Simulation of the effect of evaporation and gas composition during plasma spheroidization of titanium particles

: A 3D model was proposed that describes the in-flight behavior of titanium particles in the plasma environment, developed in the commercial CFD Ansys Fluent software, which described the heating of particles. The rate of evaporation was investigated based on the gas compositions, and the mass evaporated on the surface of the particle along the trajectory under plasma conditions. To evaluate the spheroidization rate of titanium particles, the calculated temperature and flow histories were established. Significant heat exchange behaviors are presented due to the variations in hydrogen content and feed rate. The simulation results have demonstrated that the range of 0-4% of H 2 and at a low injection feed rate of 3-10 g/min minimized the evaporation rate and increased the spheroidization rate of particles.


Introduction
The spheroidization of fine powders in thermal plasma processes has been recently increasing in various parts of the industries such as additive manufacturing, powder metallurgy, and other sectors. Irregular particles are injected into the plasma medium to undergo high heat transfer where particles quickly melt and or evaporate. This heat treatment creates a high temperature that causes particles, especially of small size to easily evaporate contrary to large particles that have difficulty completely melting and spheroidized due to insufficient heat transfer from the plasma gas to the injected particles. Although the interaction between particles and the plasma gas is not fully understood because of the short time that this reaction occurs. Different authors have put their efforts to study such effects through experimental and computational approaches to minimize the effect of evaporation and improve the heat transfer rate during their trajectories. The results presented in previous studies showed that researchers have used different assumptions, as for computational analysis different transport equations as well as approximations to resolve the issue of the low rate of spheroidization.
To improve the spheroidization ratio of particles in the plasma medium, an attempt to increase the heat transfer rate is necessary to be established for most particles with large size through adjustment of feed rate and the gas compositions to increase high enthalpy and thermal conductivity [1] in the system. Studies have shown that argon gas alone in the sheath does not efficiently generate heat transfer [2]. Particles throughout their trajectories do not undergo the same heat transfer to completely melt and spheroidized. The regulation of the reaction gas is most important because that allows the plasma temperature to propagate smoothly in the plasma region of the torch for the particles to receive enough energy during the trajectories.
In an investigation of the effect of hydrogen gas on spheroidization of molybdenum granules by Z. Hao [3], they found that the ratio of the spherical particle had increased with the addition of more content of hydrogen to argon, and this favored mostly small particle size. Also, this increment improves the heat exchange between the plasma and particles. The consequence attached to more hydrogen content in the sheath gas, its conductivity increases the plasma temperature to allow particles to melt but increases the evaporation rate. Qi Shi [4] on the other hand investigated the effect of helium gas in the preparation of Nickeltitanium in plasma spheroidization, it was found that He conductivity improved the efficiency of the produced particle to be spherical and smooth. By comparing these two gases, hydrogen has higher thermal conductivity than helium, and more content creates excessive evaporation. Another simulation work done in [5] that titanium particles ranging from 20-100 µm were treated in the mixture of Ar-H2, and their investigations revealed that the evaporation had affected mostly particles with small size in the range of the plasma temperature of 10,000 K. It is evident to say that at this temperature, particles will eventually evaporate which will further result in the poor collection of treated powder. The simulation approach to this effect [6] reveals that the composition of the mixture in the sheath gas creates extreme energy transfer that particles are heated up above their boiling point temperature, which becomes a negative impact on the spheroidization of irregular particles. The study of such effect requires optimization of boundary conditions to favor to spheroidization by melting particles within different size distribution to reduce the evaporation rate of material regardless of their initial feed rate.
We will attempt to investigate this case through numerical simulation using CFD Ansys fluent software. And this work aims to investigate the effect of evaporation and gas composition on the plasma temperature during the trajectory of particles in the numerical approach to the spheroidization process. The study is structured as follows: first, the definition of the model and the assumptions, secondly, at a power input of 10 kW, we evaluated the plasma temperature history for Ar-H2, and Ar-He, respectively. And lastly, we studied the effect of the content of these additional gas on argon and different feed rate of particles on the spheroidization of titanium materials. Figure 1 represents the model used in this study taken from [7] composed of the ICP torch and the reaction chamber, which is used in the Plasma Technology laboratory at The South African Nuclear Energy Corporation SOC Ltd, South Africa. The detail of the model is described in Table 1. The plasma model has been used for many decades for the treatment of irregular solids, and the mathematical model using the CFD has mostly improved for such a process. Boulos [8] is so far recognized as the first in implementing the CFD method and it is improved in recent times. In this current model, there is no induction of magnetic fields, the energy is generated by the source term instead for the simplicity of the model.

Assumptions
In this numerical study, the following assumptions were attributed to the model: (i) The oscillation caused by the magnetic fields is neglected, the heat transfer is generated using a

Governing equations
The governing equations that are used to simulate titanium in the spheroidization process include the drag and gravity forces that are employed in the Lagrangian frame as the equation of motion of the particle. The heat transfer was calculated for individual particles using the heat of convection including the heat loss due to radiation heat transfer. The equations (1(3) are solved using the PISO algorithm. In addition to this, we considered the melting and evaporation processes of the particles. The equations that involved these processes are presented as follows: The mass Continuity equation demonstrates the variation of the density and is denoted as: where ρ is the density of the fluid, v ⃗ is the velocity filed and S are and all additional source terms.
The momentum conservation equation is given as: where, μ, is the thermal conductivity of fluid and F ⃗ are the forces applied to the particles. The energy conservation equation is defined as: where H is the enthalpy, C P is the specific heat of the fluid at a constant temperature, and S h are the heat of chemical reaction and any other additional source term defined in the model.
The equation of motion of the particle is described as: where F D , is the drag force, u and u P are the gas and particle velocity, g is the gravitational force, ρ and ρ P are the density of the gas and particle respectively. The heat balance between the particle and plasma gas that combination of the heat convection and radiation is calculated as follows: where, Q net is the net energy required to transfer to the particle through convection and radiation, T P is the temperature of the particle, A is the surface area of the particle, T ∞ is the temperature of the plasma, T a is the ambient temperature, h is the heat transfer coefficient of 370, 02004 (2022) https://doi.org/10.1051/matecconf/202237002004 MATEC Web of Conferences 2022 RAPDASA-RobMech-PRASA-CoSAAMI Conference the particle surface, ε is the emissivity of the particle, σ s is Stefan-Boltzmann constant. The Nusselt number [9] correlation is used to find the heat transfer coefficient as follows: where Nu, is the Nusselt number, d p is the particle diameter, k is the thermal conductivity of the particle, Re is the Reynolds number, and Pr is the Prandtl number. Nu is approximated in terms of the Reynolds and Prandtl number, but in this case, since the carrier gas and the feed injection velocities are assumed to be the same, the relative velocity is zero and which will maintain the Nusselt number at 2 along the process.
The rate of evaporation is given as the ratio of the net heat required to heat a particle with the latent heat of vaporization, which describes the mass loss on the surface of the particle throughout its trajectory.

̇=
where ṁv is the evaporation rate, and L v is the latent heat of vaporization.

Boundary conditions
The numerical simulation was subjected to the following equations applied to the computational domain as displayed in Figure 1. Equations (9(11) are used for the carrier, central, and sheath gas inlets respectively, and equation (12) is applied at the exit of the chamber. The initial temperature of the material and gases and the wall temperature for both the plasma torch and the chamber were adjusted to 300 K.

Numerical conditions
To study the evaporation and gas composition effects in this work, some evaluations were considered: (1) the plasma temperature history due to the addition of hydrogen and helium gas content in a separate case, and set the same boundary condition, to analyze which composition can improve spheroidization ratio and alter the effect of particle evaporation [10], and the particle temperature along their trajectories following the percentage content of gas ranged from 0-4% that will advantage the particle to melt efficiently. For this numerical calculation, the input power was set to 10 kW in the volumetric source term for all conditions at 1 atm pressure. The flow rate in the sheath gas was set separately at 40 slpm for Argon and 370, 02004 (2022) https://doi.org/10.1051/matecconf/202237002004 MATEC Web of Conferences 2022 RAPDASA-RobMech-PRASA-CoSAAMI Conference 4 slpm for either hydrogen or helium gas. Titanium with its physical properties displayed in Table 2 was subjected to analytical calculations.

Results and discussion
The results presented here were performed on Ar-H2 and Ar-He flows in the plasma spheroidization process using a source term to generate the heat transfer in the plasma medium. In the following sections, we will present numerical results and analyze the effect of additional gas content in the reaction gas on particle temperature, followed by the evaporation rate based on the compositions and feed rate on the spheroidization rate of titanium.

The effect of additional gas on plasma temperature
The plasma temperature determines the heat transfer propagation within the torch and the downside of the chamber. It is important to analyze through simulation the rate of spheroidization of titanium. In this section, we have defined particle size as 40 µm with the numerical conditions listed in Table 2. As it can be seen that the temperature contours in Figure 2, describe three simulation cases ran at an unsteady state and at the same time steps, displays the difference in heat exchange distribution that involves additional gas into argon in reaction gas, as observed that Ar-H2 (see Figure 2b) presents higher plasma temperature of 6590 K than Ar-He 6573 K (see Figure 2c) which makes 0.3% difference. The rise in plasma temperature in the case of the argon reacting with hydrogen gas was due to its high thermal conductivity compared to helium, which may result in a high degree of spheroidization than when argon reacts with any other gas [11]. Considering the plasma propagation alongside the torch, the temperature fields presented in Figure 2a display a small zone where the plasma temperature has dissipated compared to Ar-H2 and Ar-He. Therefore, the additional gases gave effective energy transfer, that enable particles to undergo a smooth process [12].  hydrogen, and (c) 25% helium gas respectively in the sheath gas flow, for 40 µm titanium particles flowing at 10 g/min, using 10 kW input power. Figure 3 shows the particle temperature throughout their trajectories, the three solid lines represent three volume percentages of hydrogen gas numerically calculated that particles have experienced during a 1.1 m traveling distance. In this figure, it is observed that the rise in particle temperature was proportional to the volume percentage of hydrogen such as that at condition 0 vol% the particle temperature reached 3462.81 K, at 2 vol% 3542.42 K, and lastly at 4 vol% equal to 3841.42 K. The difference in the temperature has indicated that particles can be spheroidized, with an increase of the rate from 50-85% as shown in Figure  4. And this described the ability of hydrogen gas to improve the rate of spheroidization [13].  Figure 4: Effect of hydrogen content on spheroidization of titanium particle. Figure 5 shows the relationship of the particle temperatures along their axial displacement and describes the decrease of particle temperature with the increase in particle feed rate from 3 to 10 g/min in the plasma torch. It is observed that at 6 g/min there is a decrease of 19.8% and 38.6 % at 10 g/min of the particle temperature. This is explained by the fact that particles injected at a high rate present a short residence time in the plasma environment to absorb heat from the plasma and diffuse some particles from the plasma environment. Thus the spheroidization rate as shown in Figure 6 to decrease from 75% to 60.2% which may result in poor melting and spheroidization processes [14]. The interaction of particles becomes denser when the feed rate increases; this reduces the energy exchange phenomenon, which reduces the plasma temperature to affect the particle temperature [5].

Effect of evaporation rate on heat transfer
The evaporation rate presented below was calculated using equations (5) and (8), and the data is in Error! Reference source not found.. These evaporation rates are observed from 0.07586 m in the torch as the particle temperature starts to rise ( Figure 5) and increases rapidly inside the plasma torch due to high plasma temperature. The decrease is observed at the exit of the torch, this shows that particles can be efficiently heated throughout their displacement along the plasma torch, and this affects the evaporation phenomenon. In Figure 7, we have presented three cases of 0-4 vol% of hydrogen content. The simulation results presented practically the same evaporation rate, and a slow decrease towards the reactor. The high flow of hydrogen in the sheath gas increases the heat transfer consequently creating massive evaporation due to hydrogen enthalpy. Figure 8 shows the rate of evaporation as a function of axial distance.
Three cases of feed rates ranging from 3-10 g/min were analyzed. As seen in Figure 5, the injection rate does influence the temperature history along the trajectory [15]. As observed titanium particles are rapidly evaporated after being injected into the plasma environment at a low rate, contrary to the high feed rate. Particles at a low injection rate have   Three sizes of titanium ranging from 20-40 µm were chosen, which has demonstrated that particles of larger size drop the plasma temperature by absorbing more energy compared to the smaller size during their trajectories as displayed in Figure 9, which led to a rise in evaporation rate as seen in Figure 10, which displays the evaporation rate of these particles treated at the constant condition of feed rate and power input, it is observed that the evaporation rate decreases with the decrease in size, that particle with small size can evaporate earlier in the plasma torch than the larger particles that require more time to gain enough energy from the plasma gas to evaporate. It showed that particles with 40 µm have a   The spheroidization rate has demonstrated a positive impact on particle size. In Figure  11, the spheroidization rate is 90.63% for 20 µm, while it decreases to 63.89% to 40 µm, for the spheroidization of small particles is improved by the rising temperature and low evaporation rate. Particles with a size less than 40 µm can be completely spheroidized. Therefore, the initial size of particles can be restrictedly moderated. However, the results show that most 20-40 µm can spheroidized well under the given conditions.

Conclusions
In this paper, we reported the simulation analysis investigating the effect of evaporation and additional gas on the spheroidization of titanium particles. The simulation calculations are summarized as follows: Based on the simulations, the temperature fields of particles in the plasma process were obtained with the increase in vol% of hydrogen content at 4 vol% with the input power of 10 kW, the maximum temperature of the particles is 3851.14 K which has resulted in 85% spheroidization rate. the evaporation rate of particles was observed to be affected by the increase in hydrogen content where particles are mostly exposed to high plasma temperature, and at a low mass loading rate. Following the presented effects, the results gave an insight into how the operating conditions can be optimized to control the rate of spheroidization of particles.