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Development of Holistic Three-Dimensional Models for Cold Spray Supersonic Jet

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Abstract

A three-dimensional, computational fluid dynamics (CFD) model is developed to estimate cold spray gas conditions. This model is calibrated and validated with respect to thermal history of a substrate exposed to the cold spray supersonic jet. The proposed holistic model is important to track state of gas and particles from injection point to the substrate surface with significant benefits for optimization of very rapid "nanoseconds" cold spray deposition. The three-dimensional model is developed with careful attention with respect to computation time to benefit broader cold spray industry with limited access to supercomputers. The k-ε-type CFD model is evaluated using measured temperature for a titanium substrate exposed to cold spray nitrogen at 800 °C and 3 MPa. The model important parameters are detailed including domain meshing method with turbulence, and dissipation coefficients during spraying. Heat transfer and radiation are considered for the de Laval nozzle used in experiments. The calibrated holistic model successfully estimated state of the gas for chosen high temperature and high pressure cold spray parameters used in this study. Further to this, the holistic model predictions with respect to the substrate maximum temperature had a good agreement with earlier findings in the literature.

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Abbreviations

c :

Local speed of sound in fluid (m/s)

c p :

Specific heat capacity at constant pressure (m2/s2 K)

C ε1 :

k-ε turbulence model constant

C ε2 :

k-ε turbulence model constant

C μ :

k-ε turbulence model constant

C Clip :

Clip factor coefficient for turbulence energy

C Scale :

Scaling coefficient for curvature correction

g :

Gravity vector (m/s2)

h :

Specific static (thermodynamic) enthalpy (m2/s2)

h tot :

Specific total enthalpy (m2/s2)

k :

Turbulent kinetic energy per unit mass (m2/s2)

M :

Local Mach number, U/c (Dimensionless)

p′:

Modified pressure (kg/m s2)

p :

Static (thermodynamic) pressure (kg/m s2)

P k :

Turbulence energy (kg/m s3)

p ref :

Reference pressure (kg/m s2)

Prt :

Turbulent Prandtl Number, c p μt/λt (Dimensionless)

p tot :

Total pressure (kg/m s2)

R 0 :

Universal gas constant = 8.3145 (m3 Pa /K mol)

Re:

Reynolds number (Dimensionless)

Sct :

Turbulent Schmidt Number, μt/Γt (Dimensionless)

s strnr :

Shear strain rate (1/s)

t :

Time (s)

T dom :

Domain temperature (K)

T stat :

Static (thermodynamic) temperature (K)

T tot :

Total temperature (K)

U :

Velocity magnitude (m/s)

u :

Fluctuating velocity component (m/s)

ε :

Turbulent (Eddy) dissipation rate (m2/s3)

κ :

Von Karman constant (0.41)

λ :

Thermal conductivity (kg/m s3 K)

μ :

Molecular (dynamic) viscosity (kg/m s)

μ eff :

Effective viscosity, μ + μ t (kg/m s)

μ t :

Turbulent (Eddy) viscosity (kg/m s)

ρ :

Density (kg/m3)

σ k :

k-ε turbulence model constant (1)

σ ε :

k-ε turbulence model constant (1.3)

Γt :

Turbulent diffusivity (kg/m s)

θ:

Nondimensionalized temperature

T g :

Cold spray stagnation temperature (ºC)

T w :

Measured substrate temperature (ºC)

T ∞ :

Environment temperature (ºC)

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Authors and Affiliations

  1. CSIRO Materials Science and Engineering, Gate 5, Normanby Road, Clayton, VIC, 3168, Australia

    S. H. Zahiri & M. Jahedi

  2. Swinburne University of Technology, 545 Burwood Road, Hawthorn, VIC, 3122, Australia

    T. D. Phan & S. H. Masood

Authors
  1. S. H. Zahiri
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  2. T. D. Phan
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  3. S. H. Masood
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  4. M. Jahedi
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Correspondence to S. H. Zahiri.

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Zahiri, S.H., Phan, T.D., Masood, S.H. et al. Development of Holistic Three-Dimensional Models for Cold Spray Supersonic Jet. J Therm Spray Tech 23, 919–933 (2014). https://doi.org/10.1007/s11666-014-0113-2

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  • DOI: https://doi.org/10.1007/s11666-014-0113-2

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