平板紊流邊界層通過深凹穴的流場分析

A Study of Flat-Plate Turbulent Boundary Layer over a Deep Cavity

凹穴是工程上基於功能上的需求而常有的非平整結構幾何，當流體運動通過時常會造成複雜的流體力學現象，開口式的凹穴則同時也會造成噪音的產生。本文特別針對深凹穴，探討平板紊流邊界層通過這樣的區域所造成的流場現象。
本論文設定凹穴的長度L與深度D的長深比（aspect ratio）為/ 0.15 LD=，一平板邊界層流通過此一凹穴，Reynolds數（以L為特徵長度，邊界層外流場的均勻入流速度為特徵速度）則為6 1.01 10´。我們採用計算流體力學的方法來進行計算研究，將RANS方程式（Reynolds-averaged Navier-Stokes equations）離散，並採用兩種不同的網格設計（六邊形網格與多邊形網格），和兩種不同的紊流模型（realizable k-ε模型與SST k-ω模型）來進行相關的研析。相關的成果顯示，SST k-ω模型配合六面體網格所得的結果，包括平均速度分布和紊流動能，與文獻實驗數據最為吻合；據此，我們探討這樣組合所得的凹穴內部流場結構特性，結果顯示流場呈現明顯的三維特性，且紊流現象只有在凹穴口附近比較明顯（以紊流動能分布的角度來看），進到凹穴一半以上的深度處，因流體運動速度低，紊流的特性已經不明顯。另外，我們也進行unsteady RANS方程式的計算，探討凹穴開口附近的渦流演化。

Cavities are non-smooth structures commonly encountered in engineering due to functional requirements. When fluid flows pass over these cavities, complicated flow phenomena often occur, and in the case of open cavities, noise generation is also a significant issue. This study focuses specifically on deep cavities, examining the flow field phenomena created by a flat-plate turbulent boundary layer over an open cavity.
In this paper, the aspect ratio of the cavity (length-to-depth ratio) is set to a specific value, with a flat-plate boundary layer flow passing over the cavity. The Reynolds number, based on the cavity depth and the uniform inflow velocity of the outer boundary layer, is also specified. Computational Fluid Dynamics (CFD) methods are employed to conduct this study by discretizing the Reynolds-averaged Navier-Stokes (RANS) equations. Two different grid designs (hexahedral grids and polyhedral grids) and two turbulence models (the realizable k-εmodel and the SST k-ωmodel) were used for analysis. The computations indicate that the combination of the SST k-ωmodel with hexahedral grids leads to the best solution which most closely match experimental data from previous studies. Based on this combination, the flow field structure characteristics within the cavity are investigated. The findings show that the flow field exhibits significant three-dimensional characteristics. Turbulence phenomena are prominent only near the cavity opening (from the perspective of turbulent kinetic energy distribution). In regions deeper than halfway into the cavity, due to the low fluid velocity, turbu-lent characteristics become negligible.