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PIERS ONLINE, VOL. 5, NO. 7, 2009 690 Measurement of Dielectric Properties and Finite Element Simulation of Microwave Pretreatment for Convective Drying of Grapes S. R. S. Dev, Y. Gari´ epy, and G. S. V. Raghavan Department of Bioresource Engineering, McGill University, QC, Canada AbstractIn this study, the dielectric properties (dielectric constant — ε 0 and dielectric loss factor — ε 00 ) of grapes were measured on a matrix of frequencies (from 200 MHz to 10 GHz) and temperatures (5 C to 80 )C. Empirical relationships relating the dielectric properties to both temperature and frequency were developed. A Finite Element Model (FEM) of the microwave pretreatment of the grapes was made. Simulation studies were conducted for grapes subjected to 5 minutes of pretreatment under 915 MHz and 2450 MHz. Different power densities of 0.5 W/g, 5 W/g and 50 W/g were used in order to visualize and investigate the energy distribution within the berries. 1. INTRODUCTION Raisins are well known for its medicinal and nutraceutical properties. It is a good source of potassium, magnesium and fibre. Fresh grapes contain about 80–85 per cent moisture content on wet basis. In the process of raisin making it is reduced to 18 per cent (wet basis). This is done traditionally by sun drying or convective drying. The natural waxy coating on the grapes delays moisture removal. Dipping in hot water and the use of chemicals such as sulphur, NaOH, and ethyl or methyl oleate emulsions are some of pretreatments widely used for grape drying to remove the waxy coating and increase drying rate in raisin making. According to Tulasidas etal. [7] microwave processing is an energy efficient drying technique for raisin production. Due to its high moisture content heat absorption is very effective. With a view to find alternate methods that could reduce drying time without using chemicals, pre-treatment with microwaves (MW) and pulsed electric field (PEF) were studied by Dev etal. [3] and found that microwave pretreatment significantly enhances the drying rate and quality of raisins. Measurements and modelling of dielectric helps understanding, explaining, and simulating the microwave heating of the materials [4]. There are studies on the measurement and modelling of dielectric properties of grapes at 2.45 GHz for different temperatures [7]. But there is no data available on the dielectric properties of grapes at different frequency. Such data will give a better understanding of the behaviour of the grapes on a broader electromagnetic spectrum and helps further simulation studies at other permitted frequencies like 915 MHz. Yen and Clary [10] state that during microwave heating once moisture in the berry is heated to a saturation temperature, the temperature rises with pressure resulting in volume expansion causing the berry to rupture. If the rate of vaporization is controlled by the level of microwave energy applied, a puffed nature can be achieved by the rupture of different layers. In grapes, this rupturing is reported to start near the surface and propagate into the interior giving the raisins a puffy texture, thus providing the necessary pathways for moisture migration from different layers of the berry. This might enhance the drying rate in further drying process. There is poor understanding of the mechanisms involved in creating new channels for moisture migration and actual energy distribution inside the grapes when subjecting them to electromagnetic field. The electromagnetic field distribution inside the microwave oven can be traced out by solving the Maxwell’s equations [5]. Finite Element Method (FEM) is commonly used for solving Maxwell’s equations to get the energy distribution in a complex object or within a multimode cavity and it is capable of simulating power density distribution in 3-D space [8, 9]. FEM technique competes very favourably with the other numerical methods, as it is based on reducing the Maxwell’s equations to a system of simultaneous algebraic linear equations [2]. FEM can readily model heterogeneous and anisotropic materials as well as arbitrarily shaped geometries. It can also provide both time and frequency domain analyses which are important to microwave heating problems like field distribution, scattering parameters and dissipated power distribution for various materials and geometries [1].

Transcript of Measurement of Dielectric Properties and Finite Element...

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PIERS ONLINE, VOL. 5, NO. 7, 2009 690

Measurement of Dielectric Properties and Finite ElementSimulation of Microwave Pretreatment for Convective Drying of

Grapes

S. R. S. Dev, Y. Gariepy, and G. S. V. RaghavanDepartment of Bioresource Engineering, McGill University, QC, Canada

Abstract— In this study, the dielectric properties (dielectric constant — ε′ and dielectric lossfactor — ε′′) of grapes were measured on a matrix of frequencies (from 200 MHz to 10 GHz) andtemperatures (5◦C to 80◦)C. Empirical relationships relating the dielectric properties to bothtemperature and frequency were developed. A Finite Element Model (FEM) of the microwavepretreatment of the grapes was made. Simulation studies were conducted for grapes subjected to5 minutes of pretreatment under 915 MHz and 2450 MHz. Different power densities of 0.5 W/g,5W/g and 50 W/g were used in order to visualize and investigate the energy distribution withinthe berries.

1. INTRODUCTION

Raisins are well known for its medicinal and nutraceutical properties. It is a good source ofpotassium, magnesium and fibre. Fresh grapes contain about 80–85 per cent moisture contenton wet basis. In the process of raisin making it is reduced to 18 per cent (wet basis). This is donetraditionally by sun drying or convective drying. The natural waxy coating on the grapes delaysmoisture removal. Dipping in hot water and the use of chemicals such as sulphur, NaOH, and ethylor methyl oleate emulsions are some of pretreatments widely used for grape drying to remove thewaxy coating and increase drying rate in raisin making.

According to Tulasidas et al. [7] microwave processing is an energy efficient drying technique forraisin production. Due to its high moisture content heat absorption is very effective. With a viewto find alternate methods that could reduce drying time without using chemicals, pre-treatmentwith microwaves (MW) and pulsed electric field (PEF) were studied by Dev et al. [3] and foundthat microwave pretreatment significantly enhances the drying rate and quality of raisins.

Measurements and modelling of dielectric helps understanding, explaining, and simulating themicrowave heating of the materials [4]. There are studies on the measurement and modelling ofdielectric properties of grapes at 2.45 GHz for different temperatures [7]. But there is no dataavailable on the dielectric properties of grapes at different frequency. Such data will give a betterunderstanding of the behaviour of the grapes on a broader electromagnetic spectrum and helpsfurther simulation studies at other permitted frequencies like 915 MHz.

Yen and Clary [10] state that during microwave heating once moisture in the berry is heatedto a saturation temperature, the temperature rises with pressure resulting in volume expansioncausing the berry to rupture. If the rate of vaporization is controlled by the level of microwaveenergy applied, a puffed nature can be achieved by the rupture of different layers. In grapes, thisrupturing is reported to start near the surface and propagate into the interior giving the raisins apuffy texture, thus providing the necessary pathways for moisture migration from different layersof the berry. This might enhance the drying rate in further drying process.

There is poor understanding of the mechanisms involved in creating new channels for moisturemigration and actual energy distribution inside the grapes when subjecting them to electromagneticfield. The electromagnetic field distribution inside the microwave oven can be traced out by solvingthe Maxwell’s equations [5]. Finite Element Method (FEM) is commonly used for solving Maxwell’sequations to get the energy distribution in a complex object or within a multimode cavity and itis capable of simulating power density distribution in 3-D space [8, 9].

FEM technique competes very favourably with the other numerical methods, as it is based onreducing the Maxwell’s equations to a system of simultaneous algebraic linear equations [2]. FEMcan readily model heterogeneous and anisotropic materials as well as arbitrarily shaped geometries.It can also provide both time and frequency domain analyses which are important to microwaveheating problems like field distribution, scattering parameters and dissipated power distributionfor various materials and geometries [1].

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Taking into account all the above mentioned facts, in this study, measurement and modeling ofthe dielectric properties of grapes was conducted on a matrix of frequencies (from 50MHz to 10 GHz)and temperatures (5◦C to 80◦C). Using the results obtained, a Finite Element Model (FEM) ofthe microwave pretreatment of the grapes was made and simulation studies were conducted forgrapes subjected to 5 minutes of pretreatment under 915 MHz and 2450MHz and power densitiesof 0.5W/g, 5 W/g and 50 W/g in order to visualize and investigate the energy distribution withinthe berries.

2. MATERIALS AND METHODS

In this study, the mechanisms involved in enhancement of drying rate by microwave pretreatmentwere investigated by FEM simulations. At first, dielectric properties of the grapes were measuredat temperatures ranging from 5◦C to 80◦C, and at frequencies ranging from 200 MHz to 10 GHz.Empirical relationships were then obtained to express dielectric properties as a function of temper-ature and frequency. In the second part, a Finite Element Model was made in order to simulatethe microwave heating of grapes.

2.1. Measurement of Dielectric Properties2.1.1. Grape SamplesGrapes (Thomson seedless variety) were purchased from the local market. They were washed,separated, destemmed, and surface dried. Each grape berry was taken into custom made 25 mmdiameter tube for heating in a temperature controlled dry heating bath.

2.1.2. EquipmentMeasurements of the dielectric properties were made with the open ended coaxial probe technique(Agilent 8722 ES s-parameter Network Analyzer equipped with a slim type probe model 85070B,Santa Clara, USA) and controlled by a computer software (Agilent 85070D Dielectric Probe KitSoftware Version E01.02, Santa Clara, USA). According to the manufacturer, the equipment hasan accuracy of ±5% for the dielectric constant (ε′) and ±0.005 for the loss factor (ε′′) (HP, 1992).A diagram of the experimental setup used for the measurement of dielectric properties is shown inFigure 1.

2.1.3. Experimental ProcedureThe grapes taken in the 25 mm diameter tubes were placed one at a time in a temperature controlleddry heating bath (Isotempr Model: 2001FS from Fisher Scientific, USA). The temperature at thecentre point of the grape berry, which was set to be the measuring point for the dielectric properties,was measured using a K type thermocouple (Thermo Fisher Scientific, USA). The temperature ofthe dry bath was set to 2◦C higher than the measurement temperature in order to allow thegradient for steady state heat flow. Once the centre point of the grape reached the requiredtemperature, the temperature across berry was assumed to have stabilized and measurements weretaken after removing the thermocouple and inserting the dielectric probe into the berry. Thedielectric properties were measured at 100 different frequencies ranging from 200 MHz to 10GHz.

2.1.4. Data AnalysisMATLAB version R2009a was used to analyze the collected data and to establish the mathematicalrelationships for the dielectric constant and loss factor as a function of frequency and temperature.

2.2. Finite Element Modeling and SimulationA 3D Finite Element Model was developed using COMSOL Multiphysics version 3.5 (COMSOLInc., USA) software package to simulate the MW pretreatment process for grapes for three differentpower densities (0.5, 50 and 50 W/g) for regular domestic microwave oven configuration. Themeshed structure for 2.45 GHz along with the grapes is shown in Figure 2. The cavity The 915 MHzcavity had a similar structure with bigger cavity dimensions. The cavity dimensions were taken as0.267m× 0.270m× 0.188m and 1.07 m× 1.22m× 1.47m for 2.45 GHz and 915 MHz respectively.

The simulations performed were a virtual replication of the actual pretreatments performed byDev et al. [3–5] except for the power densities used, wherein the drying temperature of 65◦C wasused as a microwave cut off temperature. Also they had a microwave on/off cycle time of 60/5seconds. So the similar conditions were applied for the simulation. The grapes were heated from25◦C to 65◦C in the simulation. The temperature dependent properties of grapes like density,thermal conductivity, electrical conductivity and specific heat capacity were taken from Tulasidaset al. [7].

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Computer

Network

Analyzer

ProbeElectronic

Calibration Module

25 mm Diameter tube Slim type probe

Dry heating bath

Figure 1: Dielectric properties measurement setup. Figure 2: FEM mesh structure with grapes.

A custom built computer with two AMD Opteron quadcore 2.4 GHz processors and 32 GBprimary memory was used to run the simulations.

2.2.1. Mathematics of the Model

ElectromagneticsThe Maxwell’s equations that govern the electromagnetic phenomena evolving in a given con-

figuration resolved in 3D space were solved for the Electric field intensity (E) (V ·m−1) and HMagnetic Field Intensity (A ·m−1) [1]. The dynamically changing dielectric constant ε′ and lossfactor ε′′ were calculated using equations derived from the measurement of dielectric properties.

The time average power dissipated (Pav) in each element in a dielectric material was obtained byintegrating the poynting vector (Pc) over the closed surface S for each tetrahedral element (Eq. (1))(Jia and Jolly, 1992).

Pav = −12

S

Pc · dS (1)

where Pc = E ×H. Volumetric heat generation Q can be expressed in terms of power intensity inthree orthogonal directions as shown in Eq. (2) (Lin et al., 1989).

Q =∂Pav(x)

∂V+

∂Pav(y)

∂V+

∂Pav(z)

∂V(2)

where the suffixes x, y and z indicate time average power dissipated in the corresponding directionsand V is the volume in which the heat is generated.Boundary Conditions [8]

Perfect Electrical Conductor (PEC) boundary condition (n × E = 0) was used for the walls ofthe cavity and Perfect Magnetic Conductor (PMC) boundary condition (n×H = 0) was used forthe symmetry boundaries.

Boundary conditions at the port were taken as follows

Hy = A cos(Πx/α) cos(ωt + βy) (3)Ez = (ωµ0α/Π)A sin(Πx/α) sin(ωt + βy) (4)Hx = (βα/Π)A sin(Πx/α)sin(ωt + βy) (5)

where the x, y and z indicate the corresponding axes and A is the cross sectional area of thewaveguide, ω is the phase angle and α & β are arbitrary constants.Heat Transfer

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For an incompressible food material heated under constant pressure, the thermal energy equationis given by Eq. (14) [9]

ρCp∂T

∂t= ∇ · (K∇T ) + Q (6)

where ρ is the density (kg ·m−3), Cp is the specific heat (kJ · kg−1 ·K−1) and K is the thermalconductivity of the material and T is the absolute temperature in Kelvin.

Different mesh element sizes were used for different sub-domains based on the dielectric prop-erties of the sub-domain and the precision required in the sub-domain of interest.

3. RESULTS AND DISCUSSION

3.1. Measurement and Modelling of Dielectric Properties of GrapesThe moisture content of the grapes tested was found to be 81%w.b., based on the oven dryingmethod. The ε′ and ε′′ values obtained were much closer to that of water. At any given temperatureand frequency, repeatability of the measurements was excellent and the variances calculated amongreplicates were smaller than 0.15.

A linear additive model was used to relate ε′ or ε′′ to temperature and frequency. Its generalform of the relationship is given by Eq. (7). The ε′ for grapes were decreasing with increasingtemperature and frequency (Eq. (8)) whereas the ε′′ decreased with increase in temperature andincreases with increase in frequency (Eq. (9)).

(ε′ or ε′′) = a± b · T ± c · F (7)

where,

T is the temperature in ◦C,F is the frequency in GHz, anda, b, c are the model coefficients

Regression analysis performed on the collected data yielded the following relationships for egg white

ε′ = 79.92− 0.18 · T − 1.75 · F (R2 = 0.965) (P < 0.01) (8)ε′′ = 17.22− 0.11 · T + 2.21 · F (R2 = 0.978) (P < 0.01) (9)

Figure 3 shows the change in dielectric properties with temperature at 2450 MHz and 915MHz.

Figure 3: Change in dielectric properties with temperature at 2450 MHz and 915MHz.

3.2. Finite Element Modelling and Simulation of Microwave Pretreatment for GrapesFigures 4 and 5 show the temperature profiles and thereby the heat distribution inside the grapeberries during microwave pretreatment for 0.5 W/g, 5 W/g and 50 W/g power densities at 2450MHzand 915 MHz respectively.

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(a) (b)

(c)

Figure 4: Temperature profile of a grape berry in 2450 MHz cavity at (a) 50W/g for 5 secs, (b) 5W/g for15 secs and (c) 0.5 W/g for 60 secs.

(a) (b)

(c)

Figure 5: Temperature profile of a grape berry in 915 MHz cavity at (a) 50 W/g for 8 secs, (b) 5W/g for25 secs and (c) 0.5 W/g for 60 secs.

As 65◦C was set as the microwave cutoff temperature, several cycles of microwave heatinghappened in the pretreatment duration of 5 mins and the number of such cycles depended on thepower density applied. Due to these repeated on/off cycles, the heat got dissipated with time andthe temperature distribution was pretty uniform all over the berry in about 2–3 mins, dependingon the power density applied. The figures show the temperature gradient during the first cycle ofheating only. The heating rate was very high while using the power density of 50 W/g. Therefore

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the heating times for the first cycle were only 5 seconds and 3 seconds for 2450MHz and 915 MHzrespectively. Whereas, the maximum time limit of 60 seconds for the first was reached even beforeany part of the berry could reach 65◦C. The heating pattern corroborates very well with thetheoretical explanation given by Yen and Clary [10] for the puffy nature of the microwave driedgrapes and their scanning electron microscopic images of the microwave dried grapes. The energydistribution pattern appears to be the same for both 2450 MHz and 915 MHz. But the heatingrates were higher for 2450 MHz than 915 MHz, which is explained by the dielectric properties atthe corresponding frequencies. Though the heating time was slightly longer, the uniformity wasbetter in 915 MHz than 2450MHz which is indicated by the temperature scale in the Figures 4and 5 (only 2◦C difference between the hottest and the coldest spots for 915MHz as against 7◦Cdifference for 2450 MHz).

4. CONCLUSIONS

The dielectric properties of the grapes varied linearly with respect to temperature (5–80◦C) andfrequency (0.2–10GHz). The linear models developed can be used for further simulation studiesand for designing microwave processing equipments for grapes. The FEM simulations give a de-tailed insight into the temperature profile inside a grape berry subjected to microwave treatment.This also provides a more detailed visualization of the possible reasons for the puffy nature ofthe microwave dried raisins. Grapes can be effectively pretreated at 915MHz in the industrialscale before convective drying, as 915 MHz has its own advantages in industrial applications then2450MHz.

ACKNOWLEDGMENT

The financial support by the Natural Sciences and Engineering Research council and Le FondsQuebecois de la Recherche sur la Nature et les Technologies is gratefully acknowledged.

REFERENCES

1. Dai, J., “Microwave-assisted extraction and synthesis studies and the scale-up study withthe aid of FDTD simulation,” Ph.D. dissertation, Department of Bioresource Engg., McGillUniversity, Canada, 2006.

2. Delisle, G. Y., K. L. Wu, and J. Litva, “Couples finite element and boundary element methodin electromagnetics,” Computer Physics Communications, Vol. 68, 255–278, 1991.

3. Dev, S. R. S., T. Padmini, A. Adedeji, Y. Gariepy, and G. S. V. A. Raghavan, “Comparativestudy on the effect of chemical, microwave, and pulsed electric pretreatments on convectivedrying and quality of raisins,” Drying Technology, Vol. 26, No. 10, 1238–1243. 2008.

4. Dev, S. R. S., G. S. V. Raghavan, and Y. Gariepy, “Dielectric properties of egg components andmicrowave heating for in-shell pasteurization of eggs,” Journal of Food Engineering, Vol. 86,207–214, 2008.

5. Dev, S. R. S., V. Orsat, Y. Gariepy, and G. S. V. Raghavan, “Optimization of microwaveheating of in-shell eggs through modeling and experimental trials,” ASABE AIM, Providence,USA, June 29–July 2, 2008.

6. Tulasidas, T. N., “Combined convective and microwave drying of grapes,” Ph.D. thesis disser-tation, Dept. of Bioresource Engineering, McGill University, Canada, 1994.

7. Tulasidas, T. N., G. S. V. Raghavan, F. van de Voort, and R. Girard, “Dielectric propertiesof grapes and sugar solutions at 2.45 GHz,” Journal of Microwave Power and ElectromagneticEnergy, Vol. 30, No. 2, 117–123. 1995.

8. Fu, W. and A. Metaxas, “Numerical prediction of three-dimensional power density distributionin a multimode cavity,” Journal of Microwave Power and Electromagnetic Energy, Vol. 29,No. 2, 67–75, 1994.

9. Zhou, L., V. M. Puri, R. C. Anantheswaran, and G. Yeh, “Finite element modeling of heatand mass transfer in food materials during microwave heating — Model development andvalidation,” Journal of Food Engineering, Vol. 25, 509–529, 1995.

10. Yen, M. and C. D. Clary, “Why is the grape puff puffy? An analysis of MIVAC temperaturecurves,” Research note, VERC, Cati Publication, 1994.