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Theoretical and Experimental Investigation of Gas Flows, Powder Transport and Heating in Coaxial Laser Direct Metal Deposition (DMD) Process

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Abstract

The results of theoretical and experimental investigations of direct metal deposition (DMD) processes involving a CO2-laser with the power up to 5 kW and wave length of 10.6 μm are presented. The physical and mathematical model of multi-layer gas flows with gas-jet transportation of metal powder particles has been developed. To simulate the flows of carrier and shaping gases in annular channels of a triple coaxial nozzle, Navier-Stokes equations were applied for an axisymmetric flow. Thermodynamics and powder particles transport are calculated from a discrete-trajectory model with due regard to particle collision with solid walls of the transport nozzle. It is shown that particles may overheat on their way between the nozzle and substrate; the overheating depends on the trajectories by which particles move, on their size, and time of their retention in the laser-radiation region. The results of performed experimental researches on DMD processes visualization are presented. Some results of numerical simulation and experimental data are compared and analyzed.

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Abbreviations

t :

time

{x, y} or {x α, α = 1, 2}:

cylindrical system of coordinates

p, ρ, T, μ, λ:

gas pressure, density, temperature, viscosity, and thermal conductivity

\( \vec{V} \), V:

velocity vector and absolute value of the velocity vector of the gas

uα or u, v:

gas velocity in the x α or x, y directions, respectively

\( \vec{n},\,\vec{\uptau } \) :

normal and tangential vectors

\( \uptau_{ij} = \upmu \left( {{\frac{{\partial u_{i} }}{{\partial x_{j} }}} + {\frac{{\partial u_{j} }}{{\partial x_{i} }}} - \frac{2}{3}\updelta_{ij} {\frac{{\partial u_{k} }}{{\partial x_{k} }}}} \right) \) :

viscosity stress tensor; \( \updelta_{ij} = \left\{ \begin{gathered} \begin{array}{*{20}c} {0,} & {i \ne j} \\ \end{array} \hfill \\ \begin{array}{*{20}c} {1,} & {i = j} \\ \end{array} \hfill \\ \end{gathered} \right.; \)

Re, Pr, Nu :

Reynolds, Prandtl, and Nusselt numbers

c p , c v ,:

heat capacity at constant pressure and constant volume, respectively

γ = c p /c v :

the ratio of specific heats

R :

gas constant

E, e:

gas total energy and internal energy, respectively

\( \Upphi = \uptau_{ij} {\frac{{\partial u_{i} }}{{\partial x_{j} }}} \) :

dissipative function

\( q = - \uplambda \nabla T \) :

a heat flux

g :

acceleration of gravity

σ:

Boltzmann constant

A ab :

coefficient of laser radiation absorption

I(x, y):

laser radiation intensity

C d :

drag coefficient

Gn, Gs, Gc:

flow rate of nozzle, shaping, and carrier gas

r :

radius

φ:

nonsphericity degree of a particle

0:

initial value

p:

particle

s:

solid

m:

liquid or melting

g:

gas

n, τ:

normal and tangential components

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Acknowledgment

This research was supported by the Russian Foundation for Basic Research (Grant No. 08-08-00238_a).

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Authors and Affiliations

  1. Khristianovich Institute of Theoretical and Applied Mechanics, Siberian Branch of Russian Academy of Sciences, Novosibirsk, Russia

    O. B. Kovalev & A. V. Zaitsev

  2. Ecole Nationale d’Ingénieurs de Saint-Etienne (ENISE), DIPI Laboratory, 58 rue Jean Parot, 42023, Saint-Etienne, France

    D. Novichenko & I. Smurov

Authors
  1. O. B. Kovalev
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  2. A. V. Zaitsev
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  3. D. Novichenko
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  4. I. Smurov
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Correspondence to O. B. Kovalev.

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Kovalev, O.B., Zaitsev, A.V., Novichenko, D. et al. Theoretical and Experimental Investigation of Gas Flows, Powder Transport and Heating in Coaxial Laser Direct Metal Deposition (DMD) Process. J Therm Spray Tech 20, 465–478 (2011). https://doi.org/10.1007/s11666-010-9539-3

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  • DOI: https://doi.org/10.1007/s11666-010-9539-3

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