Fluid Dynamic Characterization of Turbo-machinery

P M V SubbaraoProfessor

Mechanical Engineering Department

Understanding the Role of Vectorial analysis !!!

The thermodynamic Variations

IncompressibleFluid

CompressibleFluid

Power Generating Machines

Hydraulic Turbines Steam/Gas/wind Turbines

Power Consuming Machines

Pumps Fan/blowers/Compressors

• 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).

Fluid Dynamics of A Turbo-machine

A Turbo-machine

The Ancient Design : Undershot Water Wheel : 4000BC

SOME TYPES OF WIND TURBINES: VAWT

SOME TYPES OF WIND TURBINES: HAWT

Various Types of Modern Turbomachine

• 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.

Why So Many?

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 through-

flow 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

kVjViVV zrˆˆˆ

Euler’s Work Equation

Torque exerted by flow on blade row = shaft output torque = Rate of change of Angular momentum of fluid =

Euler Theory:kVjViVV zrˆˆˆ