66
3 Coupling Model and Numerical Computation Method of Keyhole and Weld Pool
As for heat source model of the keyhole laser-absorbing wall, the analytical keyhole
linear heat source model commonly used in the early stage of laser welding simulation, and the dynamic keyhole multiple Fresnel absorption model are introduced.
As for tracking method of the real-time changing gas–liquid free surface during
the welding process, the commonly used VOF (volume of fluid) method and Level
Set method are mainly introduced. The precise treatment of the gas–liquid surface
boundary conditions is a guarantee essential to the calculation accuracy of mesoscale
surface flow in laser welding. The gas–liquid sharp surface method proposed by the
author can accurately treat the surface boundary conditions, avoiding the numerical
error caused by the CSF (continue surface force) model, and greatly improving the
accuracy of the simulation calculation. Therefore, the multi-phase coupling model
of the laser keyhole and weld pool established by this method is also known as laser
welding sharp surface model.
This chapter also gives a detailed introduction of the numerical solution method
and process corresponding to the multi-phase coupling model, including the algorithm based on linear heat source model, the ray tracing algorithm based on multiple
Fresnel absorption heat source, the high precision finite difference solution format
of Level Set method, the fast solving algorithm of weld pool heat transfer and
flow, the OpenMP parallel solving language, and the iterative solving process in
the coupled solution. The multi-phase coupling model introduced in this chapter has
more comprehensive considerations than the quasi-steady-state model as provided
in Chap. 2. It can describe the dynamics features of the keyhole and moving weld
pool during the entire welding process from the initial welding to the quasi-steady
state. But it is more complicated and time-consuming in calculation.
3.2 Governing Equations of Coupled Model
3.2.1 Heat Transfer and Fluid Flow Equations
It is assumed that the molten metal in the weld pool during laser welding is an incompressible fluid, and the density of the molten metal does not change during the solid–
liquid phase transition. Therefore, the mass, momentum and energy conservation is
expressed as follows
∇ ·
− →
U =0
(3.1)
ρ
∂
− →
U
∂t
+
− →
U · ∇
− →
U
= ∇ ·
μ l ∇
− →
U
− ∇ p −
μ l
K
− →
U
−
C ρ
√
K
|
− →
U |
− →
U + ρ
gβ
T − T re f
(3.2)
3 Coupling Model and Numerical Computation Method of Keyhole and Weld Pool
As for heat source model of the keyhole laser-absorbing wall, the analytical keyhole
linear heat source model commonly used in the early stage of laser welding simulation, and the dynamic keyhole multiple Fresnel absorption model are introduced.
As for tracking method of the real-time changing gas–liquid free surface during
the welding process, the commonly used VOF (volume of fluid) method and Level
Set method are mainly introduced. The precise treatment of the gas–liquid surface
boundary conditions is a guarantee essential to the calculation accuracy of mesoscale
surface flow in laser welding. The gas–liquid sharp surface method proposed by the
author can accurately treat the surface boundary conditions, avoiding the numerical
error caused by the CSF (continue surface force) model, and greatly improving the
accuracy of the simulation calculation. Therefore, the multi-phase coupling model
of the laser keyhole and weld pool established by this method is also known as laser
welding sharp surface model.
This chapter also gives a detailed introduction of the numerical solution method
and process corresponding to the multi-phase coupling model, including the algorithm based on linear heat source model, the ray tracing algorithm based on multiple
Fresnel absorption heat source, the high precision finite difference solution format
of Level Set method, the fast solving algorithm of weld pool heat transfer and
flow, the OpenMP parallel solving language, and the iterative solving process in
the coupled solution. The multi-phase coupling model introduced in this chapter has
more comprehensive considerations than the quasi-steady-state model as provided
in Chap. 2. It can describe the dynamics features of the keyhole and moving weld
pool during the entire welding process from the initial welding to the quasi-steady
state. But it is more complicated and time-consuming in calculation.
3.2 Governing Equations of Coupled Model
3.2.1 Heat Transfer and Fluid Flow Equations
It is assumed that the molten metal in the weld pool during laser welding is an incompressible fluid, and the density of the molten metal does not change during the solid–
liquid phase transition. Therefore, the mass, momentum and energy conservation is
expressed as follows
∇ ·
− →
U =0
(3.1)
ρ
∂
− →
U
∂t
+
− →
U · ∇
− →
U
= ∇ ·
μ l ∇
− →
U
− ∇ p −
μ l
K
− →
U
−
C ρ
√
K
|
− →
U |
− →
U + ρ
gβ
T − T re f
(3.2)