Bozbiei L. Improvement of the vacuum arc remelting process of the steel by using a convective structure with free boundaries

This work proposes to provide maximum homogenization of the doping impurity due to its transfer in the steel melt due to the convective flow having a stable ordered structure. It is established that in the melting of a metal at the vacuum-arc steel remelting there is a convective structure that occupies the entire volume of the melt. It has an upward flow in the center and is declining -on the periphery. Such a convective structure is similar to the isolated cylindrical convective structures observed in the horizontal layers of viscous fluid heated from below. An analytical review of scientific sources has shown that in the study ofnatural convection in unevenly heated liquid, the main attention was paid only to completely formed orderly convective currents, for example, Benard cells. The processes of the origin of convective structures, their development, and the transition from one state to another, when the most isolated cylindrical convective structures are observed, due attention is not paid. Therefore, the paper presents studies to improve the process of vacuum-arc steel remelting and to determine the laws of the convective flow in horizontal layers of the liquid.The mathematical model of convective heat transfer in elementary convective cell (ECC)with free boundaries is proposed. The analytical solutions for the velocity and perturbation (deviation of the magnitude from the equivalent in the state of mechanical equilibrium) of the temperature in the ECC are obtained. Their dependence on the axial coordinate is determined by simple harmonics, and from the radial coordinate it is presented in the form of the Bessel function of the first kind of zero (for the perturbation of the temperature and the axial component 23of the velocity) and the first order (for the radial component of the velocity). The analytical expressions for radial velocity wave numbers and eigenvalues of the problem are obtained. It is shown that the spectrum of eigenvalues is discrete in both the perturbation mode and the radial wave number.In order to increase the homogenization of the doping impurity, the design of the cathode of the vacuum arc furnace is improved. The method of calculating the geometric parameters of cavities in a cathode (the dimensionless width of the inclined circular groove, the radius of a cylindrical cathode), containing a powder of a doping impurity, is provided, in which a continuous flow of nanodispersed powder into the metal melts is provided. It is shown that in the case of zirconium dioxide powder application, they take values of 0.14 and 0.63, respectively.An expression was also obtained for determining the maximum allowable particle size of a dopant, in which it is uniformly distributed throughout the melt volume due to the convective flow. It has been established that for a steel 08X18H10T, the size of ZrO2particles should be within the range of 80− 100 nm.