Blades for Wind Turbines P M V Subbarao Professor Mechanical Engineering Department An extra-ordinary Fluid Device.....

Roles of Blade in Wind Turbine

Flow past an airfoil

Effect Based Description

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

Can We Identify the Cause?

The Natural Genius & The Art of Generating Lift

Hydrodynamics of Prey & Predators

The Art of C-Start

The Art of Complex Swimming

Development of an Ultimate Fluid machine

19th Century Inventions H F Phillips Otto Lilienthal

History of Airfoil Development

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.

Fascinating Vortex Phenomena : Kutta-Joukowski Theorem

Fascinating Vortex Phenomena : Kutta-Joukowski Theorem The Joukowsky transformation is a very useful way to generate interesting airfoil shapes. However the range of shapes that can be generated is limited by range available for the parameters that define the transformation.

Three Basic Elements in Creation of Thin Aerofoil Theory

THE COMPLEX POTENTIAL Invscid Flow field and perturbing solid(s) 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 perturbation objects The source and the sink The vortex

THE UNIFORM FLOW : Creation of 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

THE SOURCE OR SINK: The Perturbation Functions 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 The flow field is uniquely determined upon deriving the complex potential W with respect to z.

A Combination of Source & Sink

THE DOUBLET The complex potential of a doublet

Uniform Flow Past A Doublet : Perturbation of Uniform Flow The superposition of a doublet and a uniform flow gives the complex potential

Find out a stream line corresponding to a value of steam function is zero

There exist a circular stream line of radium R, on which value of stream function is zero. Any stream function of zero value is an impermeable solid wall. Plot shapes of iso-streamlines.

Note that one of the streamlines is closed and surrounds the origin at a constant distance equal to    

Recalling the fact that, by definition, a streamline cannot be crossed by the fluid, this complex potential represents the irrotational flow around a cylinder of radius R approached by a uniform flow with velocity U. Moving away from the body, the effect of the doublet decreases so that far from the cylinder we find, as expected, the undisturbed uniform flow. In the two intersections of the x-axis with the cylinder, the velocity will be found to be zero. These two points are thus called stagnation points.

To obtain the velocity field, calculate dw/dz.

Equation of zero stream line: with

Cartesian and polar coordinate system

V2 Distribution of flow over a circular cylinder The velocity of the fluid is zero at = 0o and = 180o. Maximum velocity occur on the sides of the cylinder at = 90o and = -90o.

Creation of Flow Past A Cylinder

Generation of Vorticity

Creation of Pressure Distribution

No Net Up wash Effect

THE VORTEX In the case of a vortex, the flow field is purely tangential. The picture is similar to that of a source but streamlines and equipotential lines are reversed. The complex potential is There is again a singularity at the origin, this time associated to the fact that the circulation along any closed curve including the origin is nonzero and equal to g. If the closed curve does not include the origin, the circulation will be zero.

Uniform Flow Past A Doublet with Vortex The superposition of a doublet and a uniform flow gives the complex potential

Angle of Attack Unbelievable Flying Objects

Kate Carew Interviews the Wright Brothers “Are you manufacturing any racing machines?” “Not just now, but we intend to.” “How much can I buy one for?” “Seven thousand five hundred-dollars.” “Is that all? It doesn’t seem like an outside price for a perfectly good airship?” “Airship!” shouted the Wright brothers indignantly. “Is that the wrong word?” “An airship,” said Wilbur contemptuously, “is a big, clumsy balloon filled with gas.” “Well, I don’t see why your biplane shouldn’t be called an airship, too.” “It’s a flying machine,” said Wilbur. “The name we prefer is ‘flyer,’” said Orville. “An airship would cost $50,000,” said Wilbur. “More like $150,000,” said Orville, and they argued the question.