導電溶液在平行板間受垂直電場與溫度梯度作用之穩定特性分析

本研究係以數值方法分析：兩平行板間具離子濃度及溫度分佈之導電性溶液，在通入直流電場之後，發生不穩定特性之流場參數條件。溶液導電度隨著離子濃度及溫度變化，而密度僅隨溫度做變化。溫度剖面由兩平板溫差以及內部熱源決定，離子濃度分佈為準穩態設定。使用微擾法及線性分析後，將擾動量正交展開得穩定特性方程式；使用射擊法，配合剛體邊界條件求得流場穩定特性。數值計算結果顯示：在不考慮內部熱源時，上板加熱為穩定機制，需要較大電場以擾動流場；而下板加熱為不穩定機制，且電場為零之極端情形可精確簡化至”Rayleigh-Benard convection”。在考慮內部熱源後，流場最高溫可能發生在流道中，致使流場上半部為熱不穩定，下半部為熱穩定。又因庫侖力侷限於下平板處，因此流場不穩定的情形可區分為二：其一、流場上半部為熱不穩定驅動；其二、流場下半部當庫侖力作用大於黏滯力與熱穩定機制。

關鍵字

流體穩定學；電流體力學；平行板；導電度梯度；溫度梯度

並列摘要

The onset of electro-hydrodynamic instability within two parallel plates with electrical conductivity and thermal gradients has been concerned in this study by using numerical method. Electrical conductivity depends on local ion concentration and temperature; density depends on local temperature only since the solution is diluted. The temperature profile is governed by temperature difference between two plates and internal heating. Concentration distribution has been quiescent assumed. Applying perturbation method and linear stability analysis, the stability equations can be found. The neutral stability curves are calculated by shooting method with rigid-rigid boundary conditions. The numerical results show that: without internal heating, the flow field becomes more stable when upper plate has been heated. Conversely, the hotter lower plate destabilizes the field and can be reduced to “Rayleigh-Benard convection” problem accurately. While internal heating has been concerned, the temperature profile separates the system into two parts. The upper region is mainly governed by thermal unstable mechanism. The lower region becomes unstable while electro-hydrodynamic overcomes viscous and thermal stable effect.

並列關鍵字

electrohydrodynamic instability ； parallel plates ； electrical conductivity gradient ； thermal gradient

參考文獻

[1] G. I. Taylor and A. D. McEwan, “The stability of a horizontal fluid interface in a vertical electric field”, Journal of Fluid Mechanics 1965, 22(1) p.1

[2] R. J. Turnbull and J. R. Melcher, ”Electrohydrodynamic Rayleigh - Taylor bulk instability”, Physics of Fluids 1969, 22(6) p.1160

[3] A. Castellanos and M. G. Velarde, “Electrohydrodynamic stability in the presence of a thermal-gradient”, Physics of Fluids 1981, 24(10) p.1784

[4] J. R. Melcher, “Continuum Electromechanics”, MIT, Cambridge, MA, 1981

[5] R. J. Turnbull, “Electroconvective instability with a stabilizing temperature gradient: I. theory”, Physics of Fluids 1968, 11(12) p.2588

國際替代計量

導電溶液在平行板間受垂直電場與溫度梯度作用之穩定特性分析

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