在非線性EHD動力系統內的分岔研究

Bifurcation studies in a electrical hydrodynamic nonlinear dynamical system

林鼎盛(Ting -Sheng Lin)

指導教授 ： 許文翰

國立臺灣大學/工學院/工程科學及海洋工程學研究所/碩士(2010年)

https://doi.org/10.6342/NTU.2010.03144

摘要

本論文是利用對流-擴散-反應的數值方法模擬于二維電液動非線性動力系統內的分岔行為。此一包含了受空間電荷密度影響的外加電場之Poisson方程式、由庫倫力所驅動的不可壓縮Navier-Stokes方程、以及可描述流場中帶電離子分佈的電荷守恆方程式。

本研究係在兩電極板中間以單極注入之方式造成非線性動力行為的分岔，它包括了對稱性分岔、倍頻率分岔、週期分岔、及最後所發展至渾沌狀態。吾人將利用模擬之結果說明其各個現象所代表的物理意義;並透過數值分析來了解電液動的分岔行為。

關鍵字

電液動 ； 對流-擴散-反應 ； 對稱分岔 ； 倍頻率分岔 ； 渾沌

並列摘要

This study is aimed to simulate the bifurcation behavior occurring in a two-dimensional electrical hydrodynamic nonlinear dynamical system by using the convection-diffusion-reaction (CDR) numerical method. This nonlinear system includes the Poisson equation for the external electric field that is subject to the space charge density, incompressible Navier-Stokes equations driven by the Coulomb force, continuity equation, and the charge conservation equation which describes ions distribution in the hydrodynamic field.

The dynamics in the investigated nonlinear system include the pitchfork-bifurcation, frequency-doubling, Hopf-bifurcation, and the chaotic dynamics. The simulation results are presented for the case of unipolar injection between two plane electrodes. Finally, we will use the numerical analysis to understand bifurcation behavior in the electrohydrodynamic.

並列關鍵字

Electrohydrodynamic ； convection-diffusion-reaction ； bifurcation ； symmetry ； periodic ； chaos

參考文獻

A. Castellanos (eds.), Electrohydrodynamic,

New York : Springer, 1998.

P. A. Vazquez, G. E. Georghiou, A. Castellanos, Numerical analysis of the stability of the electrohydrodynamic (EHD) electroconvection between two plates,

J. Phy. D:Appl. Phys. 41, 175303, 2008.

P. A. Vazquez, G. E. Georghiou, A. Castellanos, Characterization of injection instabilities in electrohydrodynamics by numerical modelling: comparison of particle in cell and flux corrected transport methods for electroconvection between two plates,