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

A mathematical model for the transient gas dynamics in one dimension resulting from laser vaporization of metals is presented. The model treats the case of inviscid isentropic (the material derivative of the specific entropy vanishes) flow. A general solution is obtained for the flow velocity and thermodynamic parameters as functions of time and position. The flow field is determined in terms of the time dependence of the velocity νK, which is the velocity of the vapor exiting a transition zone between the melt surface and the bulk vapor flow (known as the Knudsen layer). It was found that the stagnation parameters c0, p0, ρ0, and T0 (the sound speed, pressure, density, and temperature for the field when the flow velocity vanishes) were functions only of the specific entropy s and thus their material derivatives also vanish. The general solution is applied to a specific case in which νK is taken to be linear in time. The isentropic results are compared with the homentropic results using a quasisteady approximation. It was found that for reasonably small variations in νK, comparison of isentropic and homentropic results show them to be consistent. Thermodynamics relations derived and used to test the results are not satisfied by the quasisteady homentropic calculations but are satisfied by the isentropic results. It is concluded that the specific entropy varies with νK and the isentropic model extends the range of applicability of the flow model to all subsonic flow situations.