Rotated view of rectangular waveguide in Figure 1. 

Contexts in source publication

Context 1

... which in turn affect the EM field distribution. Solving these coupled equations for a three- dimensional (3-D) transient microwave heating process in an industrial system for foods with temperature-dependent dielectric properties is a challenging task that has not been addressed in literature. Early research used analytical models to describe EM fields inside domestic microwave ovens [Shou-Zheng and Han-Kui, 1988; Watanabe and Ohkawa, 1978], but these were suitable only for oversimplified cases that did not represent real-world systems. Numeric models were developed for EM field distribution calculations in more complicated cases [Paoloni, 1989; Webb et al ., 1983]. Coupled EM and heat transfer models were used for simple 1-D [Smyth, 1990] or 2-D cases [Clemens and Saltiel, 1995; Barratt and Simons, 1992]. Detailed 3-D treatment of numeric models for coupled equations had not been explored until recently [Burfoot et al ., 1996; Bows et al ., 1997; Clemens and Saltiel, 1995; Dibben and Metaxas, 1994; Harms et al ., 1996]. Several numerical techniques have been used to solve coupled Maxwell and heat transfer equations using the Finite Difference Time Domain (FDTD) method [Ma and Paul, 1995; Torres and Jecko, 1997], Finite Element Method [Webb et al ., 1983; Dibben and Metaxas, 1994;] and Transmission Line Method [Leo et al ., 1991]. In [Spiegel, 1984], Spiegel reviewed numeric methods for medical applications and commented that the FDTD method is best suited for coupled EM and thermal processes because it does not require matrix computation, and thus saves computer memory and simulation time. However, a major limitation of the FDTD method is the use of rectangular meshes that are not applicable for irregular geometries such as curvature surfaces. The Finite Element Method (FEM) can handle more complex geometries. In [Zhang and Datta, 2000], two commercial software employing FEM were used together to simulate coupled EM and thermal processes in a domestic oven. But FEM involves computation to inverse matrices that contain information for all elements of the discrete grids within the considered domain. This requires large computer memory and lengthy computation time, therefore making it unsuitable for complicated systems. A major development in FDTD applications with EM field simulation is the use of a conformal FDTD algorithm. This algorithm incorporates finite boundary grids that conform to geometry surfaces to accurately match detailed irregularities in a 3-D domain, while also including regular grids identical to those in the original FDTD algorithm for the other parts of the 3-D domain. References [Holland, 1993] and [Harms et al. , 1992] provide a detailed description of a conformal FDTD algorithm and its application to some simple cases. In brief, instead of Yee’s original algorithm that uses differential forms of Maxwell’s equations, the conformal FDTD algorithm uses integral forms of Maxwell’s equations for the finite grids conformed to the edge or surface of the geometry, thus avoiding the need to approximate the curved and oblique surface using staircase grid. As a result, complex geometry can be modeled without sacrificing the speed of an FDTD algorithm. This method also saves computer memory and simulation time compared to the original FDTD algorithm when applied to complex geometries. The conformal FDTD algorithm can be used to model arbitrary shape structures and inhomogeneous, nonlinear, dispersive and loss mediums. Since the FDTD method does not require computation of inverse matrices which takes extensive computer memory for fine element grids, the conformal FDTD algorithm is much more efficient compared to the FEM. For example, in [Zhang and Datta, 2000], it took six and half hours for an HP workstation to run a model consisting of 15,000 nodes for a single time step, while the conformal FDTD used in the study reported here took only three hours to complete a coupled simulation that included 720 time steps for a complicated industrial system with 500,000 cells in a 3-D domain. This paper presents a model that used conformal FDTD algorithms for EM field simulation and the regular FDTD method for heat transfer to simulate coupled processes in an microwave heating system for industrial sterilization and pasteurization applications. Validation is a critical step in developing a new and reliable numeric model. In this study, this was achieved with a single-mode microwave sterilization system developed at Washington State University. The system consisted of a rectangular cavity with one horn-shaped applicator on the top and another identical applicator on the bottom (Figures 1 and 2). Figure 1 shows a front view of the system with an exposed interior cut and vertical central plane, while Figure 2 shows the top view for the central section of the cavity. Microwave energy was provided by a 5 kW generator operating at 915 MHz through a standard waveguide that supported only TE 10 mode (Figure 3). Figure 3 provides detailed information for the top and bottom rectangular waveguide sections having a length of 128 mm and width of 124 mm. After passing through a circulator, the microwave energy was equally divided at a T-junction and fed to the two horn applicators through two standard waveguides shown in Figure 3. The length of each leg of the waveguide after the T-junction could be adjusted to control the phase difference between the microwaves at the entry port of the two horn applicators, which meant the phase shift between the two waves interacting inside the cavity could be controlled to achieve the desired field distribution. In this study, for simplification, a 0 phase shift was used between the entry ports of the top and bottom horn applicators. That was, microwaves coming to the top and the bottom entry ports of the horn applicators were in the same phase at any moment. The model, however, was able to simulate more complex cases with arbitrary phase differences. The pilot scale system combined surface heating by circulating hot water and volumetric microwave heating to improve heating uniformity and reduce heating time. Because microwave sterilization for low-acid foods (pH > 4.5) [Guan et al ., 2003] requires that food temperatures at cold spots be processed higher than 121 ̊C, the temperature of the circulation water in the cavity was set at 125 ̊C. The water was pressurized at 41 psia by compressed air through a buffer tank in the water-circulating system (not shown) to prevent boiling. To maintain the steam inside the cavity, two windows made of microwave transparent material were secured at the mouth of both horn waveguides. During thermal processing, the packaged food was positioned at the central line of the cavity. Though it was possible to simulate a heating process with moving packages, only a simple stationary case was considered to better focus on the development and validation of the numeric model. During the experiment, three fiber optic sensors (FOT-L, FISO, Québec, CANADA) were placed at three different points (within the cold and hot spots) to monitor the temperature changes with time. In addition to monitoring temperature changes at selected locations in the packaged foods, heating patterns were measured with the computer vision software IMAQ (National Instruments, TX, USA) using a chemical marker method [Pandit et al ., 2005]. This method measures color changes as a result of the formation of a chemical compound commonly referred to as M-2, a product of a Millard reaction between protein amino acids and a reduced sugar (ribose). The color changes depend upon heat intensity at temperatures beyond 100 o C and, therefore, served as an indicator of temperature distribution after heating. Detailed information about the kinetics of M-2 formation with temperature can be found elsewhere [Lau et al ., 2003; Pandit et al ., 2006]. In brief, with increasing temperature during the heating process, the density of M-2 also increased following an Arrhenius relationship with temperature and first order kinetics with time. The density of M-2 was then transferred to pixel density, which was further mapped into red, green, and blue (RGB) values, where red indicates the hottest area and blue the coldest. Whey protein gels (78% water, 20% protein, 1.7% salt, 0.3% D-ribose) were used as the model food because they have uniform properties and are easily formed. They also maintain a stable shape during the process. Dielectric properties of the whey protein gels were measured with an open coaxial cable from a HP8491B dielectric probe kit connected to an HP8491B network analyzer (Hewlett-Packard, CA, USA; Table 1). Thermal properties were measured with a KD2 device (Decagon, WA, USA) using the double needle method [Campbell et al ., 1991] (Table 2). Table 1 shows dielectric property data at temperatures up to 121 ̊C to allow for sterilization [Guan et al. , 2004]. Table 2 shows thermal properties at temperatures only up to 80 ̊C because of measurement difficulties beyond this temperature. For temperatures over 80oC, thermal properties were assumed constant. The whey protein gels were sealed in a 7 oz polymeric tray to maintain the food shape during microwave heating. Prior to the experiment, six identical food trays containing whey gel slabs (95 mm x 140 mm x 16 mm) were removed from a refrigerator where they had been stored at 9 ̊C overnight. Fiber optic sensors were inserted carefully to the locations shown in Figure 4 with seals at the tray wall entry ports to prevent leakage of water. All six trays were secured in the center plane of the cavity with equal distance from the top and bottom windows of the cavity (Figure 1). Hot water at 125 ̊C was filled at a speed of 40 lit/min into the cavity prior to microwave heating of the food. A uniform surrounding water temperature (125 ̊ C) was assumed during the heating process. The thermal properties and dielectric properties were measured using the ...

Context 2

... used analytical models to describe EM fields inside domestic microwave ovens [Shou-Zheng and Han-Kui, 1988; Watanabe and Ohkawa, 1978], but these were suitable only for oversimplified cases that did not represent real-world systems. Numeric models were developed for EM field distribution calculations in more complicated cases [Paoloni, 1989; Webb et al ., 1983]. Coupled EM and heat transfer models were used for simple 1-D [Smyth, 1990] or 2-D cases [Clemens and Saltiel, 1995; Barratt and Simons, 1992]. Detailed 3-D treatment of numeric models for coupled equations had not been explored until recently [Burfoot et al ., 1996; Bows et al ., 1997; Clemens and Saltiel, 1995; Dibben and Metaxas, 1994; Harms et al ., 1996]. Several numerical techniques have been used to solve coupled Maxwell and heat transfer equations using the Finite Difference Time Domain (FDTD) method [Ma and Paul, 1995; Torres and Jecko, 1997], Finite Element Method [Webb et al ., 1983; Dibben and Metaxas, 1994;] and Transmission Line Method [Leo et al ., 1991]. In [Spiegel, 1984], Spiegel reviewed numeric methods for medical applications and commented that the FDTD method is best suited for coupled EM and thermal processes because it does not require matrix computation, and thus saves computer memory and simulation time. However, a major limitation of the FDTD method is the use of rectangular meshes that are not applicable for irregular geometries such as curvature surfaces. The Finite Element Method (FEM) can handle more complex geometries. In [Zhang and Datta, 2000], two commercial software employing FEM were used together to simulate coupled EM and thermal processes in a domestic oven. But FEM involves computation to inverse matrices that contain information for all elements of the discrete grids within the considered domain. This requires large computer memory and lengthy computation time, therefore making it unsuitable for complicated systems. A major development in FDTD applications with EM field simulation is the use of a conformal FDTD algorithm. This algorithm incorporates finite boundary grids that conform to geometry surfaces to accurately match detailed irregularities in a 3-D domain, while also including regular grids identical to those in the original FDTD algorithm for the other parts of the 3-D domain. References [Holland, 1993] and [Harms et al. , 1992] provide a detailed description of a conformal FDTD algorithm and its application to some simple cases. In brief, instead of Yee’s original algorithm that uses differential forms of Maxwell’s equations, the conformal FDTD algorithm uses integral forms of Maxwell’s equations for the finite grids conformed to the edge or surface of the geometry, thus avoiding the need to approximate the curved and oblique surface using staircase grid. As a result, complex geometry can be modeled without sacrificing the speed of an FDTD algorithm. This method also saves computer memory and simulation time compared to the original FDTD algorithm when applied to complex geometries. The conformal FDTD algorithm can be used to model arbitrary shape structures and inhomogeneous, nonlinear, dispersive and loss mediums. Since the FDTD method does not require computation of inverse matrices which takes extensive computer memory for fine element grids, the conformal FDTD algorithm is much more efficient compared to the FEM. For example, in [Zhang and Datta, 2000], it took six and half hours for an HP workstation to run a model consisting of 15,000 nodes for a single time step, while the conformal FDTD used in the study reported here took only three hours to complete a coupled simulation that included 720 time steps for a complicated industrial system with 500,000 cells in a 3-D domain. This paper presents a model that used conformal FDTD algorithms for EM field simulation and the regular FDTD method for heat transfer to simulate coupled processes in an microwave heating system for industrial sterilization and pasteurization applications. Validation is a critical step in developing a new and reliable numeric model. In this study, this was achieved with a single-mode microwave sterilization system developed at Washington State University. The system consisted of a rectangular cavity with one horn-shaped applicator on the top and another identical applicator on the bottom (Figures 1 and 2). Figure 1 shows a front view of the system with an exposed interior cut and vertical central plane, while Figure 2 shows the top view for the central section of the cavity. Microwave energy was provided by a 5 kW generator operating at 915 MHz through a standard waveguide that supported only TE 10 mode (Figure 3). Figure 3 provides detailed information for the top and bottom rectangular waveguide sections having a length of 128 mm and width of 124 mm. After passing through a circulator, the microwave energy was equally divided at a T-junction and fed to the two horn applicators through two standard waveguides shown in Figure 3. The length of each leg of the waveguide after the T-junction could be adjusted to control the phase difference between the microwaves at the entry port of the two horn applicators, which meant the phase shift between the two waves interacting inside the cavity could be controlled to achieve the desired field distribution. In this study, for simplification, a 0 phase shift was used between the entry ports of the top and bottom horn applicators. That was, microwaves coming to the top and the bottom entry ports of the horn applicators were in the same phase at any moment. The model, however, was able to simulate more complex cases with arbitrary phase differences. The pilot scale system combined surface heating by circulating hot water and volumetric microwave heating to improve heating uniformity and reduce heating time. Because microwave sterilization for low-acid foods (pH > 4.5) [Guan et al ., 2003] requires that food temperatures at cold spots be processed higher than 121 ̊C, the temperature of the circulation water in the cavity was set at 125 ̊C. The water was pressurized at 41 psia by compressed air through a buffer tank in the water-circulating system (not shown) to prevent boiling. To maintain the steam inside the cavity, two windows made of microwave transparent material were secured at the mouth of both horn waveguides. During thermal processing, the packaged food was positioned at the central line of the cavity. Though it was possible to simulate a heating process with moving packages, only a simple stationary case was considered to better focus on the development and validation of the numeric model. During the experiment, three fiber optic sensors (FOT-L, FISO, Québec, CANADA) were placed at three different points (within the cold and hot spots) to monitor the temperature changes with time. In addition to monitoring temperature changes at selected locations in the packaged foods, heating patterns were measured with the computer vision software IMAQ (National Instruments, TX, USA) using a chemical marker method [Pandit et al ., 2005]. This method measures color changes as a result of the formation of a chemical compound commonly referred to as M-2, a product of a Millard reaction between protein amino acids and a reduced sugar (ribose). The color changes depend upon heat intensity at temperatures beyond 100 o C and, therefore, served as an indicator of temperature distribution after heating. Detailed information about the kinetics of M-2 formation with temperature can be found elsewhere [Lau et al ., 2003; Pandit et al ., 2006]. In brief, with increasing temperature during the heating process, the density of M-2 also increased following an Arrhenius relationship with temperature and first order kinetics with time. The density of M-2 was then transferred to pixel density, which was further mapped into red, green, and blue (RGB) values, where red indicates the hottest area and blue the coldest. Whey protein gels (78% water, 20% protein, 1.7% salt, 0.3% D-ribose) were used as the model food because they have uniform properties and are easily formed. They also maintain a stable shape during the process. Dielectric properties of the whey protein gels were measured with an open coaxial cable from a HP8491B dielectric probe kit connected to an HP8491B network analyzer (Hewlett-Packard, CA, USA; Table 1). Thermal properties were measured with a KD2 device (Decagon, WA, USA) using the double needle method [Campbell et al ., 1991] (Table 2). Table 1 shows dielectric property data at temperatures up to 121 ̊C to allow for sterilization [Guan et al. , 2004]. Table 2 shows thermal properties at temperatures only up to 80 ̊C because of measurement difficulties beyond this temperature. For temperatures over 80oC, thermal properties were assumed constant. The whey protein gels were sealed in a 7 oz polymeric tray to maintain the food shape during microwave heating. Prior to the experiment, six identical food trays containing whey gel slabs (95 mm x 140 mm x 16 mm) were removed from a refrigerator where they had been stored at 9 ̊C overnight. Fiber optic sensors were inserted carefully to the locations shown in Figure 4 with seals at the tray wall entry ports to prevent leakage of water. All six trays were secured in the center plane of the cavity with equal distance from the top and bottom windows of the cavity (Figure 1). Hot water at 125 ̊C was filled at a speed of 40 lit/min into the cavity prior to microwave heating of the food. A uniform surrounding water temperature (125 ̊ C) was assumed during the heating process. The thermal properties and dielectric properties were measured using the same methods as for whey protein gel. In experiments and simulation, the gel samples were preheated with circulating pressurized water at 125 ̊C. When the temperature at the cold spots (spot 1 or 2 measured in the experiment in Figure 4) of the gel reached 60 ̊C, microwave power was turned on and microwave ...

Context 3

... of food, which in turn affect the EM field distribution. Solving these coupled equations for a three- dimensional (3-D) transient microwave heating process in an industrial system for foods with temperature-dependent dielectric properties is a challenging task that has not been addressed in literature. Early research used analytical models to describe EM fields inside domestic microwave ovens [Shou-Zheng and Han-Kui, 1988; Watanabe and Ohkawa, 1978], but these were suitable only for oversimplified cases that did not represent real-world systems. Numeric models were developed for EM field distribution calculations in more complicated cases [Paoloni, 1989; Webb et al ., 1983]. Coupled EM and heat transfer models were used for simple 1-D [Smyth, 1990] or 2-D cases [Clemens and Saltiel, 1995; Barratt and Simons, 1992]. Detailed 3-D treatment of numeric models for coupled equations had not been explored until recently [Burfoot et al ., 1996; Bows et al ., 1997; Clemens and Saltiel, 1995; Dibben and Metaxas, 1994; Harms et al ., 1996]. Several numerical techniques have been used to solve coupled Maxwell and heat transfer equations using the Finite Difference Time Domain (FDTD) method [Ma and Paul, 1995; Torres and Jecko, 1997], Finite Element Method [Webb et al ., 1983; Dibben and Metaxas, 1994;] and Transmission Line Method [Leo et al ., 1991]. In [Spiegel, 1984], Spiegel reviewed numeric methods for medical applications and commented that the FDTD method is best suited for coupled EM and thermal processes because it does not require matrix computation, and thus saves computer memory and simulation time. However, a major limitation of the FDTD method is the use of rectangular meshes that are not applicable for irregular geometries such as curvature surfaces. The Finite Element Method (FEM) can handle more complex geometries. In [Zhang and Datta, 2000], two commercial software employing FEM were used together to simulate coupled EM and thermal processes in a domestic oven. But FEM involves computation to inverse matrices that contain information for all elements of the discrete grids within the considered domain. This requires large computer memory and lengthy computation time, therefore making it unsuitable for complicated systems. A major development in FDTD applications with EM field simulation is the use of a conformal FDTD algorithm. This algorithm incorporates finite boundary grids that conform to geometry surfaces to accurately match detailed irregularities in a 3-D domain, while also including regular grids identical to those in the original FDTD algorithm for the other parts of the 3-D domain. References [Holland, 1993] and [Harms et al. , 1992] provide a detailed description of a conformal FDTD algorithm and its application to some simple cases. In brief, instead of Yee’s original algorithm that uses differential forms of Maxwell’s equations, the conformal FDTD algorithm uses integral forms of Maxwell’s equations for the finite grids conformed to the edge or surface of the geometry, thus avoiding the need to approximate the curved and oblique surface using staircase grid. As a result, complex geometry can be modeled without sacrificing the speed of an FDTD algorithm. This method also saves computer memory and simulation time compared to the original FDTD algorithm when applied to complex geometries. The conformal FDTD algorithm can be used to model arbitrary shape structures and inhomogeneous, nonlinear, dispersive and loss mediums. Since the FDTD method does not require computation of inverse matrices which takes extensive computer memory for fine element grids, the conformal FDTD algorithm is much more efficient compared to the FEM. For example, in [Zhang and Datta, 2000], it took six and half hours for an HP workstation to run a model consisting of 15,000 nodes for a single time step, while the conformal FDTD used in the study reported here took only three hours to complete a coupled simulation that included 720 time steps for a complicated industrial system with 500,000 cells in a 3-D domain. This paper presents a model that used conformal FDTD algorithms for EM field simulation and the regular FDTD method for heat transfer to simulate coupled processes in an microwave heating system for industrial sterilization and pasteurization applications. Validation is a critical step in developing a new and reliable numeric model. In this study, this was achieved with a single-mode microwave sterilization system developed at Washington State University. The system consisted of a rectangular cavity with one horn-shaped applicator on the top and another identical applicator on the bottom (Figures 1 and 2). Figure 1 shows a front view of the system with an exposed interior cut and vertical central plane, while Figure 2 shows the top view for the central section of the cavity. Microwave energy was provided by a 5 kW generator operating at 915 MHz through a standard waveguide that supported only TE 10 mode (Figure 3). Figure 3 provides detailed information for the top and bottom rectangular waveguide sections having a length of 128 mm and width of 124 mm. After passing through a circulator, the microwave energy was equally divided at a T-junction and fed to the two horn applicators through two standard waveguides shown in Figure 3. The length of each leg of the waveguide after the T-junction could be adjusted to control the phase difference between the microwaves at the entry port of the two horn applicators, which meant the phase shift between the two waves interacting inside the cavity could be controlled to achieve the desired field distribution. In this study, for simplification, a 0 phase shift was used between the entry ports of the top and bottom horn applicators. That was, microwaves coming to the top and the bottom entry ports of the horn applicators were in the same phase at any moment. The model, however, was able to simulate more complex cases with arbitrary phase differences. The pilot scale system combined surface heating by circulating hot water and volumetric microwave heating to improve heating uniformity and reduce heating time. Because microwave sterilization for low-acid foods (pH > 4.5) [Guan et al ., 2003] requires that food temperatures at cold spots be processed higher than 121 ̊C, the temperature of the circulation water in the cavity was set at 125 ̊C. The water was pressurized at 41 psia by compressed air through a buffer tank in the water-circulating system (not shown) to prevent boiling. To maintain the steam inside the cavity, two windows made of microwave transparent material were secured at the mouth of both horn waveguides. During thermal processing, the packaged food was positioned at the central line of the cavity. Though it was possible to simulate a heating process with moving packages, only a simple stationary case was considered to better focus on the development and validation of the numeric model. During the experiment, three fiber optic sensors (FOT-L, FISO, Québec, CANADA) were placed at three different points (within the cold and hot spots) to monitor the temperature changes with time. In addition to monitoring temperature changes at selected locations in the packaged foods, heating patterns were measured with the computer vision software IMAQ (National Instruments, TX, USA) using a chemical marker method [Pandit et al ., 2005]. This method measures color changes as a result of the formation of a chemical compound commonly referred to as M-2, a product of a Millard reaction between protein amino acids and a reduced sugar (ribose). The color changes depend upon heat intensity at temperatures beyond 100 o C and, therefore, served as an indicator of temperature distribution after heating. Detailed information about the kinetics of M-2 formation with temperature can be found elsewhere [Lau et al ., 2003; Pandit et al ., 2006]. In brief, with increasing temperature during the heating process, the density of M-2 also increased following an Arrhenius relationship with temperature and first order kinetics with time. The density of M-2 was then transferred to pixel density, which was further mapped into red, green, and blue (RGB) values, where red indicates the hottest area and blue the coldest. Whey protein gels (78% water, 20% protein, 1.7% salt, 0.3% D-ribose) were used as the model food because they have uniform properties and are easily formed. They also maintain a stable shape during the process. Dielectric properties of the whey protein gels were measured with an open coaxial cable from a HP8491B dielectric probe kit connected to an HP8491B network analyzer (Hewlett-Packard, CA, USA; Table 1). Thermal properties were measured with a KD2 device (Decagon, WA, USA) using the double needle method [Campbell et al ., 1991] (Table 2). Table 1 shows dielectric property data at temperatures up to 121 ̊C to allow for sterilization [Guan et al. , 2004]. Table 2 shows thermal properties at temperatures only up to 80 ̊C because of measurement difficulties beyond this temperature. For temperatures over 80oC, thermal properties were assumed constant. The whey protein gels were sealed in a 7 oz polymeric tray to maintain the food shape during microwave heating. Prior to the experiment, six identical food trays containing whey gel slabs (95 mm x 140 mm x 16 mm) were removed from a refrigerator where they had been stored at 9 ̊C overnight. Fiber optic sensors were inserted carefully to the locations shown in Figure 4 with seals at the tray wall entry ports to prevent leakage of water. All six trays were secured in the center plane of the cavity with equal distance from the top and bottom windows of the cavity (Figure 1). Hot water at 125 ̊C was filled at a speed of 40 lit/min into the cavity prior to microwave heating of the food. A uniform surrounding water temperature (125 ̊ C) was assumed during the heating process. The thermal properties and dielectric properties were measured ...