Turbine Cascade
-
Upload
omprakashsingh123 -
Category
Documents
-
view
221 -
download
0
Transcript of Turbine Cascade
8/3/2019 Turbine Cascade
http://slidepdf.com/reader/full/turbine-cascade 1/37
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
8/3/2019 Turbine Cascade
http://slidepdf.com/reader/full/turbine-cascade 2/37
Gas Turbine Engines
Axial Flow Turbines
Turbine Performance
Cascade Theory
Compressor Cascade
Turbine Cascade
Conclusion
2
Elementary Cascade Theory And Gas Turbine Performance
Outline
8/3/2019 Turbine Cascade
http://slidepdf.com/reader/full/turbine-cascade 3/37
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
Elementary Cascade Theory And Gas Turbine Performance
Gas Turbine Engines
Theory Of Gas Turbine Engines
8/3/2019 Turbine Cascade
http://slidepdf.com/reader/full/turbine-cascade 4/37
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
Elementary Cascade Theory And Gas Turbine Performance
Gas Turbine Engines
Theory Of Gas Turbine Engines
8/3/2019 Turbine Cascade
http://slidepdf.com/reader/full/turbine-cascade 5/37
5
Elementary Cascade Theory And Gas Turbine Performance
Gas Turbine Engines
8/3/2019 Turbine Cascade
http://slidepdf.com/reader/full/turbine-cascade 6/37
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
Elementary Cascade Theory And Gas Turbine Performance
Gas Turbine Engines
Working Of A Simple Turbojet
8/3/2019 Turbine Cascade
http://slidepdf.com/reader/full/turbine-cascade 7/37
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
Elementary Cascade Theory And Gas Turbine Performance
Axial Flow Turbines
Axial Flow Turbines
8/3/2019 Turbine Cascade
http://slidepdf.com/reader/full/turbine-cascade 8/37
8
Elementary Cascade Theory And Gas Turbine Performance
Axial Flow Turbines
2-D Theory Of Axial Turbines
8/3/2019 Turbine Cascade
http://slidepdf.com/reader/full/turbine-cascade 9/37
Power Output:
In axial turbine stage,
Using diagram, we
express work output in
terms of rotor bladeangles
WT
Combined Velocity diagram9
Elementary Cascade Theory And Gas Turbine Performance
Axial Flow Turbines
Work Done, WT
8/3/2019 Turbine Cascade
http://slidepdf.com/reader/full/turbine-cascade 10/37
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
Elementary Cascade Theory And Gas Turbine Performance
Axial Flow Turbines
Types Of Axial Turbines
8/3/2019 Turbine Cascade
http://slidepdf.com/reader/full/turbine-cascade 11/37
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
Elementary Cascade Theory And Gas Turbine Performance
Axial Flow Turbines
Dimensionless Parameters
8/3/2019 Turbine Cascade
http://slidepdf.com/reader/full/turbine-cascade 12/37
Thus, R in terms of Exit Angles:
12
Elementary Cascade Theory And Gas Turbine Performance
Axial Flow Turbines
Gas Flow Angles in terms of ψ, φ, R
8/3/2019 Turbine Cascade
http://slidepdf.com/reader/full/turbine-cascade 13/37
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
Elementary Cascade Theory And Gas Turbine Performance
Axial Flow Turbines
ZERO EXIT SWIRL
El t C d Th A d G T bi P f
8/3/2019 Turbine Cascade
http://slidepdf.com/reader/full/turbine-cascade 14/37
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
Elementary Cascade Theory And Gas Turbine Performance
Turbine Performance
STAGE EFFICIENCY
El t C d Th A d G T bi P f
8/3/2019 Turbine Cascade
http://slidepdf.com/reader/full/turbine-cascade 15/37
Using
we obtain
Thus ηtt > ηts
Actual Turbine Work
T-S diagram: expansion ina turbine 15
Elementary Cascade Theory And Gas Turbine Performance
Turbine Performance
STAGE EFFICIENCY
Elementary Cascade Theory And Gas Turbine Performance
8/3/2019 Turbine Cascade
http://slidepdf.com/reader/full/turbine-cascade 16/37
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
Elementary Cascade Theory And Gas Turbine Performance
Cascade TheoryTurbine Performance
STAGE EFFICIENCY
Elementary Cascade Theory And Gas Turbine Performance
8/3/2019 Turbine Cascade
http://slidepdf.com/reader/full/turbine-cascade 17/37
Given
Turbine Design
Fluid at high Re
We get:
where
stagnation states 02 and 03
are at the turbine inlet and
outlet
17
Elementary Cascade Theory And Gas Turbine Performance
Cascade TheoryTurbine Performance
TURBINE STAGE PERFORMANCE
Elementary Cascade Theory And Gas Turbine Performance
8/3/2019 Turbine Cascade
http://slidepdf.com/reader/full/turbine-cascade 18/37
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
Elementary Cascade Theory And Gas Turbine Performance
Cascade TheoryTurbine Performance
OVERALL PERFORMANCE
Elementary Cascade Theory And Gas Turbine Performance
8/3/2019 Turbine Cascade
http://slidepdf.com/reader/full/turbine-cascade 19/37
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
Elementary Cascade Theory And Gas Turbine Performance
Cascade Theory
ELEMENTARY CASCADE THEORY
Elementary Cascade Theory And Gas Turbine Performance
8/3/2019 Turbine Cascade
http://slidepdf.com/reader/full/turbine-cascade 20/37
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
Elementary Cascade Theory And Gas Turbine Performance
Cascade Theory
WHY CASCADE THEORY
Elementary Cascade Theory And Gas Turbine Performance
8/3/2019 Turbine Cascade
http://slidepdf.com/reader/full/turbine-cascade 21/37
Blade Camber Angle, Θ = θ1
+ θ2 21
Elementary Cascade Theory And Gas Turbine Performance
Cascade Theory
CASCADE NOMENCLATURE
Elementary Cascade Theory And Gas Turbine Performance
8/3/2019 Turbine Cascade
http://slidepdf.com/reader/full/turbine-cascade 22/37
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
Elementary Cascade Theory And Gas Turbine Performance
Cascade Theory
COMPRESSOR CASCADE
Elementary Cascade Theory And Gas Turbine Performance
8/3/2019 Turbine Cascade
http://slidepdf.com/reader/full/turbine-cascade 23/37
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
Elementary Cascade Theory And Gas Turbine Performance
8/3/2019 Turbine Cascade
http://slidepdf.com/reader/full/turbine-cascade 24/37
Velocity
Triangle 24
y y
Cascade Theory
COMPRESSOR CASCADE
Elementary Cascade Theory And Gas Turbine Performance
8/3/2019 Turbine Cascade
http://slidepdf.com/reader/full/turbine-cascade 25/37
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
Elementary Cascade Theory And Gas Turbine Performance
8/3/2019 Turbine Cascade
http://slidepdf.com/reader/full/turbine-cascade 26/37
Velocity
Triangle 26
Cascade Theory
TURBINE CASCADE
Elementary Cascade Theory And Gas Turbine Performance
8/3/2019 Turbine Cascade
http://slidepdf.com/reader/full/turbine-cascade 27/37
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
Elementary Cascade Theory And Gas Turbine Performance
8/3/2019 Turbine Cascade
http://slidepdf.com/reader/full/turbine-cascade 28/37
28
Fixed Incidence
Loss in
Dimensionless
form
Cascade Theory
Variation of Stagnation Pressure Loss and Deflection
Elementary Cascade Theory And Gas Turbine Performance
8/3/2019 Turbine Cascade
http://slidepdf.com/reader/full/turbine-cascade 29/37
29
Nominal
Deflection = ξ*
Stalling
Deflection = ξs
Cascade Theory
Cascade Mean Deflection and Pressure Loss Curves
Elementary Cascade Theory And Gas Turbine Performance
8/3/2019 Turbine Cascade
http://slidepdf.com/reader/full/turbine-cascade 30/37
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
Elementary Cascade Theory And Gas Turbine Performance
C d Th
8/3/2019 Turbine Cascade
http://slidepdf.com/reader/full/turbine-cascade 31/37
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)
Elementary Cascade Theory And Gas Turbine Performance
C d Th
8/3/2019 Turbine Cascade
http://slidepdf.com/reader/full/turbine-cascade 32/37
Here, Drag contributes to
work. So, drag is useful
component
Drag,
Effective Lift,
Lift Coefficient
32
Cascade Theory
TURBINE CASCADE (VISCOUS CASE)
Elementary Cascade Theory And Gas Turbine Performance
C d Th
8/3/2019 Turbine Cascade
http://slidepdf.com/reader/full/turbine-cascade 33/37
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
Elementary Cascade Theory And Gas Turbine Performance
Cascade Theory
8/3/2019 Turbine Cascade
http://slidepdf.com/reader/full/turbine-cascade 34/37
Blade Efficiency,
For small CD / CL ratio = (ηb)compressor
34
Cascade Theory
TURBINE BLADE EFFICIENCY
Elementary Cascade Theory And Gas Turbine Performance
Cascade Theory
8/3/2019 Turbine Cascade
http://slidepdf.com/reader/full/turbine-cascade 35/37
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
Elementary Cascade Theory And Gas Turbine Performance
8/3/2019 Turbine Cascade
http://slidepdf.com/reader/full/turbine-cascade 36/37
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
Elementary Cascade Theory And Gas Turbine Performance
8/3/2019 Turbine Cascade
http://slidepdf.com/reader/full/turbine-cascade 37/37
Aviral Chopra
Department of Chemical Engineering
Indian Institute of Technology Kanpur 37
THANK YOU