Fluid Dynamic Characterization of Turbomachinery P M V

Fluid Dynamic Characterization of Turbo-machinery P M V Subbarao Professor Mechanical Engineering Department Understanding the Role of Vectorial analysis !!!

The thermodynamic Variations • Two main categories of turbo-machine are identified: • Firstly, those which absorb power to increase the fluid pressure or head (fans, compressors and pumps); • Secondly, those that produce power by expanding fluid to a lower pressure or head (hydraulic, steam and gas turbines). Incompressible Fluid Compressible Fluid Power Generating Machines Hydraulic Turbines Steam/Gas/wind Turbines Power Consuming Machines Pumps Fan/blowers/ Compressors

Fluid Dynamics of A Turbo-machine

The Ancient Design : Undershot Water Wheel : 4000 BC

SOME TYPES OF WIND TURBINES: VAWT

SOME TYPES OF WIND TURBINES: HAWT

Various Types of Modern Turbomachine

Why So Many? • Why so many different types of either pumps (compressors) or turbines are in use ? • Is it due to (almost) infinite range of service requirements? • As a fact, for a given set of operating/resource requirements , • there should be only one type of pump or turbine which is best suited to provide best/optimum performance.

Classification of Turbo-machines • Two main categories of turbo-machine are identified: • Firstly, those which absorb power to increase the fluid pressure or head (fans, compressors and pumps); • Secondly, those that produce power by expanding fluid to a lower pressure or head (hydraulic, steam and gas turbines).

Classification : Flow Path

Classification : Flow Path • Turbo-machines are further categorised according to the nature of the flow path through the passages of the rotor. • When the path of the through-flow is wholly or mainly parallel to the axis of rotation, the device is termed an axial flow turbo-machine. • When the path of the through-flow is wholly or mainly in a plane perpendicular to the rotation axis, the device is termed a radial flow turbo-machine. • Mixed flow turbo-machines are widely used. • The term mixed flow refers to the direction of the throughflow at rotor outlet when both radial and axial velocity components are present in significant amounts.

Solid – Fluid Interaction Level • Open flow – No casing or enclosure for the rotating device – Propeller is an open flow power consuming device. – Windmill is an open flow power generating device. Enclosed or encased flow devices

Any Unified Theory? Developed by the Father of Turbo-machines… The Mathematics of Turbo-machinery

Leonhard Euler • Leonhard Euler (1707 -1783) 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

Euler’s Work Equation Euler Theory: Torque exerted by flow on blade row = shaft output torque = Rate of change of Angular momentum of fluid = t