Gas dynamics resulting from laser vaporization of metals in one dimension. I

A mathematical model for the transient gas dynamics in one dimension resulting from laser vaporization of metals in the presence of an ambient atmosphere (air) is presented. The gas dynamics is analyzed by considering four regions: a transition zone between the melt surface and the bulk vaporized metal (known as the Knudsen layer), the bulk vaporized metal, the disturbed, and the undisturbed air. The ratios of the temperature and density across the Knudsen layer are modeled by constructing a velocity distribution which is a sum of two variably weighted Maxwellian distributions. The formation of a shock front is considered, and where appropriate the shock front location and velocity are included in the boundary conditions. Profiles in space and time for the velocity, temperature, pressure, and density are determined in a mathematically consistent way by appropriate matching across the Knudsen layer, the vapor/air interface, and the interface between the disturbed and undisturbed air (which may or may not be a shock front). The specific case of homentropic flow, in which the specific entropy in each region is constant, is taken up. The gas dynamics was completely determined by the ambient atmospheric conditions and the velocity νK of the vapor exiting the Knudsen layer, and relations were obtained for thermodynamic parameters in terms of the velocity and specific entropy. It was found that the specific entropy varied with νK, but slowly enough so that the change was perturbative over a reasonably large range of exit velocities. Results of some calculations are presented for a commercially available material. It is estimated that the homentropic model is applicable to vaporization due to laser beams in which the change in intensity is ≲0.1 MW/cm2. The model can be applied to relatively low intensity irradiation such as occurs during welding and slow drilling, and is valid near the center line of a laser beam, or in deep holes being drilled in which the sidewalls prevent lateral flow of vaporized material.