This paper describes the investigation of low pressure supersonic plasma jets as found in LPPS processes. The main objective is to develop and validate a two-dimensional axisymmetric mathematical model representing such flows. Due to the supersonic nature of the jet, insertion of a measurement probe leads to the appearance of a detached shock in front of the probe. Consequently plasma values are measured behind the probe-induced shock, namely the stagnation enthalpy ( h o ), the stagnation pressure ( p o ) and the static pressure ( p ). The first two values are taken from enthalpy probe measurements while the third value comes from a new technique. Combining these measurements, a new interpretation method enables the calculation of the free-stream supersonic plasma jet properties. The mathematical model is validated using the enthalpy probe measurements and the free-stream properties from the new interpretation method. Results show that the model does not predict a static pressure as large as the new interpretation method. The principal cause for this discrepancy is attributed to the LTE assumption which is questionable for a 40 mbar plasma jet. The modelling effort reported here confirms the need to develop more detailed mathematical models for low pressure supersonic plasma jets in the future.

On the base of gases molecular and kinetic theory a mathematical model of interaction between powder particles and plasma jet is developed. Three-dimensional description of plasma forming gas density distribution as well as particle motion in the plasma jet are a characteristic property of the model. A software for practical realization of the mathematical model is created. Said software provides the possibility to investigate an effect of low-pressure plasma spraying parameters on particle velocity and coordinates in the plasma jet. Computer simulation of particle velocity for powders from aluminium and tungsten oxides in argon plasma under 60 Mbar is conducted. A "Plasma-Technik" VPS unit is used for testing the developed model. Particle velocity measurement is made by a specially developed optical-electronic unit.

Plasma spraying process modeling is useful to understand physical phenomena and to decrease the number of experiments. In this paper, a study of the external plasma jet is proposed: the PHOENICS™ CFD code was used with a 2D axisymmetrical geometry and a standard K-ε turbulence model. In a first step, thermodynamic and transport properties were calculated from chemical equilibrium composition, thermodynamic derivatives and kinetic theory of gases. Local Thermodynamic Equilibrium (LTE) was assumed for both plasma and surrounding gases. The proposed numerical results were computed for comparison with temperature measurements realized by Brossa and Pfender in the case of an argon plasma jet discharging into air, using enthalpy probes. The predictions were found reasonably accurate. The influence of the surrounding gas nature was also verified as the validity of the parabolic assumption.

The numerical forecast constitutes an interesting way for plasma spraying to minimize the number of experiments to achieved the optimum spraying conditions. Many computational codes have been developed to predict the properties of the plasma jet (velocity, temperature) and the particles behavior within (temperature, velocity, melting state). According to the particle injection orthogonally to the plasma jet, the models have to be 3D. However, such codes need several hours if not several days of calculations to obtain the results of one condition. This is the main drawback of the existing sophisticated codes. The computing time is not compatible with industrial needs. Various clever numerical methods were developed in the past to simulate 2-D parabolic gas flows for laminar boundary layers or jets. For example, the Genmix 2-D axi-symmetric algorithm developed by Spalding and Patankar, and known as the Bikini method requires a very low-cost memory and computing time. This algorithm makes it possible, when using the proper thermodynamics and transport properties of plasma gases and the whole equation of Boussinesq-Oseen-Basset and taking into account the thermophoresis and non continuity effect for small particle, to predict in a fast and rather realistic way, the velocity and temperature fields of the plasma jet.

Many CFD software packages are commonly used for the modeling of thermal plasma jets. Unfortunately, according to some recent results reported in the literature, one may notice that two different software products do not always provide similar results for a similar case. For example, PHOENICS and FLUENT were recently used in a single study and some abnormal differences were observed in the numerical predictions [1]. After some intensive search, the reasons were identified and are explained in the present paper: it appears that all Fluent built-in k-å type turbulence models have to be modified especially for high temperature flows. Since Fluent is now extensively used for the modeling of plasma jets, it was considered useful to report the required correction to the scientific thermal spray community and this is the purpose of the present paper.

This work deals with a 3-D transient simulation of the air plasma spraying of ceramic powders using a C.F.D. commercial code ESTET v3.4 that has been adapted to thermal plasma conditions. The mathematical model computes the distribution of particle velocity, temperature, molten state and size at impact and predicts the heat transfer to the substrate by plasma jet and particles. It incorporates the conversion from electrical to thermal energy in the torch nozzle as well as coating formation on the substrate. It makes it possible to predict the shape of the coating footprint when the torch and the substrate are fixed. The projections of the model are compared with experimental results that involve flow characteristics, time-dependant particle behavior in the flow and heat flux to the substrate.

Plasma spraying using liquid feedstock makes it possible to produce thin coatings (< 100 µm) with more refined microstructures than in conventional plasma spraying. However, the low density of the feedstock droplets makes them very sensitive to the instantaneous characteristics of the fluctuating plasma jet at the location where they are injected. In this study the interactions between the fluctuating plasma jet and droplets are explored by using numerical simulations. The computations are based on a three-dimensional and time-dependent model of the plasma jet that couples the dynamic behavior of the arc inside the torch and the plasma jet issuing from the plasma torch. The turbulence that develops in the jet flow issuing in air is modeled by a Large Eddy Simulation model that computes the largest structures of the flow which carry most of the energy and momentum.

The first part of this overview on plasma spraying covers the general behavior of plasma jets generated by d.c. and r.f. plasma torches, including the fluid dynamics of such jets. In the second part, interactions of injected powders with the plasma are considered with emphasis on those processes which dominate heat and momentum transfer from the plasma to the powder particles. Both experimental studies as well as modeling efforts are included in this overview.

A simple and efficient numerical model describing the processes of nucleation, growth, and transport of multicomponent nanoparticles is developed. The approach is similar to the classical method of moments but can be applied to co-condensation of several substances. The processes of homogeneous nucleation, heterogeneous growth, and coagulations due to Brownian collisions are considered in combination with the convective and diffusive transport of particles and reacting gases within multidimensional geometries. The model is applied to the analysis of multi-component co-condensation of TaC nanoparticles within a DC plasma reactor.

A numerical model of an argon jet exiting a LPPS torch has been developed and validated against enthalpy probe measurements for a slightly overexpanded jet at a chamber pressure of 100 mbar. Visualization of the jet using a CCD camera shows the presence of a small Mach reflection in the first compression-expansion cell with only oblique shock waves in the second cell. This jet topology is also observed in the model results. The images of the enthalpy probe on the axis of the plasma jet reveal that the shock layer, or shock-probe distance, varies according to the axial location of the probe. Shock-probe distance can be as large as 3 mm and should be considered when mapping plasma jets. Paper includes a German-language abstract.

This paper presents a numerical simulation of the plasma spraying of alumina particles using a three-dimensional commercial fluid dynamics code ESTET 3.4 . The objective of this study is to investigate the effect of (i) turbulence model and turbulence radial profiles at the torch exit on plasma flow and particle behavior, (ii) particle injection conditions on particle trajectories and heating and (iii) plasma jet fluctuations on temperature and velocity flow fields. The comparison of predictions with experimental measurements of gas and particle velocity and temperature, makes it possible to determine the influential parameters and set them to pertinent values.

When spraying ceramic particles with a low thermal conductivity such as zirconia using Ar-H 2 direct-current (d.c.) plasma jets where the heat transfer is important, heat propagation phenomena take place with the propagation of melting, evaporation or even solidification fronts. Most models neglect these heat propagation phenomena assuming the particle as a lumped media. This work is aimed at developing a model coupling the effect of heat propagation with the particle dynamic within plasma jets. It uses an adaptative grid in which the coordinates of the phase change fronts are fixed. It allows minimizing the calculation costs (approximately 10 seconds on PC under windows XP against 1hour with an enthalpy model). Such calculations are illustrated for dense and porous agglomerated zirconia as well as iron particles which evaporation in an Ar- H 2 (25 vol %) plasma is important.

The modeling of thermal plasma jets is commonly used in order to obtain a better knowledge and understanding of the atmospheric plasma spray process. Many different software products are used in the literature at present but none of them present the same ease in integrating the plasma properties and none of them propose the same options: for example concerning turbulence modeling or concerning the implemented numerical methods. All that may result in differences in the converged solution and in the required computational time. For this reason, two different software products have been tested in the present study, namely the PHOENICS CFD code developed by CHAM (Wimbledon, UK) and the FLUENT CFD code developed by FLUENT Inc (Lebanon, NH, US). The comparisons concern different points such as the possibilities in implementing the plasma gas properties, the way the energy equation is considered, the available turbulence models or the implemented numerical methods. The conclusion indicates that some differences exist in the numerical results obtained using the two CFD packages.

The phenomena occurring after injection of water-ethanol suspension of fine hydroxyapatite powder are simulated numerically. The mathematical modeling starts with the calculation of the map of velocity and temperature of working plasma gases. The map is calculated by taking into account the evaporation of the liquids included in the suspension. The suspension is injected through a mechanical injector into the anode-nozzle of the SG-100 torch. The plasma was generated with the use of working gases composed of 45 slpm of Ar and 5 slpm of H 2 and with the electric power input of 30 kW. The initial droplets of suspension were supposed to be spherical with a diameter equal to that of the injector, i.e., 500 µm. The trajectory of suspension was calculated until the evaporation of liquids. Then, the simulation of the movement and heating of solid hydroxyapatite (HA) started. The HA powder was home synthesized and exhibited a bimodal size distribution with two maxima around 3 and 10 µm. The equations describing the momentum and heat transfer from hot gas to the solids took into account the small size of solid particles. In particular, the thermophoresis force, as well as, the drag coefficient modified for non-continuum effect were used in the calculation of the trajectory of small particles. Similarly, the non-continuum effect was considered in the calculation of heat transfer. The obtained trajectories were tentatively correlated with the microstructure of the suspension plasma sprayed HA coatings.

A numerical model of a supersonic compressible plasma flow has been developed with the aid of CFD software to describe the thermodynamic and transport properties of a plasma jet in order to investigate the PS-PVD process and how to optimize it for thermal barrier coatings and, in particular, the formation of columnar microstructures. The required properties of the plasma gas mixtures were obtained as a function of temperature and pressure from thermodynamic calculations in chemical equilibrium with the effect of ionization. Two-dimensional Monte Carlo simulations were conducted to provide insight on the evolution of columnar microstructure, accounting for self-shadowing and vapor incidence angle but ignoring the effect of diffusion. Simulated structures and predicted values are presented and compared with actual images and measurements.

A mathematical model of the impingement of a plasma jet on a flat structure is proposed. This model can be used to predict temperature and velocity fields in the jet and in the near substrate region, but also to estimate thermal exchanges at the surface of this substrate. Different options were tested concerning the modeling of the near wall region and results indicate that a boundary layer calculation is necessary to predict the energy flux transferred to the substrate with a good accuracy. Nevertheless, the influence of the presence of the substrate on temperature and velocity fields was found to be important only in the near substrate region, indicating that the flow fields calculated from free jet modeling are accurate over the major part of the domain.

The present study is conducted to clarify the magnetic control characteristics of a particle-laden plasma jet impinging on a substrate for the improvement of a low pressure plasma spraying process and its controllable optimization. The plasma jet is described by Eulerian approach and each injected particle is described by Lagrangian approach respectively taking into account the compressible effect, variable transport properties and plasma-particle interactions, coupled with the Maxwell's equations. The effects of the location of the applied radio-frequency electromagnetic field, and of the injected particle size on the particle trajectory, particle velocity and its phase change are clarified by numerical simulation. It is concluded that the particle trajectory is influenced effectively and the injected particle temperature can be controlled strongly by applying the radio-frequency electromagnetic field to the nozzle. The reasonable agreement of particle velocity between calculation and experiment is observed.

Low Pressure Plasma Spraying (LPPS) is a spraying technique developed in the 1970s that uses a converging-diverging nozzle (i.e. de Laval nozzle) inside a controlled atmosphere chamber. With such a set-up, it is possible to obtain a plasma jet in the supersonic flow regime, which may encounter several non-equilibrium phenomena. First, the operating pressures (i.e. chamber and torch exit) determine the aerodynamic state of the supersonic plasma jet. Operating at the nozzle design pressure insures aerodynamic equilibrium of the plasma jet while other chamber pressure brings a state of “aerodynamic non-equilibrium” for which expansion, compression and shock waves appear. Second, a low chamber pressure corresponds to a decrease in the number of collisions between electrons and heavy species (i.e. atoms and ions). This rarefaction of the plasma causes a state of “thermal non-equilibrium” for which there exist two different temperature distributions, Te and Th, respectively representing the electrons and the heavy species. Third, the high velocity of the plasma jet can bring a state of “chemical non-equilibrium” as the hydrodynamic time scale of the flow might become smaller than its chemical time scale. Hence it is a challenging task to model a phenomenon as complex as the low pressure supersonic plasma jet. The model developed in this work uses a commercial code in which recent advances in the field of plasma transport properties are implemented. It considers chemical non-equilibrium through the solution of the electrons conservation equation while the two temperature distributions each require the solution of an energy balance. The validation of the model is possible from recent measurements with a new method enhancing the capabilities of the enthalpy probe technique to supersonic jets in aerodynamic non-equilibrium. Abstract only; no full-text paper available.

Finely structured ceramic coatings can be obtained by solution precursor plasma spraying. The final structure of the coating highly depends on the droplet size and velocity distribution at the injection, the evolution of the spray in the jet, and droplet breakup and collision within the spray. This paper describes a 3D model to simulate the transport phenomena and the trajectory and heating of the solution spray in the process. O’Rourke’s droplet collision model is used to take into account of the influence of droplet collision. The influence of droplet breakup is also considered by implementing TAB and Wave droplet breakup models into the plasma jet model. The effects of droplet collisions and breakup on the droplet size, velocity, and temperature distribution of the solution spray are investigated. The results indicate that droplet breakup and collision play an important role in determining the final particle size and velocity distributions on the substrate.

Plasma spraying is a key industrial coating process that exhibits intricate nonlinear interactions among process parameters. This complexity makes accurate predictions of particle properties, which greatly affect process behavior, very challenging. Specifically, particle velocities and temperatures profoundly impact coating quality and process efficiency. Conventional methods often require empirical correlations and extensive parameter tuning due to their limited ability to capture the underlying physics within this intricate system. This study introduces Physics-Informed Neural Networks (PINNs) as a solution. By seamlessly integrating known physical laws and constraints directly into the model architecture, PINNs offer the potential to learn the underlying physics of the system. For comparison, Artificial Neural Networks (ANNs) are also developed. Computational Fluid Dynamics (CFD) simulations of a plasma generator and plasma jet model provide data to train both ANN and PINN models. The study reveals an improvement in particle velocity prediction through the proposed PINN model, demonstrating its capability to handle complex relationships. However, challenges arise in predicting particle temperature, warranting further investigation. The developed models can aid in optimizing the plasma spraying process by predicting essential particle properties and guiding necessary process adjustments to enhance coating quality.