148
5 Dynamic Behaviors of Metal Vapor/Plasma Plume …
region and condensation region for each transient state; based on the temperature
value on the wall of the keyhole, if the temperature of a certain local position is
higher than a certain value (set around the boiling point in this paper), it is set as the
evaporation boundary; otherwise, simple reflection boundaries are imposed for local
positions of the keyhole with temperatures lower than the threshold.
For the evaporation boundaries, the metal vapor generated due to evaporation of
the liquid metal on the wall of the keyhole enters inside the keyhole, and the metal
generated is driven by the surface pressure described by formula (5.11).
Assuming the mass conservation law is satisfied during the evaporation of
molten metal, the vapor density ρ g on the evaporation boundary can be obtained
approximately by the following formula:
ρ g = (
M a
N a k B
)
p r
T gb
(5.16)
where M a —molar mass;
N a —Avogadro constant.
The velocity of the metal at the evaporation boundary approximates to the
velocity of the vapor at the nearest neighboring grid, the direction is assumed to
be perpendicular to the wall. It can be expressed as follows:
− − →
∂U g
∂ − → n
=
− →
0
(5.17)
where
− →
U g —Velocity vector of metal vapor.
For the condensation area on the wall of the keyhole, the velocity of the metal
vapor meets the reflection boundary conditions. Assuming the velocity perpendicular
to the tangent direction of the boundary is reversed, the velocity direction along the
tangential direction of the boundary line remains unchanged, let
− →
U g =
u g v g w g
,
u g is the velocity component value in normal direction of
− →
U g , v g and w g are the
velocity component values in two tangential directions of
− →
U g , i and i + 1 represent
two adjacent grid nodes at the boundary, and the velocity boundary condition on the
reflection boundary can be expressed as:
u g
i+1
= −(u g ) i , (v g ) i+1 = (v g ) i , (w g ) i+1 = (w g ) i
(5.18)
With the effect of the Knudsen layer ignored, the temperature of metal vapor on
the evaporation boundary approximates to that of the wall of the keyhole.
T gb = T k
(5.19)
where T k —Wall temperature of the keyhole for the point.
5 Dynamic Behaviors of Metal Vapor/Plasma Plume …
region and condensation region for each transient state; based on the temperature
value on the wall of the keyhole, if the temperature of a certain local position is
higher than a certain value (set around the boiling point in this paper), it is set as the
evaporation boundary; otherwise, simple reflection boundaries are imposed for local
positions of the keyhole with temperatures lower than the threshold.
For the evaporation boundaries, the metal vapor generated due to evaporation of
the liquid metal on the wall of the keyhole enters inside the keyhole, and the metal
generated is driven by the surface pressure described by formula (5.11).
Assuming the mass conservation law is satisfied during the evaporation of
molten metal, the vapor density ρ g on the evaporation boundary can be obtained
approximately by the following formula:
ρ g = (
M a
N a k B
)
p r
T gb
(5.16)
where M a —molar mass;
N a —Avogadro constant.
The velocity of the metal at the evaporation boundary approximates to the
velocity of the vapor at the nearest neighboring grid, the direction is assumed to
be perpendicular to the wall. It can be expressed as follows:
− − →
∂U g
∂ − → n
=
− →
0
(5.17)
where
− →
U g —Velocity vector of metal vapor.
For the condensation area on the wall of the keyhole, the velocity of the metal
vapor meets the reflection boundary conditions. Assuming the velocity perpendicular
to the tangent direction of the boundary is reversed, the velocity direction along the
tangential direction of the boundary line remains unchanged, let
− →
U g =
u g v g w g
,
u g is the velocity component value in normal direction of
− →
U g , v g and w g are the
velocity component values in two tangential directions of
− →
U g , i and i + 1 represent
two adjacent grid nodes at the boundary, and the velocity boundary condition on the
reflection boundary can be expressed as:
u g
i+1
= −(u g ) i , (v g ) i+1 = (v g ) i , (w g ) i+1 = (w g ) i
(5.18)
With the effect of the Knudsen layer ignored, the temperature of metal vapor on
the evaporation boundary approximates to that of the wall of the keyhole.
T gb = T k
(5.19)
where T k —Wall temperature of the keyhole for the point.