Numerical simulation of electroconvection of a poorly conducting fluid in an alternating electric field

Abstract

Electroconvection of a poorly conducting fluid in an alternating electric field of a horizontal capacitor is studied. Electroconductive charge formation mechanism which is associated with the temperature dependence of electrical conductivity is considered The simulation is carried out, taking into account a finite charge relaxation time, for a set of problem parameters corresponding to real fluids used in electrical engineering, e.g. capacitor or transformer oils. A system of eight nonlinear differential equations is obtained using the Galerkin method. The system is solved by the Runge-Kutta-Merson fourth-order method. The mechanical-equilibrium stability boundary of the fluid in the capacitor is constructed on the parameter plane “modulation amplitude -external field period”. The evolution of arising flows in the supercritical area is analyzed, and the relationship between the intensity of convective flows and the dimensionless electric parameter is obtained at several frequencies. The spectral composition of the dynamic system response is determined using the fast Fourier transform. Different types of electroconvection oscillatory regimes are detected. It is shown that the solutions belong to the synchronous response at all frequencies of the external field, but they can be divided into two groups, which differ by the value of a heat flow through the capacitor. The areas of coexistence of regimes with different heat flow values are found. A transition from periodic to chaotic oscillations is investigated. It has been found that the transition to chaos is realized through a period-doubling cascade.