Compressor: compresses the incoming air to high pressure. 3. Elementary
Cascade Theory And Gas Turbine Performance. Gas Turbine Engines. Theory Of
Gas ...
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
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Axial Flow Turbines
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Turbine Performance
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Cascade Theory y Compressor Cascade y Turbine Cascade
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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:
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Compressor: compresses the incoming air to high pressure
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Elementary Cascade Theory And Gas Turbine Performance Gas Turbine Engines
Theory Of Gas Turbine Engines |
Combustor: Burns the fuel and produces high-pressure, hightemperature gas
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Turbine: Extracts the energy from the high-pressure, highenergy gas flowing from the combustion chamber
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Elementary Cascade Theory And Gas Turbine Performance Gas Turbine Engines
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Elementary Cascade Theory And Gas Turbine Performance Gas Turbine Engines
Working Of A Simple Turbojet |
Turbine extracts energy from the gas to rotate compressor
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The pressurized gas from compressor is furnished to maintain the cycle
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Burning of fuel-air mixture provides stream of hot expanding gases
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Out of the total energy development, approximately 60% is extracted to maintain the engine cycle
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The rest is available to develop useful thrust directly
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Elementary Cascade Theory And Gas Turbine Performance Axial Flow Turbines
Axial Flow Turbines |
Compared to compressor y More Efficient y Simpler Design
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Blade shape y Dependent on Stress and Cooling y Not as much on aerodynamics
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Axial Turbine Stage y Row of stationary blades: Nozzle y Row of rotating blades: Rotor
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Elementary Cascade Theory And Gas Turbine Performance Axial Flow Turbines
2-D Theory Of Axial Turbines
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Elementary Cascade Theory And Gas Turbine Performance Axial Flow Turbines
Work Done, WT
Combined Velocity diagram
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Power Output:
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In axial turbine stage,
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Using diagram, we express work output in terms of rotor blade angles WT 9
Elementary Cascade Theory And Gas Turbine Performance Axial Flow Turbines
Types Of Axial Turbines Impulse Turbines
50 % Reaction Turbines
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Entire Pressure drop in nozzle
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Pressure drop same in Nozzle and Rotor
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Symmetrical Rotor blades
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Thus, symmetrical blading
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α2 = -β3 , β2 = -α3
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Elementary Cascade Theory And Gas Turbine Performance Axial Flow Turbines
Dimensionless Parameters |
Ψ, Blade loading or temperature drop coefficient y Expresses work capacity of a stage y
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Φ, Flow coefficient =Vf / U y Ψ= Φ (tan β2 – tan β1)
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R, degree of reaction, y
y
fraction of overall enthalpy drop (or pressure drop) occurring in the rotor =
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Elementary Cascade Theory And Gas Turbine Performance Axial Flow Turbines
Gas Flow Angles in terms of ψ, φ, R |
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Thus, R in terms of Exit Angles:
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Elementary Cascade Theory And Gas Turbine Performance Axial Flow Turbines
ZERO EXIT SWIRL |
Given stator angle
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In Impulse stage, all flow velocities are higher
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Thus, lower efficiency
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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
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Useful work is shaft power
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Kinetic Energy of exhaust,
Total-to-Total Turbine Efficiency, ηtt
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Exhaust Kinetic Energy is not a loss
V32 /2 is a loss
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Elementary Cascade Theory And Gas Turbine Performance Turbine Performance
STAGE EFFICIENCY |
Using
we obtain
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Thus ηtt > ηts Actual Turbine Work
T-S diagram: expansion in a turbine
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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
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Elementary Cascade Theory And Gas Turbine Performance Turbine Performance Cascade Theory
TURBINE STAGE PERFORMANCE |
Given y y
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Turbine Design Fluid at high Re
We get:
where stagnation states 02 and 03 are at the turbine inlet and outlet
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Elementary Cascade Theory And Gas Turbine Performance Turbine Performance Cascade Theory
OVERALL PERFORMANCE |
ηtt is constant over wide range of y Rotational Speed y Pressure Ratio
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Performance is limited by 2 factors: y Compressibility y Stress
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Trade-off between maximum temperature and maximum rotor speed, U
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Thus, elaborate cooling methods are adopted
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Elementary Cascade Theory And Gas Turbine Performance Cascade Theory
ELEMENTARY CASCADE THEORY
Cascade Tunnel
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An array of blades representing the blade ring of actual turbo machinery is called the cascade.
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Turntable: to vary the incidence angle
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Pressure and velocity measurements made upstream and downstream of cascade 19
Elementary Cascade Theory And Gas Turbine Performance Cascade Theory
WHY CASCADE THEORY |
To simulate actual conditions, cascade of blades could be tested in annular form in wind tunnel
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In such case of rotating device, difficult to appreciate flow physics
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Hence, blades generally tested as straight cascade or cascade tunnel
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This way: y Mechanical complications reduced y 2-D flow conditions simplifies interpretation of test results 20
Elementary Cascade Theory And Gas Turbine Performance Cascade Theory
CASCADE NOMENCLATURE
Blade Camber Angle, Θ = θ1 + θ2
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Elementary Cascade Theory And Gas Turbine Performance Cascade Theory
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
Elementary Cascade Theory And Gas Turbine Performance Cascade Theory
TURBINE CASCADE
Note: Stagger Angel, λ is –ve here
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Elementary Cascade Theory And Gas Turbine Performance Cascade Theory
COMPRESSOR CASCADE
Velocity Triangle
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Elementary Cascade Theory And Gas Turbine Performance Cascade Theory
COMPRESSOR CASCADE |
Vm is the mean velocity that makes an angle with the axial direction αm.
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Circulation, Γ = S ( VW1-VW2 )
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Lift, L = ρVMΓ = ρVM S( VW1-VW2 )
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Lift is perpendicular to αm line
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S,C -depend on the design of the cascade
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Lift Coefficient 25
Elementary Cascade Theory And Gas Turbine Performance Cascade Theory
TURBINE CASCADE
Velocity Triangle
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Elementary Cascade Theory And Gas Turbine Performance Cascade Theory
EFFECT OF VISCOUS FLOW |
Till now, Inviscid flow assumption
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In reality, loss in pressure
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Loss in total pressure = Loss in Static pressure =
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Loss due to y Frictional loss ( boundary layer formation) y Mixing of blade wakes 27
Elementary Cascade Theory And Gas Turbine Performance Cascade Theory
Variation of Stagnation Pressure Loss and Deflection ¾Fixed Incidence ¾Loss in Dimensionless form
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Elementary Cascade Theory And Gas Turbine Performance Cascade Theory
Cascade Mean Deflection and Pressure Loss Curves |
Nominal Deflection = ξ*
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Stalling Deflection = ξs
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Elementary Cascade Theory And Gas Turbine Performance Cascade Theory
DESIGN DEFLECTION CURVES |
Test results for different geometric forms by varying y y
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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
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Elementary Cascade Theory And Gas Turbine Performance Cascade Theory
COMPRESSOR CASCADE (VISCOUS CASE) |
Due to losses in total pressure, an axial force,
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Thus, Drag,
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Lift is reduced, so Effective Lift
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Lift Coefficient
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Drag Coefficient
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Elementary Cascade Theory And Gas Turbine Performance Cascade Theory
TURBINE CASCADE (VISCOUS CASE) |
Here, Drag contributes to work. So, drag is useful component
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Drag,
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Effective Lift,
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Lift Coefficient
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Elementary Cascade Theory And Gas Turbine Performance Cascade Theory
COMPRESSOR BLADE EFFICIENCY |
Due to viscous effect, static pressure rise is reduced, so
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Blade efficiency,
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ηb is max if
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Approximation: in expression of Lift, effect of Drag is ignored.
, or 33
Elementary Cascade Theory And Gas Turbine Performance Cascade Theory
TURBINE BLADE EFFICIENCY |
Blade Efficiency,
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For small CD / CL ratio
= (ηb)compressor 34
Elementary Cascade Theory And Gas Turbine Performance Cascade Theory
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.
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Elementary Cascade Theory And Gas Turbine Performance
CONCLUSION |
Compared to axial compressors, axial turbines are simpler in design and more efficient
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Elaborate cooling techniques are adopted in turbines to have y y
Less stress at higher temperature More rotor speed
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Cascade theory gives a thorough idea about the performance of compressor and turbine blades
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Through cascade analysis, a wide database is created which aids in the design of compressor or turbine blades 36
Elementary Cascade Theory And Gas Turbine Performance
THANK YOU
Aviral Chopra Department of Chemical Engineering Indian Institute of Technology Kanpur
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