矩形水平管道內底板舖設圓形加熱面由浮力所驅動空氣混合對流之渦旋流結構實驗研究

Abstract

本文結合流場觀測與溫度量測，在開迴路混合對流實驗系統設計架構下，對具高寬高比(A=20)的水平矩形管道內底板舖設圓形加熱面由浮力所驅動空氣混合對流之渦旋流流場結構，進行廣泛而又深入的探討；實驗參數操作範圍為雷諾數 4.7 到 99.2，雷利數 3,200 至 31,500。 結果顯示在中高雷諾數所造成的低浮慣比情況下，管道內會出現縱向渦卷流。因為是圓形加熱面的關係，愈靠近管道中央所形成的縱向渦卷流它的起始位置就會愈往上游方向移動。可以看出來這和矩形加熱面導引縱向渦卷流起始位置的順序有著相反的趨勢。另外流場觀測結果發現圓形加熱面上的熱突出物在橫方向上並非等間距分佈，連帶使得往下游方向成長的渦流也失去對稱性。值得注意的是在給定雷利數的條件下 ，這些熱突出物在高雷諾數時會顯的相當不穩定，表示有慣性力驅動的不穩定性存在，因此下游渦流會有非週期性渦卷消失與再生的不穩定情況發生。但是降低雷諾數之後逐漸有穩定的縱向渦卷流出現，形成從高雷諾數到低雷諾數也就是在增加浮慣比的情況下縱向渦卷流從不穩定轉變成穩定的所謂逆勢流場轉移；再降低雷諾數則又因為浮力驅動的不穩定性而使得渦卷流再度成為不穩定狀態。 在極低雷諾數的時候，管道內會出現一個環繞在加熱板前緣呈半圓形的環狀渦流；同時在圓形加熱板上則是佈滿移動橫向渦卷流。規則移動橫向渦卷流只存在特定範圍的雷利數內而且在入口側起始位置的橫向渦卷是往上游方向彎曲的。渦流在往下游移動的過程中會拉長變直，但是進入出口側後因為加熱板面積收縮的關係，渦流再度變形。此外規則移動橫向渦卷流的分佈對管道中央垂直面而言幾乎完全對稱，而渦卷在通過管道中心的位置時會有較大的長度。特別的是在往下游移動的過程當中渦卷強度增強而且體積也有逐漸增加的趨勢，但是所有的渦卷並沒有以相同的速率往下游方向移動。另外在給定實驗參數條件下，瞬時溫度量測記錄顯示規則移動橫向渦卷流溫度震盪的情形與偵測位置有很大的關係；特別是溫度震盪的頻率會隨著雷諾數的降低而明顯地減少，但是在高雷利數的時候溫度震盪的頻率與振幅隨著雷利數變化的情形並不明顯。這些特徵和矩形加熱面所導引的規則橫向渦卷流有很大的不同。 在極低雷諾數所造成的高浮慣比情況下，回流會出現在管道入口側靠近上板的位置，而在加熱板上則是移動橫向渦卷流。回流的外型是環繞加熱板前緣呈逆時針方向旋轉的渦旋流，同時我們在稍微離開加熱板下緣處也可以看到另一個不同旋轉方向的回流，但是這個回流因為加熱板上方移動橫向渦卷流通過的影響，無法保持一個穩定的狀態。此外，上游回流隨著雷利數的增加幾乎佔據了整個管道入口的位置，渦流中心也會前移。值得注意的是溫度量測的紀錄顯示，回流的存在基本上維持穩定而與下游各種渦流的型式無關。 根據各種不同參數條件下對管道內渦旋流流場的觀察，我們整理出流場組織圖以區別各種不同的渦旋流型式並且列示發生規則移動橫向渦卷流的上下邊界關連式；另外為了量化上游回流的特徵，我們提出一個與浮慣比有關用來判別回流是否存在的法則，結果顯示臨界浮慣比會隨著雷諾數的增加而降低。其他如上游回流軸向及垂直向渦流體積的大小、回流中心的位置以及縱向渦卷流起始位置、不同渦旋流型式的邊界等，我們也分別列出了與實驗參數有關的關連式。

In this study experimental flow visualization combined with transient temperature measurement are conducted to investigate the structure of the buoyancy driven vortex flow in low-Reynolds-number mixed convection of air through a horizontal flat duct with an isothermally heated circular disk embedded in the bottom plate of the duct for the Reynolds number ranging from 4.7 to 99.2 and Rayleigh number from 3,200 to 31,500. The possible presence of various vortex flow patterns is studied by choosing a high-aspect-ratio rectangular duct (A=20) as the test section and the experiment is performed in an open loop mixed convection apparatus. How the circular geometry of the heated surface affects the vortex flow characteristics is investigated in detail. The results indicate that at low buoyancy-to-inertia ratios with moderate Reynolds numbers the generated vortex flow is in the form of longitudinal rolls. Moreover, the longitudinal vortex rolls (L-rolls) closer to the duct axis are induced at more upstream locations, which are completely opposite to those induced in a duct with a uniformly heated bottom. Besides, the thermals driven by the circular heated surface are not evenly spaced in the spanwise direction and tend to be asymmetric spanwisely. It is of interest to note that at a given Rayleigh number Ra the thermals are unstable at high Reynolds numbers, which suggests the existence of the inertia driven instability. Thus the L-rolls evolved from these thermals are also unstable with the presence of nonperiodic generation and disappearance of L-rolls. But at slightly lower Re the thermals and L-rolls are steady and regular. The vortex flow becomes unstable and irregular for a further reduction in the Reynolds number, that is obviously resulted from the buoyancy driven instability. The simultaneous presence of these two instability mechanisms explains the appearance of the reverse transition in the longitudinal vortex flow. At very low Reynolds numbers the buoyancy-induced secondary flow is characterized by the moving transverse vortex rolls (T-rolls) over the heated plate enclosed by an incomplete circular roll. The regular T-rolls are curved at the early stage of their initiation and deformed to some degree due to the presence of the incomplete circular roll around the edge of the heated plate. But in the exit half of the duct the T-rolls are nearly straight and almost spanwisely symmetric with respect to the vertical central plane. More specifically, the generated transverse rolls get stronger and bigger during the downstream moving but do not travel downstream at a constant speed. The transient temperature measurement reveals that the flow oscillation of the T-rolls driven by the circular heated plate is space dependent for given Ra and Re. Moreover, the frequency of the flow oscillation decays substantially with decreasing Reynolds number. Furthermore, the amplitude and frequency of the temperature oscillation are reduced for a raise of Ra but they are slightly affected by the increase in Ra at a higher buoyancy especially when Ra is beyond 11,600. These characteristics are very different from the transverse vortex rolls induced in a duct with a uniformly heated bottom plate. In the cases with a high buoyancy-to-inertia ratio resulted from a very low Reynolds number, a returning flow zone is formed in the entry portion of the duct and transverse vortex rolls prevail over the horizontal heated circular plate. The return flow is in the form of a semicircular roll around the upstream edge of the circular plate. In addition, a downstream return flow zone is also induced near the exit end of the duct. The upstream return flow zone almost blocks the entire duct inlet. Moreover, the return flow zone grows in size and the zone center migrates slightly towards the upstream at increasing buoyancy-to-inertia ratio. Besides, comprehensive temperature measurements suggest that the return flow maintains its steadiness in spite of the vortex flow induced in the downstream region of the duct. Based on the present data, flow regime maps are given to delineate various vortex flow patterns driven by the circular heated plate. In addition, the boundaries for the appearance of the regular transverse vortex flow patterns were empirically correlated. To provide the quantitative reverse flow characteristics, the present data for the size and center position of the upstream return flow zone at the mid-span of the duct are correlated empirically. Besides, empirical correlations for the onset points of the L-rolls and the criterion for the onset of the return flow are also provided.