=Paper=
{{Paper
|id=Vol-3293/paper24
|storemode=property
|title=Coupled Electromagnetic and Heat Transfer Model for Grain Seeds Drying in a Hybrid Dryer
|pdfUrl=https://ceur-ws.org/Vol-3293/paper24.pdf
|volume=Vol-3293
|authors=Petru-Marian Cârlescu,Ioan Țenu,Marius Băetu,Vlad Arsenoaia,Radu Roşca
|dblpUrl=https://dblp.org/rec/conf/haicta/CarlescuTBAR22
}}
==Coupled Electromagnetic and Heat Transfer Model for Grain Seeds Drying in a Hybrid Dryer==
https://ceur-ws.org/Vol-3293/paper24.pdf
Coupled Electromagnetic and Heat Transfer Model for Grain
Seeds Drying in a Hybrid Dryer
Petru-Marian Cârlescu 1, Ioan Țenu 1, Marius Băetu 1, Vlad Arsenoaia 1 and Radu Roșca 1
1
University of Life Sciences, 3 Mihail Sadoveanu Alley, Iași, 700490, Romania
Abstract
A multiphysics model that coupled electric fields and heat transfer was developed to simulate
microwave heating of maize seeds in a dryer. The hybrid dryer with the maize seeds inside was
simulated using COMSOL Multiphysics software. The dryer was equipped with three
magnetrons, with a power of 800 W each, operating at a frequency of 2.45 GHz. These
magnetrons create an electric field that is absorbed by the heating maize seeds. In order to
increase the accuracy of the results, a study regarding the independence of the discretization
grid in the field of the dryer calculation was performed. By the action of the electric field in
the dryer, the temperature in the seed layer is evenly distributed, with a maximum value of
44°C after a period of 9-12 seconds. By losing moisture, the seeds become lighter, being
transported around the top of the seed layer, and are discharged from the dryer every 3-4
seconds when the feed rate of maize seed is 500 kg/h. The spiral movement of the seeds in the
first half of the dryer in the regions where the distribution of the electric field that alternates
from maximum to minimum, makes the temperature of the seeds to be uniform in the whole
volume, achieving a uniform drying.
Keywords 1
hybrid dryer, microwave drying, heat transfer
1. Introduction
Seeds drying is a method of preservation that prevents microbial growth, increasing their shelf life.
Drying is a complex interaction of heat, mass and impulse transport, which requires time and energy
consumption. Different types of drying equipment are currently available, based on combinations of
different drying techniques. This is advantageous since it uses the best of different methods to achieve
more efficient drying [1, 2, 3, 4, 5]. Microwaves have been widely used to dehydrate food and other
materials with humidity [6, 7, 8, 9]. Microwave heating results from volumetric heating and rapid
internal vaporization of liquid water that promotes faster drying. The process does not require long
heating times and therefore results in a significant reduction in drying time (10 to 75%) and increased
drying rates - 4-8 times compared to pure convective drying [10, 11, 12, 13]. Microwave drying
characteristics are different for different sizes and shapes of the same product [14, 15]. The use of
Lambert's law was the norm to qualitatively explain the penetration of microwaves into materials [16].
The temperature distribution of materials of different shapes during microwave heating was
measured experimentally by mapping, and uneven heating was found to occur [17]. In order to address
the unevenness of heating products, two techniques were commonly used: microwave output power
control and power cycle [18]. In this study, for the drying process, a heat transfer model was coupled
with an electromagnetic one into a hybrid dryer, in order to improve the drying uniformity in the seed
layer in a short time.
Proceedings of HAICTA 2022, September 22–25, 2022, Athens, Greece
EMAIL: pcarlescu@uaiasi.ro (A. 1); itenu@uaiasi.ro (A. 2); mbaetu@uaiasi.ro (A. 3); vnarsenoaia@uaiasi.ro (A. 4); rrosca@uaiasi.ro (A. 5)
ORCID: 0000-0003-1039-0412 (A. 1); 0000-0001-5633-522X (A. 2); 0000-0003-4222-2165 (A. 5)
©️ 2022 Copyright for this paper by its authors.
Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
CEUR Workshop Proceedings (CEUR-WS.org)
108
2. Materials and Methods
In this study, a multiphysics simulation of a hybrid dryer was performed using a heat transfer model
and an electromagnetic one. The geometric model of the dryer, the properties of the material, the
equations governing the models, the initial and boundary conditions are briefly described in the
following sections.
2.1. Multiphysics Simulation
2.1.1. Geometry
The geometry of the hybrid dryer, the seed layer to be dried, as well as the positioning of the
waveguides on the dryer must be accurately described, so as not to affect the accuracy of the distribution
of the electric field inside the created cavity. Any protrusion or cavity in the wall of the dryer, as well
as the angles made by the walls can substantially change the distribution of the electric field inside,
Figure 1. The geometric model used in the simulation must be accurate for a more accurate
representation of the electric field distribution and the temperature in the dryer.
Figure 1: Truncated cone geometry of the hybrid dryer. 1 input - wet seeds and warm air; 2 truncated
cone dryer; 3 waveguides with magnetrons; 4 seeds subjected to drying; 5 output -seed dryer.
The dimensions of the hybrid dryer used in the simulation are presented in Table 1.
Table 1
Dimensions of the hybrid dryer
Elements Units (m)
Dryer length 2.5
Large diameter dryer 0.45
Small diameter dryer 0.30
Input size (air-seeds) mixture 0.2x0.1
Output size (air-seeds) mixture 0.2x0.1
In this geometric model the electromagnetic waves generated by the magnetron enter the dryer cavity
through three parallelepipedic waveguides of 2 wavelengths = 244.9 mm (attributing in COMSOL
Multiphysics 5.6 [19] the model TE10), located on the upper generator of the dryer. The frequency of
the microwaves generated by each magnetron was 2.45 GHz and the nominal microwave power was
800 W.
2.1.2. Mesh Size
Solving electromagnetic and heat transfer models required the discretization of the entire dryer in
small volumes. Thus, an appropriate mesh size in the model simulation can provide accurate simulation
109
results, with higher computation efficiency. The space discretization errors could be reduced to a quarter
when mesh size is halved, while the computation time will increase by almost 16 times [20]. To
determine the appropriate mesh size in our model, normalized power absorption (NPA) of the
processing materials has been employed to complete the mesh independent study [21]. Here, the
variation of NPA with mesh sizes is shown in Figure 2.
Figure 2: Normalized power absorption (NPA) variation of heating computations with different mesh
sizes
The manual of software QuickWave (QWED, Warsaw, Poland) suggests the use of 12 cells per
wavelength for mesh independent results, while other researchers [22] suggest that 10 cells per
wavelength would be enough. The mesh size used in this paper is defined as:
𝑐 (1)
𝑚𝑚𝑒𝑠ℎ𝑠𝑖𝑧𝑒 ≤ ,
6𝑓 √𝜀𝑟
where c is the speed of light, f is the frequency, εr is the relative permittivity.
The discretization in the air region of the dryer was based on 8 cells, compared to the region where
the seeds are located where 10 cells were (Figure 3).
Figure 3: The space discretization of dryer geometry. 1 truncated cone dryer; 2 waveguides with
magnetrons; 3 seeds subjected to drying
2.1.3. The Physical Model
The model applied in the microwave-heat transfer coupled simulation was based on the following
hypotheses: the geometry and volume of the seeds do not change during the simulation; the initial
temperature distribution is uniform in the seed; the thermal and dielectric properties of the maize seeds
are temperature dependent; density was considered at the seed (particle) level and does not vary over
time; uniform heat transfer through conduction between seeds; negligible heat transfer between the
walls of the dryer and the air inside the dryer.
The whole simulation combines two physical processes: the microwave propagation process and the
heat transfer in solid.
The electromagnetic waves generated inside the dryer cavity are reflected multiple times by the
metal walls of the dryer, forming models of stationary electromagnetic field in the dryer.
The electric field intensity 𝐸⃗ , a vector quantity, at any point in the calculation range in the dryer was
calculated from Maxwell's equations [23]. The combined waveform of Maxwell's equations is
expressed by the equation:
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2 𝑗𝜎 (2)
∇ × 𝜇𝑟−1 (∇ × 𝐸⃗ ) − (𝜔√𝜀0 𝜇0 ) (𝜀𝑟 𝜀0 − ) 𝐸⃗ = 0,
𝜔
where μr is the relative permeability, ω is the angular frequency, ε0 is the permittivity of vacuum, µ0 is
the permeability of vacuum, εr is the relative permittivity, σ is the electrical conductivity.
Then, the electromagnetic power loss Qe of the processing materials can be obtained from the
computed electric field by the following equation [24, 25]:
1 2 1 2 (3)
𝑄𝑒 = 𝜔𝜀0 𝜀 ′ 𝑡𝑎𝑛𝛿|𝐸⃗ | = 𝜔𝜀0 𝜀 ,, |𝐸⃗ | ,
2 2
where ε0 is the permittivity of vacuum, ε’ is the real part of the relative permittivity, ε’’ is the imaginary
part of the relative permittivity of the processing seeds, tan δ is the loss tangent of the processing
materials.
For the heat transfer process, only the processed materials were taken into account in order to reduce
the computation cost. The governing equation for heat transfer in solid is given as [26, 27, 28]:
𝜕𝑇 (4)
𝜌𝐶𝑝 − 𝑘∇2 𝑇 = 𝑄 = 𝑄𝑒 ,
𝜕𝑡
where ρ is the material density, Cp is the material heat capacity under atmospheric pressure, T is the
temperature, Q is the heat source and k is the thermal conductivity.
2.1.4. Input Parameters and Boundary Conditions
To complete the simulation, property parameters and boundary conditions were needed. The input
parameters are shown in Table 2. The thermal and dielectric properties of the maize seeds are obtained
from related literature [29, 30, 31, 32].
Table 2
Summary of material properties applied in the model
Parameter Value
air relative permeability μr 1
relative permittivity εr 1
electrical conductivity σ (S/m) 0
density ρ (kg/m3) 1.205
thermal conductivity k (W/mK) 2.524 x10-2
heat capacity Cp (J/kgK) 1005
relative permeability μr 1
wall relative permittivity εr 1
electrical conductivity σ (S/m) 5.998x107
relative permeability μr 1
relative permittivity εr 6.25-1.3·j
maize seed electrical conductivity σ (S/m) 0
density ρ (kg/m3) 1250
thermal conductivity k (W/mK) 0.15
heat capacity Cp (J/kgK) 1700
The complex relative permittivity is defined as the processing materials to give a near-actual model,
which is expressed as [33]:
𝜀𝑟 = 𝜀 ′ − 𝜀 ′′ = 𝜀′(1 − 𝑗𝑡𝑎𝑛𝛿), (5)
Other surfaces are all defined as a perfect electric conductor, which can be expressed as the equation:
𝑛⃗ × 𝐸⃗ = 0, (6)
where 𝑛⃗ is the unit normal vector of the corresponding surface.
The dryer wall material was defined as the thermal insulation boundary condition. The governing
equation is given as:
−𝑛⃗ ∙ 𝑞 = 0, (7)
where 𝑞 is the heat flux.
111
2.1.5. Simulation Process
In the simulation, the electromagnetic field distribution was first calculated in the frequency domain,
and then the dissipated power was calculated. Finally, the temperature rise of the material was updated
based on the heat transfer equation in the time domain. Since the electrical properties of seeds do not
vary with temperature, the electromagnetic field distribution will not change and is calculated only
once. The simulation time for the proposed model, for a period of 20 seconds, was about 6 hours with
a workstation with two processors and a 128 Gb RAM memory.
3. Results and Discussion
The simulation results show the temperature distribution in the seed layer at the bottom of the dryer,
and the distribution of the electric field in the dryer. In the hybrid dryer the seeds have reached a
temperature of 30°C due to the warm air that transports them pneumatically. As a result of the action
of the electromagnetic field, the temperature of the seeds increased progressively in volume, reaching
a maximum temperature of 44°C during the simulation of the first 12 s of the process.
According to the experiments performed on this dryer, at a feed rate with maize seeds of 500 kg/h,
and a warm air velocity of 20-25 m/s, the maximum stagnation time of the seeds in the dryer was 20 s.
The seeds were discharged from the dryer periodically, every 3-4 seconds, and their temperature
reached a maximum of 44°C. The simulation shows a maximum temperature in the seed layer of 44 °C
after a period of 9 s and 12 s respectively (Figure 4).
Figure 4: Temperature field [°C] in the seed layer for two periods of time (9 s, 12 s)
112
Due to the small size of the maize seeds compared to the size of the layer formed at the base of the
dryer, virtually all seeds will heat up evenly from inside to outside, depending on the location of the
remaining moisture in the grain. The lighter dried maize seeds, which do not settle to the base of the
dryer, are transported to the top of the layer of the warm air at an average temperature of 44 °C. The
eddy currents formed in the dryer during the pneumatic transport of the maize seeds resulted in a spiral
trajectory in the first half of the dryer, with a tendency to deposit in the second half of it. The spiral
movement of the seeds in the first half of the dryer made them benefit from the electromagnetic waves
that have maximum power in the areas near the walls of the dryer, according to the distribution of the
electric field in Figure 5.
Figure 5: Distribution of the electromagnetic field inside the dryer E (V/m)
4. Conclusions
In this paper, a model was built that combines electromagnetic phenomena with heat transfer for
drying cereal seeds, and a study was performed regarding the independence of the discretization grid in
the field of computing for a good accuracy of the results. By simulating in the COMSOL Multiphysics
software, results were obtained for the distribution of the temperature field in the maize seed layer at
the base of the dryer and of the distribution of the electric field in the hybrid dryer. The results indicated
that under the action of the electric field in the dryer, the maximum temperature in the seed layer was
44 °C after a period of 9-12 seconds. By losing moisture, the seeds become lighter, being transported
around the top of the seed layer, and discharged from the dryer every 3-4 seconds when the feed rate of
maize seed is 500 kg/h. The spiral movement of the seeds in the first half of the dryer in the regions
with maximum power distribution of the electric field lead to an uniform temperature in the seed
volume, thus achieving a uniform drying.
5. Acknowledgements
This work was supported by a grant of the Romanian Ministry of Education and Research, project
number CNCS/CCCDI-UEFISCDI, project number PN-III-P2-2.1-PED-2019-3001, within PNCDI III,
contract no. 378PED/2020. Thanks for all your support.
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