TRANSMISSION LINE-WIRE DANCING (GALLOPING) – LYAPUNOV INSTABILITY

This article describes aerodynamic losses of damping, or aerodynamic instability, which we observe in experiments and in engineering practice. As applied to industrial high-voltage lines this phenomenon is usually called galloping (dancing) of phase line wires. This phenolmenon can be explained by Lyapunov’s instability of equilibrium state of wires profile (cross-section). In addition to known condition of Grauert-den-Hartog’s instability there was obtained practical condition of instability, which depends only on stationary aerodynamic profile’s factor – dimensionless coefficient of head resistance and lift coefficient, and also on their derivative with respect to the angle of attack.

There was suggested an effective numerical-analytical method of investigation of stability for equilibrium of profile’s state in flow, which was developed at the department “Applied mathematics” of Bauman MSTU. This method allows to determine the stationary aerodynamics characteristics of profile by numerical simulation of profile flow under different angles of attack by vortex element method and later on the application of analytical conditions of stability and Lyapunov’s instability of equilibrium positions. The obtained results during the investigation of rhombic and square profiles stability, as well as general profile of iced wire, and their comparisons with the known experiments’ results in aerodynamic tubes indicate the precision of developed methods and algorithms. The usage of mesh-free Lagrange method of vortex elements and software for their realization allows to solve also dual problems of aerohydroelasticity and to carry out direct numerical simulation of profile movement in flow. In this article the investigations’ results of different authors in this field were taken into account.

aerodynamic experiment, aerodynamic instability, Lyapunov instability, method of vortex elements

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