矩形水平管道內傾斜圓形底板加熱面對於浮力所驅動空氣混合對流之渦旋流結構之穩定研究

Abstract

本論文研究藉由流場可視化及暫態溫度量測之方法，探討底板傾斜逐漸增加主流場速度對於圓形底部加熱面之梯型管道其渦流結構之穩定性，梯型管道之寬高比可藉由調整底板傾斜角度使得入口20之寬高比至出口處可達22.5或30，實驗所得結果將與底板未傾斜之水平管道做比較，主要著重於底板傾斜對於縱向渦流(longitudinal roll)、橫向渦流(transverse roll)及迴流(return flow)結構之影響；實驗操作參數範圍雷諾數介於3.7到79.7之間，雷利數則由9,040到24,000，針對底板傾斜角度0.34°及0.97°來探討穩定及暫態之渦流結構。 由實驗研究結果得知在低浮慣比下，管道底板傾斜使得縱向渦流延後產生、結構較小，並有效的壓制不穩定之縱向渦流結構；此外，相較於矩型管道，梯型管道之寬高比逐漸往下游增加導致更多的縱向渦流產生。在橫向渦流方面，圓形底板加熱面所產生之橫向渦流其流速及振盪頻率隨著往下由移動而有所不同；另外，梯型管道中之橫向渦流，除了因底板傾斜亦使得其產生被延後、不穩定結構被壓制之外，橫方向之長度將不會縮短並且振盪幅度將隨著渦流往下由移動而減小；再者，傾斜管道之底板能有效的延遲迴流的產生，並且稍微的減弱其強度。最後，根據實驗所得結果提出橫向渦流尺寸、振盪頻率、流速及迴流發生參數之經驗公式，並由流場組織圖說明在梯型管道內，不同流場型態之邊界。

In the present study an experiment combining flow visualization and temperature measurement is carried out to investigate the possible stabilization of the buoyancy driven mixed convective vortex flow of air by the main flow acceleration associated with the inclination of the bottom plate of a horizontal rectangular duct. The vortex flow is driven by a heated circular disk embedded in the bottom plate. Specifically, the duct is tapered to become trapezoidal so that its aspect ratio at the duct inlet is 20 and gradually raised to 22.5 or 30 at the exit of the duct. The results in the trapezoidal duct are compared with those in the horizontal rectangular duct. Particular attention is paid to delineating the spatial changes of the longitudinal, transverse and return vortex air flow structures with the plate inclination angle and to how the bottom plate tilting possibly suppresses and stabilizes these vortex flows. Experiments are conducted for the Reynolds number at the duct inlet ranging from 3.7 to 79.7 and the Rayleigh number from 9,040 to 24,000 for the two inclined angles of the bottom plate, 0.34° and 0.97° covering the steady and time-dependent vortex flows. The results from the present study indicate that in the rectangular duct the steady, regular longitudinal vortex rolls (L-rolls) driven by the circular heated plate at low buoyancy-to-inertia ratios are induced at more upstream locations in the duct core, which are completely opposite to those induced in a rectangular duct with a uniformly heated bottom. The results in the trapezoidal duct show a delay in the onset of L-rolls and the effective suppression of the buoyancy driven unstable longitudinal vortex flow by the bottom plate inclination. Besides, more rolls can be induced due to the increase in the aspect ratio of the duct with the axial distance and the rolls are smaller, when compared with those in the rectangular duct. In the trapezoidal duct the transverse vortex rolls (T-rolls) driven by the circular heated disk do not have the same convection speed and oscillation frequency when moving downstream. Furthermore, the T-rolls in the trapezoidal duct would not reduce their spanwise length and the amplitude of flow oscillation decays slowly in the streamwise direction. Additionally, the onset of T-rolls is delayed and the unstable T-rolls can be regularized by the bottom plate inclination. We further note that the bottom plate inclination can effectively delay the onset of the return flow and weaken it slightly. Empirical equations are provided to correlate the present data for the wavelength, oscillation frequency and convection speed of the T-rolls and for the onset of return flow in the trapezoidal duct with its bottom inclined at the large angle of 0.97°. A flow regime map is also given to illustrate the effects of the bottom plate inclination on the appearance of various longitudinal vortex flow patterns.