Mathematical methods for boundary layers

边界层的数学方法

• 批准号: EP/D507855/1
• 负责人: Jonathan Healey
• 金额: $ 4.34万
• 依托单位: Keele University
• 依托单位国家: 英国
• 项目类别: Training Grant
• 财政年份: 2006
• 资助国家: 英国
• 起止时间: 2006 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FD507855%2F1
• 关键词: Mathematical; methods; boundary; layers

When a gas or liquid flows at high speed past an aerofoil (like an aeroplane wing, or a turbine blade) thin regions of high shear form close to the aerofoil surface, which are called boundary layers. Boundary layers play a crucial role in determining the flow around the aerofoil, e.g. if there were no boundary layers, a wing could not generate any lift, but the boundary layers also contribute significantly to the drag on the wing. This drag increases sharply if the boundary layer becomes turbulent. If the boundary layers separate from the aerofoil near the leading edge the lift reduces and the drag increases (the wing stalls). These phenomena are of central importance in the aerospace industries, but boundary layers can form whenever fluid flows through, or around, a device at speed. This summer school is concerned with teaching UK based engineering PhD students about the mathematical techniques used in current research that help us to understand, and perhaps ultimately control, boundary layer separation and transition to turbulence. The relation between analytical mathematical results and numerical results will be explored, and the benefits of combining the two identified.

当气体或液体以高速流过机翼（如机翼或涡轮机叶片）时，在靠近机翼表面处形成高剪切的薄区域，称为边界层。边界层在确定翼型周围的流动中起着至关重要的作用，例如，如果没有边界层，机翼就不能产生任何升力，但边界层也对机翼上的阻力有很大的贡献。如果附面层变成紊流，这个阻力就会急剧增加.如果附面层在前缘附近与翼型分离，升力减小，阻力增加（机翼失速）。这些现象在航空航天工业中至关重要，但是当流体高速流过或围绕设备流动时，就会形成边界层。这个暑期学校关注的是教英国的工程博士生关于当前研究中使用的数学技术，帮助我们理解，也许最终控制，边界层分离和过渡到湍流。分析数学结果和数值结果之间的关系将被探讨，并确定两者相结合的好处。