In this work, a discrete element model (DEM) is developed and implemented in the open source flow solver MFiX to simulate the effective thermal conductivity of powder beds for selective laser sintering (SLS) applications, considering scenarios common in SLS such as thin beds, high temperatures, and degrees of powder consolidation. Random particle packing structures of spherical particles are generated and heat transfer between the particles is calculated. A particle–particle contact conduction model, a particle–fluid–particle conduction model, and a view factor radiation model using ray-tracing for calculation of view factors and assuming optically thick particles are used. A nonlinear solver is used to solve for the particle temperatures that drive the net heat transfer to zero for a steady state solution. The effective thermal conductivity is then calculated from the steady state temperature distribution. Results are compared against previously published experimental measurements for powder beds and good agreement is obtained. Results are developed for the impacts of very high temperatures, finite bed depth, consolidation, Young's modulus, emissivity, gas conductivity, and polydispersity on effective thermal conductivity. Emphasis is placed on uncertainty quantification in the predicted thermal conductivity resulting from uncertain inputs. This allows SLS practitioners to control the inputs to which the thermal response of the process is most sensitive.

References

References
1.
Nelson
,
J. C.
,
Xue
,
S.
,
Barlow
,
J. W.
,
Beaman
,
J. J.
,
Marcus
,
H. L.
, and
Bourell
,
D. L.
,
1993
, “
Model of the Selective Laser Sintering of Bisphenol-A Polycarbonate
,”
Ind. Eng. Chem. Res.
,
32
(
10
), pp.
2305
2317
.
2.
van Antwerpen
,
W.
,
du Toit
,
C. G.
, and
Rousseau
,
P. G.
,
2010
, “
A Review of Correlations to Model the Packing Structure and Effective Thermal Conductivity in Packed Beds of Mono-Sized Spherical Particles
,”
Nucl. Eng. Des.
,
240
(
7
), pp.
1803
1818
.
3.
Masamune
,
S.
, and
Smith
,
J. M.
,
1963
, “
Thermal Conductivity of Beds of Spherical Particles
,”
Ind. Eng. Chem. Fundam.
,
2
(
2
), pp.
136
143
.
4.
Cheng
,
S. C.
, and
Vachon
,
R. I.
,
1969
, “
Thermal Conductivity of Packed Beds and Powder Beds
,”
Int. J. Heat Mass Transfer
,
12
(
9
), pp.
1201
1206
.
5.
Gusarov
,
A. V.
,
Laoui
,
T.
,
Froyen
,
L.
, and
Titov
,
V. I.
,
2003
, “
Contact Thermal Conductivity of a Powder Bed in Selective Laser Sintering
,”
Int. J. Heat Mass Transfer
,
46
(
6
), pp.
1103
1109
.
6.
Slavin
,
A. J.
,
Arcas
,
V.
,
Greenhalgh
,
C. A.
,
Irvine
,
E. R.
, and
Marshall
,
D. B.
,
2002
, “
Theoretical Model for the Thermal Conductivity of a Packed Bed of Solid Spheroids in the Presence of a Static Gas, With No Adjustable Parameters Except at Low Pressure and Temperature
,”
Int. J. Heat Mass Transfer
,
45
(
20
), pp.
4151
4161
.
7.
Slavin
,
A. J.
,
Londry
,
F. A.
, and
Harrison
,
J.
,
2000
, “
A New Model for the Effective Thermal Conductivity of Packed Beds of Solid Spheroids: Alumina in Helium Between 100 and 500 C
,”
Int. J. Heat Mass Transfer
,
43
(
12
), pp.
2059
2073
.
8.
Xue
,
S.
, and
Barlow
,
J. W.
,
1990
, “
Thermal Properties of Powders
,”
Solid Freeform Fabrication Proceedings
, pp.
179
185
.
9.
Xue
,
S.
, and
Barlow
,
J. W.
,
1991
, “
Models for the Prediction of the Thermal Conductivities of Powders
,”
Solid Freeform Fabrication Proceedings
, pp.
62
69
.
10.
Yuan
,
M.
,
Diller
,
T. T.
,
Bourell
,
D.
, and
Beaman
,
J.
,
2013
, “
Thermal Conductivity of Polyamide 12 Powder for Use in Laser Sintering
,”
Rapid Prototyping J.
,
19
(
6
), pp.
437
445
.
11.
Sih
,
S. S.
,
1996
, “
The Thermal and Optical Properties of Powders in Selective Laser Sintering
,” Ph.D. thesis, Ann Arbor, MI.
12.
Vargas
,
W. L.
, and
McCarthy
,
J. J.
,
2002
, “
Conductivity of Granular Media With Stagnant Interstitial Fluids Via Thermal Particle Dynamics Simulation
,”
Int. J. Heat Mass Transfer
,
45
(
24
), pp.
4847
4856
.
13.
Zhang
,
H.
,
Zhou
,
Q.
,
Xing
,
H.
, and
Muhlhaus
,
H.
,
2011
, “
A DEM Study on the Effective Thermal Conductivity of Granular Assemblies
,”
Powder Technol.
,
205
(
1–3
), pp.
172
183
.
14.
Tsory
,
T.
,
Ben-Jacob
,
N.
,
Brosh
,
T.
, and
Levy
,
A.
,
2013
, “
Thermal DEMCFD Modeling and Simulation of Heat Transfer Through Packed Bed
,”
Powder Technol.
,
244
, pp.
52
60
.
15.
Widenfeld
,
G.
,
Weiss
,
Y.
, and
Kalman
,
H.
,
2003
, “
The Effect of Compression and Preconsolidation on the Effective Thermal Conductivity of Particulate Beds
,”
Powder Technol.
,
133
(
1–3
), pp.
15
22
.
16.
Feng
,
Y.
,
Han
,
K.
,
Li
,
C.
, and
Owen
,
D.
,
2008
, “
Discrete Thermal Element Modelling of Heat Conduction in Particle Systems: Basic Formulations
,”
J. Comput. Phys.
,
227
(
10
), pp.
5072
5089
.
17.
Garg
,
R.
,
Galvin
,
J.
,
Li
,
T.
, and
Pannala
,
S.
,
2012
, “
Documentation of Open-Source MFIX-DEM Software for Gas-Solids Flows
,” https://mfix.netl.doe.gov/documentation/qmomk_doc_2012-1.pdf
18.
Musser
,
J. M. H.
,
2011
, “
Modeling of Heat Transfer and Reactive Chemistry for Particles in Gas-Solid Flow Utilizing Continuum-Discrete Methodology (CDM)
,” Ph.D. thesis, West Virginia University, Morgantown, WV.
19.
Powell
,
M. J. D.
,
1964
, “
An Efficient Method for Finding the Minimum of a Function of Several Variables Without Calculating Derivatives
,”
Comput. J.
,
7
(
2
), pp.
155
162
.
20.
Batchelor
,
G. K.
, and
O'Brien
,
R. W.
,
1977
, “
Thermal or Electrical Conduction Through a Granular Material
,”
Proc. R. Soc. London, Ser. A
,
355
(
1682
), pp.
313
333
.
21.
Rong
,
D.
, and
Horio
,
M.
,
1999
, “
DEM Simulation of Char Combustion in a Fluidized Bed
,”
Second International Conference on CFD in the Minerals and Process Industries
, Melbourne, Australia, Dec. 6–8, pp.
65
70
.
22.
Marsaglia
,
G.
,
1972
, “
Choosing a Point From the Surface of a Sphere
,”
Ann. Math. Stat.
,
43
(
2
), pp.
645
646
.
23.
Zhou
,
J.
,
Zhang
,
Y.
, and
Chen
,
J. K.
,
2009
, “
Numerical Simulation of Laser Irradiation to a Randomly Packed Bimodal Powder Bed
,”
Int. J. Heat Mass Transfer
,
52
(
1314
), pp.
3137
3146
.
24.
Xiu
,
D.
, and
Karniadakis
,
G.
,
2002
, “
The Wiener–Askey Polynomial Chaos for Stochastic Differential Equations
,”
SIAM J. Sci. Comput.
,
24
(
2
), pp.
619
644
.
25.
Xiu
,
D.
, and
Karniadakis
,
G. E.
,
2003
, “
A New Stochastic Approach to Transient Heat Conduction Modeling With Uncertainty
,”
Int. J. Heat Mass Transfer
,
46
(
24
), pp.
4681
4693
.
26.
Xiu
,
D.
, and
Hesthaven
,
J.
,
2005
, “
High-Order Collocation Methods for Differential Equations With Random Inputs
,”
SIAM J. Sci. Comput.
,
27
(
3
), pp.
1118
1139
.
27.
Ganapathysubramanian
,
B.
, and
Zabaras
,
N.
,
2007
, “
Sparse Grid Collocation Schemes for Stochastic Natural Convection Problems
,”
J. Comput. Phys.
,
225
(
1
), pp.
652
685
.
28.
Smolyak
,
S. A.
,
1963
, “
Quadrature and Interpolation Formulas for Tensor Products of Certain Classes of Functions
,”
Sov. Math., Dokl.
,
4
, pp.
240
243
.
29.
Bala
,
K.
,
Pradhan
,
P. R.
,
Saxena
,
N. S.
, and
Saksena
,
M. P.
,
1989
, “
Effective Thermal Conductivity of Copper Powders
,”
J. Phys. D: Appl. Phys.
,
22
(
8
), pp.
1068
1072
.
30.
Press
,
W. H.
,
Flannery
,
B. P.
,
Teukolsky
,
S. A.
, and
Vetterling
,
W. T.
,
1992
,
Numerical Recipes in C: The Art of Scientific Computing
,
2nd ed.
, Cambridge University Press, New York.
You do not currently have access to this content.