空氣在水平扁平矩形密閉容器中接近臨界的自然對流及在扁平管中之混合對流渦旋流結構研究

Abstract

本篇論文利用流場可視化及溫度量測方式,研究對於底部加熱的空氣在水平扁平矩形密閉容器中接近臨界的自然對流及在扁平管中之混合對流渦旋流結構。首先，對於寬高比為16及長高比20的水平扁平矩形密閉容器，主要探討在接近臨界浮力值的對流渦旋流，由結果顯示在次臨界雷利數(Rayleigh number)所產生的渦旋流為沿著容器壁邊的矩形渦流及在容器中心平行於短壁邊的平行渦流。而接近臨界雷利數(Rac = 1,708) 則產生更多矩形渦流，在容器中心的平行渦流則擠壓形成彎曲渦流(serpentine rolls)。介於2,000到3,000的超臨界浮力(supercritical buoyancy)值，整個密閉容器中充滿了平行於短邊的平行渦流。在更高的浮力—雷利數4,000時則渦旋流變成不規則且和時間相關的渦旋流結構。由各種渦旋流結構轉變過程中顯示暫態時的複雜結構及改變加熱速率來升高浮力對於中間變化過程有明顯的影響。此外，在較高雷利數時，平行渦流結構會藉由渦流形成過程中的矩形渦流分裂成細胞渦流(cells)後再相互結合而形成較大的平行渦流而減少渦捲(wavenumber)數目。 其次，藉由流場可視化及對於渦旋流的時間及空間的量測探討扁平管中之空氣混合對流渦旋流結構，主要研究在1.0至5.0間的極低雷諾數及介於1,200與4,000之間低雷利數的範圍中可能出現的渦旋流結構，實驗中所使用的測試段寬高比為16。從流場觀測中除了已往常發現的縱向渦流(longitudinal rolls)、移動的橫向渦流(transverse rolls)及混合渦流(mixed longitudinal and transverse rolls)外，也發現了四種新的渦旋流包括—縱向渦流伴隨著非週期性移動的橫向渦流波(nonperiodic traversing transverse waves)、混合渦流及不規則細胞渦流、在管道入口處固定的橫向渦流及下游穩定的縱向渦流與U形渦流(U-rolls)等。其中，後面兩種渦流結構僅出現在雷諾數等於1。更進一步來說，穩定的縱向渦流、非週期性移動的橫向渦流波及在管道入口處固定的橫向渦流甚至在次臨界雷利數下產生，同時我們也獲得了這些新渦流細部的時間及空間的特性。 本研究也探討各種由浮力所帶動的渦旋流結構形成的複雜過程，例如—縱向及橫向渦流的產生、縱向及橫向渦流相互結合形成U形渦流、渦流分裂成細胞渦流及細胞渦流結合成渦流的逆向過程。此外，實驗中也觀察到橫向渦流的移動、渦流的彎曲及橫向渦流的消散及新渦流形成的過程。同時，對於縱向渦流局部產生的位置、橫向渦流的震盪頻率及對流速度也提出了關聯方程式(correlation)。 最後，根據目前的研究我們可以整理出接近臨界浮力，包含—超臨界及次臨界浮力的渦流型態流場組織圖。

The present study includes two parts. In the first part flow visualization is conducted to study the vortex flow patterns associated with the Rayleigh-Bénard convection in a horizontal shallow cavity of air. The cavity is a rectangular enclosure characterized by the aspect ratios Ax = 16 and Az = 20. Attention is focused on the convection rolls driven at slightly supercritical and subcritical buoyancies. The results show that at slightly subcritical Ra the induced vortex flow is in the form of rectangular rolls along the cavity sides and short straight parallel rolls in the cavity core. At slightly higher Ra near Rac ( = 1,708) more rectangular rolls appear and the short straight rolls in the cavity core merge together to form a serpentine roll. At slightly supercritical buoyancy with 2000 £ Ra £ 3,000 the entire cavity is filled with the straight rolls all parallel to the short sides of the cavity. At an even higher Ra of 4,000 the vortex rolls become irregular and time dependent. Moreover, the processes through which various vortex flow structures evolve during the transient stage are shown to be rather complicate and the vortex flow patterns during the flow formation are significantly affected by the heating rate in raising the buoyancy force. Furthermore, the wavenumber reduction at higher Ra for the parallel vortex roll pattern was noted to mainly result from the splitting of some rectangular rolls into cells and the subsequent merging of the cells into bigger rolls at the intermediate stage of the flow formation. In the second part of the study, combined experimental flow visualization and temperature measurement are carried out to investigate the spatial and temporal structure of the buoyancy driven vortex flow in a mixed convective air flow through a bottom heated horizontal flat duct. Particular attention is paid to the flow at a very low Reynolds number for 1.0 £ Re £ 5.0 and low Rayleigh number for 1,200 £ Ra £ 4,000. Here the possible presence of any vortex flow at subcritical Rayleigh number is also studied. The experiment is conducted in an open loop mixed convection apparatus by choosing a high aspect ratio rectangular duct ( A = 16 ) as the test section. The results from the flow visualization have revealed four new vortex flow patterns in addition to the oftenly seen patterns – longitudinal rolls (L rolls), moving transverse rolls (T rolls), and mixed longitudinal and transverse rolls (M rolls). The newly observed vortex flow patterns include stable longitudinal rolls along with nonperiodic traversing transverse waves, mixed longitudinal and transverse rolls as well as irregular cells, stable stationary transverse rolls in the duct entry and stable longitudinal rolls in the downstream, and U-rolls. The later two vortex patterns are only noted at Re = 1.0. Moreover, steady longitudinal rolls, nonperiodic traversing transverse waves and stationary inlet transverse rolls are induced even at subcritical Rayleigh number. The temporal and spatial characteristics of the new vortex flows are inspected in detail. The buoyancy driven flow formation processes resulting in various vortex flow structures are also investigated here. Many complicate processes during the vortex flow formation are noted, such as the generation of the L and T rolls, merging of L and T rolls to form U-rolls, splitting of rolls into cells and the reverse process of cell integration into rolls, aside from the moving of T rolls, roll bending and degeneration of T rolls. Moreover, the flow formation processes leading to the two new vortex flow structures are also examined carefully. Furthermore, a correlation is given to estimate the local onset locations of the longitudinal rolls. Meanwhile, the oscillation frequency and convection speeds of the transverse rolls are correlated from the present data. Finally, a flow regime map is provided to delineate various vortex flow structures observed in this study at the slightly supercritical and subcritical buoyancies.