Theory of Blade Design for Large Deflections: Part II—Annular Cascades
Theory of Blade Design for Large Deflections: Part II—Annular Cascades
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DOI：
10.1115/1.3239572
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发表时间：
1984-04
影响因子：
1.5
通讯作者：
C. Tan;W. Hawthorne;J. Mccune;C. Wang
中科院分区：
文献类型：
--
作者：
C. Tan;W. Hawthorne;J. Mccune;C. Wang
提出了一种高负荷叶片的设计方法，使其具有一定的旋流分布。这种方法是基于一种新发展的三维分析。在本应用中，假定流动是不可压缩和无粘的（环空具有恒定的轮毂和叶尖半径），并且叶片的厚度可以忽略不计。假设一个简单的自由涡旋旋流表。流速分为周平均流速和周期流速。用Clebsch公式表示周期速度，奇点用周期广义函数表示，这样就可以用本征函数的形式得到解。由叶片边界条件迭代确定叶片型线。计算机程序的结果显示了叶片数量、长径和叶尖比如何影响叶片形状。在给定的涡流计划下，叶型不仅取决于展弦比，还取决于堆积位置（即，薄叶型径向的弦向位置），平均轴向和径向速度也同样如此。无论叶片数量多或少，这些影响都会发生，我们得出结论，即使在不可压缩流动中，叶片单元或条形理论通常也不能令人满意地设计高挠度叶片。通过分析，推导出环空壁面上叶片轮廓的几何条件，这些条件在理想流动中是满足壁面边界条件所必需的，但在任何实际情况下，这些条件都会因壁面边界层和叶片厚度的存在而改变。在叶片数量趋近于无穷大的极限条件下，得到了叶片致动器风道解。不考虑壁面叶型的条件，但在相同的旋流过程中，堆积位置和展弦比仍会影响轴向和径向速度分布。
A method of designing highly loaded blades to give a specified distribution of swirl is presented. The method is based on a newly developed, three-dimensional analysis. In the present application, the flow is assumed to be incompressible and inviscid (the annulus has constant hub and tip radii), and the blades are of negligible thickness. A simple free vortex swirl schedule is assumed. The flow velocity is divided into circumferentially averaged and periodic terms. The Clebsch formulation for the periodic velocities is used, and the singularities are represented by periodic generalized functions so that solutions may be obtained in terms of eigenfunctions. The blade profile is determined iteratively from the blade boundary condition. Results from the computer program show how blade number, aspect, and hub-tip ratios affect the blade shape. The blade profiles for a given swirl schedule depend not only on the aspect ratio but also on the stacking position (i.e., the chordwise location at which this thin blade profile is radial), and so too do the mean axial and radial velocities. These effects occur whether the number of blades is large or small, and we conclude that even in incompressible flow the blade element or strip theory is not generally satisfactory for the design of high-deflection blades. The analysis derives the geometrical conditions for the blade profiles on the walls of the annulus which are needed to satisfy the wall boundary conditions in the idealized flow, but which in any practical example will be modified by the presence of wall boundary layers and blade thickness. In the limit when the number of blades approaches infinity, a bladed actuator duct solution is obtained. The conditions for the blade profile at the walls are absent, but the stacking position and aspect ratio still affect the axial and radial velocity distributions for the same swirl schedule.