以非反射性邊界探討平行平板單面加熱可壓縮自然對流現象之研究

Abstract

在工業和學術研究上，水平與垂直平行平板自然對流現象是非常重要的。為了避免求解過程的複雜性，Boussinesq 近似法假設流體密度是常數，並且常被採用於自然對流的數值模擬，而在邊界出入口處使用速度完全發展流設定，由於高溫差自然對流中低速可壓縮流場極易被邊界條件所影響，因此本研究目的使用更適合的數值方法使水平與垂直平行平板自然對流研究應符合實際物理現象。在底部加熱之水平平行平板自然對流研究熱傳問題中，為了擴展應用範圍，考慮流體的可壓縮性因此Boussinesq assumption不適用。數值方法上使用採用Roe方法與Preconditioning矩陣與dual time stepping讓程式在計算低速可壓縮流可獲得良好之收斂結果，出口設非反射性邊界條件以降低計算網格和節省大量的計算疊代時間。溫度場與流場的變化被詳細研究，結果可發現隨著加熱壁面越長，可觀察流場與溫度場從穩定到不穩定現象變化。 而垂直平行平板自然對流中，有一個特殊的現象稱為流體回流，為了研究流體回流的發生原因，兩平板的間距被視為一個變量。在垂直平行平板間距較窄，流體回流的現象在這種情況下幾乎觀察不到，相反的垂直平行平板間距較大時，可觀察到流體回流的現象。而壓力差在出入口的分佈，解釋了流體回流的發生原因。時間和面積平均的Nusselt數，與文獻實驗結果有良好的一致性。

Natural convection in horizontal and vertical parallel plates is very important for both industrial and academic research. Due to limitation of solution methods, the Bossinesq assumption, in which the density is assumed to be constant, is usually adopted when numerical studies of natural convection were investigated. Accordingly, the boundary condition of fully developed flow must be adopted on the computational domain that causes realistic situations difficultly to be simulated, and high temperature difference situations can not be investigated due to the assumption of constant density. Therefore, the aim of the thesis drives suitable numerical methods to investigate natural convection in both horizontal and vertical parallel plates more reasonably and realistically. In the investigation of natural convection in horizontal parallel plates, The heat transfer of natural convection in three dimensional horizontal parallel plates with a heated bottom surface is investigated numerically. For enlarging the application domain, the compressibility of the fluid is taken into consideration instead of the Boussinesq assumption. Numerical methods of the Roe scheme, preconditioning and dual time stepping are adopted for solving governing equations of a low speed compressible flow. A non-reflection condition is used at both apertures in order to decrease computational grids and economize massive computing time. Variations of thermal and flow fields are examined in detail. The results show that accompanied with elongating the length of the heated bottom surface, both thermal and flow fields are changed from a steady to an unsteady situation. The flow reversal is a unique phenomenon and always observed in natural convection of vertical parallel plates. Thus the investigation of the flow reversal in natural convection of vertical parallel plates is conducted. For clarifying the occurrence of flow reversal, the gap between the plates is regarded as a variable. The flow reversal is observed under broad width situations and absent under narrow width situations. Distributions of the pressure differences at the apertures are revealed to indicate the occurrence of flow reversal. The present Nusselt numbers, which mean time and area-averaged ones, display relatively good agreement with those of the existing works.