Design of Aerofoil for A Turbomachine

1. Design of Aerofoil for A Turbomachine P M V Subbarao Professor Mechanical Engineering Department A Fluid Device, Which abridged the Globe into Global Village…. Generating Hopes to turn Space into ……

2. Aerofoil Design for A Wind Turbine Blade Tip Leading Edge Airfoil NACA 65-410 Root Section

3. Streamlines & Pressure Field past an airfoil

4. Flights Flying Upside Down

5. 19th Century Inventions Otto Lilienthal H F Phillips

6. History of Airfoil Development

7. Effect Based Description

8. Can We Identify the Cause?

9. Definition of lift and drag Lift and drag coefficients Cl and Cd are defined as:

10. The Basic & Essential Cause for Generation of Lift • The experts advocate an approach to lift by Newton's laws. • Any solid body that can force the air downward clearly implies that there will be an upward force on the airfoil as a Newton's 3rd law reaction force. • From the conservation of momentum for control Volume • The exiting air is given a downward component of momentum by the solid body, and to conserve momentum, • something must be given an equal upward momentum to solid body. • Only those bodies which can give downward momentum to exiting fluid can experience lift ! • Kutta-Joukowski theorem for lift.

11. Fascinating Vortex Phenomena : Kutta-Joukowski Theorem

12. Fascinating Vortex Phenomena : Kutta-Joukowski Theorem

13. THE COMPLEX POTENTIAL Flow past any unknown object can be represented as a complex potential. In particular we define the complex potential In the complex plane every point is associated with a complex number In general we can then write

14. Now, if the function f is analytic, this implies that it is also differentiable, meaning that the limit so that the derivative of the complex potential W in the complex z plane gives the complex conjugate of the velocity. Thus, knowledge of the complex potential as a complex function of z leads to the velocity field through a simple derivative.

15. Elementary fascination Functions • To Create IRROTATIONAL PLANE FLOWS • The uniform flow • The source and the sink • The vortex

16. THE UNIFORM FLOW : Creation of Simple mass & Momentum in Space The first and simplest example is that of a uniform flow with velocity U directed along the x axis. In this case the complex potential is and the streamlines are all parallel to the velocity direction (which is the x axis). Equi-potential lines are obviously parallel to the y axis.

18. THE SOURCE OR SINK source (or sink), the complex potential of which is • This is a pure radial flow, in which all the streamlines converge at the origin, where there is a singularity due to the fact that continuity can not be satisfied. • At the origin there is a source, m > 0 or sink, m < 0 of fluid. • Traversing any closed line that does not include the origin, the mass flux (and then the discharge) is always zero. • On the contrary, following any closed line that includes the origin the discharge is always nonzero and equal to m.

19. Iso f lines Iso y lines • The flow field is uniquely determined upon deriving the complex potential W with respect to z.