Using Modeling to Select the Type of Microwave Field Emitter for Dense-Layer Grain Dryers

Abstract

The microwave field is used for drying and disinfecting grains during the pre-sowing seed treatment. The use of a microwave field in these installations leads to an increase in their productivity and a decrease in the energy consumed by them. In grain dryers, where the grain moves in a dense layer without being loosened, one of the challenges in using microwave fields is ensuring sufficient uniformity of the field distribution. In this article, waveguide design options that introduce microwave radiation into the grain layer are discussed. The objective of this study was to use application software to find the optimum type of transmitter from the three options presented. A mathematical simulation of the electromagnetic field distribution was performed with the use of CST Microwave Studio software 2019 in order to evaluate and compare horn-type, rectangular, and semicircular waveguides. The data on the standing wave ratio and radiation efficiency of these types of waveguides have been reported. The specific features of the microwave electromagnetic field distribution and radiation power in the output of these waveguides have been described. The results of mathematical simulations revealed that semicircular waveguides with slot-type radiators are preferable for processing dense grain layers.

1. Introduction

Normally, wheat grains are subjected to pre-seeding treatment and disinfection with a moisture content of 14%. In order to ensure grain viability and technological quality, grain-drying equipment has to be applied [1]. The initial water content in grains subjected to drying may vary over a wide range, from 18% to 30%. If wet grains are not dried in a timely manner, they will promote the growth of mold and self-heating of the grain. As a result, they become unsuitable for both food and feed purposes. In terms of technological convenience and price, processing plants with thick grain layers are preferable [2], such as hopper-type units [3,4]. Such processing plants are applicable for grain moisture content not exceeding 16%. Processing grains with higher moisture content requires the application of flow-through grain dryers. Depending on the grain crop under processing and the required production rate, various types of grain dryers can be used, such as vertical silage-type dryers [5], tray-type grain dryers [6], free drop flow grain dryers [7], and table-type grain dryers [8].

It should be noted that grain drying is a rather energy-demanding process that accounts for 80% of aggregate energy consumption. That is why various methods designed to reduce the energy consumed for drying, including the application of infrared radiation [9], ozone-air mixtures as drying agents [10], and processing plants with ultrasonic grain drying effect [11] are applied. Grain dryers with alternating blow-through directions in the grain layer [12] and those with grain recycling are also widely used [13]. One of the environmentally safe grain-drying methods is treatment in convective-microwave processing plants [14,15]. The application of microwaves for processing grains with the purpose of drying, disinfection, and pre-seeding treatment makes it possible to reduce energy consumption and enhance the productivity of the dedicated equipment [16,17,18]. In the course of pre-seeding treatment, there is a possibility to combine the effect of disinfection with that of improving both the viability of seeds and the yield formula [19,20].

The basic element of such processing plants is the so-called active convective-microwave treatment zone, where waveguides and air ducts are installed. Waveguides serve as microwave radiation conductors, whereas air ducts supply drying agents into the convective-microwave zone [21,22].

One of the principal disadvantages of microwave radiation application for grain processing is defined by the dependence of the penetration depth into the grain layer on the dielectric properties of the materials. The higher the moisture content of the grain, the smaller the distance of its penetration into the grain layer, and the greater the share of microwave power absorbed in the surface sublayer adjacent to the radiation source. At the same time, the maximum productivity of the convective-microwave processing plant can be attained under conditions of uniform interaction between the microwave field and grain.

Previously, the authors designed a shaft-type convective-microwave dryer on the basis of a processing unit in which microwave field sources were installed on the opposite sides of the grain processing zone [23,24] (Figure 1).

The unit in the processing plant had the following dimensions 0.3 × 0.2 × 0.2 m, and the volume of the inner space was 0.012 m³. The length of the active zone, i.e., the distance between the waveguide’s output gates, was 0.3 m. The wheat grain weight that could be processed in the convective-microwave zone was 8 kg and 9.1 kg with moisture content of 14% and 25%, respectively.

Small-power magnetrons of 0.9 kW with a radiation frequency of 2.45 GHz are normally used in grain processing units. Radiation is supplied to the microwave-active zone with the help of horn-type antennas. The experimental studies of the grain drying and disinfection processes [25,26] have shown that there is substantial nonuniformity in the electromagnetic microwave field distribution over the grain layer, reducing the efficiency of grain processing. Therefore, there is a need for the development of new design solutions for microwave field introduction into dense grain layers.

The application of rectangular and semicircular waveguides with slot radiators is also regarded as an alternative to horn-type antennas. The use of microwave radiation in grain-processing technology (drying, disinfection, and pre-seeding treatment) has its fundamental peculiarities. These installations cannot be compared to microwave ovens. Each design of microwave grain processing installations typically uses its own radiation-emitting configurations. In the construction of such installations, it is necessary to consider not only the characteristics of the microwave field distribution but also the peculiarities of drying agent delivery to the grain processing zone. For instance, the air can first cool the power blocks and magnetrons before being supplied to the grain layer. In this case, the design of the emitters is of great importance. The choice of emitter configurations can significantly alter and complicate the construction of the entire installation. This paper considers waveguide configurations that are better suited for convective-microwave grain processing installations with a dense layer. They do not have voids unfilled with grains. The application of the considered waveguide configurations entails specific features and designs of air ducts that deliver hot air to the grain layer in each case. Therefore, the proposed waveguide options are intended for convective-microwave grain-drying installations. Mathematical simulations for the microwave field distribution in the output of such waveguides have been carried out with the use of CST Microwave Studio software [27,28] in order to compare the efficiency of such design types.

2. Materials and Methods

2.1. General Provisions

The analysis of efficiency indicators and the microwave electromagnetic field distribution has been performed for three radiator types, namely: a horn radiator (see Figure 2), a 55 × 110 rectangular waveguide with slot-type emitters (see Figure 3), and a semicircle waveguide with slot-type emitters (Figure 4).

2.2. Methods

The finite method was applied for the mathematical simulation. The finite integration technique (FIT) represents a method of spatial discretization designed for the computational solution of electromagnetic field problems in both time and frequency domains. It makes it possible to retain the basic topological properties of continuous equations such as conservation of charge and energy. The main idea of this approach is to apply the Maxwell equations in their integral form to a multilayer grid.

$${\oint }_{\left(\mathsf{\Gamma }\right)}\left(H, dl\right)={\int }_{\left(S\right)}\left(j+\frac{\partial D}{\partial t}\right)dS,$$

(1)

$${\oint }_{\left(\mathsf{\Gamma }\right)}\left(E, dl\right)=-{\int }_{\left(S\right)}\left(\frac{\partial B}{\partial t}\right)dS,$$

(2)

$${\oint }_{\left(S\right)}\left(D, dS\right)={\int }_V\rho dV,$$

(3)

$${\oint }_{\left(S\right)}\left(B, dS\right)=0,$$

(4)

where E is electric field intensity (V/m),

H is magnetic field intensity (A/m),

B is magnetic induction (T),

D is electric induction (Coulomb/m²),

Γ is borderline enclosing a free-form surface (m²),

S is free-form surface (m²),

V is volume (m³),

j is electric current density (A/m³),

l is closed contour (m),

ρ is electric charge density (Coulomb/m³), and

t is time (s).

The major advantages of this method include high flexibility in geometric modeling and boundary processing, and the possibility to involve any material distribution and properties of the material. Additionally, the application of a correlated binary orthogonal grid in combination with an explicit integrating scheme in time yields effective algorithms in terms of the simulation process and storage efficiency.

The essence of the method is based on tiling the computational domain into a finite number of spatial cells. The cells are built so that they completely fit together, and the intersection of two different cells is either a void or a polygon with a one-dimensional edge, or a point shared by both cells (Figure 5).

Such a partitioning scheme yields the final integration grid that is used as the computation array. Therefore, the entire computation domain is composed of a finite number of elementary cells. Variable electromagnetic fields and flows are normally located along the elementary lines or elementary planes. Similarly, intensities directed along other edges of the cell can be calculated. The aggregate magnetic flow through a plane can be determined as the integral of the magnetic flow density through this plane. As a result, electric field densities and magnetic flows of the entire cell complex are represented in a matrix form. The solution of this equation yields the desired variables.

In the process of designing microwave devices with the help of CST Microwave Studio 2019 design, structures in a three-dimensional representation are produced by drawing simplest geometric forms (primitives) and by performing logic (Boolean) operations over them [28]. The effectiveness of radiators was evaluated with the use of the following indicators:

−

Standing wave ratio (SWR) making it possible to evaluate radiator coherence;

−

Radiation efficiency characterizing the share of energy transferred through the waveguide from magnetron;

−

Angular pattern of the microwave field. Radiation directionality diagram is drawn in 3D form, which makes it possible to evaluate uniformity of the electromagnetic field distribution in the radiator output;

−

The radiation pattern of the microwave field along the waveguide is perpendicular to the radiation;

−

Radiated microwave power distribution.

2.3. Features of Electromagnetic Field Transmission by Horn Waveguides

According to the classification, horn antennas belong to the aperture class antennas. They have emitting elements in the form of planar aperture in which angular distribution of the microwave field is achieved. Among advantages of these antennas are a relatively simple and reliable design, convenience of connecting to waveguide transmission lines, rather low energy loss and wide bandwidth [29,30]. Horn antennas are applied in a broad frequency interval ranging from decimeter to millimeter waves. Typical horn antenna design structure is a smooth transition interface between the waveguide’s open end and the radiating surface (aperture). The latter is of large size in order to enhance its radiation directionality and, therefore, to attain better matching between the radiator and the feeder transmission line. The authors used a combination of H-sectorial and pyramidal horns (see Figure 6a,b). The upper plane of the horn has H-sectorial form while the lower one is made in the form of a pyramidal horn (Figure 6c).

This design is adopted to have the ability to control the direction of the electromagnetic field as it propagates through the grain layer. Since the microwave convective processing system is assembled from modules, one of which is depicted in Figure 1, this waveguide construction allows for directional changes based on the module’s position. For instance, when grain enters the upper microwave convective module from the receiving hopper, a downward-directed horn is used. This is done to prevent the microwave field from exiting the system when the grain level in the receiving hopper decreases. In the lower modules of the system, near the discharge hopper, a downward-directed horn is also utilized. This enables the propagation of the electromagnetic field in the lower part of the system.

The opposite direction of the field of the horns in two consecutive zones is used in the lower half of the processing plant, where the moisture content in the processed grain becomes lower and, consequently, the intensity of the microwave field acting on the grain layer can be increased.

The directional gain (DG) of an aperture-type antenna is defined from the following formula [31]:

$$D=\frac{4\pi S}{{\lambda }^2}\gamma ,$$

(5)

where S is the aperture area surface (m²), λ is the radiation wavelength (m), and γ is the aperture efficiency (AE) depending on the field amplitude and phase distribution in the radiator aperture (a.u.).

The maximum value of AE (γ = 1) is attained in conditions of uniform and coherent excitation of the aperture.

In a first approximation, the field amplitude distribution in the horn aperture has a sinusoidal form, in the plane of vector H [32]:

$$\frac{E\left(y\right)}{E_{max}}\approx \sin \left(\frac{\pi y}{B}\right),$$

(6)

where B is aperture area dimension along axis y (m),

E(y) is electromagnetic field intensity along axis y, (V/m), and

E_max is the maximum value of electromagnetic field, in the aperture (V/m).

The phase of the field in the aperture changes in accordance with nearly a square law because of the curvilinear form of the wave edge surface. The change in the direction of the electromagnetic field (and its power) at the output of the horn radiator can be described by a second-order equation. The phase displacement has its maximum Φmax on the borders of the aperture area and is equal to:

$${\mathsf{\Phi }}_{max}\approx \frac{\pi A^2}{4\lambda R}·$$

(7)

For a constant length R of the horn, the aperture area S grows with the aperture size A (Figure 7), resulting in decreasing AE due to the increasing phase nonuniformity.

The gain of a horn antenna reaches its maximum at specific values of the aperture size (phase error at the edge of the aperture). For an N-sector horn, this phase error is 3π/4, and such horns are referred to as optimal [33]. The dimensions of optimal horns are determined by substituting the above-mentioned phase shift values into Equation (7) with the above values of phase displacement on the aperture edge: $A=\sqrt{3\lambda R}$, for an N-sector horn. For a frequency of 2.45 GHz, the wavelength is 122 mm. In the horn design, we adopt R = 80 mm, which is the distance from the point of radiation of the magnetron to the end of the horn. Thus, the aperture size $A=\sqrt{3·122·80}$= 171 mm. However, due to size limitations in the module block construction, where the power supplies and magnetrons are located, A is taken as 88 mm.

In this case, the aperture utilization factor will not be at its maximum. However, it should be noted that the adopted horn aperture design combines H-sectoral and pyramidal horns. Therefore, a more accurate analysis of the electromagnetic field distribution at the horn exit can be obtained through process modeling.

2.4. Features of Electromagnetic Field Transmission by Rectangular Waveguides

The outlay of the waveguide subject to the electromagnetic field distribution studies is shown in Figure 3. In these studies, a magnetron with an operating frequency of 2.45 GHz was selected as the source of microwave energy. The generator wavelength is equal to [34]:

$$\lambda =\frac{c}{f},$$

(8)

where c = 3·10⁸ m/s is speed of light.

For a frequency value of 2.45 GHz, wavelength is

$$\lambda =\frac{3·{10}^8}{2.45·{10}^9}·$$

λ = 0.122 m = 122 mm.

In microwave communication devices, the selection of particular wave types such as, H₁₀, H₀₁ and E₁₁, is essentially important [35]. Contrariwise, the wave type selection is of no importance when the microwave electromagnetic field is used for heating purposes. It is more critical to ensure loss-free transfer of the radiation to the load. That is why the focus was made on multi-wave guides. Additionally, the dielectric strength of the waveguide can be increased, and the energy loss can be reduced by increasing the dimensions of the waveguide in relation to its length [34]. We will consider wave types capable of transferring along rectangular waveguides. In this regard, let us draw a diagram of critical wavelengths for magnetic and electric-type oscillations.

a = 2b,

(9)

Assuming that a and b are dimensions of the larger and the smaller walls of the rectangular waveguide, respectively.

Critical lengths for the magnetic- and electric-type waves are defined by the following relationship [35]:

$${\lambda }_{\mathrm{c}\mathrm{r}}=\frac{2}{\sqrt{{\left(\frac{m}{a}\right)}^2+{\left(\frac{n}{b}\right)}^2}},$$

(10)

where m and n are oscillation-type indexes H_mn (E_mn). For E wave, m ≥ 1, n ≥ 1. For H-wave, one of the two indexes may be equal to zero [20].

Calculating critical waves for various oscillation types was performed with the use of MATLAB software R2020b [36,37,38]. In calculations, it was assumed that a = 1. When drawing the diagram shown in Figure 8, calculated data were multiplied by the value of a.

To ensure the possibility of propagation of all modes in waveguides, the following conditions must be observed [39,40]:

$$\lambda {<\lambda }_{\mathrm{c}\mathrm{r}}·$$

(11)

For waves of H₁₀ type, Equation (7) can be written in the following form:

$$122<2·a.$$

Dimensions of rectangular waveguides stipulated in GOST 51914-2002, for frequencies close to those discussed in this article, are as follows:

Cross-section shall be 110.00 × 55.00 mm and 90.00 × 45.00, respectively, for the frequency ranges from 1.72 GHz to 2.59 GHz and from 2.14 GHz to 3.2 GHz.

Taking into account that, in the processing plant, the microwave field has to be distributed as homogeneously as possible in the grain layer, we assume that the waveguide cross section of 110 × 55 corresponds to this requirement to a greater extent. Therefore, the critical wavelength for this waveguide is ${\lambda }_{\mathrm{c}\mathrm{r}}=2\times 110=220 \mathrm{m}\mathrm{m}$. It means that the selected waveguide dimensions comply with Requirement (11).

2.5. Features of Electromagnetic Field Transmission by Semicircular Waveguides

Selection of a semicircle waveguide is, first of all, defined by the specific technological features of the convective-microwave processing. Technical implementation of this method requires the drying agent supply into the area of material processing. With regard to the design convenience, waveguides with a semicircle cross-section are an optimal choice.

The critical wavelength in a circular waveguide, for type E_mn wave, can be found from the following equation [27]:

$${\lambda }_{\mathrm{c}\mathrm{r}}=\frac{2\pi r}{u_{mn}},$$

(12)

or, in application to type $H_{mn}$ wave:

$${\lambda }_{\mathrm{c}\mathrm{r}}=\frac{2\pi r}{u_{mn}^{\prime }},$$

(13)

where r is waveguide radius,

$u_{mn}^{ }$ are roots of Bessel functions and of their derivatives, for type E wave, and

$u_{mn}^{\prime }$ are roots of Bessel functions and of their derivatives, for type H wave.

Wave types transferred in circular waveguide, depending on its radius, are presented in Figure 9.

In a waveguide with a semicircle cross-section, as well as in a circular waveguide, the critical wavelength, for type H wave, is λ_cr = 3.41 r. For type E wave, λ_cr = 1.64 r. It means that, for an inner radius of 50 mm of the waveguide, the critical wavelength, for type H wave, is λ_cr = 170 mm, while for type E wave, λ_cr = 82 mm. Based on the values of critical wavelengths for a waveguide radius of 50 mm, the propagation of electromagnetic waves of E₁₁ type in such waveguides is problematic. Therefore, mainly waves of type H₁₁ will go through this waveguide.

3. Results

3.1. Studying Microwave Electromagnetic Field Distribution in Horn Antennas

A mathematical simulation of the microwave electromagnetic field distribution process was performed with the use of CST Microwave Studio software. The following parameters were used for the waveguides during the modeling:

For the horn antenna: the cross-section of the rectangular waveguide is 45 × 90 mm; the length of the rectangular waveguide is 104 mm; a short-circuited partition is installed at the end of the rectangular waveguide; the distance from the short-circuited partition to the magnetron output is ½ of the wavelength; the length of the horn is 37 mm; and the dimensions of the horn are 148 × 48 mm.

For the rectangular and semi-circular waveguides: the cross-section of the rectangular waveguide is 55 × 110 mm, and the diameter of the semi-circular waveguide is 110 mm; the length of the waveguides with radiating slots is 400 mm; seven radiating slots with a height equal to the length of the lateral surface and a width of 4 mm are located on the lateral side of the waveguides; the distance between the radiating slots is ½ of the wavelength; the position of the short-circuited partition to the magnetron output is ½ of the wavelength; and the distance from the output of the magnetron to the axis of the first slit is one wavelength.

For all types of radiators, the magnetron output (radiation port) was modeled based on the magnetron’s radiating part’s dimensions.

The outlay of the horn-type waveguide model used in the mathematical simulation process is shown in Figure 6c.

The frequency ranged from 2 GHz to 3 GHz with central points of 2.45 and 2.5 GHz selected for mathematical simulations. Owing to these selections, a number of dependences were deduced, presented in Figure 10a,b. Figure 10a,b show, respectively, the graph for the frequency dependence of the standing wave ratio (SWR) and that of the radiation efficiency, for the selected horn-type waveguide.

Results of the mathematical simulation show that SWR values fall close to 1.3, for the operating radiation frequency of the magnetron, which is a positive indicator providing evidence of sufficient radiator coherence. Radiation efficiency has a maximum in the radiation frequency range of magnetrons, demonstrating an acceptable level of radiator coherence, as well.

In order to evaluate the electromagnetic field spatial distribution, 3D dependencies were calculated. They are presented in Figure 11.

Results of the 3D mathematical simulations show that there exists a substantial nonuniformity of the electromagnetic field density distribution both along the perimeter of the horn aperture area and in the radiation propagation direction.

Therefore, the application of horn-type waveguides ensures rather high values of SWR (1.3) and high radiation efficiency, but the uniformity of the microwave field density distribution must be improved.

Earlier performed experimental studies [24] have shown that energy consumption of the grain drying process, in convective-microwave zones, essentially depends on the drying agent parameters and on the method of its supply into the grain drying area. Energy consumption can be minimized when the directions of microwave field propagation into the grain layer and that of the drying agent coincide with each other [24]. In this case, a certain grade of microwave field distribution uniformity and that of drying agent concentration, in the grain layer, has to be ensured. This condition is hard to fulfill for the design option of the convective-microwave zone with horn-type waveguides. That is why an attempt was made to develop a waveguide design capable of complying with the above conditions.

3.2. Studies of Rectangular Waveguides with Slot Radiators

On the basis of this waveguide, a slot radiator was designed [34,41]. For this purpose, transverse slots were cut in the broad waveguide’s wall. The transverse slot in the broad wall of the waveguide becomes excited by the direct-axis component of the current. On account of the required volume of the section, a radiator length of 400 mm was selected. Slots in the back side of the radiator are spaced 1/2 λ apart (Figure 3).

Radiator parameters were first conformed and then were input into CST Microwave Studio software for mathematical simulation of the electromagnetic field distribution from the radiator’s slots. The results of this simulation are presented in Figure 12 and Figure 13.

Mathematical simulation results show that the application of a rectangular waveguide makes it possible to achieve better homogeneity of the electromagnetic field distribution. Additionally, the rectangular waveguide features SWR equal to 1 and increased radiated power values.

That is why the use of a rectangular 55 × 110 waveguide in convective-microwave zones for processing grain is more preferable.

Apart from the rectangular 55 × 110 waveguide, mathematical simulation of the electromagnetic field distribution was performed for a waveguide with a semicircle cross-section (circular sector) and a slot radiator (Figure 4).

3.3. Studies of Semicircle Waveguide with Slot Radiator

Figure 14 and Figure 15 show mathematical simulation results for microwave field emission conditions in the output of semicircle waveguide with slot radiator.

3.4. Comparison of Radiation Patterns for the Three Types of Emitters Studied

A comparison of the radiation efficiency values for the three types of waveguides under study showed that the semicircular waveguide has the best data. However, the distribution of radiated power shown in Figure 11b, Figure 13b and Figure 15b does not fully allow us to estimate the change in the distribution of the electromagnetic field along the waveguides. Therefore, Figure 16 shows graphs of directional patterns for three types of waveguides.

Figure 16 shows the radiation patterns along the waveguide perpendicular to the radiation. The radiation patterns show that the most uniform distribution of the microwave field is observed in a semicircular waveguide. This allows you to make a choice in its favor.

In order to confirm the authors’ conclusion regarding the comparison of radiation uniformity based on the radiation pattern, further simulations were conducted. The distribution of the microwave field in the wheat grain layer with a moisture content of 14% was modeled. As a result, graphs (Figure 17) of the microwave field absorption along the length (z-coordinate) and height (y-coordinate) of the waveguide were obtained.

The change in the power absorbed by the grain completely corresponds to the change in the radiation amplitude in the radiation patterns.

There is a significant difference in the irregularity of radiation between the three types of emitters. Therefore, it is not necessary to use numerical uniformity indices in this case. The use of homogeneity indices will be more meaningful when the difference between the radiation patterns of the electromagnetic field radiation is smaller.

It should be noted that in the microwave drying of grain, the operating modes of the radiators depend on the grain heating temperature and its current moisture content. The operating modes of the radiators are not constant but vary depending on the results of real-time monitoring of the grain layer’s condition. Therefore, the coordination of waveguides is carried out based on the zone of operation within the setup (depending on the moisture content of the processed grain). The coordination of waveguides is assessed using three indicators: standing wave ratio, radiation efficiency, and uniformity of the microwave field distribution. The evaluation of coordination and “adjustment” of coordination is performed at the stage of modeling the field propagation in the grain. Thus, this work should be carried out in the next stage of modeling.

In this case, it will be necessary to consider the placement of waveguides in the microwave-active zone. The mutual arrangement of waveguides and the microwave-convective zone’s enclosure will influence the modeling results. Once the best result is achieved through modeling, experimental studies can be conducted.

4. Discussion

Results of simulations show that a proper matching between the semicircular waveguide with the slot radiators makes it possible to attain values of SWR = 1, over the entire frequency range from 2 GHz to 3 GHz. The radiation efficiency of the electromagnetic field was 94.28 dB (see Figure 14b) compared to 94.43 dB, for the 55 × 110 rectangular waveguide. With the assumption that the radiation efficiency of semicircular waveguide was due to the absence of type E₁₁ waves, we can conclude that their share is just 0.15 dB, which does not exceed 0.16% of the aggregate power transmitted through the waveguide.

It follows from the simulation results that the radiation efficiency for rectangular waveguides has a more uniform character in a wide range of waves. The radiation efficiency reduction in the range from 2 GHz to 3 GHz does not exceed 10%. In semicircular waveguides, the radiation efficiency changes stepwise, in this frequency range, and has its maximum value at its standard frequency of 2.45 GHz. Therefore, the operation conditions of magnetrons have to be tightly controlled, avoiding operation modes leading to their overheating, when semicircular waveguides are applied.

The overall efficiency of microwave energy transmission is 14.28 dB, for the semicircular waveguide (see Figure 15a), while that of the rectangular waveguide is 14.43 dB (see Figure 13a). At the same time, their radiation directionality features better uniformity compared to the 55 × 110 rectangular waveguides (see Figure 16).

In consideration of the issues discussed above, we may conclude that the application of more easily manufactured semicircular waveguides does not affect indicators of transmission efficiency and those of electromagnetic field distribution uniformity.

5. Conclusions

The characteristics obtained as a result of modeling (standing wave ratio, radiation efficiency and radiated power) for the types of microwave field emitters allowed for their evaluation and formulation of the following conclusions:

Application of horn-type waveguides in convective-microwave processing plants makes it possible to manufacture rather convenient processing equipment for processing grain. In the operating frequency range, their SWR is 1.3, and their radiation efficiency is 78 dB. However, such waveguides do not provide sufficient uniformity of microwave field distribution at their output affecting the efficiency of grain processing.

The use of rectangular 55 × 110 waveguides with a slot radiator makes it possible to ensure a more uniform radiation of electromagnetic field in the entire spectrum of wave types. Their SWR is equal to one, and the radiation efficiency amounts to 94.43 dB. At the same time, their application requires further design development related to the issues of supplying the heat-carrier to the processing area.

Semicircular waveguides with a slot radiator feature SWR equal to one over the frequency range from 2 GHz to 3 GHz. Their radiation efficiency is 94.28 dB. The electromagnetic field distribution homogeneity of such waveguides is better compared to rectangular waveguides. Additionally, the problem of supplying the heat-carrier to the area of grain processing can be solved more easily for circular waveguides.

Based on the above, the authors have given preference to semicircular waveguides. Further research will be conducted with these types of emitters.