
Group D
Group E
Group F
P ower
Figure 3.6. Step response of the six groups of infrared thermocouples for Runner type
peanuts at 36% initial mc.
129
8
34
7
32
6
30
5
28
4
26
3
24
2
22
1
20
-200
-100
Power level (kW)
Temperature (°C)
36
0
0
100
200
300
400
Time (sec)
Group A
Group B
Group C
Group D
Group E
Group F
P ower
Figure 3.7. Step response of the six groups of infrared thermocouples for Runner type
peanuts at 52% initial mc.
50
8
7
45
Temperature (°C)
40
5
35
4
3
30
Power level (kW)
6
2
25
1
20
-200
-100
0
0
100
200
300
400
Time (sec)
Group A
Group B
Group C
Group D
Group E
Group F
P ower
Figure 3.8. Step response of the six groups of infrared thermocouples for Virginia type
peanuts at 22% initial mc.
130
50
8
7
45
Temperature (°C)
40
5
35
4
3
30
Power level (kW)
6
2
25
1
20
-200
-100
0
0
100
200
300
400
Time (sec)
Group A
Group B
Group C
Group D
Group E
Group F
P ower
Figure 3.9. Step response of the six groups of infrared thermocouples for Virginia type
peanuts at 26% initial mc.
50
8
7
45
Temperature (°C)
40
5
35
4
3
30
Power level (kW)
6
2
25
1
20
-200
-100
0
0
100
200
300
400
Time (sec)
Group A
Group B
Group C
Group D
Group E
Group F
P ower
Figure 3.10. Step response of the six groups of infrared thermocouples for Virginia type
peanuts at 44% initial mc.
131
Figure 3.11. Diagram of the Labview simulation program
132
PV
SP
PID out
Figure 3.12. Simulation result for initial tuning parameters.
SP
PV
PID out
Figure 3.13. Simulation result for optimum tuning parameters.
133
PROJECT SUMMARY
Peanut dielectric properties were determined using methods previously applied to
wheat, corn and other agricultural commodities. Dielectric theory mixture equations were
found to provide good estimates of the dielectric loss and the dielectric constant as a function
density, and they proved to be very useful in determining the dielectric properties of bulk
peanuts in the microwave region of the electromagnetic spectrum. Data for dielectric
properties of peanut pods and kernels was provided for a range of moisture contents and
temperatures at microwave frequencies used in food processing (915 and 2450 MHz). The
dependence on temperature was found to be more significant at lower moisture contents. At
higher moisture contents, the significance of temperature effects on ε' and ε'' was reduced by
the high dependence on moisture content of dielectric properties. The dielectric properties of
peanuts obtained were similar to those presented in literature (Nelson, 1973), with some
variation due to differences in moisture contents and microwave frequency.
The dielectric properties of peanuts were afterward used to estimate internal
temperature and moisture distribution of farmer stock peanuts undergoing drying in a
continuous microwave applicator. The estimations were performed using transport
phenomena equations previously developed for microwave drying in multimode cavities. The
equations were successfully adapted to account for the unique distribution of the electric field
in a continuous traveling wave microwave applicator. The experimental results confirmed the
theoretical predictions that the temperature profiles were determined only by the power level
at the same moisture content and only by the moisture content at the same power level.
134
At the same moisture contents, the maximum temperatures and maximum rates of
temperature increase occurred in the same time at the same location in the microwave
applicator at all power levels tested. The negligible effect of temperature on the dielectric
properties of the farmer stock peanuts confirmed previously performed measurements. At the
same power level, the maximum temperatures were the same for all moisture contents tested,
but the rate at which that maximum was reached increased with the increasing moisture
contents. This result confirms the dependence of the dielectric loss and the attenuation
constant α on the moisture content of the peanuts.
The measured moisture losses during microwave drying were also in line with
theoretical estimations. The leveling effect of microwaves on moisture content was
confirmed through measurements, and the total moisture reduction in consecutive passes at
the same power level was determined.
A very good correlation was determined between the surface temperatures measured
using infrared technology and the internal temperatures measured using fiber optic probes.
These results were used to create an automated temperature control mechanism for the
continuous microwave drying process. Process reaction curves were determined using
surface temperature as the controlled variable and microwave power level as the manipulated
variable. Process parameters determined using process reaction curves were used to estimate
initial tuning parameters of a PI feedback control loop that maintained the surface
temperature at the desired level. Computer simulation was successfully implemented to
determine the optimum tuning parameters. The results of the simulations showed good
behavior of the system without overshooting of the controlled variable (temperature).
135
FUTURE RESEARCH
The mathematical model developed in this study for temperature distribution during
continuous microwave drying should be improved upon by integrating the convective,
radiant and evaporative cooling effects into the transport equations. Dielectric properties of
peanuts at more moisture contents need to be evaluated to help in determining a complete
heat and mass transfer model for peanut drying. Also, more data on moisture content of
peanuts while in the applicator is required to develop a viable model for microwave drying
kinetics. The models developed in this study should be tested on different materials and in
different conditions, such as higher air flow temperatures and different belt speeds.
The difference in the rate of heating and in the location of the maximum temperatures
at different initial moisture contents determined in this study should be used in combination
with infrared imaging to determine the initial moisture content of peanuts entering the
applicator, and subsequently the number of passes through similar systems to reach a desired
final moisture content. This goal can be achieved through a feed forward/feedback control
mechanism that can be coupled with data provided by various on-line moisture sensors. This
will create a comprehensive control system for the entire microwave drying process. More
advanced process control methods such as fuzzy logic should be evaluated and compared
with the performance of the feedback control loop described in this study.
136
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