Combined thermal, solutal and momentum transport. Assume a rigid mold.
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Transcript of Combined thermal, solutal and momentum transport. Assume a rigid mold.
Time (s)
Max
imum
equivalen
tstres
s(M
Pa)
0.025 0.05 0.075 0.10
5
10
15
20
25
30
35
40
451% Cu3% Cu5% Cu7% Cu9% Cu
Time (s)
Gap
size
(m)
0.025 0.05 0.075 0.10
2E-06
4E-06
6E-06
8E-06
1E-05
1.2E-05
1.4E-05
1.6E-05 1% Cu3% Cu5% Cu7% Cu9% Cu
•Combined thermal, solutal
and momentum transport.• Assume a rigid mold.• Imperfect contact and air gap
formation at metal/mold interface
Design of mold surface topography during early stage solidification of
Al alloysPI: Prof. Nicholas Zabaras Participating students: Deep Samanta, Lijian Tan
Material Process Design and Control Laboratory
D. Samanta and N. Zabaras, “A coupled thermomechanical, thermal transport and segregation analysis of the solidification of Aluminum alloys on molds of uneven topographies ”, Materials Science and Engineering: A, in press.
Lijian Tan, Nicholas Zabaras, “A thermomechanical study of the effects of mold topography on the solidification of Aluminum alloys", Materials Science and Engineering: A, Vol. 404, 197-207, 2005.
D. Samanta and N. Zabaras, “Numerical study of macrosegregation in Aluminum alloys solidifying on uneven surfaces”, International Journal of Heat and Mass Transfer, Vol. 48, 4541-4556, 2005.
L. Tan, D. Samanta and N. Zabaras, “A coupled thermomechanical, thermal transport and segregation analysis of the solidification of aluminum alloys on molds of uneven surface topographies”, Proceedings of the 3rd M.I.T. Conference on Computational Fluid and Solid Mechanics, Massachusetts Institute of Technology, Cambridge, MA, June, 2005 .
Selected publications
Parametric analysis for the following parameters:
1) Wavelength(λ) 2) Concentration (CCu) 3) Superheat (ΔTmelt)
Time (s)
Airgap
size
(m)
0.025 0.05 0.075 0.10
2E-06
4E-06
6E-06
8E-06
1E-05
1.2E-05
superheat = 0 oCsuperheat = 30 oCsuperheat = 45 oC
Time (s)
Max
imum
equivalen
tstres
s(M
Pa)
0.025 0.05 0.075 0.1
10
15
20
25
30
35
40 superheat = 0 oCsuperheat = 30 oCsuperheat = 45 oC
Time (s)
Max
imum
equivalen
tstres
s(M
Pa)
0.025 0.05 0.075 0.15
10
15
20
25
30
35
40
45 = 3 mm= 5 mm= 7 mm= 9 mm
Time (s)
Airgap
size
(m)
0.025 0.05 0.075 0.1
2E-06
4E-06
6E-06
8E-06
1E-05
1.2E-05
1.4E-05
1.6E-05= 3 mm= 5 mm= 7 mm= 9 mm
low solid fraction high solid fractionLow solid fractions usually accompanied by melt feeding.
With increase in solid fraction, there is an increase in strength and bonding ability of dendrites.
13 T sh sw T I
qe
Left: Evolution of pressure at trough with time at selected wavelengths.Right: Mean shell thickness at gap nucleation time.
Cornell UniversityCollege of Engineering
Sibley school of Mechanical and Aerospace Engineering
Surface defects in casting
Sub-surface liquation Crack formation Ripple formation
Uneven mold surface topography effects
Undesirable growth using plain mold
Desirable growth using uneven mold
Modeling effects of uneven mold surface on solidification
Fluid flow
Heat transfer
Casting domain
Heat transfer
Mold
Contact pressure/ air gap criterion
Solute transport
Inelastic deformation
Phase changeand mushy zone
evolution
Deformable or non-deformable mold
• Heat transfer in the mold, solid shell and melt.• Heat transfer causes deformation (thermal stress).• Gaps or contact pressure affect heat transfer.• Solidification after air-gap nucleation not modeled.
Gap nucleation time (comparison with analytical study)
Maximum equivalent stress (MPa)
Frontu
nev
ennes
s(m
)
16 20 24 28 320
0.0004
0.0008
0.0012
0.0016
With inverse segregationWithout inverse segregation
= 1 mm
= 9 mm= 7 mm
= 3 mm= 5 mm
Copper concentration (wt %)
Equivalen
tstres
sat
den
drite
roots
(MPa)
0 2 4 6 8 100
2
4
6
8
10
12
14
16
18
Al-Cu alloy with 1.8% Cu is most susceptible to hot tearing
Wavelength less than 5mm
corresponds to an optimum
3 2
45 , 1 , 0.5 ,
, ( 93 10 / )
oV wall liquid
Platform liquid liquid
height mm
J m
Surface tension effects
Initial contact between mold and liquid
The size of micro-gap
Heat flux at early stages of solidification
Surface quality of aluminum casting
Mold topography Surface energy Gravity
A change of surface tension drastically changes the solidification speed at very early stages of solidification.
4
10 ,
2 10 ,
0.6wall liquid
height m
P Pa
Micro-scale effects
Macro-scale effects
4
10
10
height m
P Pa
4
10
2 10
height m
P Pa
10
25o
height m
27.124.421.719.016.313.610.98.15.42.7
891.1878.7866.2853.8841.3828.9816.4804.0791.5
901.5886.9872.3857.7843.1828.5813.9799.3784.7770.1
18.316.114.412.610.89.07.25.43.61.8
Equivalent stress (t = 0.1 s) Isotherms (t = 0.1s)
λ = 3 mm
λ = 5 mm