Selection of Stator-Rotor Combinations

How to Execute Conservation of Rothalpy ??Enthalpy

Kinetic Energy

Velocity Vector Field

Fluid Dynamics

Generation of Change in rate of angular momentum

(An Action)

Who Will take the Reaction ???

Shaft Torque is the final need as

Reaction

Basic Rules for Design of An Ideal Turbine Flow Path

• Created highest usable form of a resource.• Creation of initial velocity/kinetic energy using Stator.• X1 (Impulse)+X2(Reaction)+(1-X1-X2)(centripetal)

• Y1 (Radial)+(1-Y1 )(Axial)• Design of Flow Path using Conservation of rothalpy.• Design blade cascade using conservation of mass and

momentum.• A design of an Ideal Machine …..• Each stage can do finite amount of action….!!!• Many stages are needed to complete the action….

Flow in Stator-Rotor Inter stage Gaps

Geometrical Details along the Third Direction

• True flow through a turbo-machinery is three-dimensional. • Flow and tangential flow velocities are very important for

better operation of a turbo-machine.• The third component, which is normal to flow and

tangential directions is in general of no use.• This direction can better represented as blade height

direction.

Third Direction of an Axial Flow Turbo-Machines

• The third direction in an axial flow machine is the radial direction.

• The direction of Centrifugal forces!• Strong centrifugal forces are exerted on blades & fluid in

radial direction. • The centrifugal field distorts the flow velocity profiles

considerably.• Fluid particles tend to move outwards rather than passing

along cylindrical stream surfaces as classically assumed.

• Particularly in tall blade (low hub: tip) ratio designs.• An approach known as the radial equilibrium method,

widely used for three-dimensional design calculations in a an axial flow machine.

Radial Equilibrium Theory of Turbo-machines

P M V SubbaraoProfessor

Mechanical Engineering Department

A Model for Stable Operation of A Machine

A guiding equation for distribution of load along blade length ….

Radial Variation of Blade Geometry

Radial Equilibrium Theory

• Assumes that flow is in radial equilibrium before and after a blade row.

• Radial adjustment takes place through the row.• More important for Axial Flow Machines.

Radial Equilibrium Analysis

The centrifugal force = (rdrd)2r V = r

The centrifugal force is

The pressure force on the element

drdVF lcentrifuga2

rdpdFpressure

If the two forces are the only ones acting (viscous and other effects neglected), the particle will move at constant radius if:

lcentrifugapressure FF

rdrVdp 2

drdVrdpd 2

Equilibrium Condition for A Rotating Fluid

A mechanical equilibrium of a fluid elements demands thermodynamic equilibrium.The fluid must be facilitated to adjust radially as per the requirements.This process of radial adjustment of fluid parcels is well assumed to be isentropic.

0dpdhvdpdhTds

dpdh

rdrVdh 2

The radial variation of whirl velocity should be according to above equation.

How to implement on a machine?

rdrVdp 2

2222

2222

0VVV

hV

hh rf

0222

222

0

VVV

hddh rf

Implementation of Radial Equilibrium

Stagnation enthalpy should conserve, as there are not interactions with rotor at inlet or exit.

rdrVdh 2

0222

2222

0

VVV

drdrVdh rf

0222

22220

VVV

drd

rV

drdh rf

02

0 dr

dVVdr

dVVdr

dVV

rV

drdh r

rf

f

Radial component of velocity should be constant (zero) along radial direction for radial equilibrium of flow.

02

0 dr

dVVdr

dVV

rV

drdh f

f

Constant in a turbo-machine along meridoinal Plane

021 2

drrVd

rV

drdV f

Stagnation enthalpy is Constant in a turbo-machine along radial direction at intake and discharge.

Constant21: 22

,2 bladerelx UVVhIRothalpy

Twisted Blades for Large Turbines

021 2

drrVd

rV

drdV f