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Design of a radio frequency heating system for electrolytic liquids and sludges Ferdous, Md. Saimoom 2015

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  DESIGN OF A RADIO FREQUENCY HEATING SYSTEM FOR  ELECTROLYTIC LIQUIDS AND SLUDGES by Md. Saimoom Ferdous   B.Sc., Bangladesh University of Engineering and Technology, 2012  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF  MASTER OF APPLIED SCIENCE in THE COLLEGE OF GRADUATE STUDIES (Electrical Engineering)  THE UNIVERSITY OF BRITISH COLUMBIA (Okanagan)  January 2015  © Md. Saimoom Ferdous, 2015   ii Abstract A radio frequency (RF) heating system has been designed to heat electrolytic liquids and sludges in a pressurized test vessel. The RF heating system is designed to heat a 400 ml load volume at a frequency of 13.56 MHz using a 1 kW RF generator.  The primary application for the heating system is to conduct experimental work on the pretreatment of waste activated sludge, a byproduct of wastewater treatment plants. The dielectric properties of waste activated sludge were analyzed and it was determined that ionic conduction heating at a low frequency would be more efficient than microwave heating at a frequency of 2.45 GHz. The RF heating system was tested with sludge and salt water loads over a temperature range of 20°C to 120°C. Power transfer efficiency from the generator to the load was excellent and exceeded 86% over the entire temperature range for both loads. An important part of this work was the design of the RF applicator. The applicator consists of two circular electrodes mounted inside a Teflon cylinder to uniformly heat the load. The Teflon cylinder has seals and can heat loads under pressure. The load cylinder is enclosed in a coaxial housing and the geometry of the load cylinder and enclosure are designed to provide a nominal impedance of 50 Ω to match the RF generator impedance. The applicator has a thermocouple embedded in an electrode and a software control system is implemented in LabView to adjust the generator power for a target ramp rate or to maintain a steady state temperature. Extensive electromagnetic simulations were done to verify and optimize the applicator design. Analytic, simulation and experimental results are compared and very good agreement is obtained.   iii Table of Contents Abstract .......................................................................................................................... ii Table of Contents ......................................................................................................... iii List of Tables ................................................................................................................. vi List of Figures .............................................................................................................. vii List of Abbreviations ................................................................................................... xii Acknowledgements ..................................................................................................... xiii Dedication ................................................................................................................... xiv Chapter  1: Introduction ............................................................................................... 1 1.1 Literature Review.............................................................................................. 2 1.1.1 Heating Pretreatment Methods for Waste Activated Sludge .................... 2 1.1.2 Other Applications of RF Heating ............................................................ 3 1.2 Research Objectives .......................................................................................... 4 1.3 Overview of Chapters ....................................................................................... 5 Chapter  2: Selecting a Frequency for the RF Heating System ................................ 7 2.1 Conventional Heating versus Electromagnetic Heating ................................... 8 2.2 Principles of Electromagnetic Heating ............................................................. 9 2.2.1 Conductivity ............................................................................................ 10 2.2.2 Ohmic Heating ........................................................................................ 13 2.2.3 Dielectric Heating ................................................................................... 14 2.3 Electrical Properties of Materials.................................................................... 18 2.3.1 Relaxation, Dispersion and the Debye Model ........................................ 18 2.3.2 Electrical Models for Cells and Tissues.................................................. 21   iv 2.3.3 Dielectric Properties of Waste Activated Sludge .................................... 24 2.4 Selecting a Frequency for Heating Waste Activated Sludge .......................... 26 Chapter  3: Design of the RF Heating System .......................................................... 30 3.1 Electrical Properties of the Load..................................................................... 30 3.1.1 Waste Activated Sludge .......................................................................... 31 3.1.2 Equivalent Salt Water Loads .................................................................. 32 3.2 Heating Applicator Physical Design ............................................................... 36 3.3 Electrical Models of the RF Heating System .................................................. 43 3.3.1 Power Transfer ........................................................................................ 44 3.3.2 Equivalent Model for the Load ............................................................... 47 3.3.3 Electrical Model for the Enclosure ......................................................... 51 3.4 Analytic and Simulated Results for Power Transfer Efficiency ..................... 55 Chapter  4: Experimental Results .............................................................................. 60 4.1 Design of the Experimental Test Bed ............................................................. 60 4.1.1 RF Generator ........................................................................................... 62 4.1.2 Coaxial Cable Interconnect ..................................................................... 64 4.1.3 Heating Applicator .................................................................................. 67 4.1.4 Temperature Measurement System ......................................................... 78 4.1.5 Control Software ..................................................................................... 80 4.2 Thermal Profiles of the RF Heating System ................................................... 83 4.2.1 Thermal Ramp Rate for a Salt Water Load ............................................ 83 4.2.2 Thermal Ramp Rate for Waste Activated Sludge ................................... 84 4.2.3 Thermal Settling Time for Heating at Constant Temperature ................ 86   v 4.2.4 Thermal Gradient between the Electrodes .............................................. 88 4.3 Impedance and Power Transfer Measurements .............................................. 96 4.3.1 Salt Water Load ...................................................................................... 96 4.3.2 Waste Activated Sludge ........................................................................ 100 4.4 Comparison of Analytic, Simulated and Measured Results ......................... 102 Chapter  5: Conclusion ............................................................................................. 105 5.1 Contributions................................................................................................. 105 5.2 Future Work .................................................................................................. 107 Bibliography .............................................................................................................. 109    vi List of Tables  Table 3.1  Electrical properties of waste activated sludge at a frequency of                   13.56 MHz and at a temperature of 25°C. ............................................................. 31 Table 3.2  Comparison of the electrical properties of salt water and waste                   activated sludge at a temperature of 25°C. ............................................................ 34 Table 3.3  Equivalent circuit and geometrical parameters for WAS and                   salt water loads at 25°C. ........................................................................................ 49 Table 3.4  Capacitance and inductance of the connecting coaxial cable. ............................... 52 Table 3.5  Intrinsic capacitance and inductance for the heating apparatus. ............................ 54 Table 4.1  Effect of EMI on temperature measurements. ....................................................... 79 Table 4.2  Ramp rate of the RF heating device with 0.03315 N salt water load. ................... 84 Table 4.3  Comparison of ramp rates for 0.03315 N salt water and 4.5% WAS. ................... 86 Table 4.4  Summary of maximum and minimum temperatures across a                   0.03315 N salt water load. ..................................................................................... 94    vii List of Figures Figure 2.1  Conventional and electromagnetic heating temperature profiles across the load. . 9 Figure 2.2  Conduction current flow through a metallic conductor. ....................................... 11 Figure 2.3  Ionic current flow through a salt water electrolyte. .............................................. 12 Figure 2.4  Ohmic heating from conduction current (left) and ionic current (right). ............. 13 Figure 2.5  Electric dipole synchronization with frequencies; left: perfect                  synchronization at low frequencies; right: phase lag (relaxation loss)                   at high frequencies. ............................................................................................... 15 Figure 2.6  Equivalent circuit for a medium with complex permittivity. ............................... 16 Figure 2.7  The real part (blue) and imaginary (part) of the complex permittivity                   of water at 30ºC. ................................................................................................... 20 Figure 2.8  Single cell equivalent circuit. ............................................................................... 21 Figure 2.9  Current flow through tissues and cells. ................................................................ 22 Figure 2.10  Maxwell-Wagner effect. ..................................................................................... 23 Figure 2.11  Typical electrical properties of waste activated sludge. ..................................... 25 Figure 2.12  Complex permittivity of 4.5% waste activated sludge                      (figure based on data obtained from [17]). ......................................................... 27 Figure 2.13  Complex permittivity of 18% waste activated sludge                      (figure based on data obtained from [17]). ......................................................... 28 Figure 3.1  DC conductivity of salt water solution as a function of temperature. .................. 35 Figure 3.2  Real part of relative permittivity of salt water solution                   as a function of temperature. ................................................................................. 35 Figure 3.3  Electric fields for a parallel plate structure (top) and a coaxial   viii                   structure (bottom).................................................................................................. 37 Figure 3.4  Electric fields in the environment around a parallel plate applicator. .................. 38 Figure 3.5  Parallel plate applicator enclosed in a coaxial cylinder. ....................................... 40 Figure 3.6  Dimensions and material specifications of the heating applicator                    for a 0.03315 N salt water load. ........................................................................... 42 Figure 3.7  Dimensions and material specifications of the heating applicator                     for a 0.069 N salt water load. ............................................................................... 43 Figure 3.8  RF heating system: (a) block diagram with equivalent circuit;                   (b) power flow diagram. ....................................................................................... 46 Figure 3.9  Equivalent circuit representation of (a) WAS and (b) salt water solution. .......... 48 Figure 3.10  Impedance of salt water and WAS as a function of temperature. ...................... 50 Figure 3.11  Power transfer efficiency of salt water and WAS load                     as a function of temperature. ............................................................................... 50 Figure 3.12  Connecting coaxial cable geometry: (a) cross section; (b) side view. ............... 52 Figure 3.13  COMSOL models of the heating applicator for                      0.03315 N salt water (a) and 0.069 N salt water (b). .......................................... 55 Figure 3.14  Impedance of the RF heating system for a 0.03315 N salt water load. .............. 56 Figure 3.15  Impedance of the RF heating system for a 0.069 N salt water load. .................. 57 Figure 3.16  Power transfer efficiency of the RF heating system                      for a 0.03315 N salt water load. .......................................................................... 58 Figure 3.17  Power transfer efficiency of the RF heating system                      for a 0.069 N salt water load. .............................................................................. 58 Figure 3.18  Electric field across the load as function of distance (arc length)    ix                    for (a) 0.03315 N salt water load and (b) 0.069 N salt water load....................... 59 Figure 4.1  Pictures of the experimental test bed: (a) RF heating system                    and software control; (b) components of the RF heating system.......................... 61 Figure 4.2  Components of the RF generator. ......................................................................... 63 Figure 4.3  Connecting coaxial cable (RG 58). ...................................................................... 65 Figure 4.4  Photo of the top electrode assembly in the heating apparatus. ............................. 69 Figure 4.5  Photos of the Teflon load vessel. .......................................................................... 71 Figure 4.6  Photos of the aluminum enclosure. ...................................................................... 73 Figure 4.7  Photo of the heating apparatus and the corresponding equivalent circuit model. 75 Figure 4.8  Measured intrinsic capacitance of the heating                    applicator as a function of frequency. ................................................................... 77 Figure 4.9  Measured and modeled impedance of the heating applicator                    with a 0.03315 N salt water load for a frequency range of 10-15 MHz. .............. 78 Figure 4.10  RF generator voltage (a) and load temperature (b) as a function of time. .......... 80 Figure 4.11  LabView front panel control interface: (a) temperature graph                   and other control display/knobs; (b) instantaneous ramp rate and                      PA input voltage display. .................................................................................... 82 Figure 4.12  Ramp rate measurement for salt water load with 250 V (blue line),                    200 V (magenta line), 150 V (red line) and 100 V (yellow line)                       input to the PA. .................................................................................................. 83 Figure 4.13  Ramp rate measurement for a 4.5% WAS load with 100 V input to the PA. .... 85 Figure 4.14  Settling time for a target temperature of 120 ̊C (blue line:                     250 V and red line: 100 V). ................................................................................ 87   x Figure 4.15  Settling time for a target temperature of 30 ̊C (blue line:                      250 V and red line: 100 V). ................................................................................ 88 Figure 4.16  Thermometer tip positions for measuring temperature across load. .................. 89 Figure 4.17  Marks on the mercury thermometer used to set insertion depth in the load. ...... 90 Figure 4.18  Thermal profile across 0.03315 N salt water load for a target                     temperature of 30°C and 40°C with 250 V (blue line), 200 V (red line),                      150 V (cyan line), 100 V (blue circle). .............................................................. 91 Figure 4.19  Thermal profile across 0.03315 N salt water load for a target                    temperature of 50°C and 60°C with 250 V (blue line), 200 V (red line),                       150 V (cyan line), 100 V (blue circle). .............................................................. 91 Figure 4.20  Thermal profile across 0.03315 N salt water load for a target                    temperature of 70°C and 80°C with 250 V (blue line), 200 V (red line),                       150 V (cyan line), 100 V (blue circle). .............................................................. 92 Figure 4.21  Thermal profile across 0.03315 N salt water load for a target                     temperature of 90°C with 250 V (blue line), 200 V (red line),                       150 V (cyan line), 100 V (blue circle). .............................................................. 92 Figure 4.22  Temperature gradient across the load due to heat conduction loss. ................... 95 Figure 4.23  Temperature gradient across the load due to heat conduction                      loss and water density variation. ........................................................................ 96 Figure 4.24  Measured impedance of the RF heating applicator with a                      0.03315 N salt water load for two different ramp rates. ..................................... 97 Figure 4.25  Impedances for the RF applicator and the RF applicator                       plus the coaxial cable (overall system) with a 0.03315 N salt water load. ........ 98   xi Figure 4.26  Measured power transfer efficiency with a 0.03315 N salt water load. ............. 99 Figure 4.27  Measured impedance for the RF heating system with                      a 4.5% waste activated sludge load................................................................... 100 Figure 4.28  Measured power transfer efficiency for the RF heating system                     with a 4.5% waste activated sludge load. ......................................................... 101 Figure 4.29  Impedance comparison for the RF heating system between                      salt water and WAS load. .................................................................................. 103 Figure 4.30  Power transfer efficiency comparison for the RF heating system                     between salt water and WAS load. ................................................................... 104                 xii List of Abbreviations CIH Conventional induction heating DC Direct current EM  Electromagnetic EMI  Electromagnetic interference HA  Heating applicator ISM  Industrial, scientific and medical MW  Microwave OH Ohmic PA  Power amplifier. RF  Radio frequency WAS  Waste activated sludge      xiii Acknowledgements I would like to express my sincere thanks and gratitude to my supervisor, Dr. Thomas Johnson for his generous support, guidance and encouragement throughout my research. Besides teaching me scientific research know-how, he is an icon of enormous motivation and patience that has helped me to focus and overcome many obstacles throughout my research. I heartily thank Dr. Cigdem Eskicioglu and Dr. Kenneth Chau for supporting and encouraging my research work. I also sincerely thank Dr. Jake Bobowski and Ehssan Hosseini for their altruistic help and fruitful discussions during my research. I am also grateful to NSERC (Natural Sciences and Engineering Research Council) of Canada for funding my research. Finally, I especially want to thank my parents for their selfless support and encouragement to pursue education and scientific discovery.   xiv Dedication  To my loving parents and brother Md. Sadman Ferdous.    1 Chapter  1: Introduction This thesis is part of a larger research project focused on investigating methods to enhance the bio-gas production from sludge generated by wastewater treatment plants. The Bioreactor Technology Group at UBC is leading this work and several years ago a multidisciplinary research team was setup to investigate electromagnetic heating methods to pre-treat the water treatment sludge. More precisely, the sludge is called wasted activated sludge, and the acronym WAS will be used interchangeably with the word ‘sludge’. The motivation for heating WAS is to breakdown the organic particles in the sludge and preferably breakdown cell membranes to release intracellular material into the liquid phase. After pretreating, the sludge is moved to a digester where anaerobic micro-organisms convert proteins and complex carbohydrates into methane gas that can be captured and used as an energy source. Pretreatment methods also have other advantages such as increasing the throughput rate through the digester which reduces the volume of the digesters requirement, killing pathogens and reducing the residual organic mass left after the digester phase. WAS is a mixture of liquids and organic solids called bio-solids. The mass ratio of solids to liquids is controlled and two common ratios are 4.5% and 18% where the ratio specifies the percent content of solids in the total mass of the sludge. Although the original intent of this research project was to investigate methods to heat waste activated sludge, the work has led to the design of a RF heating apparatus that in general can be used to heat liquids and sludges provided the material has certain electrical properties that are compatible with the frequency of the generator used in this system. The application of the apparatus to other potential applications is discussed in the conclusion.   2 Within the environmental and civil engineering research community, experiments to develop improved pretreatment methods to enhance the production of bio-gas from WAS has been going on for many years. Amongst the various methods which have been evaluated to pretreat WAS, microwave pretreatment and conventional heating are included. In microwave pretreatment, the sludge is heated in a commercial microwave heating system used for laboratory applications. These systems heat loads at a frequency of 2.45 GHz and are very similar to domestic microwave ovens in that the principal heating mechanism relates to the dielectric relaxation of water molecules. Conventional heating is a process where the load is heated by a source using thermal convection. Ovens are an example of conventional heating systems. The motivation for this research project is to answer the broader question: what is the most efficient way to heat WAS? 1.1 Literature Review 1.1.1 Heating Pretreatment Methods for Waste Activated Sludge In 1977, Haug et al. [1] demonstrated that adding a thermal pretreatment stage before anaerobic digestion enhances the bio-degradability of organic materials. The enhanced bio-degradability in this context means improved bio-gas production in the anaerobic digesters as well as improvements in the ability to dewater the sludge and reduce the volume and cost of disposing of the residual solids. The experiments conducted in Huang’s study used conventional heating. Over the past several decades many other pretreatment processes have been evaluated. These methods include chemical and enzyme additives, high pressure homogenization, microwave heating and exposure to pulsed electric fields [2-5]. The motivation for all these pretreatment methods is to make organic materials present in the sludge more biodegradable   3 by physically reducing the size of organic structures and puncturing or rupturing cell membranes [4]. Amongst all the pretreatment methods, thermal pretreatments have been very effective for improving biogas production from WAS [6]. Studies have shown that both conventional and microwave heating pretreatment methods can improve the bio-gas production from WAS. In a recent study by Mehdizadeh et al. [6], a comparison was made between conventional heating and microwave heating at 2.45 GHz. The study showed, that under identical heating profiles, similar amounts of bio-gas are produced. Therefore, there is no current evidence that the heating method of sludge has a significant impact on bio-gas production. More important factors appear to be the thermal ramp rate and the operating temperatures involved in the pretreatment process. From a system perspective, the energy input to the heating system and the efficiency of converting the energy to heat the load are very important. The evaluation of heating efficiency involves both the electrical design of the heating system as well as an evaluation of the heating uniformity across the load. There has been much less work focused on investigating efficient heating methods and the question of how best to heat WAS has motivated this research project. 1.1.2 Other Applications of RF Heating As will be explained in Chapter 2, a radio frequency (RF) heating system for treating WAS was selected with an operating frequency of 13.56 MHz. Therefore, it is relevant to consider other applications of RF heating systems. Examples of other RF heating applications include food and agriculture processes and wood drying [7]. RF heating methods were first employed in food processing as early as 1940 [8]. RF heating has been used to dehydrate vegetables and fruits [9], bake cookies and crackers [10],   4 cook meat products [11], kill navel orangeworms in walnuts [12] and reduce microbial action in fruit juices [13, 14]. Advantages of RF over conventional heating are improved product quality and faster heating times. Most RF heating systems in these applications use a frequency of 27.12 MHz which corresponds to an allocated frequency band reserved for industrial, scientific and medical (ISM) applications. Two other ISM frequency bands which can be used for RF heating are 13.56 MHz and 40.68 MHz and a few papers have reported on RF heating systems in these bands [15, 16].  Although RF heating has been employed in different industrial applications, most of the published work focuses on optimizing the process rather than optimizing the electrical design of the heating system. Also, the majority of these systems are designed to heat loads up to moderate temperatures usually below 100ºC. One of the requirements in this research project was to heat liquid and sludge loads to temperatures up to 120ºC under constant volume conditions. Consequently, a heating apparatus that can work under high pressure is required. 1.2 Research Objectives The primary objective of this research project was to design an electromagnetic heating applicator that can efficiently heat WAS. After designing and implementing the heating apparatus, the equipment will be used to conduct experiments to measure how effective the heating method is in terms of enhancing bio-gas production from anaerobic digesters. Unlike other published work on pretreatment methods using microwave or conventional heating, this research began with a study of the electrical properties of WAS. The dielectric properties of WAS were measured over a wide frequency range from 100 kHz   5 to 40 GHz and these results were published several years ago by other members of the UBC research team [17]. The dielectric study provides a fundamentally different starting point for investigating the efficiency of using electromagnetic heating by first focusing on analyzing the electrical properties of the material and then selecting an optimum heating frequency. Selecting an optimum heating frequency involves more than a study of material properties and other important requirements are uniform heating throughout the load volume, efficient high power RF generators, efficient matching between the generator and the load, and constraints in terms of frequency bands which can be used for industrial heating applications. After selecting a frequency, the next objective was to design an applicator which could heat liquid and sludge loads over a temperature range of 20ºC to 120ºC. The minimum load volume for the apparatus was 400 ml and the volume and temperature range requirement relates to future experimental work on bio-gas production. Other requirements included thermal ramp rates up to 15ºC per minute and a temperature measurement system that can be used to control the heating rate. 1.3 Overview of Chapters In Chapter 2, background on electromagnetic heating methods is presented. The different mechanisms which can create heating in WAS are reviewed. It is shown that WAS has significant ionic conductivity and that the bio-solids have a dielectric dispersion called β dispersion related the electrical characteristics of cell membranes in the organic material. Based on the electrical properties of WAS, a frequency of 13.56 MHz is selected to efficiently heat the sludge. In Chapter 3, the electrical design of a RF heating applicator is described. Analytic models of load impedance as a function of temperature are derived based on matching the   6 ionic conductivity of WAS with an equivalent salt water load. The analytic models are used to design an applicator which creates a uniform electric field between two electrodes. The electrodes are mounted in a Teflon pressure vessel and the entire pressure vessel is enclosed in a coaxial cylinder. A significant part of the design methodology is associated with matching the load impedance to a 50 Ω high power RF generator. The final design is simulated and optimized in an electromagnetic simulator. Chapter 4 focuses on experimental results. The RF heating applicator was built and tested. The RF heating test bed consists of a RF generator, an applicator, and software to measure load temperature and control RF generator power. The applicator was tested with salt water loads and samples of WAS. Loads were heated from room temperature to 120ºC and impedance measurements of the applicator and load were made to verify the design. Excellent results have been obtained and the RF heating applicator shows significant promise as a method of heating liquid and sludge loads. As with any design, improvements can be made. A summary of design improvements and other potential applications for the RF heating system are described in the concluding chapter.          7 Chapter  2: Selecting a Frequency for the RF Heating System The theory of how electromagnetic fields interact with biological materials is essential to the design of the heating system for WAS. A time varying electromagnetic field has both an electric and magnetic field and the relations between the two fields are described by Maxwell’s equations. From the heating perspective, heat is generated in dielectric and metallic materials principally by the interaction of the electric field and charge. Two important electrical properties of materials which relate to the efficiency of heating using electromagnetic fields are conductivity and permittivity. Conductivity and permittivity are frequency dependent properties and consequently electromagnetic heating is frequency sensitive. The frequency dependence then raises the question: what frequency is best for heating WAS? Although the frequency dependence of material properties is important to assess, there are other constraints which affect the selection of a heating frequency for WAS. The penetration depth of the electromagnetic wave affects the heating profile through the material. Since penetration depth varies inversely with frequency, a low frequency source has advantages over high frequencye. Other practical constraints include regulatory issues which limit specific frequency bands for heating applications as well as the cost and power efficiency of the amplifiers used to generate the high frequency signals to heat the material. The remainder of this chapter is organized as follows. Background is given on the electrical properties of materials and how the properties affect the heating process. The electrical properties of materials are frequency dependent and these relations are described for materials relevant to the WAS application. Finally, a frequency of 13.56 MHz is selected   8 for this design and a discussion of the factors which were considered in the selection of this frequency is presented. 2.1 Conventional Heating versus Electromagnetic Heating Heat is generated in a material from molecular agitation. Based on how agitation is created in the material, heating methods can be broadly classified into two categories: conventional and electromagnetic. In conventional heating, a heat source is applied outside the material and thermal energy transfers by convection through the material from a region of high temperature to low temperature. An example of conventional heating is a kitchen oven where heating coils are the source and heat is conducted through the material created by the temperature gradient between the source and load. Drawbacks of conventional heating are uneven heating across the load because of the thermal conduction gradient and slow heating rates. Uneven heating arises from the conventional heating can be made quite even by inserting multiple electrodes inside the load, which requires intervening into the materials. The second method of heating uses time varying electromagnetic fields. In an electromagnetic heating process, the electric field interacts directly with the molecules in the load and increases the kinetic energy of the molecules to heat the load. Electromagnetic waves propagate with very high velocity, and providing the electric field penetrates through the load, uniform and near instantaneous heating can be obtained. Because the field penetrates the entire volume, the term volumetric heating is sometimes used to distinguish it from conduction heating. The primary drawback of electromagnetic heating is that its efficiency depends significantly on the electrical properties of the material. Typical temperature profiles for conventional and electromagnetic heating processes are shown in Figure 2.1.   9 TemperatureDistanceTemperatureDistanceMolecular vibrationConventional heating Volumetric heating Figure 2.1 Conventional and electromagnetic heating temperature profiles across the load. 2.2 Principles of Electromagnetic Heating When an electromagnetic field interacts with a material, power can be dissipated. The dissipation of power in a material from electromagnetic waves is described by the fundamental equations of electromagnetics given by Maxwell’s equations. The fields defined by Maxwell’s equation are linked by three constitutive parameters which relate to the material properties and the fields that can exist in the material. The constitutive parameters are: conductivity ( ), permittivity (  ) and permeability (  ). Of the three material properties, conductivity and permittivity are relevant to heating for non-magnetic materials.       10 2.2.1 Conductivity Conductivity, which is denoted asDC , is a material property that is described by a purely real number and ideally measured at DC (0 Hz)1.  The conductivity of a material relates to the movement of free charge. When an electric field is present in a material, the electric field exerts a force on free charge, and the charge drifts through the material. The relationship between charge ( q ), electric field (E ) and force ( F ) is given by the fundamental definition of an electric field:  qF E (N). (2.1)  Examples of free charge are electrons that move through a metal lattice in a conductor or free ions that move through an electrolyte.  The movement of electrons through a conductor is called electronic current flow and does not involve the net movement of mass. Electrons in the valence band of a metal are easily removed by a low energy electric field and they drift from atom to atom. The movement of free charge is created by electron-hole pairs and the atomic lattice is unchanged by the movement of charge. An illustration of electronic conduction current flow is shown in Figure 2.2. Current flow through a metallic conductor does not involve any electrochemical reactions at the electrodes (anode and cathode) and the only chemical reaction is in the battery which provides an electromotive force to sustain current flow.                                                  1 Experimental measurements of conductivity at DC can be complicated by electrochemical reactions between the electrodes and the material being measured. Therefore, DC conductivity may be extrapolated from low frequency measurements where electrochemical reactions do not contribute significantly to experimental errors in the measurement of conductivity.   11  Figure 2.2 Conduction current flow through a metallic conductor. Ionic current flow is distinct from electronic current flow. In ionic current flow, ions (atoms or molecules with a net charge) physically move and there is a net movement of mass. Under a static (DC) electric field, ions will drift in an electrolyte and eventually current flow can cease if there is no mechanism for generating new ions. An illustration of ionic current flow through salt water (NaCl) is shown in Error! Reference source not found.. Salt water is an electrolyte and salt molecules separate into positively charged sodium cations (Na+) and negatively charged chlorine anions (Cl-). In an electric field created by the potential difference between the two electrodes, ions drift to the charged electrodes. The positive electrode is called the cathode and attracts negatively charged chlorine ions, while the negatively charged electrode is called the anode and attracts positively charged sodium ions. At the electrodes, a chemical reaction is required to generate free electrons which can then create electronic current flow through the wires to the battery.   12 The electrochemical reaction at the electrodes creates chlorine gas at the cathode and hydrogen gas at the anode. As times goes by, due to chemical reactions at the electrode interfaces, all the ions in the electrolyte will eventually be depleted. Neutrally charged molecules build up at the electrodes and this leads a condition known as electrode polarization.   Figure 2.3 Ionic current flow through a salt water electrolyte. From a heating application, the electrochemical reactions at the electrodes are undesirable because they produce gas and the electrochemical processes can be reduced by converting to an alternating current source with a sufficiently high frequency. For salt water, the electrochemical reactions are negligible above 10 MHz. Biological material has   13 significant electrolytic properties and ionic current flow is relevant to the heating mechanism used in this research project.   2.2.2 Ohmic Heating As electrons or ions drift through a material in the presence of an electric field, collisions with atoms and molecules generate heat. The amount of energy released depends on the mobility of the charge carriers (conductivity) and the intensity of the electric field. Heat generated by conduction current, either electronic or ionic, is called ohmic heating. An illustration of electronic and ionic ohmic heating is shown in Figure 2.4. ++ ++-------- -2H O2H O2H O2H OCl-Na+ Na+Na+Na+Na+Cl-Cl-Cl-Cl--Electron NucleusAnionCationDipolar moleculeResistor Electrolyte++- - Figure 2.4 Ohmic heating from conduction current (left) and ionic current (right). Ohmic heating is described by Ohm’s law. The conduction current density Jc through a material with conductivity DC  is  DCcJ E (A/m2) (2.2) The power dissipated per unit volume in the material is   14  2c DCp  E (W/m3) (2.3) The total power dissipated in a volume is found by integrating the power density over the volume. In general, the electric field varies as a function of the spatial position ( )x, y,z  in the volume and a triple integral is required to calculate the total power dissipated in the material.  2c c DCv vP p dv (x, y, z) dv   E(W) (2.4) In this work, the integral is evaluated numerically using an electromagnetic modeling tool called COMSOL. The power dissipated in the material creates heat.  Conductivity is a temperature dependent material property; therefore, as the material is heated, the conductivity increases because of the increased mobility of charges. If the conductivity changes significantly with temperature, then the net energy absorbed by a load depends on time and the current temperature of the load. The temperature dependence of materials is important in this work and ranges from    20ºC to 120ºC. 2.2.3 Dielectric Heating When a material with bound charge is placed in an electric field, a polarization charge (P ) is induced within the material. The polarization charge can be visualized as the atomic realignment of charge where electrons are attracted in a direction of increasing potential and positive charge is repelled in a direction of decreasing potential. The atomic structure and chemical bonds in the material may prevent the charge from moving and the charge redistribution is localized within the atomic lattice; hence the name bound charge. Materials may also be composed of polar molecules. An example of a polar molecule is water. The orientation of polar molecules is affected by the presence of an electric field and there can be a net alignment of molecules which also creates a polarization charge in the material.   15 When material is exposed to a time varying electric field, the polarization charge oscillates as the polarity of the electric field changes direction. As frequency increases, the polarization charge cannot maintain perfect synchronization with the oscillating electric field and the polarization charge starts to lag behind the polarity of the electric field. The phase lag means energy from the electric field is absorbed by the material and dissipated as heat. This type of energy loss is called relaxation loss. Relaxation loss is frequency dependent and the physical characteristics of this loss mechanism are captured in the imaginary component of the dielectric constant   . Figure 2.5 illustrates the dielectric relaxation loss mechanism. +-Following delay+-Following delay+- +-Low frequencyHigh frequency (~22 GHz)Electric fieldElectric fieldDipolar molecule orientation Figure 2.5 Electric dipole synchronization with frequencies; left: perfect synchronization at low frequencies; right: phase lag (relaxation loss) at high frequencies. To show that the imaginary part of the complex permittivity results in dissipation, consider the time harmonic form of Maxwell’s equation  ( )j  H = E (2.5) Expand the right hand side by replacing   with j   :  ( - j )( )        H = E + j EE + j E (2.6)   16 The term    contributes to an effective conduction current ( cJ ) that leads to dissipation in the material. The real part of complex permittivity is associated with a reactive current flow called displacement current (dJ ). The distinction between conduction current flow and displacement current flow in a material can be used to construct an equivalent circuit model of the medium. The circuit consists of a shunt conductance (resistance) and a capacitance. To show this, assume a material is sandwiched between two parallel plates as shown in Figure 2.6. -Q+QCharge dPlate area, A+     -+     -+     -+     -+     -+     -Electric field, ELossy Dielectric+-Susceptancedue to Dielectric Conductance due to dielectric loss r 01B=XAȦİ (Ȧ)İdr 01G=RA+ İ (Ȧ)İd( +     -+     - Figure 2.6 Equivalent circuit for a medium with complex permittivity. Assume the plate area is large and fringing fields are small such that the electric field between the plates is uniform. The capacitance of the parallel plate structure is  AC d (F) (2.7)   17 where    is the complex permittivity, A is the area of the plates and d is the distance between the plates. The admittance of the capacitor is ( ) jY C    which expands into  ( )( )( ) ( )d dj AY jdA Aj G jBd d          (S) (2.8) The admittance ( )Y  of the dielectric material can be modeled by a shunt conductance ( )dG   and a shunt capacitance with susceptance ( )dB  . If the material also has finite conductivity, then there is a second shunt conductance term equal to  cAG d(S) (2.9) for the parallel plate structure. Note that unlike the conductance in the dielectric model where ( )dG  is a function of frequency, the conductance dG  is independent of frequency. The total equivalent admittance of the material including permittivity and conductivity is  ( ) ( ) ( ) ( )( )c d dY G G jBA Ajd d         (S) (2.10) This equation shows that an equivalent circuit model for modeling conductivity and complex permittivity is a shunt conductance and capacitance. The equivalent circuit model is very useful and enables the design of matching circuits to couple power to the material. The equivalent circuit model also provides a way to use measurements of admittance or impedance to determine the values of the material properties. To show how measurements of admittance can be used to extract conductivity and permittivity, rewrite (2.10) as   18  0r0( ) ( ) +[ ( )]rAY j jd         (S) (2.11) Let 0 0 /C A d  which is the capacitance of the test structure assuming the dielectric is a vacuum. The normalized admittance is then  0 0( ) ( ) - ( ) +( )r rY jj C        (S) (2.12) The equation shows that the material properties as function of frequency can then be obtained from measurements of admittance as function of frequency. The real component of the right hand side of (2.12) is the real relative permittivity, ( )r  , and the imaginary component is dependent on both the imaginary component of the complex permittivity, ( )r  , as well as the conductivity of the material. The conductivity dominates the low frequency characteristics while the imaginary part of the complex permittivity dominates the high frequency characteristics. Examples plots of the right hand side of (2.12) are shown later. 2.3 Electrical Properties of Materials The complex permittivity of a material depends on frequency and there are models that have been developed to relate the characteristics to the atomic structure of the material. An important model that is widely used is called the Debye model. The Debye model leads to dispersion which means that the permittivity does not have linear characteristics as a function frequency. 2.3.1 Relaxation, Dispersion and the Debye Model As described earlier, polarization charge oscillates in a time varying electric field. For low frequencies, polarization charge can follow the field variation, but as frequency is increased, the polarization charge starts to lag the variation in the field. The lag between the   19 polarization charge and the electric field can be modeled in the time domain by a relaxation time constant. Let (t)D  be the electric flux density as a function of time and assume the flux density is to be changed from an initial state D  to a new state 0D . An external electric field is pulsed to create the flux density change in the material. Similar to the transient response of a circuit with a conductance in shunt with a capacitance, the response can be modeled as an exponential with a relaxation time constant . The flux density is then given by  0( )( (1 ))tD t D D D e      (2.13) Equation (2.13) is called the Debye dispersion equation. The equation shows that in one time constant, the flux reaches 63.2% of its final value, and in 5 , the flux is 99.3% of the final value0D . For example, water has a relaxation time of 7.2 ps at a temperature of 30ºC. The Debye dispersion equation can also be written in the frequency domain by taking the Laplace transform of (2.13) and then evaluating the transform along the imaginary axis ( j  in the complex frequency plane) to obtain the corresponding frequency response. The Debye model for complex permittivity in the frequency domain is expressed as  ( ) ( ) j( 1) ( )rrsrj           (2.14) where, s  is the steady state (DC) dielectric constant,   is the dielectric constant at optical (infinite) frequencies, and   is the relaxation time. As an example, the Debye model for water at a temperature of 30ºC is s = 76.47,  = 4.9, and   = 7.2 ps. A plot of the real and imaginary parts of the complex permittivity of water is shown in Figure 2.7.    20 10610710810910101011101201020304050607080Frequency (Hz)Complex relative permittivity ( r )22.1GHz Figure 2.7 The real part (blue) and imaginary (part) of the complex permittivity of water at 30ºC. As shown, significant dispersion in the dielectric properties occurs in a frequency range from 2 GHz to 200 GHz. Below 2 GHz, r s    and above 200 GHz, r   . Around 22 GHz, the imaginary part of the permittivity peaks and this frequency corresponds to the frequency where the most power is dissipated in the water. A microwave oven operates at a frequency of 2.45 GHz and balances dissipation (heating), penetration depth (uniform heating) and the cost of the microwave power source. In more complex materials with heterogeneous molecules, there may be multiple dispersion regions which relate to multiple relaxation time constants. Also, high ionic conductivity in electrolytes can significantly dominate low frequency characteristics. Biological materials are examples of materials with more complex characteristics and these are described in the next section.     21 2.3.2 Electrical Models for Cells and Tissues The electrical properties of cells and tissues have been the subject of much research [18]. From this research, equivalent circuit models for cells and tissues have been developed. An example of an electrical model is shown in Figure 2.8. Intracellular fluidExtracellular fluidCell membraneEquivalentResistanceEquivalent capacitance Figure 2.8 Single cell equivalent circuit. Plant and animal tissues are heterogeneous cellular structures and tissues are composed of many cells of varying types and sizes. Each cell within a tissue is encapsulated by a cell membrane that separates intracellular fluid from extracellular fluid in the tissue. If two parallel plate electrodes are inserted into the extracellular fluid, current can be passed through the tissue and cells. The current flow is frequency dependent because the medium is   22 heterogeneous with different electrical properties for different parts of the tissue. The extracellular and intracellular fluids are electrolytic and an ionic conduction current can flow through the fluids. The cell membrane is permeable but has much lower conductivity and membrane can be modelled as dielectric sandwiched between the inner and outer ionic (conductive) mediums. Therefore the cell membrane is analogous to a parallel plate capacitor structure and current flow through the cell membrane is primarily displacement current rather than conduction current. Based on the circuit model, at DC and very low frequencies, ionic conduction current can flow between the electrodes, and the current path is primarily through extracellular fluid. As the frequency increases, a displacement current can flow through the cell membrane and the net current flow between the electrodes is composed of both conduction and displacement currents. The current flow paths are illustrated in Figure 2.9.  Intracellular fluidExtracellular fluidCell membraneLow frequency current pathHigh frequency current path Figure 2.9 Current flow through tissues and cells.   23    The current flow through the cell membrane is more complex than shown in the simplified model of Figure 2.8. At the exterior interface between the cell membrane and the extracellular fluid, and at the interior interface between the cell membrane and the intracellular fluid, there is a wet dielectric boundary. In general, each medium at an interface has different conductivity ( ) and permittivity (  ) properties as shown in Figure 2.10.  Frequency(Hz)Relative permittivitydldl1f =2ʌIJd l dl 1İ2İ1ı2ı1R 2R1C2C Figure 2.10 Maxwell-Wagner effect. The conductivity in each medium can be modeled as a conductance and the permittivity can be modelled as a capacitance. For a parallel plate structure, the capacitance and conductance of the mediums is given by (2.9) and (2.11), respectively. The conductance and capacitance in each medium are connected in shunt and the electrical circuit has a time constant,   24 /dl C G  . The time constant is similar to the relaxation time constant in the Debye model except that it arises from a different physical phenomenon where free charge carriers accumulate at the interface surface of the two media. The accumulation of a charge layer created by different time constants at a dielectric interface is called the Maxwell-Wagner effect [18]. The Maxwell-Wagner effect creates an effective frequency dependent complex permittivity in a double layer (dl) composite medium. The effective complex permittivity is given by  0dldl dl j     (2.15) and the effective time constant is /dl dl dl   . The Maxwell-Wagner effect leads to a dielectric dispersion that is similar to a Debye dispersion and an example of the dispersion characteristic is shown in Figure 2.10. In biological materials, the dispersion characteristic created by the cell membrane interface is called β dispersion. 2.3.3 Dielectric Properties of Waste Activated Sludge The primary load to be heated is WAS which is a complex mixture of organic solids immersed in an inorganic liquid composed mostly of water and electrolytes. The solid content in WAS is specified by a mass ratio of solids to liquids and two common mixture ratios are 4.5% and 18%. The solid content in WAS, also called floc, is composed of a heterogenous mixture of inorganic and organic solids where the organic solids have properties similar to biological tissues. An example of a floc structure is shown in [19]. A dielectric study of 4.5% and 18% WAS was made by the UBC research group several years ago [17]. The results of these measurements have been analyzed and an example of the typical WAS electrical properties is shown in Figure 2.11.    25 106107108109101010111012050100150Frequency (Hz)( ' r )106107108109101010111012100102104Frequency (Hz)( " r+/0 )bulk water relaxation dispersionDominant biological characteristicsBulk watercharacteristics22.1GHzIonic conduction loss13.56MHz Figure 2.11 Typical electrical properties of waste activated sludge. The electrical characteristics are shown in the form of (2.14) where the real part is r   and the imaginary part is0r DC   . At low frequencies below 300 MHz, ionic conductivity dominates the imaginary component of the dielectric characteristics. The liquid is composed of electrolytes such as salt which makes the sludge conductive. The ionic component corresponds to the term 0DC   and this leads to a straight line slope on a log-log plot. Within the 1-10 MHz range, dispersion is evident in the real part r   of the complex permittivity. The response can be compared to the graph shown in Figure 2.10 (Maxwell -Wagner effect). The β dispersion is attributed to the organic nature of the bio-solids in the sludge. From 10 MHz to 5 GHz the real part of the permittivity is approximately flat and equal to the permittivity of water (~80). At a frequency of 22 GHz, the Debye relaxation associated with water is clearly visible. This leads to a decrease in the real part of permittivity and a corresponding peak in the imaginary component. The power absorbed by   26 water molecules is maximized at a frequency of 22 GHz but the penetration depth of the electromagnetic wave is very shallow. Microwave ovens balance penetration depth with the optimum frequency for heating water and a frequency of 2.45 GHz is used in most microwave heating systems. The imaginary part of the complex permittivity determines how efficient the material can be heated using electromagnetic waves. Microwave heating at 2.45 GHz falls in the valley between the low frequency slope and the dispersion at 22 GHz. Below 100 MHz, it is clear that heating is even more efficient than the dispersion peak at 22 GHz. Furthermore, the rising slope as frequency decreases suggests a lower frequency is the best. 2.4 Selecting a Frequency for Heating Waste Activated Sludge Based on the electrical properties of WAS, a low heating frequency appears to be the most optimal in terms of maximizing the dissipated power density in the load. A low frequency also has advantages in terms of a long wavelength which leads to deep penetration depth. According to the slope in Figure 2.11, one might be tempted to conclude that the best heating frequency would be 0 Hz; in other words DC. The issue with heating at DC is that electro-chemical reactions are necessary at the electrode interfaces to create free electrons which can flow through the external circuit. This was illustrated earlier in Error! Reference source not found.. The electro-chemical reactions have other byproducts including the generation of gases and polarization charge on the surface of the electrodes. Therefore, there are issues with operating at too low a frequency. A summary of the different heating mechanisms and the associated dielectric characteristics for WAS is shown in Figure 2.12 and Figure 2.13.   27  Figure 2.12 Complex permittivity of 4.5% waste activated sludge (figure based on data obtained from [17]).    28  Figure 2.13 Complex permittivity of 18% waste activated sludge (figure based on data obtained from [17]). The problems with electro-chemical reactions and electrode polarization are significantly reduced for frequencies above a few MHz [17] (region B in the figures). There are also limitations in the available frequency bands which can be used for industrial heating   29 applications. The appropriate frequency bands for heating are associated with frequency bands reserved for industrial, scientific and medical (ISM) applications. The lowest frequency band which falls near the low end of the MHz frequency range is at 13.56 MHz. The corresponding free space wavelength at 13.56 MHz is 22 meters which means the field variation over distances of a few meters is nearly constant. The other advantage of operating at a frequency of 13.56 MHz is that it falls very near the β dispersion associated with cell membranes (region B). Since the objective of the heating process is to disassociate tissues and cells, absorption of power in the cell membranes is beneficial and this heating mechanism is absent in region C. However, the heating associated with dispersion is expected to be much less than ionic conduction heating and the outcome of bio-gas production from pretreatment at this frequency needs to be evaluated. More discussion on the relative power dissipation for ionic heating and dielectric relaxation heating from β dispersion is discussed in the next chapter. Therefore, based the preceding analysis of heating at different frequencies, it was decided to implement a design at a frequency of 13.56 MHz.           30 Chapter  3: Design of the RF Heating System In this chapter, the electrical design of a RF heating applicator is described. Analytic models of the load impedance as a function of temperature are derived based on matching the ionic conductivity of WAS with an equivalent salt water load. The analytic models are used to design an applicator which creates a uniform electric field between two electrodes. The electrodes are mounted in a Teflon pressure vessel and the entire pressure vessel is enclosed in a coaxial cylinder. A significant part of the design methodology is associated with matching the load impedance to a 50 Ω high power RF generator. The final design is simulated and optimized in an electromagnetic simulator and then compared with the analytic model. 3.1 Electrical Properties of the Load  After selecting a frequency of 13.56 MHz for the RF heating system, detailed electrical properties of the load at a frequency of 13.56 MHz need to be known to design a RF applicator that is impedance matched to a 50 Ω RF generator. The dielectric characteristics of WAS were obtained from another study which was carried out by the UBC research group [17]. From this study, values for conductivity and complex permittivity of WAS are known. Although heating WAS is the final objective of this project, it is very useful to work with a controlled load with well-known electrical characteristics. Salt water, with a controlled molarity, can be prepared to have similar conductivity to WAS. Advantages of salt water include a homogenous composition relative to the heterogeneous composition of sludge, accurate DC conductivity, and a load that is free of bio-hazards which makes handling and testing easier. There are also excellent literature references which have empirical equations for predicting how conductivity and complex permittivity vary with temperature. The   31 temperature characteristics of salt water are used in the design to predict how the impedance match between the load and the generator will vary over temperature. The electrical properties of WAS and an equivalent salt water load are presented next. 3.1.1 Waste Activated Sludge WAS samples consist of a liquid with a controlled amount of bio- solid content. The samples are specified by a ratio of the mass of the solids to the mass of the liquid and two ratios, 4.5% and 18%, are commonly available from wastewater treatment plants. Based on the experimental measurements presented in [17], the electrical properties of WAS are summarized in Table 3.1. Table 3.1 Electrical properties of waste activated sludge at a frequency of 13.56 MHz and at a temperature of 25°C. Material property 4.5% WAS 18% WAS r   92.5 138.8 r   2.8           35.6 1 -1( )DC m   .34 .68 Important limitations of this data should be noted. First, the electrical properties were measured at a single temperature of 25°C. Second, the measurements are based on a small number of samples and some variation in the electrical characteristics is expected. Third, the extraction of r   from the original measurement data reported in [17] is sensitive to measurement error at a frequency of 13.65 MHz because r   is much less than 0/  . Despite these limitations, within the scope of this project, the reported measurements are used as a basis for the applicator design. As shown later in Chapter 4, experimental results   32 differ from the design target, but the variation is within acceptable margins and efficient heating is obtained despite the variability in the load. The total amount of power which is dissipated in WAS at a frequency of 13.56 MHz can be found by modifying equation (2.3) in Chapter 2 to include dielectric heating losses and a time-harmonic electric field. The total power density is  2 2DCDC r 0 r 001 1( ) ( )2 2p        E E(W/m3) (3.1) which can be decomposed into a conduction heating component  2DC12cp  E(W/m3) (3.2) and a dielectric heating component  2012d rp   E(W/m3) (3.3) Using these equations and Table 3.1, the ratio of ohmic heating to total heating can be calculated. For 4.5% sludge, ohmic heating accounts for 99.4% of the dissipation in the load, while ohmic heating accounts for 96.2% in 18% sludge. Clearly, at frequency of 13.56 MHz, ohmic heating is expected to be the dominant heating mechanism. 3.1.2 Equivalent Salt Water Loads At a frequency of 13.56 MHz, the primary heating mechanism in WAS is ohmic heating. As described earlier, it is convenient to have a controlled load for testing the heating apparatus. Given that heating in WAS is dominated by ionic ohmic heating at a frequency of 13.56 MHz, salt water is a good choice for creating an equivalent load with similar heating properties. Stogryn et al. [20], presented a method of determining the amount (molarity) of sodium chloride salt required in pure distilled water to achieve specific dielectric   33 characteristics. A model for the complex permittivity of a saline water solution (SW ) as a function of temperature (T) in degrees Celsius, salinity (N) in moles per liter of solution and frequency (ω) is   0_ _ __0( , ) - ( , )( , , ) 1- ( , )SW W DC SWSW WSWT N T NT N jj T N          (3.4) In this equation, _W  is the high frequency permittivity of water and equal to 4.9. The other terms in the equation are dependent on temperature and salinity, and the equations for these terms are given below [19].  4 2 6 30_ ( , ) (87.74- 4 9.39 10 1.41 10 ) ( )SW T N T T T a N       (3.5)  -10 12 14 2 16 3( , ) (1.11 10 -3.83 10 6.94 10 5.09 10 ) ( , )SW T N T T T b T N          (3.6)  -2 -5 2_SW _SW-5 -5 -5 -6( , ) (25, )[1-1.96 10 8.08 10- {3.02 10 3.92 10 (1.72 10 6.85 10 )}]DC DCT N NN N              (3.7)  2 2 3 3( ) 1 .25 5.15 10 6.88 10a N N N N       (3.8)  2 2 3 3( , ) .15 10 1 .05 .03 5.64 10b T N NT N N N        (3.9)  2 3 -2 4_ (25, ) (10.39- 2.37 .68 -.13 1.01 10 )DC SW N N N N N N     (3.10)  25 T    (3.11) Using the salt water model equations, the molarity of the solution can be found to have a dissipation at 13.56 MHz which is equivalent to WAS. For 4.5% WAS, the equivalent molarity (N) is 0.03315 N, and for 18% sludge, the equivalent molarity is 0.069 N. The electrical properties of the equivalent salt water loads are summarized in Table 3.2.    34 Table 3.2 Comparison of the electrical properties of salt water and waste activated sludge at a temperature of 25°C.  r   0DCr  r  DC  4.5% WAS 92.5 454 2.8 .34 0.03315 N salt water 77.69 454.11 0 .342 18% WAS salt water 138.8 937 35.6 .68 0.069 N 76.99 937.56 0 .705 Comment WAS has higher rİ  because of the presence of β dispersion. Dissipation terms matched for WAS and salt water. No β dispersion in salt water. Dominant loss mechanism in both WAS and salt water. The electrical property equations (3.4) through (3.11) are very useful to model the impedance changes in the load as a function of temperature. In order to gain insight into the temperature sensitivity of conductivity andr  , the equations are plotted for a temperature range of 20°C to 120°C in Figure 3.1 and Figure 3.2, respectively. The temperature range corresponds to the operating temperature range of the RF heating applicator. The DC conductivity of 0.03315 N and 0.069 N salt water changes significantly and increases by approximately a factor of four from 20°C to 120°C. The relative permittivity of salt water changes less and decreases from approximately 79 at 20°C to 55 at 120°C. The temperature   35 variations of the material properties are used later to find the best compromise in terms of matching the RF generator impedance to the load impedance. 20 30 40 50 60 70 80 90 100 110 12000.511.522.53Temperature (oC)DC conductivity (S)  0.069 N salt water0.03315 N salt water Figure 3.1 DC conductivity of salt water solution as a function of temperature. 20 30 40 50 60 70 80 90 100 110 12050556065707580Temperature (oC)Real part of relative permittivity (' r)  0.03315 N salt water0.069 N salt water Figure 3.2 Real part of relative permittivity of salt water solution as a function of temperature.    36 3.2 Heating Applicator Physical Design The physical geometry of the heating applicator is very important and affects the heating profile across the load as well as the load impedance. Many different design concepts were evaluated and a summary of the methodology employed to arrive at the final design is summarized. Uniform heating across the load requires a uniform electric field. An electric field is created by applying a potential difference across two electrodes, and of all possible geometries, a parallel plate structure is the only geometry that creates a uniform electric field. An example of a parallel plate structure is shown in Figure 3.3. Although the ideal parallel structure has a uniform electric field, a practical parallel plate structures has a fringing electric fields that need to be minimized.    37 dABVE= =constantdAABBUniform electric fieldElectric fieldNon-uniform electric field1E(E field decays w ith (r))rr Figure 3.3 Electric fields for a parallel plate structure (top) and a coaxial structure (bottom).  Other geometric configurations of electrodes could be used and the geometry could be scaled to minimize the variation of the electric field throughout the volume of the load. For example, in Figure 3.3, a design with coaxial electrodes is shown. For this geometry the electric field between the two plates varies as 1/r where r is the radial distance from the center of the cross-section. If the inner conductor diameter is large such that the distance between the electrodes is small, then the field variation can be reduced. The disadvantage of   38 the coaxial design is that there would be a large volume in the center which cannot be used. Therefore, to create a compact design, a parallel plate structure is selected. Although the parallel electrode structure provides a starting point for the design it is not ideal. First, the electrodes need to be connected to a coaxial connector to interface to the RF generator. The electrode connections and wiring introduce parasitic inductance and capacitance that must be minimized and controlled. Second, the load is a liquid and needs to be enclosed in a container. The container must be physically capable of operating under pressure as the maximum operating temperature is above 100°C. Third, very high electric fields are used to heat the load and the radio frequency fields can radiate into the surrounding environment causing electromagnetic interference (EMI). Therefore, it is very desirable to completely shield the load and the electrodes. These factors are illustrated in Figure 3.4. dAB Electric field in between parallel plate capacitor                   +-Leakage electric field spread into space  Electric field inside coaxial cableCoaxial cableInner conductorOuter conductor Figure 3.4 Electric fields in the environment around a parallel plate applicator. As a way to control the electric fields from the connector interface to the parallel plate applicator, a hybrid design is created which encloses the parallel plate structure in a coaxial   39 structure. The design concept is shown in Figure 3.5. At the top of the enclosed structure is a coaxial cable which connects to the RF generator. The cable is physically attached to the applicator through a coaxial connector. The outside of cylinder is grounded and completely envelopes the load. The bottom electrode is connected to the outside shield through an elevated post. The top electrode is attached by a second post which connects to the center conductor of the coaxial cable. Since the outside structure is a cylinder, the electrodes are circular disks. The fringing fields inside the enclosure are controlled by adjusting the distance between the electrodes and the outside walls.   40  Figure 3.5 Parallel plate applicator enclosed in a coaxial cylinder. There are thermal and mechanical considerations that must be considered in selecting the materials for the heating applicator. Starting with the load, a vessel is required to contain the liquid load and attach the electrodes to the load. The container must be a dielectric and Teflon is selected for the load container. Teflon has excellent electric characteristics with very low dielectric losses. Teflon also has excellent thermal properties. The thermal conductivity of Teflon is 0.25 W/m/K and has approximately half the thermal conductivity of   41 water, 0.58 W/m/K. Because the load container is operated under pressure, the wall thickness of the Teflon pressure vessel must be large to handle the mechanical stress. The electrodes contact the load and they need to be electrically conductive. Suitable materials include copper or aluminum. Aluminum electrodes are selected as aluminum has lower thermal conductivity (238 W/m/K) than copper (401 W/m/K) which reduces thermal losses through the electrodes. Aluminum is also lighter than copper, 2700 kg/m3 versus 8960 kg/m3. The electrical conductivity of aluminum (3.77×107 S/m) is lower than copper (5.9×107 S/m), but still has much higher conductivity than the load and ohmic losses in the electrodes are negligible. Another consideration is electrode corrosion. In this application, the pH of WAS is approximately neutral (7) and electrode corrosion is not expected to be a significant issue.  The outside enclosure needs to be electrically conductive and the diameter was selected based on the availability of standard sizes of aluminum piping. In this design, 8 inch diameter piping with a wall thickness of 5/16 inch is used. The posts used to provide electrical connections to the electrodes are also machined from aluminum stock. The optimization of the heating applicator geometry including load matching was done using an electromagnetic simulator (COMSOL). The final dimensions for the heating applicator are shown in Figure 3.6 and Figure 3.7. Two different designs are made to match to the two different loads: 0.03315 N salt water or 4.5% WAS and 0.069 N salt water or 18% WAS. The electrical circuit model of the load corresponding to the final geometry is described in the next section.   42 Outer conductor(Aluminium)LoadInner conductorOuter conductorInner conductor(Aluminium)AirDielectric(Teflon)25.86.27.691.273.256.27.42.6321.48 1.2824.612.06.22.1 2.54(All digits are in cm)20.2410.45 Figure 3.6 Dimensions and material specifications of the heating applicator for a 0.03315 N salt water load.   43 Inner conductorOuter conductorInner conductor(Aluminium)Outer conductor(Aluminium)AirLoadDielectric(Teflon)30.866.27.691.272.736.27.42.6321.48 1.2829.6617.12.22.1 2.54(All digits are in cm)10.4520.24 Figure 3.7 Dimensions and material specifications of the heating applicator for a 0.069 N salt water load. 3.3 Electrical Models of the RF Heating System The RF heating apparatus is designed to transfer power from a source to a load. The source in this system is a high power RF amplifier and the load is salt water or WAS. The overall heating efficiency of the system depends on the how much power is transferred from the source to the load. Electrically, power transfer from the source to load is maximized   44 providing the impedance of the load is conjugately matched to the impedance of the amplifier. Since the load impedance in this system changes with temperature, the amount of power delivered to the load varies with temperature. When the source and load are not matched, there is a mismatch loss which reduces the efficiency of transferring power to the load. In the design of the RF heating applicator it is important to analyze the mismatch loss in the system over temperature and maximize power transfer over the operating temperature range. The analysis of the power transfer from the source to load is done by converting the load and the applicator into an equivalent circuit model. The equivalent circuits are derived from the geometry of the load and applicator as well as the electrical properties of the load. In the next section, a brief summary on the concept of matching and transfer is described. This is followed by a description of equivalent circuit models for the load and the RF applicator. After the electrical models for the load and RF applicator are available, power transfer from the amplifier to the load is analyzed. The equivalent circuit models provide a way to optimize the geometry of the RF applicator to maximize power transfer to the load. 3.3.1 Power Transfer A model of the RF heating system is shown in Figure 3.8 (a). The source consists of a 13.56 MHz oscillator followed by a 1 kW power amplifier. The amplifier is designed to drive a 50 Ω load. The RF heating apparatus and load are generically called the load. The load impedance is LZ  and the impedance is temperature dependent because the dielectric properties and conductivity of the load change with temperature. If the load is 50 Ω, then the maximum available power Pav from the amplifier is delivered to the load. When the load impedance is not 50 Ω, there is a mismatch loss and the total power delivered to the load is   45  2(1- )L L avP P   (W) (3.12) where L   is the load reflection coefficient defined as  00-( )LLLZ ZZ Z   (3.13) The reference impedance 0Z  is equal to 50 Ω and the reflection coefficient is zero when0LZ Z . Under this condition, L avP P . If the reflection coefficient is not zero because of an impedance mismatch between the source and load, thenL avP P . The power flow diagram of the RF heating system is shown in Figure 3.8 (b) and a transfer efficiency of power from the generator to the load can be defined as  Transfer efficiency ( ) 100%LavPP  (3.14)   46 LoadloadRloadCHALHACCCLCCCACSR =50ΩEQZCoaxial cable(CC)Heating applicator(HA) including load13.56 MHz oscillator and power amplifierRF generatorHAZloadZLPU(a)(b)avPLPrefP Figure 3.8 RF heating system: (a) block diagram with equivalent circuit; (b) power flow diagram.     47 3.3.2 Equivalent Model for the Load As shown in Figure 3.5, the load is a cylindrical volume sandwiched between two circular plates. The plates have area A  and are separated by distance d . With reference to (2.11), the dielectric and conductivity characteristics of the load can be separated into three components: 1) the real part rİ  of the complex permittivity, 2) the imaginary part r   of the complex permittivity, and 3) the DC conductivityDC . Each of these three parts can be associated with an electrical model. A lossless parallel plate capacitor is created by the dielectric r    sandwiched between the two electrodes. The capacitance is  0r AC d  (F) (3.15) A shunt conductor modeling dielectric losses is created by the imaginary component of the dielectric and given by  0( )DE rAG d  (S) (3.16) where   is the frequency of the oscillator in the heating system. A second shunt conductance is created by the ionic conductivity of the load and equal to  DC( )DC AG d (S) (3.17) The total admittance of the load is YL and equal to  0L DC DE L LY G G j C G jB    (S) (3.18) The admittance is complex and the real part is conductance (LG ) and the imaginary part ( LB ) is susceptance. The equivalent circuit for the salt water and WAS loads are shown in Figure 3.9. The salt water load consists of two circuit elements: a capacitance created by the dielectric   48 constant of water and a shunt conductance to model the ionic conductivity of the solution. WAS is modeled by three circuit elements: a capacitance created by the real part of the dielectric constant, a shunt conductance associated with the imaginary part of the dielectric constant which relates to the β dispersion characteristics of the biological material, and a second shunt conductance corresponding to the ionic conductivity of WAS. The two conductances in the circuit model for WAS can be combined into a single shunt conductance as shown in Figure 3.9. WASB_WAS DCG_WAS betaG_ _WAS WAS DC WAS betaG G G salt WASB BWAS saltG G(a)(b) Figure 3.9 Equivalent circuit representation of (a) WAS and (b) salt water solution. As shown in (3.15) through (3.18), the electrical model is dependent on the ratio of the area of the plates to the separation of the plate, /A d . The physical scaling ratio /A d  can therefore be used to adjust the admittance or impedance ( 1/L LZ Y ) of the load. Since the electrical properties of the load are temperature dependent, the physical scale ratio is selected   49 to create the best matching condition at the mid-point of the temperature range. The operating temperature range for the heating system is from room temperature (20°C) to 120°C with a mid-point temperature value of 70°C.  At 70°C, the physical scale ratio is adjusted such that the real part of the load impedance is equal to 50 Ω. The residual imaginary part of the load impedance, which is capacitive, is compensated in the design of the RF heating apparatus by adding series inductance so that the overall impedance of the load is ideally 50 Ω at a temperature of 70°C. The design values for the plate area and plate separation are summarized in Table 3.3 for a load volume of 400 mL. The table also includes circuit values for the load. Table 3.3 Equivalent circuit and geometrical parameters for WAS and salt water loads at 25°C. Load B (S) GDE (S) GDC (S) r (cm) d (cm) A (cm2) .03315 N salt water 47.97 10  - 34.65 10  3.25 12.06 33.18  4.5% WAS 49.48 10  52.87 10  34.62 10  .069 N salt water 31.65 10  - 22 10  2.73 17.125 23.38 18% WAS 32.97 10  21.93 10  47.63 10  Although the design so far includes only the load, it is insightful to evaluate the transfer efficiency at this point. The impedance and transfer efficiency of the analytic load model is shown in Figure 3.10 and Figure 3.11. It turns out that the imaginary component of the load impedance (reactance) is quite small relative to the real part of the load impedance and the transfer efficiency is nearly 100% at a temperature of 70°C. Over the entire operating   50 temperature range, the power transfer efficiency is greater than 84.5%. The results confirm that using the physical area and separation of the plates shown in Table 3.3 provide a good match to the RF amplifier. 20 30 40 50 60 70 80 90 100 110 120-40-20020406080100120Temperature (oC)Impedance ()  R0.03315NX0.03315NR4.5%WASX4.5%WASR0.069NX0.069NR18%WASX18%WAS25oC Figure 3.10 Impedance of salt water and WAS as a function of temperature. 20 30 40 50 60 70 80 90 100 110 1208486889092949698100Temperature (oC)Power transfer efficiency in (%)  0.03315 N salt water4.5% WAS0.069 N salt water18% WAS25oC Figure 3.11 Power transfer efficiency of salt water and WAS load as a function of temperature.    51 3.3.3 Electrical Model for the Enclosure The coaxial load enclosure and the cable interface from the RF applicator add additional capacitance and inductance to the system. Since the total load impedance presented to the amplifier is measured at the connector interface to the amplifier, the additional capacitance and inductance modifies the net load impedance. An equivalent circuit model for the complete heating apparatus is shown in Figure 3.8 (a). The load is modeled by a shunt resistor loadR  and shunt capacitor with reactance loadX . The load model corresponds to the equivalent circuits developed before in section 3.3.2. The coaxial enclosure that encapsulates the load also has stray capacitance and series inductance. The capacitance is primarily associated with the top plate which is electrically isolated from the grounded outside cylinder that shields the load. The metal post which connects the top electrode to the center conductor of the coaxial connector and the metal post that connects the bottom electrode to ground have a small amount of inductance. The capacitance and inductance of the enclosure are modeled by an LC section with inductance HAL   and HAC  as shown in Figure 3.8 (a). The last section of the equivalent circuit model is a LC section which models the capacitance and inductance of the coaxial cable which connects the amplifier to the heating apparatus. A short length of the RG-58/U coaxial cable is used for the connection and analytical models for the capacitance and mutual inductance of the cable are readily available from any introductory book on electromagnetics [21]. In this design, the cable length is 30.48 cm, the inner conductor has a radius of 1.1 mm and the dielectric has a radius of 3.57 mm. A diagram of the cable geometry is shown in Figure 3.12. The dielectric is Teflon with a   52 relative permittivity of TF  = 2. With these values, the capacitance and inductance of the cable can be calculated as shown in Table 3.4. 1.1inr mmout3.57r mm(a)(b)30.48cm Figure 3.12 Connecting coaxial cable geometry: (a) cross section; (b) side view. Table 3.4 Capacitance and inductance of the connecting coaxial cable. CXL = 0 outinln( )2rr(nH) CXC = 0outin2ln( )TFrr   (pF) ZCX= CXCXLC (Ω) 71.85 28.77 49.97 All element values of the equivalent circuit model are known except for the enclosure capacitance and inductance. There are no readily available equations to calculate these values   53 because the geometry involved is complex. An alternate way to determine the equivalent circuit values is to find the energy stored in the electric and magnetic fields and then calculate capacitance and inductance from energy. The energy in the fields can be obtained from electromagnetic simulations of the enclosure. A simulation tool called COMSOL is used for the simulating the fields in the enclosure. Once the fields are found, the electric energy eW   and the magnetic energy mW  can be found. The stored energy is partitioned between the load which corresponds to the fields within the cylindrical load between the electrodes, and the stray fields inside the enclosure but outside the load cylinder. If the total electric energy stored inside the heating apparatus is eW  and the total electric energy stored within the load cylinder is ,e loadW , then  2_1- 4e e load HA mW W C V(J) (3.19) In this equation HAC   is the effective capacitance of the enclosure (see Figure 3.8) and mV  is the peak voltage of the source used in the simulation. In this work, there are two different physical design configurations corresponding to the design of a heating applicator for 4.5% WAS and 18% WAS. The equivalent salt water loads are 0.03315 N and 0.069 N, respectively, and from electromagnetic simulations using salt water loads, the capacitance,HAC , is estimated to be 9.6 pF and 11.3 pF, respectively.  A similar calculation can be made to estimate the inductance of the enclosure. Unlike the calculation of the equivalent capacitance of the enclosure where the load and enclosure both have capacitance, the load does not have significant inductance and the inductance is primarily related to the enclosure only. Recall that the load models in section 3.3 do not include any inductive elements - only resistance and capacitance. Therefore, the total   54 magnetic energy integrated over the interior volume of the enclosure can be used to estimate the equivalent inductance of the enclosure. The relation between magnetic energy mW  and the inductance of the enclosure HAL  is  214m HA mW L I(J) (3.20) where mI  is the peak current of the source used in the simulation. Using this method, the estimated inductance of the enclosure for 4.5% WAS is 117 nH and for 18% WAS is 143 nH. The estimated values of the capacitance and inductance of the enclosure were obtained from electromagnetic simulations using a salt water load at a temperature of 70°C. The equivalent model values are ideally constant and independent of the load temperature. However, the stray electric field does change slightly because the load capacity changes and there is a small variation in the equivalent component values of the enclosure depending on the temperature used in the simulation. The results are summarized in Table 3.5. As shown the maximum variation in capacitance is 0.5 pF and the maximum variation in inductance is 3.7 nH. The variations are within 5% of the average values, and in the following sections, the equivalent circuit model for the enclosure uses the average values to calculate transfer efficiency.  Table 3.5 Intrinsic capacitance and inductance for the heating apparatus. Load HAL (nH) (Average) HAL (nH) (Maximum) HAL (nH) (Minimum) HAC (pF) (Average) HAC (pF) (Maximum) HAC (pF) (Minimum) 0.03315 N 116.7 117.6 113.9 9.68 9.70 9.16 0.069 N 143.4 144.4 140.7 11.27 11.07 11.22    55 3.4 Analytic and Simulated Results for Power Transfer Efficiency The equivalent circuit models developed in the previous section are used to calculate analytic values for the impedance and power transfer efficiency as a function of temperature. In this section, the analytic results are compared with a full electromagnetic simulation of the heating applicator. The COMSOL models for the two different heating applicator designs are shown in Figure 3.13. The DC conductivity is larger for the higher molarity (0.069 N) load; consequently, the area of the electrodes is reduced and the spacing between the electrodes is increased relative to the 0.03315 N design to maintain a nominal 50 Ω load impedance. The simulation includes conductivity and dielectric material property changes as a function to temperature. (a)(b) Figure 3.13 COMSOL models of the heating applicator for 0.03315 N salt water (a) and 0.069 N salt water (b).   56 By measuring the ratio of the phasor voltage over the phasor current at the coaxial connector interface, the equivalent impedance of the heating applicator can be determined from the simulation. The simulation results for the two applicator designs are shown in Figure 3.14 and Figure 3.15. The figures include the corresponding analytic results derived from the equivalent circuit models for the enclosure and load. As shown, the simulated and analytic results are nearly identical. 20 30 40 50 60 70 80 90 100 110 120-50050100Temperature (oC)Impedance ()  Analytical (resistance)Analytical (reactance)Simulation (resistance)Simulation (reactance) Figure 3.14 Impedance of the RF heating system for a 0.03315 N salt water load.   57 20 30 40 50 60 70 80 90 100 110 120-50050100150Temperature (oC)Impedance ()  Analytical (resistance)Analytical (reactance)Simulation (resistance)Simulation (reactance) Figure 3.15 Impedance of the RF heating system for a 0.069 N salt water load. The simulated impedance results can be used to predict the efficiency of transferring RF generator power to the load using (3.12) through (3.14). The simulated efficiency characteristics are shown in Figure 3.16 and Figure 3.17. Analytic model results are included for comparison and similar to impedance, there is close agreement between simulated and analytic results.   58 20 30 40 50 60 70 80 90 100 110 120828486889092949698100Temperature (oC)Power transfer efficiency (%)  AnalyticalSimulation Figure 3.16 Power transfer efficiency of the RF heating system for a 0.03315 N salt water load. 20 30 40 50 60 70 80 90 100 110 1208486889092949698100Temperature (oC)Power transfer efficiency (%)  AnalyticalSimulation Figure 3.17 Power transfer efficiency of the RF heating system for a 0.069 N salt water load. The COMSOL electromagnetic simulation results can also be used to predict the uniformity of the electric field between the electrodes. The simulator calculates the electric field in a three dimensional model and the field variation in a YZ plane that passes through   59 the center of the load is shown in Figure 3.18. The field intensity between the electrodes is plotted as a function of distance from the top electrode. The input power is 1 kW and the electric field is approximately 37 V/cm for the 0.03315 N load and 26 V/cm for the 0.069 N load. A larger field is expected for the 0.03315 N load, since the electrodes are spaced closer than in the 0.069 N design. In both designs, the field is uniform and uniform heating is expected.  Figure 3.18 Electric field across the load as function of distance (arc length) for (a) 0.03315 N salt water load and (b) 0.069 N salt water load.    60 Chapter  4: Experimental Results A prototype RF heating applicator was built and tested. The RF heating system includes the RF generator, the applicator, and software to measure load temperature and control RF generator power. The applicator was tested with salt water loads and samples of WAS. Loads were heated from room temperature to 120ºC and impedance measurements of the applicator and load were made to verify the design. Excellent results were obtained and the RF heating applicator shows significant promise as a method of heating liquid and sludge loads. 4.1 Design of the Experimental Test Bed As described in Chapter 3, the RF heating system consists are three main components: 1) the RF generator, 2) the RF heating applicator, and 3) a coaxial cable to connect the RF generator to the applicator. A software control system is also required to control the load temperature in the applicator. An experimental test bed for heating WAS with a 4.5% bio-solid content was implemented. Pictures of the test bed are shown Figure 4.1 and annotations are added to identify the primary components in the system. A detailed description of the implementation of each of the heating system components is described in the following sections.   61  Figure 4.1 Pictures of the experimental test bed: (a) RF heating system and software control; (b) components of the RF heating system.   62 4.1.1 RF Generator The RF generator is the source in the heating system and delivers the required power to heat the load in the applicator. As described in section 2.4, a frequency of 13.56 MHz was selected for the design based on the dielectric properties of the load and the frequency falls within a band that is allocated to industrial, scientific and medical applications. The RF generator consists of a 1 kW class E power amplifier (PA). The power amplifier module is commercially available as an evaluation unit from Directed Energy, Inc, Colorado, model number PRF-1150. The input signal to the amplifier is a sinewave source generated by an arbitrary waveform generator, Standford Laboratories model DS345. The power amplifier module requires three external power supplies. A 5 V power supply (Agilent 6824A) is required for DC logic and control circuits in the module, a 15 V power supply (Agilent E3632A) is required for the driver stage, and the output power stage requires a high voltage DC supply (Ametek XFR 300-4) that can range from 100 V to 300 V. The power amplifier, waveform signal generator, and the DC power supplies are shown in Figure 4.2. The entire RF generator system is equivalent to a sinusoidal source at a frequency of 13.56 MHz with 50 Ω output impedance.   63 PA  Voltmeter  Signal generator  15V DC p wer supply   300V DC power supply     5V DC power supply     ACsR =50Ω Figure 4.2 Components of the RF generator.   64 The amplitude of the RF generator is dependent on the high voltage DC supply voltage which powers the amplifier module. Power is proportional to the square of voltage; therefore there is ideally a square law relationship between the DC supply voltage and the power delivered to the load. The square law relationship is ideal and does not consider the losses in the amplifier circuit. The implication of losses is that the power efficiency of the amplifier varies with the supply voltage which leads to a deviation from the square law relation between supply voltage and the power delivered to the load. 4.1.2 Coaxial Cable Interconnect A short length of coaxial cable (RG-58/U) is used to connect the RF generator to the heating applicator. A photograph of the coaxial cable is shown in Figure 4.3. The coaxial cable has a length of 30.5 cm with two male BNC connectors attached to each end of the cable. The output connector on the power amplifier module is a female BNC connector. The heating applicator has a female N-type coaxial connector and an adapter (BNC to N) is used to connect the cable to the applicator. The cable and connectors have a characteristic impedance of 50 Ω, and if the generator and load are perfectly matched, the cable does not introduce any significant mismatch loss in the heating system.   65 CXLCXC Figure 4.3 Connecting coaxial cable (RG 58). Since the load is not a constant 50 Ω impedance, the impedance presented to the RF generator interface is modified by the coaxial cable. In Chapter 3, the cable was modeled as a LC lumped element circuit. The equivalent circuit component values can be determined experimentally by measuring the input impedance of the cable for different termination conditions at the other end of the cable. Impedance measurements are made with an Agilent model 5061A vector network analyzer. The network analyzer measures impedance as a function of frequency at a   66 calibrated reference plane. With reference to Figure 4.3, the equivalent circuit model for the coaxial cable consists of a series inductor series inductor CXL  and a shunt capacitor CXC . The model is valid at low frequencies and the cable length is much less than the wavelength at 13.56 MHz. The inductance and capacitance of the cable are found by measuring the input impedance of the cable with a short circuit termination at the other end of the cable. With a short circuit on the right-hand interface in Figure 4.3, the input impedance looking in from the left-hand side is a parallel resonant circuit. At low frequencies, the impedance of the parallel resonant circuit is dominated by the inductor, while at high frequencies, the circuit is dominated by the capacitance. There is also a resonant frequency where the reactance of the two elements completely cancels and the input impedance is nearly zero because of the short circuit termination. Therefore, at low frequencies (lowf )  2in low CXZ j f L (Ω) (4.1) and at resonance (rf )  210 (2 )in CX r CXZ C f L   (4.2) Input impedance measurements were made over a frequency sweep range of 300 kHz to 500 MHz with a short circuit termination. At a low frequency (lowf ) of 300 kHz, the extracted value of the inductance is 75 nH. The input impedance had a parallel resonance at a frequency of 339.8 MHz from which an equivalent cable capacitance of 29.2 pF is obtained. In Chapter 3, the analytic and modeled values for the equivalent circuit were presented, and the cable inductance was 72 nH and the cable capacitance was 28.7 pF. The analytic and measured values are similar, and the close agreement supports the choice of the equivalent circuit model topology used for analysis.   67 4.1.3 Heating Applicator The electrical design of the RF heating applicator was described in Chapter 3, and for a 4.5% WAS load, the dimensions of the applicator were given in Figure 3.6. From the electrical design, the size and spacing of the electrodes were determined to provide a good match between the load and the RF generator for a load volume of 400 ml. The electrical design included modeling the coaxial connector interface to the electrodes and the coaxial enclosure which shields the applicator.  Although the electrical design determined the principal geometry of the applicator, there are also very important mechanical design requirements for the heating applicator. Since the apparatus is designed to heat liquid and sludge loads above 100°C, the applicator must heat the load under pressure to maintain a constant volume. In other words, the RF heating applicator can be thought of as a RF or electromagnetic pressure cooker. Since the applicator operates under pressure, the design requires materials, seals, and safety valves that are consistent with a maximum operating temperature range of 120°C. The mechanical design of the heating system was done by another member of the research team, Ehssan Koupaie. Ehssan is a PhD student in environmental engineering and he will use the RF heating applicator to conduct experiments with WAS. The heating applicator was built in the machine shop at UBC and a picture of the final prototype is shown in Figure 4.1. The prototype consists of three main parts: 1) a top electrode assembly which includes an aperture for a pressure relief valve and a temperature sensor, 2) a thick walled Teflon pressure vessel with seals and a capacity of 400 ml, and 3) a coaxial aluminum enclosure that has the RF connector which connects to the RF generator. More detailed photographs of the top electrode assembly are shown in Figure 4.4. The   68 electrode is an aluminum disk cut from half inch aluminum plate. The electrode has blind holes that are used to mount the electrode to a Teflon cap and aluminum plate. The Teflon cap matches the outside diameter of the Teflon pressure vessel and the aluminum plate is used to clamp the assembly to the outside aluminum enclosure.   69  Figure 4.4 Photo of the top electrode assembly in the heating apparatus.   70 The Teflon pressure vessel is shown in Figure 4.5. At the bottom of the vessel is the bottom electrode which is connected to a coaxial N type connector. An O-ring seal is sandwiched between the electrode and the Teflon vessel. At the top of the Teflon vessel, a second O-ring seal is used to seal the top electrode to the container walls.   71  Figure 4.5 Photos of the Teflon load vessel.   72 Photographs of the aluminum enclosure are shown in Figure 4.6. Looking in from the top of the enclosure shows a hole where the RF connector on the Teflon pressure vessel passes through to the outside of the enclosure. Since the bottom electrode is sealed inside the Teflon pressure vessel, the port for the connector does not require additional seals. The enclosure is made from 8’’ aluminum pipe with a 5/16’’ wall thickness. Two flanges are welded to the enclosure. The top flange has holes to bolt the top plate of the applicator to the enclosure. The bottom flange is used as a base for the applicator.   73  Figure 4.6 Photos of the aluminum enclosure.   74 After fabricating the prototype, the electrical characteristics of the applicator were measured. As described in Chapter 3, the load in the pressure vessel can be modeled as a shunt resistor and capacitor. The resistance and capacitance are temperature dependent and designed to be matched to 50 Ω at a temperature of 70°C. The enclosure adds parasitic inductance (HAL ) and capacitance ( HAC ), and the values are measured experimentally to compare with values obtained from electromagnetic simulations. Figure 4.7 shows the applicator and the equivalent circuit model.   75  Figure 4.7 Photo of the heating apparatus and the corresponding equivalent circuit model.   76 A two-step process was used to measure and extract the equivalent circuit model for the applicator. First, an impedance measurement is made without a load in the applicator. The load capacitance is small in this case because the dielectric is air. From this measurement, the capacitance of the enclosure is estimated. A second measurement was made with a calibrated salt water load. The load was a salt water solution of 0.03315 N at a temperature of 22.8°C, and the equivalent circuit values for the load are derived from the analytic model in Chapter 3. Starting with the no load measurement, the capacitance is measured over a frequency range from 10 MHz to 15 MHz. In this case, the capacitance is the sum of the capacitance of the enclosure, HAC , and the capacitance of the load cylinder, loadC , estimated to be 0.25 pF. The capacitance of the enclosure is then determined by subtracting the load cylinder capacitance from the measured capacitance.  The inductance, HAL , does not contribute significantly to the impedance measurement. Therefore, under this condition  12 ( )in CX loadZ j f C C (Ω) (4.3) The corresponding capacitance of the enclosure extracted using this method is shown in Figure 4.8. At a frequency of 13.56 MHz the intrinsic capacitance of the enclosure is approximately 13.9 pF.   77 10 10.5 11 11.5 12 12.5 13 13.5 14 14.5 1513.8613.8813.913.9213.9413.9613.98Frequency (MHz)Capacitance (pF)13.91 pF Figure 4.8 Measured intrinsic capacitance of the heating applicator as a function of frequency. Once the capacitance of the heating applicator is known, the impedance is measured with a calibrated salt water load. Since HAC  , loadR  and loadC  are all known, the inductance HAL  is found by tuning the impedance of the analytic model until it matches the experimental results. A Smith chart is used to compare the experimental and model values as shown in Figure 4.9. Over a frequency range of 10-15 MHz, the inductance of the enclosure is estimated to be 115 nH. Note that it is difficult to see the two traces in Figure 4.9 which shows that the modeled and measured values match very well. The extracted value of 115 nH is very close to 117 nH which was the value derived from COMSOL simulations shown in Chapter 3. The experimental values of the enclosure capacitance and inductance are used later to generate power transfer models for the experimental heating apparatus.   78  Figure 4.9 Measured and modeled impedance of the heating applicator with a 0.03315 N salt water load for a frequency range of 10-15 MHz. 4.1.4 Temperature Measurement System The purpose of the RF heating system is to heat the load in a predictable and controlled way. Therefore, temperature measurements and temperature profiles across the load are very important. A K-type thermocouple, model GK11M from Test Product International, Inc. is used to measure the temperature of the load. A small hole is drilled through the top electrode and the tip of the thermocouple extends about 1 mm into the load. Because the vessel is under pressure, the thermocouple is sealed into the top electrode using an adhesive called JB Weld. The location of the temperature sensor on the top electrode is shown in Figure 4.4. A thermocouple consists of two different metals, and at the tip, the metals are joined. Through a diffusion process, a potential difference is developed across the two wires which can be measured with a digital voltmeter. The digital voltage meter is shown in Figure 4.2. The voltmeter is an Agilent 34401A unit and measurements of the thermocouple voltage are read by a computer controlled interface to the instrument. Software implemented in LabView   79 converts the voltage measurements into temperature and displays the temperature of the load on a graph. The temperature of the load is calculated using the following equation  0 slope TCT T K V   (4.4)  In this equation, 0T  is room temperature,  slopeK  is temperature constant for the K type thermocouple (24.454°C/mV), and TCV  is the thermocouple voltage. The K-type thermocouple has an operating temperature range of -40°C to +510°C. The room temperature calibration constant 0T  was determined by measuring a load in thermal equilibrium using a mercury thermometer and the thermocouple. One problem with the thermocouple measurement system is the susceptibility to electromagnetic interference (EMI). It was found that the electric fields at the surface of the electrodes are sufficiently large to create significant errors in the measurement of thermocouple voltage. Experiments were made to shield the thermocouple wires but the results always had significant error. An example of the interference problem is shown in Table 4.1 where thermocouple temperature measurements are compared with a mercury thermometer. The errors increase as the supply voltage (electric field) increases. Table 4.1 Effect of EMI on temperature measurements. Applied voltage (V) Thermocouple temperature reading, Ttc (°C) Mercury thermometer temperature reading, Tmt (°C) Error=tc mttcT -T 100T  % 100 41.7 51.5 19.03 200 21.6 51.5 58.06    80 As a way to mitigate the sensitivity of the thermocouple to electromagnetic interference, temperature measurements are made periodically by turning of the DC supply to the power amplifier module. The DC supply is pulsed off for 2 seconds while a temperature measurement is made and then turns on for 10 seconds. Using this method, accurate temperature measurements are obtained from the thermocouple. An example of temperature measurements with and without the pulsing scheme is shown in Figure 4.10. 0 10 20 30 40 50 6010152025Time (sec)Temperature (oC)  0 10 20 30 40 50 60050100Time (sec)DC power supply voltage (V)EMI free measurementEMI prone measurement(b)(a) Figure 4.10 RF generator voltage (a) and load temperature (b) as a function of time. 4.1.5 Control Software There are two modes that will be used with the heating apparatus. The first mode heats the material under test at a specific thermal ramp rate specified in °C per minute. The second mode heats the material at a target steady state temperature for a specific length of time. In both heating modes, the heating rate is controlled by the DC voltage applied to the RF power amplifier. The output power from the amplifier is proportional to the DC voltage and, by   81 measuring the temperature of the load, software implemented in LabView can control the thermal ramp rate and heat material at a constant temperature. Although an open loop control method can be implemented using a look-up table, there are limitations to this method. Ideally, the power delivered to the load has a square law relation with the power supply voltage. However, the load impedance is nonlinear which creates deviation from the square law relation. Other significant limitations of open loop control include increasing thermal losses as the temperature gradient between the load and ambient temperature increases, as well as the nonlinear relationship between the power efficiency of the amplifier and the DC supply voltage. Given the limitations of open loop temperature control, a closed loop temperature control system is implemented. An adaptive control loop is implemented using the least mean square algorithm. The algorithm measures the error between the desired (reference) temperature and the actual temperature measured using the thermocouple. The power supply voltage is then periodically adjusted in a direction dependent on the magnitude and sign of the error. At steady state, there is a small oscillation and the magnitude of the variance at convergence depends on a step size parameter µ.  All the software control is implemented in LabView 2013. The software includes graphs that show the load temperature as a function of time as well as power supply control panels. A picture of the user interface is shown in Figure 4.11.   82  Figure 4.11 LabView front panel control interface: (a) temperature graph and other control display/knobs; (b) instantaneous ramp rate and PA input voltage display.     83 4.2 Thermal Profiles of the RF Heating System Experiments were made to verify the operation of the RF heating system. The experiments include heating salt water and WAS at different thermal ramp rates, as well as heating loads at a constant temperature. Experiments were also made to measure the temperature variation across the load volume since uniform heating is important. 4.2.1 Thermal Ramp Rate for a Salt Water Load The first test conducted to verify heating profiles was to measure the thermal ramp rate for a salt water load. A salt water load of 0.03315 N is used and the DC voltage was set to four different voltages: 100 V, 150 V, 200 V, and 250 V. The salt water was initially at room temperature, approximately 22.5°C, and heated to a target temperature of 80°C. The time required to reach the target temperature was recorded and the corresponding thermal ramp rate was calculated from the measurements. The experimental results are summarized in Figure 4.12 and Table 4.2.  0 10 20 30 40 50 602030405060708090Time (minute)Temperature (oC)   Figure 4.12 Ramp rate measurement for salt water load with 250 V (blue line), 200 V (magenta line), 150 V (red line) and 100 V (yellow line) input to the PA.   84 Table 4.2 Ramp rate of the RF heating device with 0.03315 N salt water load. Applied voltage (V) Room temperature (̊C) Target temperature (̊C) Time to reach 80 ̊C (min) Ramp rate (̊C/min) 250 22.5 80 4.22 13.63 200 22.58 80 6.635 8.66 150 22.8 80 10.06 5.68 100 24.9 80 36.68 1.502 For 100 V, the thermal ramp rate is 1.5°C per minute and progressively higher ramp rates are measured for higher voltages. The highest thermal ramp rate is 13.6°C per minute for a voltage of 250 V. The data show that the thermal ramp rate and the corresponding voltage are not linear. For example, the thermal ramp rate increases from 1.5°C to 5.7°C for a 50 V change from 100 V to 150 V, while the thermal rate changes from 8.7°C to 13.6°C for a 50 V step from 200 V to 250 V. The nonlinear relationship between the voltage step and the thermal ramp rate step is related to the square law relationship between voltage and power as well as differences in the power efficiency of the amplifier as a function of DC supply voltage. The amplifier is most efficient at high power (high voltage) and power efficiency decreases for lower operating voltages. 4.2.2 Thermal Ramp Rate for Waste Activated Sludge Limited samples of WAS were available for testing and, at this point in the research project, testing was conducted for 100 V only.2 The results for heating 4.5% WAS are shown                                                  2 Testing is conducted in a conservative manner with the least aggressive ramp rate first. This caution was exercised as the RF amplifier can be damaged if a test did not work as expected.   85 in Figure 4.13. For comparison, the heating for an equivalent salt water load is shown. The sludge was heated from an initial temperature of 22.2°C to a final temperature of 80°C over a time interval of 42.5 minutes. Therefore the average ramp rate for the sludge is 1.35°C per minute compared to 1.5°C per minute for the equivalent salt water load (see Table 4.3). Although salt water has similar electrical characteristics compared to sludge, the physical characteristics of sludge and salt water are different. Sludge is heterogeneous and has 4.5% bio-solid content from organic matter, while salt water is homogenous and the thermal characteristics of salt water are primarily determined the properties of water. The measurements show that a slightly lower thermal ramp rate can be expected for the sludge.  Figure 4.13 Ramp rate measurement for a 4.5% WAS load with 100 V input to the PA.      86 Table 4.3 Comparison of ramp rates for 0.03315 N salt water and 4.5% WAS. Load Room temperature (̊C) Target temperature (̊C) Time to reach 80 ̊C (min) Ramp rate (̊C/min) 0.03315 N salt water 24.9 80 36.68 1.502 4.5% WAS 22.2 80 42.52 1.35  4.2.3 Thermal Settling Time for Heating at Constant Temperature After ramping the temperature of the load to a target temperature, the load needs to be maintained at a constant temperature. At a constant temperature, the load loses heat to the ambient environment. The load is contained in a Teflon vessel and the enclosure is aluminum. Each of these materials conducts heat from the load and power must be periodically applied to maintain a constant temperature. For this project, a steady state temperature is obtained when the load temperature is within ± 0.5°C of the target temperature. After experimenting with different pulsing schemes to maintain constant temperature, the DC power supply is pulsed on at a voltage of 75 V after reaching the target temperature. Using this scheme, the settling times for a salt water load were measured and the results are shown in Figure 4.14. For a low thermal ramp rate of 1.5°C per minute using a 100 V supply, the settling time is negligible. The load has been ramped up to a temperature of 120°C and the pulsing scheme maintains a steady state temperature of 120°C. A second experiment was run for the most aggressive thermal ramp rate (13.6°C per minute) using a 250 V supply. For the fast ramp rate, the load is heated quickly and once the target temperature is reached there   87 is an initial overshoot in temperature. For this experiment with salt water, it took 9.53 minutes for the load to settle to the target temperature of 120 ± 0.5°C. 0 10 20 30 40 50 60 70 8020406080100120140Time (minute)Temperature (oC)  settling time= 9.53 minutesSteady state regionTransientregiontolerancelimitHeatingregionsettling time=0 minute Figure 4.14 Settling time for a target temperature of 120 C̊ (blue line: 250 V and red line: 100 V). The thermal gradient between the load and the ambient environment is large at a target temperature of 120°C. If the target temperature is reduced, then the thermal settling time is reduced. This is illustrated by measurements for a target temperature of 30°C as shown in Figure 4.15. Similar to the experiment with a target temperature of 120°C, a low ramp rate using 100 V does not require any settling time. For an aggressive thermal ramp rate using a 250 V supply, the thermal settling time is 6.1 minutes, approximately 3.5 minutes less than for a 120°C target temperature. Based on these experiments, a thermal settling time of 10 minutes is recommended to cover the fastest thermal ramp rate and highest target temperature which can be obtained using the experimental heating system.   88 0 2 4 6 8 10 12 1420222426283032Time (minute)Temperature (oC)settling time=0 minutessettling time= 6.1 minutestolerance limit Figure 4.15 Settling time for a target temperature of 30 ̊C (blue line: 250 V and red line: 100 V). 4.2.4 Thermal Gradient between the Electrodes An important objective for the RF heating system was to design a heating system which produces uniform heating across the load. The electrical design of the apparatus consists of two electrodes, and providing the leakage fields outside the Teflon cylinder are small, the field is expected to be approximately uniform across the load.  The electromagnetic simulations of the electric field profile across the load were shown earlier in section 0. If there were no thermal losses in the system, a uniform electric field would create uniform heating and the temperature would be constant across the load. However, there are thermal losses in the RF heating system which creates a deviation from a uniform thermal profile. Thermal conduction losses include heat loss through the aluminum electrodes, the Teflon vessel, and the aluminum enclosure. The thermal profile of the temperature between the electrodes was measured by inserting a mercury thermometer into the load through a small hole in the electrode. The hole   89 in the top electrode was shown earlier in Figure 4.4 and the hole is normally used for a connection to the pressure relief valve. An illustration of the measurement method is shown in Figure 4.16. The thermometer is inserted into the load at five different depths. The five depths are uniformly spaced across the load in 30.15 mm increments. In order to calibrate the insertion depth, the thermometer was marked as shown in Figure 4.17.  Figure 4.16 Thermometer tip positions for measuring temperature across load.   90  Figure 4.17 Marks on the mercury thermometer used to set insertion depth in the load. A large number of experiments were run with the salt water load to measure the temperature gradient across the load. Measurements were made at steady state temperatures from 30°C to 90°C in 10°C steps. A thermal settling time of ten minutes was used before each measurement was made. The upper limit of 90°C is the maximum temperature before the volume of the load expands significantly and starts to bubble through the hole in the top electrode. For each temperature step, the thermal gradient was measured for four different initial ramp rates using 100 V, 150 V, 200 V and 250 V. The results for each steady state temperature measurement are shown in Figure 4.18 through Figure 4.21.    91 0 20 40 60 80 100 120 1401020304050Distance across load (mm)Temperature (oC)0 20 40 60 80 100 120 1402030405060Distance across load (mm)Temperature (oC)Top heating plate Bottom heating plate Figure 4.18 Thermal profile across 0.03315 N salt water load for a target temperature of 30°C and 40°C with 250 V (blue line), 200 V (red line), 150 V (cyan line), 100 V (blue circle). 0 20 40 60 80 100 120 1403040506070Distance across load (mm)Temperature (oC)0 20 40 60 80 100 120 1404050607080Distance across load (mm)Temperature (oC) Figure 4.19 Thermal profile across 0.03315 N salt water load for a target temperature of 50°C and 60°C with 250 V (blue line), 200 V (red line), 150 V (cyan line), 100 V (blue circle).   92 0 20 40 60 80 100 120 1405060708090Distance across load (mm)Temperature (oC)0 20 40 60 80 100 120 14060708090100Distance across load (mm)Temperature (oC)11.3mmregion of -2oC lower than target temperature Figure 4.20 Thermal profile across 0.03315 N salt water load for a target temperature of 70°C and 80°C with 250 V (blue line), 200 V (red line), 150 V (cyan line), 100 V (blue circle).  0 20 40 60 80 100 120 140707580859095100105110Distance across load (mm)Temperature (oC) Figure 4.21 Thermal profile across 0.03315 N salt water load for a target temperature of 90°C with 250 V (blue line), 200 V (red line), 150 V (cyan line), 100 V (blue circle).     93 From the experiments, the following observations are made: 1. The thermal gradients are independent of the initial ramp voltage. This provides additional confirmation that ten minutes is an adequate settling time for the RF heating apparatus. 2. The temperature near the top electrode where the temperature sensor is located is close to the target temperature. 3. The temperature in the middle of the load is slightly higher than the target temperature. 4. The temperature near the bottom electrode is less than the target temperature and the deviation from the target temperature increases as the temperature increases. The maximum and minimum temperatures measured across the load are summarized in Table 4.4. For a target temperature of 40°C the maximum temperature deviation is +2/-3°C and for a target temperature of 90°C the maximum temperature deviation is +2/-11°C. 5. The thermal gradient near the bottom electrode is confined to a small region of approximately 1 cm. As an example, with reference to Figure 4.20, for a target temperature of 80°C and with a voltage ramp of 250 V, the temperature varies from 78°C at a distance of 11.3 mm from the bottom electrode to a temperature of 70.8°C (Table 4.4) at the surface of the bottom electrode. Over the remainder of the load volume, the temperature is within 2°C of the target temperature.      94  Table 4.4 Summary of maximum and minimum temperatures across a 0.03315 N salt water load. Target temperature ( ̊C) Maximum temperature ( ̊C) Minimum temperature ( ̊C) 30 30.8 28 40 42 37 50 52.5 46 60 62.8 55.8 70 73 64.5 80 83.1 70.8 90 92 79 A temperature gradient near the electrodes is expected because of the thermal conduction through the aluminum electrodes. Thermal conduction through the electrodes was considered in the design phase and thin posts are used to connect the electrodes the electrical source. Since the mechanical design of the top and bottom electrodes is similar, a uniform thermal conduction gradient was expected as shown in Figure 4.22. Obviously the measurements show an asymmetric thermal gradient in the region of near the electrodes, and upon further analysis, the asymmetric gradient can be explained by a change in density as the load is heated. With reference to Figure 4.23, as the load is heated, the density decreases because of the increase in kinetic energy of the molecules in the load. The less dense molecules float to the top of the Teflon enclosure and gravity acts on the colder molecules that are denser. The movement of mass is a thermal convection process, and in steady state, the temperature at the bottom of the vessel is cooler than the top of the vessel. The same observation can be made after heating a cup of water in a microwave oven. Therefore, the   95 primary reason for the steeper temperature gradient at the bottom electrode arises from the orientation of the experimental apparatus where the electrodes are in a vertical profile. Improvements in the apparatus could include mechanisms to rotate or stir the load. These recommendations are included in Chapter 5 under the discussion of future work.  Figure 4.22 Temperature gradient across the load due to heat conduction loss.   96  Figure 4.23 Temperature gradient across the load due to heat conduction loss and water density variation. 4.3 Impedance and Power Transfer Measurements Experimental measurements of impedance were made with an Agilent model 5061A vector network analyzer. The impedance measurements were made at different temperatures, and from the impedance data, the transfer efficiency of power from the RF generator to the load can be calculated using equations shown in section 3.3. The experimental results for a salt water load and WAS are described next. 4.3.1 Salt Water Load A series of impedance measurements were made for a 0.03315 N salt water load over a temperature range of 30°C to 120°C. The load was heated using two different ramp rates and then held at a steady state temperature for ten minutes before making an impedance   97 measurement with the network analyzer. The ramp rates correspond to 100 V and 250 V power supply voltages, and for each ramp rate, the load temperature was increased in 10°C steps from 30°C to 120°C. At each temperature step, a dwell time of ten minutes was used such that the load reached a steady state temperature. After reaching a steady state temperature, the RF heating applicator was disconnected from the RF generator and connected to the vector network analyzer to measure impedance. Two impedance measurements were made at a frequency of 13.56 MHz. The first measurement was made at the RF generator interface to measure the total impedance of the overall system presented to the RF generator and the second measurement was made at the connector interface to the applicator (see Figure 3.8). The impedance measurements for all the experiments are summarized in Figure 4.24 and Figure 4.25. 30 40 50 60 70 80 90 100 110 120-20020406080100Temperature (oC)Impedance ()  Resistance (100 V)Resistance (250 V)Reactance (100 V)Reactance (250 V) Figure 4.24 Measured impedance of the RF heating applicator with a 0.03315 N salt water load for two different ramp rates.   98 30 40 50 60 70 80 90 100 110 120-20020406080100Temperature (oC)Impedance ()  Resistance (HA including load)Reactance (overall system)Resistance (overall system)Reactance (HA including load) Figure 4.25 Impedances for the RF applicator and the RF applicator plus the coaxial cable (overall system) with a 0.03315 N salt water load. Several observations can be made from the impedance measurement data. 1. The impedance measurements for the 100 V ramp rate and the 250 V ramp rate are very similar (see Figure 4.24). This result is expected because the load is held at a steady state temperature for each temperature step and the ramp rate only affects how fast the load can be heated. 2. The real part of the impedance (resistance) is very close to 50 Ω at a temperature of 70°C (see Figure 4.24). The 70 °C reference point for the best match is consistent with the design objective where the match is optimum near the midpoint of the operating temperature range. These measurements confirm that the experimental apparatus meets the original design specifications for a calibrated salt water load. 3. With reference to Figure 4.25, the impedance measurements of the RF heating apparatus and the measurements with the addition of the coaxial cable (overall   99 system) are similar. This shows that when the applicator is designed to be matched to 50 Ω, the additional coaxial transmission line with a characteristic impedance of 50 Ω does not significantly modify the impedance presented to the RF generator. The impedance measurements can be used to calculate the efficiency of power transfer from the RF generator to the load using equations shown in section 3.3. The corresponding power transfer characteristics are shown in Figure 4.26. The power transfer efficiency is greater than 93% over the entire operating temperature range, and peak efficiency occurs between 60°C and 70°C. The peak efficiency point is where the load impedance is very close to 50 Ω. 30 40 50 60 70 80 90 100 110 1209293949596979899100Temperature (oC)Power transfer efficiency (%)  Heating applicatorOverall system Figure 4.26 Measured power transfer efficiency with a 0.03315 N salt water load.      100 4.3.2 Waste Activated Sludge The input impedance of the RF heating apparatus was measured with WAS. The load was heated using a 100 V ramp and then held at a steady state temperature for ten minutes before making an impedance measurement with the network analyzer. Impedance measurements were made in 10°C increments over a temperature range from 30°C to 120°C. At each temperature point the impedance was measured at both the connector reference plane and at the RF generator plane which includes the coaxial cable. The real (resistive) and imaginary (reactive) components of the impedance measurements are shown in Figure 4.27. 20 30 40 50 60 70 80 90 100 110 120-20- 001020304050607080Temperature (oC)Impedance ()  Resistance (HA including load)Reactance (overall system)Resistance (overall system)Reactance (HA including load) Figure 4.27 Measured impedance for the RF heating system with a 4.5% waste activated sludge load. From the impedance measurements, the real part of the impedance is approximately 50 Ω at a temperature of 40°C. The design objective was to match the real part for a temperature range of 70°C which is the midpoint of the 30°C to 120°C operating temperature range. The difference between the measured result and the design objective can be attributed to the variation in the dielectric properties of the sludge. The design was based on a dielectric study   101 carried out several years ago and the samples tested for this experiment were recently obtained from the Kelowna water treatment plant. Although both samples have a bio-solid content of 4.5% the ionic conductivity of the samples is different. Many more samples would have to be tested to determine the standard deviation of the dielectric characteristics and this is recommended in future work. Despite the variance in the dielectric characteristics of WAS, sludge samples can still be heated very efficiently using the RF heating system. This is illustrated by the power transfer efficiency graphs shown in Figure 4.28. Power efficiency from the generator to the load is greater than 86% over the entire operating temperature range. Efficiency peaks around 40°C which corresponds to the temperature where the real part of the load impedance is 50 Ω as shown in Figure 4.28. The results demonstrate that the sludge can be heated very efficiently using the RF heating apparatus. 20 30 40 50 60 70 80 90 100 110 12086889092949698100Temperature (oC)Power transfer efficiency (%)  Heating applicatorOverall system Figure 4.28 Measured power transfer efficiency for the RF heating system with a 4.5% waste activated sludge load.    102 4.4 Comparison of Analytic, Simulated and Measured Results As a summary of the RF heating system, a comparison is made between analytic results, electromagnetic simulation results and experimental results. An important design objective has been to implement a system that is matched to 50 Ω. Factors which affect the match are the load impedance, the area of the electrodes, the distance between the electrodes, and the parasitic inductance and capacitance of the enclosure and the coaxial cable. The load impedance is the most significant variable in the design and the load impedance varies with temperature. The operating temperature range of the heating system is 20°C to 120°C, and the impedance match is designed for a temperature of 70°C such that the overall power transfer to the load remains high over the entire operating temperature range. A summary of the impedance characteristics of the overall heating system including the coaxial cable is shown in Figure 4.29. For the salt water load with a concentration of 0.03315 N there is very close agreement between analytic, simulated and measured results. Salt water is a homogenous load with well controlled electrical characteristics that make it ideal for design and verification. After verifying the RF heating system with a salt water load, the system was tested with WAS. The sludge samples were obtained from effluent at the Kelowna wastewater treatment plant and the electrical properties of sludge are much more variable than a prepared salt water solution. The sludge is heterogenous and has 4.5% organic solid content. The experimental results in Figure 4.29 show that a 50 Ω match is obtained at approximately 40°C compared to the salt water load which is matched at 70°C. Since the resistance of the sludge is lower than the salt water load, the ionic conductivity of the sludge is higher than the salt water load.   103 20 40 60 80 100 120-50050100Temperature (oC)Impedance ()  Resistance of salt water (measurement)Resistance of salt water (simulation)Resistance of salt water (analytical)Reactance of salt water (simulation)Reactance of salt water (analytical)Resistance of WAS (measurement)Reactance of WAS (measurement)Reactance of salt water (measurement) Figure 4.29 Impedance comparison for the RF heating system between salt water and WAS load. The impedance characteristics shown in Figure 4.29 can be used to calculate the power transfer efficiency from the generator to the load (Figure 4.30). When the load is not equal to the source impedance (50 Ω) there is a mismatch loss that reduces the efficiency of delivering power to the load. The analytic, simulated and measured power transfer characteristics for a salt water load are similar and peak efficiency is centered at 70°C. The power transfer efficiency curve for WAS is also shown. The efficiency peaks at 40°C and remains above 86% efficiency over the entire operating range. Therefore, despite the shift in peak efficiency from a 70°C target, the load can still be heated very efficiently.   104 20 30 40 50 60 70 80 90 100 110 120828486889092949698100Temperature (oC)Power transfer efficiency (%)  Measurement (salt water)Analytical (salt water)Simulation (salt water)Measurement (WAS) Figure 4.30 Power transfer efficiency comparison for the RF heating system between salt water and WAS load.                105 Chapter  5: Conclusion The motivation for this research project was to design an electromagnetic heating system for treating WAS. The heating process is used as a pretreatment method to breakdown cell walls in organic material, and after pretreatment, the organic waste is processed in an anaerobic digester to generate bio-gas. The heating methods used in research projects to investigate the pretreatment of sludge have so far been limited to conventional heating process using thermal conduction and microwave heating at a frequency of 2.45 GHz. These heating processes have been selected primarily based on the convenience of accessing commercial equipment that is readily available for conventional and microwave heating, and there appears to be no prior work that has investigated the design of more optimal heating systems for WAS. 5.1 Contributions The dielectric properties of WAS were measured over a wide frequency, and based on these measurements, a frequency of 13.56 MHz was selected for heating. The dielectric properties show that sludge has significant ionic conductivity as well as β dispersion associated with the cell membrane. At a frequency of 13.56 MHz, WAS has significant ionic electrical properties that can lead to efficient ohmic heating. There is also dielectric heating associated with β dispersion, although the heating associated with this mechanism is expected to be much less than ohmic heating.  The efficiency of ohmic heating could be increased by reducing the frequency below 13.56 MHz but other issues including electro-chemical reactions and electrode polarization start to become problems. Therefore, heating at a frequency of 13.56 MHz is a good compromise.   106  Other advantages of heating at a frequency of 13.56 MHz include uniform volumetric heating through the load rather than conventional heating processes that rely on thermal gradients. The wavelength of a 13.56 MHz source transmitting electromagnetic power through a liquid medium like water is 16.6 meters and therefore, the depth of penetration of the electric field is large. Microwave heating on the other hand has a wavelength of .092 meters in water and has a much shallower penetration depth. RF heating at 13.56 MHz also has other advantages over microwave heating in terms of the power efficiency of the generator. A typical domestic microwave oven has a 1.2 kW microwave tube with a power efficiency of approximately 60%. By comparison, the RF power module in this research project delivers 1 kW with a power efficiency of 85% and the design is implemented with solid-state devices in a compact module. Therefore, RF heating has advantages in terms of the power efficiency of the RF generator and higher penetration depth compared to microwave heating systems. Once the frequency of the RF heating apparatus was selected, the impedance characteristics of the load were known, and an applicator to uniformly heat a load was designed. Different design concepts were evaluated using electromagnetic simulation tools and eventually a design based on a coaxial enclosure with two electrodes was selected. The geometry of the design was optimized to intrinsically match the load to 50 Ω generator impedance over an operating temperature range of 20°C to 120°C. The design included important mechanical design requirements to operate under pressure and maintain a constant load volume. The design was fabricated and tested. A salt water load with similar electrical characteristic to WAS was initially used to verify the design. Analytic, simulated and   107 experimental results using the salt water load were in close agreement. Thermal ramp rates from 1.5°C to 13.5°C were measured and measurements were also made to evaluate the temperature across the load. Uniform heating across the load was measured and the only significant deviation occurred near the bottom electrode. A change in density with temperature and convection flow in the load reduces the temperature near the bottom electrode. Methods to improve uniform heating are discussed in the next section on future work. After salt water load testing, the RF heating apparatus was used to heat samples of WAS. The dielectric characteristics of sludge are much more variable than salt water, and despite the variation, sludge was efficiently heated to a temperature of 120°C. The RF heating apparatus will now be used by the environmental engineering group at UBC to evaluate pretreatment methods for WAS at a frequency of 13.56 MHz, and the heating method will be compared with conventional and microwave heating methods. 5.2 Future Work The RF heating system is very attractive for heating electrolytic liquids and sludges. In addition to heating, the design can operate under pressure, and there are many other potential applications for this technology; examples include heating processes for food and biofuels, and heating to treat organic sludges from beer and wine making processes. There are many design improvements which could be made to improve the RF heating system. The temperature gradient near the bottom electrode could be reduced by changing the orientation of the applicator or incorporating a way to stir or turn the load. Other ways to improve uniform heating could be the implementation a tapered cylinder such that the heating at the bottom of the pressure vessel is higher to compensate for the density and   108 convection flow in the load. Larger volumes could be heated with an array of electrodes. Separate RF generators could be used to power different sets of electrodes to improve heating uniformity across large volumes. A dynamic matching structure with tunable inductors or capacitors could be used to track the load impedance as a function of temperature and maintain very high power transfer efficiency to the load. Thermal conduction losses from the pressure vessel could be reduced by changing the electrodes from aluminum to stainless steel. Also, insulation could be added to the air cavity in the coaxial enclosure to reduce the thermal gradient between the pressure vessel and the ambient environment. With many possible improvements to this design, future research projects are possible and these may lead to useful commercial applications of this RF heating technology.                109 Bibliography [1] R. Haug, "Sludge processing to optimize digestibility and energy production,"  Journal (Water Pollution Control Federation), pp. 1713-1721, 1977.  [2] L. Appels, J. Baeyens, J. Degrève and R. Dewil, "Principles and potential of the anaerobic digestion of waste-activated sludge,"  Progress in Energy and Combustion Science, vol. 34, pp. 755-781, 2008.  [3] C. Eskicioglu, K. Kennedy and R. Droste, "Enhanced disinfection and methane production from sewage sludge by microwave irradiation,"  Desalination, vol. 248, pp. 279-285, 2009.  [4] M. Saha, C. Eskicioglu and J. 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Moyer and E. Stotz, "The blanching of vegetables by electronics,"  Food Technol., vol. 1, pp. 252-257, 1947.  [10] J. Rice, "RF technology sharpens bakery's competitive edge," in Food Proc, 1993, pp. 18-24. [11] L. Laycock, P. Piyasena and G. Mittal, "Radio frequency cooking of ground, comminuted and muscle meat products,"  Meat Sci., vol. 65, pp. 959-965, 2003.  [12] S. Wang, J. Ikediala, J. Tang, J. Hansen, E. Mitcham, R. Mao and B. Swanson, "Radio frequency treatments to control codling moth in in-shell walnuts,"  Postharvest Biol.  Technol., vol. 22, pp. 29-38, 2001.    110 [13] M. Demeczky, "Continuous pasteurization of bottled fruit juices by high frequency energy," in Proceedings of IV International Congress on Food Science and Technology, 1974, pp. 11-20. [14] D. J. Geveke, C. Brunkhorst and X. Fan, "Radio frequency electric fields processing of orange juice,"  Innovative Food Science & Emerging Technologies, vol. 8, pp. 549-554, 2007.  [15] Q. Zhong, K. Sandeep and K. Swartzel, "Continuous flow radio frequency heating of water and carboxymethylcellulose solutions,"  J.  Food Sci., vol. 68, pp. 217-223, 2003.  [16] Z. Cserhalmi, Z. Márkus, B. Czukor, Á Baráth and M. Tóth, "Physico-chemical properties and food utilization possibilities of RF-treated mustard seed,"  Innovative Food Science & Emerging Technologies, vol. 1, pp. 251-254, 2000.  [17] J. S. Bobowski, T. Johnson and C. Eskicioglu, "Permittivity of waste-activated sludge by an open-ended coaxial line,"  Progress in Electromagnetics Research Letters, vol. 29, pp. 139-149, 2012.  [18] O. G. Martinsen and S. Grimnes, Bioimpedance and Bioelectricity Basics. Academic press, 2011. [19] S. Szilveszter, B. Ráduly, S. Bucs, B. Ábrahám, S. Lányi and D. N. Robescu, "Activated sludge floc characterization by confocal laser scanning microscopy,"  Environmental Engineering and Management Journal, vol. 11, pp. 669-674, 2012.  [20] A. 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