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

  • Timothy J. Vincent
  • Markus P. Rumpfkeil
  • Anil Chaudhary
Article

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.

Keywords

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

Nomenclature

Acell

= local mesh face surface area

At

= track cross-sectional area

α

= liquid phase fraction

Cp

= Specific heat

d

= powder nozzle diameter

\(\hat {d}\)

= vector in the direction of the laser beam

Dc

= D’arcy phase coefficient

\(D_{c_{l}}\)

= D’arcy liquid coefficient

\(D_{c_{s}}\)

= D’arcy solid coefficient

Di

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

δij

= Kronecker delta

erf

= Gauss error function

𝜖

= emissivity

η

= laser bulk beam efficiency

ftop

= set of all faces on the top boundary

g

= gravity constant

γ

= surface tension

Ht

= track height

h

= nozzle standoff height

hd

= depth from surface

hc

= convection coefficient

Hf

= 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

pf

= focal point of powder streams

pr

= vector from powder focal point to arbitrary point p

prgh

= pρgh d

qlaser

= laser heat flux

Rt

= radius of deposit track

ρ

= density

r0

= laser beam radius

rc,i

= radius of powder cloud

rn

= distance of spray nozzle outlet from laser axis

rp,i

= perpendicular distance from powder stream axis to point p

s

= powder nozzle spacing

σsb

= Stefan Boltzmann constant

T

= temperature

T

= ambient temperature

Tl

= alloy liquidus temperature

Ts

= alloy solidus temperature

Tm

= average melting temperature

Tsub

= ambient solid temperature

ti

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

𝜃0

= angle between powder jet streams projected into the horizontal plane

𝜃d

= powder jet divergence angle

𝜃j

= powder jet angle

ui

= liquid velocity

Vi

= solid velocity

\(\dot {V}\)

= powder feed rate

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

= powder flow rate flux

vd,i

= vector from powder nozzle outlet to powder stream focal point

vp

= locally averaged velocity of powder crossing into melt pool

Wt

= track width

Notes

Acknowledgements

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

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Applied Optimization, Inc.FairbornUSA
  2. 2.Department of Mechanical and Aerospace EngineeringUniversity of DaytonDaytonUSA

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