Potential flow through a cascade of aerofoils: direct and inverse problems
Potential flow through a cascade of aerofoils: direct and inverse problems
复制标题
通过级联翼型的势流：正问题和反问题
DOI：
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发表时间：
2018
期刊：
影响因子：
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通讯作者：
Lorna J. Ayton
中科院分区：
文献类型：
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作者：
Peter J. Baddoo;Lorna J. Ayton
通过无限级联翼型的势流被视为正问题和逆问题。在每种情况下，都假设关于背景均匀流的扰动展开，其中扰动的大小与翼型的纵横比相当。这种扰动必须在上游很远的地方衰减，并且还满足特定的边缘条件，包括每个后缘的库塔条件。在直接问题中，计算通过已知几何形状的级联翼型的流场。通过将情况重新转换为仅在和弦上规定虚值的黎曼-希尔伯特问题，可以通过分析解决此问题。当翼型之间的距离趋于无穷大时，可以看到解决方案收敛到单个翼型的已知解析表达式。表面速度、升力和偏转角的解析表达式被表示为翼型几何形状、迎角和交错角的函数；这些结果与数值结果非常吻合。在反问题中，机翼几何形状是根据沿弦的指定切向表面速度和上游攻角计算的。这是通过求解机翼弦上规定的奇异积分方程找到的。
The potential flow through an infinite cascade of aerofoils is considered as both a direct and inverse problem. In each case, a perturbation expansion about a background uniform flow is assumed where the size of the perturbation is comparable to the aspect ratio of the aerofoils. This perturbation must decay far upstream and also satisfy particular edge conditions, including the Kutta condition at each trailing edge. In the direct problem, the flow field through a cascade of aerofoils of known geometry is calculated. This is solved analytically by recasting the situation as a Riemann–Hilbert problem with only imaginary values prescribed on the chords. As the distance between aerofoils is taken to infinity, the solution is seen to converge to a known analytic expression for a single aerofoil. Analytic expressions for the surface velocity, lift and deflection angle are presented as functions of aerofoil geometry, angle of attack and stagger angle; these show good agreement with numerical results. In the inverse problem, the aerofoil geometry is calculated from a prescribed tangential surface velocity along the chords and upstream angle of attack. This is found via the solution of a singular integral equation prescribed on the chords of the aerofoils.