Numerical and Experimental Analysis of the Vacuum Corn Seed Degassing System

Abstract

Vacuum degassing of seeds is a basic preliminary stage of the treatment process to improve the viability of seeds of various crops. In this work, the degassing process of corn seeds was experimentally and numerically analyzed by removing air or other gases from around the seeds, specifically from the seed coating, in a rough vacuum chamber. Two complementary variants were employed to understand and optimize this process to improve the quality and germination rate of the seeds. The average germination percentage on the first day was about 98%, and the germination speed of 5.0 days. Several experiments were conducted with well-established durations of 10 min and masses of 5 kg and masses of corn seeds at different temperatures to observe and record the behavior of the system, facilitating the modeling of the degasification process in the vacuum compartment. Modeling the degasification operation in the vacuum chamber allowed for determining the pressure profiles on the vacuum chamber and its lid. Numerical simulations were either conducted using a simulation program developed in the Visual Basic Applications (VBA) language for Microsoft Excel to model the degassing process in the vacuum chamber or with the assistance of specialized software (transient structural analysis and simulation program in the ANSYS Workbench environment). Statistical analysis of the correlation between experimental and estimated pressure values revealed that both the proposed mathematical model and the solution method are well-chosen, with differences expressed through the absolute error (EA) being very small, only 1.425 mbar. Structural dynamic analysis carried through the Finite Element Method (FEM) highlights that the chosen materials for manufacturing the vacuum chamber vessel (316 stainless steel—yield strength 225 MPa and tangent modulus 2091 MPa) or the chamber lid (transparent acrylic plastic—yield strength 62.35 MPa and shear modulus 1445.3 MPa) are durable and capable of withstanding the desired pressure and temperature demands in the seed treatment process. Additionally, through structural dynamic analysis, it was possible to study the deformation of system components, providing a detailed perspective on their structural distribution. Thus, the paper aims to improve the quality and survival/germination rate of corn seeds as an important step to improve corn yield through simulations and analyses (numerical and experimental) of the vacuum corn seed degassing system. The degassing process of the vacuum chamber was simulated with a simulation program developed for Microsoft Excel for Microsoft 365 MSO (Version 2401 Build 16.0.17231.20236) 64-bit in the VBA language and software (transient structural dynamic analysis in the ANSYS environment through FEM). Vacuum degassing of corn seeds involves the removal of air or other gases around the seeds or products, which is crucial in various fields such as the food, pharmaceutical, or space technology industries.

1. Introduction

Treating seeds in vacuum chambers is a procedure used to boost the quality and germination rate of seeds. This method involves exposing the seeds to an environment with reduced pressure for the complete elimination of air around them in a special chamber called a vacuum chamber [1,2,3] for the following reasons:

• By removing the air (degassing) around the seeds, oxidation and decomposition are prevented, contributing to their long-term preservation;
• Seeds become more permeable, allowing them to absorb treatment evenly and more efficiently, facilitating the subsequent absorption of water and nutrients necessary for germination [4,5,6,7];
• The vacuum environment can help destroy and eliminate harmful microorganisms or reduce the number of pathogens and pests that may be present on the surface of the seeds, potentially affecting germination and plant health [3,8];
• Vacuum treatment can activate certain enzymes in seeds, accelerating the biochemical processes necessary for germination [9,10,11,12,13];
• By using vacuum treatment, the required quantity of treatment substances can be minimized, reducing waste and potential environmental impact [14,15].

The retention of essential elements in the seed is appropriately regulated and sheltered by physical and chemical barriers facing external biotic factors. This nutrient package is indispensable for germination, leading to the development and replication of plants [4,5].

The vacuum treatment process can vary depending on the plant species and treatment objectives. Generally, seeds are placed in a special vacuum chamber where atmospheric pressure is reduced or eliminated [16]; this can be achieved through a vacuum system or by evacuating the air from a sealed chamber. Physical treatments are challenging to implement as there is a delicate balance between effectively eradicating seed-transmitted diseases and causing harm to the seeds [14,17]. Not all seed batches react the same way to all treatments, making it difficult to predict how physical treatments will affect seed germination and vigor [5,7,8,16,18]. Chemical treatments that do not have phytotoxic effects on seeds are available, but methods for complete internal penetration have not been identified [14,17].

Treating seeds in vacuum chambers is commonly used in agricultural and horticultural settings to improve seed quality and germination rates, leading to enhanced crop yields and plant health [6,11,13,18]. However, it is crucial to ensure that seed treatment is carried out with appropriate equipment and under controlled conditions to avoid seed damage or the onset of undesirable negative effects. Seed treatment practices must always adhere to safety and environmental regulations.

In a complete vacuum, the temperature of the air cannot be measured in the usual sense, as a vacuum represents a space devoid of matter, including air particles [19]. Temperature is a measure of the average kinetic energy of molecules in a system. The absence of particles in a vacuum makes it impossible to measure the usual temperature of air, as there are no particles to generate thermal motion or interact with a thermometer. There are only concepts related to radiation and radiant temperature, which are different from the air temperature encountered under normal conditions [18].

On the other hand, in a vacuum system, there are primarily three sources of gas, known as the gas load, namely [20], residual gas in the system, vapors in equilibrium with the present materials, gases produced or introduced by leaks (also, “virtual leaks” of captured gas without penetration through the walls), degassing (adsorption), permeability (gas transfer through a solid, through porous materials, glass, etc.).

Therefore, in this work, vacuum pressure testing was performed through dynamic Finite Element Method (FEM) analysis of the system designed for treating corn seeds. The FEM analysis is crucial to understanding and optimizing the degassing process of corn seeds because it offers the possibility that seed treatment is carried out with appropriate equipment and under controlled conditions to avoid seed damage or the onset of undesirable negative effects. Thus, the degassing process of corn seeds was experimentally and numerically analyzed by removing air or other gases from around the seeds, specifically from the seed coating, in a vacuum chamber.

The mathematical modeling of the seed degassing process in vacuum chambers is of particular importance in acquiring information about the processes or treatment systems. Numerical analysis represents a valuable experience that demonstrates how mathematical concepts are useful in aiding our quest for a better understanding of the physical world. The goal was to understand and optimize the process, as well as to improve the quality and germination rate of the seeds [10,11,12,13].

This was achieved by modeling the degassing process in the vacuum chamber using specialized software (transient structural analysis and numerical simulation program in the ANSYS Workbench environment developed in the Visual Basic Applications language). ANSYS—Workbench 2022 R2 is a software platform that combines basic solving capabilities with a set of product management tools for the effective handling of elements and data.

Our study brings a valuable contribution to the field of modeling the degassing process in the vacuum chamber by addressing new aspects or issues or by improving existing methods and techniques. The practical relevance may lie in the development of more precise and efficient degassing techniques, optimizing the design and operations of vacuum chambers, or improving the quality of products obtained through the degassing process.

Experimental analysis and numerical simulations of the degassing process of seeds in a vacuum chamber are complementary methods used to understand and optimize this process. Degassing involves removing air or other gases from around seeds or products, which is crucial in various fields such as the food industry, pharmaceuticals, or space technology.

Simulations can aid in visualizing gas flows around the seeds and provide detailed information about the time needed to achieve a certain degree of degassing, pressure distribution, temperature, etc. Using simulations, virtual tests can be conducted to optimize the vacuum chamber’s geometry or evaluate different degassing strategies, thus reducing costs and time required for real experiments.

Both experimental analysis and numerical simulations contribute to a deeper and more comprehensive understanding of the seed degassing process in a vacuum chamber. The obtained results can be used to enhance the process and make informed decisions in designing and optimizing degassing systems.

2. Materials and Methods

For experimental analysis, the seeds are first cleaned and sorted to remove any debris, damaged seeds, or foreign materials. They are then placed inside the vacuum chamber in a way that ensures uniform distribution and avoids overcrowding. The chamber is sealed, and a vacuum with low pressure is created, aiding in the removal of air bubbles and ensuring consistent treatment for all seeds. While the seeds are in the vacuum, various substances or treatments that promote growth or beneficial microorganisms can be applied. After the treatment is complete, the chamber is filled again with ordinary atmospheric air by releasing the vacuum.

The experimental analysis was conducted in a setup whose schematic is presented in Figure 1a–d, illustrating the porous structure of corn seeds, allowing the observation, and recording of seed behavior under vacuum conditions.

The seeds were deposited in the container of the vacuum compartment, and then the pressure inside it was gradually reduced until it reached the desired vacuum pressure using the vacuum system (see Figure 1). Subsequently, various parameters were monitored, such as the degassing rate, the quantity of gases eliminated, and changes in the volume of the seeds, etc.

The experimental results can deliver useful knowledge about the efficiency of the degassing process, the time required to achieve a certain degree of degassing, and other relevant aspects. On the other hand, numerical simulations can be conducted using specialized software, with programs for structural analysis and Computational Fluid Dynamics (CFD) for fluid dynamics analysis.

For the experimental analysis, 5 experiments were performed, each lasting 10 min, using a mass of 5 kg of corn seeds at different temperatures (27.7, 20.3, 14.2, 8.5, and 4.8 °C) to observe and record the system’s behavior.

To perform a numerical simulation, data about the vacuum chamber geometry, material characteristics of the seeds and gases, as well as initial and boundary conditions, are required.

Analysis of mechanical elements or assemblies through the Finite Element Method (FEM) primarily unfolds in three distinct stages, as shown in Figure 2 [21,22,23].

• Pre-processing—the model was defined (by building a mathematical model applied to a 3D geometric element created with SolidWorks 2022 CAD software and divided into smaller bodies) to be analyzed, along with the ambient environmental factors applied to it;
• Analysis and solving constitutive mathematical equations (performed on computers with high computing power Ultrabook Acer 14″ Swift SF314-51, FHD IPS, (Processor Intel^® Core™ i7-6500U 3.10 GHz, 8GB DDR4, 1TB SSD, GMA HD 520);
• Post-processing of results (using powerful graphic visualization devices Intel Iris Xe, the simulation results were analyzed and interpreted, as well as identifying issues in the studied structure.

The 3D geometric modeling of the vacuum seed treatment system was designed in SolidWorks 2022, while the structural analysis was performed using the ANSYS—Workbench software [24], which is capable of solving with a set of product management tools and combining them for effective handling of elements and data.

The design and construction of the vacuum chamber took into consideration three main components: (1) their arrangement, (2) the vacuum structure, and (3) the heat exchange system. The thermal transfer (heat exchange) system is represented by an electric resistance of 155 W, a type K thermocouple for temperature measurement, and a bi-positional control system (thermostat), as can be seen in Figure 3a (in the bottom right corner). In this work, the first two components will be described and analyzed. The vacuum space was constructed and manufactured to meet the following requirements:

➢

Provide the necessary conditions to achieve specific processing conditions for cereal seeds (such as removing dust particles before applying a thin layer of fungicides, insecticides, and bactericides and evaporating water from the material for conditioning);

➢

Be capable of maintaining elevated and cold temperatures for an extended period;

➢

Produce a vacuum environment that encompasses pressures from atmospheric down to 100 Pa at a minimum;

➢

Have an interior size of at least 20 L.

To achieve a higher level of vacuum (i.e., lower pressures), special systems and pumps are used to evacuate more gas from the system. The lower the pressure, the fewer gaseous particles the space contains, which is crucial in many scientific and technological applications.

Thus, the vacuum chamber was fabricated from one-piece cast 316 stainless steel, which is highly durable and capable of withstanding temperatures as low as −70 °C, with the chamber’s lid made of acrylic Plexiglas. This material was chosen for being ordinarily applied in the manufacturing of thermal vacuum containers due to its high resistance [9]. The material for the chamber vessel has the following characteristics: density of 7.985 × 10⁻⁶ kg/mm³, Poisson’s coefficient of 0.25, Young’s modulus of 1.95 × 10⁵ MPa, stiffness of 1.3 × 10⁵ MPa, shear strength of 76,923 MPa. The lid material has the following properties: density of 1.185 × 10⁻⁶ kg/mm³, Poisson’s coefficient of 0.3952, elastic modulus of 3225 MPa, stiffness of 5182.9 MPa, shear strength of 1167.9 MPa.

The vacuum chamber has a cylindrical vessel structure with dimensions specified in

Table 1. Technical specifications of the vacuum chamber.

Maximum rated vacuum	482.6 mmHg at sea level	Maximum operating temperature	70 °C
Volume	20 L	Lid dimensions (diameter × thickness)	240 × 15 mm
Length of steel wire hose	1250 mm	Dimensions of the vacuum chamber (diameter × height × thickness)	240 × 40 × 3 mm

Notes: The choice/selection of materials with the dimensions and specifications in this table was made to ensure the durability and performance of the system, considering their mechanical properties (tensile strength and deformation, hardness, rigidity, thermal and chemical properties, availability, machinability, even and the cost, and other requirements application specific). These specifications have been optimized and validated through FEM analysis that allows the system components’ structural behavior to be evaluated under different operating conditions and loads, confirming whether the chosen material meets the performance requirements and identifying any problems or critical areas.

(outer diameter of 240 mm, height of 240 mm, and wall thickness of 3 mm). Based on structural analysis using FEM, the 3 mm thickness of the vessel wall ensured the required constructive integrity for the vessel. The end plate of the chamber not only exhibits high strength and impact resistance but also provides sufficient visibility to observe the interior state. The thick and transparent lid, made of acrylic material with a thickness of 15 mm, is equipped with a silicone ring for effective sealing [7]. Figure 3 illustrates the physical system created for this study, and the technical specifications of the vacuum chamber and lid are presented in Table 1.

To obtain the required vacuum pressure inside the vessel, a low-pressure pump was employed. The vacuum pump is a rotary vane mechanical pump (Value, 2020) with a maximum rotation speed of 1440 rpm, a power of 200 W, and a flow rate of 42 L/min at 220 V/50 Hz. The pump has the necessary capabilities for high vacuum, is equipped with a built-in manometer to measure rough vacuum, and can reach pressures in the range from atmospheric pressure to 20 Pa. To quantify medium and high vacuum pressures inside the vessel, a portable Testo 552 device was implemented, as shown in Figure 4.

The checking of the qualitative improvement and the germination rate of corn seeds after vacuum treatment was performed in a specialized laboratory. A rectangular tub with the dimensions of 2 × 1.5 m, the germinal bed, was prepared with a loose depth of fertile soil (shredded on the surface, no weeds, with a large reserve of water, preferred by corn for grains), a known number of corn grains were sown at a certain distance at room temperature (around 20 °C), after being treated in the vacuum chamber. By viewing every day, the degree of germination was followed, and after the fifth day from sowing, the grains germinated, and by counting, the degree of germination in percentages and the speed of germination were estimated.

Then, the modeling of the degasification process in the vacuum chamber considers two aspects, namely:

(a)

Finite element mathematical modeling

The developed mathematical model applies to dynamic systems with a finite number of degrees of freedom through the analytical formulation of structure dynamics with added damping. The analytical model of this formulation (the matrix differential equation of vibrational motion) is the one from classical dynamic analysis. In this context, loads or loading conditions vary over time and are applied instantaneously. Dynamic loads involve oscillating weights, impacts, collisions, and unpredictable amounts, and therefore, this case is supposed to involve [25]:

➢

Transient dynamic evaluation is employed to calculate the feedback of a structure to external loads that fluctuate unpredictably over the period.

• In dynamic analysis, the matrix equations for force equilibrium are applied to a dynamic system [25,26]:

  -

  For a structure without foreign load:

  $$\left[M\right]\times \left[\ddot{X}\right(t\left)\right] + \left[C\right]\times \left[\dot{X}\right(\mathrm{t}\left)\right] + \left[K\right]\times \left[X\right(t\left)\right] = 0$$

  (1)

  -

  For a system with an external load:

  $$\left[M\right]·\left[\ddot{X}\right(t\left)\right] + \left[C\right]·\left[\dot{X}\right(t\left)\right] + \left[K\right]·\left[X\right(t\left)\right] = \left[F\right(t\left)\right]$$

  (2)

where M—mass; $\ddot{X}$—acceleration; C—Rayleigh damping; $\dot{X}$—velocity; K—stiffness; X—displacement; and F—load (all variables are in matrical form), t—time.

By solving the Equations (1) and (2), we can obtain the natural frequencies of a structure. The types of loads used in a static analysis are the same as those of a dynamic. The expected results from the software include natural frequencies, displacements, deformations, and stresses. All these outcomes can also be acquired in the total deformation, where δ_t is a scalar quantity, and:

$${\delta }_t=\sqrt{{\delta }_x^2+{\delta }_y^2+{\delta }_z^2},$$

(3)

where δ_x,y,z—the components of deformation along coordinate axes can be obtained in either global or local coordinates.

The associated differential equation has the form [15]:

$$M^{+}·\ddot{X}\left(\mathrm{t}\right)+C^{+}·\dot{X}\left(\mathrm{t}\right)+K^{+}·X\left(t\right)=F^{+}\left(t\right),$$

(4)

in which the matrices and vectors are specific to the dynamic model with added mass (M⁺) connected to the primary system through elastic connections (stiffness coefficient K⁺), damping connections (damping coefficient C⁺), and F⁺—appropriate load.

(b)

Numerical modeling

Here, an approach to mathematical modeling established on the utilization of computational instruments for numerical simulations is presented [27]. The process involves transitioning from problem formulation and equation establishment to the implementation of computational algorithms and analysis of results.

The factors depicted beyond an evaluation of the pumping time should fundamentally differ for evacuating a vessel in the rough vacuum region compared to evacuating in the regions of medium and high vacuum.

In the case of gas evacuation of a vessel in gross vacuum mode (excluding supplementary quantities of gas or vapor), the effective pumping speed, s_ef of the pump–vacuum chamber assembly, depends only on the required pressure, p (after time t), on the volume, V of the chamber and the pumping time, t.

Accompanied by an invariable pumping speed, s_ef and supposing that the maximum pressure reached, p_f (the final/desired pressure) by the chosen pump model, is such that p_f << p, the pressure drop over time, p(t) in a vessel of vacuum is provided by the differential equation of the first order [2]:

$$-\frac{dp}{dt}=\frac{s_{ef}}{V}·p, \mathrm{or} \frac{dp}{p}=-\frac{s_{ef}}{V}dt,$$

(5)

which by integration, considering that the pressure varies from the initial pressure, p₀ = 1003 mbar at the time t = 0 to a minimum value, p (after the time, t), then the effective pumping speed, s_ef could be estimated as a function of the pumping time, t from Equation/relation (5) as follows:

$${\int }_{1003}^p\frac{dp}{p}=-\frac{s_{ef}}{V}·t=>ln\frac{1003}{p}=-\frac{s_{ef}}{V}·t,$$

(6)

where from result:

$$s_{ef}=\frac{V}{t}·ln\frac{1003}{p}.$$

(7)

Noting $ln\frac{1003}{p}=\sigma$—the dimensionless pressure factor and substituting in Equation/relation (7), we obtain that the association amongst the effective speed, s_ef and the pumping duration, t, becomes:

$$s_{ef}=\frac{V}{t }·\sigma .$$

(8)

The ratio (V/s_ef) = τ is commonly defined as a time-invariant. Consequently, the pumping duration, t, of a vacuum vessel from atmospheric load to a value of pressure p, will be:

$$t=\tau ·\sigma$$

(9)

The dependency of the σ parameter on the wished-for pressure is presented in Figure 5. It must be mentioned that the pumping speed of ordinary pumps drops less than 10 mbar with gas ballast and less than 1 mbar without gas heft. This elementary attitude varies for pumps of different capacities, but it is recommended not to be overlooked in determining the pumping time relying on the pump size. It is emphasized that Equations (6)–(9) and also Figure 5 apply only when the final pressure reached alongside the pump applied is several orders of amplitude lower than the wanted pressure.

The nomogram in Figure 5 (obtained based on Equations (5) and (8)) provides a method for selecting the value of the dimensionless factor required for calculating the effective gas pumping rate [20]. This is much smaller compared to the effective pumping speed needed to maintain the desired final pressure and depends mostly on the gas load and leak rates.

In the gross vacuum regime, the capacity of the chamber is determined for the duration engaged in the pumping routine. In the high and ultrahigh vacuum areas, the release of gases from the walls (of the corn seeds and the vessel) exhibits a significant function; in the medium vacuum region, the evacuating process is affected by both quantities. Additionally, in the medium vacuum zone, especially in the situation of rotary pumps, the maximum pressure that can be reached is not insignificant.

3. Results and Discussion

3.1. Analytical and Numerical Modeling

If the amount of gas accessing the chamber is established to be Q (in mbar·L/s) from the gas release from the seed enclosures, the chamber, and the leaks, the differential Equation (5) for the pumping operation changes into [2]:

$$\frac{dp}{dt}=-\frac{s_{ef}\left(p-p_f\right)-Q}{V},$$

(10)

and through the integration of this Equation (11), we obtain:

$$t=\frac{V}{s_{ef}}ln\frac{\left(p_0-p_f\right)-Q/s_{ef}}{\left(p-p_f\right)-Q/s_{ef}}.$$

(11)

Unlike Equation/relation (7), Equation/relation (11) does not allow for a definition of the solution for the effective pumping velocity, s_ef; therefore, the s_ef for a well-known gas release cannot be obtained derived from the pressure drop curve over time without additional knowledge, Figure 6. It is mentioned that the method used to ensure the accuracy of the simulation program in predicting pressure variations over time was “Mesh and model refinement”.

Therefore, in usage, the strategy will necessitate a pump with enough upward pumping speed, calculated from Equation/relation (7) as an outcome of the volume of the gas-free chamber and the wanted pumping duration. Instead, the ratio Q/s_ef between the gas release velocity and this pumping speed is established. This ratio must be less than the needed pressure; for protection, it should be approximately ten times smaller. If the corresponding situation is not met, a pump with a comparable elevated pumping speed must be selected. In a situation where the pumping process is dominated by residual gas, pumping in a high vacuum region can be described by the relation [2]:

$$p=p_0·exp\left[-\frac{\left(s_{ef}/V_t\right)}{t}\right],$$

(12)

where V_t—is the total volume of the system.

However, by far, the most significant uncertainty associated with pump performance, pressure, flow, and external leaks is due to gas release. Gas release rates can differ by several orders of amplitude, according to the component of a surface, its external intervention, humidity, temperature, and the exposure duration to vacuum. As it usually approaches asymptotically to the final pressure of a system, even small changes in gas loads result in significant differences in evacuation times (see Figure 6). Vacuum analysis, which aided in selecting a roughing pump, relied solely on the relationship between pressure and the time to reach this pressure, assuming the following relevant hypotheses for such an analysis: the system has no leaks, the pump is 100% productive, and nothing will vaporize in the vacuum vessels.

The calculation application was developed using Microsoft Excel, but any equivalent software to Microsoft Office 365 that includes a spreadsheet with similar features to Excel can be used, making the adaptation of the application relatively easy. The choice of an Excel spreadsheet to simulate the variation of the vacuum system pressure over time is due to its capability to perform numerical description (in a table), applying symbolic statements as thoroughly as visual description using tables constructed for this purpose. The skill to activate and explore numerical, symbolic, and visual descriptions dynamically makes the spreadsheet an essential instrument for promoting conceptualization and algebraic reflection [27]. Excel uses the VBA (Visual Basic for Applications) language, which is now widely used. It should be emphasized that VBA is a complex programming language. With its help, data can be manipulated, complex tasks automated, interactions with other Office applications can be performed, and much more [28,29].

Using a spreadsheet, we can generate the graph of the precedent response (12) that reveals the relationship between the initial time, t, and the gas load pressure in the vacuum chamber, p(t), Figure 7. At the aforementioned, it is also feasible to see the so-called state curves, which represent the parametric error (quantified in the paragraphs below) of estimation based on experimental data at each moment of the system’s operation.

Since the particular solution (12) is a function that depends on parameters, s_ef (pumping speed in steady-state), V (volume of the vacuum chamber), and implicitly by σ (the dimensionless pressure factor), as well as the initial pressure of the gas load, p₀, at the initial moment t₀ = 0, it can be seen how the graphic elements are constructed that can be interactively modified using sliders for the constructive parameters of the chamber, diameter, D and height, H, Figure 7. The design of the spreadsheet itself is indispensable to the development of the calculation section.

It should be emphasized that VBA is a complex programming language. With its help, data can be manipulated, complex tasks automated, interactions with other Office applications performed, and much more [29,30]. Consequently, the relevant VBA editor was used and adapted accordingly for processing and analyzing the results obtained from the simulation. The interface of the “Vacuum Chamber Pressure Variation Simulation.xls” program on the “Pressure” page is presented in Figure 8.

Figure 8 represents the main interface of the program created in Excel and the graphic interface of the seed degassing process simulation program with the GUI user and allows a person to communicate with the program through the use of symbols and visual metaphors with indications. Additionally, to significantly increase the level of understanding, a screenshot of a portion of the “Data Processing” page has been introduced.

In the figure, it is important to note that the values in the cells for D, H, s_ef, and V of the vacuum chamber, as well as the dimensionless parameter of pressure, σ, can also be controlled by components called scrollbars. The same is valid for the variables for the initial conditions t₀ and p₀. To identify the real or correct values, the absolute error (EA) was calculated. The real values were considered to be the mean values of the data resulting from multiple measurements in physical experiments with corn seeds. The measured average real value for the gas load pressure in the vacuum chamber was 44.273 mbar.

The procedure for measuring the real value of the gas load involves turning on the vacuum pump (see Figure 1a) and simultaneously following the indications of the manometer incorporated in the pump body and the portable device (see Figure 4, also visible in Figure 3) implemented in the vacuum chamber, through its lid (see Figure 1a). Finally, on the display of the system data logger, gas pressure and temp (see Figure 1a) are followed by the real measured average value of the gas load.

The graph of the data obtained from measurements for the pressure variation over time is presented in Figure 9a. The estimated values of pressure over time for three different values of σ (dimensionless pressure factor), σ = 23.73; 27.05; 32.18, were calculated using the mathematical model adopted in the simulation program, and the data can be observed in Figure 9b. The average values of the estimated pressures for each of the three data sets of his σ were 51.031, 45.920, and 40.140 mbar, respectively, and the estimated average value for all three data sets was 45.698 mbar. For each measurement, the following formula is applied to obtain EA:

EA = |Estimated value − Real value|

(13)

The variation of EA for the three sets of estimated pressure data with the created simulation program is presented in Figure 9c. The trend of the error variation is similar for the three curves shown, with a peak at the moment t = 0.33 s. The highest peak value of 132.472 mbar was recorded in the dataset with σ = 23.73, while the lowest peak value of 21.269 mbar was encountered in the curve with σ = 32.18, and for σ = 27.05, the peak had a value of 85.035 mbar.

It is observed for all three curves that after approximately 2 min, the error value significantly decreases, reaching a steady-state value of about 5.161 mbar, which indicates that the system has reached equilibrium and is operating consistently at this pressure level without significant fluctuations.

Then, if there are multiple measurements, errors can be summed to obtain the total EA, or the average of absolute errors can be calculated by dividing the sum of absolute errors by the number of measurements. The calculation of the average EA for the estimated pressure with the simulation model was performed using the relation:

Average:

EA = (EA₁ + EA₂ + EA₃)/3 = (6.758 + 1.651 + 4.133)/3 = 1.425 mbar.

(14)

Therefore, the calculated values of EA and their analysis showed that a very small value justifies the correlation between the results obtained by simulation and the real ones. Usually, to conclude, multiple measurements are needed, then the total EA (by summing partial EAs) or the average EAs (as an arithmetic average), and based on the obtained values, the calculation efficiency of the simulation program can be evaluated, and optimizations can be made to improve the system performance. All this implies a comprehensive approach aimed at improving the time of execution, the use of system resources, calculation algorithms, and data management.

3.2. Finite Element Procedure

For the structural dynamic analysis of the vacuum system under certain loads, the Finite Element Method (FEM) was used, considering the capabilities of the vessel made of stainless steel 316 and the lid made of acrylic plastic. The materials selection/choice for vessel and lid considered the consideration of several factors (mechanical properties, corrosion resistance, mass and density, and thermal conductivity, including performance requirements, working environment, costs, durability, etc.) that may significantly influence the performance and structural behavior of the structure of the material, including the results obtained in FEM analysis. The dynamic analysis process is carried out in the subsequent stage.

➢

The first stage is the selection of the material and some details. Several materials can be checked under vacuum pressure; however, the most regular categories used are metals, plastics, and their composites [23]. The ANSYS material library provided characteristic values for the materials of the chamber and the lid, as mentioned above, while the temperature and other experimental conditions are detailed below.

➢

The second step involves creating the 3D geometry of both the chamber vessel and the lid in the Solid Works 2022 program (Figure 10) according to the dimensions (Table 1) of the experimental physical model (Figure 5).

Modeling the contact-type connections between the vessel and the lid was automatically achieved through the Augmented Lagrange method for solving the nonlinear model of frictionless contacts (Figure 11a). The discretization was performed automatically with default parameters for both the vacuum chamber and the chamber lid. Using the adaptive meshing method, a total of 10,546 nodes and 4572 elements resulted (8968 nodes and 4363 elements for the vessel; 1578 nodes and 209 elements for the lid). Modeling the constraints was performed by fixing the lower edge of the cylindrical vessel. Modeling the loading with variable vacuum pressure over time (the request is for a time-varying pressure lower than/below atmospheric pressure), normally applied to the surface, according to the relationship, was also performed [31]:

p = 101,325·exp(−0.023·t) + 40 [Pa],

(15)

The application of the load (due to variable vacuum pressure over time) was achieved by selecting the interior surfaces of the vessel and the lid (Figure 11b). The setting of the unit system was conducted by choosing the metric system (mm, kg, N, s, mV, mA, radians, rad/s, degrees Celsius).

The solution of the physical nonlinear model (without friction) in an average time of 2.45 min was performed on an Acer Swift 3 laptop with an Intel CORE I7 6500U processor at a frequency of 2.5 GHz, using 0.31 GB of the available 8 GB RAM. The information is available in the resolution statistical report, presented below.

The convergence graphs of force and displacement for the solution of the nonlinear problem are visualized in Figure 12 and Figure 13.

The image presented in Figure 14 illustrates the maximum deformation occurring at the bottom of the chamber as well as the deformation of the lid due to pressure. The maximum deformation of 0.009 mm was observed in the middle part of the lid and decreased radially towards the exterior. On the bottom of the vessel, we find deformations almost halved in order of magnitude, of about 0.004–0.005 mm, with the same decreasing radial distribution.

In addition,

Table 2. The total deformations produced by the vacuum pressure with the help of ANSYS simulations.

Time [s]	Minimum [mm]	Maximum [mm]	Average [mm]
10	0	4.51 × 10−1	2.82 × 10−2
20		0.35917	2.24 × 10−2
30		0.28578	1.78 × 10−2
40		0.22737	1.42 × 10−2
50		0.18093	1.13 × 10−2
…		…	…
550		1.57 × 10−3	1.03 × 10−4
560		1.57 × 10−3	1.03 × 10−4
570		1.57 × 10−3	1.03 × 10−4
580		1.57 × 10−3	1.03 × 10−4
590		1.57 × 10−3	1.03 × 10−4
600		1.57 × 10−3	1.03 × 10−4

summarizes the sample deformation values obtained by structural dynamic analysis depending on the pressure in the vacuum chamber of the test experiment by simulations.

To correlate the deformations observed in the chamber and cover with the pressure applied over time, it is necessary to compare the deformation and pressure profiles over time and identify the discrepancies or similarities between them, which are to be investigated later after an experimental analysis to identify possible errors or model inconsistencies. However, the theoretical or numerical analysis offers us a more detailed perspective and deeper understanding of the relationship between deformations and pressure. At the same time, these simulations can provide a structural behavior prediction under different conditions and can identify critical areas where deformations or stresses are higher.

As the pressure stresses the walls of the vacuum chamber, von Mises internal stresses occur in them due to the loading (compressive forces). According to Hooke’s law, within the elastic limit, stress is directly proportional to deformation, and here, the induced effort in the material of the walls and lid is the reaction to the applied compressive force [7]. The observed values of von Mises stresses are presented both in tabular and graphical form. Figure 15a shows the stress distribution in the walls of the vacuum chamber and lid, with a maximum value in the central area of the vessel bottom due to stress concentration. Figure 15b depicts the variation of equivalent stresses over time, considering elastic loading, and the results are presented in

Table 3. The equivalent of von Mises stresses as a function of time.

Time [s]	Minimum [MPa]	Maximum [MPa]	Average [MPa]
10	0.55818	63.982	9.9335
20	0.4394	50.826	7.8945
30	0.34646	40.381	6.2738
40	0.27352	32.094	4.9861
50	0.21614	25.52	3.9634
…	…	…	…
550	3.28 × 10−4	0.23396	3.12 × 10−2
560	3.25 × 10−4	0.23391	3.12 × 10−2
570	3.22 × 10−4	0.23387	3.12 × 10−2
580	3.20 × 10−4	0.23384	3.12 × 10−2
590	3.19 × 10−4	0.23381	3.12 × 10−2
600	3.17 × 10−4	0.23379	3.12 × 10−2

, obtained using structural dynamic analysis.

Following the analysis of the obtained results, as a result of modeling and post-processing, the following highlights emerge:

• In the deformation process of the subassembly elements due to the action of vacuum pressure (Figure 15b), increased displacements are observed (max. 0.001569 mm) in the central area of the vessel bottom and (max. 0.000869 mm) in the central area of the lid.
• The equivalent von Mises stress has increased values (max 63.92 MPa) in the body of the vessel in the middle area of the lower part, while on the lid, the values are insignificant.
• From the analysis of the maximum stress, the main compression load on the chamber body is highlighted, with a maximum value of 74.242 MPa in the connection area from the outside, and the tensile stress is reduced in the contact area with the body of the lid.
• The radial normal stresses, especially compression, have reduced values (52.643 MPa) in the joining area of the vertical wall of the vessel with the lower end portion.
• Increased values (21.434 MPa) of tangential (circumferential) stresses are highlighted in the body of the chamber in the area with the maximum diameter of its bottom, along with a significantly reduced tensile stress in the body of the lid.
• The total maximum value of the system energy over time was 617.65 mJ, with a predominance of 617 mJ in deformation energy and only 2.0225 × 10⁻⁶ mJ in kinetic energy. A small deviation was acquired, demonstrating the validity of the conducted virtual experiment. The energy stored in bodies due to deformation is calculated from stress and strain results and includes the plastic strain energy as a result of material plasticity.
• It is specified that energy distribution analysis helps detect anomalies and problems in system operation. Unexpected variations in energy distribution may indicate equipment malfunctions, energy losses, or other issues that require investigation and remediation.

The significantly reduced values of the structural error field (max 2.4669 mJ) obtained for the chamber body indicate that the stress values are appropriate and close to the real ones. Additionally, Figure 15 highlights the rapid convergence (79 steps—see also Table 3) of the solution algorithm, and the computation time is reduced (an average of approximately 16.7 min cumulatively).

Therefore, there are real and practical perspectives of the findings on the design and operation of vacuum chambers in seed treatment processes and their potential in other applications, namely:

-

Optimization of the seed treatment process: Using the vacuum chamber in the seed treatment process can offer multiple benefits, such as improving treatment uniformity and reducing processing time. Energy distribution analysis over time can provide a deeper understanding of how energy is distributed and used inside the vacuum chamber, helping to optimize process parameters such as temperature, pressure, and treatment duration to achieve desired results.

-

Ensuring product quality: Using the vacuum chamber in the seed treatment process can contribute to improving the quality and yield of crops. Uniform energy distribution during treatment can ensure proper coverage of seeds with treatment substances, thereby reducing the risk of contamination and ensuring healthy and uniform plant growth. Thus, in laboratory conditions, it was proven that after five days from the sowing of corn seeds treated in a vacuum, the average germination percentage on the first day was about 98%, and, therefore, the germination speed of 5.0 days.

-

Extending applications to other fields: The principles and technologies used in vacuum chambers for seed treatment can be adapted and extended to other fields and applications. For example, vacuum chambers can be used in heat treatment processes, sterilization, food preservation, pharmaceutical production, chemical processes, and many others, where precise control of process parameters and uniform energy distribution are essential for achieving desired results.

4. Conclusions

The existing technological variants for seed treatment are generally directed towards a combined method of priming followed by vacuum infiltration to facilitate the deep penetration of antibiotics or other substances into the seeds. The application of the degassing method before seed infiltration may capture the interest of farmers eager to reduce the use of chemical fungicides, thus ensuring maximum penetration into the seeds to eradicate diseases that occur deep within the seed. In this way, any type of seed can be treated, from most vegetable crops to ornamental plants and agronomic crops.

The numerical and experimental analyses conducted are considered vital for testing material strength under various stresses. In this study, vacuum pressure testing was performed through dynamic Finite Element Method (FEM) analysis of the system designed for corn seed treatment. The equipment and specimens were designed according to ASTM D256 standards. All simulation tests were conducted on the following materials: stainless steel 319 for the chamber vessel and acrylic Plexiglas for the vacuum chamber lid.

The structural dynamic analysis accomplished using FEM highlights that the maximum deformation was found at the center of the lid, in order of about 0.004–0.009 mm, and almost zero at the support handle due to the fixation on the frame. For stress analysis, the outcomes express that the effort is maximum at the junction of the lower end of the vessel with the vertical wall, in the range of 63.920–74.242 MPa.

As a result of solving the nonlinear FEM model, adopting the convergence method for force and displacement, results with increased accuracy were obtained. The values of the obtained parameters (displacements, stresses, structural error) are useful for optimizing the shape and dimensions of the lid.

Statistical analysis of the correlation between experimental and estimated pressure values highlighted that both the proposed mathematical model and the used method are well-chosen, with differences expressed through absolute error (EA) being very small, of only 1.425 mbar.

Further research aims to analyze the experimental and numerical dynamics of the heating and cooling system in the degassing process of seeds in the vacuum chamber. Modal and harmonic analysis will be conducted to determine the natural frequency and mode shape of a structure, respectively, as well as the structure’s response to variable harmonic loads over time.