A rotary radiation structure for microwave heating uniformity improvement

Accepted Manuscript A Rotary Radiation Structure for Microwave Heating Uniformity Improvement Huacheng Zhu, Jianbo He, Tao Hong, Qianzhen Yang, Ying Wu, Yang Yang, Kama Huang PII: DOI: Reference:

S1359-4311(17)37274-5 https://doi.org/10.1016/j.applthermaleng.2018.05.122 ATE 12261

To appear in:

Applied Thermal Engineering

Received Date: Revised Date: Accepted Date:

22 November 2017 7 February 2018 28 May 2018

Please cite this article as: H. Zhu, J. He, T. Hong, Q. Yang, Y. Wu, Y. Yang, K. Huang, A Rotary Radiation Structure for Microwave Heating Uniformity Improvement, Applied Thermal Engineering (2018), doi: https://doi.org/ 10.1016/j.applthermaleng.2018.05.122

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A Rotary Radiation Structure for Microwave Heating Uniformity Improvement Huacheng Zhua, Jianbo He a, Tao Hongb, Qianzhen Yang a, Ying Wua, Yang Yanga*, Kama Huanga a College of Electronics and Information Engineering, Sichuan University, Chengdu 610065, China; [email protected] (J.H.); [email protected] (Y.W.); [email protected] (Y.Y.); [email protected] (K.H.) b School of Electronic Information Engineering, China West Normal University, Nanchong 637002, China; [email protected](T.H.) * Correspondence: [email protected]; Tel.: +86-28-85470659 Abstract: A novel microwave heating method with rotary radiation structure has been proposed to improve heating uniformity. Through time division of the whole heating process, static heating assumption of each time step and temperature inheritance between time steps, a simulation model has been built and computed based on the finite element method combined with programming. A quantitative validation of simulation results has been performed with physical experiments. Heating uniformity and heating efficiency of the proposed method has been compared with those of two traditional methods, by which a potato slice is heated with a turntable and heated statically. The results show that the rotary radiation structure has an obvious superiority. What is more, influences of positions of the waveguide that feeds microwave and its placing directions of the proposed method have also been discussed. Keywords: microwave heating; rotary radiation structure; heating uniformity improvement; efficient heating. 1. Introduction Traditional heating methods are mainly based on principles of heat radiation, convection and conduction. Materials are thus heated in an outside-in orientation. On the contrary, the burgeoning microwave heating technology processes materials through direct interaction with the inner polar molecules and charged particles of materials. Due to its unique heating principle, microwave heating is characterized by efficient heating, internal heating and environmentally friendly heating [1-5]. However, there are also some natural drawbacks of microwave heating and non-uniformity heating is the most common one [6]. Non-uniformity heating can easily cause local overheat problems and hot spots, which lead to thermal runaway problems as a surge in the system temperature, which will cause quality degradation of final products [7-10] and even cause the burning and * Corresponding author： Yang Yang, e-mail address: [email protected].

explosion [11-12]. Therefore, great efforts have been made by experts to invent new methods to improve heating uniformity in microwave heating applications. The common methods to improve microwave heating uniformity can be classified into two categories [13]: to improve the uniformity of the electromagnetic field in microwave cavity; to improve the uniformity of microwave energy absorption. For the former one, it is usually realized by optimization of microwave power feeding situations(such as port number, feeding positions, feeding frequency and so on) [14-17], introduction of mode stirrers [18-19], application of conductive beads to cause random scatterings of microwave [20-21] and optimization of heating chamber structure [22-23]. For the latter one, it is usually realized by analyzing the effects of heated material’s different positions and its dynamic motion during heating by the introduction of components such as rotating turntable and conveyor belt [24-25]. there are also studies [21, 26-27] on the influence of processing materials’ physical properties, such as shapes, sizes and so on. Laura Analía Campañone et al. [14] studied heating materials with two equal and coherent fronts incident waves. By altering the phases of the incident waves, uniform heating results can be achieved. D Luan et al. [15] found that adjusting the dimension of the cavity in the dominant direction and the phase of standing wave within the microwave heating cavity, heating uniformity can be improved. Plaza-Gonzalez et al. [16-17] studied several kinds of mode stirrer configurations and the effect resulted from improving the electric field uniformity, and they have found that stirrers moving in the vicinity of the processed materials could result in a noteworthy improvement on the distribution uniformity of microwave. Yoshinori Itaya et al. [18] proposed a technology to apply electrically conductive beads into a fluidized bed. The random movement of the conductive beads could lead to the scattering of microwave disordered and thus give the processing materials a better uniformity of the electric field intensity. Similar studies have been done by Ruifang Wang [19] who heated materials with conductive beads in a microwave oven. Nomenclature Le length of the waveguide n simulated in model (m) wavelength of microwave at λ certain frequency in free space (m) width of the standard WR340 a waveguide (m) c speed of light (3×108 m/s) frequency of the feeding f microwave (Hz)

Cp

heat capacity under atmospheric pressure (J/(kg·K))

T

temperature (℃)

Q

heat source (W/m3)

k

thermal conductivity (W/(m·K)) rotation angle of the radiation disk (°) computation updating frequency of heat transfer part (dimensionless) initial space temperature

phi

H

magnetic field intensity (A/m)

N

J

ampere density (A/m2)

Tinitial_

distribution in the Nth time step (x,y,z) (℃) T final space temperature the electric field strength initial_ E distribution in the Nth time step N-1 (V/m) (x,y,z) (℃) real part of relative permittivity t time (s) ε' (dimensionless) unit normal vector of the magnetic induction intensity B n corresponding surface (T) (dimensionless) electric displacement vector D q heat flux (J/(m2·s)) 2 (C/m ) heat transfer coefficient ρe electric charge density (C/m3) h (W/(m2·K)) relative permeability temperature of the air inside the μr Tair (dimensionless) cavity (℃) wave number in free space normalized power absorption k0 NPA (dimensionless) (dimensionless) ε(T relative permittivity mmeshsi size of the unit mesh cell (m) ) (dimensionless) ze point temperature of the selected ω angular frequency (rad/s) Ti region (℃) permittivity of vacuum coefficient of variation ε0 COV -12 (8.85×10 F/m) (dimensionless) average temperature of the σ electrical conductivity (S/m) Ta selected region (℃) permeability of vacuum total number of the point of the μ0 n -7 (4π×10 H/m) selected region (℃) electromagnetic power loss initial average temperature of Qe T0 (W/m3) the selected region (℃) imaginary part of relative average temperature of the ε" Tp permittivity (dimensionless) tangent plane (℃) distance between the feeding 3 ρ material density (kg/m ) S window and the center of the rotating disk. (mm) S. Ryynänen and T. Ohlsson [21] studied how the physical and chemical properties of the processed materials affect the final heating uniformity and found it is mainly decided by the arrangement and geometry of components and type of tray instead of chemical modifications and other factors. While studying the effect of changing materials’ position, Geedipalli et al. [22] found that the rotation of a turntable could increase the temperature uniformity of the processing food by about 40%. In this paper, a novel rotary radiation structure for microwave heating is proposed to solve the common non-uniformity heating problem. In section two, a theoretical model has been built and simulated through multiphysics coupling and finite element method combined with programming. Based on simulation results, physical experiment system has been designed and N

performed to complete the validation work. In section three, quantitative analysis of the comparative results between the experiment and simulation has been conducted. Along with the following analysis of heating uniformity and efficiency compared with those of other methods, the superiority and applicability of the proposed method have been discussed. In addition, model sensitivity has been computed to show its influence on heating uniformity and efficiency. 2. METHODOLOGY 2.1. Multiphyscis Simulation 2.1.1. Geometry The simulation model consists of four components, a cavity as heating oven, a waveguide to feed microwave power, an aluminum rotary disk on one surface of the cavity to realize rotary radiation structure, a slice of potato as the processing material and a support disk to put the potato slice on. The model structure is showed in Fig. 1.

2

43.2

10

40 10

40

166

91

Fig. 1. Geometry of the 3-D simulation model (unit: mm). The waveguide simulated in model is in the standard WR340 waveguide size, namely with its basic width and height as 86.4×43.2 mm. The length of the waveguide Len has been fixed to be half of the waveguide wavelength under the simulation frequency to approximate the WR340 waveguide coaxial adapter used in actual experiment. Len is defined as 

(1 ) where the λ is the wavelength of microwave at certain frequency in free space, a is the width of the standard WR340 waveguide, c is the speed of light, f is the frequency of the feeding microwave. 2.1.2. Governing equations Len  

1 (

2a

)2 ,   c / f

Simulation of the model is coupled by two parts: the microwave propagation part and the heat transfer part. To compute the former part, Maxwell’s equations are employed as E t B E   t B  0   D  e

H  J 

(2)

where H is magnetic field intensity, J is ampere density, E is the electric field strength, t is time, B is magnetic induction intensity, D is electric displacement vector and ρe is electric charge density. Governing equation of electric field can thus be derived from equation (2) and be written as Helmholtz equation [28] j     r 1    E   k0 2   (T ) 0  E0    k0    0  0

(3)

where μr is the relative permeability, k0 is the wave number in free space, ε(T) is the relative permittivity, ω is the angular frequency, ε0 is the permittivity of vacuum, σ is the electrical conductivity and μ0 is the permeability of vacuum. Then the electromagnetic power loss Qe could be gained from the computed electric field by the following equation [29-30] (4 ) where ε" is the imaginary part of relative permittivity of processing material. To compute the temperature distribution situation, governing equation for heat transfer is given as [31-33] 1 2 Qe   0 " E 2

C p

T  k  2T  Q  Qe t

(5)

where ρ is the material density, Cp is the material heat capacity, T is the temperature, t is the time, Q is the heat source and k is the thermal conductivity. For the rotary radiation structure, phi is given to define the rotation angle of the aluminum rotary disk. Equation can be expressed as phi  360

N 1 N

(6)

where N is the computation updating frequency of heat transfer part. The value of N refers to the number of time that a complete rotation cycle is divided into for heat transfer computation. In other words, during a complete rotation cycle as total turn angle of 360°, heat transfer computation will be done for every angle of phi and in total N times. 2.1.3. Solution methods To accomplish the simulation, COMSOL Multiphysics (which is based on FEM) combined with Matlab programming has been employed. The main steps involved to imitate the real rotary heating situation are showed in Fig. 2.

Fig. 2. Overall flowchart. The whole heating and rotation process is actually divided into several time steps and N is given to define the appropriate value. During each step, the rotary disk is assumed to be still and the model is computed through the multiphysics computation process showed in Fig.2. Between time steps, Matlab programming is introduced to perform the geometric transformation of model and the result temperature inheritance, which means the final temperature distribution of the last step is defined as the initial temperature distribution in the next step Tinitial _ N ( x, y, z)  Tfinal _ N 1 ( x, y, z)

(7)

By increasing of the value of N, the simulation results would finally converge and fit with physical truth. Moreover, due to the rotation of the rotary disk, the mesh differences in the processing materials caused by remeshing are little, the error caused by the remeshing would be low [34]. 2.1.4. Input parameters and boundary conditions For model computation, necessary property parameters and boundary conditions are needed. Related input parameters of simulation are showed in Table1. The thermal and dielectric properties of potatoes are obtained from the literature [35]. The complex permittivity of the processing material is defined to give a near-actual model. Variable enactment of temperature-depending permittivity has been employed to fulfill the updating of permittivity with temperature, as the step (11) showed in Fig.2, which is defined as [36]  (T )     j   (5.5  A

A  5.5 A  5.5 )  j  (9.652  105  e2143.84T  ) 1  (9.652  105  e2143.84T )2 1  (9.652  105  e2143.84T )2

(56.25  1186.78  e2143.84T  16.57  T )2  2178  T 2 (56.25  1186.78  e2143.84T  16.57  T )  12  T 12  T

(8)

where ε' are the real part the relative permittivity. The whole surfaces of the heating system except the feeding port on the waveguide are defined as perfect electric conductor. The governing equation can be expressed as n E  0

(9)

where n is the unit normal vector of the corresponding surface. The feeding port of the waveguide here is defined as rectangular with microwave in TE10 mode while it then becomes multimode as entering the cavity and becoming standing wave. For heat transfer boundary condition, convection heat transfer boundary condition has been applied to the surface of the potato slice to approximate the natural heat convection of the potato slice to air, which is governed as k T n  h  (T  Tair )

(11 )

where ∂T/∂n is the temperature gradient, Tair is the temperature of the air, and h is the heat transfer coefficient, of which the value is 10 W/(m2∙K), a typical value used for natural convective heat transfer in air [37]. The thermal boundary between potato slice and the support disk is set as insulation boundary conditions. Table 1. Summary of material properties applied in the model. Applied Property Value Source domains Air 1 Ref [35] Potato ε(T) Ref [36] Relative permittivity Polyethylene 2.3 Ref [35] Air 1 Ref [35] Aluminum 1 Ref [35] Relative permeability Potato 1 Ref [35] Polyethylene 1 Ref [35] 0 Air Ref [35] 3.774 × Aluminum Ref [35] 107 Conductivity (S/m) Potato Ref [35] 0 Polyethylene Ref [35] 0 Heat conductivity coefficient Potato 0.648 Ref [35] (W/m∙K) Potato 1050 Ref [35] Density (kg/m3) Heat capacity at constant Potato 3640 Ref [35] pressure (J/kg∙K) 2.1.5. Mesh size Appropriate mesh size is important in model simulation. The space discretization errors could be down to a quarter when mesh size is halved while computation time will increase by almost 16 times and memory requirements eight times [38].

To define appropriate mesh sizes for the proposed model, mesh independence study has been carried out involved with the normalized power absorption, which can be expressed as NPA 

power absorbed by the processing materials power fed into the system

(12 )

When the value of NPA almost doesn't change with thinner mesh sizes, it can be concluded that a convergence has been reached and the results with that mesh size are accurate. Manual of software QuickWave [38] suggests 12 cells per wavelength are needed for mesh independent results while other researchers [39-40] suggest at least 10 cells per wavelength. Here the NPA with mesh size study has been studied and showed in Fig.3-4 and Table 2. According to mesh independence study, the mesh size used in this paper is defined as mmeshsize 

(13 )

c 8 f 

where mmeshsize is the size of the unit mesh cell. 0.45 0.40

NPA

0.35 0.30 0.25 0.20 0.15 0.10 0

2

4

6

8

10

12

14

16

Cell number (per wavelength)

Fig. 3. NPA variation of heating computations with different mesh sizes.

Fig. 4. Diagrammatic sketch of the finite element mesh used in simulation. The mesh has a total of 202,489 elements. Table 2. Computation information about the mesh independence study. Cell number (per Total number of Time (s) wavelength) elements 0.2 67090 466 0.5 66672 463 1 67347 487 2 72815 984 4 89098 681 6 129216 920 8 202489 1304 10 321160 2042 11 398559 2454 12 494827 3273 14 738426 5102 16 1053061 10777 2.1.6. Computation updating frequency To reduce computation time as well as get accurate simulation results, comparisons have been done to determine the best value of N, in other words, to determine the updating frequency of the rotary heating computation [41]. Here the whole heating process is set as 12s with rotary disk at a speed of 30°/s, which speed is selected as it is the speed of the electrical machinery used in corresponding experiments. Heating computation is updated every 10°, 15°, 20°, 30°, 60°, 90°, namely with N value as 36, 24, 18, 12, 6 and 4 to approximate continuous rotation of the rotary disk in real heating. Normalized power absorption (NPA) [34, 42] has been employed to analyze the convergence of heating results. According to the final results showed in Fig.5, N=18 was observed to be sufficiently close to the continuous situation.

N=4

N=6

N=12

N=18

N=24

N=36

(a)

NPA

0.4

0.2

0.0 0

5

10

15

20

25

30

35

40

N

Fig.5 (a) Temperature distribution of heating computations with different updating frequency (temperature unit: °C); (b) NPA variation of heating computations with different updating frequency. As the computation updating frequency affirmed, the mesh situation of each time step, where the rotary disk is assumed to be still as described in the previous section, has also been checked to show the credibility of the solution methods to the proposed structure. The mesh during each time step have been showed in Fig.6 and Table 3. The changing of the rotation angle phi would cause a standard deviation of 0.61% on the total number elements to the initial model but no influence on the elements in the simulated sample, which means the error caused by the remeshing would be little in the result temperature inheritance.

Fig. 6. Diagrammatic sketch of the finite element mesh at each time step. Table 3. Mesh information at each time step. Elements in the Total number of phi (°) sample (potato elements slice) region 0 202489 33911 20 198308 33911 40 198169 33911 60 198021 33911

80 100 120 140 160 180 200 220 240 260 280 300 320 340

198096 198380 198324 198086 197805 200664 197846 197370 197228 198432 198335 197949 198364 198103

33911 33911 33911 33911 33911 33911 33911 33911 33911 33911 33911 33911 33911 33911

2.2. Experimental setup 2.2.1. Experimental system To validate the computational modeling results, physical experiments need to be completed. In accordance with the modeling system, a physical heating oven has been processed to complete verification work. As the processing model showed in Fig. 7, the physical cavity has a lid with a cut-off waveguide on its top side to give a conventional operation and observation entrance. For rotary structure, it is realized by a disk that could rotate by the handle to drive the feeding waveguide coaxial adapter connected to it. A lateral view of the disk has been showed in Fig. 7 to further illustrate the structure of the disk. The disk actually consists of three separate metal disks, of which the middle one fit with the circular opening on the oven while the other two is a little bit larger to clamp the whole structure on the system.

Fig. 7. Overall view of processed cavity and its rotary structure.

Other equipment involved to complete the experiments includes a microwave solid source, a fiber optic temperature sensor, a thermal imager, a waveguide coaxial adapter in standard WR340 size and corresponding cables. The schematic structure of the system is showed in Fig. 8. Cut-off waveguide Optical fiber

Waveguide coaxial adapter

Cavity Sample

Optical fiber thermometer

Rotary disk Support disk Microwave generator

Fig. 8. Schematic of the laboratory microwave heating system. 2.2.2. Experimental procedures As the experiment system showed in Fig.6, the real heating process is carried by a solid-state power generator (WSPS-2450-200M, Wattsine, Chengdu, China) to feed microwave. Power of 165W at 2.45 GHz has been used to heat the potato slice on the support floor. The support disk here is made of polyethylene, a kind of material that has a small real part of permittivity so its influence on the electric field is little. For the same consideration, a fiber optic temperature sensor (FISO FOT-NS-967A, FISO Technologies, Quebec, QC, Canada) is used to obtain the temperature changing in a single point of the potato slice instead of thermoelectric thermometers. The rotation radiation structure is realized by the rotation of the rotary disk along with the waveguide coaxial connector (CAWG-26-N, Euler, Nanjing, China) and source. For temperature validation, the center point of the processing potato slice’s top surface has been selected to perform a temperature measurement during the heating process by the fiber optic temperature sensor (as shown in Fig. 9) while the final temperature distribution of the top surface is measured by the thermal imager (VarioCAM hr inspect 500, InfraTec., Dresden, Germany). 3. Results and discussions 3.1. Model validation Top surface temperature distributions of the simulation and experiment after 30 seconds’ heating have been showed in Fig. 9. To define the differences in temperature distributions to be discussed then, the coefficient of variation (COV) of the selected region’s temperature has been employed. The COV could be expressed as COV 

 T  T  i

n

n

a

(Ta  T0 )

(14 )

where Ti is the point temperature of the selected region, Ta is the average temperature of the selected region, n is the total number of the point of it and T0 is the initial average temperature. Simulation result based on the proposed method has shown four areas on the top surface with a higher temperature, which could be observed from experimental results in the similar positions but with a better heat conduction effect. Simulation and experimental results based on direct static materials heating have both shown two areas with higher temperature. Top surface center point temperature variations of simulation and experiments based on the proposed method have been showed in Fig. 10. General temperature distributions between simulations and experiments fit have shown consistence. For the proposed method, temperature COV of the top surface is 0.3985 in simulation while 0.3469 in experiment, which has a difference of 12.9%. And the average surface temperature is 32.37℃ in simulation while 31.32℃ in experiment, which has a difference of 3.24%. For direct static materials heating, temperature COV of the top surface is 0.4769 in simulation compared with 0.4632 in experiment, which has a difference of 2.87%. And the average surface temperature is 23.23℃ in simulation while 23.41℃ in experiment, which has a difference of 0.769%. The experiment heating results have shown a different uniformity and average temperature rise compared to simulation. It may be caused by two reasons: the first is the computation mistake by the simplification of the physical situation and the properties differences between simulation and experiment. The physical process of heating the potato involves more than heat transfer and convection, such as the phase change of water in potatoes, the flow of air in the cavity. These simplifications would bring errors to the heating results between simulations and experiments. Besides, the properties of relative materials, especially the potato slice, used in simulation can't match the practical situation perfectly and thus would also bring differences on final temperature distribution results. The second comes from the experimental procedures. The errors of the device itself and the delay in data acquisition have played a not negligible part, not to speak of the operation delays such as the roughly 4 to 6 seconds needed to remove the lid of the cavity to take the thermal imaging of temperature distribution on potato surface.

Center point

Center point

(a)

(b)

(c)

(d)

Fig. 9. Comparisons between experimental and simulated surface temperature distributions of potatoes subjected to 30 s in heating cavity (temperature unit: °C): (a) simulation heating result by the proposed method; (b) experiment heating result by the proposed method; (c) simulation result of direct static materials heating; (d) experiment result of direct static materials heating. Experiment Simulation

50

Temperature (℃ )

45 40 35 30 25 20 15 0

5

10

15

20

25

30

Time (s)

Fig. 10. Top surface center point temperature variations of simulation and experiments based on the proposed method 3.2. Analysis of model’s heating uniformity and sensitivity 3.2.1. Heating uniformity analysis To investigate the effect caused by rotary radiation structure on the heating uniformity of the microwave heating, heating processes using conventional methods, namely heating with a turntable, the proposed method and direct static

materials heating are computed. Comparisons of the heating results are conducted under similar conditions, namely the processing potato slice and its position, the cavity and power conditions have all stayed the same. As the computed spatial temperature profiles showed in Fig. 11, heating with rotary radiation structure and heating materials on a turntable could observably improve the heating uniformity compared with heating with static materials. Heating with the proposed method has also shown a higher heating efficiency. To define their effect quantitatively, the coefficient of variation (COV) and the average body temperature T at the end of the heating process are also employed as showed in Fig. 11. All the temperature profiles are drew in a range of 20℃ to 40℃. The rotary speed of the turntable and rotary disk is all defined as 30°/s.

(a)

(b)

(c)

Fig. 11. Spatial temperature profiles of potatoes heated by different methods (temperature unit: °C): (a) heating with a turntable, COV=0.3014, T=29.62; (b) heating materials with rotary radiation structure, COV=0.3122, T=41.20; (c) direct static materials heating, COV=0.6332, T=24.63. Geedipalli et al. [25] have found that although the introduction of turntable could improve the heating uniformity of the processing materials on the same layer. But for different layers, the thermal inhomogeneity is still obvious. ChunFang Song et al. [43] have studied the local temperature and moisture uniformity in a drying chamber and found that the temperature and moisture gradients mainly occurred in the vertical direction of the drying cavity. Table 4 has shown some computational heating results of several selected layers from processing materials heated by turntable and by the proposed method, including the average temperature of the tangent plane Tp and the COV value of the tangent plane. For the whole processing material, heating with turntable could get a better uniformity with a COV of 0.3014 compared to 0.3122 in heating with the proposed method. When taking different layer’s heating results into consideration, the mean square error of different layer’s COV in heating with a turntable is 0.05462 while it is 0.06010 in heating with a radiation structure. But for direct comparisons of different layer’s average temperature between those two methods, the mean square error is 1.745 when using a turntable compared to 0.7025 when the proposed method is employed. Fig. 12 has shown the temperature distributions of the selected planes to give a more intuitive comparison. In addition, heating with rotary radiation structure could bring more modes of microwave and thus give a more efficient heating. The average

body temperature of rotary radiation structure is 41.20℃ compared to 29.62℃ of the turntable structure. Hence, microwave heating with rotary radiation structure does be superior to other methods discussed here. Table 4. Comparison between the turntable structure’s and the proposed structure’s average surface temperature and COV of horizontal sections at different height of the potato slice Rotary radiation structure

Turntable

Section height (mm) 10 7.5 5 2.5 0 Whole material Mean square errors

Tp (C )

COV

Tp (C )

COV

27.74 29.46 31.71 29.75 27.37

0.2135 0.1670 0.2915 0.2930 0.2177

41.86 41.36 40.06 41.52 41.57

0.3985 0.3499 0.2633 0.2607 0.2890

29.62

0.3014

41.20

0.3122

1.745

0.05462

0.7025

0.06010

Rotary radiation structure

Turntable structure

Section height (mm)

10

7.5

5

2.5

0

Fig. 12. Comparison between the turntable structure’s and the proposed structure’s surface temperature distribution of horizontal at with different height of the potato (temperature unit: ℃) 3.2.2. Sensitivity analysis To study the effect of rotary radiation structure on heating uniformity and efficiency, positions and placing directions of the waveguide have been analyzed. Position changes and placing direction changes of the waveguide to feed microwave power are analyzed based on the structure view and corresponding simulation results showed in Fig. 13 and Fig. 14. Data of COV value and average body temperature have also been performed. S is given to define the distance between the microwave feeding port and the center of the rotary disk as showed in Fig. 13. The results have shown that the position change of the

waveguide has a linear effect on the heating uniformity and the average temperature T. With the increasing S, temperature distribution results show a more efficient heating while the heating uniformity gets worse. Taking changes of waveguide’s placing direction into comparison, heating with vertical waveguide has a better heating uniformity but with a lower heating efficiency.

Fig. 13. Structure view of the position and placing direction of feeding port: (a) horizontal waveguide; (b) vertical waveguide.

Fig. 14. Horizontal waveguide’s and vertical waveguide’s spatial temperature profiles with different positions. (temperature unit: °C) 4. Conclusions A novel heating category based on rotary radiation structure has been presented in this work. With coupled electromagnetic field and heat transfer situation computed based on finite element method combined with programming, a microwave heating model based on the proposed structure has been realized. Physical equipment has been processed and employed to test the validity of the proposed method, which was further verified by the computation results. Comparisons between the proposed method and other two heating methods, heating with turntable and direct static materials heating, have shown that the proposed method has a better heating uniformity compared with heating with static materials as the COV value 0.3122 to 0.6332. Although

heating materials on turntable has gained a better COV value of 0.3014, a worse uniformity can be observed when different layers of the processing materials are taken into consideration. And the proposed method has shown a higher heating efficiency as the average body temperature 41.20℃ compared with 29.62℃ of the heating with turntable and 24.63℃ of static materials heating. In addition, positions and placing directions of the waveguide have also been analyzed. It shows that changeing the waveguide’s position, either horizontal waveguide or vertical waveguide, will increase the final temperature and the value of COV with the increase of S. Nevertheless, heating with horizontal waveguide has resulted in a higher heating efficiency but a worse heating uniformity. Acknowledgments This work was supported by the NSFC (Grant No. 61601312, 61501311). Science Foundation of the Sichuan Province (Grant No. 2016FZ0070). Young scientist foundation of Sichuan University (Grant No. 2016SCU11001). References [1] L. A. Campanone, N. E. Zaritzky, Mathematical analysis of microwave heating process, Journal of Food Engineering, 69(2005) 359-368. [2] D. Adam, Microwave chemistry: Out of the kitchen, Nature, 421(2003) 571–572. [3] S. O. Ozkoc, G. Sumnu, S. Sahin, Chapter 20-Recent Developments in Microwave Heating, Emerging Technologies for Food Processing press, 2014. [4] W. S. Sutton, Microwave processing of ceramics-an overview. in: R.L. Beatty, W.S. Sutton, M.F. Iskander (Eds.), Microwave Processing of Materials III, Materials Research Society, Pittsburgh, 269(1992) 3-20. [5] N. Ferrera-Lorenzo, E. Fuente, I. Suárez-Ruiz, et al., KOH activated carbon from conventional and microwave heating system of a macroalgae waste from the Agar-Agar industry, Fuel Processing Technology, 121(2014) 25-31. [6] R. Vadivambal and D. S. Jayas, Non-uniform temperature distribution during microwave heating of food materials-A review, Food Bioprocess Technol., 3(2010) 161–171. [7] M. Kubota, T. Hanada, S. Yabe, et al., Water desorption behavior of desiccant rotor under microwave irradiation, Applied Thermal Engineering, 31(2011) 1482-1486. [8] V. Lopez-Avila, J. Benedicto, K. M. Bauer, Stability of Organochlorine and Organophosphorus Pesticides when Extracted from Solid Matrixes with Microwave Energy, Journal of Aoac International, 81(1998) 1224-1232. [9] V. SEBERA, A. NASSWETTROVA, K. NIKL, Finite element analysis of mode stirrer impact on electric field uniformity in a microwave applicator, Drying Technology, 30(2012) 1388-1396. [10] D. E. CLARK, W. H. SUTTON, Microwave processing of materials, Annual Review of Materials Science, 26(1996) 299-331. [11] A. Stadler, B. H. Yousefi, D. Dallinger, et al., Scalability of Microwave-Assisted Organic Synthesis. From Single-Mode to Multimode

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Simulation model

Physical Experiment Cut-off waveguide

Optical fiber

Cavity

2

Sample

Waveguide coaxial adapter

Optical fiber thermometer

Rotary disk Support disk

43.2 Cavity

Microwave generator Front view of the rotary disk

10 166

Lateral view of the rotary disk

40 10

40

43.2 mm

172 mm 170 mm

91

92.8 mm

1 mm 43.2 mm 86 mm

2 mm

2 3 mm mm

Highlights： 1. A novel cavity structure for uniform and efficient heating is developed. 2. A time subsection method for physical continuous rotary situation is performed. 3. The multiphysics model is verified by experiments. 4. Thermal inhomogeneity problem in materials’ different layers is analyzed.