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


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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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


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

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Corresponding author

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).

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