Analysis Of Electric Field Distribution Within A Microwave .
Journal of Food Engineering 188 (2016) 87e97Contents lists available at ScienceDirectJournal of Food Engineeringjournal homepage: www.elsevier.com/locate/jfoodengAnalysis of electric field distribution within a microwave assistedthermal sterilization (MATS) system by computer simulationDonglei Luan a, 1, Juming Tang a, *, Patrick D. Pedrow b, Frank Liu a, Zhongwei Tang aabDepartment of Biological Systems Engineering, Washington State University, P. O. Box-646120, Pullman, WA 99164-6120, USASchool of Electrical Engineering and Computer Science, Washington State University, P.O. Box-642752, Pullman, WA 99164-2752, USAa r t i c l e i n f oa b s t r a c tArticle history:Received 24 August 2015Received in revised form26 April 2016Accepted 11 May 2016Available online 13 May 2016Microwave heating holds potential to improve food quality of low acid shelf-stable or chilled meals ascompared to conventional thermal processes. Several thermal processes based on pilot-scale 915 MHzsingle-mode microwave assisted thermal sterilization (MATS) systems have received acceptances fromregulatory agencies in USA. In this study a comprehensive computer simulation model was developed tostudy microwave distributions within waveguides and applicators of the MATS system. A threedimensional model was developed based on Maxwell equations using the finite difference timedomain method. It was validated and then used to analyze electric field distribution in different partsof the MATS waveguide configuration and in a microwave heating cavity. Simulation results indicatedthat the TE10 mode was consistent within the waveguide elements. The dominant electric fieldcomponent within the microwave heating cavity controlled the heating pattern in the food packages.Adjusting the dimension of the cavity in the dominant direction should help improve heating uniformity.Food packages immerged in water reduced the edge heating of packaged foods. Adjusting the phase ofstanding wave within the microwave heating cavity can improve the heating uniformity in the directionof the thickness. The information from this study should assist design of industrial systems withimproved heating uniformity in food packages. 2016 Elsevier Ltd. All rights reserved.Keywords:Microwave heatingComputer simulationPropagation modeWaveguide wavelengthPhase shiftElectric field distribution1. IntroductionA 915 MHz single model microwave assisted thermal sterilization (MATS) system was developed at Washington State University,Pullman, WA, USA, to explore industrial applications of microwavevolumetric heating in thermal processing of pre-packaged foods(Tang et al., 2006, 2008). It was also used for developing knowledges and collecting data for regulatory filing and industrial scaleup. In October 2009, a filing for a MATS process of prepackagedmashed potato was accepted by the US Food and Drug Administration (FDA). This marked the first FDA accepted microwave process for sterilization of pre-packaged low acid food in the UnitedStates. Since then, two additional processes were accepted by FDA,one in 2011 (salmon fillet) at Washington State University and* Corresponding author.E-mail address: jtang@wsu.edu (J. Tang).1Current address: Engineering Research Center of Food Thermal-processingTechnology, Department of Food Science and Technology, Shanghai Ocean University, Shanghai, .0090260-8774/ 2016 Elsevier Ltd. All rights reserved.another in 2014 (mashed potato) at AmeriQual Foods, Evansville,IN. A non-objection letter was received from US Department ofAgriculture Food Safety and Inspection Services (USDA FSIS) formicrowave sterilization and pasteurization of shelf-stable or chilledfoods containing more than 2% meat, poultry or egg products (Tang,2015). These successes have generated great confidence and interest for scaled-up systems used in industrial production.A MATS system consists of four sections: preheating, microwaveheating, holding and cooling, which represents four steps of anindustrial process (Resurrection et al., 2013). Each of these foursections had a separated water circulation system with differenttemperature settings. Packaged foods are immerged in water bedand transported through MATS system via a conveyor belt. In thepreheating section, packaged foods are equilibrated to a uniforminitial temperature. They are then moved through interconnectedmicrowave cavities in the microwave heating section and heated toa target temperature (i.e. 121 C) for sterilization. The food packagescontinue moving in hot water of 123 C through holding section toachieve designed thermal lethality. The residence times for eachpackage in the microwave heating and holding sections are
88D. Luan et al. / Journal of Food Engineering 188 (2016) 87e97between 3 and 5 min depending on product formulation andthickness of the food package. The packages are then moved into acold water section for cooling to room temperature. The design ofthe microwave applicators in the microwave heating section determines heating uniformity and processing time and, thus, is oneof the most important parts of a MATS system. In support of processfiling to FDA, computer simulation models were developed to assistdesign of microwave applicators (Pathak et al., 2003), and to predictand study stability of heating patterns in packages foods in MATSsystems (Chen et al., 2007; Resurrection et al., 2013, 2015). Simulation models were also used to support determination of coldspots in food packages by chemical markers (Chen et al., 2008;Resurrection et al., 2013, 2015; Lau et al., 2003; Pandit et al.,2007) and to analyze interference of microwave intensity on accuracy of temperature measurement by mobile metallic temperature sensors (Luan et al., 2013, 2015). All those studies onlyconsidered MATS cavities in the simulation models, withoutconsidering waveguide configurations that connected microwavecavities to 915 MHz generators. There is a need to develop a morecomprehensive simulation model to study microwave standingwaves within the complete waveguide system to reveal howwaveguide and applicator design could influence heatinguniformity.A major challenge in scaling-up the MATS system is the nonuniform heating pattern caused by the uneven electric field distribution. Hot and cold spots occur at locations of high and lowelectric field intensity, respectively. The non-uniform heating canbe severer when using high microwave power in industrial scaleMATS systems. It is because microwave energy absorbed by food isproportional to the square of the electric field intensity. Furthermore the dielectric loss factor of food materials in general increaseswith increasing temperatures (Datta, 2001). Hence, the temperature difference between the hot spot and cold spot will continuously increase as long as high microwave power is applied. Thistype of non-uniform heating affects the selection of thermal process parameters. Thus, a systematic analyses of the electric fielddistribution and the formation of heating pattern within the complete MATS system will provide the fundamental information forimproving heating uniformity and guidelines for designing industrial systems.The objective of this study was to analyze microwave propagation mode and electric field distribution inside the MATS systemthrough numerical simulation. These results could give insight intothe dominating factors that control electric field pattern in theMATS system and provide guidelines for designing MATS systemsin industrial scale.2. Theories2.1. Electromagnetic wave and governing equationsMicrowaves are electromagnetic (EM) waves within a frequencyrange of 300 MHz to 300 GHz (Decareau, 1985). EM waves have two!components: electric field component ( E ) and magnetic field!component ( H ). These two components are vector quantities thathave both magnitude and direction. EM wave is a transverse wave.That is, the directions of field components are perpendicular to thepropagating direction of energy and wave. The traveling EM wavesare governed by the Maxwell’s equations. The differential form ofMaxwell’s equations describe and relate the electric and magneticfield vectors, current and charge densities at any point in space atany time. The differential forms of Maxwell’s equations are shownbelow (Balanis, 1989):!!!vBvH¼ mV E ¼ vtvt(1-a)!!!!! vDvEV H ¼ sE þ¼ J þεvtvt(1-b)!V D ¼ r(1-c)!V B ¼ 0(1-d)!!!where E is electric field intensity, D is electric flux density, H is the!!magnetic field intensity, B is magnetic flux density, J is volumecurrent density. Some of the above variables are related as!!!! !!B ¼ m H D ¼ ε E , J ¼ s E . Each of the variables is a function of! !space coordinates and time, for example, E ¼ E ðx; y; z; tÞ. Thevariable r is the volume charge density. The constitutive parametersε, m and s are permittivity, permeability and conductivity, respectively; they are the electric and magnetic properties of the material.In free space, the values of permittivity and permeability areε0 ¼ 10 9/(36p) F/m and m0 ¼ 4p 10 7 H/m, respectively. Theconductivity in free space is zero.2.2. Boundary conditionsThe differential form of Maxwell’s equations is valid where thefield vectors are continuous functions of position and time andthese functions have continuous derivatives. Along the boundarieswhere the electrical properties of the two media are not continuous, the field vectors are also discontinuous. The boundary conditions describe these vectors’ behavior across the interface of thetwo media (medium 1 and medium 2) with different electricalproperties: b n b n!!E2 E1!!H2 H1 ¼0(2-a)!¼ Js(2-b) !!b D 2 D 1 ¼ qsn(2-c) !!b B 2 B 1 ¼ 0n(2-d)!where J s is the induced electric current density due to the existence of electrical charges; qs is the surface charge density at theboundary plane. Eqs. (2aed) are the general form of boundaryconditions which can be modified for different media. If the twomedia are both dielectric materials without electrical charges andhave constitutive parameters of ε1, m1, s1 and ε2, m2, s2, respectively,the boundary condition can be written as:b n b n!!E2 E1!!H2 H1 ¼0(3-a)¼0(3-b)
D. Luan et al. / Journal of Food Engineering 188 (2016) 87e97 !!!!b ε2 E 2 ε1 E 1 ¼ 0b D 2 D 1 ¼ nn(3-c) !!!!b B 2 B 1 ¼ nb m2 H 2 m1 H 1 ¼ 0n(3-d)Eqs. (3-a) and (3-b) indicate that the tangential component ofelectric and magnetic field intensity across the interface is continuous; Eqs. (3-c) and (3-d) indicate that the normal component ofelectric and magnetic flux density across the surface is continuous.The normal component of electric and magnetic field intensity is,however, not continuous.2.3. Propagation mode in rectangular waveguideThe propagation modes of microwaves within a metallicwaveguide are the results of possible solutions of the wave equations that satisfy the boundary conditions. Within a rectangularwaveguide, assuming that the microwave propagation direction isalong z axis (Fig. 1A), the following three configurations can beobtained from the solutions of wave equations (Dibben, 2001):transverse electromagnetic (TEMz): components of both electricand magnetic fields in the propagation (z) direction are equal tozero, Hz ¼ Ez ¼ 0.transverse magnetic (TMz): the magnetic field component in thepropagation (z) direction is equal to zero, Hz ¼ 0.transverse electric (TEz): the electric field has no component inthe propagation (z) direction, Ez ¼ 0.However, the TEMz mode does not satisfy the boundary condition of the waveguide wall. Fig. 1A illustrates the dimension of arectangular waveguide that transmitting EM energy in positive zdirection. Considering a TEz mode as an example, the solutions ofEM waves in this waveguide are (Balanis, 1989):Exþ ¼ AmnbyεEyþ ¼ AmnEzþ cosðbx xÞsin by y e jbzbxε sinðbx xÞcos by y e jbz z¼0Hxþ ¼ Amn(4-a) by bzcosðbx xÞsin by y e jbz zumεHzþ ¼ jAmn b2x þ b2ycosðbx xÞcos by y e jbz zumε(4-e)(4-f)In whichb2x þ b2y þ b2z ¼ b2 ¼ u2 mε(5-a)bx ¼mpa(5-b)by ¼npb(5-c)where Exþ , Eyþ , Ezþ , Hxþ , Hyþ and Hzþ represent the electric and magnetic field intensity in each component within the rectangular coordinate system; the superscript (þ) indicates that the EM wave ispropagating in þz direction; bx, by and bz are the components ofphase constant b in each coordinate direction; a and b represent thedimensions of the waveguide in x and y directions; m and n areinteger numbers which are not zero at the same time in a solution(m s n ¼ 0, 1, 2, ); Amn is the amplitude constant of the solutioncorresponding with m and n. From physical standpoint, the propagating EM wave (in z direction) forms standing waves in x and ydirections. The integer number m and n indicates the number ofsemi-sinusoidal variations (anti-node) in the x and y direction,respectively. Fig. 2 displays the electric field distributions for someTE modes with different semi-sinusoidal combinations (m and n).Solution with different values of m and n leads to differentmodes. With a given mode, there is a matching cutoff frequency (fc)for each type of waveguide. The EM wave cannot propagate withinthe waveguide if its frequency is lower than the cutoff frequency.The cutoff frequency could be derived from:(4-b)(4-c) bx bzsinðbx xÞcos by y e jbz zumεHyþ ¼ Amn89(4-d)ðfc Þmn ¼1pffiffiffiffiffi2p ffiffiffi mp 2 np 2þab(6)In a waveguide, the transmitted microwave mode with lowestfrequency is called the dominant mode. The dominant TE10 modeis always the normal operation mode of a rectangular waveguidefor power transmission (Fig. 1B).Fig. 1. Rectangular waveguide (A) and its dominant mode (B). For TE10 mode, Ez ¼ 0, Ex ¼ 0. The electric field component in y direction (Ey) formed a standing wave in x directionwith one semi-sinusoidal variation.
90D. Luan et al. / Journal of Food Engineering 188 (2016) 87e97Fig. 2. Electric field distribution of some TEmn modes: A: m ¼ 3, n ¼ 0; B: m ¼ 3, n ¼ 1; C: m ¼ 3, n ¼ 2; D: m ¼ 3, n ¼ 4.3. Methodology3.1. Physical modelThe MATS system installed at Washington State Universityconsists of four sections, i.e. preheating, microwave heating, holding and cooling. The packaged foods are transported through thesefour sections in sequence by a microwave transparent conveyor beltthat immersed in a thin bed (76 mm) of circulating water. Eachsection has its own water circulating system with different settingsof water temperature. The structure of MATS system and thedetailed operation process was described by Resurrection et al.(2013). Among these four sections, the microwave heating sectionis the key element in reducing processing time and improving foodquality.The microwave heating section contains four connected microwave heating cavities. Fig. 3 shows a typical microwave heatingcavity and the attached waveguide elements through which microwave power is delivered from the generator to the heatingcavity. Each cavity has two windows (top and bottom) made from ahigh temperature resistant polymer (Ultem 1000). Microwavesare delivered to the heating cavity through the Ultem windows thatare connected to two identical horn shaped applicators on the topand bottom. The horn applicator is a tapered shape parallelogramwith wide end connected to the window and narrow endconnected to a standard WR975 waveguide element that having aninner cross sectional dimension of 247.7 mm by 123.8 mm.A tee junction is used to split the microwave power equally tothe top and bottom horn applicators. On the bottom two connectedE-bend waveguides direct the microwave to the narrow end of thehorn applicator. On the top, two short waveguides are used toconnect E-bend with horn applicator and tee-junction. These twoshort waveguides are installed for phase adjustment. Severalstandard WR975 rectangular waveguide elements are used toconnect the generator and the tee-junction including an H-bendwaveguide. The E-bend or H-bend waveguide is used to change thepropagating direction of microwaves. In Fig. 3, an H-bend waveguide is shown to change the microwave propagating from x to ydirection.3.2. Computer simulation model for electric field distributionanalysisComputer simulation model was developed using the commercial software QuickWave version 7.5 (QW3D, Warsaw, Poland)based on the physical model of the MATS system and finite difference time domain (FDTD) method. The mesh size in different materials was set following the rules of more than ten cells perwavelength (Rattanadecho, 2006). The metal wall was assumed asperfect electric conductor (PEC). The dielectric and thermalFig. 3. Microwave heating cavity and waveguide assembly.
D. Luan et al. / Journal of Food Engineering 188 (2016) 87e97properties of water and food were updated with changing temperatures, the detailed data were reported in Resurrection et al.(2013). Only one microwave heating cavity with attached waveguide elements was built up in this study (Fig. 3) to analyze themicrowave propagation mode and electric field component distribution from waveguide to the microwave heating cavity.A sinusoidal microwave source with TE10 mode was set at theport. In a rectangular waveguide with a lateral dimensions a and b(a b), as shown in Fig. 1A, the dominant propagation mode ofelectromagnetic (EM) wave was TE10 mode. The symbol TE indicated that the electric field component was perpendicular to thepropagation direction (i.e. z direction in Fig. 1A). The symbols 1 and0 in a mode type denoted the number of semi-sinusoidal variationsin x and y direction, respectively (Fig. 1B). For a TE10 mode propagating in the coordinate system described in Fig. 1A, the electricfield had no component in z (Ez) and x (Ex) directions. Thecomponent in y direction (Ey) formed a standing wave in x direction with one semi-sinusoidal variation.The numerical method and steps of developing a simulationmodel based on the software of QuickWave have been described indetail in previous studies (Resurrection et al., 2013; Luan et al.,2013, 2015). This study focused on utilizing the validated modelto analyze the electric field distribution within the waveguide elements and the microwave heating cavity.3.3. Experimental validationThe heating pattern obtained from experimental test via MATSsystem was used to validate the computer simulation model. Preformed whey protein gel (WPG, 95 140 16 mm3) containing75.4% water, 23.3% protein, 1% D-ribose and 0.3% salt was utilized asmodel food in the experimental test. The procedure described byWang et al. (2009) in preparing WPG was used. The detailedoperation process for experimental validation was reported byResurrection et al. (2013). Chemical marker (M-2) method andcomputer vision method (Lau et al., 2003; Pandit et al., 2007) wereapplied to obtain the heating pattern of food. The production of M2 was irreversible and dependent on accumulated effect of timeand temperature. Thus, the intensities of brown color (color of M-2)represented the heating treatment pattern of WPG. The originalheating pattern showing brown color distribution was processed bycomputer vision method to create a heating pattern in pseudo color91(Fig. 4A). In this study, only the temperature distribution, whichrepresents the electric field distribution, was concerned (Fig. 4B).4. Results and discussion4.1. Validation of the computer simulation modelThe experimental and simulation results for heating patterns offood in top view (x-y plane) in the middle layer in z direction areshown in Fig. 4. Similar heating patterns were observed betweenexperimental and simulation results, which verified that thesimulation model was reliable. Thus, the predicated propagation ofmicrowave from the port, through the waveguide, horn shapeapplicator to the microwave heating cavity was reliable.4.2. Electric field distribution in waveguidesNatural biological materials, such as food, interact with only theelectric part of the electromagnetic field (Mudgett, 1986). Thuselectric field distribution is of the most concern. Fig. 5
The objective of this study was to analyze microwave propa-gation mode and electric field distribution inside the MATS system through numerical simulation. These results could give insight into the dominating factors that control electric field pattern in the MATS system and provide guideli
The electric field is stronger where the field lines are closer together. 16.8 Field Lines Electric dipole: two equal charges, opposite in sign: 16.8 Field Lines The electric field between two closely spaced, oppositely charg
16.8 Field Lines The electric field between two closely spaced, oppositely charged parallel plates is constant. 16.8 Field Lines Summary of field lines: 1. Field lines indicate the direction of the field; the field is tangent to the line. 2. Th
Introduction to Maxwell’s Theory Z X Y Q1 Q2 F2 1 E ( r ) THE ELECTRIC FIELD Figure 4.1: The Electric Field and Electric Forces Maxwell said that electric and magnetic forces were due to the presence of the electric and magnetic field. In this figure, the electric force on Q 2 is due to the presence of the field at its location, F 21 .
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Access to Accounting Software – SAMS – Assessment book . 2 . Notes for students . This sample assessment is designed to demonstrate as many of the possible question types you may find in a live assessment. It is not designed to be used on its own to determine whether you are ready for a live assessment. In a live assessment, you will be required to upload documents as part of your evidence .
