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Ch. 31 - 1
The World of Energy
31.1. Gas Turbine Fundamentals
Chapter 31 LNG Gas Turbine
Ch. 31 - 2
First gas turbine was developed in 1872 by Dr. F. Stolze
Generates thrust by mixing compressed ambient air with fuel and combusting the mixture through a nozzle to propel an object forward or to produce shaft work.
Gas Turbine History
Ch. 31 - 3
What is a gas turbine ?
A Heavy Duty GT is a single shaft turbo-machine with:
1 compressor, 1 combustion system, 1 expansion
turbine
Ch. 31 - 4
Turbine and Compressor Design
Ch. 31 - 5
Gas Turbine Issues
Compressor and Turbine Design
Cooling
Dynamic Surge
Stall Propagation
Ch. 31 - 6
How Does it Work?
As the working fluid is exhausted out the nozzle of the gas turbine engine, the object that the engine is attached to is pushed forward
In the case of generating shaft work, the shaft turns a generator which produces electrical power.
Ch. 31 - 7
How Does it Work?
Shaft
Exhaust Gas
Ambient Air In
Ch. 31 - 8
Gas Turbine Components
Ch. 31 - 9
Gas Turbine Components
Ch. 31 - 10
heatexchanger
Closed Brayton cycle
turbinecompressorWnet
QH
QL
heatexchanger
Ch. 31 - 11
Open Brayton cycle
turbine
exhaust
compressor
air intake
combustion
chamber
Gas turbine cycle
fuel
Wnet
Ch. 31 - 12
turbine
exhaust
compressor
Air intake
combustion
chamber
fuel
Wnet
regenerator
Brayton cycle with regeneration
Ch. 31 - 13
Brayton Cycle: The Ideal Cycle for Gas Turbine Engines
Ideal Brayton Cycle
In reality, gas turbines operate on an open cycle
Fresh air is continuously drawn into the compressor and exhaust gases are thrown out
Ch. 31 - 14
Brayton Cycle: The Ideal Cycle for Gas Turbine Engines
Ideal Brayton Cycle (cont.)
The open gas-turbine cycle can be modeled as a closed cycleThe combustion process is replaced by a constant-pressure heat-addition process and the exhaust process is replaced by a constant-pressure heat-rejection process
Ch. 31 - 15
Gas Turbine Schematic
Ch. 31 - 16
Land Base Gas Turbine Cutaway
1. Air Intake Section2. Compression Section3. Combustion Section4. Turbine Section5. Exhaust Section6. Exhaust Diffuser
Ch. 31 - 17
Gas Turbine Operation
Compressor is connected to the turbine via a shaft. The turbine provides the turning moment to turn the compressor.
The turning turbine rotates the compressor fan blades which compresses the incoming air.
Compression occurs through rotors and stators within the compression region.
Rotors (Rotate with shaft)
Stators (Stationary to shaft)
Ch. 31 - 18
Types of Gas Turbines
Centrifugal
Compressed air output is around the outer perimeter of engine
Axial
Compressed air output is directed along the centerline of the engine
Combination of Both
Compressed air output is initially directed along center shaft of engine and then is compressed against the perimeter of engine by a later stage.
Ch. 31 - 19
Example of Centrifugal Flow
Intake airflow is being forced around the outside perimeter of the engine.
Centrifugal Compressor
Airflow being forced around body of engine
Ch. 31 - 20
Example of Axial Flow
Intake airflow is forced down the center shaft of the engine.
Multistage Axial Compressor
Center Shaft
Ch. 31 - 21
Example of Combination Flow
Intake Air Flow
Axial Compressor
Centrifugal Compressor
Intake air flow is forced down the center shaft initially by axially compressor stages, and then forced against engine perimeter by the centrifugal compressor.
Ch. 31 - 22
Major Components of Interest
Compressor
Axial
Centrifugal
Turbine
Axial
Radial
Axial Compressor
Centrifugal Compressor
Ch. 31 - 23
Axial Compressor Operation
A&P Technician Powerplant Textbook published by Jeppesen Sanderson Inc., 1997
Axial compressors are designed in a divergent shape which allows the air velocity to remain almost constant, while pressure gradually increases.
Average Velocity
Ch. 31 - 24
The airflow comes in through the inlet and first comes to the compressor rotor.
Rotor is rotating and is what draws the airflow into the engine.
After the rotor is the stator which does not move and it redirects the flow into the next stage of the compressor
Air flows into second stage.
Process continues and each stage gradually increases the pressure throughout the compressor.
Axial Compressor Operation
Ch. 31 - 25
An axial compressor stage consists of a rotor and a stator.
The rotor is installed in front of the stator and air flows through accordingly. (See Fig.)
www.stanford.edu/ group/cits/simulation/
Axial Compressor Staging
Ch. 31 - 26
Centrifugal compressors rotate ambient air about an impeller. The impeller blades guide the airflow toward the outer perimeter of the compressor assembly. The air velocity is then increased as the rotational speed of the impeller increases.
Centrifugal Compressor Operation
Ch. 31 - 27
Axial Turbine Operation
Hot combustion gases expand, airflow pressure and temperature drops.
This drop over the turbine blades creates shaft work which rotates the compressor assembly.
Axial Turbine with airflowAirflow around rotor
Airflow through stator
Ch. 31 - 28
Radial Turbine Operation
Same operation characteristics as axial flow turbine.
Radial turbines are simpler in design and less expensive to manufacture.
They are designed much like centrifugal compressors.
Airflow is essentially expanded outward from the center of the turbine.
Radial Flow Turbine
Ch. 31 - 29
Gas Turbine Issues
Gas Turbine Engines Suffer from a number of problematic issues:
Thermal Issues
Blade (airfoil) Stalls
Dynamic Surge
http://www.turbosolve.com/index.html
Ch. 31 - 30
Thermal Issues
Gas Turbines are limited to lower operating temperatures due to the materials available for the engine itself.
Operating at the lower temperature will decrease the efficiency of the gas turbine so a means of cooling the components is necessary to increase temperatures at which engine is run.
Ch. 31 - 31
Cooling Methods
Spray (Liquid)Passage Transpiration
Ch. 31 - 32
Spray Cooling
The method of spraying a liquid coolant onto the turbine rotor blades and nozzle
Prevents extreme turbine inlet temperatures from melting turbine blades by direct convection between the coolant and the blades.
Ch. 31 - 33
Passage Cooling
Hollow turbine blades such that a passage is formed for the movement of a cooling fluid.
DOE has relatively new process in which excess high-pressure compressor airflow is directed into turbine passages.
http://www.eere.energy.gov/inventions/pdfs/fluidtherm.pdf
Ch. 31 - 34
Transpiration Cooling
Method of forcing air through a porous turbine blade.
Ability to remove heat at a more uniform rate.
Result is an effusing layer of air is produced around the turbine blade.
Thus there is a reduction in the rate of heat transfer to the turbine blade.
Ch. 31 - 35
Blade (airflow) Stalls
When airflow begins separating from the compressor blades over which it is passing as the angle of attack the blades exceeds the design parameters
The result of a blade stall is that the blade(s) no longer produce lift and thus no longer produces a pressure rise through the compressor.
Separation Regions
Ch. 31 - 36
Occurs when the static (inlet) air pressure rises past the design characteristics of the compressor.
When there is a reversal of airflow from the compressor causing a surge to propagate in the engine.
Essentially, the flow is exhausted out of the compressor, or front, of the engine.
Result, is the compressor no longer able to exhaust as quickly as air is being drawn
http://www.turbosolve.com/index.html
Compressor Inlet
Turbine Exit
Dynamic Surge
Ch. 31 - 37
Dynamic Surge Effects
Cause: Inlet flow is reversed
Effect: Mass flow rate is reduced into engine.
Effect: Compressor stages lose pressure.
Result: Pressure drop allows flow to reverse back into engine.
Result: Mass flow rate increases
Cause: Increased mass flow causes high pressure again.
Effect: Surge occurs again and process continues.
Result: Engine surges until corrective actions are taken.
Ch. 31 - 38
outm
P
V
Surge Point, Flow Reverses
No Surge Condition
Compressor Pressure Loss Occurs
Flow reverses back into engine
Corrective Action Taken
inm
outm
Dynamic Surge Process
Ch. 31 - 39
Axial Compressor Design
Assumption of Needs
Determination of Rotational Speed
Estimation of number of stages
General Stage Design
Variation of air angles
Ch. 31 - 40
Assumption of Needs
The first step in compressor design in the determination of the needs of the system
Assumptions:Standard Atmospheric Conditions
Engine Thrust Required
Pressure Ratio Required
Air Mass Flow
Turbine inlet temperature
Ch. 31 - 41
Rotational Speed Determination
First Step in Axial Compressor Design
Process for this determination is based on assumptions of the system as a whole
Assumed: Blade tip speed, axial velocity, and hub-tip ratio at inlet to first stage.
Rotational Speed Equation
Ch. 31 - 42
Derivation of Rotational Speed
First Make Assumptions:
Standard atmospheric conditions
Axial Velocity:
Tip Speed:
No Intake Losses
Hub-tip ratio 0.4 to 0.6
U t 350m
s
C a 150 200m
s
Ch. 31 - 43
Compressor Rotational Speed
Somewhat of an iterative process in conjunction with the turbine design.
Derivation Process:First Define the mass flow into the system
is the axial velocity range from the root of the compressor blades to the tips of the blades.
AUmdot where U =1aC
1aC
Ch. 31 - 44
Axial Velocity Relationship
a
t
ra C
r
rC *1
2
1
Radius to root of blade
rr
tr Radius to tip of blade
Ch. 31 - 45
Tip Radius Determination
2
11
2
1t
ra
dott
r
rC
mr
By rearranging the mass flow rate equation we can obtain an iterative equation to determine the blade tip radius required for the design.
Now Looking at the energy equation, we can determine the entry temperature of the flow.
p
a
c
CTT
2
2
101
22
2
11
2
00
UTc
UTc pp
Ch. 31 - 46
Isentropic Relationships
Now employing the isentropic relation between the temperatures and pressures, then the pressure at the inlet may be obtained.
Now employ the ideal gas law to obtain the density of the inlet air.
1
0
101T
TPP
1
11
RT
P
Ch. 31 - 47
Using the equation for tip speed
Rearranging to obtain rotational speed.
Finally an iterative process is utilized to obtain the table seen here.
NrU tt 2
t
t
r
UN
2
Finally Obtaining Rotational Speed
Ch. 31 - 48
Make keen assumptions
Polytropic efficiency of approximately 90%.
Mean Radius of annulus is constant through all stages.
Use polytropic relation to determine the exit temperature of compressor.
n
n
P
PTT
1
01
020102
n = 1.4, Ratio of Specific Heats, Cp/Cv
is the pressure that the compressor outputs
To1 is ambient temperature
02P
Determining Number of Stages
Ch. 31 - 49
Assuming that Ca1 = Ca
is the work done factor
Work done factor is estimate of stage efficiency
Determine the mean blade speed.
Geometry allows for determining the rotor blade angle at the inlet of the compressor.
NrU meanm 2
a
m
C
U1tan
Determine Temperature Change
Ch. 31 - 50
Temperature Rise in a Stage
p
ams
c
CUT 210
tantan
1
1cos
aCV
This will give an estimate of the maximum possible rotor deflection.
Finally obtain the temperature rise through the stage.
2
2cosV
Ca
Determine the speed of the flow over the blade profile.
Velocity flow over blade V1.
DeflectionBlade_12
Ch. 31 - 51
Number of Stages Required
The number of stages required is dependent upon the ratio of temperature changes throughout the compressor.
sT
TStages
0
ambTTT 2
is the temperature change within a stage
is the average temperature change over all the stagessT
T
0
Ch. 31 - 52
Make assumptions
Assume initial temperature change through first stage.
Assume the work-done factors through each stage.
Ideal Gas at standard conditions
Determine the air angles in each stage.
Designing a Stage
Ch. 31 - 53
Stages 1 to 2
Determine the change in the whirl velocity.
Whirl Velocity is the tangential component of the flow velocity around the rotor.
Ch. 31 - 54
Change in whirl velocity through stage.
12 www CCC
m
p
wU
TcC
11 tanaw CC
Alpha 1 is zero at the first stage.
a
w
a
wm
C
C
C
CU
22
22
tan
tan
Stage 1 to 2
Ch. 31 - 55
Compressor Velocity Triangles
Ch. 31 - 56
Pressure ratio of the Stage
10
01
03 1amb
sss
T
T
P
PR
9.0s
The pressure ratio in the stage can be determined through the isentropic temperature relationship and the polytropic efficiency assumed at 90%.
Ch. 31 - 57
The analysis shows that the stage can be outlined by the following attributes:
1.) Pressure at the onset of the stage.
2.) Temperature at the onset of the stage.
3.) The pressure ratio of the stage.
4.) Pressure at the end of the stage.
5.) Temperature at the end of the stage.
6.) Change in pressure through the stage.
Example of a single stage
Stage Attributes
Ch. 31 - 58
Assume the free vortex condition.
Determine stator exit angle.
Then determine the flow velocity.
constrCw2
13 tantana
m
C
U
3
3cos
mUC
Variation in Air Angles of Blade
Ch. 31 - 59
Alpha 1 is 0 at the inlet stage because there
Thus, Ca1=C1, and Cw1 is 0
Note: This is the whirl velocity component and not a blade spacing!
Air Angle Triangle
Ch. 31 - 60
Red is
Green is
Blue is
Velocity Triangle
aC
aC
aC
Ch. 31 - 61
Variation in Air Angles of Blade
Determine the exit temp., pressure, and density of stage 1
Determine the blade height at exit
Finally determine the radii of the blade at stator exit.
p
a
c
CTT
2
2
03
1
03
3033T
TPP
3
33RT
P
meanr
Ah
2
3
2
hrr meants 2
hrr meanrs
a
dot
C
mA
3
3
Ch. 31 - 62
Variation in Air Angles of Blade
Determine the radii at the rotor exit.
Determine the whirl velocities at the blade root and tip.
2
tstritr
rrr
2
rsrrirr
rrr
Note: That is the radius of the blade at the tip at rotor inlet.
trir
Note: That is the radius of the blade at the root at rotor inlet.
rrir
rr
meanmwrwr
rCC 22
tr
meanmwtwr
rCC 22
Note: because there is no other whirl velocity component in the first stage.
22 wmw CC
Ch. 31 - 63
a
twtrt
a
mwmm
a
rwrrr
a
twt
a
mwm
a
rwr
C
CU
C
CU
C
CU
C
C
C
C
C
C
22
22
22
22
22
22
tan
tan
tan
tan
tan
tan Stator air angle at root of blade
Stator air angle at middle of blade
Stator air angle at tip of blade
Deflection air angle at root of blade
Deflection air angle at middle of blade
Deflection air angle at tip of blade
Finally determine the Air Angles
Ch. 31 - 64
Compressor Design Example
Design of a 5 stage axial compressor:
98.0
150
5.452
288
2262.0
2
sm
a
a
t
C
KT
KT
mrGivens:
Use this and chart to get Rotational speed of engine.
Once rotational speed is found, determine mean blade tip speed.
Ch. 31 - 65
Example
s
mNrU
mrr
r
meanm
rtmean
6.2662
1697.02
KTTT amb 5.1642
Determine the total temperature rise through the first stage.
We are designing for more than just one stage, so we need to define an average temperature rise per stage:
KStages
TT s 9.32
#0
Ch. 31 - 66
2
0
1
12
1
1
55.126
0
64.60tan
w
m
sp
w
w
www
a
m
Cs
m
U
TcC
s
mC
CCC
C
U
Example (Air Angle Determination)
Ch. 31 - 67
s
mCV
C
CU
a
a
wm
21.205cos
03.43tan
2
2
21
2
15.40tan 21
2
a
w
C
C
Example (Air Angle Determination)