Numerical Simulation of Molten Flow in Directed Energy Deposition Using an Iterative Geometry Technique

Abstract

The complex, multi-faceted physics of laser-based additive metals processing tends to demand high-fidelity models and costly simulation tools to provide predictions accurate enough to aid in selecting process parameters. Of particular difficulty is the accurate determination of melt pool shape and size, which are useful for predicting lack-of-fusion, as this typically requires an adequate treatment of thermal and fluid flow. In this article we describe a novel numerical simulation tool which aims to achieve a balance between accuracy and cost. This is accomplished by making simplifying assumptions regarding the behavior of the gas-liquid interface for processes with a moderate energy density, such as Laser Engineered Net Shaping (LENS). The details of the implementation, which is based on the solver simpleFoam of the well-known software suite OpenFOAM, are given here and the tool is verified and validated for a LENS process involving Ti-6Al-4V. The results indicate that the new tool predicts width and height of a deposited track to engineering accuracy levels.

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Abbreviations

A c e l l :

= local mesh face surface area

A t :

= track cross-sectional area

α :

= liquid phase fraction

C p :

= Specific heat

d :

= powder nozzle diameter

\(\hat {d}\) :

= vector in the direction of the laser beam

D c :

= D’arcy phase coefficient

\(D_{c_{l}}\) :

= D’arcy liquid coefficient

\(D_{c_{s}}\) :

= D’arcy solid coefficient

D i :

= self-dyadic tensor of the unit vector in the direction of vd,i

δ i j :

= Kronecker delta

erf :

= Gauss error function

𝜖 :

= emissivity

η :

= laser bulk beam efficiency

f t o p :

= set of all faces on the top boundary

g :

= gravity constant

γ :

= surface tension

H t :

= track height

h :

= nozzle standoff height

h d :

= depth from surface

h c :

= convection coefficient

H f :

= latent heat of fusion

I :

= identity matrix

\(\mathscr {I}\) :

= total bulk intensity

k :

= thermal conductivity

μ :

= dynamic viscosity

N :

= number of powder nozzles

\(\hat {n}_{i}\) :

= normal vector

\(\mathscr {P}\) :

= Laser power

p :

= pressure

p :

= arbitrary point in global coordinate system

p f :

= focal point of powder streams

p r :

= vector from powder focal point to arbitrary point p

p r g h :

= pρgh d

q l a s e r :

= laser heat flux

R t :

= radius of deposit track

ρ :

= density

r 0 :

= laser beam radius

r c,i :

= radius of powder cloud

r n :

= distance of spray nozzle outlet from laser axis

r p,i :

= perpendicular distance from powder stream axis to point p

s :

= powder nozzle spacing

σ s b :

= Stefan Boltzmann constant

T :

= temperature

T :

= ambient temperature

T l :

= alloy liquidus temperature

T s :

= alloy solidus temperature

T m :

= average melting temperature

T s u b :

= ambient solid temperature

t i :

= distance from powder nozzle center to point p along vector vd,i

𝜃 0 :

= angle between powder jet streams projected into the horizontal plane

𝜃 d :

= powder jet divergence angle

𝜃 j :

= powder jet angle

u i :

= liquid velocity

V i :

= solid velocity

\(\dot {V}\) :

= powder feed rate

\(\dot {V}^{\prime \prime }\) :

= powder flow rate flux

v d,i :

= vector from powder nozzle outlet to powder stream focal point

v p :

= locally averaged velocity of powder crossing into melt pool

W t :

= track width

References

  1. 1.

    Kim, Y.D., Kim, W.S.: A numerical analysis of heat and fluid flow with a deformable curved free surface in a laser melting process. Int. J. Heat Fluid Flow 29, 1481–1493 (2008)

    Article  Google Scholar 

  2. 2.

    Mullen, L., Stamp, R., Brooks, W., Jones, E., Sutcliffe, C.: Selective laser melting: a regular unit cell approach for the manufacture of porous, titanium, bone in-growth constructs, suitable for orthopedic applications. J. Biomed. Mater. Res. B Appl. Biomater. 89(2), 325–334 (2009)

    Article  Google Scholar 

  3. 3.

    Shen, Y., McKown, S., Tsopanos, S., Sutcliffe, C., Mines, R., Cantwell, W.: The mechanical properties of sandwich structures based on metal lattice architectures. J. Sandw. Struct. Mater. 12(2), 159–180 (2010)

    Article  Google Scholar 

  4. 4.

    Kumar, A., Roy, S.: Effect of three-dimensional melt pool convection on process characteristics during laser cladding. Comput. Mater. Sci. 46, 495–506 (2009). https://doi.org/10.1016/j.commatsci.2009.04.002

    Article  Google Scholar 

  5. 5.

    Gan, Z., Yu, G., He, X., Li, S.: Numerical simulation of thermal behavior and multicomponent mass transfer in direct laser deposition of co-base alloy on steel. Int. J. Heat Mass Transf. 104, 28–38 (2017)

    Article  Google Scholar 

  6. 6.

    Bedenko, D., Kovalev, O.: Modelling of heat and mass transfer in the laser cladding during direct metal deposition. Thermophys. Aeromech. 20(2), 251–261 (2013)

    Article  Google Scholar 

  7. 7.

    Ahsan, M.N., Pinkerton, A.J.: An analytical–numerical model of laser direct metal deposition track and microstructure formation. Model. Simul. Mater. Sci. Eng. 19(5), 055,003 (2011)

    Article  Google Scholar 

  8. 8.

    Wang, Q., Li, J., Gouge, M., Nassar, A.R., Michaleris, P.P., Reutzel, E.W.: Physics-based multivariable modeling and feedback linearization control of melt-pool geometry and temperature in directed energy deposition. J. Manuf. Sci. Eng. 139(2), 021,013 (2017)

    Article  Google Scholar 

  9. 9.

    Weller, H.G., Tabor, G., Jasak, H., Fureby, C.: A tensorial approach to computational continuum mechanics using object-oriented techniques. Comput. Phys. 12(6), 620–631 (1998)

    Article  Google Scholar 

  10. 10.

    Assuncao, E., Williams, S., Yapp, D.: Interaction time and beam diameter effects on the conduction mode limit. Opt. Lasers Eng. 50(6), 823–828 (2012)

    Article  Google Scholar 

  11. 11.

    Geuzaine, C., Remacle, J.F.: Gmsh: a three-dimensional finite element mesh generator with built-in pre- and post-processing facilities. Int. J. Numer. Methods Eng. 79(11), 1309–1331 (2009)

    Article  MATH  Google Scholar 

  12. 12.

    Premnath, K.N., Pattison, M.J., Banerjee, S.: Generalized lattice boltzmann equation with forcing term for computation of wall-bounded turbulent flows. Phys. Rev. E 79(2), 026,703 (2009)

    MathSciNet  Article  Google Scholar 

  13. 13.

    Boivineau, M., Cagran, C., Doytier, D., Eyraud, V., Nadal, M.H., Wilthan, B., Pottlacher, G.: Thermophysical properties of solid and liquid Ti-6Al-4V (TA6v) alloy. Int. J. Thermophys. 27(2), 507–529 (2006)

    Article  Google Scholar 

  14. 14.

    Voller, V.R., Prakash, C.: A fixed grid numerical modelling methodology for convection-diffusion mushy region phase-change problems. Int. J. Heat Mass Transf. 30(8), 1709–1719 (1987)

    Article  Google Scholar 

  15. 15.

    Rösler, F., Brüggemann, D.: Shell-and-tube type latent heat thermal energy storage: numerical analysis and comparison with experiments. Heat Mass Transf. 47 (8), 1027–1033 (2011)

    Article  Google Scholar 

  16. 16.

    Aune, R., Battezzati, L., Brooks, R., Egry, I., Fecht, H.J., Garandet, J.P., Mills, K.C., Passerone, A., Quested, P.N., Ricci, E., Schneider, S., Seetharaman, S., Wunderlich, R.K., Vinet, B.: Surface tension and viscosity of industrial alloys from parabolic flight experiments - results of the ThermoLab project. Microgravity Sci. Technol. 16, 11–14 (2005)

    Article  Google Scholar 

  17. 17.

    Stadler, M., Masquère, M., Freton, P., Franceries, X., Gonzalez, J.: Experimental characterization of the weld pool flow in a tig configuration. In: Journal of Physics: Conference series, vol. 550, pp. 012005. IOP publishing (2014)

  18. 18.

    Sahoo, P., Debroy, T., McNallan, M.J.: Surface tension of binary Metal–Surface active solution systems under conditions relevant to welding metallurgy. Metall. Trans. B 19B, 483–491 (1988)

    Article  Google Scholar 

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Acknowledgements

This work was partially supported by US Navy SBIR N111-077-0790.

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Correspondence to Timothy J. Vincent.

Additional information

This work was partially supported by US Navy SBIR N111-077-0790.

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Vincent, T.J., Rumpfkeil, M.P. & Chaudhary, A. Numerical Simulation of Molten Flow in Directed Energy Deposition Using an Iterative Geometry Technique. Lasers Manuf. Mater. Process. 5, 113–132 (2018). https://doi.org/10.1007/s40516-018-0057-3

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Keywords

  • LENS
  • DED
  • Additive manufacturing
  • OpenFOAM
  • Ti-6Al-4V