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Numerical Study on Particle–Gas Interaction Close to the Substrates in Thermal Spray Processes with High-Kinetic and Low-Pressure Conditions

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Abstract

In thermal spray processes, the interaction between the gas jet and the particulate feedstock can affect the coating build-up mechanisms considerably. In particular under high-kinetic and low-pressure conditions, small particles are subjected to rapid deflection and velocity changes close to the substrate. In this work, numerical studies were carried out to investigate the interaction between gas and particles in the substrate boundary layers (BL). Typical conditions for suspension plasma spraying (SPS), plasma spray-physical vapor deposition (PS-PVD), and aerosol deposition (AD) were taken as a basis. Particular importance was attached to the consideration of rarefaction and compressibility effects on the drag force. Typical Stokes numbers for the different thermal spray processes were calculated and compared. Possible effects on the resulting coating build-up mechanisms and microstructure formation are discussed. The results show that just for larger particles in the SPS process the laminar flow attached to the particles begins to separate so that the drag coefficients have to be corrected. Furthermore, slip effects occur in all the investigated processes and must be considered. The comparison of calculated Stokes numbers with critical values shows that there is a disposition to form columnar microstructures or stacking effects depending on the particle size for PS-PVD and SPS, but not for AD.

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Abbreviations

c :

Sonic speed (m s−1)

C :

Coefficient (–)

d :

Diameter (m)

f :

Correction factor (–)

F :

Force (N)

k B :

Boltzmann constant (1.381 × 10−23 J K−1)

Kn :

Knudsen number (–)

m :

Mass (kg)

Ma :

Mach number (–)

p :

Pressure (Pa)

Pr :

Prandtl number (–)

r :

Radial coordinate (m)

R :

Specific gas constant (J kg−1 K−1)

Re :

Reynolds number (–)

St :

Stokes number (–)

t :

Time (s)

T :

Temperature (K)

v :

Velocity (m s−1)

z :

Axial coordinate (m)

α :

Fitting parameter (–)

β :

Fitting parameter (–)

γ :

Specific heat capacity ratio (–)

δ :

Fitting parameter (–)

κ :

Curvature (m−1)

λ :

Mean free path length (m)

µ :

Dynamic viscosity (Pa s)

ρ :

Density (kg m−3)

τ :

Characteristic time (s)

Crit:

Critical

D:

Drag

E:

External

g:

Gas

jet:

Jet

Kn :

Related to Knudsen number

M :

Molecular

p :

Particle

PG:

Pressure gradient

Re :

Related to Reynolds number

rel:

Relative

sub:

Substrate

∞ :

Ambient, not influenced by the substrate

\(\dot{}\) :

First derivation with respect to time

\(\ddot{}\) :

Second derivation with respect to time

‘:

Corrected

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  1. Institute of Energy and Climate Research: IEK-1, Forschungszentrum Jülich GmbH, 52425, Jülich, Germany

    Georg Mauer

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Mauer, G. Numerical Study on Particle–Gas Interaction Close to the Substrates in Thermal Spray Processes with High-Kinetic and Low-Pressure Conditions. J Therm Spray Tech 28, 27–39 (2019). https://doi.org/10.1007/s11666-018-0810-3

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  • DOI: https://doi.org/10.1007/s11666-018-0810-3

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