電暈放電產生之電液動流場數值模擬

Abstract

針對電暈放電產生之電液動的問題，本研究利用有限體積法發展出一套電場與流場耦合之數值方法。首先，單獨針對電場做測試，其問題包括具解析解的一維、二維及三維靜電場，採用兩種不同之邊界條件，結果發現給定電荷密度之邊界條件比給定電流解較為貼近解析解。電場與流場以One-way及Two-way兩種方式耦合，One-way耦合忽略流場對電場之影響，較解省計算時間，Two-way方式則完整考慮流場及電場之交互影響，計算中需來回多次疊代，因而計算時間大幅增加，對兩種方式做測試所得結果相近，這顯示流場對電場的影響甚小。最後探討一實際利用電液動改善散熱問題，藉由改變電壓及改變電極間距，分析發熱片附近之速度及溫度分布等，由模擬結果發現，提高電壓或降低間距使電場強度越強，使庫倫力增強加快速度，提高散熱效果。與實驗比較，兩者整體趨勢相同，但模擬之發熱片中心溫度一般皆比實驗值低，此誤差主要來源是由於模擬時發熱片僅單面為熱源，不考慮其餘面散至環境之能量，由於密閉空間，實驗時散失之能量仍存在腔體內，故整體計算之能量較低，此外，模擬中腔體表面假設為固定的常溫，與實際狀態不大相符。

The main concern of this study is the Electrohydrodynamic flows induced by corona discharge, with use of finite volume method a numerical method is developed to simulate the flow field coupling with electric field. The method is first tested on 1-D, 2-D and 3-D electrostatic for which theoretical solutions are available. Two different boundary conditions are employed. It is found that the use of electric charge density, rather than the use of electric current, as boundary condition leads to better results. The coupling between the electric field and the flow field is treated by using either one-way or two-way methods. In the one-way method, the effect of the flow on the electric field is neglected and it saves more time than two-way method. In the two-way method, because the interaction of the flow field and the electric field need lots of iterations, the time of computation will greatly increase. The results of these two methods are similar, so it shows that the influence of the flow field on electric field is very slight. In the end, we discuss the cooling issue by the Electrohydrodynamic. We adjust various distances of electrode gap or voltages to analyze the temperature distribution at the heater and velocity profiles near that. The results show that when we increase the voltage or decrease the distance of electrode gap, the electric field and the Coulomb's force will be stronger. Then the velocity will increase and the effect of heat transfer will be enhanced. Compared with experiment results, the numerical results are the same trend, but the temperature at middle of heater is lower. The main error is caused by that in the simulation case we only consider one side of the heater as heat source without considering the energy loss from other sides. In the real case, heat loss is still in the chamber which is confined space, so the whole energy is lower in the simulation case. In addition, in the simulation case, the other error is caused by that the temperature of the wall is fixed ambient temperature which is different with the real case.