Journal of Thermal Spray Technology

, Volume 28, Issue 1–2, pp 108–123 | Cite as

Modeling the Continuous Heat Generation in the Cold Spray Coating Process

  • Ozan C. OzdemirEmail author
  • Qiyong Chen
  • Sinan Muftu
  • Victor K. ChampagneJr.
Peer Reviewed


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.


Al 6061 CFD cold spray FEA heat generation simulation 

List of symbols


Cell surface area (m2)


Biot number


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


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


Nozzle exit diameter (m)


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


x-axis index notation


y-axis index notation


z-axis index notation


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


Characteristic length (m)


Cell mass (kg)


Mass input into the domain (kg)


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


Computational approximation factor


Average Nusselt number over a flat plate


Local Nusselt number on flat plate in impinging jet zone


Prandtl number


Radial distance from nozzle axis (m)


Reynolds number over flat plate


Reynolds number for jet flow


Heat flux (W)


Surface heat flux (W)


Conductive surface heat flux (W)

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

Convective surface heat flux (W)


Thermal energy source generated from particle impact (W)


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


Time (s)


Temperature (°K)


Melting temperature (°K)


Reference fluid temperature (°K)


Room temperature (°K)


Particle impact velocity (m/s)

\(U_{\infty }\)

Far-field fluid velocity (m/s)


Axis in Cartesian coordinate system (m)


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


Axis in Cartesian coordinate system (m)


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


Axis in Cartesian coordinate system (m)


Adjusted z-coordinate (m)

Greek letters


Solid material thermal diffusivity


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


Mass flow distribution x-direction mean (m)


Mass flow distribution y-direction mean


Vector differential operator


Temperature difference (°K)


Average temperature difference (°K)


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


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


Mass flow distribution x-direction standard deviation (m)


Mass flow distribution y-direction standard deviation (m)


Non-dimensional temperature


Non-dimensional adiabatic wall temperature


Non-dimensional radial distance from nozzle axis



x-axis index notation


y-axis index notation


z-axis index notation







Time index notation



Computational fluid dynamics


Finite element analysis


Probability density function


Thermal energy



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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Copyright information

© ASM International 2018

Authors and Affiliations

  • Ozan C. Ozdemir
    • 1
    Email author
  • Qiyong Chen
    • 1
  • Sinan Muftu
    • 1
  • Victor K. ChampagneJr.
    • 2
  1. 1.Department of Mechanical and Industrial EngineeringNortheastern UniversityBostonUSA
  2. 2.U.S Army Research LaboratoryAberdeen Proving GroundUSA

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