Thermocapillary flows in the weld pool formed during laser welding, investigated mathematically

Abstract

The action of a laser generates a keyhole in the work piece surrounded by a molten weld pool when it is used for the deep penetration welding of metals. The boundary of the weld pool is the melting isotherm of the metal and its cross sectional shape varies with depth when viewed from above the pool. The circulation pattern is the combined result of the translation of the work piece relative to the laser beam and the flow induced by variation of the surface tension caused by the presence of the substantial temperature gradients that exist in the weld pool. The derivative of the surface tension with respect to the temperature can, furthermore, change sign in the presence of suitable traces of contaminants whose concentration need only be to the extent of a few parts per million. Powerful thermocapillary surface forces result which can cause a rapid flow near the surface of the weld pool. This paper formulates the problem of modelling mathematically the flow in the weld pool caused by a combination of the translation of the work piece and the presence of these thermocapillary flows. It is shown that the three-dimensional flow in the weld pool can be studied using a representation of the thermocapillary boundary layer as a surface condition imposed on the otherwise inviscid equations of motion for the flow in the weld pool.The action of a laser generates a keyhole in the work piece surrounded by a molten weld pool when it is used for the deep penetration welding of metals. The boundary of the weld pool is the melting isotherm of the metal and its cross sectional shape varies with depth when viewed from above the pool. The circulation pattern is the combined result of the translation of the work piece relative to the laser beam and the flow induced by variation of the surface tension caused by the presence of the substantial temperature gradients that exist in the weld pool. The derivative of the surface tension with respect to the temperature can, furthermore, change sign in the presence of suitable traces of contaminants whose concentration need only be to the extent of a few parts per million. Powerful thermocapillary surface forces result which can cause a rapid flow near the surface of the weld pool. This paper formulates the problem of modelling mathematically the flow in the weld pool caused by a combination of the tr...