大寬長比之平行平板單邊加熱自然對流之研究

Abstract

本研究利用數值方法模擬二維垂直平行平板單邊加熱之可壓縮自然對流現象，流場以有限差分法進行計算，而計算方法可分為兩部分：第一部分為非黏滯性項之尤拉方程式採用Roe方法計算通量，並加入Preconditioning矩陣，使程式在計算低速可壓縮流可獲得良好的收斂結果；第二部分為黏滯性項，採用二階中央差分法做計算。在時間項則採用LUSGS隱性法，出入口設定非反射性邊界條件避免可壓縮流中壓力波的干擾且減少計算網格數量。 垂直平行平板非對稱加熱之自然對流在出口處會產生不穩定流體回流現象，由於加熱壁面對流體所造成的密度差，在近加熱面流體沿著壁面加速向上流動，經由入口周圍的流體吸入到平行平板間的量無法完全補足在出口流出平行平板的量，故出口周圍的流體被強制吸入到垂直平行平板中，以補足其不足量。隨著平板間距的增加，觀察到在平板上部區域之流體回流會有向下直接沿著絕熱壁面流出入口之向下穿透流，故以此研究來分析其加大寬長比後的垂直平行平板自然對流之不穩定現象。

An unsteady flow reversal of natural convection in vertical parallel plates with an asymmetrically heated wall is investigated numerically. For clarifying the occurrence of flow reversal, the width of the plates is regarded as a variable, and the non-reflecting boundary condition is adopted at apertures. The methods of the Roe scheme, preconditioning and dual time stepping matching LUSGS are simultaneously used to solve governing equations which are available for a low speed compressible flow problem. 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. As the width of the parallel increases, the flow reversal will form the flow downward-penetration through the inlet. The present Nusselt numbers, which mean time and area-averaged ones, display relatively good agreement with those of the existing works.