A Confrontation of Lattice Boltzmann, Finite Difference and Taguchi Experimental Design Results for Optimizing Plasma Spraying Operating Conditions Toward Deposit Requirements

A Confrontation of Lattice Boltzmann, Finite Difference and Taguchi Experimental Design Results for Optimizing Plasma Spraying Operating Conditions Toward Deposit Requirements

Ridha Djebali (ISLAIB, University of Jendouba, Béja, Tunisia & UR: Matériaux, Energie et Energies Renouvelables (MEER), University of Gafsa, Tunisia)
Copyright: © 2017 |Pages: 19
DOI: 10.4018/IJEOE.2017100102
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The aim of the present work is the confrontation of three numerical techniques results to optimize the operating conditions of thermal plasma spraying process. The Lattice Boltzmann method (LBM) is used to scrutinize dispersion effects of injection parameters on droplet impact characteristics when impacting substrate. The validation of the developed model shows good agreement with former findings. The results of spraying Zirconia particles give the values Kmin=88.2, Kmax=367.4, Kmean=273.8 and a standard deviation of 48.0 for the Sommerfeld number. The Taguchi experimental design study is conducted for five operating parameters of two levels. The ensuing retained factors combination give Kmean=258.9. To assess drawn conclusions, confirmation test was performed using the Jets&Poudres software. The results show that the prior way is to coat and particles of dp< 40.3 µm have evaporated, particles 40.3 = dp = 49 µm are fully molten and all particles of dp = 71.9 µm arrive fully solid.
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Nowadays, the material and energy consumption control is a major challenge in the sustainable development context. Greenhouse gas emissions, growing energy consumption and materials development costs intensified research on renewable energies, biomaterials, rationalization of consumption and preserving the environment (White & Ali, 2016; Tamali, Boumedienne and Ahmed, 2016). The rule is to align with the topical directions of scientific research which highlights the importance of the international trilogy: Materials - Energy - Environment.

Besides, thin films obtained in surfaces treatment by plasma spraying is an important manufacturing process which was and remains extensively used in industrial applications. This process is used to enhance the performance of engineering components such as coating of pistons, piston rings and shafts, and improving resistance to thermal degradation, corrosion and wear. As many are the experimentations in the process field, there is a huge interest to conduct numerical works to achieve high performance and to reduce experimental cost and efforts. Moreover, the arc plasma spraying processes are of high level complexity due to the various parameters involved in many stages.

The aim of this work falls into this objective. A scrutiny of spray jet and impact characteristics under dispersion effects of powder injection parameters will be presented to show whether injection parameters are influencing the spray stream and then the impact conditions. In a second part, a Taguchi experimental design study will be conducted to explore the weighting of some spraying parameters on the characteristics of the formed coat. Experimental design technique, which is required in the industrial practice of experiments design, has met with growing interest in engineering process. Chen et al. (1993) conducted a D-optimal experimental design to characterize the effects of the APS process parameters on in-flight particle temperature and velocity, and on the oxide content and porosity in the coatings based Alloy 625. Authors concluded that the optimum spraying conditions produced a coating with less than 4% oxide and less than 2.5% porosity. The spray distance, particle size, and current have largest effects on porosity. The particle size, current, and Ar flow rate have an influence on particle velocity and temperature.

Steeper et al. (1993) conducted an experimental study on plasma spraying of Alumina-Titania powder. The coating experiments were conducted using a Taguchi methodology. It has been concluded through the Taguchi evaluation that hydrogen flow and traverse rate were the most significant contributors to porosity. Authors concluded also that the spray distance dominated the insulator plate and tube resistance and the surface finish is influenced the most by primary nitrogen flow.

See the Nomenclature for this article in Table 1.

Table 1.
Vector Quantities
Gas velocity (m/s)
Particle velocity (m/s)
Particle position (m)
Drag force (N)
Gravity force (N)
Force due to additive mass (N)
Thermophoretic force (N)
Gravitational field (=9.81m/s2)
Physical Parameters
aThermal accommodation coefficient
ApParticle surface, = πdp2
CDDrag coefficient
CppParticle specific heat (J/mol.K)
dinjInjector diameter (m)
dpParticle diameter (m)
fknCorrective factor related to Knudsen effect
fpropCorrective factor related to boundary layer effect
hfConvective heat transfer coefficient (W/m2/K)
Kn*Knudsen number
kpParticle conductivity (W/m2/K)
LeMaterial latent heat of boiling (J/kg)
LmMaterial latent heat of melting (J/kg)
mpLiquid-solid averaged particle mass (kg)
NfModified Nusselt number
PrwPrandtl number of hot gas at Tw
QconvConvective heat flux received by the particle (W/m2)
QnetTotal heat flux received by the particle (W/m2)
QradRadiative heat flux received by the particle (W/m2)
ReRelative Reynolds number,
RepParticle Reynolds number,
tParticle time (s)
TPhysical gas temperature(k)
TLocal jet temperature (k)
TaAmbient temperature, 300K
TeMaterial boiling point (k)
TmMaterial melting point (k)
TpParticle temperature,
TwParticle-wall temperature
XpVolumetric melt fraction of the particle
Gas density (kg/m3)
Particle density (kg/m3)
Gas dynamic viscosity (kg/m/s)
Specific heat ratio
Subscripts, Superscripts and Abbreviations
maAdditive mass
propGas property
FDFinite Differences
LTELocal Thermal Equilibrium
ODEOrdinary Differential Equations
PSPPlasma Spraying Process
Far from particle
Rate of mass vaporization
minMinimum value
maxMaximum value
avAverage value

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