Study of dimensionless quantities to analyse front and rear wall of keyhole formed during laser beam welding

Abstract

Fluid flow mechanisms present in Keyhole (KH) during Laser Beam Welding (LBW) process influence the associated heat and mass transfer. In an attempt to describe these complexities for eventual optimization of LBW parameters, a dimensionless analysis using Mach (Ma), Raleigh (Ra), Reynolds (Re) and Marangoni (Mg) numbers have been carried out. This analysis describes hydrodynamics of melt and vapour phase appearing in the front and rear wall of KH. The non-dimensional hydrodynamic quantities describe the mechanism behind flow pattern present in melt-vapour in terms of ratio of convection–conduction heat transfer occurring within KH. The analysis shows that the higher Marangoni number indicates stronger Marangoni convection in the KH causing relatively higher capillary flow in the melt pool. The laminar-turbulent flow of melt-vapour in KH medium is described in terms of ratio of Reynolds and Mach numbers (Re/Ma). The pressure distribution in the KH accounts for the melt-vapour ejection rate. A relationship between depth and radius of KH has been obtained as a function of delivered laser power.

Symbols

r _kh :

Keyhole radius

σ _coeff :

Surface tension coefficient

p _abl :

Ablation pressure due to recoil pressure

δρ _g :

Excess pressure due to gas flowing

μ :

Kinematic viscosity

C _g :

Gas flow parameter

Re:

Reynolds number

Mg:

Marangoni number

δ :

Melt thickness

σ :

Surface tension force

α :

Thermal diffusivity

ρc _p :

Ratio of thermal conductivity to volumetric heat capacity

$-(\partial \gamma /\partial T)$ :

Temperature coefficient of surface tension

ρ :

Melt density

c _p :

Specific heat capacity

V _kh :

Keyhole volume

ΔT :

Temperature difference in the keyhole

τ :

Relaxational dimensionless parameter

β :

Volumetric thermal expansion coefficient

$\boldsymbol{c}$ :

Speed of sound

g :

Acceleration due to gravity

Gr:

Grashof number

h _kh :

Depth of keyhole

Pr:

Prandtl number

Ma:

Mach numbers

Nu:

Nusselt number

V _o and V _c :

Object and sound velocity in keyhole medium

χ :

Heat conductivity

γ :

Adiabatic coefficient

Pe:

Peclet number

Ra:

Raleigh number

r _b :

Beam radius

FWKH:

Front wall of keyhole

RWKH:

Rear wall of keyhole

V_wel :

Spacimen velocity

W_kh :

Width of keyhole at half of maximum depth

Lwp:

Length of weld pool