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A Numerical Investigation of the Cold Spray Process Using Underexpanded and Overexpanded Jets

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Abstract

The impact velocity of particles during the cold spray process is crucial to the optimisation of coating quality and spraying costs. In the present investigation, both underexpanded and overexpanded impinging jets are employed to accelerate Aluminium particles towards a substrate. The impact velocity and angle statistics are generated by injecting polydisperse particles into the jet and the particle dynamics are characterised using the velocity and trajectories of the particles. The optimum particle size corresponding to the maximum impact speed is recast in terms of the Stokes number and shown to have a value of approximately one. Finally, a normal shock model is proposed which may be employed to estimate the particle impact speed using the nozzle exit conditions. It is shown that owing to artificial viscosity associated with the total variation diminishing scheme, this model tends to underestimate the speed.

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Abbreviations

D :

nozzle diameter, m

θ:

nozzle divergence angle

d p :

particle diameter, m

d m :

mean particle diameter, m

m :

particle mass, kg

A :

particle cross-sectional area, m2

σ:

standard deviation

Δt :

time step

Δ:

grid size in r and z direction

z :

jet axis

r :

radial axis

u :

axial velocity

v :

radial velocity

P :

pressure

ρ:

density

T :

temperature

E :

internal energy

t :

time

Z :

stand off distance

L :

computational domain length

τ:

shear stress terms

q :

heat flux terms

μ:

dynamic viscosity

κ:

thermal conductivity

τA :

particle aerodynamic response time

τB :

fluid time scale

PR:

pressure ratio

C D :

drag coefficient

St :

Stokes number

Ma :

Mach number

Co :

Courant number

Re :

Reynolds number

R :

gas constant

γ:

specific heat ratio

0:

stagnation conditions

k:

particle parcel index

t:

nozzle throat

e:

nozzle exit

a:

ambient conditions

p:

particle phase

s:

post shock conditions

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Acknowledgments

The correspondence author would like to thanks the ARC Center of Excellence for Design in Light Metals and the CSIRO Direct Manufacturing Center for their funding of this research. The outcomes presented in the article could not have been achieved without their support and encouragement. The principal author would also like to acknowledge the contributions of Dr. Chong Yau Wong in proof reading the manuscript.

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Authors and Affiliations

  1. Laboratory for Turbulence Research in Aerospace & Combustion, Department of Mechanical and Aerospace Engineering, Monash University, Clayton, VIC, 3800, Australia

    S. Li & J. Soria

  2. ARC Centre of Excellence for Design in Light Metals, Monash University, Clayton, VIC, 3800, Australia

    B. Muddle

  3. CSIRO Materials Science and Engineering, Clayton, VIC, 3169, Australia

    M. Jahedi

Authors
  1. S. Li
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  2. B. Muddle
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  3. M. Jahedi
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  4. J. Soria
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Correspondence to S. Li.

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Li, S., Muddle, B., Jahedi, M. et al. A Numerical Investigation of the Cold Spray Process Using Underexpanded and Overexpanded Jets. J Therm Spray Tech 21, 108–120 (2012). https://doi.org/10.1007/s11666-011-9691-4

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  • DOI: https://doi.org/10.1007/s11666-011-9691-4

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