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Thermal gradient in polymeric particles during the cold spray process

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Abstract

Understanding the particle history during the cold spray process is primordial to better apprehend the particle's mechanical behavior during the impact. If the particle velocity can easily be measured using a high-speed camera, measuring the particle temperature remains a challenge. A solution is to perform numerical simulations of the process using computational fluid dynamics (CFD) simulations. However, most CFD simulation results only give an idea of the particle average temperature. Although it would be valid for metallic particles which exhibit a small temperature difference between the particle core and surface with high thermal stability, it is not the case for polymeric material, because of their low thermal conductivity. In this paper, the thermal gradient of a polymer particle is investigated. While small particles exhibit a uniform temperature distribution, a large temperature gradient is observed for particle diameter larger than 30 µm. In addition, assuming that the particle is spherical without rotation during the flight, the particle exhibits melting at the front. Such a phenomenon can have considerable consequences on the particle behavior during the impact. Furthermore, the influence of the feeding rate on the particle temperature distribution is investigated. If the particles are well diluted inside the nozzle (low feeding rate), the difference in the average temperature of two successive particles is limited to 5 K.

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Abbreviations

\({\mathcal{B}}_{\mathrm{i}}\) :

Biot number

\({\mathcal{N}}_{\mathrm{u}}\) :

Nusselt number

\({\mathcal{P}}_{\mathrm{r}}\) :

Prandtl number

\({\mathcal{R}}_{\mathrm{ep}}\) :

Particle Reynolds number

E:

Total energy per unit of mass (J kg−1)

\({E}_{\text{melt}}\) :

Energy of melting of the crystalline lamellae (J)

\({E}_{\mathrm{T}}\) :

Energy to increase the particle temperature (J)

\(\mathbf{F}\) :

Force (N)

\({G}_{k}\) :

Generation of turbulence kinetic energy due to mean velocity gradients (W m−3)

\({G}_{\mathrm{b}}\) :

Generation of turbulence kinetic energy due to buoyancy (W m−3)

\(k\) :

Turbulent kinetic energy (J kg−1)

\(p\) :

Gas pressure (Pa)

\(t\) :

Time (s)

\(T\) :

Absolute temperature (K)

\({\varvec{u}}\) :

Velocity (m s−1)

\({Y}_{M}\) :

Contribution of the fluctuation dilatation in compressible turbulence to the overall dissipation rate (W m−3)

\(\varepsilon \) :

Turbulent dissipation rate (m2 s−3)

\(h\) :

Convective heat transfer coefficient (W m−2 K−1)

H:

Enthalpy (J kg−1)

\({\varvec{q}}\) :

Heat flux by conduction (W m−2)

\({\mathcal{Q}}_{s}\) :

Heat sources by conduction (W m−3)

\({\mathcal{Q}}_{f}\) :

Heat sources by convection (W m−3)

\(\overline{\overline{\tau }}\) :

Viscous stress tensor (Pa)

\({c}_{p}\) :

Heat capacity at constant pressure (J kg−1 K−1)

\({d}_{\mathrm{p}}\) :

Particle diameter (m)

\({H}_{100\%}\) :

Enthalpy of fusion of a 100% crystalline material (J kg−1)

\({m}_{\mathrm{p}}\) :

Particle mass (kg)

\({\alpha }_{p}\) :

Thermal expansion coefficient (K−1)

\(\Delta T\) :

Temperature difference

\(\Gamma \) :

Thermal conductivity (W m−1 K−1)

\({\mu }_{g}\) :

Viscosity (Pa s)

\({\mu }_{\mathrm{t}}\) :

Turbulent viscosity (Pa s)

\(\rho \) :

Density (kg m−3)

\(\%{\chi }_{\mathrm{c}}\) :

Crystallinity ratio

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Acknowledgements

The authors would like to acknowledge the Institute of Fluid Science at Tohoku University, which supported this research through the Grants J21Ly08 and J22Ly09 under the label of the LyC Collaborative Research Project.

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Authors and Affiliations

  1. Frontier Research Institute for Interdisciplinary Sciences, Tohoku University, Sendai, Japan

    C. A. Bernard

  2. ELyTMaX IRL3757, CNRS, Univ Lyon, INSA Lyon, Centrale Lyon, Université Claude Bernard Lyon 1, Tohoku University, Sendai, Japan

    C. A. Bernard, K. Ogawa & J.-Y. Cavaillé

  3. Fracture and Reliability Research Institute, Tohoku University, Sendai, Japan

    C. A. Bernard & K. Ogawa

  4. Institute of Fluid Science, Tohoku University, Sendai, Japan

    H. Takana

  5. Lyon Center, IFS -Tohoku University, Université de Lyon, INSAVALOR, 69621, Villeurbanne, France

    H. Takana & J.-Y. Cavaillé

  6. Micro System Integration Center, Micro/Nano-Machining Research and Education Center, Tohoku University, Sendai, Japan

    G. Diguet

  7. Materials Engineering and Science (MateIS), CNRS, INSA-Lyon, UMR5510, Université de Lyon, Villeurbanne, France

    O. Lame

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In the following, the subscript "p" refers to the particle while the subscript "g" refers to the gas. Parameters in bold are vectors.  ̿ refers to 3×3 tensors.

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Bernard, C.A., Takana, H., Diguet, G. et al. Thermal gradient in polymeric particles during the cold spray process. Comp. Part. Mech. 10, 1697–1716 (2023). https://doi.org/10.1007/s40571-023-00583-0

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