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Numerical Investigation of Substrate Melting and Deformation During Thermal Spray Coating by SPH Method

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Abstract

The fluid–solid coupling model is developed to simulate substrate melting and deformation during molten droplet impact. In this model, the liquid and solid parts of splat and substrate are governed by the SPH formulations of the Navier–Stokes equations and the conservation equations of continuum mechanics, respectively. This is the first time that the fluid–solid coupling by the SPH method is applied to simulation of the interaction between droplet and substrate during thermal spray coating. The simulation results on formation of the crater are presented to study the Ni droplet impacting onto the Sn substrate, and Mo droplet impacting onto the Steel, Al, and Brass substrates, respectively. It is found that the initial temperatures and thermal properties of droplet and substrate have great effects on the substrate melting and the morphologies of the splat and the substrate.

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Abbreviations

c p :

Specific heat (J/kg K)

d :

Droplet diameter (m)

D :

Parameter in the form of the repulsive force

f :

Force (N)

g :

Gravity force (N)

G :

Shear modulus (Pa)

h :

Smoothing length (m)

I :

Unit tensor

J 0 :

Yield stress (Pa)

Ja :

Jakob number (= c pl (T m −T B )/L f )

k :

Thermal conductivity (W/m K)

K :

Permeability (m2)

L :

Latent heat (J/kg)

m :

Particle mass (kg)

p :

Pressure (Pa)

R :

Rotaotion rate tensor

Re:

Reynolds number (= ρVd/μ)

t :

Time (s)

T :

Temperature (K)

u :

Internal energy (J/kg)

U :

Velocity (m/s)

\( \vec{v} \) :

Particle velocity vector (m/s)

W :

Smoothing function (m−3)

r :

Particle position (m)

δ :

Dirac notation

ε :

Strain rate tensor

μ :

Viscosity coefficient (kg/m s)

ρ :

Particle density (kg/m3)

τ :

Viscous stress tensor, deviatoric stress tensor

∇ :

Gradient operator

α, β :

Coordinate direction

i,j :

Particle index

m:

Melting

l :

Liquid

s :

Solid

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Acknowledgment

The first author acknowledges the support from National Natural Science Foundation of China (Grant No. 10742002 and 10802011).

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Authors and Affiliations

  1. Institute of Applied Physics and Computational Mathematics, Beijing, 100088, China

    Mingyu Zhang

  2. Department of Engineering Physics, Tsinghua University, Beijing, 100084, China

    Hui Zhang

  3. School of Aerospace, Tsinghua University, Beijing, 100084, China

    Lili Zheng

Authors
  1. Mingyu Zhang
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  2. Hui Zhang
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  3. Lili Zheng
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Correspondence to Mingyu Zhang.

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Zhang, M., Zhang, H. & Zheng, L. Numerical Investigation of Substrate Melting and Deformation During Thermal Spray Coating by SPH Method. Plasma Chem Plasma Process 29, 55–68 (2009). https://doi.org/10.1007/s11090-008-9158-7

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  • DOI: https://doi.org/10.1007/s11090-008-9158-7

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