Creation of A Better Energy Harvester !!!?!?!?! P M V Subbarao Professor Mechanical Engineering Department I I T Delhi Harvesting of the Useful Energy of the Bountiful Fluid

Wild Solutions to Utilize Available Energy

The Family of Steam Engines

The definition of Work The term work was introduced in 1826 by the French mathematician Gaspard-Gustave Coriolis as "weight liftedthrough a height“. This is based on the use of early steam engines to lift buckets of water out of flooded ore mines.

The Basic & Essential Cause for Generation of motive work The experts advocate an approach to action by Newton's laws. Any solid body that can generate an action on the continuously flowing fluid clearly implies that there will be a reaction on the solid body as a Newton's 3rd law reaction. From the conservation of momentum for control Volume: If an exiting stream from a solid body is given a downward component of momentum by the solid body, 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 reactive force !

Reaction leading to Torque The concept of torque, also called moment or couple, originated with the studies of Archimedes on levers. The rotational analogues: Force – Torque Mass – Inertia Acceleration -- angular acceleration

Simple Turbine : Harvester of Useful Fluid Energy in out T

Acquisition of Work from Riverine Bounty

Hydraulic Turbine : Harvester of Kinetic Energy

The Hydro Power House

Wind Turbine : Harvester of Kinetic Energy

SOME TYPES OF WIND TURBINES

Macro Analysis of A Turbine A Turbine Fluid in Fluid out

Leonhard Euler Leonhard Euler ( ) was arguably the greatest mathematician of the eighteenth century. One of the most prolific writer of all time; his publication list of 886 papers and books fill about 90 volumes. Remarkably, much of this output dates from the last two decades of his life, when he was totally blind. Euler's prolific output caused a tremendous problem of backlog: the St. Petersburg Academy continued publishing his work posthumously for more than 30 years.

Theoretical and Rigorous Work of French Bernoulli and Leonhard Euler. 1750:Euler offered a memoir containing analysis and equations for hydraulic turbines. 1754: An idealized theoretical application of Newton’s Law to centrifugal impellers. Known as Euler Equation. Did much to help the development of hydraulic machinery. 1767: Relation between Torque and Change in moment of momentum of the fluid as it passed through the machine.

Applications of Euler’s Equation Euler equation applies to all kinds of turbomachines. Wind turbines ---- Pumps --- Gas turbines. Axial flow machines to Radial flow to Mixed flow. Energy extraction machines – Energy consuming machines. For a turbine the value of Equation is negative. For pumps, fans, blowers and compressors it is positive.

The Superiority of Vector Parameters in A Cylindrical Coordinate System

Order of Velocity Vectors The real flow through any turbomachine is three dimensional. Axial, Radial and Circumferential. Axi-symmetry: Inter blade row space. Axi-symmetry assumes an average value to represent the state of working fluid in the blade-to-blade plane.

The Reference Plane of Euler Equation : Meridional Plane The momentum balance is considered in a plane constructed through axis of rotation and radial axis. This Plane is called Meridional Plane.

Euler’s Vision of Vector

Macro Analysis of A Steam Turbine Fluid in Fluid out

Euler’s Version of Newton’s Second Law In turbo-machines much useful information is obtained by employing Newton’s second law in the form where it applies to the moments of forces. This form is of central importance in the analysis of the energy transfer process in turbo-machines.

Euler’s Statement for Second Law For a system of mass m, the vector sum of the moments of all external forces acting on the system about some arbitrary axis A--A fixed in space is equal to the time rate of change of angular momentum of the system about that axis, i.e.

Torque exerted by flow on blade row = shaft output torque = Rate of change of Angular momentum of fluid =  Euler Theory: Define, L as Angular momentum : Angular momentum is moment of linear momentum of angular velocity, V 

For a steady flow through a turbo-machine: Inlet rate of angular momentum : Exit rate of angular momentum at exit: Change in Rate of angular momentum:

Euler Theory: Power : A change in Whirl Velocity of fluid is essential to establish Power Exchange between fluid and rotor in a turbo-machine ! Euler Turbine Equation

Infinitesimal Euler Turbine Equation

Euler Turbine Power Equation. Conservation of Energy for An Ideal Turbine

For a Turbomachine: Combination of Euler and SFEE Over an ideal turbomachine blade along flow direction rothalpy remains constant