CONTROL OF MICROWAVE HEATING IN RECTANGULAR WAVEGUIDE

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1 ISTP-16, 2005, PRAGUE 16 TH INTERNATIONAL SYMPOSIUM ON TRANSPORT PHENOMENA CONTROL OF MICROWAVE HEATING IN RECTANGULAR WAVEGUIDE Kazuo AOKI*, Masatoshi AKAHORI*, Kenji OSHIMA** and Masato MORITA* *Nagaoka University of Technology, **Union Tool Co. Corresponding author: phone: , fax: Keywords: Microwave Heating, Electromagnetic Field, Rectangular Waveguide, Reflection Abstract Using the microwave of TE 10 mode and frequency of 2.45GHz in rectangular waveguide, we have investigated two effects of a reflecting plate and an incident wave controlling plate on the characteristics of microwave heating, and have indicated the guideline for the optimization of microwave heating by controlling reflected and transmitted waves. 1 Introduction Microwave heating has the features in a transmission, absorption and reflection of an electromagnetic wave. The performance of the heating strongly depends on the interference of the transmitted wave and reflected wave in materials. In the previous papers, we had investigated the characteristics of heating [1], melting [2] and drying [3, 4] due to microwave using a rectangular waveguide theoretically and experimentally. In this study, in order to obtain the optimum conditions for microwave heating in a rectangular waveguide, we have investigated the effects of a reflecting plate and an incident wave controlling plate on microwave heating theoretically and experimentally. 2 Analysis Figure 1 shows the analytical model for the microwave heating using rectangular waveguide. Since microwave of TE 10 mode which propagates in rectangular waveguide is uniform in y-direction, the electromagnetic field can be considered in two-dimensional model on x-z plane. Corresponding to electromagnetic field, temperature field also can be considered to be two-dimensional. The model proposed is based on the following assumptions. (1) The absorption of microwave by air in rectangular waveguide is negligible. (2) The walls of rectangular waveguide are perfect conductors. (3) The sample heated is an isotropic medium and thermal properties are constant. (4) The effect of the sample container on the electromagnetic and temperature fields can be neglected. 2.1 The Maxwell's equation Assuming the microwave of TE 10 mode, the governing equations for the electromagnetic field can be written in term of the component notations of electric and magnetic field intensities, E H H εε 0 r + σe = z x H E x y µµ 0 r = z Hz Ey µµ 0 r = x y x z y (1) where E and H are electric and magnetic field intensities, respectively, ε is permittivity, µ is magnetic permeability and σ is electric conductivity, ε r and µ r are relative permittivity and relative magnetic permeability. The subscript 0 denotes the value concerning vacuum condition. 2.2 The energy equation Considering the rate of volumetric heat generation due to the absorption of microwave, 1

2 Kazuo AOKI, Masatoshi AKAHORI, Kenji OSHIMA, Masato MORITA Microwave Generator π x Ey = Eyin sin sin( 2π ft ) L x 0 z = B 1 z = B 2 z = B 3 z = B ref z = B end z Incident Wave Wave controlling plate Sample Transmission Wave Reflected Wave x = L x x Absorbing B.C. Ey Ey = υ (Equ. of G.Mur). z Perfectly Conducting Walls Et = 0, Hn = J (Ampere s Low) s D = σ, B = 0 t t n Continuity Condition Et1 = Et 1, Hn1 = Hn 1 (Ampere s Low) D = D, B = B t t n1 n Continuity Condition Et = E t2, Hn = H n2(ampere s Low) 2 2 D = D, B = B t t n n Continuity Condition Et = E t3, Hn = H (Ampere s Low) n3 3 3 D = D, B = B t t n n Reflecting Plate Et = 0, H = J n s D = σ, B = 0 t t n Fig.1 Analytical model (Ampere s Low) the governing equation of energy is represented by 2 2 T T T q = a x z ρcp (2) where a is the thermal diffusivity of the sample. The rate of volumetric heat generation due to the absorption of microwave, q, is represented by the following equation. q 2 f tan Ey 2 = π ε δ (3) where f is frequency of microwave and tanδ is dielectric loss coefficient. 2.3 Boundary conditions Corresponding to the analytical model, boundary conditions for the electromagnetic field [5] can be given as shown in Figure 2. The inner wall surface of a rectangular waveguide is perfect electric conductor. Boundary conditions along the interface between different layers are continuity conditions. At both ends of the rectangular wave guide, the first order absorbing conditions proposed by G. Mur [6] are applied. Oscillation of the electric and magnetic field intensities by magnetron is given by the following equations. π x Ey = E sin yin sin( 2π ft ) Lx Eyin π x Hx = sin sin( 2π ft ) Z H L x (4) where E yin is the input value of electric field intensity, L x is the length of rectangular wave guide in x-direction, Z H is the wave impedance in cases where microwave propagates in the rectangular wave guide. The boundary conditions for the temperature field are assumed to be adiabatic. 2.4 Numerical procedure In order to obtain the electromagnetic field, a finite difference time domain (FDTD) method was applied. Concerning the discritization of the governing equation of heat transport, finite volume method in space and fully implicit method in time was used. Because the propagating velocity of microwave is very fast compared with the rate of heat transfer, the different time steps of dt = 1 [ps] and 0.1 [s] were used for the computation of the electromagnetic and temperature fields, respectively. The spatial step size was dx = dz = [mm]. 3 Experimental apparatus and procedure Figure 2 shows the experimental apparatus used here. A monochromatic wave of TE 10 mode and frequency of 2.45 GHz generated by magnetron propagates in rectangular waveguide having inner dimensions of mm long mm wide, and is irradiated to the sample material. The microwave passing through the sample is perfectly absorbed at the end of the waveguide using water load. The sample heated is a packed bed which is composed of glass beads of 0.15 mm in diameter and water. An incident wave controlling plate and a reflecting plate are installed over and under the sample, as shown in Figure 2. Temperatures in the sample are measured using an infrared radiation thermometer and light fiber sensors which are placed in the center of the sample at each 5 mm interval. The electric powers of incident, 2

CONTROL OF MICROWAVE HEATING IN RECTANGULAR WAVEGUIDE @ A B C F E z Microwave Wave Control Plate Sample Reflecting plate 109.22[mm] y x 54.

2 Experimental apparatus Model 1 1.2 5 É @ Magnetron DLight Fiber Sensor APower Monitor EDetector BComputer FRectangular Wave Guide CThermometer GIsolater Fig.

3 CONTROL OF MICROWAVE HEATING IN RECTANGULAR A B C F E z Microwave Wave Control Plate Sample Reflecting plate [mm] y x 54.61[mm] Rectangular Wave Guide Movable Experimental results Model 1 Calculated results Model 2 Fig.4 Temperature distributions in the sample for normal heating D 1.5 É G Fig.2 Experimental apparatus Model Magnetron DLight Fiber Sensor APower Monitor EDetector BComputer FRectangular Wave Guide CThermometer GIsolater Fig.3 Sample Model 2 Electric field E y /E yin [-] Sample length [mm] (a) Model 1 (resonance state) reflected and transmitted waves are measured by wattmeter using a directional coupler. We used two packed beds having 30 mm (model 1) and 25 mm (model 2) in thickness. As shown in Figure 3, the thickness in model 1 corresponds to 1.5 times of the wavelength in packed beds (λ = 20 mm) and leads to the resonance state in the sample. The thickness in model 2 corresponds to 5 times and leads to the anti-resonance state. 4 Results and discussion 4.1 in rectangular waveguide In microwave heating, the temperature distributions in the sample depend on the interference of transmitted wave and reflected wave. First, we show the normal heating of the sample installed in a rectangular waveguide. Figure 4 shows the comparison of the temperature distributions between model 1 and model 2 after the 10 seconds with the incident power of 1.5 kw. The temperature in model 1 is higher than that in model 2, because the transmitted and reflected waves in the sample Electric Field E y /E yin [-] Sample length [mm] (b) Model 2 (anti-resonance state) Fig.5 Typical electromagnetic fields in the sample resonate for model 1 and anti-resonate for model 2. The calculated results of the temperature distributions are in agreement with the experimental results measured by infrared radiation thermometer. In order to clarify the difference in the electromagnetic field, we show typical electromagnetic fields in the sample along with the center line of rectangular wave guide in Figures 5(a) and 5(b), corresponding to the model 1 and 2. The vertical axis represents the 3

When the sample length is the integer multiple of half wavelength corresponding to model 1, the transmitted and reflected waves in the sample resonate and the intensity of electric field becomes

4 Kazuo AOKI, Masatoshi AKAHORI, Kenji OSHIMA, Masato MORITA Experimental results Mode1 1 Calculated results Mode1 2 Fig.6 Temperature distribution in the sample with a reflecting plate intensity of electric field E y, which is normalized to the amplitude of input electromagnetic wave, E yin. When the sample length is the integer multiple of half wavelength corresponding to model 1, the transmitted and reflected waves in the sample resonate and the intensity of electric field becomes larger than that in model Effect of reflecting plate Next, we explain the effect of a reflecting plate on microwave heating. When a reflecting plate is attached at the bottom of the sample, transmitted wave passing through the sample is absolutely reflected on it and the reflected wave becomes the reverse phase against the transmitted wave at the bottom. This means that the interference state in the sample changes from resonance to anti-resonance in model 1 and from anti-resonance to resonance in model 2. Figure 6 shows the comparison of the temperature distributions between model 1 and model 2. In this case, the temperature in model 2 is higher than that in model 1. Figure 7 shows the change of the energy absorbed in the sample against the sample length for both cases with and without the reflecting plate. The absorbed energy depends on the sample length and has some peaks corresponding to the resonance state. The peak values of the absorbed energy are higher in case with the reflecting plate because of the effect of the reflected wave. Since the position of the reflecting plate affects the interference of transmitted wave and reflected wave, it is possible to make resonance state by changing the distance between the 1.8 Power 1500W 1.6 Elapsed time 1s With reflecting plate at bottom of the sample Fig.7 Absorbed energy against sample length for both cases with and without reflecting plate Distance between a sample and reflecting plate / Wave length in air [-] Fig.8 The optimum distance between sample and reflecting plate against the sample length Power 1500W Elapsed time 1s With a reflecting plate Fig.9 Effect of reflecting plate on absorbed energy sample and the reflecting plate. Figure 8 shows the optimum distance between the sample and the reflecting plate against the sample length. It is found that the optimum distance which means to lead to the resonance state in the sample changes in the interval of a quarter wavelength. Figure 9 shows the comparison of absorbed energy between the normal heating and the 4

5 CONTROL OF MICROWAVE HEATING IN RECTANGULAR WAVEGUIDE heating in case that the reflecting plate is installed in the optimum position. It is found that the absorbed energy increases by installing the reflecting plate in the suitable position. 4.3 Effect of incident wave controlling plate When an incident microwaves is directly irradiated to a high dielectric material, major part of wave is reflected on the surface of the material. In order to avoid the reflection, it is available to attach a low dielectric material on the high dielectric material. The optimum relative permittivity of the wave controlling plate where the rate of reflection becomes the smallest is obtained from the following relationship. ε = ε ε (5) rc ra rs where ε r is relative permittivity, and the subscripts a, c and s denote air, wave controlling plate and sample, respectively. In general, when the sample is infinite, the optimum thickness of the wave controlling plate is a quarter wavelength. While the thickness of the sample is finite, the optimum thickness depends on the sample thickness because of the influence of the reflected wave occurring at the end of the sample. Figure 10 shows the optimum thickness of the wave controlling plate against the sample length. When the length of the sample is short, the optimum thickness of the wave controlling plate depends strongly the sample length. As the sample becomes long, the optimum thickness becomes around a quarter wavelength because the influence of the reflected wave becomes small. Figure 11 shows the comparison of the energy absorbed in the sample between the normal heating and the heating with the incident wave controlling plate. It is found that the absorbed energy increases by attaching the wave controlling plate having the suitable thickness, even if the standing wave formed in the sample become resonance or anti-resonance states. 4.4 Multiple effects of two plates Figure 12 shows the comparison of the energy Wave controlling plate length / Wave length in the plate [-] Fig.10 The optimum thickness of the wave controlling plate against the sample length Power 1500W Elapsed time 1s With a wave controlling layer Sample length / Wave length in sample[-] Fig.11 Effect of incident wave controlling plate on absorbed energy With a reflecting plate Power 1500W 1.8 With a wave controlling plate Elapsed time 1s With both plates 1.6 Fig.12 Multiple effects of reflecting plate and incident wave controlling plate on absorbed energy 5

6 Kazuo AOKI, Masatoshi AKAHORI, Kenji OSHIMA, Masato MORITA absorbed in the sample between the normal heating and the heating with the reflecting plate and the incident wave controlling plate. When the reflecting and the wave controlling plates are simultaneously attached, the absorbed energy becomes very higher in comparison with the normal heating. 5 Conclusions In order to clarify the optimization of microwave heating using rectangular waveguide, we proposed two procedures that the incident wave controlling plate and the reflecting plate were installed in upper and lower parts of the sample. It was found that the performance of microwave heating could be improved by attaching both plates under the optimum conditions. We indicated guideline for the optimization of microwave heating by controlling reflected and transmitted waves. References [1] Padungsak R, Aoki K. and Akahori M., Experimental Validation of a Combined Electromagnetic and Thermal Model for a Microwave Heating of Multi- Layered Materials Using a Rectangular Wave Guide, ASME J. Heat Transfer, 124(5), pp , [2] Padungsak R, Aoki K. and Akahori M., Characteristics of Microwave Melting of Frozen Packed Bed Using a Rectangular Wave Guide, IEEE Trans. on Microwave Theory and Techniques, 50(6), pp , [3] Padungsak R, Aoki K. and Akahori M., Influence of Irradiation Time, Particle Sizes and Initial Moisture Content During Microwave Drying of Multi-Layered Capillary Porous Materials, ASME J. Heat Transfer, 124(1), pp , [4] Aoki K, P. Padungsak R, Mikawa T., Akahori M., During of Moisture Packed Beds due to Microwave Heating Using a Rectangular Wave Guide, Proc. of the 12th. Int. Heat Transfer Conf., France, [5] Tada, S., Echigo, R., and Yoshida, H., Numerical analysis of electromagnetic wave in a partially loaded microwave applicator, Int. J. Heat and Mass Transfer, Vol. 41, pp , [6] Mur G., Absorbing boundary conditions for the finite-difference approximation of the time-domain electromagnetic field equations, IEEE Transcations of Electromagnetic Compatibility, Vol. EMC-23, NO. 4, pp ,

The Characteristics of Microwave Melting of Frozen Packed Beds Using a Rectangular Waveguide

IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 50, NO. 6, JUNE 2002 1495 The Characteristics of Microwave Melting of Frozen Packed Beds Using a Rectangular Waveguide Phadungsak Ratanadecho,