Transition to chaos in electro-thermo-convection of a dielectric liquid in a square cavity
Tianfu Li, Zheng-Gang Su, Kang Luo, Hong-Liang Yi
Abstract
The transition process from laminar to chaotic flow in electro-thermal convection of a dielectric liquid is numerically investigated using a unified lattice Boltzmann method. The liquid is confined in a closed square cavity, and free charges are introduced into the system through a strong unipolar injection mechanism. Three cases with different Rayleigh numbers are considered. With the increase of electric Rayleigh number, various complicated dynamical behaviors are observed and three diverse transition routes to chaos are identified, namely, the quasi-periodic sequence involving four incommensurable frequencies, the intermittency sequence, and the alternating periodic-chaotic sequence. Numerical results are illustrated using time histories, Fourier frequency spectra, and phase portraits. The chaotic behavior is quantitatively analyzed through the calculation of fractal dimension and Lyapunov exponent. Typical flow patterns for both steady-state regime and periodic regime are also presented and discussed.