Methods for simulating oxides in aluminum castings
View Patent ↗A method of simulating aluminum oxides defects in aluminum castings comprises determining the free surface area for a plurality of particles of aluminum in an aluminum melt, storing the free surface area for each particle of aluminum, tracking the free surface area change during mold filling, and calculating the total area of entrained or surface oxide films based on the free surface area change during mold filling. The method may further comprise a scalar variable method and a discrete particle method coupled together to simulate the aluminum oxide defects in aluminum castings.
1. A method of simulating aluminum oxides defects in aluminum castings comprising:
providing a casting mold and a mold filling approach for casting an aluminum melt;
determining the free surface area for a plurality of particles of aluminum in the aluminum melt;
storing the free surface area for each particle of aluminum;
tracking the free surface area change during filling of the casting mold;
calculating the total area of entrained or surface oxide films based on the free surface area change during filling of the casting mold in accordance with the mold filling approach;
determining the total area of bifilms created, wherein the total area of bifilms are calculated by storing the area of contact between fluid fronts meeting at angles of more than 135 degrees for each of the plurality of particles and summing over all particle areas;
determining the total area of cold shuts created, wherein the total area of cold shuts are calculated by storing the area of bifilms created at temperatures below the median temperature of a freezing range;
determining a velocity of the aluminum melt at multiple locations; and
optimizing the casting mold and mold filling approach to minimize the aluminum oxide defects based on one of the determined free surface area for a plurality of particles of aluminum in the aluminum melt, and determined total area of bifilms created, determined total area of cold shuts created, and determined velocity of the aluminum melt at multiple locations;
wherein the velocity of the aluminum melt is determined using the algorithm
δρ
u
x
δ
t
=
-
[
δ
P
δ
x
]
-
(
δρ
u
x
u
x
δ
x
+
δρ
u
y
u
x
δ
y
+
δρ
u
z
u
x
δ
z
)
-
(
δτ
xx
δ
x
+
δτ
xy
δ
y
+
δτ
xz
δ
z
)
+
ρ
g
x
δρ
u
y
δ
t
=
-
[
δ
P
δ
y
]
-
(
δρ
u
x
u
y
δ
x
+
δρ
u
y
u
y
δ
y
+
δρ
u
z
u
y
δ
z
)
-
(
δτ
yx
δ
x
+
δτ
yy
δ
y
+
δτ
yz
δ
z
)
+
ρ
g
y
δρ
u
z
δ
t
=
-
[
δ
P
δ
z
]
-
(
δρ
u
x
u
z
δ
x
+
δρ
u
y
u
z
δ
y
+
δρ
u
z
u
z
δ
z
)
-
(
δτ
zx
δ
x
+
δτ
zy
δ
y
+
δτ
zz
δ
z
)
+
ρ
g
z
wherein u x , u y , and u z is the velocity in x, y, and z direction (m/s), respectively; P is pressure (Pa); ρ is the aluminum density (g/cm^3); t is time (s); δ x , δ y , and δ z is small increment in x, y, z direction (mm), respectively; τ is shear stress (Pa); and g is gravity (m/s^2).
2. The method of claim 1 , wherein the free surface area is tracked using the algorithm
δρ
F
δ
t
=
-
[
δ
δ
x
(
u
x
ρ
F
)
+
δ
δ
y
(
u
y
ρ
F
)
+
δ
δ
z
(
u
z
ρ
F
)
]
wherein u x , u y , and u z is the velocity in x, y, and z direction (m/s), respectively; ρ is the aluminum density (g/cm^3); t is time (s); δ x , δ y , and δ z is small increment in x, y, z direction (mm), respectively; and F is the force (N).
3. A method of simulating aluminum oxides defects in aluminum castings comprising:
providing a casting mold and a mold filling approach for casting an aluminum melt;
determining the free surface area for a plurality of particles of aluminum in the aluminum melt;
storing the free surface area for each particle of aluminum;
tracking the free surface area change during filling of the casting mold; and
calculating the total area of entrained or surface oxide films based on the free surface area change during filling of the casting mold in accordance with the mold filling approach;
determining a velocity of the aluminum melt at multiple locations; and
optimizing the casting mold and mold filling approach to minimize the aluminum oxide defects based on one of the determined free surface area for a plurality of particles of aluminum in the aluminum melt and determined velocity of the aluminum melt at multiple locations;
wherein the velocity of the aluminum melt is determined using the algorithm
δρ
u
x
δ
t
=
-
[
δ
P
δ
x
]
-
(
δρ
u
x
u
x
δ
x
+
δρ
u
y
u
x
δ
y
+
δρ
u
z
u
x
δ
z
)
-
(
δτ
xx
δ
x
+
δτ
xy
δ
y
+
δτ
xz
δ
z
)
+
ρ
g
x
δρ
u
y
δ
t
=
-
[
δ
P
δ
y
]
-
(
δρ
u
x
u
y
δ
x
+
δρ
u
y
u
y
δ
y
+
δρ
u
z
u
y
δ
z
)
-
(
δτ
yx
δ
x
+
δτ
yy
δ
y
+
δτ
yz
δ
z
)
+
ρ
g
y
δρ
u
z
δ
t
=
-
[
δ
P
δ
z
]
-
(
δρ
u
x
u
z
δ
x
+
δρ
u
y
u
z
δ
y
+
δρ
u
z
u
z
δ
z
)
-
(
δτ
zx
δ
x
+
δτ
zy
δ
y
+
δτ
zz
δ
z
)
+
ρ
g
z
the free surface area is tracked using the algorithm
δρ
F
δ
t
=
-
[
δ
δ
x
(
u
x
ρ
F
)
+
δ
δ
y
(
u
y
ρ
F
)
+
δ
δ
z
(
u
z
ρ
F
)
]
and the mass conservation is ensured using the algorithm
δρ
δ
t
=
-
[
δ
δ
x
(
ρ
u
x
)
+
δ
δ
y
(
ρ
u
y
)
+
δ
δ
z
(
ρ
u
z
)
]
wherein u x , u y , and u z , is the velocity in x, y, and z direction (m/s), respectively; P is pressure (Pa); ρ is the aluminum density (g/cm^3); t is time (s); δ x ,δ y , δ z is small increment in x, y, z direction (mm), respectively; F is the force (N), τ is shear stress (Pa); and g is gravity (m/s^2).
4. The method of claim 3 wherein the movement of a discrete entrained oxide particle is described by the algorithm
V
P
ρ
P
∂
u
P
∂
t
=
V
P
(
-
∇
P
+
ρ
g
)
-
V
P
ρΔ
A
2
[
∂
u
P
∂
t
-
∂
u
∂
t
-
u
P
·
∇
u
]
-
V
P
g
(
ρ
-
ρ
P
)
+
π
r
P
2
2
ρ
C
d
(
u
P
-
u
)
u
P
-
u
-
6
r
P
2
πρμ
∫
0
t
[
∂
u
P
∂
t
-
∂
u
∂
t
-
u
P
·
∇
u
]
ⅆ
t
t
-
s
wherein Vp is the particle volume (mm^3); Δ A is the free surface area change, ρ and ρ p are liquid aluminum and particle density, respectively (g/cm^3); u and u p are fluid and particle velocity, respectively (m/s); P is pressure (Pa); g is gravitational acceleration vector (m/s^2); r P is particle radius (mm); C d is drag coefficient (dimensionless); t is time (s); μ is dynamic viscosity (cm^2s^−1); and s is dimensional time (s).
5. The method of claim 4 , wherein the method is performed by a computer with the algorithms programmed therein.
6. A method of simulating aluminum oxides defects in aluminum castings comprising:
providing a casting mold and a mold filling approach for casting an aluminum melt;
determining the free surface area for a plurality of particles of aluminum in the aluminum melt;
storing the free surface area for each particle of aluminum;
tracking the free surface area change during filling of the casting mold; and
calculating the total area of entrained or surface oxide films based on the free surface area change during filling of the casting mold in accordance with the mold filling approach;
wherein a scalar variable method and a discrete particle method are coupled together to simulate the aluminum oxide defects in aluminum castings;
determining a velocity of the aluminum melt at multiple locations; and
optimizing the casting mold and mold filling approach to minimize the aluminum oxide defects based on one of the determined free surface area for a plurality of particles of aluminum in the aluminum melt, calculated total area of entrained or surface oxide films, determined velocity of the aluminum melt at multiple locations; and simulated aluminum oxide defects;
wherein:
the velocity of the aluminum melt is determined using the algorithm
δρ
u
x
δ
t
=
-
[
δ
P
δ
x
]
-
(
δρ
u
x
u
x
δ
x
+
δρ
u
y
u
x
δ
y
+
δρ
u
z
u
x
δ
z
)
-
(
δτ
xx
δ
x
+
δτ
xy
δ
y
+
δτ
xz
δ
z
)
+
ρ
g
x
δρ
u
y
δ
t
=
-
[
δ
P
δ
y
]
-
(
δρ
u
x
u
y
δ
x
+
δρ
u
y
u
y
δ
y
+
δρ
u
z
u
y
δ
z
)
-
(
δτ
yx
δ
x
+
δτ
yy
δ
y
+
δτ
yz
δ
z
)
+
ρ
g
y
δρ
u
z
δ
t
=
-
[
δ
P
δ
z
]
-
(
δρ
u
x
u
z
δ
x
+
δρ
u
y
u
z
δ
y
+
δρ
u
z
u
z
δ
z
)
-
(
δτ
zx
δ
x
+
δτ
zy
δ
y
+
δτ
zz
δ
z
)
+
ρ
g
z
the free surface area is tracked using the algorithm
δρ
F
δ
t
=
-
[
δ
δ
x
(
u
x
ρ
F
)
+
δ
δ
y
(
u
y
ρ
F
)
+
δ
δ
z
(
u
z
ρ
F
)
]
;
the mass conservation is ensured using the algorithm
δρ
δ
t
=
-
[
δ
δ
x
(
ρ
u
x
)
+
δ
δ
y
(
ρ
u
y
)
+
δ
δ
z
(
ρ
u
z
)
]
;
and
wherein u x , u y ,and u z is the velocity in x, y, and z direction (m/s), respectively; P is pressure (Pa); ρ is the aluminum density (g/cm^3); t is time (s); δ x , δ y , and δ z is small increment in x, y, z direction (mm), respectively; g x , g y and g z is gravity in the x, y, z direction m/s^2), τ is shear stress (Pa); and F is the force (N); and
the movement of entrained or surface oxide films is described by the algorithm
δρ
C
δ
t
=
-
∇
·
ρ
u
C
+
∇
·
(
ρη
(
D
+
μ
t
σ
C
)
∇
C
)
.
wherein c is the variable of interest (oxide film concentration for mass transfer, mm^2/mm^3); D is the mass diffusivity for particle motion (mm^2/s); u is the velocity (mm/s); ∇ represents gradient or divergence; μ t is turbulent viscosity (cm^2s^−1); σ c is the turbulent Schmidt number (dimensionless); and η is dimensional normal distance (mm).