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
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.
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.
\label{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.}
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.
Correlation by computational simulation