DEVELOPMENT OF AN OHMIC THAWING APPARATUS FOR ACCURATE
MEASUREMENT OF ELECTRICAL RESISTANCE
By
RANDY ALLEN CLEMENTS
A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
2006
Copyright 2006
by
Randy Allen Clements
To my wife Tammy and my sons Kyle and Austin
ACKNOWLEDGMENTS
Many individuals that have made this work possible. There are more than can be
reasonably listed, but I would like to extend special thanks to Dr. Murat O. Balaban for his
encouragement, support and guidance in completing this work. I am indebted to my
graduate committee for their patience and persistence. I also wish to thank Dr. Randolf
Hook for his friendship, help and engaging conversations on this research. Completion of
this work would not have been possible without the support of my family throughout the
process.
iv
TABLE OF CONTENTS
page
ACKNOWLEDGMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv
LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii
LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix
LIST OF OBJECTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi
ABSTRACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii
CHAPTER
1
INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
2
LITERATURE REVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
Traditional Heating . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Volumetric Heating . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Microwave . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Ohmic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Historical Overview of Ohmic Heating . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Ohmic Thawing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3
3
4
4
5
5
9
MATERIALS AND METHODS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
Physical Test Sample . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Gel Type . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Sample Cell . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Cylindrical housing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Interior insulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Exterior insulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Electrodes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
End caps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Probes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Cell Holder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Temperature Control Chamber . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Power Supply . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
v
13
13
14
14
15
16
16
17
18
20
21
22
Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Manual control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Automated control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Alternative direct current . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Leads and plugs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Data Collection Hardware and Software . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Data Acquisition Card . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Interfacing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Backplane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Signal Conditioning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Signal Conditioning Housing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Data Logging Digital Multimeter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Software . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Data collection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Data visualization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Equipment Cart . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Apparatus Construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Probe Construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Assembly . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Sample Cell Construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Assembly . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Sample Cell Holder Construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Assembly . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Signal Conditioning Housing Construction . . . . . . . . . . . . . . . . . . . . . . . . . .
Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Assembly . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Apparatus Wiring . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Meters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Backplane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Screw terminal panel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Experimental Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Data Collection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Laptop computer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Data logging digital multimeter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Laboratory notebook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Temperature Probe Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Gel Preparation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Gel Density Determination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Freezing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Environment Characterization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Continuous Running . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
vi
22
23
23
23
24
24
24
24
25
25
26
27
28
28
29
29
31
31
31
32
34
34
36
39
39
39
41
41
41
42
43
46
47
48
49
50
50
51
52
52
54
55
56
58
58
Cycling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Thermal Damping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Automatic Power Control Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Relay set up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Power control validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Resistance Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Unfrozen sample . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Frozen sample . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Ohmic Thawing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4
59
59
60
60
61
62
62
64
66
RESULTS AND DISCUSSION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
Data Collection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
Temperature Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
Theoretical . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
Experimental . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
Experimental Gel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
Total Mass Percent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
Density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
Freezing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
Environmental Characterization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
Automatic Power Control Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
Resistance Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
Unfrozen Gel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
Frozen Gel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
Combined Temperature Ranges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
Ohmic Thawing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
Error Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
Temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
Resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
5
CONCLUSIONS AND RECOMMENDATIONS . . . . . . . . . . . . . . . . . . . . . . . . 117
APPENDIX
A
ALTERNATE NEUMANN’S SOLUTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
B
TEMPERATURE ERROR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
C
RESISTIVITY ERROR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
BIOGRAPHICAL SKETCH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
vii
LIST OF TABLES
Table
page
4-1. Calibration Offset Values. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
4-2. Percent of Total Mass of Gelatin in Gel. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
4-3. Gel Density. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
viii
LIST OF FIGURES
Figures
page
3-1. Cylindrical Housing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
3-2. Sketch of PVC Cell. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
3-3. Electrode Sketch and Picture. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
3-4. Probe Sketch. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3-5. Probe Assembly Bench Rail. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3-6. Sample Cell Holder. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3-7. Housing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3-8. Box Arrangement. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3-9. Shell With Ports. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
3-10. Sample Holder Picture Front and Side Views. . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
3-11. Detailed Sample Power Wiring. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
3-12. Probe Positions and Naming Conventions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
3-13. Relays. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
3-14. Additional Fiberglass Insulation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
4-1. Calibration Setup Features. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
4-2. Probe Calibration Data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
4-3. Calibration Warming Data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
4-4. Calibration Noise. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
ix
4-5. Noise Under High Voltage. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
4-6. Temperature Cycling. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
4-7. Cycling and Adjacent Probe Temperature Differences. . . . . . . . . . . . . . . . . . . . . . 87
4-8. Sample and Environmental Warming. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
4-9. Unfrozen Gel Temperature, Voltage and Current Plots. . . . . . . . . . . . . . . . . . . . . 90
4-10. Unfrozen Gel Temperature, Voltage and Current Plots. . . . . . . . . . . . . . . . . . . . 91
4-11. Unfrozen Gel Resistance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
4-12. Unfrozen Gel Resistivity and Maximum Temperature Difference. . . . . . . . . . . . . 93
4-13. Unfrozen Gel Resistivity Before and After Freezing. . . . . . . . . . . . . . . . . . . . . . . 94
4-14. Unfrozen Resistivity with Cubic Polynomial Fit. . . . . . . . . . . . . . . . . . . . . . . . . 95
4-15. Frozen Gel Temperature, Voltage and Current Plots. . . . . . . . . . . . . . . . . . . . . . 97
4-16. Frozen Gels Resistance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
4-17. Frozen Resistivity and Maximum Temperature Difference. . . . . . . . . . . . . . . . . . 99
4-18. Frozen Resistivity with Cubic Polynomial Fit. . . . . . . . . . . . . . . . . . . . . . . . . . . 100
4-19. Unfrozen and Frozen Resistivity Cubic Fits. . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
4-20. Ohmic Thawing Voltage and Current Data. . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
4-21. Ohmic Temperature Data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
4-22. Ohmic Temperature and Current Data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
4-23. Ohmic Apparent Resistivity and Maximum Temperature Difference. . . . . . . . . . 109
4-24. Power Applied. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
4-25. Frozen Resistivity Error. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
4-26. Frozen Resistivity Error and Maximum Temperature Difference. . . . . . . . . . . . 114
4-27. Unfrozen Resistivity Error. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
x
LIST OF OBJECTS
Objects
page
3-1. PVC_Cell.jpg . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
3-2. SampleCell.jpg . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
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xii
Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy
DEVELOPMENT OF AN OHMIC THAWING APPARATUS FOR ACCURATE
MEASUREMENT OF ELECTRICAL RESISTANCE
By
Randy Allen Clements
May 2006
Chair: Murat O. Balaban
Department: Agricultural and Biological Engineering
Heating occurs when an electrical current is passed through an object. The
amount of heat generated in the object is dependent on the electrical resistance of the
object. This form of heating is commonly referred to as ohmic heating. The application of
this heat to a frozen object to change the material phase from frozen to unfrozen is ohmic
thawing. The electrical resistance of a food is heavily influenced by temperature. Foods
undergoing thawing commonly exhibit two orders of magnitude decrease in their
resistance. Accurate knowledge of the electrical resistance is vital to practical ohmic
applications in food processing.
This research presents the development of an apparatus for measuring the
electrical resistance of a food item in both its frozen and unfrozen states. A model food
substance was used to illustrate the capabilities of the apparatus. The model food
xiii
substance used in this research was a gelatin gel. The electrical resistance of the gel was
measured in both the frozen and unfrozen state. The resistance data for the gel were
converted to resistivity data. The resistivity data for the frozen gel were fitted with a
cubic polynomial (y = -35.9628 x3 + 162.3497 x2 - 526.1101 x + 67.9648), where y was
the resistivity in ohm-meters and x was the temperature in degrees Celsius, while the
frozen resistivity data were fitted with (y = -0.0004 x3 + 0.0270 x2 - 1.0960 x + 31.3939).
The fits generated R2 values of 0.9977 and 0.9953, respectively. The errors associated
with the data and the fits were discussed and presented. It was shown that temperature
measurement error was an important aspect in the accuracy of the resistivity data
calculated.
This research produced a useful apparatus for measuring an important food
property in the application of ohmic thawing. The research also provided new data in an
area where very little published data exists. This data will prove useful to the food
engineering community for both future comparative and modeling purposes in the further
development of ohmic heating technology.
xiv
CHAPTER 1
INTRODUCTION
Low temperature storage of food materials is a common method of food
preservation. The low temperatures used are often in the frozen range of a food product.
These temperatures reduce the activity of microorganisms and enzymes (Baird and
Gressgott 1978). As a result the freezing of foods has been extensively studied. Cleland
and Earle (1984) reported that the published work done with just freezing time prediction
methods has hundreds of contributors. Prediction of freezing phenomenon is important
because the design of commercial processes without this knowledge leaves only laboratory
and pilot scale experiments to make design decisions. These are not eliminated with
predictive abilities, but can be reduced for to a minimum for cost savings (Heldman 1983)
and optimization of process design.
For the purpose of modeling freezing, Singh (1994) reported that there are several
key properties of foods that must be taken into consideration. He listed among these key
properties: density, thermal conductivity, enthalpy, specific heat, and thermal diffusivity.
Singh also reported that there have been several major reviews of reported data on
published literature for some of these properties, as well as a computerized data base for
the published data that he developed in 1993. All of the work on freezing has helped
commercial freezing become a relatively efficient and reasonably understood process for
the food industry.
1
2
Hendricks and others (1988) reported that in the past freezing has been more
important than thawing, but due to greater quantities of frozen food receiving further
processing by manufacturers, thawing was gaining more industrial interest. Thawing
operations are not simply inverse freezing operations. Thawing of frozen foods brings
several unique problems that freezing does not exhibit. It also has physical methods that
have no freezing corollary. This research examined one of those methods.
Ohmic thawing uses the electrical resistance of a frozen food product to
volumetrically generate the heat required for thawing within the food product itself, as an
electrical current is passed through the food product. The electrical resistance of the
frozen food product is additional knowledge not required by a freezing process. A direct
result of this included very little published data on a key property needed for predictive
modeling of ohmic thawing. This research developed an experimental apparatus capable
of measuring this key property for a gel in both the frozen and unfrozen states. The
apparatus developed was also capable of performing ohmic thawing. In this second mode
it can gather data simultaneously for time, temperature and resistance that would be useful
for model verification of predictive methods to be developed for ohmic thawing.
CHAPTER 2
LITERATURE REVIEW
Traditional Heating
Traditional methods of heating food products involve applying thermal energy to
the surface of the product. The thermal energy is delivered to the surface by direct
exposure to a thermally radiative source or by direct contact with a fluid, gas or solid of
higher temperature. These heat delivery methods account for radiative, convective and
conductive boundary conditions at the food surface. Once the energy is applied the
surface temperature will rise and heat will begin to flow into the product. The energy
transfer now will be governed by thermal conduction. The heat flow can be described by
the following differential equation:
(1-1)
In this equation k is thermal conductivity; T is temperature; r is the position vector; t is
time, D is density; Cp is specific heat. This equation indicates the limits of the rate of
temperature change in the food product. The thermal conductivity, density, and specific
heat in equation (1-1) are properties inherent to a given food product. One method of
inducing high rates of temperature change is by using very high temperatures at the
surface. Surface temperatures for food products are limited by thermal sensitivity foods
have in their structural and organoleptic properties. Another method is to reduce the path
for conduction heat transfer. This can be achieved by forcing the food product to have a
shape that presents a very short conduction path. This can be a viable option for certain
liquid food products, but generally not for solid food products.
3
4
Volumetric Heating
Volumetric heating does not suffer the same limitations as traditional heating
methods. With volumetric heating the heat source is internal to the food product. The
entire volume of the food is stimulated by an external energy source to produce heat
internally. The external energy can be delivered by electromagnetic waves. These include
high frequency waves, microwaves, and radio waves. These electromagnetic waves would
also include frequencies at which electricity is commercially transmitted and even direct
electrical current.
Microwave
Microwave heating has received the most study and application in relation to
heating food products. Microwave heating requires no direct contact with the food
product, but does require the food product to be enclosed so the microwaves are
contained for human safety. The use of microwaves is limited by how they are absorbed
by the food material. The depth of penetration is limited for microwaves, and water can
preferentially absorb them. The preferential absorption by water has been thought to be a
major cause for localized overheating (Li and Sun, 2002). Localized overheating is
referred to as runaway heating. It is called runaway heating because it has a cascading
effect. The absorption properties tend to increase as the temperature rises, and as a result
even more energy is absorbed by the localized area. This then leads to a greater
temperature rise and absorption properties becoming even more favorable, driving the
local heating process out of control to food damaging temperatures. Control of this
phenomenon when driven by microwaves is very difficult.
5
Ohmic
Ohmic heating, unlike microwave, requires some type of direct contact with the
food product. Ohmic heating uses electrical energy to drive the volumetric heating
process. In ohmic heating the food product acts as a resistor in an electrical circuit. A
voltage is applied across the food product and a current flows. This can be described by
Ohm’s law. Equation 1-2 lists Ohm’s law.
(1-2)
In this equation V is voltage; I is current; and R is electrical resistance. True volumetric
heating occurs as the current flows through the food product. Since nearly all the energy
goes into the food as heat from this process, ohmic heating is more efficient than
microwave ( de Alwis and Fryer, 1990c; Li and Sun, 2002).
Historical Overview of Ohmic Heating
The application of ohmic heating to food dates back more than 100 years. One of
the earliest uses cited in the literature was credited to Fowler in 1882 for a device that held
meat or fish in a box with a salt solution containing electrodes (de Alwis and Fryer, 1990c;
Halden and others, 1990). Other food products also saw early work according to de
Alwis and Fryer (1990c), such as liquids in 1897, in can sterilization in 1900 and milk
pasteurization in 1914. The authors also mentioned other early firsts reported in the
literature such as blanching of potatoes in 1951 by Schade. This was the same year that
the authors cited Tanaka and Tanaka as having shared work on attempting the thawing of
frozen meat chunks with little success. Ohmic heating saw interest in the early half of the
20th century, but only saw one brief commercial success with milk pasteurization. In the
6
opinion of de Alwis and Fryer (1990c) the problems were primarily related to lack of
suitable electrode materials and control systems.
Interest in possible commercial applications of ohmic heating continued into the
1970's. The Ukranian Meat and Dairy Industries Institute was reported in 1972 to have
developed an experimental aseptic line for manufacturing skinless frankfurters using a
combined ohmic and conventional process by Ruchkovski and others, according to de
Alwis and Fryer (1990c). A commercial blanching process required by potatoes before
deep frying was also reported by Electro-food AB and called the OSCO process (de Alwis
and Fryer, 1990c). Successful study of blanching corn on the cob was reported by
Mizrahi and others (1975). He reported the complete inactivation of peroxidase in only 3
minutes with an ohmic process, while the conventional process of using boiling water
would take 17 minutes.
Ohmic heating used for baking was reported to reduce process times by about
60% when compared to conventional methods in 1985 and 1986. These reports were
credited to Danilesko by de Alwis and Fryer (1990c). The late 1980's marked the
beginning of a widespread interest in investigating ohmic heating. The primary catalyst for
this would be work done by the UK Electricity Council Research Centre. A process was
developed for using ohmic heating in continuous sterilization of particulate foods. This
process was licensed to APV Baker who developed it into a commercial system (de Alwis
and Fryer, 1990c).
Following this commercial process development, there has been a great deal of
research into ohmic heating. The bulk of the research has been centered around the
heating of particulate foods. The research has been carried out in several important ways.
7
The process has been experimentally modeled and examined in a static ohmic cell where
the particulate is stationary. Early work in this area included that of de Alwis and Fryer
(1990a, 1990b) and Zhang and Fryer (1993) at the University of Cambridge in the United
Kingdom. Other early work included that of Sastry and Palaniappan (1992a, 1992b) at
the Ohio State University. The usefulness of studying a static cell related to the
continuous process was further illustrated by later works of Khalaf and Sastry (1996).
This area of research continued through the 1990's as illustrated with work by Davies and
others (1999), as well as work by Fu and Hsieh (1999). The most recent published work
related to using static cells have been by Ye and others (2003) and Zareifard and others
(2003).
The work with static cells relating to processing food particulate has been
accompanied by work with continuous flow. Early research was undertaken by Sastry
(1992) as well as Zhang and Fryer (1994). The work continued through the 1990's as
illustrated with further work by Khalaf and Sastry (1996). The complexities of flow
caused many problems with the early works and many simplifying assumptions typically
had to be undertaken. The gains in understanding from early work and the work done
with static cells, when coupled with the steep decline in computing cost, has led to greater
research interest in the continuous flow process. Work since 2000 includes that of
Benabderrahmane and Pain (2000), Eliot-Godéreaux and others (2001a, 2001b), Tucker
and others (2002), and Ayadi and others (2004).
The static and continuous flow research inspired by the APV Baker process also
created other areas of ohmic research. Ohmic heating of a particle in a liquid creates an
enhanced diffusion effect from the particle to the liquid. Some early published work on
8
this was by Stapley and others (1995) and Imai and others (1995). Further research in the
area would consider how this phenomenon affects hot air drying rates and juice yields of
certain foods (Lima and Sastry, 1999). Further work in drying rates and extraction yields
has continued as reported by Wang and Sastry (2002), Zhong and Lima (2003), and
Lakkakula and others (2004). These ohmic heating applications have no thermal analog,
since the effects are due to the electric field applied and not only the heat generated.
The most important food property when applying ohmic heating is the electrical
resistance of the food product. Before the commercialization of the APV Baker process
little data existed on the electrical resistance values of foods or the inverse value of
conductance. The research related to static and continuous cells would give rise to
research specifically to determine electrical conductivity values for certain food products.
The first published work in the area is Halden and others (1990), which was followed by
Palaniappan and Sastry (1991a, 1991b). Later work would be done with pacific whiting
surimi paste (Yongsawatdigul and others, 1995) and starch gels (Wang and Sastry, 1997).
Work in this area has continued as reported by Fu and Lin (2003) who also has made
measurements on a variety of meats, vegetables, and fruits. Castro and others (2004)
reported on conductivity values for strawberry products, while Shirsat and others (2004)
reported on conductivity values for cuts of pork. The most recent reporting of
conductivity values were related to tylose (sodium carboxy methyl cellulose), which is
used as a food analog for modeling lean beef (Icier and Ilicali, 2005).
Ohmic heating can be applied to thawing of food products. There has been very
little research related to ohmic thawing (Li and Sun, 2002). According to de Alwis and
Fryer (1990c), Rao and Mathen in 1974 reported using ohmic thawing for frozen blocks
9
of prawns for quick quality checks. Segars and Kasalis were reported to have used ohmic
thawing and heating of precooked frozen casserole items (Naveh and others, 1983; de
Alwis and Fryer, 1990c). Naveh and others (1983) proposed a method applying ohmic
thawing to frozen meat chunks. The method did not have direct contact with the meat but
instead used a carrier fluid that contacted both the meat and the electrodes. Similar
research was credited to Yun and others in 1998 by Li and Sun (2002).
At the University of Florida in 1993 preliminary work on the technical and
economic feasibility of applying ohmic thawing to frozen shrimp was done by Henderson
(1993). The positive findings led to the further work with frozen shrimp blocks. The
electrical conductivity of frozen shrimp and flounder were reported by Luzuriaga and
Balaban (1996). These values were unique because of how little data has been published
on frozen foods. A prototype automated ohmic thawing unit was designed and tested in
1994 (Roberts, 1994; Roberts and others, 1998). The work successfully demonstrated the
technology of thawing frozen shrimp blocks with ohmic heating and automated control.
Ohmic Thawing
Thawing of food products refers to the specific change of state of the water in the
product from a frozen state to unfrozen state. The heating required is generally separated
into sensible and latent heat. The sensible heat is the heat actually associated with
temperature change, and the latent heat is associated with only the change of phase. The
latent heat of food products is high because of their high water content.
Thawing of food products presents several problems. The thermal conductivity of
food products is dependent on temperature. Normally their thermal conductivity is high
when frozen. This is not surprising since most food products have a high water content,
10
and water has a lower thermal conductivity than ice. Everington (1971) reported that
regarding the thermal conductivity for fish muscle the frozen conductivity was three times
that of the unfrozen conductivity. This means that a food product that undergoes
conventional thawing, where heat is applied to the surface, will develop what is essentially
a layer of insulation. The heat required to thaw the center of the product must pass
through the insulating or thawed layer before reaching an unthawed inner layer of product.
This causes significant problems in trying to rapidly thaw a food product by conventional
heating methods. This problem is further compounded by the fact the specific heat of a
frozen food product will be lower than the unfrozen product. The unfrozen insulation
layer then will not only conduct heat more slowly, but requires more energy to raise the
temperature in this layer.
Rapid thawing has been of interest because uncontrolled slow thawing can negate
the high quality of a food product achieved by controlled rapid freezing and cold storage
(Everington, 1971; Naveh, 1983; de Alwis and Fryer, 1990c). In order to increase the
heat transfer at the surface of the frozen product, water has been commonly used as a
working fluid to thaw meats, fish, egg as well as other food stuffs (Everington, 1971).
Water can leach soluble constituents from the food product (Jason and Sanders, 1962;
Everington 1971; Roberts, 1998). The water used becomes a waste stream that must be
dealt with often at cost to the processor (Henderson, 1993). Water used in direct contact
with a food product must be potable. This can also be a burden to a processor due to cost
and or limited availability (Roberts, 1998). The water temperature has been commonly in
the range of 18 to 21 °C (65 to 70 °F) (Everington, 1971). This can lead to the exterior of
11
the food product being heated into a range that microbial growth is a problem before the
product can be completely thawed or processed.
Volumetric heating methods offer solutions to thawing problems. Volumetric
heating does not require large amounts of water. It does not raise the surface temperature
of the food product to undesirable levels. This form of heating is more rapid because the
food product’s thermal conductivity is not controlling the thawing rate.
The electrical resistance of the food product is the controlling food property for
ohmic thawing. This property also has a dependence on temperature. It changes greatly
as the food product goes from the frozen to unfrozen state for a food product. Frozen
fish muscle wass reported to have a specific resistance that changes by several orders of
magnitude by Jason in de Alwis and Fryer (1990c). A similar finding is reported for
shrimp (Luzuriaga and Balaban, 1996). The drastic change in this controlling property
leads to runaway heating in a fashion very similar to microwave runaway heating. One
difference with ohmic would be that the runaway heating would not be a phenomenon that
could be supported in a single pocket surrounded by frozen material. It would require a
path of unfrozen material or low resistance material from one conducting electrode to
another.
Electrical resistance of a food product is not typically measured directly. The
resistance is normally calculated from knowledge of the voltage and current. In a simple
circuit that contains only a resistor if the voltage and current are measured the resistance
can be calculated from Ohm’s Law presented earlier. An important property of a resistor
is that its value is mainly determined by its physical dimensions and the resistivity of the
material of which it is composed (Peebles and Giuma, 1991). The resistance measured by
12
any experimental set up would be specific to that experimental set up and the food
product’s physical dimensions. The resistivity has broader application as it can be applied
to find the resistance of the same food product with different dimensions. The resistance
R for a resistor of constant cross sectional area A, length L, and resistivity De is written in
equation 1-3 (Peebles and Giuma, 1991).
(1-3)
It is easy to determine from the equation that if resistance is in ohms, length in meters and
area in meters squared, then resistivity will have units of ohm meter. In an experimental set
up that is measuring both the voltage and current simultaneously, it is also very easy to
calculate the power that is applied. The power will simply be the product of the voltage
and the current.
CHAPTER 3
MATERIALS AND METHODS
This research has been considered in two major areas. The first area was the
physical test sample under consideration, and the second area was related to data collection
from the test sample. Items related to the physical test sample included the sample itself
and objects in direct contact with the sample. This also included anything that was used to
control the physical state of the sample. The second area was inclusive of all data
collection hardware and software used. In addition to the two major areas there was a third
minor area related to the physical mounting and interconnecting of the first two.
Several distinct methods were used in this research. Preliminary methods were
considered to encompass the procedures for generating the materials. These included
construction and assembly techniques for custom materials, as well as overall system design
and assembly. Methods also comprised the operational validations, characteristics and
calibration needed by the experimental apparatus before its use.
The experimental use of the apparatus was also considered a method topic. This
included the actual procedures used in data collection, reduction, and visualization. These
varied according to the purpose of the experiment that was preformed by the apparatus.
Physical Test Sample
Gel Type
The physical test sample considered in this study was a simple food gel.
Specifically, it was a unflavored gelatin gel. The gelatin was manufactured by the Knox®
13
14
Company (Parsippany, NJ), which was a unit of Nabisco Incorporated. Their standard
retail box package of 28 grams (one ounce) subdivided into four individual unhydrated
packages was procured locally. The average density of the hydrated gelatin gel used in the
research was 1.02 g/cm3. The average percent ratio of the unhydrated product to water
added was 6.6 %. In the unfrozen state it was transparent with some slight yellow
coloring. In the frozen state it was only partially translucent.
Sample Cell
The gel during the experiment was contained in a sample cell. It consisted of
several parts. The major component was the rigid polyvinyl chloride (PVC) cylindrical
housing threaded for end caps on both ends. Insulation layers existed on both the interior
and exterior radial surfaces, as well as on both of the electrode exteriors. The electrodes
were also considered part of the sample cell, since they formed the axial boundaries for the
gel. Temperature probes in the sample were likewise considered a part of the cell, since
they were essentially fixed in place once the gel was formed in the sample cell.
Cylindrical housing
This housing (Figure 3-1) consisted of 76.2 mm (3") schedule-40 PVC pipe fittings,
Charlotte Pipe and Foundry Company (Charlotte, NC) part numbers PVC 101 and PVC
105 (http://charlottepipe.com). Both ends were threaded on the interior, with a smooth
walled transition between the threaded areas. The smooth walled transition to the
threading was separated by an interior shoulder. The smooth walled or central region of
the housing had an axial line of 3 holes on each side of a diameter of the housing, that were
equally spaced over that region. This placed the center set at the center of the axial height
of the smooth region with the other two sets halving the remaining half heights. A sketch
of these features can be seen in Figure 3-2.
15
Figure 3-1. Cylindrical Housing.
Object 3-1. PVC_Cell.jpg (2.59 MB).
Interior insulation
The insulation on the radial interior of the cell was PermaSeal™ by Perma “R”
Products Incorporated (Johnson City, TN ). This insulation was a closed cell insulation
normally used in construction for creating a sill seal. It came in a standard 6.35 mm x
139.7 mm x 15.24 m (1/4"x5.5"x50') white roll. It was sized to fit the gel column height of
the smoothed walled portion of the cylindrical housing. A standard utility knife was used
for the sizing. This insulation was resilient to being compressed, due to its closed cell
nature with relatively large air pockets.
16
Figure 3-2. Sketch of PVC Cell.
Object 3-2. SampleCell.jpg (43 KB).
Exterior insulation
The insulation on the radial exterior of the cell was Great Stuff™ by Dow Chemical
Company (Midland, MI). It was an expanding foam sealant sold in a pressurized can.
This insulated the radial exterior in the region of the smooth transition between the
threaded regions of the cylindrical housing. It also sealed the close tolerance passages for
the probes that came in through the radial exterior of the cell.
Electrodes
A circular stainless steel electrode rested on each interior shoulder that separated
the smooth interior from the threaded interior. The electrodes were approximately 3.2 mm
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(1/8") thick. Each had a 10-24 12.7 mm (½") stainless bolt welded to the backside. This
bolt along with two nuts and two washers, formed the electrical input connector for each
electrode. The front side of the electrode which contacted the sample had a surface finish
consistent with random orbital sanding with a fine emery cloth. Figure 3-3 is a sketch of
the electrode and a picture of the gel contacting surface.
Figure 3-3. Electrode Sketch and Picture.
Object 3-3. ElectrodeSketch.jpg (211 KB).
End caps
Three separate materials were used in series to form the end caps for the cylindrical
housing. The first material in direct contact with the electrode was 19 mm (3/4") thick
foamed polystyrene insulation. The next layer was a 3 mm (1/8") thick 3 ply wood disk.
Contacting the disk layer was a standard threaded plug. The plug was filled with the same
insulating material as the interior of the cell. This provided and effective fill for the plug
that allowed the power conductor to pass through this section. The end of the plug was
drilled to allow passage of the electrical connection.
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Probes
The temperature probes were custom made for the experiment. They were
essentially type T thermocouples. The uniqueness of the probes was in the fact that they
were two separate thermocouples bonded together and electrically isolated from one
another. This allowed for two separate temperature measurements to be taken for
essentially one geometric position inside the sample.
The probe has been broken into the following components. The first was a
Omegatite® 200 ceramic insulator (Omega Engineering, Inc., Stamford, CT, model
number TRM-164116-6) that made up the rigid electrically insulating portion. The
insulator was a cylindrical tube shape, and had two round channels that protected and
electrically isolated the thermocouple wires. The diameter of the tube was 1.5 mm (1/16
in.),while the channel diameters were 0.4 mm (1/64 in.). The published approximate
thermal conductivity was 0.712 W/m K (1.333 BTU/hr ft °F).
The second part of the probe was the actual thermocouple junctions. Each junction
consisted of the two thermocouple wires, one a 0.254 mm copper and the other a 0.254
mm constantan (Omega Engineering, Inc. part numbers SPCP-010 and SPCC-010
respectively), wound together and soldered. The solder and wire combination conformed
to the ceramic insulator’s exterior diameter. This acted as an end cap on the ceramic
insulator. A sketch of the probe was made in Figure 3-4.
The third part of the probe was the electrical insulation for the exposed portion of
the thermocouples. The electrical insulation was a QuickTite® super glue by Loctite®
(Avon, OH ). It was a cyanoacrylate type adhesive. Cyanoacrylates have an electrical
resistivity of greater than 1015 Ohm mm, and a dielectric strength of 25 kilovolts per mm.
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Figure 3-4. Probe Sketch.
Object 3-4. Probe.jpg (90 KB)
The insulator being an adhesive allowed it to serve a second role as the bonding agent
between the probe tips or end caps. These probe tips were also bonded to the ceramic
insulator with this material.
The last physical part of the probe was the junctions that connected the transmission
leads. Omega part number SMPW-T miniature connectors were used. The female portion
of the two bladed copper-constantan connectors were used on the probe end of these
junctions. The two piece design of the female portion allowed it to be attached directly to
each end of the probe by clamping over the ceramic insulator portion of the probe.
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The probes were also considered to include their assembly bench. This was custom
made to manufacture the probes. The bench rail was an angled piece of aluminum. Figure
3-5 has a sketch of the assembly bench rail. The bench had an open section in its center
allowing for adhesives to be applied to the thermocouple ends. The rail was fastened by
two screws to a pair of small wood blocks cut at 45° angles. These were the bench
foundations and lifted the rail for center access. Small spring loaded clamps were utilized
to bind the probe portions onto the rail interior corner.
Cell Holder
The test cell had a custom holder to make it easier to be moved, and protected its
thermocouple leads during movement. A diagram of the cell holder can be seen in Figure
3-6. It was constructed of wood. The holder had specific features that assisted in the
experiments. The top handle allowed the holder to be easily gripped when the sample was
being moved from the temperature control chamber. The sides had three holes bored in
them to provide for stress relief to the thermocouples when the sample was being moved.
The short legs were utilized to allow the sample holder to rest on its side, when a gel was
being poured. The large opening between the test cell and the handle allowed the sample
to be clamped during freezing. A 304.8 mm (12") Craftsman C style screw clamp was used
Figure 3-5. Probe Assembly Bench Rail.
Object 3-5. ProbeBench.jpg (37 KB).
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Figure 3-6. Sample Cell Holder.
Object 3-6. SampleHolder.jpg (120 KB).
on the cell for clamping purposes. The clamp was considered a part of the cell holder even
though it was only applied during the freezing phase of the experiments.
Temperature Control Chamber
The temperature control chamber was a small chest type freezer, manufactured by
General Electric (Louisville, KY). Its model number was FCM5DMA WH. It had several
features that were very beneficial to the experimental needs. The first feature was an
adjustable thermostat and included a continuous run mode switch. This allowed the
temperature to be cycled on different ranges or simply be taken to the equipmental limit
and held. The front of the freezer also had a drain portal at the bottom center. This acted
22
as a power lead access point during experimentation. The interior of the freezer was lined
with aluminum. The gasket sealing the top was very flexible and approximately 12.5 mm
(1/2") thick, and 25 mm (1") wide. The flexibility of the gasket allowed for the
thermocouple transmission leads to be routed into the top of the freezer between this
gasket and the lid. The thickness let the freezer maintain its top seal even with the leads in
place.
The chamber also had enough room for thermal dampers. The thermal dampers
were two, one gallon jugs of distilled water. These two gallons when frozen acted as
dampers to rapid temperature changes in the chamber. This allowed for very slow warming
when the freezer was shut off. They also had the added benefit of damping the cycling of
temperature when the freezer is running in a cycling mode.
Power Supply
The primary power supply used was made by STACO Energy Products (Dayton,
OH) type 6020CT-2S. This supply utilized 220 volt AC input to provide variable output
from 0 to 500 volts AC. The power supply for experimental purposes was also considered
to include other facets of providing power to the test cell. These included control of power
through voltage adjustment and current limiting. The leads and plugins required to deliver
the power to the test cell electrodes, as well as, alternative DC power arrangements
possible were other items grouped with the power supply.
Control
Control of applied power to the sample cell had two layers. The first layer was
manually controlled by the operator of the power supply. The second layer was an
automated layer. Both types of control were used any time power was applied to the test
cell.
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Manual control
The first layer was the manual breaker switch to the power supply itself that
controled the 220 volt input to the supply system. The output of the power supply also had
a manual breaker switch. These manual controls were combined to give independent onoff control for both the input to the supply and its variable output voltage. The voltage
output level was set with a manual rotary dial that adjusted the voltage output from 0100% of the supply’s voltage range.
Automated control
The automated control was applied to the current output of the power supply. A
Crompton meter with two optional attachments was the first part of this control. This
meter continuously monitored the current level and cuts it off above a specified range. It
achieved this by controlling the supply voltage to another relay better suited for the high
voltages used in the experiment. This primary relay was a Crydom D4812 by Crydom
Electronics (San Diego, CA).
The automated control also included a separate test instrument constructed to show
that the control worked correctly. This instrument was a simple light fixture wired to be
plug compatible with the system output plug. The light produced by the resistance bulb
gives visual verification that the manual and automated controls were operating correctly.
Alternative direct current
The power set up was flexible. It allowed for an alternative DC source to be
inserted into the ciruit. This source had only manual control of the voltage. The power
supply for the DC source ws a LBK type 3371C by LBK Electronics. This supply could
provide DC voltages up to the 1200 volt range, but was limited to 60 mA output current.
24
Leads and plugs
Several leads and plugs were used in the interconnecting of power. The primary
plugs for carrying current to the test sample were three bladed plugs and receptacles. The
power supply side were all receptacles for safety. The lead to the test cell electrodes had a
compatible male plug on one end and insulated ring tongue terminals on the other. There
was also a special lead that was essentially a double ended male plug. This lead was the
bridge for the AC power to the test leads. This bridge when removed allowed a DC lead to
be inserted into the plug. The DC lead had a compatible male plug on one end and banana
plugs on the other for connecting the DC source.
Data Collection Hardware and Software
To ultimately gather useful information, several different forms of data were
collected. These data types were collected by two separate instruments, each with
supporting hardware and software. These supporting parts assisted in signal routing and
conditioning, as well as data reduction and visualization.
Data Acquisition Card
The data acquisition card used in this investigation was a Keithley Electronics
(Cleveland, Ohio) PCI 3107. This was a 16 bit 16 channel PCI card. It was housed in a
Toshiba docking station V plus model number PA2710U. This docking station was where
the Toshiba Tecra™ 8000, model number PAT80AU laptop connects. The laptop served
as a controlling interface to the data acquisition card, as well as a storage medium for data
collected by the card.
Interfacing
The Keithley card used a 36 pin D style connector to the external signals to be
sampled. A Keithley model CAB-1284-.5 cable interfaced the connector. The other end of
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the cable interfaced with a Keithley model STA36 screw terminal panel. The screw
terminal panel then could be connected to simple wiring that required no special connectors
for interfacing. The wiring connected to the screw terminal was a standard 28 gauge
ribbon wire. The opposite end of the ribbon wire had a 26 pin female connector. This
connector interfaced with the I/O plugs on signal conditioning backplane.
Backplane
The backplane was an Analog Devices Incorporated (ADI) (Norwood, MA) model
5B01 (http://www.analog.com). This backplane was designed to house plug-in signal
conditioning modules. It also was used as an interface for external signal leads. The
backplane had screw terminal inputs on each of its 16 data lines, which served this purpose.
These lines went through an ADI signal conditioning module or directly to one of the two
26 pin I/O connectors on the backplane.
Signal Conditioning
All of the raw data signals were conditioned before being sampled by the Keithley
card. There were three types of conditioning used. One type was used for temperature
probes. The other two were used for voltage data.
ADI 5B37-T-03 signal conditioning modules provided the temperature signal
conditioning. These modules were specific for T type thermocouples. They were optically
isolating and provided a linearized output from 0-5 volts for their temperature range of 100° to +400° C.
Voltage data were more challenging to condition for reading by the Keithley card.
The range of interest in this investigation was from 0-500 volts. This was far beyond the
card range of 0 to 10 volts. A Crompton 262-30 digital panel meter was used to sample
the raw signal, and gave a visual display of the reading. The Crompton meter had an
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optional backpack attached that provided a continuous analog current output. This output
was linearly related to an adjustable input range.
The analog output signal was a selectable current range. In this investigation the
industry standard 4-20 mA current output was used. This current signal then must be
converted to a voltage signal that the Keithley card could recognize. This conversion was
handled by using a precision resistor. The resistor was a 250 ohm resistor made by
Precision Resistor Co., Inc. (Largo, Florida) with a stated tolerance of 0.01 percent. This
resistor was connected to the screw terminals of the ADI backplane, where the current
signal was connected. The arrangement rendered a 1-5 volt signal.
Signal Conditioning Housing
The signal conditioning equipment and connections were housed together. This
housing was a converted tower style computer case. The case had an external power
switch, which turned on and off both of the Crompton meters used in this investigation.
The Crompton meters were securely mounted in the former external drive bay area for
clear viewing. Directly below the meters, still in the former external drive bay area, the
Keithley screw terminal was mounted. Only its cable connector was visible from the
outside. Figure 3-7 shows the housing and docking laptop. The ADI backplane was not
visible from the outside. It was mounted internally and positioned like a motherboard.
The housing had five basic points of access used in this investigation. The first was
the Keithley screw terminal connector. The other four were on the back of the case. Three
used a 19 mm (3/4") diameter connector to provide a portal into the case. One of these
three carried the experimental power lead into and out of a Crompton meter. It was not
shielded outside the case, only inside. It ran its interior route inside a 19 mm (3/4")
flexible tubular metal shielding. The power lead for the meters was run with shielding on
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the interior, but not the exterior. The thermocouple leads on the other hand were not
shielded inside the case, but were shielded on the exterior. Flexible tubular 19 mm (3/4")
metal shielding was used.
The third line coming into the rear of the case was shielded cabling. It had four
leads. One pair carried the voltage signal to be sampled from the AC power supply. The
other pair of leads carried the control signal for the Crydom relay used for automatic
control of power to the thawing system.
Data Logging Digital Multimeter
Another device used to collect data was a data logging digital multimeter. An
Extech (Waltham, MA) model ML720 was used. It could store up to 43,000 data points.
It featured an infrared communication port, which coul be linked to a PC via the serial port.
This allowed the data to be transmitted after the actual data collection process had ended,
and stored on a permanent basis, elsewhere.
Figure 3-7. Housing.
Object 3-7. Tower-Laptop.jpg (349 KB).
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Software
There were three significant ways in which software was utilized in this investigation
related to data. It was used to manipulate, control, and observe the data collection
process. After data collection, software was used to reduce and combine the data, and its
final use was for data visualization. The first two represented mainly custom programming,
while the third relied on commercially available graphics software.
Data collection
A custom written Visual Basic 6 (Microsoft, Redmond, Washington) program was
used to control the data acquisition card. It utilized a DLL driver interface known as
Driver Linx provided by Keithley. The Visual Basic program also converted the raw bit
data into meaningful units of measure. It was responsible for saving all data points in a
comma delimited text file. The program controlled the data collection, manipulated the
data and saved it, while the user saw the data in real time as it was collected.
Another software program was used to collect the alternating current data from the
data logging multimeter. This program was called Bs81-5x Data Logging System. The
software was provided by Extech with the multimeter. The program was used to decode
the data transmission from the data logging digital multimeter. It could also display the
data, and save the data in a standard comma delimited text format or a proprietary format.
Other custom written Visual Basic programs assisted in combining and reducing the
data. One program merged the two separate data files containing voltage and temperature
in the first, and current data in the second. This program created a third synchronized data
file that was further manipulated. These further manipulations, such as resistance
calculations, were preformed by another custom Visual Basic program.
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Data visualization
The primary software used in this investigation for the visualization of data was
Axum 6.0 by MathSoft Engineering & Education, Inc. (Cambridge, MA). Axum was used
in preference to a spreadsheet such as Excel by Microsoft or Quatro Pro by Corel Corp.
(Ottawa, ONT, Canada). The inability of either to deal with large data sets for graphing,
was the primary reason for preference given to a dedicated graphing program. Axum was
capable of easily graphing data sets of more than 175,000 points. This size data set was
common in this investigation.
Equipment Cart
For ease of use in investigation, several key components were mounted on an equipment
cart. The cart was the same cart described in Roberts (1994). It was custom made for
that work. It retained its general form, but was modified to fit the needs of this
investigation. As in the original form the cart had the AC power supply mounted under its
top surface. Both of the manual circuit breakers were intact and left positioned as in the
original set up.
The modifications started on the top surface. The signal conditioning housing was
mounted there. It was securely fastened by six screws and washers. A vertical plywood
surface from the original design was used to mount the plugs needed to connect the test
cell. The Crydom relay was mounted inside a plug box here. Female banana jacks for the
Data logging digital multimeter were also located in a separate plug box fastened to this
surface. Another plug box had a female sub D mini 9 pin connector used for connecting
the voltage sampling leads, and the control signal for the Crydom relay. A picture of the
layout can be seen in Figure 3-8.
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Figure 3-8. Box Arrangement.
Only one of the fold down shelves of the cart was utilized during this research.
This shelf provide a working space where the docking station for the laptop and other
miscellaneous items used during experiments were placed. The data acquisition card
housed in the docking station could then be connected by the 0.5 m data cable to the signal
conditioning housing. This also placed the laptop at a convenient height in which to view
and control the processes during data collection.
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Apparatus Construction
The construction of the apparatus was broken into the physical elements that make up each
portion of the apparatus. Each element had a number of constraints or characteristics that
had to be adhered to in order to meet the needs of the experimental work. These design
considerations were an essential part of the construction in addition to the actual
construction methods used.
Probe Construction
Design
The temperature probe design reflected the specific needs of the experiment. In the
experiments, the probe had to remain stationary when it was in contact with a liquid. It
also had to maintain its position during phase change related expansion or contraction.
This led to selecting a rigid probe. If the sensor end of the probe were placed inside the
sample, the sensor area at the tip would have had only one support point. The probe
needed to be supported at both ends for greater stability and accuracy in placement. The
support problem was solved by adding another linear section to the probe. This gave the
completed probe two fixed support points as it spanned the diameter of the test cell. The
new linear section also had the opportunity to become a second sensor holder for the same
location. The linear design also aided in determining location of temperature sensor on the
probe in the sample. This design allowed for two independent sensors to gather data at the
same geometric location in the sample cell.
The probes were at times exposed to electric fields on the order of 500 volts. Thus,
the probes had to be electrically non-conductive. By selecting a rigid ceramic with two
round channels in it, bare thermocouple wires could be used inside the probe. These bare
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wires helped to keep the total diameter of the probe small. The smaller the probe diameter,
the less heat could flow to or from the external environment through the probe which
could have acted as a fin. The choice of a glass ceramic that had a low thermal
conductivity assisted in reducing this finning effect. Finning by the thermocouple leads
themselves was addressed by using small thermocouple wires in the probes, since the metal
of the wire had a large thermal conductivity.
Assembly
The first step in constructing the probes was to break the ceramic insulator into two
sections. The insulator came in a standard 152 mm (6") length. The length was scored at
one of two positions depending on where the probe was intended to be used. If used as a
center probe, the center of the insulator was scored and broken. If on the hand, it was to
be used as a top or bottom probe the score is made off center. This score location reflected
the approximate half radius length for the sample. By having different lengths, each probe
had approximately the same length that protruded from the sample cell from each different
location that a probe occupied. The breaks were sanded as needed to have a reasonably
flat end.
The next step was to insert the thermocouple wires into the channels of the ceramic
insulator. The clearance was low and care was exercised not to bend the bare leads. The
leads were then be twisted together at the end where the break was initiated. The leads
were soldered together after twisting. This gave a solid probe tip formed from the solder
and thermocouple leads. The shape of the tip at this point of construction was similar to a
tear drop with a flat bottom. The tear drop shape was machined by filing and sanding to
conform to the exterior diameter of the ceramic insulator. Further machining of the axial
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direction then flattened the tip and reduced the axial height. The final form of this tip was a
disk at the probe end, or an end cap to the partial probe length.
At this point in the probe construction a special construction bench was used to
finish the probe assembly. The custom construction bench was specifically designed to
allow the probe sections to be assembled in a straight line. The simple geometric relation
that a line is formed if two planes intersect was used. The bench created a line by utilizing
the two perpendicular planes of the rail on the bench. The rail of the bench was where the
probe lengths were placed contacting both planes simultaneously. Thus, the probes lie
parallel to the intersection of two planes, which was a straight line by definition.
Once a probe was in position on the rail, the end caps could be glued, first to
ceramic insulator and then to one another. The bench rail had an open slot to allow access
to the junction between the end caps. This slot kept the adhesive from contacting the
bench and bonding the probe to it. The shallow lip of the rail allowed simple clips to be
applied to the probe. These clips served two purposes. First, they held the probe tightly to
both of the intersecting planes of the rail enforcing the straight line condition. Second, the
clips held the probe so it could not move during the curing process or during later
application of the adhesive.
The adhesive used to bond the end caps to one another was the electrical insulator
between the two separate thermocouple end caps. This electrical isolation was verified by
checking with a digital multimeter for continuity between the leads that protrude from each
end of the probe. After isolation was verified, a layer of adhesive was applied on the
exposed surface of the two bonded end caps. This layer acted as the electrical insulation
for the exposed radial section of the thermocouples. The bench was again instrumental in
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holding the probe during this application, and allowed the layer to be applied around the
entire circumference in one application.
The probes were then a straight line double sensor devices with loose wire leads on
both ends. To enhance connectivity of the probes to data acquisition leads, the loose wires
on one end were connected to the male end of a two bladed connector. The two piece
Omega connector physically clamped over the end of the ceramic, where it could be easily
connected to its female counterpart on the data acquisition lead. The final male connector
could not be put in place until the probe was in position in the sample cell.
Sample Cell Construction
Design
The process of designing the sample cell involved identifying the most important
constraints related to the research, and then finding ways to satisfy them. The cell had to
be able to provide the structural rigidity for holding the probes in a fixed position. It acted
as a form, to shape the liquid gel during its phase change from liquid to solid. In addition,
it had to be able to protect the probes during the volume change that the gel undergoes
when being frozen. The cell eliminated alternate electrical paths around the sample it held.
It needed a geometric shape that could be reduced dimensionally from a three dimensional
structure to a two dimensional shape for simpler numerical models. The overall design
required a minimum of machining, with preference given to readily available parts.
The first task in the design was selecting the geometric shape and material of the
sample cell. This shape was also the solid shape of the gel. A simple cylinder was used.
The cylinder provides a three dimensional shape that could be reduced to two dimensions
due to its axisymetric nature. This shape is common in piping, and thus readily available.
35
PVC piping was readily available as a construction material, and had the additional benefit
of a very high electrical resistance. In standard schedule 40 form, it was very rigid for
short spans, and was easily machined.
The cell was closed on both ends by the electrodes, which directly contacted the
gel. This configuration created a fixed volume cavity for the gel bounded by the electrodes
on the ends. Unfortunately, the gel underwent expansion during freezing on the same order
as that of water during freezing or roughly ten percent, and a rigid cavity would have been
cracked or broken. Additionally, any rigid probe that entered the cavity radially, would
have been sheared if expansion was allowed in the axial direction. The design challenge
was then broken into 2 parts, first to maintain the unfrozen geometry and second to protect
the inserted temperature probes.
One part of the design solution was to make sure the electrodes could be
constrained from moving during the phase change expansion. This then dictated the sample
must undergo expansion only in the radial direction. Since the PVC was rigid, a
compressible layer was added to its interior that allowed for radial gel expansion. This
maintained the basic geometry of a cylinder keeping the original height intact and changing
only the diameter of the sample. It also protected the probes entering radially from
encountering any axial shearing during the phase change expansion.
The last constraints that were satisfied were not as challenging. They included
accounting for how the gel will be poured into the cavity. This required a liquid tight seal
on the axial bottom and radial surfaces. The cell was drilled for the probes and electrical
leads to allow their entry.
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Assembly
The first phase in assembly was to create the basic PVC plastic shell. The shell was
made from two standard 76 mm (3") PVC fittings. The first was a female drain, waste and
vent (DWV) fitting. This fitting was female threaded for a standard 76 mm (3") threaded
plug that transitions to a female slip joint. The second fitting was a 76 mm (3") male DWV
adapter. This fitting had a male slip side that transitions to a female thread. The two slip
joints were glued together with a standard PVC glue.
The shell was then modified to accommodate the temperature probes. The center
height for the smooth section was drilled with an 2.41 mm (0.095") diameter bit
perpendicular and in line with the axis of the cylinder. The cylinder was then rotated 180°
and the second center hole drilled. The same procedure was used to drill the two quarter
heights. The three collinear points on each side defined diameters that cross the cylinder’s
smooth section at it’s axial 1/4 height, 1/2 height, and 3/4 height. In order to insure
accuracy of the placement of the holes, these modifications where preformed by a machinist
on a milling machine.
The shell had two key features now completed. The shell could hold rigid probes in
place at prescribed height locations. It also had a natural shoulder at the transition from
threaded to smooth at each end. These shoulders acted as the defining stops for the
electrodes. The height of the experimental cylinder was now fixed. Figure 3-9 is a picture
of the finished shell.
The electrodes had to be held in place. Two separate compression methods were
constructed for this purpose. The first used standard male threaded 76.2 mm (3") drain
plugs. These plugs could be screwed into the ends of the shell. By using a spacer, the plug
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could apply an axial force to the electrode. This configuration allowed each electrode to be
independently held in place
Two spacers were used in the research. The first was a simple 51 mm (2") PVC
slip coupling that fitted inside the threaded area. The second spacer was custom made. It
used one inch thick polystrene foam to contact the electrode across its complete surface.
The foam insulation was split into two semi-circles for easy placement and removal. It had
a central hole just large enough to allow the electrical connection to pass through. The
foam required a stiff surface to apply a relatively even load from the end plug to the
electrode beneath the foam. A 76 mm (3") diameter plywood circle was fitted to construct
Figure 3-9. Shell With Ports.
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the rigid surface between the end plug and foam. The wood circle was sawed on a radius,
and the center drilled to allow for passage of an electrical lead to the electrode. The
threaded plugs were modified for the electrical lead also. They had a hole drilled in the axial
center that was approximately 10 mm (3/8") allowing passage of the electrical connector.
The second method used a 305 mm (12") cast iron screw style C clamp, and
standard 19 mm (3/4") copper slip couplings. The couplings acted as a spacers to protect
the electrode electrical connectors, when the axial load was applied by the clamp. The
second method allowed the clamping force to be externalized from the shell. It also
allowed the electrodes to be viewed while in the clamped state. However, it did not allow
for the clamping of only one electrode like the drain plug method.
The defined cylinder inside the shell could be fitted with the interior insulation at
any time after the shell construction was complete. The insulation was cut with a utility
knife to dimensions of 254 mm (10") by 49.21 mm (1 15/16"). This was slightly oversized
in both the dimensions of length and width. The extra length helped the insulation form a
tight joint to each cut end as the insulation had to compress slightly to fit in the interior
circumference shell. The extra height did the same for the bottom surface that contacted
the electrode.
The exterior insulation was not placed on the sample cell until it was secure on its
holder. The temperature probes were in place at this time. The expanding foam was
sprayed onto the area corresponding to the central smooth interior area that eventually
contained the sample in the cell. It was allowed to expand in place and seal around the
probes. The foam required eight hours to cure and become stiff.
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Sample Cell Holder Construction
Design
Several requirements and conditions were identified that played a role in the sample
cell holder design. The sample cell was not self standing. It required a stand that could
hold it in a fixed position. The required fixed positions were sample cell axis horizontal, or
axis vertical. The cell holder was able to transition from one position to the other without
requiring the sample cell to be removed. The sample cell holder restrained the sample cell
as it moved to and from the temperature controlled chamber. It was desirable for it to be
easily gripped during these transitions. The holder protected the probes from bending
stresses at all times from the thermocouple leads that connected to the data collection
housing.
Assembly
The cell holder was constructed of wood. The layout can be seen in Figure 3-6.
First, the base was cut out of 50 mm x 152 mm (2"x6") spruce. Then, the carriage portions
were cut from 50 mm x 101 mm (2"x4") spruce. The carriage portions were then
positioned centered with respect to the long edge of the base. The space between their
inside edges was set to equal two radial ridges on the exterior of the sample cell. This
created two stops preventing the cell from sliding in its axial direction. The carriage
portions were then fastened to the base by drywall type wood screws. The uprights were
cut from 50 mm x 101 mm (2"x4") spruce. The upright was then centered on the base
short side with its end flush with the base bottom. It was attached in this position to the
base with the same type screws. The handle was cut from 19 mm x 38 mm (3/4"x1-1/2")
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spruce. It was centered on top of the upright, flush with the edges, and attached by a
drywall type screw on each end.
The sample cell was then placed in the carriage to determine the height of the
probes. This height was then marked and drilled with identical spacing to the sample cell.
The cell holder then had integral thermocouple lead holes. These 38 mm deep holes
allowed the thermocouple leads to approach the sample cell in a linear fashion. They also
prevented the leads from applying any bending stress on the probes during movement of
the holder when the cell was in place. A picture of the cell holder at this point of
construction was taken (Figure 3-10).
The last parts to be assembled were the horizontal legs. The legs were cut from
craft sticks. The lengths were adjusted to allow the holder to sit level with clearance for
the sample cell, in the horizontal position. Each leg was clearance drilled for the screw that
attached it. A drywall screw with an additional flat steel washer was used to attach each
leg into its position.
Figure 3-10. Sample Holder Picture, Front and Side Views.
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Signal Conditioning Housing Construction
Design
The design of the signal conditioning housing addressed several issues. First the
housing acted as an electrical shield for the signal conditioning equipment. The housing
was easy to access. It also provided a convenient manner for viewing the Crompton meter
displays. Easy access to an external power switch for the same meters was also desired,
since they required standard 110/120v input to operate. Overall housing size was impacted
by the need to provide adequate room for mounting the backplane and signal conditioning
modules on the interior. Readily available parts and supplies were given preference to
minimize cost. Construction techniques that required only simple hand tools were given
preference as well.
Assembly
The first part of construction was selecting a suitable match for the general physical
characteristics the housing fulfilled. A tower style computer case was selected. It provided
the required room, shielding, and ease of access. The case was then modified for the
specific needs of the equipment it housed. The interior of the case was cleaned out leaving
only the drive bay substructure and the computer power switch. The top two drive bays
was used to mount the Crompton meters. By being mounting close to the top of the case,
they were easy to view. The exterior covers for the drive bays were removed making room
for the meters. The opening was then closed down in height with metal to match the
mounting cases of the Crompton meters. The exposed area that was prreviously closed by
metal was now taped over with aluminum tape to improve the exterior appearance. The
meters were then attached to the case via their mounting cases.
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The Keithley screw terminal was mounted to the bottom of the drive bay section. It
was physically placed on the inside of the case. Two 25 mm (1") self-tapping sheet metal
screws were used to secure it in place. These screws penetrated the bottom of the 133 mm
(5-1/4") drive bays. This screw connection to the drive bay bottom held the connection
point to link the data acquisition transmission cable rigid enough to withstand locking and
unlocking the connector. This protected the interior connection made across the screw
terminal from damage that movement could cause. A drive bay cover was modified by
making a square cut out. The cut out matched the size of the connector for connecting the
screw terminal to its transmission cable. The drive cover was then installed.
Next the ADI backplane was mounted to the computer case siding, where
previously the motherboard and expansion cards had resided. In order to easily
accommodate the fixed mounting points of the backplane, a 508 mm x 203 mm x16 mm
(20"x8"x5/8") piece of plywood was mounted directly to the interior case wall to provide a
mounting platform. This plywood was positioned and mounted with drywall type screws
through existing holes in the interior case wall. The backplane was then positioned on
plywood without regard to the interior case wall design, which had insufficient height to
accommodate all the mounting points of the backplane. The backplane was secured to the
plywood by seven drywall screws that ran through its integrated standoffs that were in
direct contact with the plywood platform.
Apparatus Wiring
Custom wiring of the apparatus was an integral part of the design. Wiring was
necessary for several reasons. It acted as a conduit for power to be delivered to the
apparatus, and it was needed to deliver the power to the sample through a custom circuit.
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The wiring also served to carry signals for control and data sampling purposes. The
backplane utilized also had a certain amount of custom wiring to accommodate the needs
of the apparatus and connecting it to the data acquisition card.
Power
The Crompton meters needed a 120 volt AC power supply. This line was routed
from source to the back of the signal conditioning housing, and upon transition to the
interior, it was cased in an electrically insulating shielding. It ran from there to the power
switch of the computer case, which had been rewired to service the Crompton meters.
Between the power switch and each Crompton meter was an inline replaceable fuse holder
with a one amp fuse. With this wiring set up, an easy to access power switch on the
exterior of the housing was available for turning on and off the Crompton meters, and the
supply to each meter was independently fuse protected.
A 120 volt power bar with an on/off switch was attached to one leg of the
equipment cart. This allowed the cart to have a single point connection for up to six
standard 120 volt plugs. The Crompton meters as well as the laptop computer were
connected here. Devices used with the laptop such as external drives could also be
connected to the power bar. Direct current for experimenting was powered from this
location. The power bar itself had a meter long cord for connecting to an external
extension cord that routes the power from a standard 120 volt outlet.
A higher voltage supply was needed by the experimental sample power supply. It
required a 240 volt source. This was connected with a standard plug at the end of a
flexible lead that was approximately 3 meters long. The lead ran to a I-T-E enclosed
switch made by Siemens (catalog number CNFR-222). This general duty switch was a
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plug fuse type. It had an external lift lever and integrated light. This gave the sample
supply a convenient protected on-off switch that indicated visually when power was on to
the power supply. From the enclosure switch the wiring was routed inside a flexible metal
shielding to the power supply itself.
The wiring to deliver power to the sample is shown in Figure 3-11. This diagram
shows the important features of how the power was routed from supply to sample. The
leads for power exited the supply in flexible metal shielding and entered a Square D
(Palatine, IL) heavy duty safety switch (catalog number H-361-N). This 600 VAC 30 amp
switch had an external lever arm for actuation from the open to closed position. The
power leads were then routed from the bottom of this switch enclosure.
The leads were connected to two separate metal outlet boxes mounted to plywood.
The physical layout of the boxes is indicated in Figure 3-8. The top box provided the
connection point for the Crompton meter that acted as an ammeter and current controller.
This lead then exited behind the plywood and was routed into the center box where a
Crydom D4812 solid state relay was mounted. This box had a solid face since the power
did not need to enter or exit the face of the box. The lead then exited the mount side of the
box and was routed to the bottom box. The bottom box made use of the same standard
female plug. This was where the other lead from the Square D switch was routed directly,
and entered from the mount side. This plug now had both power leads connected and was
capable of power supply. In order to facilitate the easy and safe connection of the external
data logging multimeter and the Crompton meter measuring voltage, another series of
three boxes were mounted to the plywood as presented in Figure 3-8. The bottom box had
the same type female plug as the supply. This acted as an input point. A custom male to
45
Figure 3-11. Detailed Sample Power Wiring.
Object 3-8. DetailedPowerCircuit.jpg (58 KB).
male connector jumper was constructed to route the power out of the lowest right box into
the lowest left box. The leads then exited this box from its mount side.
The leads entered the top left box from the mount side behind the plywood. One
was connected directly to the female connector seen on the box’s face, while the other was
connected to a standard female banana jack at the top side of the box. The banana jack
was one of a pair of female jacks on the top of the box. The other of the pair was
connected to the female connector on the front of the box. This gave safe standard
connections for the data logging multimeter via a male to male banana plug jumper that
was used to route one leg of the power leads through the multimeter.
The top left box acted as the interface to the experimental sample leads. The
sample leads were approximately two meters in length. One end had a male connector
compatible with the female connector on the output box mounted to the plywood in the
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upper left position on the experiment cart. The other ends of the leads had insulated ring
tongue terminals. These were placed on the electrodes and secured to the bolt connectors.
The ring tongue terminals were small enough to be routed directly through the bottom
drain port of the temperature control unit.
Meters
The two Crompton meters had additional wiring besides what was already
presented. One meter was configured to read the voltage supplied to the sample. The
signal was sampled before it went through the data logging multimeter. A sub D mini 9 pin
connector was used to act as an easy plugin connection. This 9 pin connector had four
active connections, two to carry the voltage signal to a Crompton meter and two to carry a
control signal from the other Crompton meter.
This female side of this connector was mounted in the center left box (see Figure 38). The four leads exited the side of this box. Three leads, two for control and one for
voltage sampling, went to the center right box and entered through its side. Here they
connected to the Crydom relay. The two that completed a five volt circuit connected to
the control terminals on the relay, and the third lead was connected on the voltage output
side of the relay. The fourth lead entered the bottom right box and was connected to the
female output connector where the other leg of the experimental supply attached. The
leads were clamped on exit and entry from the boxes to prevent strain on the connections.
The leads were carried up to the signal conditioning housing via a custom
constructed lead. One end of the lead had the mating male sub D 9 pin mini connector.
The other end of the lead was stripped wires that were connected directly to the
appropriate connection points on the Crompton meters. The lead itself was 32 AWG
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shielded wire type with four conductors. It ran directly into the signal conditioning housing
via a close tolerance existing hole. The wires were left shielded inside the housing until
very close to the connection points on the Crompton meters. The lead was clamped next
to the interior of the housing to prevent strain on the interior connections from the exterior
portion of the lead.
The Crompton meter responsible for current control was outfitted with a dual relay
pod (262-RLY). This pod had two “change over” relays with a common wiper. The relay
controled a five volt signal provided by the data acquisition card. The wiring connection to
the relays came from the screw terminal panel which interfaced the data acquisition cable
connected to the data acquisition card.
Backplane
The ADI backplane plane had two roles, and wiring specific for each. First, it acted
as the interfacing point for the six thermocouple leads connected to individual channel
screw terminal connectors on the backplane. The number 2 and number 3 connectors of
each set were used on channel positions 5, 7, 9, 11, 13, 15. No further on board wiring
was needed for these channels. They routed through the ADI conditioning module and to
the pin out connector of the backplane.
The second role the backplane was to act as an interfacing point for the analog
output of the Crompton meters. The Crompton meter output was a scaled current and was
converted to a scaled voltage signal. One 250 ohm precision resistor was placed close to
the number 2 and number 3 screw connector on channel 1 and on channel 3 of the
backplane, respectively. The resistor was physically connected to each of the analog
current output leads to complete the current circuit. The connection was made with a wire
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twist type connector. Each junction had an extra lead wire also attached that was routed to
one of the screw terminals. Each twist on connector thus had three wires it connected,
with the last one being the voltage sampling lead. Both the lead to the meter and the screw
terminal were 18 AWG insulated copper leads. This configuration placed the sampling
leads on each end of the precision resistor for voltage sampling. Since no ADI module was
in place on the backplane for channels 1 and 3, direct jumpers were installed to route the
signal across the module plug interface. The jumpers were made from 18 AWG wire, and
fit the board female pin connectors designed for 0.0965 mm (0.038") pins. The signal was
then routed by the backplane to the backplane pinout connector.
The backplane had no external connections to the individual input screw terminal
connectors of channels 0, 2, 4, 6, 8, 10, 12, and 14. These channels were each grounded to
the backplane. The grounding connection was made on each channel where an ADI
conditioning module was placed. A jumper was installed on each to accomplish this. The
jumper was again 18 AWG wire connected to the appropriate female pin connectors. This
provided a grounded channel between each of the eight channels that were read by the data
acquisition card.
Screw terminal panel
The backplane pin connector had only 26 pins, and was not pin compatible with the
Keithley data acquisition card. The Keithley screw terminal panel acted as the wiring
interface between the data acquisition card and the backplane. The screw terminal front
had an integral connector specific for the Keithley data aquisition cable. This connector
locked the data acquisition cable into place preventing accidental disconnection of the cable
from the screw terminal. The other end of the screw terminal panel allowed for a screw
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clamp connection to each of the 36 discreet lines that come via connecting cable from the
Keithley data acquisition card. These screw terminals were used to interface to the
backplane.
The wiring between the backplane and the screw terminal was custom made by the
following process. A section of 40 conductor hard drive cabling (28 AWG flat ribbon
cable) was reduced to 26 lines.
A 26 pin clamp on female connector was attached to the
flat ribbon cable. The other end of the ribbon conductor was stripped, separating the
individual conductors. The individual leads were then matched to the appropriate screw
terminal for input to the Keithley data acquisition card.
The screw terminal also acted as the connection point for a pair of 18 AWG
conductors. These were connected to the screw terminals that carried a five volt DC
source from the data acquisition card. These leads were then connected via wire nuts to 2
more 18 AWG conductors providing a wiring split. One side of the split went to the
backplane to power the ADI signal conditioning modules mounted on the backplane. The
interface for the lead on the backplane was a screw terminal on the backplane. The other
halves of the splits routed power to the Crydom sample power relay. As presented in the
previous section, these leads were connected to the control relay on the Crompton meter
that was measuring current.
Experimental Methods
In the course of developing the apparatus several experimental investigations
utilizing various techniques were performed. The methods of data collection will first be
discussed, as they were relevant to all experiments undertaken. Then, the experimental
calibration of the temperature probes is presented. This is followed by the method of gel
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preparation used, and the method of determining the gel density. Experiments follow with
some very simple gel freezing trials that later helped to further refine design decisions.
They also provided information that helped to characterize certain components of the
experimental apparatus and the gel used in the research. Other experiments were designed
to validate certain operational procedures of the equipment.
With the knowledge gained through all the initial experiments, the final experiments
were designed. The final experiments included measuring the electrical resistance of the gel
and making continuous measurements on a gel as it was subjected to ohmic thawing.
Data Collection
Data collection occurred at several locations simultaneously. The primary location
was at the laptop where the voltage and temperature data were collected during an
experiment. The secondary locations included the data logging digital multimeter. The
final location was the laboratory notebook where observational information was recorded.
These methods of collecting data are further detailed below.
Laptop computer
The laptop was running a custom Visual Basic program that utilizes the software
polling capabilities of the Keithley data acquisition card. The program utilized user input to
start the process. Once the process was started the laptop’s internal clock was used as the
trigger. The program allowed the user to set how many data points on a single collection
channel were averaged per second by the program. The program then scanned the
channels for the set number of sweeps each second.
The raw data points were averaged and converted to meaningful units. The raw
data were in bits representing a zero to five volt signal measured by the acquisition card.
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This signal was conditioned previous to acquisition. The signal conditioning components
scaled and linearized it. The converted and now meaningful data were then written to the
hard drive with a time stamp that the program read from the laptop clock at the beginning
of the polling sequence. The program then waited for the next second to register on the
laptop clock to initiate another collection. This process continued until the user prompted
the program to stop. The number of points averaged per second on all experiments
preformed were 100. The one exception was initial runs with the program.
These initial runs were executed with various numbers of sweeps over the data
acquisition channels. The purpose of these initial data runs were to validate the operation
of the program and refine the interface. It also aided in finding the limit of how many scans
each second the card, laptop and software combination could be expected to execute. By
making runs with increasing numbers of points to be averaged and observing the time
stamps, the maximum number of scans per second was determined. These observations
additionally indicated an approximate time per scan.
Data logging digital multimeter
The data collected with the logging digital multimeter involved a multi-step
process. The initial step was to set the digital multimeter to the property to be measured.
The rotary dial on the digital multimeter was used for this step. The second step of the
process was setting the data scanning rate for the digital multimeter. This was
accomplished through its integral button and readout interfaces. The rate used was one
reading per second. This rate was used on all experiments utilizing the data logging digital
multimeter. Next, the digital multimeter was triggered by button interface to start
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acquiring data. It continued to collect data sequentially till the user prompted it to stop or
it reached 43,000 data points, the maximum storage capacity for the meter.
The data collected resided in the internal memory of the digital multimeter, and
needed transferring to a computer. The transfer was possible by using the digital
multimeter’s IR port. A special cable connected the IR port to a computer standard RS232
serial port. A software program written by the digital multimeter manufacturer then
interpreted the incoming signal to the computer’s serial port and translated it to a
meaningful data stream. The manufacturer’s program was utilized because the transmitted
data stream was non-standard for a RS232 serial connection. The data captured by the
program were saved in several formats including one proprietary to the software and a
simple comma delimited form. The comma delimited form sequentially numbered the data,
which effectively gave a time stamp in seconds referenced to the start of the experiment
with the chosen data collection rate.
Laboratory notebook
The laboratory notebook was important for keeping track of data that were not
being collected electronically. These observations were recorded by pen in a standard
format utilizing the guidelines of Kanare (1985). It also acted as a recorder of all methods
employed and important observations during experiments.
Temperature Probe Calibration
The temperature probes required calibrating to assure the desired degree of
accuracy. The experimental calibration utilized the phase change temperature of water. A
simple experiment design that continuously monitored the temperature of water, as the
water was cooled to its phase change temperature was utilized.
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In this experiment the sample cell was assembled with the bottom electrode in
place. The electrode was seated on the bottom shoulder of the sample cell. A coating of
petroleum jelly was applied to the shoulder via a 5ml hypodermic syringe. This ensured a
water tight seal on the bottom surface between sample cell shoulder and electrode. The
electrode was held in place with an end cap spacer combination.
The temperature probes were inserted. The order of the probes with their
respective data names are indicated in Figure 3-12. This arrangement and naming were
consistent for all experiments. After insertion, the exterior clearance area between the
probe and the cell were sealed with petroleum jelly. The same 5 ml hypodermic syringe
was used to deliver the petroleum jelly to the desired region. The probe was now in
position so that the second set of connectors could be attached. The sample cell holder
was prepared for receiving the sample cell by routing the thermocouple transmission leads
through its exterior. The lead pairs were then connected to their respective connectors.
The sample cell was then secured in the sample cell holder, and the connectors were
attached from probe end to transmission lead end.
Figure 3-12. Probe Positions and Naming Conventions.
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The cell holder was moved to the temperature control chamber. The cell was in an axis
vertical position with its top open. The temperature data collection was started. Deionized
water was added to the cell. The control chamber was closed and the water began to cool.
The temperature was monitored. At phase change the temperature remained constant. The
cell was removed from the chamber at this point and allowed to warm.
The data collection process was stopped. The collected data were copied to a
compact disk. The data were plotted to determine which region represented the phase
change temperature for water. The temperature readings then offset to the actual phase
change temperature.
Gel Preparation
The method of preparing the food gel for each experiment was consistent for all
experiments where the gel was placed in the sample cell. The first step in preparing the gel
was to weigh two of the retail envelopes on a laboratory balance (Ohaus model GT410).
The weights were then recorded in the laboratory notebook. A 250 mL beaker was used to
hold approximately 150 mL of deionized water on a hot plate. A 400 mL beaker was used
to hold another 125 mL of dionized water that was not heated. The 125 mL of water was
measured with a 100 mL graduated cylinder.
The gel envelopes were opened, and the powder poured into the beaker that
contained the 125 mL of room temperature deionized water. The gel powder was left to
absorb the water for approximately two minutes. At the end of the two minutes, 100 mL
of almost boiling hot water from the 250 mL beaker was measured with a graduated
cylinder and added to the gel. The mixture was stirred with a stainless steel spatula, and
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placed on an electric hotplate. The stirring was continued till all granules were dissolved,
which occurred in approximately one minute.
The beaker was taken by bare hand from the hot plate. The solution was then
poured into the sample cell to the desired fill level. A separate 30 mL beaker was used to
collect the remaining solution. This additional sample of the gel was covered by Parafilm®
“M”. The sample was used later to determine the density of the gel. The liquids then
solidified at room temperature. The last steps weighed the empty gel envelopes and
recorded the weights in the laboratory notebook.
Gel Density Determination
The method for determining the gel density utilized a Quantachrome Instruments
(Boynton Beach, FL) multipycnometer and a laboratory scale. The first step in utilizing the
multipycnometer was to verify its calibration. The small sample cell and two small
calibration balls were used. The volumes of the calibration balls were known. Three
repeated measures were made using the instrument. The measurements were then
compared with the known value. This procedure insured that the operator of the
instrument was using it correctly.
The multipycnometer was ready to determine accurate volumes for samples of the
gel. The gel sample from the 30 mL beaker was uncovered and cut with a coring tool. The
core was weighed on the laboratory scale and the weight recorded in the laboratory
notebook. The core was placed in the small sample cell of the multipycnometer. The
volume measurement by the multipycnometer was repeated six times for each core sample.
Three core samples were taken from each gel sample examined.
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The density was calculated from the weight measured by the laboratory scale, and
the volume calculated from the pressure measurements made by the multipycnometer. The
pressure measurements were transferred from the laboratory notebook to a spreadsheet.
The volume calculations using the pressure measurement were done in the spreadsheet to
speed up the repetitive calculations. Ultimately the density calculations were made in the
spreadsheet as well. Having all the calculation in a spreadsheet format allowed comparison
of the data from different gel samples.
Freezing
Experiments in gel freezing helped to characterize the changes the gel underwent in
the solid-solid (unfrozen to frozen) phase transition. The first basic experiment was an
observation experiment. Gel was mixed and poured to form an inch thick slab in a beaker.
The gel was then allowed to transition from liquid to solid. The top of the beaker was
covered with Parafilm slowing water exchange with the surrounding atmosphere. The top
surface of the gel was unconstrained. The gel was placed in a freezer and frozen. The
frozen gel was removed from the freezer and observations recorded on shape. These
observations discussed in Chapter 4, lead to the next iteration of the freezing experiments.
The next iteration was pouring a gel into the sample cell without the internal
insulation. In this experiment the gel top surface was poured even with the upper shoulder,
and covered by the top electrode. The top electrode was in contact with the liquid gel.
The electrode was not constrained other than the shoulder it rested on. This shoulder kept
the electrode from initially sinking into the gel. The gel was refrigerated to speed up the
liquid to solid phase transition. Once congealed the gel was placed in a freezer and frozen.
The sample was removed and observations recorded.
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With the observations of the previous experiments for guidance, a new experiment
was designed. The sample cell was fitted with interior insulation. The gel was poured
inside what was the second iteration cell with interior insulation, and the electrode placed
on the top gel surface. The gel was refrigerated to congeal. The only variation at this
point was the new interior insulation.
After congealing the cell was removed from refrigeration. The constraining end cap
on the bottom of the cell was removed. The C-clamp and copper spacers were positioned
to constrain the electrodes in an axial manner. The clamped cell was placed in a freezer to
undergo the solid to solid phase transition. After the gel was frozen, it was removed from
the freezer. The clamp was removed to expose the electrodes. The electrodes were
warmed by tap water to facilitate their release from the frozen gel.
An inertial method was used to extract the frozen sample from the sample cell. In
this method the cell was raised above the laboratory bench top and dropped to it. The
frozen gel and insulation then slid in the axial direction of the cell. Once slippage has
occurred, the gel and insulation easily pushed in the axial direction for removal from the
sample cell. Once the gel was removed the insulation can be pulled away from the radial
surface of the frozen gel.
Observations were recorded, when the electrodes were removed. These
observations primarily record the surface conditions. More observations were recorded
after the insulation was removed from the sample. This set of observations recorded the
condition of the radial edge and overall geometry of the sample. More observations were
taken as the sample was allowed to make the solid to solid phase transition back to the
unfrozen state. The observational emphasis was the overall geometric shape.
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A variation of this final freezing experiment was preformed with a set of sample
probes in place. The primary difference in this variation was sample probes positioned in
the liquid gel before it is set. The gel sample now resembled the actual set up that was
utilized for tracking the temperature of the gel sample. Upon removal from the sample cell
by the inertial method, the probes were sheared at the cell wall interface. The design of this
experiment allowed for further observational validation of the freezing geometry, as well as
the effect of the solid to solid phase change on inserted probes.
Environment Characterization
The environmental control chamber interacted with the sample. The interactions
were characterized to help design and control experiments. Several methods were used to
gain insight into how it impacted the sample temperature, and the capabilities of the
chamber.
Continuous Running
The control chamber could be operated in a continuous mode. This mode turned
on the unit’s compressor and left it in the running state until it was manually switched back
to a temperature cycling state. This allowed the minimum possible temperature of the
control chamber to be determined. The method employed was to set the chamber into the
continuous run state and monitor its temperature. The chamber was allowed to stay in this
state for at least 12 hours. The temperature inside the chamber was monitored and
recorded. When this method was used with a gel sample, the freezing of the sample
occurred in the minimum time allowable by the equipment. This helped to provide
consistent freezing of different gel samples.
59
Cycling
The chamber was also operated in a more standard fashion. This was a cycling
mode that automatically turned on the compressor when a high temperature set point was
crossed, then automatically shuts off the compressor when the low temperature set point
was reached. The chamber did not have a precise manner for selecting the upper and lower
set points. It utilized a manual rotary control with numbering for selecting from a range
predetermined by the manufacturer. The numbering of the scale gave reference points from
the lowest cycling temperatures to the highest cycling temperatures and had no units of
measure.
The method for determining the impact of cycling on the gel sample of interest was
straight forward. The temperature of the frozen gel sample was monitored during an
extended time up to 7 hours. These temperatures were graphed. The cycling nature of the
chamber became visible. The prominent features such as magnitude of sample temperature
change and frequency of the changes were extracted. The method used for evaluating the
cycling, also yielded information about probe finning discussed in chapter 4.
Thermal Damping
The final characteristic interaction between the chamber and sample that needed to
be understood was how the sample warms up when the chamber is no longer actively
running in either mode. The method for gaining this information was to track a frozen gel
sample’s temperature when the chamber was turned off. This procedure was used to
determine how rapidly the sample warmed.
A second iteration involved increasing the thermal mass inside the chamber. In this
experimental set up 7.5 L (2 gallons) of distilled water in standard 3.75 L (1 gallon) plastic
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milk style jugs were frozen in a separate freezer. The frozen water jugs were then placed in
the chamber along with the sample. The freezer was then shut off and the temperature of
the sample tracked. This increased thermal mass acted as a thermal damper. The data
graphed and the impact of the thermal damping determined.
Automatic Power Control Method
Relay set up
A single relay option pack for the Crompton Meter was used for controlling the
maximum current applied to a sample during ohmic thawing. The relay pack was two
relays that utilized a single wiper (See Figure 3-13). The relays were used in series. The
incoming lead carried the 5 volt control signal that attached to connection 1 in Figure 3-13.
The outgoing lead to the Crydom relay attached to connection 5. The first relay was set to
be a low alarm, and the second relay was set to be a high alarm. The first relay had a 5
second delay, and the second had no delay. The relays also had user defined hysterisis.
The low level alarm was set at a 0.05 amps, and the high level alarm was set to 0.4
amps. The hysterisis level on the low alarm was set to coincide with the high level alarm,
and the high level alarm hysterisis was set to coincide with the low level alarm. When the
meter was turned on and no power is being transmitted, the low level alarm was active and
closed the first relay, and it stayed in this state until its hysterisis value was reached. The
second relay was already closed and stayed closed until the high level alarm value was
exceeded. Power could then be applied, and when the high level alarm was tripped the
control signal circuit was broken. The voltage value dropped with both relays in an open
position until the second relay reset at its hysterisis point.
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Figure 3-13. Relays.
The low level alarm was activated also, but it had a 5 second delay before it changed state.
The delay from an over current shut down to the applying power allowed the operator to
adjust the voltage to a lower value. This current limitation prevented the power supply
from delivering undesirable levels of power to the sample.
Power control validation
The relay configuration was verified prior to the ohmic experiment runs by the
following method. An incandescent electric light bulb was made wire compatible with the
experimental apparatus output. This allowed the voltage supplied to the light bulb to be
varied, which in turn led to the current supplied to the bulb being varied. The light was
supplied a current that was less than the high alarm state. The current was increased until it
trips the high alarm and shuts off the output. The result was visible both on meter readings
from the Crompton meter and no light being emitted from the bulb. After a five second
delay the system once again supplied power to the light bulb and was verified by both
meter reading and light emission. The system then immediately shut down, because the
voltage was not adjusted to a lower value. During the next five second delay the voltage
was reduced and power did not shut down.
62
Resistance Measurement
The experimental determination of the sample resistance employed two methods both
used the same equipment. The difference in resistance property magnitudes required a
different approach depending on the physical state of the sample. The first method was
used with the sample in an unfrozen state. The second method was used with the sample in
a frozen state.
Unfrozen sample
The first step was to prepare a gel as discussed previously. Just before the gel was
poured into the instrumented sample cell the data acquisition was started and recorded the
temperature history of the liquid gel as it cools and became a solid at room temperature.
After the gel was poured the second electrode was put into place on the top of the sample.
A small amount of liquid sample formed a bead between the sample cell edge and the
electrode. Then the top of the electrode was covered with a thin layer of gel. This
prevented any dehydration from occurring to the gel located between the electrodes, while
the sample congealed.
Once the gel was set, the top electrode was attached to the power lead and the end
cap put in place preventing the electrode from pulling away from the sample. The bottom
end cap was removed allowing the bottom electrode to be connected to the other power
lead. The instrumented sample with power leads connected was placed into the
environmental control chamber. The sample was ready for thermal conditioning.
The chamber was turned on and two jugs of ice introduced. This was very similar
to the method of thermal damping. The air temperature of the chamber was monitored
with an external temperature measuring device. One device was the multimeter which has
63
type K thermocouple direct input for temperature monitoring. When it was not available
due to collecting current data, a simple inexpensive thermistor probe was used. These
probes were not calibrated. They showed good agreement between each other when
referenced to the thermocouple probes. Calibration was not required since high accuracy
was not necessary in monitoring the air temperatures.
The chamber was initially cooled to slightly below freezing and then turned off.
The temperature of the sample monitored. The manual cycling of the temperature in the
chamber was continued bringing the sample slowly close to freezing. Once the temperature
was in the desired range then data collection for determining resistance began.
The power supply was set to a predetermined value, with the final manual switch
left open. The multimeter and data acquisition software were started. The power was now
switched on and the temperature readings for the sample monitored. The power was left
on for approximately 30 seconds then switched off. The sample was ohmically heated by
the application of the power, and its temperature rose on the order of 0.5° C during the
power application. The power was then switched off for approximately 30 seconds. This
allowed for internal thermal relaxation of the sample. This cycling was continued until the
temperature difference between probe locations was on the order of 0.2° C.
Once the run finished, the data were downloaded from the multimeter. The
chamber was then thermally conditioned to a new temperature. The new temperature was
chosen to overlap a portion of a previous run. This provided multiple data points at the
same temperature. The general data collection procedure of this method was repeated until
the temperature range of interest was adequately covered.
64
The resistance was calculated from the collected data. The data were first reduced
by a custom program that detected the edges of each current cycle, and aligned that with
the edge of each voltage cycle. The combined data had the matched voltage and current
values which indicated the resistance. The average temperature versus resistance was
graphed and fitted with a polynomial. The graphing and fitting were done with the Axum
software. A third order polynomial was chosen, with the inverse of the maximum
temperature difference between probes used as a weight for each point. This gave slightly
more weight to points that show closer temperature agreement between all three locations.
Frozen sample
The frozen sample went through the same gel preparation as the unfrozen. After
the unfrozen state measurements were finished, the sample was removed from the
environmental control chamber for freezing preparations. The end caps were first removed
so the electrode connections could be accessed. Then, the electrodes were disconnected to
allow clamping for freezing. The layer of excess gel was removed from the top electrode
during this process.
The smple was ready to be frozen after clamping. The unfrozen sample was placed
in the environmental control chamber set to continuous run mode. The sample temperature
was monitored by the data acquisition system which collected the sample phase change
information. The chamber was turned off when the sample had reached the limiting
temperature of the chamber, approximately -35° C.
The frozen sample was removed and prepared for data collection in the frozen
state. The first step was to reconnect the electrodes to the power supply, and put axial
insulation and end caps in place. The exterior of the sample holder was covered with
65
additional layers of fiberglass insulation. This was held in place by mesh fiberglass tape
(Figure 3-14). The new configuration was placed back into the freezer. Cycling and
warming data were taken for the new configuration.
Due to the extremely high electrical resistance of the frozen sample it was thermally
conditioned before resistance measurements. This time the conditioning was to warm the
frozen sample to a range of interest that was still below freezing. The thermal damping
method discussed previously was utilized to bring the sample temperature close to -5° C.
This was the starting point in the frozen state for the electrical resistance values.
The high resistance of the frozen state allowed the data to be collected as a single
continuous stream. The warming of the sample in this case was not driven by the ohmic
portion of heating since the total power applied was very low. To maintain this effect as
the temperature warmed, the voltage was reduced one time during the collection. With
close monitoring of the temperature rise of the sample and previous knowledge of the
Figure 3-14. Additional Fiberglass Insulation.
66
warming, it was possible to take data very close to 0° C without crossing the phase change
boundary of the sample gel. The data collection was stopped at approximately -0.2° C.
The process of cooling the sample was repeated to set up for another data
collection run. The data collected from these runs were analyzed much the same way as
the unfrozen data. A custom program did edge detection to assure alignment of the
voltage and current data points taken with the two different instruments. The combined
data were then used to calculate the resistance values.
The transformed data were then graphed and fitted with Axum software. Again, a
third order polynomial wass used with the same type weighting factors. The weighting
factor was used for consistency between the two sets. The temperature spread between
probes for the unfrozen state experiments were much more than that for the frozen. The
spread on the frozen state experiments were at or below approximately 0.1° C or less, with
the majority of the data showing a spread more on the order of 0.05° C.
Ohmic Thawing
The final experimental method involved collecting data during an ohmic thawing
process. The sample at this point has already undergone resistance measurements in the
unfrozen and the frozen states. The gel preparation and details of those measurements are
discussed in previous sections. At the end of the frozen resistance measurements, the gel
was still frozen in the chamber which was in a cycling mode. The first step was to
thermally condition the sample to the desired temperature range to start the process. The
air temperature was also monitored to bring it close to the sample temperature just before
power was applied to the sample.
67
The automatic power control was configured to switch the system off if the current
rose above 0.4 amps. The power supply was set to its maximum output, approximately
490 volts AC. The data logging multimeter was connected and set on the milliamp scale in
alternating current mode. This allowed the current to be read initially in hundreds of
milliamps on the four digit display with automatic switch over to milliamps once the
reading exceeded 50 milliamps. The frequency for the logging on the multimeter was set at
one Hertz.
The data acquisition was initiated simultaneously with the software controlled card
and manually controlled data logging multimeter. The system was ready to begin ohmic
heating. The power switch closed to apply power to the sample. The sample temperature
monitored on the screen as it was recorded. Notes were maintained in the laboratory
notebook on the approximate chamber temperature.
The system was allowed to run until the sample has a 0.5° C difference between
temperature measuring points in the gel. The power was manually turned off. The system
was allowed to thermally relax before power was applied again. The power was applied a
second time to approximately the same temperature difference and turned off. The sample
was allowed to relax again just below the phase transition point. Note at this point all
temperatures were reading below the sample phase transition point.
The sample was then powered through the phase transition. Following the phase
transition the automatic power control took over, shutting off the power and a manual turn
off applied that controlled the power off time. The applied voltage was adjusted to reduce
the power supplied to heat the sample. The sample was taken from the environmental
chamber once it was through the phase transition. This further enhanced the insulated
68
boundary conditions, since the sample was warmer than the environmental chamber and
was closing in on ambient room temperature. The sample was further heated to slightly
above ambient room conditions following the same cycling of limited power and voltage
adjustments.
The data acquisitions were stopped. The data logging digital multimeter data were
downloaded. The sample was placed back in the environmental control chamber. It was
still a solid gel at this point. The sample was ready to have another round of thermal
conditioning. The conditioning prepared the sample for unfrozen resistance measurement
a second time.
After a second set of unfrozen data was acquired, the sample was ready for physical
examination. The outer layer of fiberglass insulation was removed first. Then the end caps
and associated insulation were removed, so the electrode connections could be taken apart.
The electrodes were then removed from both ends of the sample for photographing. Notes
were made in the laboratory notebook on the physical observations about the gel and the
electrodes contacting it. The collected data were ready for consolidation and reduction.
Software again assisted in further analysis. The results were then graphically displayed.
CHAPTER 4
RESULTS AND DISCUSSION
This research yielded many results. They were grouped with the same structure as
the Materials and Methods chapter.
Data Collection
There were two data collection experiments with results of interest. The first was
determining an acceptable rate for temperature polling and characterizing the data.
Through progressively increasing the polling rate, it was determined that the hardware and
software combination had an upper limit of approximately 500 Hertz for looping the 16
channels. Above this level it was noted that the data taken no longer had sequential
seconds as the time stamp.
From simple division it was deduced, that the loop rate was on the order of 0.002
seconds. Since all experiments were run by averaging 100 loops, each data point
represented a time slice of approximately 0.2 seconds long. Another way of describing the
polling rate was to look at the number of data points that were collected based on each
loop. There were 16 points collected for each loop. This meant that the system collected
1600 points when it polled 100 loops. These were then reduced to 16 averaged points
before recording. The advantage of looking at the number of data points on a single loop
was this gave some insight to collection time capability of a single data point by the
hardware software combination. A single data point took on the order of 1.25 x 10-4 s.
Further, it was observed that the time between consecutive points on the same channel
were equal to the loop time of 0.002 seconds, when 16 channels were scanned, as was the
case in all of this research.
69
70
The 16 channels being sampled were ordered specifically to include a grounded
channel between each data channel of interest. Since software polling was being used in all
cases, this gave voltage values of the backplane ground. The advantage of the
configuration was in creating a more flexible data collection device. The Keithley data
acquisition board had a DMA (direct memory access) mode that allowed significantly faster
acquisitions in which the settling time between readings could be enhanced by referencing a
ground before each measurement. The data collection rate based on a per point basis then
could be pushed to the board limit or 100,000 kHz.
The data collection software ran under Windows 98 and exhibited one limitation. It
began to stall after taking a large number of averaged points. The system showed slowing
marked by longer than one second intervals between averaged points. This slowing was
not an issue in the research, because of the high number of points that had to be taken to
see the phenomenon. It was exhibited when the number of looped averages exceeded
approximately 25,000. This translated to almost seven hours of continuous data taking.
All physical phenomena of interest in the experiments took a shorter period to capture.
The cause for the eventual slow down was not determined, as it had no practical impact on
the research.
Temperature Calibration
Theoretical
In any temperature measuring instrument the greatest accuracy is achieved by multipoint calibration. In this research a single temperature reference point was used. The
theoretical justification for a single point being enough for our purposes was two fold. The
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first was the method of temperature measurement used, and the second was the range of
temperatures measured.
In this research the temperature probes were thermocouples. These thermocouples
were not read directly, instead a conditioned output signal was read. Their output signal
was conditioned by the ADI signal conditioning modules. The modules were designed to
specifically condition for T-type thermocouples. The manufacturer’s specifications for the
module’s accuracy were dependent on several factors. The first was the span of
temperature range for the module’s design. The next was a voltage signal reading accuracy
along with the accuracy of a cold junction compensation sensor for each channel. When
the errors were evaluated and the square root of the sum of their squares taken, the order
of magnitude of the error was 0.5 °C. This represented the accuracy expectation with no
further calibration applied. By referencing a known temperature the accuracy was
improved. It was noted from the single point values presented later, that indeed the
modules required an offset of less than the manufacturer’s error range.
The main issue was the nonlinearity of the output, which was linearized by the
signal conditioning module. The nonlinearity of the module according to the
manufacturer’s specifications was +/- 0.02% of the range. The range during experiments
never exceeded 50 °C from the calibrated point. The nonlinearity was then expected to be
on the order of 0.01 °C. This coupled with the fact that the range of interest in the
research was relatively small, indicated that a single calibration point close to the middle of
the range was sufficient to expect accuracy more on the order of the nonlinearity. This was
coupled with the resolution of the device reading the module and the apparent levels of
72
noise in the system which yielded a final order of magnitude expected for the temperature
measurement errors.
The calibration of the temperature sensors utilized a classic theoretical problem.
The problem is commonly referred to as the Stephan Problem. It is a simple homogeneous
phase change from liquid to solid. A solution to this one dimensional problem is given in
Carslaw and Jaeger (1959). The solution is referred to as the Neuman solution for the
semi-infinite problem. The problem maintains the initial surface at x=0 to be at zero
temperature. The rest of the body is initially at a constant temperature above the
substance’s melting point. The solution to this one dimensional problem is arrived at by
making an assumption that the position of the phase change surface is proportional to the
square root of time. The authors arbitrarily chose a form that includes the thermal
diffusivity of the solid phase. The solution can be shown to be equivalent to the same
assumption using the thermal diffusivity of the liquid phase. A derivation of this second
form of the solution can be found in Appendix A.
The theoretical problem then inherently is a conduction heat transfer problem. It
allows for different thermal properties in each of the two phases. It assumes the density of
both phases to be the same with no volume changes accounted for.
Experimental
The experimental problem for calibration looked very similar to the theoretical.
The important features were shown in Figure 4-1. This, under ideal conditions, was a one
dimensional heat transfer set up. It was recognized that the data collected with the
experimental apparatus reflected several features that the theoretical solution did not
exhibit. The first was that the physical properties were functions of temperature as well as
73
Figure 4-1. Calibration Setup Features.
phase. The experimental set up also only approximated the ideal boundary conditions that
were represented by the theoretical problem. The upper surface in reality has something
other than a constant temperature boundary condition that drove the heat transfer. The
differences initially looked relatively minor, but due to water’s unique properties the
theoretical solution had no comparative value to actual data taken for calibrating the
sensors.
The informative part of a calibration run at first appeared to seek only a
temperature plateau. A visible plateau indicated constant temperature, when in fact there
was energy transfer occurring in the form of cooling. This then yielded a reference point
for the phase change temperature of the liquid in the sample cell. The actual data from a
calibration run were plotted in Figure 4-2.
It was immediately striking that there was a much more complicated system in play
than a simple conduction problem explained. The initial part of the graph showed that all
temperatures were tracking one another very closely. This was explained by the convective
mixing that would have been driven by a process where the liquid upper surface upon
74
Figure 4-2. Probe Calibration Data.
Object 4-1. Cal3_85x11.jpg (174 KB).
cooling becomes more dense and sinks down. Water’s maximum density was at 4 °C, so
the convective process was not maintained all the way to the freezing point at 0 °C .
The graph clearly showed that in the area of 4 °C another physical phenomenon was
occurring. The interesting point here was that one could actually see the expected
transition from a convection driven process to a conduction driven process. The cool top
layer became the less dense layer, no longer sinking and causing the natural convection to
occur. This cool layer then rested in place and thermal stratification began when the
primary heat transfer mode was conduction. During the entirety of the research endeavor
several similar calibration experiments were carried out and consistent observations were
made on each of the runs.
75
The data captured by the experiment also showed another expected phenomenon.
Sub-cooling of the liquid was also apparent. This was yet another physical phenomenon
that the simple theoretical model could not account for, but one was expected to occur.
Following the sub cooling on the graph, there was a plateau where phase transition was
trying to initiate. This area was where the offset numbers for calibration were collected. A
short span of the data was linearly regressed and yielded a slope to verify that it was
virtually horizontal. An average value then was used to calibrate each sensor. The values
arrived at for three calibration runs are listed in Table 4-1.
Table 4-1. Calibration Offset Values.
Calibration Offset Values (°C )
Thermocouple Probe Designation
Calibration Run #
Chan5
Chan7
Chan9
Chan11
Chan13
Chan15
1
0.248
0.319
0.246
0.209
0.472
0.258
2
0.259
0.329
0.260
0.211
0.464
0.272
3
0.263
0.341
0.260
0.216
0.471
0.288
0.257
0.330
0.255
0.212
0.469
0.273
Average Values
Figure 4-3 plotted data collected while the water sample warmed up. The time count
was restarted at zero, when the sample was removed from the temperature control
chamber. It was interesting to note how the warming water showed a physical
phenomenon around same 4 °C point. This time it appeared as if the warming was initiated
from the bottom, since it was the lowest sensors that were showing the warmer
temperatures initially upon leaving the plateau area. This could have been related to the
lack of a perfectly insulated boundary condition applied at the bottom. Coupled with the
fact that on the cooling side the bottom slightly led when convective mode was dominant,
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Figure 4-3. Calibration Warming Data.
Object 4-2. Cal6_85x11.jpg (157 KB).
the data seemed to indicate that the bottom insulated condition was indeed slightly
imperfect. The insulated condition probably was not the main cause for the leading of the
bottom set in temperature change. In both cases there would have been convection
favoring the bottom being colder in the first case, and warmer in this second case. When
viewing the warming it has to be remembered that the warmer temperature below 4 °C was
actually the more dense water and was expected to be found at the bottom. It was relevant
to note that in both cases the initial part of the data reflected conditions supporting natural
convection, while after crossing the 4 °C mark both tended to support conduction and
stratification in the temperature profiles.
77
Other factors could have been also influencing the temperature response of the
system. The radial insulated boundary condition could have been playing a role. If there
was heat leakage through this surface, it would have been enhancing to the effects of the
convective heat transfer of the system during periods when natural convection was favored
in the system. The energy level of the water as reflected through the temperature readings
at different depths when all sensors were at the phase change temperature would not have
been expected to be equal. This was due to the fact the energy was being extracted mainly
from the water’s top surface. Since the top surface was assumed to have a lower energy
level, that may have also indicated the lowest level of water would have been more greatly
impacted by imperfection of the radial condition, along with any imperfection in the bottom
boundary condition.
Ultimately, when the water reached its maximum density the top driven conduction
process took over. Thermal stratification exhibited was expected as the warmer less dense
water was on the top, and the heat delivered primarily also on the top. The stratification
from the top to middle was greater than what was observed from the middle to the bottom.
This lended support to the insulated boundary conditions having been violated slightly.
The warmer water produced at the side or bottom would have impacted the lower and
upper readings the most. The lowest and highest positions in the water would have been
expected to have their temperatures slightly higher. The center located at the radial origin
would not have been expected to reflect any breakdown of the insulated boundary
conditions unless those break downs were of a large magnitude relative to the top heat flux
applied. Based on the insulations used on the siding and the bottom this was what one
would intuitively have expected as well.
78
The calibration data yielded more information than just an offset value for the
sensors. It also gave insight into how complex a real Stephan problem could be involving a
complex fluid such as water. The data also implied that if water was cooled to its
maximum density first there would probably have been a much better approximation to the
theoretical, since thermal stratification would have made the primary mode of heat transfer
conduction. Furthermore, the analogous thawing problem would have run into difficulties,
if the thawing was initiated from the top since once a layer was formed over the ice, the
warmest uppermost layer would initially have been more dense and initiated natural
convection until it reached maximum density temperature for water.
The calibration data gave a first look at the apparent noise in the temperature
measurements. Figure 4-4 took slices of the uncalibrated data in the region of the phase
change temperature. The graphs represented isothermal slices of time temperature data
from three different calibration experiments. The spread of the data on individual channels
(Chan5 - Chan15) was not attributable to changes in temperature and were correlated to
noise in the system. The figure showed that the data looked to be bounded by roughly
+/- 0.04 °C. This represented an apparent noise for the system while it was not undergoing
ohmic heating.
It was important to look at a slice of data while the sensors were in the high voltage
field conditions that were more representative of ohmic conditions. Figure 4-5 plotted a
time slice, when the applied electric field was approximately 500 volts AC. It appeared to
show that the spread attributable to noise was on the same order of magnitude as before.
This time though there was not the luxury of looking at an isothermal time slice.
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Figure 4-4. Calibration Noise.
Object 4-3. CalNoise3.jpg (1000 KB).
The low noise level exhibited by these thermocouple sensors was attributed to several
factors. First, care was taken to properly shield the transmission portions of the
thermocouples, which helped prevent intrusion of stray electrical signals. The ADI
modules had built in noise suppression optimized for 60 hertz signals. The thermocouples
in the high voltage field area were designed to be perpendicular to the applied voltage field
to reduce induced voltages from the applied alternating field. Each data point was an
average of 100 points which further aided in reducing the noise in the readings.
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Figure 4-5. Noise Under High Voltage.
Object 4-4. HighVoltageNoise.jpg (233 KB).
The temperature data were collected by the Keithley data acquisition board in the
form of a linearized voltage that had been scaled from 0 to 5 VDC. It had been noted that
this was also inherently a part of the temperature error since the board converted the
analog signal to a digital one. The Keithley board was a 16 bit board, and therefore could
resolve the signal to 216 or 65,536 parts. This yielded a volts per bit of roughly 76.3x10-6.
The linearized °C/V was obtained by dividing the range of the ADI module by its linearized
output range. The linearized °C/V then was 100. The product of the last two quantities
yielded the °C/bit that the card was reading. Carrying out the calculation, this value was
determined to have been 7.62x10-3 °C/bit.
The noise and conversion to a digital signal even when combined linearly were less
than half of the nonlinearity of the module which was 0.1 °C. Based on these numbers the
calibrated sensors were judged to be of acceptable accuracy for this research.
81
Experimental Gel
Total Mass Percent
The gel used in the experiment was prepared in a consistent manner each time. The
mass percent of five separate runs involving the gel were recorded in Table 4-2. It could
be seen that the retail packages had a small amount of variation. Since the water used to
hydrate the gel was kept constant, this variation ultimately led to slight variations in the
mass percent of the different gels. The gels fell into a range of 6.1 +/- 0.2% total mass.
Table 4-2. Percent of Total Mass of Gelatin in Gel.
Percent of Total Mass of Gelatin in Gel
Sample
1
2
3
4
5
Full Packets Empty Packets
Mass (Grams)
16.630
1.544
16.700
1.543
16.380
1.527
16.056
1.607
16.314
1.540
Net Gelatin Water
Gelatin
(Grams)
(mL) (Percent of Total Mass)
15.086
225
6.71
15.157
225
6.74
14.853
225
6.60
14.449
225
6.42
14.774
225
6.57
Average: 6.61
Density
The average density for three separate gel preparations was recorded in Table 4-3.
These values were the average values of three core samples from each gel preparation.
Each of the core samples were measured by the multipycnometer a total of 5 times. This
translated to 15 total measurements for each average which consisted of 5 repetitions of 3
different core samples for each of the gel samples. The densities for all samples were in the
range of 1.02 +/- 0.01 g/cm3. The data results were consistent between gel preparations.
They also compared well to the density of water which made up almost 94% of the gel on a
total mass basis.
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Table 4-3. Gel Density.
Gel Density
Measured Density
Sample
Grams/cm3
1
1.014
2
1.024
3
1.019
Average: 1.020
Standard Deviation
.003
.003
.004
Freezing
The freezing experiments were started with a very simple concept and became more
refined. The refinements between iterations were due to the observations from each
previous experiment. The freezing experiments are discussed in the order of their iterative
changes, which mirrors the presentation order in the Materials and Methods section.
The first most basic freezing experiment yielded some very important qualitative
results. The unconstrained top surface of the samples did not remain planar. The surface
was observed to fracture and rose unevenly. This was unacceptable for applying a flat
electrode, as well as not exhibiting an ideal geometry. The translucence of the gel was
decreased in the frozen state as well.
Based on these observations an experiment was designed to try to control the top
surface flatness while freezing. The top gel surface was set with the electrode in place.
From this configuration the freezing was initiated from the top surface of the gel. The hope
was that this would have addressed the surface flatness and the geometry issues. The gel in
this case was allowed to rise in the axial direction. The observation when the experiment
was carried out was that while the electrode might remain in contact the geometry had
significantly changed from the unfrozen initial geometry. The top and bottom planes of the
sample which started out parallel were no longer parallel by a significant and visible
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amount. It was even noted in some cases the electrode did not stay in complete contact
with the upper surface of the gel.
The expansion in the axial direction was not ideal for rigid probes that were
entering radially into the sample. If only one probe at the center was used the issue might
have been addressed by allowing both the top and bottom planes to have moved during
freezing. A probe in a central plane would not have been expected to move axially. The
goal was to make multipoint measurements, and therefore axial expansion was deemed
unacceptable.
The next iteration of freezing experiments provided several important solutions.
The initial concept was to allow the sample to expand in the radial direction only. This
meant that the top and bottom planes were constrained to be flat and parallel. The known
volume of the sample cell gave an estimate of how much extra volume was needed based
on the expansion that water undergoes during freezing. A suitable compressible material of
an appropriate thickness was chosen to line the inside of the sample cell. This decreased
the sample cell volume and allowed for radial expansion. The rigid outer shell only saw
very minor pressure applied from the compressed lining. The electrode interfaces with the
gel surfaces were expected to stay in complete contact with this arrangement. The probes
were not expected to see any shearing stress as the gel movement was in the probe axial
direction.
The first runs of this new configuration were made with no probes installed. The
initial observations after freezing were that the electrodes maintained their parallel
positions. The frozen gel when extracted from the sample cell holder and unwrapped from
the interior insulation (the compressible material), showed close adherence to the sought
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after final frozen geometry. The radial exterior had some slight texturing, where it
conformed to the insulation during the gel setting phase. When the electrode was removed,
it was noted to have maintained contact with the gel. This was expected because the
electrode was initially set into the liquid before it congealed. Other important observations
were made about the gel at this point. The transition back to unfrozen gel proceeded with
very little water loss from the sample. The sample appeared to return to its initial state as a
gel with only very minor visible defects after a freeze and thaw cycle.
The next iteration placed probes in a sample, and subjected the sample to a freeze
thaw cycle. The experiment ultimately sacrificed the probes that were installed. After
freezing, the only way to remove the frozen gel intact was by shearing the probes at the
rigid wall of the sample holder. The probes were then observed from the end view with
both of the electrodes removed. With the sample removed from the sample holder and the
insulation removed, the probes were observed from the radial direction of the sample. The
probes had maintained their positions in the sample.
Environmental Characterization
The environmental chamber used in the experiments had several of its features
characterized. The first was the minimum maintainable temperature. By setting the system
to a continuous run mode overnight and measuring the temperatures inside, it was
determined that the system was capable of cooling to approximately -33 C". This
temperature was much lower than required for our purposes, but made the system capable
of a greater range of applications for future investigations.
The system was normally operated in a cycling mode. Data for cycling were
captured intermittently during the experimental investigations. One set of representative
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data were plotted in Figure 4-6. This data showed how the internal temperature for the
sample gel typically varied and approximately how the air temperature varied. The sample
in this data was in exactly the same physical set up as the ohmic experiments discussed
later. All three layers of insulation were in place on the sample holder. The data for the
freezer air temperatures were collected with the digital multimeter and a manufacturer
supplied type K thermocouple which had a much lower temperature resolution than the
sample probes.
The graphs of Figure 4-6 showed the relevant characteristics of cycling. The graph
labeled Temperature Cycling One gave a visual comparison of the two different
temperature cycles. It was interesting to note that while the air temperature typically
Figure 4-6. Temperature Cycling.
Object 4-5. CyclingAllMar22.jpg (1471 KB).
86
varied about 7 °C over one cycle , the gel temperature only varied about 0.1 °C. The
following graph utilized a second Y axis which allowed the gel temperatures to be more
closely observed. The graph labeled Temperature One Cycle contained approximately one
cycle of data for the gel, while the last graph in the figure had the valley section of this
single cycle.
The data for the air temperature were resolved in 1 °C steps, but the cycling
characteristics were still obvious. The data were very useful, as it gave an idea of how the
sample responded to external changes in temperature. Another piece of dynamic
information was observed in the Temperature One Cycle graph. The temperature probes
did not seem to show any significant finning of external heat within the range of the cycling
temperatures. If finning were significant, the probes with the least penetration (Figure 312) into the sample would have led in both the cooling and heating. The observation made
though was the probes tracked very closely even with the reversal during cycling from
heating to cooling. The differences between a probe pair were graphed and no trends
appeared (Figure 4-7).
The temperature range of interest for the gel was warmer than the cycling
temperature of the environmental control unit. The temperature of the sample had to be
raised. After the installation of thermal dampers, the temperature change in the air and the
sample inside the unit were tracked. The configuration was again just as it was in the
actual ohmic thawing experiments with all insulation in place. Figure 4-8 shows how the
sample and the chamber interior air conditions varied after the unit was turned off. After
an initial period, the air temperature and sample temperature had approximately the same
slope. When we regressed the linear section, the slope there was determined to be 4.856 x
87
Figure 4-7. Cycling and Adjacent Probe Temperature Differences.
Object 4-6. Cyc15-13DiffAll.jpg (985 KB).
10-4 °C/s. This was approximately 0.029 °C per minute or 1.748 °C/hr. The temperature
difference between sample and air was roughly 7 °C.
Automatic Power Control Validation
The automatic power control validation experiment verified that the system could
automatically shut down the power to prevent too much current from being supplied to the
sample. An interesting observation was captured during the experiment. The set up used
an incandescent resistance light bulb to provide the resistance. The upper alarm was set
based on the wattage of the bulb rated for 120 VAC. When the circuit was closed with the
voltage set at the upper end of this wattage, but below where it should have triggered the
high alarm, the alarm was tripped. This was due to an initial spike in the current when the
88
Figure 4-8. Sample and Environmental Warming.
Object 4-7. WarmingAll.jpg (719 KB).
circuit closed. The spike was visible on the meter display also. Once the bulb was on and
the filament hot, the voltage was adjusted up to the same level without tripping the alarm.
This was not surprising as the resistance of cold filament was different than that of a hot
one. This unplanned facet of the experiment gave a further insight in how the relays
reacted to a very fast ramped current input.
Resistance Measurement
Unfrozen Gel
One of the primary functions of the experimental apparatus was to make electrical
resistance measurements. These values were the result of combining the data from both
data collection devices that were an integral part of the apparatus. A sample of initial
89
voltage data for the unfrozen gelatin were plotted in Figure 4-9 and Figure 4-10. The
voltage applied looked very much like a square wave. This was a result of the cycling
pattern chosen for the experiment. During the determination of resistance as a function of
temperature many samples of data like these were collected. Figure 4-9 indicated that this
sample was taken over roughly a 2.5 °C range. The ranges of each sample varied slightly
but were generally over a 2.5 to 6 °C span. The ranges sampled had overlap and gave
repeated temperature points for the final determination of the resistance versus
temperature.
The current data plot for each sample set of data was plotted in Figure 4-9 and
Figure 4-10 below the voltage and temperature data plots. Both figures indicated the
voltage was maintained at a roughly constant value while the current increased. The
trapezoidal shape the current assumed was a direct result of the rectangular shape of the
voltage input. This was expected, since the temperature of the gel was changing during the
application of the voltage. The figures also illustrated the temperature changes in each
voltage power on cycle. The regions with the voltage power off showed slight temperature
decreases. This represented the thermal relaxation occurring in the system. The
temperature drop was less when the 6 end temperatures of a power on cycle were more
tightly grouped.
It was observed that even with a relatively low level of voltage applied there was
ohmic heating that occurred in the unfrozen gel. The temperature distribution within the
gel started out relatively uniform. The ohmic heating caused the temperature distribution
to vary in the sample. For calculation purposes the average temperature of all 6 of the
temperature sensors were used.
90
Figure 4-9. Unfrozen Gel Temperature, Voltage and Current Plots.
Object 4-8. UF-Resist-TVC1.jpg (323 KB).
91
Figure 4-10. Unfrozen Gel Temperature, Voltage and Current Plots.
Object 4-9. UF-Resist-TVC2.jpg (381 KB).
92
The reasons for taking the data in a cycling fashion were illustrated from the points
already given. If the complete system of gel and all boundary conditions were perfect, the
gel would have heated uniformly. The system though was a real system, and had a gel that
was not perfectly homogenous or perfectly isothermal, therefore the gel exhibited
temperature increases that were not entirely uniform. A specification was set on how close
to isothermal the sample initially appeared to start a cycle and the maximum spread
between sensors that would not be exceeded. This ultimately allowed the error to be
estimated.
A representative plot of all the unfrozen resistance measurements was made, Figure
4-11. The average temperature values on this plot as well as other plots represented the
Figure 4-11. Unfrozen Gel Resistance.
Object 4-10. UF_ResistAll.JPG (114 KB).
93
average of all 6 temperature readings taken for a single point. The resistance data were
transformed to resistivity data for the gel by use of the consistent geometric shape. The
resistivity appeared as scaled resistance values. The resistance values were scaled by the
area of the sample divided by the height. The numerical value for this was 69.82 x 10-3 m.
The data were plotted in terms of resistivity, see Figure 4-12.
In Figure 4-12 the maximum temperature difference (MTD) is plotted
simultaneously with the resistivity. The maximum temperature difference represented the
largest difference between any 1 of the 6 averaged readings and the average value. The
channel that sustained the highest temperature was also identified and recorded. The plot
Figure 4-12. Unfrozen Gel Resistivity and Maximum Temperature Difference.
Object 4-11. UF_Resisty_MTDiffAll.jpg (235 KB).
94
showed that the upper bound to the temperature spread was 0.25 °C . While this was the
upper bound, the bulk of the data were collected at a level below 0.15 °C maximum
difference. By use of this method for collecting and reducing the data, the average
temperature had meaning with respect to error associated with the measurement of
temperature at a point by the system. It also let the isothermal nature of the gel be defined
and verified while the system was measuring the electrical resistance.
The data on the unfrozen gel were collected at two distinct experimental phases.
The first data set was taken before the gel was frozen. The second data set was taken after
the gel had been frozen and subjected to ohmic thawing. In Figure 4-13 the two sets of the
Figure 4-13. Unfrozen Gel Resistivity Before and After Freezing.
Object 4-12. UF_Resisty_MTDiff_All_Sep10.jpg (226 KB).
95
resistance data were separated and indicated. For easier visual inspection the graph had
only every tenth data point of each set plotted. Data before freezing were over a smaller
temperature range than that taken after the thawing. This was done to be conservative
initially, and avoided driving the gel back to a liquid state. The agreement between the
before and after data were very good. It indicated that from an electrical resistance
standpoint the gel was virtually unchanged by a freeze/thaw cycle.
Figure 4-14 shows all the unfrozen resistance data reduced to every tenth point and
a polynomial fitted to the data. A third order polynomial worked nicely to fit the unfrozen
resistance measurements with an R2 value of 0.9977. The equation for the polynomial is
given below as equation 4-1, where y is resistivity (ohm meters) and x is temperature (°C).
(4-1)
Figure 4-14. Unfrozen Resistivity with Cubic Polynomial Fit.
Object 4-13. UF-Resisty-All-wFit.jpg (121 KB).
96
It was derived by fitting all the data points in Axum and using a weighting factor of the
inverse of the maximum temperature difference. The inclusion of the weighting factor was
designed to favor points on which there was less variation in the gel temperature.
Frozen Gel
The measurement of resistance for the frozen sample was very similar to the unfrozen
from a procedural stand point. The main difference was that longer continuous blocks of
data were possible, because the ohmic heating was less. Figure 4-15 reflected the voltage
applied during data collection for this run. It was noted that this was a complete run over
the temperature range of interest approximately -5 °C to 0 °C . The range was slightly
larger than 5 °C. The temperature profile showed the effects of ohmic heating. The drop
in voltage to a lower level clearly changed the rate the temperature was rising in the sample
corresponding to the ohmic heating. It was noted that this collection was over a two hour
period, while a sample run presented for the unfrozen gel was much shorter. Both the
frozen and unfrozen runs covered approximately the same amount of temperature rise. The
difference in the magnitudes of the voltages applied were apparent. The initial voltage
applied to the frozen gel was roughly three times the magnitude of the voltage applied to
the unfrozen gel.
The current measured during the run was plotted in the bottom plot of Figure 4-15.
This was a single continuous stream of data. The curvature of the data suggested that the
resistance was changing quite rapidly, and the resistance was not linearly related to the
temperature. The voltage step down point was clearly visible from the view of voltage
data on the graphs. The current drop at this point was immediately followed by the current
increasing again.
97
Figure 4-15. Frozen Gel Temperature, Voltage and Current Plots.
Object 4-14. Frozen-Resist-TVC.jpg (273 KB).
98
Figure 4-16 had frozen resistance data for 2 gels and 2 data runs for each of the gels.
The second gel first data run was the same data set that was used in Figure 4-15. The
second gel was represented in the unfrozen measurements presented previously. This was
also the gel system used in the ohmic experiment. The resistance plot was included again
for consistent presentation and gave a feel for the resistance values that were measured.
These resistance values like the unfrozen gel values could be converted to resistivity values.
A resistivity plot for the same set of data used in Figure 4-15 was made, see Figure
4-17. This graph simultaneously plotted the maximum temperature differences. The
maximum temperature differences in the figure gave insight as to how the gel was reacting
to the process. It indicated that the temperature spread before the run started was slightly
higher than during part of the data acquisition. This phenomenon was easily explained
Figure 4-16. Frozen Gels Resistance.
Object 4-15. Frozen-Resist-All.jpg (130 KB).
99
Figure 4-17. Frozen Resistivity and Maximum Temperature Difference.
Object 4-16. Frozen_Resisty_MTDiff21-10.jpg (221 KB).
when when taken in consideration with how the sample arrived at the initial start
temperature. The sample had to warm from the cycling temperature to this range. There
would have been a minor gradient in the sample during this warming. The sample was then
subjected to very minor warming due to ohmic heating. One expected to see the gradient
that was causing the warming to eventually reverse as the gel started at some point to lose
heat instead of gaining it from the environment. The temperature difference data values
went down again when the voltage was reduced. This corresponded to the ohmic heating
being reduced. The temperature differences between probes were very minor for this entire
run with the bulk of the data below a maximum temperature difference of 0.05 °C.
The 4 frozen resistivity data sets were plotted in Figure 4-18. The resistivity data
had a third order polynomial fitted to it. The fitted polynomial is listed as equation 4-2,
where y is resistivity (ohm meters) and x is temperature (°C).
100
(4-2)
It was arrived at in the same manner as the polynomial for the unfrozen resistivity data and
made use of the same form of weighting coefficients. Use the weighting coefficients in this
case provided consistency in analysis, since the temperature spread from the average
temperature was very small for all of the data. The R2 for the fit was 0.9953.
Combined Temperature Ranges
The resistivity measured for the sample gel is presented for both solid phases
unfrozen and frozen. These phases represent two non overlapping temperature ranges. A
third order polynomial can adequately reflect the nature of data in each of those
temperature ranges. It is noted though that they are not the same polynomial. Figure 4-19
Figure 4-18. Frozen Resistivity with Cubic Polynomial Fit.
Object 4-17. Frozen-Resisty-All-wFit.jpg (124 KB).
101
Figure 4-19. Unfrozen and Frozen Resistivity Cubic Fits.
Object 4-18. ResistyFitsBoth.jpg (105 KB).
presents the two fits applied to the data on a single plot. With a single scale applied to
both sets of data, the difference in magnitude between the resistivity in each phase was
graphically evident. This gave a clear picture of what was expected to happen to the
electrical resistivity of finite volumes within the gel as they under went transition both in
temperature and phase during thawing.
Ohmic Thawing
The ohmic thawing data is presented in similar order as the resistance data to
emphasize the similarities and differences between the two types of data. It was previously
noted that the resistance data collection runs involved ohmic heating of the gel sample.
102
The ohmic thawing data actually captured information on the solid to solid phase change
that was occurring in the gel. The temperature range was roughly the full span of all the
resistance data, and included the gap area where the phase change occurred that no
resistance data existed.
The voltage application during the experiment was plotted in Figure 4-20 on the top
plot. The voltage was basically a step input with various amounts of time between its
application. The step nature of the input was a result of the switching used to control the
power application. The first power application cycle was applied and the sample allowed
to thermally relax so that the temperatures were more uniform. The same procedure was
followed for the second power application cycle. Both of these cycles were manually
controlled by the operator. The third power application cycle was different. It was
stopped by the current limiting control system of the apparatus. During the five second
window of the automatic shutdown, the voltage was manually adjusted by the operator.
The system automatically started the next cycle at the end of the programmed delay. This
was carried out 2 more times as indicated by the graph. The shut down was then manual to
allow for thermal relaxation similar to the initial power off cycles. The next section showed
the applied voltage had been adjusted, and the power control was initiated by the
automatic but overridden by manual control. The system shut down automatically and the
circuit was manually opened to allow for more thermal relaxation, and was manually closed
again to initiate another cycle.
The current data for the ohmic experiment were plotted in Figure 4-20 on the lower
plot. The current data clearly indicated where automatic shut off was used. Each current
peak at 0.4 amps represented one of these cases. The peaks below this level represented
103
Figure 4-20. Ohmic Thawing Voltage and Current Data.
Object 4-19. OhmicVC.jpg (225 KB).
104
manual power shut off. The plot of the current data indicated periods of thermal relaxation
with plateau areas having a zero value. The fully automated power off to power on cycles
were identifiable by the steep drop and rise 5 seconds later. The time scale of the plot
makes this appear as though it was almost immediate. The nonlinear nature of the
resistance values was very clear from the shape of the current data when viewing the
corresponding voltage data. The curvature of the current data during application was quite
a contrast to the voltage data which were very flat during application.
In Figure 4-21 the temperature data for the ohmic experiment were presented in 2
plots. The top plot in this figure represented a short period just before the power was
applied. It was essentially the initial temperature condition of the gel sample. The
temperature data plotted indicated the sample were basically isothermal with a temperature
spread of approximately plus or minus 0.05 °C.
The complete temperature data colleted for the ohmic experiment were plotted in
the lower plot of Figure 4-21. This range covered data from the plot above it to a point in
time well after the last power application was ended. It was seen that the gel did not heat
in a perfectly uniform manner. The temperature data as it related to phases of the sample
were easier to interpret with the addition of the current data.
Two additional plots of the temperature data were plotted in Figure 4-22. The
upper plot was all of the temperature data with the current data. The new plot allowed the
region before phase change to be easily identified from the temperature data. This was
where the initial manually controlled power cycles were. The region where phase change
was occurring could then be identified as areas where automatic control of the power
105
Figure 4-21. Ohmic Temperature Data.
Object 4-20. OhmicTempBoth.jpg (418 KB).
106
Figure 4-22. Ohmic Temperature and Current Data.
Object 4-21. OhmicCurrentTempBoth.jpg (417 KB).
107
application was being used from looking at the current data. The final region with power
cycles after the phase change could also then be easily identified.
It was evident that before phase change much less current was being delivered to the
sample for heating, just as was expected from the known resistivity data of the sample gel.
The current applied for phase change and beyond was much greater and in all but one case
was controlled by the automatic cut off value. The temperature spreads between different
geometric positions in the sample were relatively small in the frozen region even during
heating. These spreads began to increase significantly when the sample began to change
phase.
The phase change region was shown in the lower plot of Figure 4-22. This plot
showed more detail of the phase change region. It started at the end of the second thermal
relaxation region and spanned to one cycle past all temperature data over the phase change.
The current increase over the first span of a very small change indicated that some portion
of the sample was undergoing phase transition. The rise in current, if not controlled, would
have led to run away heating at that point. The temperature readings appeared to converge
for a brief period with the voltage reduced. The next power cycle ended as one pair of
sensors (Chan5 and Chan7) started to show a temperature rise.
The data illustrated how the temperatures from a finite set of points would not have
been sufficient to detect the initiation of phase change in the sample. The current data gave
an early indication that somewhere in the sample the gel was undergoing a large change in
its resistivity value. The temperature data from the phase change region showed other
interesting points with respect to geometric positions of the sensors. Two sensors at the
same position diverged in readings once the temperature was above the phase change
108
temperature. It was interesting to note that the highest readings consistently came from the
same side of the sample. The most probable explanation was that the sensors were seeing a
finning effect on the probe itself inside the gel from a heated region. A localized volume of
the gel that was experiencing run-a-way heating would have been much higher in
temperature than other volumes of the gel. This hot volume could have finned heat
through the probe body to the temperature probe tip. The impact on a single end of the
probe would have been related to the position of the higher temperature volume to the
probe section. The probe arrangement left very little chance that this effect could have
impacted both ends of the probe set equally. This point illustrated the difficulty in
establishing validity of a single probe temperature measurement in a solid that was not
isothermal where there would have been no second probe to show the phenomenon.
A plot of the maximum temperature differences and gel sample apparent resistivity
for average gel temperatures were made in Figure 4-23, and contrasted temperature spread
for an ohmic data experiment compared to an experiment designed to measure resistivity.
It was clear that very little of this data could be used to get the resistivity at a given
temperature due to the temperature differences within the gel sample. The value of the
data were in already knowing the resistivity, then theoretically a temperature range for a
sample could be set with a temperature distribution that would create the same total
resistivity. The overlaps in data were a result of thermal relaxation where the average
temperature went down while power was not supplied.
The apparent power supplied to the sample during the ohmic thawing experiment
was plotted in Figure 4-24. The graph had both the instantaneous and the cumulative
amount supplied. The cumulative was arrived at by summing the individual average
109
Figure 4-23. Ohmic Apparent Resistivity and Maximum Temperature Difference.
Object 4-22. OhmicResistyAveTempMTD.jpg (158 KB).
apparent power application measurements. The average was the sum of the previous
second plus the current second divided by 2. This was an estimate that assumed the input
was constant over the one second interval that the average measurement represented. With
the time interval being small (1 second), this provided a good estimate. The units for the
cumulative power was VA seconds. The final value for the cumulative power was 79140
VA seconds. The highest instantaneous input occured during phase change.
Error Analysis
Temperature
The temperature error was dependent on several factors as mentioned in the
calibration section. The main error sources of concern were the data acquisition system
110
Figure 4-24. Power Applied.
Object 4-23. OhmicPowerAppCumu.jpg (132 KB).
resolution, signal conditioning error and level of noise. These primary sources provided a
useful estimate of the temperature measurement error expected from the calibrated system.
The resolution of the data acquisition system was calculated to be 76.3 x 10-3 °C
per bit. The signal conditioning error had already been estimated at the linearity of the
signal conditioning module which was 0.01 °C . The noise was estimated from looking at
data that were expected to be isothermal with respect to time and had little slope, then
noting the range of values. The noise on this basis appeared to be roughly 0.04 °C. The
assumption was made that these errors were independent, and then they could be added in
quadrature to get a final value. This yielded a final estimate on the temperature error of
approximately 0.042 °C. The break down of the calculations were placed in Appendix B.
111
Resistance
The resistance error included a greater number of measured quantities, making it
more complex. It was dependent on the error associated with both the voltage and current
measurements. To address the resistance measurement error at a specific temperature, the
temperature error was also be taken into account to avoid giving a range for both
temperature and resistance. They were coupled through the third order polynomial fitted
to the resistance versus temperature data. The usefulness of being able to fit the resistance
versus temperature data with a polynomial was then apparent.
The polynomial was used to establish, through its derivative, the slope at a given
average temperature data point. The slope was then in Ohms/°C. This slope was
multiplied by the average temperature error to provide the temperature error impact on the
reading of the resistance. The average temperature error accounted for the fact that the gel
was not expected to have been completely isothermal. The average temperature error took
the maximum temperature difference and the temperature measurement error then
combines the values by adding them in quadrature. The original errors associated with the
measurement and calculation of the resistance were then added to this value in quadrature
to give an estimate of the resistance error at a given temperature. The temperature was
assumed to be exact now, since all the error associated with it had been placed into the
value of the resistance error.
The resistivity error was not simply a scaled resistance error. The problem for
resistivity involved the fact that the length of the sample was measured, and the cross
sectional area was calculated from a diameter measurement. This introduced another
source of error that was accounted for when resistivity error was examined. The error in
112
resistivity as it related to temperature error was handled in the same manner as presented
for resistance error as it related to temperature error. An example calculation was made
and included in Appendix C. The appendix was generated as a Mathcad (MathSoft
Engineering and Education Inc., Cambridge, Massachusetts) sheet that was set up to verify
calculations carried out to transform the data already in Axum to be graphed.
The results of the error analysis were graphed. A fitted curve with the frozen
resistivity on the first y-axis was plotted in the top plot of Figure 4-25. The percent
resistivity error was placed on the second y-axis.
The total percent resistivity error was inclusive of the temperature measurement
error, while the resistivity error had only the resistivity error without the temperature
measurement error included. The total theoretical percent error increased as the
temperature increased. The scale of the graph made the data look as if it were becoming
closer to the fit and less spread out.
The lower plot of Figure 4-25 was the same data on a new scale zoomed to
approximately the last 1.5 °C of data. On this scale the spread from the third order
polynomial was easily seen. The importance of including a temperature measurement error
in the total error was easily verified from this plot. The resistivity error was not large
enough to account for the spread of values found experimentally. The total error gave a
realistic value that accounted for the spread found experimentally. The higher the
temperature in this span the more dominant the error due to temperature error became, and
the larger the total error. The resistivity error alone would have led one to believe the
opposite.
113
Figure 4-25. Frozen Resistivity Error.
Object 4-24. ErrorPercFrozResistyBoth.jpg (576 KB).
114
The maximum temperature difference’s role in the total resistivity error was also illustrated
graphically. A plot of the maximum temperature differences and the total error were made
in Figure 4-26. The shape of the total error was very similar to that of the maximum
temperature difference. A rise in the maximum temperature difference value led to a
substantial rise in the total error.
The unfrozen resistivity data were plotted in Figure 4-27. The plot in this figure
was similar to the upper plot in Figure 4-25. The scale values for each of the axes were a
contrasting feature of this plot. This was expected for the resistivity values, but carried
over to the error values as well. The total percent error was very close to being constant
around 3.3 percent. It did not vary more than one tenth of one percent from this value.
The frozen data exhibited a much wider range of total percent error. It included values that
were almost 10 times that amount.
Figure 4-26. Frozen Resistivity Error and Maximum Temperature Difference.
Object 4-25. ErrorPercFrozMTDResisty.jpg (417 KB).
115
Figure 4-27. Unfrozen Resistivity Error.
Object 4-26. ErrorPercUnfrozResistyAll.jpg (185 KB).
contrasting feature of this plot. This was expected for the resistivity values, but carried
over to the error values as well. The total percent error was very close to being constant
around 3.3 percent. It did not vary more than one tenth of one percent from this value.
The frozen data exhibited a much wider range of total percent error. It included values that
were almost 10 times that amount.
The unfrozen resistivity measurement was less sensitive to temperature error. The
resistivity error without compensating for the temperature error was very close to the total
value as was indicated in Figure 4-27. The maximum temperature differences presented in
Figure 4-12 showed that in contrast to the frozen data this data had larger differences. The
maximum differences for the unfrozen data were more than twice as large as the frozen
data. The lower sensitivity of the unfrozen measurements was related to the slower rate of
116
change of the resistivity in the unfrozen state. The rate of change for the frozen range was
much greater when contrasted to the unfrozen, and magnified any temperature error.
Figure 4-19 visually verified the last point.
CHAPTER 5
CONCLUSIONS AND RECOMMENDATIONS
The research was successful in designing and constructing an apparatus capable of
making accurate measurements needed for determining the electrical resistivity of a gel in
both the unfrozen and frozen states. The system design was capable of continuously taking
data on a frozen gel as it under went ohmic thawing. The research also validated the
importance of knowing approximately how isothermal a gel was in terms of reporting the
theoretical error. The data collected on unfrozen gel resistivity did not indicate that the
freezing or the thawing processes impacted the gel electrical properties.
Calibration of the experimental apparatus presented data that was identified with
different methods of heat transfer. Conduction and convection were both present in the
calibration experiment. The data indicated that assuming conduction from the top surface
for the classic Stephan problem of water freezing was probably reasonable up to the
maximum density temperature of water. The calibration data carried further implications in
the reverse process, thawing, that convection would have played a role early in the process
up to the maximum density temperature, but after that point conduction from the top
surface dominated.
During the operation further challenges of making measurements on a gel system
undergoing phase change were identified. Internal finning of heat by the probes could
impact the temperature measurements. The planar probe arrangement was unable to
distinguish between symmetric geometric heat source locations on opposite sides of the
117
118
plane of the probes. Single temperature locations were unlikely to capture the initiation of
phase change. The initiation of phase change could occur anywhere randomly in the
sample and the event would only be evident when a probe location was thermally impacted
by the event. The physical size of the probe compared to the sample made it highly
unlikely that the probe was located exactly where phase change initiated.
There were several recommendations for further research. The experimental
apparatus could undergo a second design iteration. The probe diameters could be reduced
to help minimize internal finning. The probe geometric layout could be changed so that
each probe would enter at 60° angles to one another. This would divide the gel into 6
sectors and yield more geometric information on locations of heat sources. Ohmic thawing
experiments could be designed with gels that have solid inclusions of simple geometric
nature of another gel or food material with different electrical properties. The experimental
data gained from this research and further research in the area should be used for validating
numerical models of the ohmic thawing process.
APPENDIX A
ALTERNATE NEUMANN'S SOLUTION
This sheet created with Mathcad 2001© provides a derivation of the λ equation
1
assuming the front location has the form of X = 2⋅ λ ⋅ ( κ 2⋅ t) insead of assuming
2
1
2
X = 2⋅ λ ⋅ ( κ 1⋅ t) as in Carslaw & Jaeger (1959). The symbols are consistent with
those in the original derivation.
κ1
Thermal diffusivity of solid
κ2
Thermal diffusivity of the liquid
λ
Numerical constant
ρ
Density of liquid and solid phases
A,B
Numerical constants
c1
Specific heat of the solid
c2
Specific heat of the liquid
K1
Thermal conductivity of the solid
K2
Thermal conductivity of the liquid
L
Latent heat of fusion
T1
Melting point temperature
v1
Temperature in solid phase
v2
Temperature in liquid phase
119
120
V
Initial Temperature of liquid phase
x
Position
X
Position of the phase change front
erf ( 1) = 0.843
erfc ( x) := 1 − erf ( x)
v1 = A⋅ erf ⎡
d
erf ( x) =
dx
x
⎢
1
⎢
2
⎣ 2⋅ ( κ 1⋅ t)
⎤
⎢
1 ⎥
⎢
2 ⎥
κ
⋅
t
(
)
⎣ 2
⎦
x = X ( t)
X
⎤ = V − B⋅ erf ⎡ X
⎢
⎥
⎢
1
1
⎢
⎥
⎢
2
2
⎣ 2⋅ ( κ 1⋅ t) ⎦
⎣ ( κ 2⋅ t)
T1
erf ⎡
X
⎢
1
⎢
2
⎣ 2⋅ ( κ 1⋅ t)
B=
⎤
⎥
⎥
⎦
x
Phase Surface boundary condition
A⋅ erf ⎡
A=
π
( 2)
⋅ exp −x
v2 = V − B⋅ erf ⎡
⎤
⎥
⎥
⎦
When
v1 = v2 = T1
2
⎤
⎥ = T1
⎥
⎦
V − T1
erfc ⎡
⎤
⎢
1 ⎥
⎢
2 ⎥
⋅
⋅
t
2
κ
(
)
2
⎣
⎦
X
1
X = 2⋅ λ ⋅ ( κ 2⋅ t)
K 1⋅
2
λ=
1 X
⋅
2 κ 2⋅ t
d
d
d
v1 − K2⋅ v2 = L⋅ ρ ⋅ X
dx
dx
dt
1
K 1⋅
d ⎡
A⋅ erf ⎡
⎢
⎢
dx
⎢
⎣
x
1
⎢
2
⎣ 2⋅ ( κ 1⋅ t)
⎤ ⎤ − K ⋅ d ⎡ V − B⋅ erfc ⎡ x
2
⎥⎥
⎢
1
dx ⎢
⎥⎥
⎢
⎢
2
⎦⎦
⎣
⎣ ( κ 2⋅ t)
⎤ ⎤ = L⋅ ρ ⋅ d 2⋅ λ ⋅ ( κ ⋅ t) 2
2
⎥⎥
dt
⎥⎥
⎦⎦
121
⎡ −1 x2 ⎤
⎡ −x2 ⎤
exp ⎢ ⋅
exp ⎢
⎥
⎥
4 ( κ 1⋅ t) ⎦
κ 2⋅ t) ⎦
(
A
B
λ
⎣
⎣
K 1⋅
⋅
− 2⋅ K2⋅
⋅
= L⋅ ρ ⋅
⋅κ2
π
κ 1⋅ t
κ 2⋅ t
π
κ 2⋅ t
Substitute in for A and B
K 1⋅
T1
⎛ erf ⎛ 1 ⋅ X ⎞ ⋅ π ⎞
⎜ ⎜2
κ 1⋅ t ⎠
⎝ ⎝
⎠
−K2⋅
⎡ −1 x2 ⎤
exp ⎢ ⋅
⎥
4
κ
⋅
t
(
)
1
⎣
⎦ + ...
⋅
κ 1⋅ t
( V − T1)
⎛ erfc ⎛ 1 ⋅ X ⎞ ⋅ π ⎞
⎜ ⎜2
κ 2⋅ t ⎠
⎝ ⎝
⎠
⎡ −1 x2 ⎤
exp ⎢ ⋅
⎥
4 ( κ 2⋅ t) ⎦
λ
⎣
⋅
= L⋅ ρ ⋅
⋅κ2
κ 2⋅ t
1 X
Recognizing the λ terms, and rewriting.λ = ⋅
2 κ 2⋅ t
K 1⋅
⎛
2 κ2 ⎞
⎝
κ1 ⎠
exp ⎜ −λ ⋅
T1
⎛
κ2 ⎞
erf ⎜ λ ⋅
⋅ π
κ1 ⎠
⎝
⋅
κ 1⋅ t
− K 2⋅
( V − T 1)
erfc ( λ ) ⋅ π
κ 2⋅ t
2
1 X
λ = ⋅
4 κ 2⋅ t
2
⋅
( 2) = L ⋅ ρ ⋅
exp −λ
κ 2⋅ t
λ
κ 2⋅ t
⋅κ2
Dividing by T1 and multiplying by square root of π
K 1⋅
1
⎛
κ2 ⎞
⎝
κ1 ⎠
erf ⎜ λ ⋅
⎛
2 κ2 ⎞
⎝
κ1 ⎠
exp ⎜ −λ ⋅
⋅
κ 1⋅ t
V − T1) exp ( −λ 2)
(
⋅
⋅
− K2
erfc ( λ )
T 1⋅ κ 2⋅ t
1
= L⋅ ρ ⋅
λ
T1⋅ κ 2⋅ t
⋅ κ 2⋅ π
2
122
Dividing through by K2, getting ready to recognize the c2
⎛
⎛ 2 κ2 ⎞ ⎞
1
exp ⎜ −λ ⋅
⎜
2
K1
κ1 ⎠
1
⎝
⎟ − ( V − T1) ⋅ exp ( −λ ) = L⋅ ρ ⋅ λ ⋅ κ 2⋅ π 2
⋅⎜
⋅
K2 ⎜ ⎛
K2 T1⋅ κ 2⋅ t
⎟ erfc ( λ ) T1⋅ κ 2⋅ t
κ2 ⎞
κ 1⋅ t
⎜ erf ⎜ λ ⋅
κ1 ⎠
⎝ ⎝
⎠
Utilizing
⎛
K1
K2
κ2 =
ρ ⋅ c2
2 κ2 ⎞
exp ⎜ −λ ⋅
⋅
K2
and mutiplying by
κ 1 ⎠ κ 2 ( V − T1)
⎝
⋅
−
⋅
κ1
erfc ( λ )
⎛
κ2 ⎞
erf ⎜ λ ⋅
κ1 ⎠
⎝
κ 2⋅ t
⎛
2 κ1 ⎞
⎝
κ2 ⎠
exp ⎜ −λ ⋅
T1
1
=
L λ
2
⋅ ⋅π
c2 T1
1
2
Now you have a form for the λ from assuming X = 2⋅ λ ⋅ ( κ 2⋅ t) instead of
1
X = 2⋅ λ ⋅ ( κ 1⋅ t)
2
as in Carslaw & Jaeger (1959).
APPENDIX B
ERROR IN TEMPERATURE MEASUREMENT
Error in Temperature Measurement
Components of that error:
Data Acquisiton Resolution
Signal Conditioning Error
Level of Noise
Data Acquisition Resolution
16
2
=
3
65.536 × 10
5V
16
−
2
=
−6
76.295 × 10
Volts per Bit
V
1
500
= 100
5
°C/V
−6
100⋅ 76.295 × 10
=
Degrees Celsius per linearized Volt output
−3
7.63 × 10
Resolution in Degrees Celsius per Bit
Signal Conditioning Error
Linearity of the Signal Conditioning Module (Total Range of Module)
500⋅ 0.0002 = 0.1
°C
Nonlinearity of the Conditioning Module
Range of Interest is less than 50 therefore less than 1/10 of
total nonliearity or 0.01
Level of Noise
0.04
°C
Level of noise from data based on observation of Calibration and
other data, roughly 5 bits
Summation of the Errors in Quadrature Yields Expected Error in Degrees Celsius
(.01)2 + (0.00763)2 + (0.04)2 = 0.042
°C
123
Expected Error in Degrees Celsius
APPENDIX C
RESISTIVITY ERROR
Resistivity error with no temperature error
Voltage := 67.89447V
Data Value
Current := 0.1566A
Data Value
Resistance :=
Voltage
Current
Resistance = 433.553 Ω
First Examine the Voltage Measurement Error
Voltage Measurement by Crompton Meter Converted to Current by Output Pod.
Current Converted to Voltage by DAC Reading Voltage across Precision Resistor.
( 20 − 4)mA = 0.016 A
Span of output pod
250Ω ⋅ 0.0001 = 0.025 Ω
Accuracy of the Precision Resistor
4mA⋅ 250Ω = 1 V
Low side output
20mA⋅ 250Ω = 5 V
High side output
−5
16mA⋅ 0.0007 = 1.12 × 10
A
Since V=IR, need to look at dV =
Accuracy of Current output (Manufacturer
Specification 0.07% of Span)
d
d
V⋅ R +
V⋅ I, which will be done in quadrature.
dI
dR
( 11.2 × 10− 6⋅ A⋅ 250Ω) 2 + ( 25 × 10− 3Ω⋅ 20mA) 2 = 2.844 × 10− 3 V
This would be the scaled voltage error, before converting back to Voltage applied to sam
The value can be converted by dividing by the original scaling factor, where the original
volt range of the Crompton meter was converted to a effective 4 volt range by current out
4
500
124
125
−3
2.844293 × 10
⎛ 4 ⎞
⎜
⎝ 500 ⎠
V
= 0.356 V
Accuracy of Voltage, which can be
considered as Measure of Error
−3
Voltage_Error := 355.536625 × 10
V
Renaming the Error to a variable
Examine the Current Error
Current Read by Extech DMM
−5
50.0mA⋅ 0.0006 + 0.03mA = 6 × 10
Manufacturer Specification of 0.6%+3d
this leads to 2 values, determined by the
Range that the DMM is reading
A
−6
Low Range 60⋅ 10
A
−6
High Range 600⋅ 10
−6
Current_Error := 600⋅ 10
⋅A
A
Renaming the Error to a variable
2
Voltage
1
⎞
⎞
Ohms_Error := ⎛⎜
⋅ Current_Error + ⎛⎜
Voltage_Error
2
Current
⎠
⎝ Current
⎠ ⎝
2
Ohms_Error = 2.813 Ω
Ohms_Percent_Error :=
Ohms_Error
⋅ 100 Ohms_Percent_Error = 0.649
Resistance
Length := 49mm
Length of the sample cell
Length_Error := .5mm
Radius := 33mm
Radius of the sample cell
2
Area := π ⋅ Radius
Area_Error := 2⋅ π ⋅ Radius⋅ .5mm
−3 2
Area = 3.421 × 10
m
Assumes Diameter error equal to the Length Error,
which implies Radius error would be the same.
126
Resistivity := Resistance ⋅
Area
Length
Resistivity = 30.271 Ω ⋅ m
Take the derivative for the Resistivity and add the parts in quadrature.
For presentation a substitution will be made for the each part.
OE :=
Area
⋅ Ohms_Error
Length
AE :=
Resistance
⋅ Area_Error
Length
LE :=
Resistance ⋅ Area
2
⋅ Length_Error
Length
Resistivity_Error :=
2
2
( OE) + ( AE) + ( LE)
2
Resistivity_Error = 0.988 Ω ⋅ m
Resistivity_Percent_Error :=
Resistivity_Error
⋅ 100
Resistivity
Resistivity_Percent_Error = 3.263
Temperature Contribution
Temperature_accuracy := 0.042 °C
From Temperature Error Analysis
Max_Temperature_Diff := 0.10 °C
From Data at each Point
Temperature_Unknown :=
2
Temperature_accuracy + Max_Temperature_Diff
2
Apply the slope at the given temperature for the data point by taking the derivative of the
cubic polynomial that was fitted at that point, and multiply by the temperature unknown
2
Slope := 3⋅ −35.9628⋅ Temperature + 2⋅ 162.3497⋅ Temperature + −526.1101
Resistivity_Unknown :=
2
Resistivity_Error + ( Slope⋅ Temperature_Unknown)
2
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BIOGRAPHICAL SKETCH
Randy A. Clements was born January 24, 1966, to Larry and Sue Clements of
Davenport, Florida. Randy graduated high school in 1984 from Haines City High School
in Haines City, Florida. He attended Polk Community College for 2 years before
transferring to the University of South Florida. He married Tammy Moody, his junior high
sweetheart, in 1988. Then, he graduated with a bachelor’s degree in physics during the fall
of 1990. His oldest son Kyle was born March 24, 1995. He earned a bachelor’s degree
and a master’s degree in mechanical engineering in the summer of 1995 from the University
of South Florida. The summer of 1995 also marked admission to the University of Florida
as a USDA National Needs Fellow. He has pursed research in ohmic heating under Murat
Balaban during his graduate studies at the University of Florida. His second son Austin was
born November 3, 1998.
131