本研究透過數值模擬與實驗方法，探討可壓縮流場中橢圓形凹槽的內部流動結構、流動轉變以及側壁曲率所引發的三維效應。研究中所分析的自由流馬赫數分別為0.83、0.70和0.64，凹槽的偏心率則設定為0.87、0.66和0.47，長深比（L/H）則涵蓋2.10至21.50的範圍。
根據實驗與數值模擬的結果，橢圓形凹槽流場可區分為開放型（open cavity）、過渡型（transitional cavity）以及封閉型（closed cavity）三種流動，取決於凹槽的幾何結構。表面壓力分布顯示，當L/H達到約8.60時，流場明顯從開放型轉變為過渡型；而當L/H超過14.33時，流場則轉變為封閉型。這樣的轉換趨勢與圓形凹槽的文獻結果一致。油流實驗也證實了此流動的轉變，在L/H為8.60時，凹槽內的反向流（reversed flow）的分離線消失，並於14.33時剪切層（shear layer）明顯附著於凹槽底部。數值模擬馬赫數為0.83時，隨著L/H的增加，凹槽內的渦流（recirculation vortex）受到壓迫，其核心逐漸前移且尺寸縮小。模擬也明確呈現了渦流顯著的變形行為：在較低L/H時，渦流主要沿著橫向方向旋轉；隨著長深比的增加，渦流逐漸轉向垂直方向旋轉，凸顯出因側壁曲率所誘導的三維效應增強。在偏心率影響方面，研究結果顯示較低偏心率（即較寬的凹槽）顯著增強了凹槽內部流動的三維性。在長深比2.10且偏心率為0.87時，流動結構接近二維，呈現出明確的前渦流、渦流和後渦流。然而，隨著偏心率降低（凹槽變寬），前半部的流場逐漸出現類龍捲風渦流（tornado-like vortex），這種結構強化了由曲面側壁驅動的橫向運動，隨著長深比進一步提高，這類龍捲風渦流成為流場中的主導結構，並促使流場逐漸轉為封閉型流態。頻譜分析結果則指出，在L/H為2.10的開放型凹槽流場中存在明顯的Rossiter模態（Rossiter modes）。但隨著長深比的增加，前面三個Rossiter模態的振幅逐漸減弱，這主要歸因於剪切層與迴流之間交互作用遭到抑制所致。當流場轉變為封閉型時，模擬結果指出剪切層直接附著於凹槽底部，進一步破壞了流場中的回饋迴路（feedback loop），使得自持震盪 (self-sustained oscillations)逐漸消失。偏心率的改變雖然對Rossiter模態的震盪頻率與振幅影響不大，但較高的偏心率卻顯著增強了凹槽內的橫向運動，使原本集中的Rossiter模態能量重新分配至寬頻雜訊中。

This numerical and experimental study investigates the internal flow structures, flow regime transitions, and three-dimensional effects induced by curved sidewalls in compressible elliptical cavity flows. The analyses cover freestream Mach numbers of 0.83, 0.70, and 0.64; the cavity eccentricities of 0.87, 0.66, and 0.47; and cavity length-to-depth (L/H) ratios ranging from 2.10-21.50. Pressure-sensitive paint, oil flow visualization, and dynamic pressure sensors were used in the experimental analysis.
Elliptical cavity flows are categorized into three regimes: open, transitional, and closed cavity flows. The type of cavity flow is primarily influenced by the cavity geometry. Surface pressure measurements conducted in this study indicated that a distinct transition from an open flow to a transitional flow occurred at L/H = 8.60. Moreover, a transition from a transitional flow to a closed flow occurred for L/H > 14.33. As the cavity’s L/H ratio increased, the recirculation vortex shifted forward and became progressively constrained to a smaller area, with its size decreasing because of shear layer compression. Furthermore, this vortex underwent considerable deformation, transitioning from exhibiting a primarily spanwise-aligned rotation for L/H ≤ 4.43 to an almost vertical rotation orientation at L/H = 14.33.
Spectral analysis indicated the existence of distinct Rossiter modes within open cavity flows when the L/H = 2.10. These Rossiter modes diminished with an increase in the L/H because of the suppression of the interactions between the shear layer and recirculation vortices. Simulation results revealed that in transitional and closed cavity regimes, attachment of the shear layer to the cavity floor disrupted the feedback loop, effectively eliminating self-sustained oscillations. Although eccentricity variations had minimal effects on the oscillation frequency, increased eccentricity notably enhanced spanwise fluid motion, redistributing spectral energy from discrete Rossiter tones into a broader frequency range.
Overall, this study provides detailed insights into flow regime transitions and three-dimensional effect for compressible flows in elliptical cavities, thus considerably enhancing the understanding of cavity flows and their implications for aerodynamic design and flow control applications.

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