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首页> 外文会议>IUTAM Symposium on Diffraction and Scattering in Fluid Mechanics and Elasticity Jul 16-20, 2000 Manchester, United Kingdom >THE WAVENUMBER SURFACE IN BLADE-VORTEX INTERACTION
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THE WAVENUMBER SURFACE IN BLADE-VORTEX INTERACTION

机译：叶片-涡旋相互作用中的波数表面

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This paper determines the wavenumber surface describing the production of sound when convected vorticity strikes the leading edge of an aircraft wing or fan blade. The acoustic part of the wavenumber surface consists of four sheets, namely an ellipsoid, half an elliptic cylinder, and two parallel planes. The half-cylinder, which has two infinite straight edges, is wrapped around the ellipsoid, i.e. is tangential to it along a half-ellipse. Each of the parallel planes contains an edge of the half-cylinder, and is tangential both to the half-cylinder and the ellipsoid; and each plane contains a special point at which there is a triple tan-gency of the plane, the half-cylinder, and the ellipsoid. The wavenumber surface also contains a fifth sheet, describing convection of vorticity with the mean flow; this sheet is a plane, perpendicular to the two acoustic planes. The four acoustic sheets determine the asymptotic properties of the radiated sound field; in particular the half-ellipse, two straight edges, and two triple points determine the special functions describing the sound radiated in certain special directions. The author believes that the wavenumber surface has not previously been determined for a diffraction problem. Intriguingly, the knife-edge in physical space leads to knife-edges in wavenumber space, a result which can be expected in general. The method in the paper for determining the wavenumber surface applies to any half-plane diffraction problem, e.g. the scattering of sound by a half-plane, the scattering of an elastic wave by a crack, or the scattering of a Rossby wave by a vertical barrier.
机译：本文确定了描述对流涡旋撞击飞机机翼或风扇叶片前缘时产生声音的波数表面。波数表面的声学部分由四张薄片组成，即一个椭圆体，一个半椭圆圆柱体和两个平行平面。具有两个无限直边的半圆柱体包裹在椭圆形周围，即沿半椭圆形切向它。每个平行平面都包含半圆柱体的边缘，并且与半圆柱体和椭圆体均相切；每个平面都包含一个特殊的点，在该点上，该平面，半圆柱体和椭球体具有三重相切。波数表面还包含第五张图，描述了涡旋与平均流的对流。该片是垂直于两个声平面的平面。四个声片确定了辐射声场的渐近特性。特别是半椭圆，两个笔直的边缘和两个三点确定了描述在某些特定方向上辐射的声音的特殊功能。作者认为，波数表面以前尚未确定是否存在衍射问题。有趣的是，物理空间中的刀刃会导致波数空间中的刀刃，这通常是可以预期的结果。本文中确定波数表面的方法适用于任何半平面衍射问题，例如声音在半平面上的散射，弹性波在裂缝上的散射或罗斯比波在垂直屏障下的散射。

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