Novel Cooling Rate Correlations in Molten Metal Gas Atomization

The cooling rate in molten metal gas atomization is the key determining factor for the microstructure of metal powders. Mathematical expressions for cooling rates often include the melt droplet diameter and a pre-exponential factor describing the materials and gas properties. A new mathematical cooling rate correlation for rapidly solidified melt droplets is proposed based on heat flow considerations during gas atomization. The model approach takes process conditions such as gas-to-melt mass flow ratio and the initial gas temperature into account. The mathematical formulation was experimentally developed using secondary dendrite arm spacing method. For this purpose, a Cu-6wt pct Sn alloy was atomized with close-coupled (CCA) and free-fall atomization (FFA). A novel approach was made to predict the pre-exponential factor that allows the transferability to other materials. Our correlation for the cooling rate and the pre-exponential factor was validated by experimental data from the literature. The novel correlation type is valid for two different atomizing systems (FFA and CCA), suggesting that it may be applicable to entirely different gas atomization systems.

• 14 February 2019

  Author notes two two typos in Equation 2.

a :

Constant to calculate the cooling rate through SDAS

a _i :

Model parameters

c _g :

Specific heat capacity of the gas, J kg⁻¹ K⁻¹

\( c_{{{\text{p}}_{\text{L}} }} \) :

Specific heat capacity of the liquid melt droplet, J kg⁻¹ K⁻¹

\( c_{{{\text{p}}_{\text{S}} }} \) :

Specific heat capacity of the solid melt droplet, J kg⁻¹ K⁻¹

CR:

Cooling rate, K s⁻¹

D :

Nozzle outlet diameter, m

d _p :

Droplet diameter, m

d _50,3 :

Mass median particle diameter, m

f _s :

Solid fraction

h :

Heat transfer coefficient, W m⁻² K⁻¹

k _g :

Thermal conductivity of the gas, W m⁻¹ K⁻¹

k _l :

Thermal conductivity of the melt droplet, W m⁻¹ K⁻¹

L :

Distance between first adjacent arm to the last, m

m :

Constant to calculate the SDAS

\( \dot{m}_{G} \) :

Gas mass flow rate, kg s⁻¹

\( \dot{m}_{L} \) :

Melt mass flow rate, kg s⁻¹

n:

Constant to calculate the cooling rate through SDAS

n _arms :

Number of counted arms to calculate SDAS, #

p :

Atomization pressure, MPa

q :

Heat flux, W m⁻²

r :

r-axis, m

R:

Residuum

T ₀ :

Ambient gas temperature (293 K)

T _G :

Gas temperature, K

\( T_{{G_{0} }} \) :

Initial gas temperature, K

T _L :

Liquidus temperature, K

T _m :

Temperature of the melt droplet at solid fraction = 0.5, K

T _M :

Melt temperature, K

T _s :

Solidus temperature, K

u _d :

Droplet velocity, m s⁻¹

u _g :

Gas velocity, m s⁻¹

z :

z-axis, m

Δh :

Latent heat of fusion, J kg⁻¹

Δt :

Solidification time, s

ΔT :

Temperature difference between melt droplet and surrounding gas, K

ΔT _M :

Superheated melt temperature, K

Δu :

Relative velocity m s⁻¹

η :

Dynamic viscosity of the gas, N s m⁻²

λ ₁ :

Primary dendrite arm spacing, m

λ ₂ :

Secondary dendrite arm spacing, m

ρ _g :

Density of the gas, kg m⁻³

ρ _f :

Density of the melt droplet at solid fraction = 0.5 kg m⁻³

σ _g :

Geometric standard deviation

ψ :

Materials and gas properties

Bi:

Biot number

CCA:

Close-coupled atomization

FFA:

Free-fall atomization

GMR:

Gas-to-melt mass flow ratio

HG:

Hot gas atomization

Nu:

Nusselt number

Pr:

Prandtl number

Re:

Reynolds number

RT :

Atomization at ambient temperature

SDAS:

Secondary dendrite arm spacing, m

Financial support of subprojects S01 ‘Process to Generate Rapidly Cooled, Homogenous Samples’ and U01 ‘Generation of spherical microscopic samples with single droplet solidification’ of the Collaborative Research Center SFB 1232 “Farbige Zustände” by the German Research Foundation (DFG) is gratefully acknowledged. We also thank F. Peschel, R. Lehmann, S. Evers for their experimental support. Additionally, the authors wish to thank F. Mostaghimi, J. Eitzen, C. O’Fuarthain for useful discussions and their helpful comments on this work.

Authors and Affiliations

1. Faculty of Production Engineering, University of Bremen, Badgasteiner Straße 1, 28359, Bremen, Germany

   N. Ellendt, G. Coulthard, E. Soares Barreto, L. Mädler & V. Uhlenwinkel

2. Leibniz Institute for Materials Engineering IWT, Badgasteiner Straße 3, 28359, Bremen, Germany

   N. Ciftci, N. Ellendt, G. Coulthard, E. Soares Barreto, L. Mädler & V. Uhlenwinkel

Corresponding author

Correspondence to V. Uhlenwinkel.

Manuscript submitted August 27, 2018.

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