turbine cascade

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ELEMENTARY CASCADE THEORYAND

GAS TURBINE PERFORMANCE

INDO-GERMAN WINTER ACADEMY 2007

AVIRAL CHOPRA

DEPARTMENT OF CHEMICAL ENGINEERINGIIT KANPUR

TUTORS:

DR. G. BIWAS,DR. S. SARKAR



Gas Turbine Engines

Axial Flow Turbines

Turbine Performance

Cascade Theory

Compressor Cascade

Turbine Cascade

Conclusion

2

Elementary Cascade Theory And Gas Turbine Performance

Outline



A gas turbine engine extracts energy from a flow of hot gas

produced by combustion of gas or fuel oil in a stream of

compressed air. The system has three major parts:

Compressor: compresses the incoming air to high pressure

3


Gas Turbine Engines

Theory Of Gas Turbine Engines



Combustor: Burns the fuel and produces high-pressure, high-

temperature gas

Turbine: Extracts the energy from the high-pressure, high-

energy gas flowing from the combustion chamber

4


Gas Turbine Engines

Theory Of Gas Turbine Engines



5


Gas Turbine Engines



Turbine extracts energy from the gas to rotate compressor

The pressurized gas from compressor is furnished to maintain

the cycle

Burning of fuel-air mixture provides stream of hot expandinggases

Out of the total energy development, approximately 60% isextracted to maintain the engine cycle

The rest is available to develop useful thrust directly

6


Gas Turbine Engines

Working Of A Simple Turbojet



Compared to compressor

More Efficient

Simpler Design

Blade shape

Dependent on Stress andCooling

Not as much on

aerodynamics

Axial Turbine Stage

Row of stationary blades:

Nozzle

Row of rotating blades: Rotor

7


Axial Flow Turbines

Axial Flow Turbines



8


Axial Flow Turbines

2-D Theory Of Axial Turbines



Power Output:

In axial turbine stage,

Using diagram, we

express work output in

terms of rotor bladeangles

WT

Combined Velocity diagram9


Axial Flow Turbines

Work Done, WT



Entire Pressure drop in

nozzle

Symmetrical Rotor blades

Pressure drop same in

Nozzle and Rotor

Thus, symmetrical blading

α2 = -β3 , β2 = -α3

Impulse Turbines 50 % Reaction Turbines

10


Axial Flow Turbines

Types Of Axial Turbines



Ψ, Blade loading or temperature drop coefficient

Expresses work capacity of a stage

Φ, Flow coefficient =Vf / U Ψ= Φ (tan β2 – tan β1)

R, degree of reaction, fraction of overall enthalpy drop (or pressure drop) occurring in

the rotor

= 11


Axial Flow Turbines

Dimensionless Parameters



Thus, R in terms of Exit Angles:

12


Axial Flow Turbines

Gas Flow Angles in terms of ψ, φ, R



Work capacity Ψ

and degree of reaction

R of axial turbine stages design for zeroexit swirl.

Given stator angle

In Impulse stage, all

flow velocities are

higher

Thus, lower efficiency

13


Axial Flow Turbines

ZERO EXIT SWIRL

El t C d Th A d G T bi P f



Useful work is shaft power

Kinetic Energy of exhaust,

V32

/2 is a loss

Exhaust Kinetic Energy is

not a loss

Total-to-Static Turbineefficiency, ηts

Total-to-Total TurbineEfficiency, ηtt

14


Turbine Performance

STAGE EFFICIENCY

El t C d Th A d G T bi P f



Using

we obtain

Thus ηtt > ηts

Actual Turbine Work

T-S diagram: expansion ina turbine 15


Turbine Performance

STAGE EFFICIENCY




Estimation of stage losses and η is difficult

Loss Coefficients for Nozzle and Rotor are defined using cascadetests

Effect of loss expressed as difference in static enthalpy

Enthalpy loss coefficient for nozzle,

Enthalpy loss coefficient foe rotor,

Thus, and 16


Cascade TheoryTurbine Performance

STAGE EFFICIENCY




Given

Turbine Design

Fluid at high Re

We get:

where

stagnation states 02 and 03

are at the turbine inlet and

outlet

17



TURBINE STAGE PERFORMANCE




ηtt is constant over wide range of

Rotational Speed

Pressure Ratio

Performance is limited by 2 factors:

Compressibility Stress

Trade-off between maximum temperature and maximum rotor speed, U

Thus, elaborate cooling methods are adopted18



OVERALL PERFORMANCE




An array of blades

representing the blade ring

of actual turbo machinery iscalled the cascade.

Turntable: to vary theincidence angle

Pressure and velocity

measurements madeupstream and

downstream of cascadeCascade Tunnel

19


Cascade Theory

ELEMENTARY CASCADE THEORY




To simulate actual conditions, cascade of blades could be

tested in annular form in wind tunnel

In such case of rotating device, difficult to appreciate flow

physics

Hence, blades generally tested as straight cascade or

cascade tunnel

This way:

Mechanical complications reduced

2-D flow conditions simplifies interpretation of test results

20


Cascade Theory

WHY CASCADE THEORY




Blade Camber Angle, Θ = θ1

+ θ2 21


Cascade Theory

CASCADE NOMENCLATURE




Stagger angel, λ (+ve here)

(b/w Axis and chord line) Blade inlet angle, α1

I = λ + θ1

Blade outlet angle α2I = λ – θ2

Air inlet Angle, α1

= λ + θ1

+ i

Air outlet Angle, α2 = λ - θ2 + δ

Deflection, ξ = α1 – α2

= θ

+ i -

δ

Deviation, δ = α2 – α2I

Incidence Angle, i = α1 – α1I

22


Cascade Theory

COMPRESSOR CASCADE




TURBINE CASCADE

Note: Stagger Angel, λ is –vehere

23

e e ta y Cascade eo y d Gas u b e e o a ce

Cascade Theory




Velocity

Triangle 24

y y

Cascade Theory

COMPRESSOR CASCADE




Vm is the mean velocity that makes an angle with the axial direction αm.

Circulation, Γ = S ( VW1-VW2 )

Lift, L = ρVMΓ = ρVM S( VW1-VW2 )

Lift is perpendicular to αm line

S,C -depend on the design of the cascade

Lift Coefficient

25

y y

Cascade Theory

COMPRESSOR CASCADE




Velocity

Triangle 26

Cascade Theory

TURBINE CASCADE




Till now, Inviscid flow assumption

In reality, loss in pressure

Loss in total pressure

= Loss in Static pressure

=

Loss due to

Frictional loss ( boundary layer formation)

Mixing of blade wakes

27

Cascade Theory

EFFECT OF VISCOUS FLOW




28

Fixed Incidence

Loss in

Dimensionless

form

Cascade Theory

Variation of Stagnation Pressure Loss and Deflection




29

Nominal

Deflection = ξ*

Stalling

Deflection = ξs

Cascade Theory

Cascade Mean Deflection and Pressure Loss Curves




Test results for different

geometric forms by varying

Camber

Pitch/ Chord ratio

In the range of incidencelikely to be used, ξ* is

mainly dependent on:

Pitch/ chord ratio

Air outlet angle

30

Cascade Theory

DESIGN DEFLECTION CURVES


C d Th



Due to losses in total pressure,

an axial force,

Thus, Drag,

Lift is reduced, so Effective Lift

Lift Coefficient

Drag Coefficient31

Cascade Theory

COMPRESSOR CASCADE (VISCOUS CASE)


C d Th



Here, Drag contributes to

work. So, drag is useful

component

Drag,

Effective Lift,

Lift Coefficient

32

Cascade Theory

TURBINE CASCADE (VISCOUS CASE)


C d Th



Due to viscous effect, static pressure rise is reduced, so

Blade efficiency,

ηb is max if , or

Approximation: in expression of Lift, effect of Drag is ignored. 33

Cascade Theory

COMPRESSOR BLADE EFFICIENCY


Cascade Theory



Blade Efficiency,

For small CD / CL ratio = (ηb)compressor

34

Cascade Theory

TURBINE BLADE EFFICIENCY


Cascade Theory



If Drag is not neglected

in expression of Lift

Nature of variation of ηb

wrt mean

flow angle αm

Note: ηb does not vary much in the range 15°

≤ αm

≤

75°, which provides

flexibility in design.35

Cascade Theory

BLADE EFFICIENCY




Compared to axial compressors, axial turbines are simpler in

design and more efficient

Elaborate cooling techniques are adopted in turbines to have

Less stress at higher temperature

More rotor speed

Cascade theory gives a thorough idea about the performance

of compressor and turbine blades

Through cascade analysis, a wide database is created which

aids in the design of compressor or turbine blades

36

CONCLUSION




Aviral Chopra

Department of Chemical Engineering

Indian Institute of Technology Kanpur 37

THANK YOU

turbine cascade

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