Calculating the lift on a finite stack of cylindrical aerofoils
Calculating the lift on a finite stack of cylindrical aerofoils
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计算有限堆叠的圆柱形翼型的升力
DOI：
10.1098/rspa.2005.1631
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发表时间：
2006
期刊：
影响因子：
--
通讯作者：
D. Crowdy
中科院分区：
文献类型：
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作者：
D. Crowdy
经典的精确解由于Lagally（Lagally，M。1929年，在两个村庄里，reibungslose strömung。Z. Angew. Math.Mech.9，299-305.）对于流过两个圆柱形翼型（或障碍物）的流动，本文将其推广到任意有限个圆柱形翼型的情况。给定翼型的几何形状、迎面均匀流的速度和方向以及单独的圆形翼型环流，在可以保形映射到流体区域的参数前像区域中以解析形式找到与流相关联的复势。然后根据两个区域之间的保角映射的知识来完全确定流动。在翼型都是圆形的特殊情况下，从参数原像区域到流体域的保角映射是莫比乌斯映射。在这种情况下，复势的解可与Blasius定理结合使用，以计算多翼型构型上的水动力分布。
The classic exact solution due to Lagally (Lagally, M. 1929 Die reibungslose strömung im aussengebiet zweier kreise. Z. Angew. Math. Mech. 9, 299–305.) for streaming flow past two cylindrical aerofoils (or obstacles) is generalized to the case of an arbitrary finite number of cylindrical aerofoils. Given the geometry of the aerofoils, the speed and direction of the oncoming uniform flow and the individual round-aerofoil circulations, the complex potential associated with the flow is found in analytical form in a parametric pre-image region that can be conformally mapped to the fluid region. A complete determination of the flow then follows from knowledge of the conformal mapping between the two regions. In the special case where the aerofoils are all circular, the conformal mapping from the parametric pre-image region to the fluid domain is a Möbius mapping. The solution for the complex potential in such a case can then be used, in combination with the Blasius theorem, to compute the distribution of hydrodynamic forces on the multi-aerofoil configuration.