Design of Aerofoil for A Turbomachine P M

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 ……

Aerofoil Design for A Wind Turbine Blade Tip Leading Edge Root Section Airfoil NACA 65410

Streamlines & Pressure Field past an airfoil

Flights Flying Upside Down

19 th Century Inventions H F Phillips Otto Lilienthal

History of Airfoil Development

Effect Based Description

Can We Identify the Cause?

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

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 3 rd 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.

Fascinating Vortex Phenomena : Kutta-Joukowski Theorem

Fascinating Vortex Phenomena : Kutta-Joukowski Theorem

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

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.

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

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.

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.

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