elementary cascade theory and gas turbine performance

INDO-GERMAN WINTER ACADEMY 2007

ELEMENTARY CASCADE THEORY AND GAS TURBINE PERFORMANCE

AVIRAL CHOPRA DEPARTMENT OF CHEMICAL ENGINEERING IIT KANPUR TUTORS: DR. G. BIWAS, DR. S. SARKAR

Elementary Cascade Theory And Gas Turbine Performance

Outline |

Gas Turbine Engines

|

Axial Flow Turbines

|

Turbine Performance

|

Cascade Theory y Compressor Cascade y Turbine Cascade

|

Conclusion 2

Elementary Cascade Theory And Gas Turbine Performance Gas Turbine Engines

Theory Of Gas Turbine Engines |

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


Theory Of Gas Turbine Engines |

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

|

Turbine: Extracts the energy from the high-pressure, highenergy gas flowing from the combustion chamber

4


5


Working Of A Simple Turbojet |

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 expanding gases

|

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

|

The rest is available to develop useful thrust directly

6

Elementary Cascade Theory And Gas Turbine Performance Axial Flow Turbines

Axial Flow Turbines |

Compared to compressor y More Efficient y Simpler Design

|

Blade shape y Dependent on Stress and Cooling y Not as much on aerodynamics

|

Axial Turbine Stage y Row of stationary blades: Nozzle y Row of rotating blades: Rotor

7


2-D Theory Of Axial Turbines

8


Work Done, WT

Combined Velocity diagram

|

Power Output:

|

In axial turbine stage,

|

Using diagram, we express work output in terms of rotor blade angles WT 9


Types Of Axial Turbines Impulse Turbines

50 % Reaction Turbines

|

Entire Pressure drop in nozzle

|

Pressure drop same in Nozzle and Rotor

|

Symmetrical Rotor blades

|

Thus, symmetrical blading

|

α2 = -β3 , β2 = -α3

10


Dimensionless Parameters |

Ψ, Blade loading or temperature drop coefficient y Expresses work capacity of a stage y

|

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

|

R, degree of reaction, y

y

fraction of overall enthalpy drop (or pressure drop) occurring in the rotor =

11


Gas Flow Angles in terms of ψ, φ, R |

|

|

|

|

Thus, R in terms of Exit Angles:

12


ZERO EXIT SWIRL |

Given stator angle

|

In Impulse stage, all flow velocities are higher

|

Thus, lower efficiency

13

Work capacity Ψ and degree of reaction R of axial turbine stages design for zero exit swirl.

Elementary Cascade Theory And Gas Turbine Performance Turbine Performance

STAGE EFFICIENCY Total-to-Static Turbine efficiency, ηts

|

Useful work is shaft power

|

Kinetic Energy of exhaust,

Total-to-Total Turbine Efficiency, ηtt

|

Exhaust Kinetic Energy is not a loss

V32 /2 is a loss

14

Elementary Cascade Theory And Gas Turbine Performance Turbine Performance

STAGE EFFICIENCY |

Using

we obtain

|

|

Thus ηtt > ηts Actual Turbine Work

T-S diagram: expansion in a turbine

15

Elementary Cascade Theory And Gas Turbine Performance Turbine Performance Cascade Theory

STAGE EFFICIENCY y

Estimation of stage losses and η is difficult

y

Loss Coefficients for Nozzle and Rotor are defined using cascade tests

y

Effect of loss expressed as difference in static enthalpy

y

Enthalpy loss coefficient for nozzle,

y

Enthalpy loss coefficient foe rotor,

y

Thus,

and

16


TURBINE STAGE PERFORMANCE |

Given y y

|

Turbine Design Fluid at high Re

We get:

where stagnation states 02 and 03 are at the turbine inlet and outlet

17


OVERALL PERFORMANCE |

ηtt is constant over wide range of y Rotational Speed y Pressure Ratio

|

Performance is limited by 2 factors: y Compressibility y Stress

|

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

|

Thus, elaborate cooling methods are adopted

18

Elementary Cascade Theory And Gas Turbine Performance Cascade Theory

ELEMENTARY CASCADE THEORY

Cascade Tunnel

|

An array of blades representing the blade ring of actual turbo machinery is called the cascade.

|

Turntable: to vary the incidence angle

|

Pressure and velocity measurements made upstream and downstream of cascade 19


WHY 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: y Mechanical complications reduced y 2-D flow conditions simplifies interpretation of test results 20


CASCADE NOMENCLATURE

Blade Camber Angle, Θ = θ1 + θ2

21


COMPRESSOR CASCADE y

Stagger angel, λ (+ve here) (b/w Axis and chord line)

y

Blade inlet angle, α1I = λ + θ1

y

Blade outlet angle α2I = λ – θ2

y

Air inlet Angle, α1 = λ + θ1 + i

y

Air outlet Angle, α2 = λ - θ2 + δ

y

Deflection, ξ = α1 – α2 =θ+i-δ

y

Deviation, δ = α2 – α2I

y

Incidence Angle, i = α1 – α1I 22


TURBINE CASCADE

Note: Stagger Angel, λ is –ve here

23


COMPRESSOR CASCADE

Velocity Triangle

24


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


TURBINE CASCADE

Velocity Triangle

26


EFFECT OF VISCOUS FLOW |

Till now, Inviscid flow assumption

|

In reality, loss in pressure

|

Loss in total pressure = Loss in Static pressure =

|

Loss due to y Frictional loss ( boundary layer formation) y Mixing of blade wakes 27


Variation of Stagnation Pressure Loss and Deflection ¾Fixed Incidence ¾Loss in Dimensionless form

28


Cascade Mean Deflection and Pressure Loss Curves |

Nominal Deflection = ξ*

|

Stalling Deflection = ξs

29


DESIGN DEFLECTION CURVES |

Test results for different geometric forms by varying y y

|

Camber Pitch/ Chord ratio

In the range of incidence likely to be used, ξ* is mainly dependent on: y y

Pitch/ chord ratio Air outlet angle

30


COMPRESSOR CASCADE (VISCOUS CASE) |

Due to losses in total pressure, an axial force,

|

Thus, Drag,

|

Lift is reduced, so Effective Lift

|

Lift Coefficient

|

Drag Coefficient

31


TURBINE CASCADE (VISCOUS CASE) |

Here, Drag contributes to work. So, drag is useful component

|

Drag,

|

Effective Lift,

|

Lift Coefficient

32


COMPRESSOR BLADE EFFICIENCY |

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

|

Blade efficiency,

|

ηb is max if

|

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

, or 33


TURBINE BLADE EFFICIENCY |

Blade Efficiency,

|

For small CD / CL ratio

= (ηb)compressor 34


BLADE EFFICIENCY |

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


CONCLUSION |

Compared to axial compressors, axial turbines are simpler in design and more efficient

|

Elaborate cooling techniques are adopted in turbines to have y y

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


THANK YOU

Aviral Chopra Department of Chemical Engineering Indian Institute of Technology Kanpur

37