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Modeling the Continuous Heat Generation in the Cold Spray Coating Process

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Abstract

In cold spray, 5-150-µm particles (of metal, ceramic, composite, and other materials) are accelerated to supersonic velocities through a de Laval nozzle with an inert gas (generally He or N2) that can reach 1000 °C. In the process, the gas jet impingement on the target and the extreme plastic deformation of impacting particles cause heat generation in the coating layers and the substrate. The heat generation has been argued to cause residual stress, which may cause coating–substrate delamination. In this study, heat generation due to gas impingement and particle plastic deformation has been predicted from CFD and FEA simulations, respectively. Furthermore, a finite volume method has been presented for transiently simulating the coating buildup and bulk heat generation in the coating and the substrate. The model is intended to assist researchers to understand thermal affects in the coating process and help design more informed coating patterns to reduce negative thermal effects.

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Abbreviations

\(A\) :

Cell surface area (m2)

\(Bi\) :

Biot number

\(C_{\text{m}}\) :

Solid material specific heat capacity \(( {\text{J}}/({\text{kg}}\;^\circ {\text{K}}))\)

\(C_{\text{p}}\) :

Fluid specific heat capacity \(( {\text{J}}/({\text{kg}}\;^\circ {\text{K}}))\)

\(D_{\text{e}}\) :

Nozzle exit diameter (m)

\(h_{\text{f}}\) :

Heat transfer coefficient \(( {\text{W}}/({\text{m}}^{2} \,^\circ {\text{K}}))\)

\(i\) :

x-axis index notation

\(j\) :

y-axis index notation

\(k\) :

z-axis index notation

\(k_{\text{f}}\) :

Fluid thermal conductivity \(( {\text{W}}/({\text{m}}\,^\circ {\text{K}}))\)

\(L_{\text{ch}}\) :

Characteristic length (m)

\(m_{\text{m}}\) :

Cell mass (kg)

\(m_{\text{in}}\) :

Mass input into the domain (kg)

\(\dot{m}_{\text{in}}\) :

Mass flux into the domain (deposition rate) (kg/s)

\(n\) :

Computational approximation factor

\(\overline{Nu}_{\text{L}}\) :

Average Nusselt number over a flat plate

\(Nu_{\text{jet}}\) :

Local Nusselt number on flat plate in impinging jet zone

\(Pr\) :

Prandtl number

\(r\) :

Radial distance from nozzle axis (m)

\(Re_{\text{L}}\) :

Reynolds number over flat plate

\(Re_{\text{jet}}\) :

Reynolds number for jet flow

\(\dot{q}\) :

Heat flux (W)

\(\dot{q}_{\text{surf}}\) :

Surface heat flux (W)

\(\dot{q}_{\text{cond}}\) :

Conductive surface heat flux (W)

\(\sum \dot{q}_{\text{conv}}\) :

Convective surface heat flux (W)

\(S_{\text{impact}}\) :

Thermal energy source generated from particle impact (W)

\(\varvec{S}_{{\varvec{impact}}}\) :

Thermal energy source generated from particle impact per volume \(( {\text{W/m}}^{3} )\)

\(t\) :

Time (s)

\(T\) :

Temperature (°K)

\(T_{\text{m}}\) :

Melting temperature (°K)

\(T_{\text{ref}}\) :

Reference fluid temperature (°K)

\(T_{\text{room}}\) :

Room temperature (°K)

\(U_{\text{pi}}\) :

Particle impact velocity (m/s)

\(U_{\infty }\) :

Far-field fluid velocity (m/s)

\(x\) :

Axis in Cartesian coordinate system (m)

\(x_{\text{N}}\) :

Nozzle x-coordinate position in the Cartesian coordinate system (m)

\(y\) :

Axis in Cartesian coordinate system (m)

\(y_{\text{N}}\) :

Nozzle y-coordinate position in the Cartesian coordinate system (m)

\(z\) :

Axis in Cartesian coordinate system (m)

\(z_{\text{adj}}\) :

Adjusted z-coordinate (m)

\(\alpha_{\text{m}}\) :

Solid material thermal diffusivity

\(\mu_{\text{f}}\) :

Fluid dynamic viscosity \(( {\text{kg}}/({\text{m}}\,{\text{s}}))\)

\(\mu_{{{\text{m}}x}}\) :

Mass flow distribution x-direction mean (m)

\(\mu_{{{\text{m}}y}}\) :

Mass flow distribution y-direction mean

\(\nabla\) :

Vector differential operator

\(\phi\) :

Temperature difference (°K)

\(\phi_{\text{avg}}\) :

Average temperature difference (°K)

\(\rho_{\text{f}}\) :

Fluid density \(( {\text{kg/m}}^{3} )\)

\(\rho_{\text{m}}\) :

Solid material density \(( {\text{kg/m}}^{3} )\)

\(\sigma_{{{\text{m}}x}}\) :

Mass flow distribution x-direction standard deviation (m)

\(\sigma_{{{\text{m}}y}}\) :

Mass flow distribution y-direction standard deviation (m)

\(\theta\) :

Non-dimensional temperature

\(\theta_{\text{aw}}\) :

Non-dimensional adiabatic wall temperature

\(\zeta\) :

Non-dimensional radial distance from nozzle axis

\(i\) :

x-axis index notation

\(j\) :

y-axis index notation

\(k\) :

z-axis index notation

\({\text{m}}\) :

Melting

\({\text{N}}\) :

Nozzle

\(t\) :

Time index notation

CFD:

Computational fluid dynamics

FEA:

Finite element analysis

PDF:

Probability density function

TE:

Thermal energy

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Acknowledgments

This work was sponsored in part by the US Army Research Laboratories under the Grant No. W911NF-15-2-0026. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the US Government.

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Authors and Affiliations

  1. Department of Mechanical and Industrial Engineering, Northeastern University, Boston, MA, 21005, USA

    Ozan C. Ozdemir, Qiyong Chen & Sinan Muftu

  2. U.S Army Research Laboratory, Aberdeen Proving Ground, MD, 21005, USA

    Victor K. Champagne Jr.

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  1. Ozan C. Ozdemir
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  2. Qiyong Chen
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Correspondence to Ozan C. Ozdemir.

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Ozdemir, O.C., Chen, Q., Muftu, S. et al. Modeling the Continuous Heat Generation in the Cold Spray Coating Process. J Therm Spray Tech 28, 108–123 (2019). https://doi.org/10.1007/s11666-018-0794-z

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  • DOI: https://doi.org/10.1007/s11666-018-0794-z

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