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.