不同形狀凸緣氣罩開口的勢流流場

The Potential Flow Field Generated by the Flanged Hood Openings of Various Shapes

根據以往實驗觀察與紊流模式計算的結果顯示，外裝式無限凸緣氣罩開口吸氣所造成的氣流流場可運用較簡單的勢流理論求解。在使用勢流理論時，開口可視為一由均勻分佈消失點（sink）所構成的範圍，於是開口吸氣所造成的流場便可將消失點的綜合效應積分求得。本文採用碎形積分（fractal integration）求解不同形狀開口所造成的流場。也就是由大量矩形元素組成的碎形（fractal）幾何形狀近似各種形狀開口，各元素對流場的效應則可使用既有的理論數學式直接計算。根據積分範圍的可加性質，此碎形範圍抽氣所形成的流場可近似特定形狀開口抽氣所產生的流場。經比較等面積與等抽氣風量矩形、橢圓（含圓形）與直角三角形開口流場，發現在對等面積半徑歸一的座標中，無論開口形狀為何，中央面與中軸風速均具有相當的類似性，且與開口長寬比相關。於是既有的矩形開口流場理論解經修改延伸後，可用以快速推估不同形狀開口的中央面與中軸風速。

Consider a flanged exterior hood as an opening on an infinite plane. Results obtained from experimental and turbulence model computation results in related investigations have confirmed that the flow field originating from the sucking effect at the opening can be calculated by a relatively simpler potential theory. Applying the potential flow theory, allows us to treat the opening as a domain with a constant sink distributed upon it. Hence, the flow field can be determined by integrating the effect of the sink within the domain. This study presents a numerical algorithm to evaluate the flow field generated by the openings of various shapes. Based on the additive property of the integration, the opening is filled with rectangular elements in which the closed-form solutions are available. A sufficient number of elements forms a fractal resembling the concerned domain. In addition, the flows generated by the rectangular, elliptic (including circular) and right-triangular openings are evaluated and compared under the same opening area and sucking flow rate. According to those results, at the same aspect ratio but different shapes of the opening, the central-plane and central-axis velocities closely resemble each other if the coordinate is normalized to the equivalent-area radius. Therefore, the closed-form solutions for the rectangular opening can be modified to quickly estimate central-plane and central-axis velocities generated by the openings of various shapes.