Journal of Thermal Spray Technology

, Volume 28, Issue 1–2, pp 27–39 | Cite as

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

  • Georg MauerEmail author
Peer Reviewed


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.


aerosol deposition LPPS PVD/CVD modeling particle plume interaction processing suspension spraying 

List of Symbols


Sonic speed (m s−1)


Coefficient (–)


Diameter (m)


Correction factor (–)


Force (N)


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


Knudsen number (–)


Mass (kg)


Mach number (–)


Pressure (Pa)


Prandtl number (–)


Radial coordinate (m)


Specific gas constant (J kg−1 K−1)


Reynolds number (–)


Stokes number (–)


Time (s)


Temperature (K)


Velocity (m s−1)


Axial coordinate (m)


Fitting parameter (–)


Fitting parameter (–)


Specific heat capacity ratio (–)


Fitting parameter (–)


Curvature (m−1)


Mean free path length (m)


Dynamic viscosity (Pa s)


Density (kg m−3)


Characteristic time (s)













Related to Knudsen number






Pressure gradient


Related to Reynolds number





Ambient, not influenced by the substrate



First derivation with respect to time


Second derivation with respect to time



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Copyright information

© ASM International 2018

Authors and Affiliations

  1. 1.Institute of Energy and Climate Research: IEK-1Forschungszentrum Jülich GmbHJülichGermany

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