The condition for application of the Crocco integral in the mathematical description of a laser welding plasma plume

Based on the theoretical approach developed in the article by G.A. Turichin et al. (High Temperature. 2006. Vol. 44. No. 5. Pp. 647−655), the characteristics of the plasma plume forming in the keyhole laser welding have been investigated. A condition corresponding to the existence of the Crocco integral was defined, making it possible to simplify the system of gas dynamics equations and obtain analytical solutions for a plasma plume in the form of a classical submerged jet. These solutions were analyzed for a wide range of metal vapor velocities and temperatures at the keyhole top. For some of the selected values, an agreement with the numerical calculations of other authors was found.