Introduction

Plasma sputtering presents an efficient method for acquiring functional coatings [1; 2]. By precisely managing plasma parameters and deposition conditions, it becomes feasible to achieve top-quality coatings [3]. Extensive research exists concerning the examination of how deposition process parameters impact the characteristics of the resultant functional coatings [4–6]. Additionally, plasma spraying serves as a technique for generating powders that find application in additive technologies [7–10].

The finite element method serves as a convenient and precise tool for predicting and elucidating the influence of various factors on both powder production and coating application processes. Computer simulations are in high demand, especially for the investigation of functional coatings composed of high-entropy alloys like GdTbDyHoSc and GdTbDyHoY [11]. studies related to coating deposition [12–14], software packages such as ANSYS, SolidWorks, and JmarPro were employed. For simulating the powder production processes using the plasma method, researchers utilized ANSYS [15], FLOW-3D [16] and COMSOL [17].

The trajectories of particles within a plasma flow significantly affects the characteristics of coatings and the properties of the resulting powders. Conversely, it is also influenced by the particle size of the raw powder material. Additionally, among the contributing factors, the shape of the internal channel, which is defined by the components of the plasma head and the operational features of the facility, plays a pivotal role. While there are publications that discuss the impact of factors like nozzle shape [18], operating modes [19], powder material introduction methods [20], interelectrode inserts [21] and gas swirler shapes [22], insufficient attention has been given to exploring the effect of powder particle size on particle motion trajectories within the plasma flow.

The primary objective of this study was to investigate how three particle sizes (1, 50 and 100 µm) of titanium powder, used as raw material, influence the trajectories of particles within a vertically directed plasma flow.

Experimental

A computer model of the plasma facility was developed to predict plasma flow parameters, employing the finite element method. The SolidWorks Flow Simulation software package (version 2016) served as a valuable tool for computational fluid dynamics (CFD). Subsequently, the results of the computer experiment underwent verification. In the numerical solution process, the Euler and Navier-Stokes equations were employed. In order to accurately represent surface, subsurface, and intermediate processes occurring within the flow, a finite element grid size of 0.24 mm was chosen. This grid size ensured that a minimum of 8 elements were positioned within the narrowest section of the three-dimensional computer model of the plasmatron, specifically, the plasma-forming gas inlet channel of the swirler with a diameter of 2 mm [23].

In order to carry out a computer experiment, a three-dimensional model was created based on the MAK-10 laboratory facility, which is located at the premises of IMET, Ural Branch, Russian Academy of Sciences. The design and parameters of this facility are depicted in Figгure 1.

The initial data for the computer experiment are as follows:

• plasma forming gas flow rate: 20 l/min;

• gas type: argon;

• gas pressure in the supplying system: 2 atm;

• diameter of the central hole of swirlers: 24 mm;

• plasma-forming gas is supplied in a tangential pattern through 6 channels, each with a diameter of 2 mm;

• the chosen raw material is titanium powder VT1-0, selected from the library of standard materials within the software package (State Standard GOST 19807-91) with the following composition (wt. %, not exceeding): N – 0.04, C – 0.07, H – 0.01, Fe – 0.25, Ni – 0.04, Si – 0.1, O – 0.2).

The environmental conditions are set as follows:

• gas type: air;

• absolute gas pressure at the outlet of the anode unit is 98,100 Pa, equivalent to the altitude of Yekaterinburg;

• temperature corresponds to room temperature, at 293 K.

The study focused on particle motion trajectories within the plasma flow for particle sizes of 1, 50 and 100 μm. The mass flow rate for each fraction was set at 1 g/s.

An indirect-acting plasmatron was employed with the following specifications:

• voltage: 26 V;

• current: 250 A;

• spraying direction: vertically, directed upwards;

• reactor length: 2.8 m;

• diameters of respective segments: 250 and 500 mm.

Results and discussion

In Figure 2 the trajectories of 100 particles for each of the three fractions are depicted. It’s important to note that the particle sizes in the figure do not correspond to scale and have been chosen arbitrarily for illustration purposes. We assumed that the temperature at which titanium powder begins to glow and produce bright sparks is above 1573 K. This determination was based on reference data regarding the colors of heated titanium (bright red – 900 °C, yellow – 1200 °C, white – 1300 °C) [24]. Through computer simulation, several key findings were obtained, including the dimensions of the torch containing the luminous powder fraction with temperatures exceeding 1573 K, as well as the maximum distance covered by powder particles within the flow.

The obtained data is presented below:

As observed, there is a negative correlation between particle size and the length of the luminous fraction, as well as the distance particles are carried by the flow away from the plasma torch’s end. Conversely, the width and opening angle of the plasma flow torch increase with larger particle sizes. This phenomenon can be attributed to the influence of gravity acting upon powder particles entrained by the plasma flow. Notably, smaller powder particles tend to follow longer flight paths within the flow, resulting in greater distances from the plasma head.

In order to validate the outcomes of the computer experiment, two full-scale experiments were conducted. The first experiment aimed to compare the width and length of the torch containing luminous particles of PTM-1 titanium powder, which was sprayed using a laboratory facility (TU 14-22-57-92). In terms of chemical composition, PTM-1 corresponds closely to the titanium powder VT1-0 employed in the computer experiment (wt. %, not exceeding: N – 0.08, C – 0.05, H – 0.35, Fe + Ni – 0.4, Si – 0.1, Ca – 0.05, Cl – 0.004). The second full-scale experiment was designed to determine the temperature of the plasma flow during the plasma torch’s idle mode (without powder particle spraying). This measurement aimed to assess the correspondence of this value to the one determined through the computer experiment.

Each of the full-scale experiments was conducted in five separate runs to ensure robust and reliable measurement results. In order to enhance the accuracy and credibility of the measurements, we applied statistical processing using scatter plots and the calculation of their average values [25–27].

In the first full-scale experiment, a granulometric analysis of PTM-1 titanium powder was conducted using CAMSIZER-XT (Germany). The data obtained revealed that 90 % of the powder had a size of less than 91 μm, while 50 % had a size of less than 50 μm. Furthermore, 98.1 % of the powder material exhibited a sphericity coefficient exceeding 0.9 (the ratio of the smallest particle size or diameter to the largest), and 90.9 % of the studied powder displayed sphericity coefficients exceeding 0.9. The particle size range of PTM-1 titanium powder fell within the range of 1–97 µm. Figure 3 presents a visual representation of the data from both full-scale and computer experiments.

In the first full-scale experiment, the initial conditions were as follows:

• plasma-forming gas flow rate: 20 l/min;

• gas type: argon; purity 99.993 % (complying with State Standard 10157-2016);

• gas pressure in the supplying system: 2 atm;

• diameter of the central hole of the swirlers: 24 mm;

• plasma-forming gas was introduced in a tangential pattern through 6 channels, each with a 2 mm diameter.

The environmental conditions were set as follows:

• gas type: air;

• absolute gas pressure at the outlet of the anode unit: 98,100 Pa, equivalent to the altitude of Yekaterinburg;

• temperature was maintained at room temperature – 293 K.

The study focused on analyzing the motion trajectories of particles within the plasma flow, encompassing particle sizes ranging from 1 to 97 μm. The mass flow rate for each fraction was set at 1 g/s. An indirect-acting plasmatron was employed, with the following specifications:

• voltage: 26 V;

• current: 250 A;

• spraying direction: vertical, directed upwards;

• reactor length: 2.8 m;

• diameters of respective segments: 250 and 500 mm.

During the experiment, measurements were taken for the length and width of the luminous fraction of titanium powder, which amounted to 600 mm and 65 mm, respectively. As a result, the deviation from the results of the computer experiment did not exceed 7.7 %.

In the second full-scale experiment, conducted during the idle mode of the plasmatron (without the use of powder), the temperature of the plasma flow on its axis was studied. To achieve this, a method involving the placement of rods with known melting temperatures within the plasma flow was employed. Specifically, 3 rods with a 3 mm diameter, composed of copper M1 (compliant with State Standard GOST 859-2014), steel 10 (in accordance with State Standard GOST 1050-2013) and lanthanized tungsten (as per Specifications TU 48-19-27-88) were selected. These materials were chosen for their varying melting points. The rods were fixed in a manner where one end was securely clamped, and the other end was left free to be exposed to the plasma flow. The head of the plasmatron was mounted on a manipulator, which enabled its uniform movement along the axis toward the rod at a speed of 10 mm per minute. The distance between the free end of the rod and the end plane of the anode of the plasmatron’s head unit was meticulously recorded throughout the experiment. The initial distance between the free end of the rod and the plasma torch’s head was assumed to be 0.5 m. When the melting process commenced on the rod’s surface, the distance from the rod to the plasma torch was recorded.

In order to determine the temperature of the rod’s surface at the point of melting onset, an optical pyrometer (EOP-66, Type No. 240, compliant with GOST 5.278) was employed. This pyrometer is specifically designed for accurately estimating the brightness temperatures of heated objects through their thermal radiation, covering a range from 900 to 10,000 °C. The measurement error does not exceed 5 °С.

In the second full-scale experiment, the initial conditions were as follows:

• plasma-forming gas flow rate: 20 l/min;

• gas type: argon; purity 99.993 % (complying with State Standard 10157-2016);

• gas pressure in the supplying system: 2 atm;

• diameter of the central hole of the swirlers: 24 mm;

• plasma-forming gas was introduced in a tangential pattern through 6 channels, each with a 2 mm diameter.

The environmental conditions for this experiment were as follows:

• gas type: air;

• absolute gas pressure at the outlet of the anode unit: 98,100 Pa, equivalent to the altitude of Yekaterinburg;

• temperature was maintained at room temperature – 293 K.

For this experiment, an indirect-acting plasmatron with the following specifications: was utilized:

• voltage: 26 V;

• current: 250 A;

• spraying direction: vertical, directed upwards;

• reactor length: 2.8 m;

• diameters of respective segments: 250 and 500 mm.

The data derived from the second full-scale experiment indicated that the onset of melting for each of the rods occurred at temperatures closely aligned with the reference data for each rod material, with a slight deviation of no more than 22 K. A comprehensive account of this experiment can be found in [28] and the results are visually presented in Figure 4 and detailed in the accompanying Table.

Thus, the comparative analysis of the computer and field experiments demonstrated a satisfactory level of agreement, with the discrepancy not exceeding 5 %.

Conclusions

A comparative analysis of the motion trajectories of titanium powder particles of varying sizes in a vertically directed plasma flow has been successfully conducted. The study revealed that the size of powder particles significantly influences various parameters, including the dimensions of the luminous fraction, the opening angle of the plasma torch, and the distance of particles carried by the plasma flow from the plasma head. These findings are of great significance for processes involving coating and powder production.

Furthermore, the development of a computer model describing a laboratory plasma facility for applying functional coatings and producing powder materials represents a valuable contribution. This model can be employed to predict outcomes in powder production processes. Additionally, it enables the determination of optimal reactor (powder receiving chamber) dimensions and shapes, with the dual goal of reducing internal volume and mitigating issues such as molten particles adhering to chamber surfaces. This optimization is essential for minimizing the material consumption of process equipment, reducing facility dimensions, and cutting operational costs, especially when inert gases are used to fill the receiving chamber. A well-designed chamber shape not only lowers the unit cost of produced powder but also prevents contamination of internal reactor surfaces.

In the context of vertically upward plasma flow, the influence of gravity leads to a natural separation of sprayed powder into different fractions. Finer particles exhibit a larger scatter radius, while coarser ones are concentrated closer to the plasma jet’s axis. This phenomenon can be harnessed for the selective collection of powdered material. As part of the chamber’s design improvement, the proposal to introduce additional internal walls for particle deposition based on size is an innovative approach.

Overall, the use of gravity’s effect in vertically directed spray patterns serves as an additional tool for segregating the produced powder material.

These study results hold particular utility in the application of functional coatings, aiding in the optimal positioning of the substrate on which they are applied. The computer model offers the capability to predict plasma flow torch characteristics, such as the opening angle and width, in relation to the distance from the plasmatron. This information is invaluable for estimating the coating area, determining the number of required passes of the plasma torch for surface coverage and considering particle temperatures. Moreover, it assists in defining the optimal substrate-to-plasma head distance and inclination.

The choice of directing the atomization process vertically upwards, taking advantage of the natural tendency of heat to rise due to the pressure difference in heated gases, offers several advantages over directing the plasma flow vertically downwards. In this configuration, the heat flow from the plasma is directed toward the substrate positioned above the plasma source. This setup minimizes the risk of overheating and potential damage to the plasma equipment’s components, reducing the likelihood of plasma source failure. Additionally, when the plasma flow is directed upwards, the substrate receives more effective heating.

These recommendations have practical significance for both consumers and developers of technological equipment used in coating processes and powder production. By employing a computer model, it becomes feasible to anticipate process outcomes and make adjustments by manipulating influencing factors.

Furthermore, the results of the computer experiment were validated through a full-scale experiment and the comparative analysis of their findings demonstrated a satisfactory level of agreement.