The physical factors and conditions leading to the formation of stable vortex structures in internal turbulent swirling currents occurring in complex channels of various energy and heat exchangers are considered. The possibility of applying the theory of screw flows and the equation for the rate of helicity change to determine the critical conditions for the occurrence of a deterministic vortex structure of turbulent flows and to predict the effects of the occurrence of large-scale vortex formations in various elements of energy systems is substantiated. The phenomenon of the swirl flow crisis is described. It is shown that the use of thermodynamic stability analysis to describe complex vortex flows makes it possible to expand the applicability of mathematical modeling methods to describe the processes of formation of vortex structures. The results of computational and theoretical modeling of vortex formation processes during the flow of a swirl flow in pipelines of variable cross-section, which are elements of pipeline systems of a nuclear power installation, are presented.