tailieunhanh - KUNDU Fluid Mechanics 2E Episode 16

Tham khảo tài liệu 'kundu fluid mechanics 2e episode 16', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | to. IẦftũiịỊ I MU Theory of Prandll and iMiicheiiter 649 Figure Lift and induced drag on a wing element dy. Because the aspect ratio is assumed large is small. Each element dy of the finite wing may then be assumed to act as though it is an isolated two-dimensional section set in a stream of uniform velocity ue at an angle of attack ae. According to the Kutta-Zhukhovsky lift theorem a circulation r superimposed on the actual resultant velocity i e generates an elementary aerodynamic force dLc pUer dy which acts normal to uc. This force may be resolved into two components the conventional lift force dL normal to the direction of flight and a component dDi parallel to the direction of flight Figure . Therefore dL dLe cos pUer dy cos pur dy dDị dLesỉne pucr dysine pwrdy. In general w r ue and ac are all functions of y so that for the entire wing These expressions have a simple interpretation Whereas the interaction of u and r generates L which acts normal to u the interaction of w and r generates Di which acts normal to w. Induced Drag The drag force Dị induced by the trailing vortices is called the induced drag which is zero for an airfoil of infinite span. It arises because a wing of finite span continuously creates trailing vortices and the rate of generation of the kinetic energy of the vortices must equal the rate of work done against the induced drag namely DịU. For this reason the induced drag is also known as the vortex drag. It is analogous to the wave drag experienced by a ship which continuously radiates gravity waves during its motion. As we shall see the induced drag is the largest part of the total drag experienced by an airfoil. 650 Aerodynamiai A basic reason why there must be a downward velocity behind the wing is the following The fluid exerts an upward lift force on the wing and therefore the wing exerts a downward force on the fluid. The fluid must therefore constantly gain downward momentum as it goes past the wing. See the .