Nomenclature
Nusselt number Particle diameter
Reynolds number Velocity
Prandtl number Pressure,
Film temperature Density
Plasma Kinematic viscosity,
Heat capacity g Gravitational acceleration
Thermal conductivity Drag coefficient
Temperature radius surface
  1. Introduction
In order to improve the characteristics of the deposits and their applicability under extreme conditions, metal ceramic deposits with specific properties have been developed. At the same time, advances in knowledge of materials and coating processes are currently very advanced. Among the known processes, thermal spraying is without doubt one of the most appreciated techniques. Plasma spraying is part of the thermal spraying which includes a set of methods in which powdered form material (particle size less than 100 µm) are deposited in a molten or semi-molten on previously prepared substrates [1, 2]. Historically, the first spraying process is Flame spraying Developed by Schoop (1909). This technique was used initially for low-melting metals, such as tin or lead, and was later extended to more refractory metals and even ceramics. Thermal spraying developed at the first time an empirical and expensive way limiting its use to the aerospace, nuclear and military [3-5]. Over time, progress, through both basic and applied research, has improved the quality and reproducibility of the repository, while lowering the cost of production. These advances have made it possible to broaden the applications of plasma processes that currently cover the fields of textiles, chemicals, petrochemicals, electronics and biomedical. However, the results are not yet quite satisfactory and the widening of applications requires a better understanding of the phenomena occurring during the deposition, in order to improve the quality and reliability of the projected layers. Additionally, the higher added value required today on materials for energy and smart applications increase the need to understanding refined and minor phenomena to increase efficiency. Recently, simulation appears as a promising way to study physical phenomena like the plasma, and allows reproducing the observed ones. From theoretical models as well as the preparation of experiments, the simulation is based on the principle that physical laws are formulated mathematically, and by its low cost, it allows to identify the needs and the conditions of the experience in a relatively short time period [6, 8]. Indeed in plasma spraying, metal or ceramics (of the order of microns) are projected at high velocity in a molten or semi melted on previously prepared substrates [9-10]. The plasma allows very high temperatures (6000 K to 12000 K) which ensure the melting of particles of more refractory materials. The impact velocity of the drops is high and it is difficult to describe their behavior during the impact on the substrate. Impact behavior is directly influenced by the thermal and dynamic history of the particle in the flame. This dynamic behavior is written by numerical simulations to evaluate independently the static axisymmetric flow of the plasma jet and the behavior of the injected particle within it. We propose here a numerical study in order to obtain a better understanding of the phenomena of transfer and thus to validate and identify domains of validity of semi-empirical correlations.
  1. Basic considerations

Thermal spraying technique has continuously gained increasing interest in the scientific terminology. Extensive development efforts reflected by an important research made over the last years have uncovered the potential of thermal spraying with suspensions [11]. The use of suspensions allows a direct processing of Micro-powders.

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A typical thermal spray system consists of plasma spraying which has the advantage that it can spray very high melting point materials; the material in the form of powder is injected at high temperature plasma jet, where it is rapidly heated to a high velocity. As a consequence, molten droplets are then sprayed onto the substrate by using a high velocity air stream to atomize and propel the material (Fig.1).
Heat treatment of particles in a plasma environment depends not only on the operating parameters of the torch but also on thermodynamic properties and on transport of plasma gas. The latter are strongly non-linear on a wide range of temperatures and it is useful to explain, according to the gas mixture used. The most used gases are argon, binary mixtures (Ar-H2, Ar-He, N2-H2), and ternary mixtures (Ar-He-N2).
Argon is a heavy gas, allowing a transfer of most important momentum. In addition, the torches are more stable with argon. Furthermore, changes in the thermal conductivity of reaction are essentially due to the phenomena of dissociation and ionization. The addition of hydrogen has the effect to increase the heat transfer in the vicinity of dissociation temperatures (around 3700 K for H2 Ar75%) [Fig. 2 ] (All calculation affected with T&TWinner code [12]).
For study heat transfer between plasma jet and spherical particulate is becoming increasingly important to establish reliable Nusselt Number correlations. The Ranz and Marshall correlation, established in 1952 [13], can explain the heat transfer between a spherical particle and the surrounding plasma gas. This correlation can be written:
Where Nu is the Nusselt number, Re is the Reynolds number and Pr is the Prandtl number for gas surrounding.
The Ranz-marshal equation was developed for a spherical particle immersed in a cold fluid, and is not entirely satisfactory and numerous corrections are made to it. We present below the main corrections proposed in the literature.
Lewis and Gauvin [14] studied experimentally the motion of small particles (30 -140 µm in diameter) immersed in argon plasma jet at high velocity to predict the particle velocity, acceleration and temperature along its trajectory, following this study they are given correlation below:
A numerical method is presented by Fiszdon [15] for calculating the motion and heating including phase changes for Al2O3particles during their movement in the high temperature plasma jet:
Lee and Pfender [16] are developed a mathematical model for the simulation of thermal plasma jet, including the mixing phenomena between the jet and the surrounding gases by generalizing the governing equations .for simple mixing flows. Also included is the density fluctuation effect by extending the model.
Kalganova and Klubnikin [17] studied the Convective heat transfer for sphere in a stream for low temperatures of the incoming flow (Tf < 20 000 K) and different Reynolds numbers.
The purpose of this work was to study by direct numerical simulation heat transfer Nusselt number for fine spherical particles in H2-Ar75% as plasma gas from 1100 to 9100 K at atmospheric pressure using fluids with different thermos-physical properties, particles with 50 µm diameters, and different fluid temperature. The objectives were to compare numerical data predicted both for small particles immersed in a moving plasma gas at high temperature.
  1. Correlation by computational simulation