Stability and stabilization of garnissage on surface in cylindrical channel

Abstract

Abstract The developed mathematical models of parametric oscillations on the phase change boundaries in a cylindrical channel are presented in a continuation of the previously published paper, which made an introduction to the subject. Analysis of the advanced models and processes described by them, together with the computer simulations, revealed a number of important features of the complex systems with dynamical boundaries of the phase change. Influence of the diverse factors and parameters with their interconnections is investigated in detail: the Peclet number, Bio number, modified Bio number (for the heat flux control system), the ratios of physical properties for the liquid and solid phases, a thickness of a solid layer, and the wave numbers of oscillations. Parameters of a garnissage on the internal surface of a cylindrical channel and the regularities of its instability are discussed for the linear and nonlinear cases. A possibility for the system s stabilization against unstable perturbations is examined using the automatic heat flux control. The control parameters are estimated in computer simulation for a wide range of the variable parameters. The results may be useful for the wall s protection against destruction with the artificially controlled garnissage in the metallurgical machines, as well as in some other applications.