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Combined Cycle Power Plants 1. Fundamentals of Gas Turbines 1 /115
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1. Fundamentals of Gas Turbines
Combined Cycle Power Plants 1. Fundamentals of Gas Turbines 2 /115
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Thermodynamics 53 2
Fundamentals for Gas Turbines 2 1
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Coal
Gas
Oil
Water
Nuclear
Wind
Solar
Geothermal
Biomass
Variety of Fuels Competitive Machine
Effic
iency
Availa
bili
ty
Opera
tin
g
Fle
xib
ility
Em
issio
ns
Co
sts
Power Generation Requirement
Combined Cycle Power Plants 1. Fundamentals of Gas Turbines 4 /115
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Starter &
gear box
Air inlet Compressor Combustor
Turbine Exhaust
VIGV
Air extraction
ports Diffuser
Transition
piece
Cold section Hot section
A Typical Gas Turbine for Power Generation
7FA, GE
Combined Cycle Power Plants 1. Fundamentals of Gas Turbines 5 /115
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In a gas turbine, the working fluid for transforming thermal energy into rotating mechanical energy is the hot
combustion gas, hence the term “gas turbine.”
The first power generation gas turbine was introduced by ABB in 1937. It was a standby unit with a thermal
efficiency of 17%.
The gas turbine technology has many applications. The original jet engine technology was first made into a
heavy duty application for mechanical drive purposes.
Pipeline pumping stations, gas compressor plants, and various modes of transportation have successfully
used gas turbines.
While the mechanical drive applications continue to have widespread use, the technology has advanced into
larger gas turbine designs that are coupled to electric generators for power generation applications.
Gas turbine generators are self-contained packaged power plants.
Air compression, fuel delivery, combustion, expansion of combustion gas through a turbine, and electricity
generation are all accomplished in a compact combination of equipment usually provided by a single
supplier under a single contract.
The advantages of the heavy-duty gas turbines are their long life, high availability, and slightly higher overall
efficiencies. The noise level from the heavy-duty gas turbines is considerably less than gas turbines for
aviation.
Gas Turbine
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Idealized Brayton Cycle [1/3]
Compressor
Fuel Combustor
Turbine
Air
Power
Exhaust gas 1
2 4 3
p
2
1
T
(h)
s
qin
3
4 1
2
3
4
qout
win wout
win
wout
qin
qout
Combined Cycle Power Plants 1. Fundamentals of Gas Turbines 7 /115
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The entering air is compressed to higher pressure.
No heat is added. However, compression raises the air temperature so that the discharged air has
higher temperature and pressure.
The mechanical energy transmitted from the turbine is used to compress the air.
Compression Process (1 2)
Compressed air enters the combustor, where fuel is injected and combustion occurs.
The chemical energy contained in the fuel is converted into thermal energy.
Combustion occurs at constant pressure. However, pressure decreases slightly in the practical process.
Although high local temperatures are reached within the primary combustion zone (approaching
stoichiometric conditions), the combustion system is designed to provide mixing, burning, dilution,
cooling.
Combustion mixture leaves with mixed average temperature.
Combustion Process (2 3)
Idealized Brayton Cycle [2/3]
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The thermal energy contained in the hot gases is converted into mechanical work in the turbine.
This conversion actually takes place in two steps:
• Nozzle: the hot gases are expanded and accelerated, and a portion of the pressure energy is
converted into kinetic energy.
• Bucket: a portion of the kinetic energy is transferred to the rotating buckets and converted into
mechanical work.
Some of the work produced by the turbine is used to drive the compressor, and the remainder is used to
drive load equipment, such as generator, ship propeller, and pump, etc.
Typically, more than 50% of the work produced by the turbine section is used to power the compressor.
Expansion Process (3 4)
Exhaust Process (4 1)
This is a constant-pressure cooling process.
This cooling is done by the atmosphere, which provides fresh, cool air as well.
The actual cycle is an “open” rather than “closed”.
Idealized Brayton Cycle [3/3]
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Variation of Major Parameters
m/s bar C
700 21 2100
600 18 1800
500 15 1500
400 12 1200
300 9 900
200 6 600
100 3 300
0 0 0
Pressure (po)
Temperature (To)
Velocity
Combined Cycle Power Plants 1. Fundamentals of Gas Turbines 10 /115
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Terminology Meaning
Combined cycle
• Combined cycle = Brayton cycle (topping cycle) + Rankine cycle (bottoming cycle)
• Combined cycle can be defined as a combination of two thermal cycles in one plant. When
two cycles are combined, the efficiency that can be achieved is higher than that of one cycle
alone.
• Gas turbine + Steam turbine
• Normally the topping and bottoming cycles are coupled in a heat exchanger.
Simple cycle
• The term simple cycle is used to distinguish this configuration from the complex cycles, which
utilizes additional components, such as heat exchanger for regeneration, intercooler, reheating
system, or steam boilers.
Heavy duty gas
turbines
• In general. it means gas turbines for power generation because they differ from aeronautical
designs in that the frames, bearings, and blading are of heavier construction .
Aeroderivative gas
turbines
• The aero-engines transformed into land based gas turbines successfully.
• P&W JT8/FT8, GE J79/LM1500, GE CF6/LM2500, CF6/LM5000, CF6/LM6000
• The LM2500 has been the most commercially successful one.
Mechanical drive
gas turbines
• Sometimes, it includes heavy duty gas turbines, aeroderivative gas turbines, gas (oil) pumping
gas turbines, and gas turbines for marine applications.
• Generally, this means the industrial gas turbines that are used solely for mechanical drive or
used in collaboration with a recovery steam generator differ from power generating sets in that
they are often smaller and feature a "twin" shaft design as opposed to a single shaft. The
power range varies from 1 MW up to 50 MW.
Terminology
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Compressor
Fuel
Combustor
Turbine
Inlet
air
Steam
turbine
G
G
Condenser
Deaerator
Condensate
pump HP boiler feed pump
LP boiler feed pump
HP superheater
HP evaporator
HP economizer
LP superheater
LP evaporator
LP economizer
HP
drum
LP
drum
Exhaust
gas
HRSG
In simple cycle mode, the gas turbine is operated alone, without the benefit of recovering any of energy
in the hot exhaust gases. The exhaust gases are sent directly to the atmosphere.
In combined cycle mode, the gas turbine exhaust gases are sent into HRSG. The HRSG generates
steam that is normally used to power a steam turbine.
Combined Cycle Power Plants [1/11]
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Cycle Diagram for a 3 Pressure Reheat Cycle (F-Class Gas Turbine)
Combined Cycle Power Plants [2/11]
Condenser
G
G
Fuel
Air
Gas turbine
Heat recovery steam
generator
IP steam LP
steam Cold reheat
steam
Hot reheat
steam
Main
steam
Steam turbine
Condensate pump
Steam
Water
Fuel
Air
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Combined cycle power plants have a higher thermal efficiency because of the application of two
complementary thermodynamic cycles
T-s Diagram for a Typical CCPPs
Combined Cycle Power Plants [3/11]
Condenser
(heat out)
T
s
Topping cycle
Bottoming cycle
Combustion
(heat In)
Stack
(heat
out)
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TH
TL
QL
W
QH
Steam turbine
TH
TL
QL
W
QH
Gas turbine
W Steam turbine
HRSG
[ Fossil / Nuclear ] [ Combined cycle]
The Second Law of Thermodynamics
Combined Cycle Power Plants [4/11]
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구분 Topping cycle Bottoming cycle
Main Components GT ST/HRSG
Working Fluid Air Water/Steam
Temperature High Medium/Low
Thermodynamic Cycle Brayton Rankine
Coupling Two Cycles Heat Exchanger
Topping cycle Coupling Bottoming cycle
Cycle Characteristics
Combined Cycle Power Plants [5/11]
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Combined cycle power plant means a gas turbine operated with the Brayton cycle, is combined with a heat
recover steam generator and steam turbine operated with the Rankine cycle, in one plant.
When two cycles are combined, the efficiency increases higher than that of one cycle alone.
Thermal cycles with the same or with different working fluid can be combined.
In general, a combination of cycles with different working fluid has good characteristics because their
advantages can complement one another.
Normally, when two cycles are combined, the cycle operating at the higher temperature level is called as
topping cycle. The waste heat is used for second process that is operated at the lower temperature level,
and is called as bottoming cycle.
The combination used today for commercial power generation is that of a gas topping cycle with a
water/steam bottoming cycle. In this case heat can be introduced at higher temperature and exhausted at
very low temperature.
Temperature of the air used as a working fluid of gas turbines can be increased very high under lower
pressure. Water/steam used as a working fluid can contain very high level of energy at lower temperature
because it has very high specific heat.
Normally the topping and bottoming cycles are coupled in a heat exchanger.
Generals [1/2]
Combined Cycle Power Plants [6/11]
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Air is used as a working fluid in gas turbines having high turbine inlet temperatures because it is easy to get
and has good properties for topping cycle.
Steam/water is an ideal material for bottoming cycle because it is inexpensive, easy to get, non-hazardous,
and suitable for medium and low temperature ranges.
The initial breakthrough of gas-steam cycle onto the commercial power plant market was possible due to
the development of the gas turbine.
In the late 1970s, EGT reached sufficiently high level that can be used for high efficiency combined cycles.
The breakthrough was made easier because gas turbines have been used for power generation as a simple
cycle and steam turbines have been used widely.
For this reason, the combined cycle, which has high efficiency, low installation cost, fast delivery time, had
been developed easily.
Generals [2/2]
Combined Cycle Power Plants [7/11]
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Gas turbine Steam turbine
Combustion Internal External
Thermodynamic cycle Brayton Rankine
Cycle type Open Closed
Working fluid Air Water/Steam
Max. pressure, bar 23 (40 for Aviation) 350 (5050 psig)
Max. temperature, C(F) 1350 (2462) 630 (1166)
Blade cooling Yes No
Shaft cooling No Yes (USC only)
Max. cycle efficiency, % 40 49 (USC only)
Max. number of reheat 1 2
Power density High Low
Steam conditions of the steam turbines for combined cycle applications are lower than those for
USC steam turbines.
GT vs. ST
Combined Cycle Power Plants [8/11]
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Fuel energy
100%
GT 37.6%
ST 21.7%
Condenser
31.0%
Stack 8.6%
Loss in HRSG
0.3%
Loss
0.5%
Loss
0.3%
Three pressure
reheat cycle Im
pro
ve
d
Heat Balance of CCPPs
Combined Cycle Power Plants [9/11]
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G
Natural gas
G
IP
9
HP
8
LP
10
1
2
3
4
5
6
7
11 12
13
14
15 16
17
18
19 20 1 Dual HP superheater/reheater 2,4,6 HP,IP,LP evaporators 3 HP economizer/IP superheater 5,7 Dual HP/IP economizer 8,9,10 HP,IP,LP drums 11 HP steam turbine 12 IP/LP steam turbine 13,14,15 HP,IP,LP steam bypasses 16 Condenser 17 Condensate pump 18 Deaerator 19,20 IP,HP feedwater pumps
Three Pressure
Reheat Cycle
Flow Diagram of a Typical CCPP
Combined Cycle Power Plants [10/11]
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Three Pressure
Reheat Cycle
Heat Balance Diagram of a Typical CCPP
Combined Cycle Power Plants [11/11]
Air
G
Natural gas
473 MW
G
P 33.7
T 240
P 33.7
T 240
P 33.7
T 240
P bar T C M kg/s X Rel. humidity
Gross output = 280.5 MW
Gross effi. (LHV) = 59.3%
P 1.013 T 15 X 60 %
P 0.045 T 31 M 67
P 28.5 T 565 M 65.1
P 115.2 T 565 M 59.2
P 120 T 568
P 30.0 T 568
P 32.1 T 369 M 5.9 P 4.6
T 150 M 5.4
M 0
M 0
P 5.0 T 152 M 5.4
M 11.3 M 59.2
M 0
M 3.5
P 0.2 T 60
P 1.013 T 103 M 386.7
T 647 M 386.7
178 MW
M 0
102.5 MW
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Simple cycle gas turbines for electricity generation are typically used for standby or peaking capacity and
are generally operated for a limited number of hours per year. Peaking operation is often defined as fewer
than 2,000 hours of operation per year.
In mechanical drive applications, and for some industrial power generation, simple cycle gas turbines are
base-load and operate more than 5,000 hours of operation per year.
Some plants are initially installed as simple cycle plants with provisions for future conversion to combined
cycle.
Gas turbines typically have their own cooling, lubricating, and other service systems needed for simple
cycle operation. This can eliminate the need to tie service systems into the combined cycle addition and will
allow continued operation of the gas turbine during the conversion process and, with proper provisions,
during periods when the combined cycle equipment is out of service.
If future simple cycle is desired, a bypass stack may be included with the connection of the HRSG. A typical
method for providing this connection is to procure a divert damper box at the outlet of the gas turbine.
Simple Cycle
[ with Bypass Stack ] [ without Bypass Stack ]
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Heavy duty gas turbines Aeroderivative gas turbines
• Newly designed for power generation
• High aspect ratio (long, thin) turbine blades with tip
shrouds to dampen vibration and improve blade tip
sealing characteristics
• Single-shaft
• Electrical output of up to 340 MW
• Standardized
• Manufactured on the base of sales forecasts rather
than orders received
• Series of frame sizes
- shorter installation time
- low costs
• Derived from jet engines (lightweight components,
compact design, and high efficiency) and frequently
incorporating a separate power turbine
• Low aspect ratio turbine blades with no shroud
• Two- or three-shaft turbine with a variable speed
compressor (This is an advantage for part-load
efficiency because airflow is reduced at low speeds)
• Higher part load efficiency because of variable
speed
• Two-shaft turbines are usually used for compressor
or pump drives
• The size is limited to 100 MW due to the maximum
size of aircraft
MS7001F, GE LM6000, GE
Heavy Duty vs. Aeroderivative GT [1/3]
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Aero Trent
Trent 60 Gas Turbine (Mechanical Drive)
① New LP compressor replaces fan
② LP bleed added for low speed operation
③ DLN combustor replaces annular aero combustor
④ Last two stages of LPT and exhaust redesigned
⑤ Rear drive added
Aero Trent
MT30
Heavy Duty vs. Aeroderivative GT [2/3]
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Both heavy duty and aeroderivative gas turbines are used in combined cycle applications. However, the
majority of the gas turbines used in power generation are heavy duty gas turbines.
The exhaust gas temperatures of heavy duty gas turbines are typically higher than those of aeroderivative
machines.
In addition, the exhaust flow per unit gas turbine output is higher for the heavy duty gas turbines.
In combined cycle mode, this allows more steam with higher superheat temperatures to be generated with
the heavy duty machines, which translates into more electrical output from the steam turbine.
In general, for smaller ratings, the overall heat rate for a heavy duty gas turbine based combined cycle is
slightly higher than that for an aeroderivative based combined cycle plant of similar size.
However, combined cycle power plants with larger heavy duty gas turbines having higher TITs have lower
heat rates compared to aeroderivative based combined cycle plants.
The heavy duty gas turbines are based on more rugged design and can use a much wide range of fuels
than the aeroderivative gas turbines.
Advanced metallurgy and cooling technologies developed for jet engines have enabled heavy duty gas
turbines to achieve higher TIT and efficiency.
Heavy Duty vs. Aeroderivative GT [3/3]
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Hot-end drive Cold-end drive
• In the hot-end drive configuration, the output shaft
extends out the rear of the turbine.
• The designer is faced with many constraints, such
as output shaft length, high EGT, exhaust duct
turbulence, pressure drop, and maintenance
accessibility.
• Insufficient attention to any of these details, in the
design process, often results in power loss,
vibration, shaft or coupling failures, and increased
down-time for maintenance.
• This configuration is difficult to service as the
assembly must be fitted through the exhaust duct.
• In the cold-end drive configuration, the output shaft
extends out the front of the compressor.
• The single disadvantage is that the compressor
inlet must be configured to accommodate output
shaft.
• The inlet duct must be turbulent free and provide
uniform, vortex free, flow over the all operating
range.
• Inlet turbulence may induce surge in the
compressor resulting in complete destruction of the
unit.
MS7001E, GE MS7001F, GE
Hot-End Drive vs. Cold-End Drive
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~ ~
Single-shaft Multi-shaft
• Cold-end drive
• Power generation only
• Efficient exhaust
• 50/60 Hz direct drive for large units
• Higher starting power
• Low speed operation is not possible because of
surge
• Hot-end drive
• Both power generation and mechanical drive
• The free power turbine is coupled
aerodynamically with HP turbine
• The speed of the free power turbine is variable
• Optimum solution for emergency power
• The gas turbine is easier to start, especially in
cold weather
• The load does not transmit vibration into the gas
generator
• Less efficient exhaust
• Power turbine over-speed risk at load rejection
Single-Shaft vs. Multi-Shaft [1/2]
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When the operation flexibility is important, such as marine applications, a mechanically independent power
turbine is used.
Compressor and high pressure turbine combination acts as a gas generator for the power turbine.
Fuel flow to the combustor is controlled to achieve variation of power. This will cause a decrease in cycle
pressure ratio and maximum temperature.
At off-design conditions the power output reduces with the result that the thermal efficiency deteriorates
considerably at part loads.
Compressor
Fuel Combustor
LP turbine
(power turbine)
Air
Power
Exhaust gas
HP turbine
Two-Shaft GT
Single-Shaft vs. Multi-Shaft [2/2]
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Base load Intermediate load Peak load
Operating
hours [hr/a] 5000 2000 to 5000 2000
Generating
units
• Nuclear plant
• High-performance steam
turbine plant
• High efficient combined cycle
plant
• Hydropower plant
• Simple steam turbine plant
• Old base-load plant
• Combined gas and steam
plant
• Gas turbine
• Diesel engine
• Pumping-up power plant
• Old simple steam turbine
plant
Characteri-
stics
• Operated at full load as long as
possible during the year
• High efficiency and lowest cost
• Poor load change capability
(take more time to respond load
demand)
• Operated on weekdays and
shutdown at night and on the
weekend
• The efficiency is higher than
that of peak-load plants, but
lower than that of base-load
plants
• Low capital investment, but
highest operating costs
• Ease in startup
• Used as standby or
emergency also
Type of Plants
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2004 2006 2008 2010
Bill
ions o
f d
olla
rs (
20
07
)
3
6
9
12
15
18
Commercial aviation
Electrical generation
Military aviation
Mechanical drive
Marine propulsion
Gas Turbine Production by Sector Source: Davis Franus, Forecast International
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열역학적 성능 향상
온도 향상
압력 향상
유체역학적 성능 향상
2차유동손실 최소화
누설손실 최소화
배기손실 최소화
기타
대형화
Options for Power
Enhancement
USC Steam Turbine H-Gas Turbine
발전설비 성능향상
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A-USC USC SC
(Supercritical) SC
(Subcritical)
TIT, C = 1104 1316 1427 1600
PR = 15 15 20-23 23
th (SC/CC) = 37/55 39/58 --/60 40/61
T, F(C) = 1000(538) 1100(593) 1130(610) 1292(700)
P, psig = 2400 3500 4500 4500
th = 38 44 49 ?
Gas Turbine
Steam Turbine
Thermodynamic Improvement
J-class H-class F-class E-class
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Evolution of GE Gas Turbine
Combined Cycle Power Plants 1. Fundamentals of Gas Turbines 34 /115
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S106B
S107EA
S109E
S106FA
S107FA
S107FB
S109FA
S109FB
S107H S109H
Second Generation • B & E Gas Turbine Technology
• Non-Reheat, 3-Pressure Steam Cycle
Third Generation • F Gas Turbine Technology
• Reheat, 3-Pressure Steam Cycle
Fourth Generation • H Gas Turbine Technology
• Reheat, 3-Pressure Steam Cycle
0 50 100 150 200 250 300 350 400 450 500 550
64
61
60
58
56
54
52
50
48
46
Ne
t E
ffic
ien
cy,
% (
Ba
se
d o
n L
HV
)
Net Plant Output, MW
STAG Product Line Ratings
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Core Technologies
• Materials / coatings
• Cooling / sealing
• 3D aerodynamic designs
• Tools and talent
• Installed base learning
Plant Performance
• Higher efficiency
• Higher output
• Higher reliability
• Lower emissions
• Lower O&M costs
Compressor
Pressure ratio
Combustor
Dry low NOx
Turbine
TIT
Superiority
• Lower cost of electricity
• Higher market share
Why Technology Matters ?
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The gas turbine will continue to play an important role in meeting power generation requirements as
technology advances and as the product and cycle designs respond to changes in fuel economics and
allowable plant emissions.
• Higher efficiency (3D)
• Higher PR
• Larger air flow
• Smaller stages
• Low leakage flow
• Low vibration
• No stall and surge –
variable stators
• Lower emissions
• Low pressure loss
• Higher combustion efficiency
• Less cooling air
• Low vibration / high reliability
• High fuel flexibility
• Uniform outlet temp distribution
• Higher turbine efficiency
• Lower stage loading
• Higher output (larger
enthalpy drop = higher TIT)
• Advanced blade materials
• Coating technologies
• Cooling technologies
• Improved sealing
• Cycle analysis
Required Technologies
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The last 30 years has seen a large growth in gas turbine technologies.
The growth is provided by the increase in compressor pressure ratio, advanced combustion techniques, the
growth of materials technology, new coatings, and new cooling schemes.
The increase in gas turbine efficiency is dependent on two basic parameters, such as pressure ratio and TIT.
The aerospace engines have been the leaders in most of the gas turbine technologies. The design criteria
for these engines was high reliability, high performance, with many starts and flexible operation throughout
the flight envelope.
The industrial gas turbines have always emphasized long life and rugged operation. Therefore, those have
been conservative in pressure ratio and TITs, thus lower efficiency than aerospace ones.
However, this concept has been changed in the last 10 years, and performance gap between these two
types of gas turbines has been reduced greatly.
Currently, axial compressor produces pressure ratio of up to 40:1 in some aerospace applications, and a
pressure ratio of 30:1 in some industrial units.
TITs are similar between these two types of gas turbines, and single crystal materials are used in those two
types of gas turbines.
Gas Turbine Technologies
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Acquire the last proven technology and not the latest. The latest technology contains a high technological
risk.
All possible failure modes are still unknown for the latest generation of gas turbines.
Any operation of the gas turbine outside the ideal operating conditions (base load, ISO conditions)
significantly affects its performance and durability.
Cyclic operation of combined cycles is still vague. (emissions, fuel, part-load, etc.)
Within the lifecycle cost of a combined cycle plant, the maintenance cost is (approximately) twice the initial
cost.
The design of a gas turbine has always being improved.
There is a need for (regulation and) certification of component repair for gas turbine technology.
Approximately between 70-80% of the cost of electricity corresponds to the cost of fuel.
Main technology risks:
• Mechanical component failures: Thermo-mechanic fatigue, creep, …
• Problems due to high TITs: Materials & coating life, cooling effectiveness,...
• Rotor & blading integrity: Rotor assembly, vibrational/rotordynamic integrity, …
• Combustion process: Flame instability, NOx control, etc.
Users Point of View
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Increased pressure ratio
• Higher engine efficiency requires higher engine pressure ratio.
• Higher pressure ratios will also increase the number of stages and potentially longer rotors.
• The number of turbine stage has been changed from three to four as the pressure ratio increases.
• Variable stator has adopted to control compressor stall and to increase efficiency during part load
operation.
Increased specific flow
• Specific flow will continue to increase and approach aero-engine technology.
• Siemens: 820 kg/s (latest 50 Hz engine); MHI: 860 kg/s (J-class)
• GE: 745 kg/s (9FB.05), 440 kg/s (7FA), 558 kg/s (7H)
• The absolute maximum of today is around 1000 kg/s@3000 rpm, but this can be achieved only with mul
ti-spools.
• GE and Alstom have upgraded compressor with aero-engine technology.
All major OEMs have on-line compressor vibration measurements and associated protection system.
Developmental Trends
Compressor [1/7]
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Previous Designs New Designs Risk
2D double circular arc or NACA 65 profiles 3D or Controlled Diffusion-shaped Airfoil
(CDA) profiles
Large number of airfoils Reduced airfoils
Repeating stages Stages unique
Shorter chords Longer chords
Low/modest aspect ratios High aspect ratios
Large clearances Small clearances
Low/modest pressure ratios Much high pressure ratios
Low/modest blade loading per stage High blade loading per stage
Wider operating margin Narrow operating margin
Thicker leading edges Thinner leading edges
Dry operation Wet operation
Lower costs Higher costs
Developmental Trends
Compressor [2/7]
Combined Cycle Power Plants 1. Fundamentals of Gas Turbines 41 /115
HIoPE
Pressure Ratio P
ressure
ratio
7E/9E
501ATS
7EA/9EC
V84.2/V94.2
7H/9H
V84.3A/
V94.3A
V84.3
501F/701F
7F/9F
7FA/9FA
GT24/GT26
GT13E2
GT11N2
501G/701G
35
30
25
20
15
10
5
80 78 84 82 88 86 92 90 96 94 00 98
501D5A
/701D
GE
Siemens
Alstom
WH/MHI
Compressor [3/7]
Combined Cycle Power Plants 1. Fundamentals of Gas Turbines 42 /115
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10
Pre
ssu
re r
atio
8
66 70 78 74 86 82 98 94 90 02
14
12
18
16
22
20
24
MS9001E
MS5001M
MS7001H
MS6001B
MS9001H
MS7001EF MS9001F MS7001EA
MS9001B
MS7001C
MS7001B MS7001A
MS5001P
MS7001E
MS5001N
MS9001FA
Pressure Ratio - GE
Compressor [4/7]
Combined Cycle Power Plants 1. Fundamentals of Gas Turbines 43 /115
HIoPE
200
0
66 70 78 74 86 82 98 94 90 02
600
400
1000
800
1400
1200
1600
MS9001E
MS5001M/R
MS7001H
MS6001B MS6001A
MS9001H
MS7001EF
MS7001FA
MS9001FA
MS7001EA
MS9001B
MS7001C
MS7001B
MS7001A
MS5002A MS5001P MS5002B
MS5001N
Air flo
w, lb
/se
c
MS7001E
Air Flow - GE
Compressor [5/7]
Combined Cycle Power Plants 1. Fundamentals of Gas Turbines 44 /115
HIoPE
200
0
1940 1950 1970 1960 1990 1980 2010 2000
600
400
1000
800
1400
1200
Air m
ass flo
w, kg
/se
c
TIT
, C
TIT
Air mass flow
Historical Development of Maximum Air Flows and TITs
Compressor [6/7]
Combined Cycle Power Plants 1. Fundamentals of Gas Turbines 45 /115
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High Pressure Packing
Sealing became an important issue
as the pressure ratio increases
Brush seals
• Minimize air leakage
• Tolerant of misalignments
• More durable than labyrinth seals
Compressor [7/7]
Combined Cycle Power Plants 1. Fundamentals of Gas Turbines 46 /115
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The TIT defines the technology level of the gas turbine. The primary objective of increasing the TIT is to
allow for higher power output for a given engine size. Due to the improvements in material science and
blade cooling techniques, the allowable TIT has steadily increased by 10 K every year over the last few
decades and there is hope that this trend will continue. Unfortunately, however, the life of the turbine blade
is halved by each 15 K rise in temperature, hence new technologies are always being sought to suppress
creep, thermal fatigue and oxidation which are the primary mechanisms that limit blade life.
Considerable effort has also been made in developing efficient cooling techniques and surface coating, so
that TITs can be increased.
The TIT will increase to 1600C to get higher combined cycle efficiency.
It seems that the engines have TIT higher than 1600C will little market penetration because of the
necessity of steam cooling. Steam cooling engines will not meet user’s requirements for rapid startup and
steep ramp rates.
The fact that 60 percent efficiency could be obtained only by employment of steam cooling has definitely
proven false.
Higher TITs force the steam turbine throttle temperature above 600C.
The number of turbine stage increased to four as the pressure ratio increase. There is an efficiency gain
associated with the fourth stage because the stage loading will be reduced and larger exhaust area.
Siemens H-class machines have reverted back to DS blades instead of SC blades because of cost
problems.
Recent research activities have been focused in the area of new materials that can withstand higher
temperatures and higher stresses at the same time. This would enable improvement in cycle efficiencies,
decrease the number of turbine stages.
Developmental Trends
Turbine [1/6]
Combined Cycle Power Plants 1. Fundamentals of Gas Turbines 47 /115
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Turbine Inlet Temperature T
urb
ine
In
let Te
mp
era
ture
, C
7E/9E
501ATS
7EA/9EC
V84.2/V94.2
7H/9H
V84.3A/V94.3A
V84.3
GT11N2
501F/701F
7F/9F
7FA/9FA
GT24/GT26 GT13E2
501G/701G
1600
1500
1400
1300
1200
1100
1000
80 78 84 82 88 86 92 90 96 94 00 98
501D5A/701D
GE
Siemens
Alstom
WH/MHI
Turbine [2/6]
EGT increases with TIT. The HRSG efficiency increases with EGT.
Combined Cycle Power Plants 1. Fundamentals of Gas Turbines 48 /115
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Advanced Vortex Blades
Turbine [3/6]
Combined Cycle Power Plants 1. Fundamentals of Gas Turbines 49 /115
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Precision Casting
• Equi-axial material
• Directional solidification
• Single crystal
Coating
• Oxidation resistance
• Corrosion resistance
• Thermal barrier
Heat Resistance Alloy
Forging
Production Technologies
Turbine [4/6]
Combined Cycle Power Plants 1. Fundamentals of Gas Turbines 50 /115
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Cooling Technologies
Turbine [5/6]
Te
mp
era
ture
, C
1500
1965
Allowable Gas
Temperature Film Cooling
Closed-loop
Cooling
U700
IN738 IN939
IN92DS
1st Gen. SX
2nd Gen. SX
Maximum Material
Temperature 1000
700
TBC; Thermal Barrier Coating
DS; Directional Solidification
SX; Single Crystal
1975 1985 1995 2005 2015
Benefits of
Cooling
Combined Cycle Power Plants 1. Fundamentals of Gas Turbines 51 /115
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Advanced Seal Systems
Turbine [6/6]
Combined Cycle Power Plants 1. Fundamentals of Gas Turbines 52 /115
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Gas Turbine Steam Turbine Remarks
2차유동손실
최소화
배기손실
최소화
• GT: 1) Hot-End Drive
Cold End Drive
2) TBN: 3 4 stages
(large exhaust area)
• ST: 1) Advanced LP exhaust
hood
2) longer LSB
누설손실
최소화
• 작동압력 증가에 따라 누설
제어 중요
• Brush seal 적용
내열소재 Single Crystal
Cooling Technology Ni-alloy Creep 특성 향상
Mechanical Improvement
Combined Cycle Power Plants 1. Fundamentals of Gas Turbines 53 /115
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Thermodynamics 2
Fundamentals for Gas Turbines 1
Combined Cycle Power Plants 1. Fundamentals of Gas Turbines 54 /115
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Turbomachinery Research Development Design Manufacturing Maintenance
Fluid Mechanics
Thermodynamics
Heat Transfer
Solid Mechanics
Vibration
Rotor Dynamics
Material Science
Acoustics
Manufacturing Engineering
Mathematics
Numerical Analysis
Control System
Electrical Engineering
Turbomachinery research, analysis, design, computation, and development involve the interaction of
various subjects. A large turbomachinery company will have experts and groups in most of areas
indicated in this figure.
It would be useful to review some basic concepts and equations in both thermodynamics and fluid
dynamics that are useful for better understanding of turbomachinery.
Which Subject ?
Combined Cycle Power Plants 1. Fundamentals of Gas Turbines 55 /115
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발전설비는 가장 대표적인 열기관
열기관은 열에너지를 기계적인 에너지로 변환시키는 기계장치
열기관에서의 에너지 변환은 열역학 및 유체역학을 이용 분석 (발전설비는 가장 대표적인 열유체기계)
발전설비의 효율 극대화를 위해 극단적인 열 및 유동 조건 적용
• Thermodynamics: the higher maximum cycle temperature and pressure, the greater specific power output and thermal efficiency (A-USC coal-fired power plants, & H-class GTs)
• Fluid dynamics: supersonic flow, stall, surge, choking, cooling
• Materials: heat resistant materials (creep), erosion, corrosion, coating
• Others: reliability/availability
A Typical Gas Turbine for Power
Generation
A Typical Steam Turbine for
Power Generation
Heat Engines
1. Change of State
Combined Cycle Power Plants 1. Fundamentals of Gas Turbines 56 /115
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열역학은 일(work)과 열(heat)을 다루는 과학
• 일: 어떤 물체를 힘을 가해서 이동시켰을 때, 힘과 변위의 곱으로 주어지는 물리량
• 열: 온도차가 존재하는 경우에 계의 경계를 넘어서 이동하는 에너지
• 일과 열은 열역학적 상태량이 아니라 물질의 에너지 상태 및 열역학적 상태량을 달라지게 하는 열역학적인 양(thermodynamic quantities)으로서 일과 열은 에너지 전달이다
일은 쉽게 열로 변환 가능
열 또한 일로 변환 가능. 그러나 열을 일로 바꾸는 것은 쉽지 않음. 이는 일을 하기 위해서는 힘이 필요한데 열 속에는 힘의 요소가 없기 때문에 열을 직접적으로 일로 바꾸기 힘들며, 열을 일로 변환시키기 위해서는 반드시 열기관 필요
열기관은 열에너지를 이용해서 동력을 얻는 장치로서 공기 또는 증기와 같은 물질의 압력 및 온도가 쉽게 변하는 성질을 이용하여 열을 일로 변환시키는 기계적 장치
공기나 증기와 같은 물질을 작동유체(working fluid)라 함
즉, 작동유체는 계 내부를 채우고 있거나 계를 통과하여 흘러가는 유체로서 열에너지를 저장(보관)할 수 있는 능력을 가지고 있으며, 이는 작동유체의 열역학적 상태변화를 통해서 확인 가능
따라서 열기관을 해석하기 위해서 작동유체의 상태변화를 이해하는 것이 매우 중요
열기관에서 작동유체의 상태변화는 여러 가지 과정(process)으로 나타남
대표적인 열역학적 상태량: 온도, 압력, 비체적, 내부에너지, 엔탈피, 엔트로피 등
1. Change of State
Combined Cycle Power Plants 1. Fundamentals of Gas Turbines 57 /115
HIoPE
Working
Fluids
Water Steam Combustion
Gas
Hydraulic Turbine Steam Turbine Gas Turbine
Air
Wind Turbine
작동유체 종류에 따른 터빈 분류
1. Change of State
Combined Cycle Power Plants 1. Fundamentals of Gas Turbines 58 /115
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상 (phase): 기체, 액체, 고체처럼 화학적 성질과 분자식은 같지만 분자가 모여있는 구조가 다르며, 상질도 약간 다른 모습이 존재하는 것을 말한다. 얼음, 물, 증기의 경우 분자식은 H2O로 같지만 얼음의 경우 분자는 가깝게 모여있고, 액체인 물의 경우 조금 더 떨어져 있고, 증기의 경우에는 훨씬 더 떨어져 있다.
상태 (state): 계를 구성하는 작동유체(working fluid)의 물리적화학적 특성
상태량: 물질의 존재 방식을 나타내는 양
• 대표적 상태량: 온도, 압력, 체적, 질량, 밀도 등
• 추상적 상태량: 내부에너지, 엔트로피 등
• 거시적 상태량: 물질이 다수의 분자로 이루어짐에 따라 이들 양의 조합에 의해 물질의 상태를 나타낼 수 있을 때 이들 양을 거시적 상태량이라 함 (밀도, 온도, 압력 등)
• 미시적 상태량: 분자 수준의 상태로 나타낼 수 있는 양 (질량, 운동량, 에너지 등)
상태변화: 계를 구성하는 작동유체가 열(heat)이나 일(work)에 의하여 한 상태에서 다른 상태로 변화되는 것 (예: 계의 온도나 압력의 변화)
p
1
2
1. Change of State
Combined Cycle Power Plants 1. Fundamentals of Gas Turbines 59 /115
HIoPE
열역학은 에너지(energy)와 평형(equilibrium)을 다루는 과학
어떤 한 물질(substance)의 열역학적 상태는 에너지를 나타낼 수 있는 상태량(properties)과 평형상태에 이르게 하는 에너지 전달에 의하여 기술
A
B C
비체적 (specific volume): 단위질량당 체적 (종량성 상태량인 체적을 강도성 상태량으로 나타내기 위함)
= V /m [m3/kg]
밀도 (density): 단위체적당 질량
= m /V [kg/m3] ( = 1 / )
상태량 [Properties]
강도성 상태량 종량성 상태량
• 물질의 질량과 관계 없음
• 압력, 온도, 밀도,
• 비체적, 비엔탈피, 비엔트로피, 비내부에너지
• 열역학에서 주로 사용하며, 소문자로
표시
• 물질의 질량에 정비례하여 변함
• 질량, 체적, 엔탈피, 엔트로피, 내부에너지
• 대문자로 표시
1. Change of State
Combined Cycle Power Plants 1. Fundamentals of Gas Turbines 60 /115
HIoPE
과정(process): 상태가 변해가는 연속적인 경로(path)
과정 종류: 정압과정, 정적과정, 등온과정, 단열과정, 등엔트로피과정, 폴리트로픽과정
가역과정 (reversible process): 어떤 진행된 과정을 거꾸로 진행시켰을 경우 계 및 주위가 최초 상태로 되돌려질 수 있는 과정. 마찰손실을 수반하지 않는 과정 (유체마찰과 열전달이 없는 경우 가역과정이 가능하지만 유체가 흘러가는 동안 마찰과 열전달이 필수적으로 수반되기 때문에 가역과정은 실질적으로 불가능)
비가역과정 (irreversible process): 과정이 진행되는 동안 마찰손실을 수반하는 과정
p
1 2
[ 정압과정 ] [ 정적과정 ] [ 등온과정 ] [ 단열과정 ]
T 1 2
s
T
1
2
s
p
1
2
과정 [Process]
1. Change of State
Combined Cycle Power Plants 1. Fundamentals of Gas Turbines 61 /115
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2. Heat and Work
Heat Work Work Heat
pA
피스톤 운동
dx
W
W
2
1
2
1
2
112 pddxFww
[ 밀폐계에서의 절대일 ]
일(work) = 힘 거리
일은 경로함수(path function) – 불완전미분 (미분기호 “ ” 사용)
m
온도계
낙하추
교반기
액체
[ 줄의 실험장치 ]
줄(Joule)은 단열용기에 물을 채운 상태에서 낙하추를 떨어뜨리는 실험을 통하여 다음 사항을 확인함.
1 kcal = 427 kgf‧m (낙하추 일 마찰열+유체 교란)
p
d
1 2
Combined Cycle Power Plants 1. Fundamentals of Gas Turbines 62 /115
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2. Heat and Work
열역학적 상태량은 상태변화가 일어난 경로(path)에 좌우되어 그 변화량이 결정되는 상태량이 있는 반면에 경로에는 무관하게 최초상태와 최종상태에 의해서만 상태변화량이 결정되는 상태량이 있다.
예를 들면, 열과 일은 상태변화가 일어난 경로에 따라 상태변화량 크기가 달라지는 경로함수(path function)이며, 상태변화량은 수학적으로 불완전미분을 이용해서 구해진다.
이에 반해서 내부에너지의 상태변화량 크기는 상태변화가 일어난 경로에 무관하고 최초상태와 최종상태에 의해서만 상태변화량이 결정되는 점함수(point function)이며, 상태변화량은 수학적으로 완전미분을 이용해서 구해진다.
열역학에서 완전미분에 대해서는 미분기호 d , 불완전미분에 대한 미분기호는 를 사용한다.
완전미분과 불완전미분을 통해서 구해진 상태변화량 크기를 서로 구분하기 위하여 각각 다음과 같이 표현한다.
2
112ww
Path Function vs. Point Function
2
112 hhdh
p 2
1
1 2
b
a
d
Combined Cycle Power Plants 1. Fundamentals of Gas Turbines 63 /115
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[ 열과 일에 대한 방향성 ]
System
Win () Wout (+)
Qout ()
Qin (+)
경계
• The rotor changes the stagnation
enthalpy, kinetic energy, stagnation
of the working fluid.
• In a compressor, the energy is
imparted to the working fluid by a
rotor.
• In a turbine, the energy is
extracted from the fluid.
일의 방향
There are two types of fluid machines, power-
producing and power-absorbing machine. In both
power-producing and power-absorbing machines,
energy transfer takes place between a fluid and a
moving machine part.
The representative power-producing machines are
steam and gas turbines, which extract energy from
fluid.
The representative power-absorbing machines are
compressors and pumps, which transfer energy to
fluid.
2. Heat and Work
Combined Cycle Power Plants 1. Fundamentals of Gas Turbines 64 /115
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Heat
2. Heat and Work
열역학적으로 평형에 도달하는 과정에서 열은 고온체로부터 저온체로 흘러가며, 열평형에 도달한 후에 열은 더 이상 전달되지 않는다.
즉, 열 (heat)은 계와 주위 또는 다른 계와의 온도차에 의하여 이동하는 에너지로서 Q로 표시.
열에 의한 에너지 전달은 다음 식으로 표현한다.
(or )
비열(c)은 단위 질량을 가지는 물질의 온도를 1℃ 상승시키는 데 필요한 열량을 의미한다.
TmcQ mcdTQ
한편, 단위질량당 전달된 열량을 나타내기 위하여 소문자 ‘q'를 사용한다.
열역학적 계에서 전달된 열이 없는 경우 단열(adiabatic)이라 한다.
열은 부호를 가지며, 계로 유입되는 열을 양(+)의 열, 계를 빠져나가는 열을 음(-)의 열이라 한다.
일과 마찬가지로 열도 에너지 전달이다. 그러나 일이 거시적으로 조직화된 에너지 전달인 반면에 열은 미시적으로 비조직화된 에너지 전달이다.
이에 대한 이해를 돕기 위하여 기체로 채워진 밀봉된 용기를 가열하는 경우를 살펴보기로 한다. 이 경우 열역학적 상태량인 온도와 압력을 조사하면 비록 가해진 일이 없더라도 기체의 에너지 상태가 바뀌었다는 것을 알 수 있다. 열역학적 개념에서 열은 이런 에너지 전달을 나타내는 것이다. 그러나 계가 일단 평형상태에 도달하면 에너지가 열에 의해서 전달되었는지 아니면 일에 의해서 전달되었는지 확인하기 어렵다.
Combined Cycle Power Plants 1. Fundamentals of Gas Turbines 65 /115
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열의 방향
Fuel in =
qin (+)
Fuel in =
qin (+)
Exhaust gas =
qout ()
Exhaust gas =
qout ()
Exhaust gas =
qout ()
Fuel in =
qin (+)
2. Heat and Work
Combined Cycle Power Plants 1. Fundamentals of Gas Turbines 66 /115
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1 kcal = 물 1 kg의 온도를 1℃ (14.5℃15.5℃)상승시키는데 필요한 열량
1 Btu = 물 1 lbm의 온도를 1℉(63℉ 64℉) 상승시키는데 필요한 열량
1 kcal = 4.185 kJ
1 Btu = 0.252 kcal = 1.055 kJ
일의 단위: J(Joule) = N‧m (일 = 힘 거리)
열의 단위:
1) 국제단위계: J
2) 공학단위계: kcal or Btu,
일과 열의 관계: 1 kcal = 427 kgf‧m = 4.185 kJ (Joule’ experiment)
열과 일의 단위
2. Heat and Work
Combined Cycle Power Plants 1. Fundamentals of Gas Turbines 67 /115
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단위계
2. Heat and Work
대부분의 국가에서 국제단위계 사용
단위계 국제단위계 공학단위계 단위 환산
기본단위 길이 (m) 질량 (kg) 시간 (sec)
길이 (m) 힘 (kgf)
시간 (sec)
질량 kg kgfs2/m
힘 N (Newton) kgf 1 kgf = 9.81 N
압력 Pa (=N/m2) kgf/m2 1 kgf/cm2 = 98,069 Pa
일(에너지) J (Joule) kgfm 1 kgfm = 9.81 J
열량 J (Joule) kcal or Btu 1 kcal = 427 kgfm = 4.185 kJ
1 Btu = 778 lbfft = 1.055 kJ
동력 W (Watt) PS 1 PS = 75 kgfm/s = 735.5 W
Combined Cycle Power Plants 1. Fundamentals of Gas Turbines 68 /115
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열역학 제1법칙 = 에너지 보존법칙
국제단위계: Q = W [kJ]
공학단위계: Q = AW [kcal], JQ = W [kgf‧m] (1 kcal = 427 kgf‧m or 1 Btu = 778 lbf‧ft)
A: 일의 열당량 (A = 1/427 kcal/kgf‧m)
J: 열의 일당량 (J = 427 kgf‧m/kcal)
열역학 제1법칙에 대한 표현:
1) 열은 에너지의 한 형태로서 일을 열로 변환시키는 것과 역으로 열을 일로 변환시키는 것이 가능
2) 열을 일로 변환시킬 때 혹은 일을 열로 변환시킬 때 에너지 총량은 변화하지 않고 일정
3) 에너지를 소비하지 않고 계속해서 일을 발생시키는 기계인 제1종 영구기관을 만드는 것은 불가능
3. The First Law of Thermodynamics
754 MJ/s (100%)
205 MW (27.2%) 203 160 119 MW = 482 MW (63.9%)
277 MW (Net Output = 36.7%)
272 MJ/s (36.1%)
가스터빈에서 열과 일의 변화 (국제단위계)
Combined Cycle Power Plants 1. Fundamentals of Gas Turbines 69 /115
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3. The First Law of Thermodynamics
c1
c2 q
w z1
z2
1
2
q w
[ Closed system ]
[ Open system ]
wdeq
계에 가해진 열량은 일부가 일로 변화되고 나머지 일부는 에너지 변환으로 나타남
기계공학(열유체기계) 계에 관계된 에너지는 내부에너지, 유동에너지, 운동에너지, 위치에너지
PEKEFEue
1212
2
1
2
2112212122
1wzzgccppuuq
1212
2
1
2
212122
1wzzgcchhq
일반식:
밀폐계:
개방계:
121212 wuuq
1212
2
1
2
2112212122
1WzzgccppuumQ
wPEdKEdFEdduq )()()(
12
2
11
2
22122
1
2
1wchchq
121212 whhq
wdhq
121,2,12 whhq oo (ho: stagnation enthalpy)
(If KE is small)
Combined Cycle Power Plants 1. Fundamentals of Gas Turbines 70 /115
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Flow energy (flow work) is the work associated with the masses crossing the control surface.
The term p11 represents the work done by the fluid in the flow channel just upstream of the inlet to move
the fluid ahead of it into the system (control volume), and it thus represents energy flow into the system.
Similarly, p22 is the flow work done by the fluid inside the system to move the fluid ahead of it out of the
system. It represents energy transfer as work leaving the system.
pdmpmddVpdlApFE
Flow Energy [유동에너지]
c1
c2 q
w z1
z2
1
2
[ Open system ]
3. The First Law of Thermodynamics
Combined Cycle Power Plants 1. Fundamentals of Gas Turbines 71 /115
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wduq 밀폐계에 대한 열역학 제1법칙:
밀폐계 정압과정에 대한 일의 크기는,
따라서 다음과 같은 관계식 성립
결론적으로, 밀폐계 정압과정에서 가열한 열량의 크기는 최종상
태와 초기상태 사이의 (u + p) 상태량 변화와 같아졌으며, 이를
특별한 열역학적 상태량인 엔탈피라한다.
여기서 p를 유동에너지(또는 유동일)라고 한다. 그러므로 엔탈
피는 내부에너지와 유동에너지의 합이다.
2
1112212 pppdww
11122212 pupuq
puh
pA
피스톤 운동
dx
W
W
[ 정압 가열과정]
1212 hhq
Enthalpy
3. The First Law of Thermodynamics
[Exercise 1.1]
1) 발전설비에서 정압가열이 중요한 이유를 설명하시오.
2) 발전설비에서 정압가열 후 가장 중요하게 취급되는 열역학적 상태량은 무엇인가?
Combined Cycle Power Plants 1. Fundamentals of Gas Turbines 72 /115
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Cycle
3. The First Law of Thermodynamics
Cycle: 계를 구성하는 작동유체가 일련의 과정을 거쳐서 최초의 상태로 다시 돌아왔을 경우 사이클(cycle)을 이루었다고 함
Brayton Cycle - Open System Otto Cycle - Closed System
흡입 압축 연소 배기
p
2
1
3
4
2
1
3
4
p
Combined Cycle Power Plants 1. Fundamentals of Gas Turbines 73 /115
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2
1
3
2
4
3
1
4qqqqqqcycle
열역학 제1법칙은 사이클을 겪는 계에 대해서도 성립
WQ
41342312 qqqq
2
1
3
2
4
3
1
4wwwwwwcycle
41342312 wwww
Cycle Integration
3. The First Law of Thermodynamics
[ Otto Cycle ]
[ Sabathe Cycle ]
2
1
3
4
p
1
5
2
3 4
p
Combined Cycle Power Plants 1. Fundamentals of Gas Turbines 74 /115
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wdhq
개방계에서의 열역학 제1법칙과 열역학
제2기초식을 비교하면,
dpdhq
2
112 dpw
다음과 같은 공업일을 구할 수 있다.
p
2
1
p2
dp
p1
펌프(비압축성유체)인 경우 :
12112 ppw
4. 공업일 (Technical Work)
Combined Cycle Power Plants 1. Fundamentals of Gas Turbines 75 /115
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4. 공업일 (Technical Work)
p
2
1
dp
1
2
0
2 1
p1
p2
1 2
과정 11:
• 흡입과정
• 일의 크기 = p11
과정 12:
• 팽창과정
• 일의 크기 = 면적 1-2-2-1-1
과정 22:
• 배기과정
• 일의 크기= -p22
과정 21:
• 공급압력 상승
• 일의 크기= 0
유동가스가 한 공업일의 크기 =
2
1dp
Combined Cycle Power Plants 1. Fundamentals of Gas Turbines 76 /115
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p
2
1
1 2
b
a
d
절대일 (absolute work) 공업일 (technical work)
p
2
1
p2
dp
p1
밀폐계에서의 일 개방계에서의 일
절대일 vs. 공업일
4. 공업일 (Technical Work)
Combined Cycle Power Plants 1. Fundamentals of Gas Turbines 77 /115
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Brayton Cycle
4. 공업일 (Technical Work)
p
2
1
3
4
win
(a)
p
2
1
3
4
wout
(b)
p
2
1
3
4
wsys
(c)
Combined Cycle Power Plants 1. Fundamentals of Gas Turbines 78 /115
HIoPE
cdTq dT
qc
dT
dh
dT
qc
p
p
dT
du
dT
qc
dTcdh p
dTcdu
(열역학 제2기초식 참조)
(열역학 제1기초식 참조)
mcdTQ
c
cp : Specific heat ratio
단원자 가스 : = 5/3 (= 1.67)
2원자 가스 : = 7/5 (= 1.40)
다원자 가스 : = 4/3 (= 1.33)
5. Specific Heat
[ Exercise 1.2 ]
Solid materials have one specific heat. However, all gases
have two different specific heats. Discuss for this.
W
pA
dx
W
Combined Cycle Power Plants 1. Fundamentals of Gas Turbines 79 /115
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물: 지구상에 존재하는 물질 가운데 비열이 가장 크다.
물이 풍부한 지방이 온화; 겨울 동안 공기(cp=1004.7 J/kgK) 온도가 내려감에 따라 물에서 공기로 열이 전달되기 때문에 공기 온도 증가. 미국 서해안에는 겨울 동안에 동풍이 불기 때문에 동쪽의 육지로 따뜻한 공기가 유입. 따라서 미국의 경우 겨울엔 기후가 온화한 서해안 선호.
Substance J/kgK kcal/kgK
Aluminium 900 0.215
Beryllium 1,820 0.436
Cadmium 230 0.055
Copper 387 0.0924
Germanium 322 0.077
Gold 129 0.0308
Iron 448 0.107
Lead 128 0.0305
Silicon 703 0.168
Silver 234 0.056
Glass 837 0.20
Ice (-5C) 2,090 0.50
Wood 1,700 0.41
Alcohol (ethyl) 2,400 0.58
Mercury 140 0.033
Water (15C) 4,186 1.00
Steam (100C) 2,010 0.48
Specific Heats of Some Substances at 25C and
Atmospheric Pressure
해변에서 공기의 순환
한여름 더운 낮에 모래 위의 차가운 공기는 물 위에 있는 공기보다 더 빨리 가열. 따뜻해진 공기가 부력에 의해 상승하면 물 위의 차가운 공기가 모래사장 쪽으로 유입.
5. Specific Heat
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기체의 비열은 각종 엔진의 성능을 계산하는데 필수적으로 사용되는 매우 중요한 물리량 임. 따라서 비열은 매우 정확하게 구해야 함
가스터빈엔진에 있어서 통상적으로 다음과 같은 비열 값과 비열비가 사용
Cold end gas properties: cp = 1004.7 J/kg-K, = 1.4
Hot end gas properties: cp = 1156.9 J/kg-K, = 1.33
이는 Cold end gas는 공기(2원자 가스)이며, Hot end gas는 CO2, H2O, NOx 등과 같은 다원자 가스이기 때문임
그러나 이렇게 일정한 값을 가진다고 가정하여 성능을 계산하는 경우 최대 5% 정도의 오차를 보이는 것으로 알려져 있음
한편, 비열에 대한 정확한 값을 계산하기 위해서는 연료 종류 및 연소 생성물 등을 고려하여 계산해야 함
5. Specific Heat
Combined Cycle Power Plants 1. Fundamentals of Gas Turbines 81 /115
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c
cp (1.4 for air)
Rc1
1
Rcp1
puh
Specific Heat for Ideal Gases
RTuh
RdT
du
dT
dh
Rccp
An ideal gas model assumes that internal energy is only a function of temperature u=u(T). Therefore,
shows that enthalpy is also a function of temperature only.
From this equation and the ratio of specific heat, we can get
RTuh
5. Specific Heat
Combined Cycle Power Plants 1. Fundamentals of Gas Turbines 82 /115
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T1
(hot)
T2
(cold)
q
Heat transfer
There exists a useful thermodynamic variable called entropy (s).
A natural process that starts in one equilibrium state and ends
in another will go in the direction that causes the entropy of the
system plus the environment to increase for an irreversible
process and to remain constant for a reversible process.
T
qds
Entropy = Energy + Tropy
Tropy = Transformation (in Greek)
엔트로피 물질의 열적 상태를 나타내는 물리량 (1865년 Clausius가 제안)
전통적으로 엔트로피라는 물리량은 신비에 싸여 있음 엔트로피가 다른 물리량들에 비해 훨씬 덜 명확함
이는 엔트로피는 그 절대적인 값보다는 그 변화량에 관심을 두기 때문임
압축과정이나 팽창과정에서 엔트로피가 증가된다는 것은 열에너지(thermal energy)가 유용한 일(useful work)로 사용할 수 없는 마찰로 손실된다는 것을 의미
6. Entropy
Combined Cycle Power Plants 1. Fundamentals of Gas Turbines 83 /115
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A
uA
sA
B
uB
sB
A
B
q
,uss
ds
duu
sds
u
pdduTds
Tdsq
Gibbs Equation
pdduq
(Gibb’s equation)
(The first law of thermodynamics)
T
s
2
1
s2 s1 ds
2
112 Tdsq
Tdsq
revT
qds
(for a simple compressible substance)
6. Entropy
Combined Cycle Power Plants 1. Fundamentals of Gas Turbines 84 /115
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정량적 계산
From Gibbs’ equation and first law of thermodynamics,
and integrating. This gives
Entropy is assigned the value zero at the reference state, Tref = 0 K and pref = 1 atm. The value of entropy at
temperature T and pressure p is then calculated from
p
dpR
T
dTcds
dpdhTds
p
1
21122 ln,,
12
p
pR
T
dTTc
T
dTTcpTspTs
T
Tp
T
Tp
refref
ref
T
Tp
p
pR
T
dTTcpTs
ref
ln,
6. Entropy
Combined Cycle Power Plants 1. Fundamentals of Gas Turbines 85 /115
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All engine cycles are illustrated schematically by both p- and T-s diagram.
The amount of work produced or supplied can be predicted by p- diagram.
Similarly, the amount of heat supplied or exhausted can be predicted by T-s diagram.
2
112 pdvw
p
2
1
1 2 d
2
112 Tdsq
T
s
2
1
s2 s1 ds
q=Tds
Why we need T-s diagram ?
6. Entropy
Combined Cycle Power Plants 1. Fundamentals of Gas Turbines 86 /115
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Rankine Cycle
T
s
1
2
3
4
qout
T
s
2
3
qin
1
4
T
s
1 2
3
4
qsys
(a) (b) (c)
T-s diagram
6. Entropy
Combined Cycle Power Plants 1. Fundamentals of Gas Turbines 87 /115
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Otto Cycle / Diesel Cycle / Brayton Cycle
과정의 s-축에 대한 투영면적이 계로 공급되거나 계를 빠져나간 열량을 나타냄
엔트로피가 증가하면 계 내부로 열량 공급, 엔트로피가 감소하면 계 외부로 열량 배출 의미
(a) (b) (c)
T
s
2
1
3
4
qin
T
s
2
1
3
4
qout
T
s
2
1
3
4 qsys
T-s diagram
6. Entropy
Combined Cycle Power Plants 1. Fundamentals of Gas Turbines 88 /115
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p
p = const.
adiabatic
T
s
=
const.
T = const.
T = const.
s =
co
nst.
(ad
iab
atic)
= const.
p = const.
p- and T-s Diagrams
6. Entropy
Combined Cycle Power Plants 1. Fundamentals of Gas Turbines 89 /115
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Isentropic Efficiency & Loss
6. Entropy
Ava
ilab
le e
ne
rgy
Use
ful e
ne
rgy
A
B C
D
pi
po
Loss ds
Reduction in useful energy
(Performance degradation)
Increase in entropy due to aging
AB : Isentropic expansion line
AC : Original expansion line
AD : New expansion line due to aging
pi : Pressure at the inlet of turbine
po : Pressure at the outlet of turbine
ds : Increase of entropy due to the loss
h
s
th = Useful energy
Available energy
Combined Cycle Power Plants 1. Fundamentals of Gas Turbines 90 /115
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dT
qds
= entropy increase by heat transfer
= entropy increase due to internal irreversibility, such as friction
T
q
d
T
LWd
= lost work LW
Friction is ignored in thermodynamics, thus this equation is not used generally. However, isentropic
process can be expressed very clearly by this equation.
The Second Law of Thermodynamics
6. Entropy
Combined Cycle Power Plants 1. Fundamentals of Gas Turbines 91 /115
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12
12
12
12
TT
TT
hh
hh ssC
ss
TTT
TT
hh
hh
43
43
43
43
Efficiency of compressor (or pump)
Efficiency of turbine
Efficiency
6. Entropy
T
s
1
2 2s
3
4s 4
[ Brayton cycle T-s diagram ]
Combined Cycle Power Plants 1. Fundamentals of Gas Turbines 92 /115
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① 보일러(HRSG)급수펌프에서 다양한 손실 발생 – 펌프 자체효율 존재
② 보일러는 보일러 배관에서 발생하는 마찰손실, 외벽을 통해 빠져나가는 열손실, 연도가스 통로 압력손실, 굴뚝으로 빠져나가는 열손실, 보일러 자체의 열전달 효율이 존재 - 보일러 자체효율 존재
③ 가스터빈/증기터빈에서 다양한 손실 발생 – 가스터빈/증기터빈 자체효율 존재
④ 복수기 손실 발생
⑤ 기계적 손실 발생 – 가스터빈/증기터빈에서 생산된 동력이 발전기에 전달되면서 베어링에서 기계적 손실 발생
⑥ 발전기 자체효율(대개 98~99%) 존재 – 전기적 손실 및 기계적 손실
⑦ 발전소 보조기기(오일펌프, 팬 등)에 사용되는 전력 존재
복합발전에서 Heat Rate를 사용하는 이유
Heat rate는 열입력을 발전기 출력으로 나눈 값
Heat rate는 열효율과 역수 관계
실질적으로 다양한 손실을 반영하여 정확하게 효율을 계산
하기 어려움
7. Heat Rate
Combined Cycle Power Plants 1. Fundamentals of Gas Turbines 93 /115
HIoPE
1 kcal = 물(water) 1 kg의 온도를 1C 상승시키는데 필요한 열량
1 Btu = 물(water) 1 lb의 온도를 1F 상승시키는데 필요한 열량
1 kcal = 427 kgfm = 427 kg 9.81 m/s2 m = 4185 Nm = 4.185 kJ
1 Btu = 1 kcal 1/2.204619 5/9 = 0.252 kcal = 1.055 kJ
양변을 시간 h로 나누면,
1 Btu/h = 1.055 kJ/3600 s = 1.055/3600 kW
1 kWh = 3600/1.055 Btu = 3412.14 Btu
따라서 이상적인 경우(열효율 100%)에 1 kWh의 전기를 생산하기 위해서는 3412.14 Btu의 열량이
필요. 그러나 실제적으로는 다양한 손실로 인하여 1 kWh의 전기를 생산하기 위해서는 이상적인
경우보다 더 많은 열량이 요구.
]kJ/kWhorBtu/kWh,[outputgenerator
inputheatrateheat
발전설비 열효율은 각 구성품에서 발생하는 비가역성으로 인하여 계산하기 어렵다. 따라서 열효율 대신에 열입력을 발전기 출력으로 나누어준 열율을 많이 사용
]kJ/kWh[
3600
]Btu/kWh[
14.3412
rateheatrateheatth 열율과 열효율 관계:
7. Heat Rate
Combined Cycle Power Plants 1. Fundamentals of Gas Turbines 94 /115
HIoPE
The net plant efficiency is affected by three main components, such as net turbine heat rate (NTHR), boiler
efficiency, and auxiliary power consumption.
The net plant efficiency or its reciprocal term net plant heat rate (NPHR) is a key evaluation parameter for
the cost of electricity.
In the US, the net plant efficiency is defined as the ratio of net generated electric energy by the fuel energy,
on a higher heating value (HHV) basis.
NPHR = NTHR/ ((Blr/100) (100%AP)/100) [kJ/kWh (Btu/kWh)]
Where, NTHR = net turbine heat rate, Btu/kWh, input heat by steam divided by net generator output
power.
Blr = boiler fuel efficiency, %, this is the fuel higher heating value energy input to steam.
%AP = percent auxiliary power in % of gross power generation.
Boiler fuel efficiency is the percent of fuel input heat absorbed by the steam.
Boiler efficiency is typically in a range from about 85 to 92%.
Net Plant Efficiency
7. Heat Rate
Combined Cycle Power Plants 1. Fundamentals of Gas Turbines 95 /115
HIoPE
C + O2 = CO2 + 33.9 MJ/kg
H2 + 1/2O2 = H2O(water) + 143.0 MJ/kg (HHV)
H2 + 1/2O2 = H2O(vapor) + 120.6 MJ/kg (LHV)
S + O2 = SO2 + 9.28 MJ/kg
Combustion
7. Heat Rate
Combined Cycle Power Plants 1. Fundamentals of Gas Turbines 96 /115
HIoPE
The heat rate will be different by the type of heating value.
In the US, the standard is HHV, whereas in Europe the practice is to use LHV.
The fuel HHV is obtained by laboratory analysis in an oxygen bomb calorimeter.
The LHV of the fuel is computed by subtracting the latent heat of vaporization for water produced by fuel
hydrogen combustion and fuel moisture content.
LHV = HHV – Hfg (M + 8.94H2)/100
where, M is fuel moisture % by weight, Hfg is water latent heat at reference temperature 25C, H2 is fuel
hydrogen % by weight.
The lower heating value of the gas is one in which the H2O in the products has not condensed. The lower
heating value is equal to the higher heating value minus the latent heat of the condensed water vapor.
Heating Value [1/2]
7. Heat Rate
Combined Cycle Power Plants 1. Fundamentals of Gas Turbines 97 /115
HIoPE
[Exercise 1.3]
어떤 발전소 열효율이 HHV를 기준으로 45%이다. 이 발전소의 열효율을 LHV를 기준으로 계산하시오. 이 발전소에 사용하는 석탄의 HHV는 12540 Btu/lb이며, 석탄은 5.2%의 수분과 4.83%의 수소를 포함하고 있다.
[Solution]
Heat rate를 구하면 다음과 같다.
th,HHV = 3412.14/HRHHV = 0.45 HRHHV = 7,582.5 Btu/kWh
LHV를 계산한다.
LHV = HHV – Hfg (M + 8.94H2)/100 = 12540 – 1049.7 (5.2 + 8.94 4.83)/100
= 12032.15 Btu/lb
LHV/HHV를 계산한다.
LHV/HHV = 12032.15/12540 = 0.9595
따라서 LHV를 기준했을 때 heat rate는 다음과 같다.
HRLHV = HRHHV 0.9595 = 7275.41 Btu/kWh
th,LHV = 3412.14/HRLHV = 3412.14/7275.41 = 46.9%
Heating Value [2/2]
7. Heat Rate
Combined Cycle Power Plants 1. Fundamentals of Gas Turbines 98 /115
HIoPE
8. Cycle Analysis
p
2
1
3
4
2 1 3
T
s
1 2
3 4 TH
TL
qout ()
qin (+)
s2 s1
The Carnot cycle is the most efficient cycle that can operate between two constant temperature
reservoirs. This is because its processes are reversible.
The Carnot cycle is very useful to compare with other power producing cycles.
The Carnot cycle is an ideal cycle that could not be attained in practice.
Isothermal
compressor
Isentropic
compressor
Isothermal
turbine
Isentropic
turbine
q q
Carnot Cycle
Combined Cycle Power Plants 1. Fundamentals of Gas Turbines 99 /115
HIoPE
Process Work Heat
12 Compression at constant temp. w12 = RT1 ln(1/2) (= win) q12 = w12 = T1(s1s2) (= qout)
23 Adiabatic compression w23 = (u3u2) = c(T3T2) (= win) q23 = 0
34 Expansion at constant temp. w34 = RT3 ln(4/3) (= wout) q34 = w34 = T3(s4s3) (= qin)
41 Adiabatic expansion w41 = u4u1 = c(T4T1) (= wout) q41 = 0
wduq
in
out
in
outin
in
sys
in
sys
thq
q
q
q
q
q
w
input
output
1
H
LCarnotth
T
T
T
T
ssT
ssT
111
3
1
343
211,
8. Cycle Analysis
Carnot Cycle
41342312 wwwwwwOutput sys
[Exercise 1.4]
카르노사이클 열효율 향상방법 두 가지를 제시하시오. 1) 2)
121212 wuuq
Combined Cycle Power Plants 1. Fundamentals of Gas Turbines 100 /115
HIoPE
T
s
1
2
3
4 qC
wT qB
qB
qB
wP
a
Process Component Heat Work Process
12 Pump q12 = qP = 0 w12 = wP = (h2h1) Power in (adiabatic compression)
23 Boiler q23 = qB = h3h2 w23 = wB = 0 Heat addition at constant pressure
34 Turbine q34 = qT = 0 w34 = wT = h3h4 Power out (adiabatic expansion)
41 Condenser q41 = qC = (h4h1) w41 = wC = 0 Heat release at constant temperature
1212
2
1
2
212122
1wzzgcchhq
Rankine Cycle
8. Cycle Analysis
Combined Cycle Power Plants 1. Fundamentals of Gas Turbines 101 /115
HIoPE
Process Component Heat Work Process
12 Compressor q12 = qC = 0 w12 = wC = (h2h1) Power in (adiabatic compression)
23 Combustor q23 = qB = h3h2 w23 = wB = 0 Heat addition at constant pressure
34 Turbine q34 = qT = 0 w34 = wT = h3h4 Power out (adiabatic expansion)
41 Exhaust q41 = qE = (h4h1) w41 = wE = 0 Heat release at constant pressure
1212
2
1
2
212122
1wzzgcchhq
p
2
1
T
(h)
s
qin
3
4 1
2
3
4
qout
win
wout
win
wout
qin
qout
Brayton Cycle
8. Cycle Analysis
Combined Cycle Power Plants 1. Fundamentals of Gas Turbines 102 /115
HIoPE
Steam is used in more of today’s power plants than any other working fluid.
The physical properties of steam are complex because any one steam property is changed, such as
pressure, temperature, specific volume, energy or moisture, all the other properties will also change.
The Mollier diagram has been developed to show this interrelationship of steam properties, and how they all
fit together.
The vertical axis is enthalpy(kJ/kg or BTU/lb) which is defined as internal energy plus flow energy of the
working fluid, and the horizontal axis is entropy(kJ/kg-K or BTU/lb-F) representing energy loss.
Mollier diagram shows lines of constant pressure, constant temperature, constant moisture, and the steam
saturation line (below which the steam is wet, and above which the steam is dry and superheated.
h-s Diagram [Mollier Diagram]
8. Cycle Analysis
h-s 선도는 이상기체와 다른 성질을 가지는 실재기체의 상태변화를 실험을 통하여 확인하여 표와 선도로 나타낸 것이다.
h-s 선도는 1906년 R. Mollier가 개발
h를 종축, s를 횡축으로 설정하여 증기의 상태(p, , T, x)를 나타낸 선도.
증기의 상태량(T, p, , x, h, s) 가운데 2개를 알면, h-s 선도로부터 다른 상태량을 알 수 있다.
주로 연소기체나 수증기를 대상으로 하기 때문에 가스터빈 및 증기터빈의 사이클 해석에 이용된다.
압축수의 엔탈피는 파악하기 어렵다.
Combined Cycle Power Plants 1. Fundamentals of Gas Turbines 103 /115
HIoPE
h-s Diagram [Mollier Diagram]
8. Cycle Analysis
Combined Cycle Power Plants 1. Fundamentals of Gas Turbines 104 /115
HIoPE
Wilson line
T
(h)
s
1
2
3
4
win
wout
qin
qout
h-s Diagram [Mollier Diagram]
8. Cycle Analysis
[Exercise 1.5]
작동유체가 공기(이상기체)인 경우 T-s 선도와 h-s 선도가 동일한 형상을 가지는 이유에 대해서 설명하시오.
Combined Cycle Power Plants 1. Fundamentals of Gas Turbines 105 /115
HIoPE
s
h
Turbine
Efficiency 0%
25%
75%
1
h2 at 25%
h2 at 50%
h2 at 75%
h2 at 100%
50%
100%
h2 = h1 at 0%
Turbine efficiency decreases as
the entropy increases during
expansion process.
h-s Diagram [Mollier Diagram]
8. Cycle Analysis
Combined Cycle Power Plants 1. Fundamentals of Gas Turbines 106 /115
HIoPE
9. Throttling Process
유체가 노즐이나 오리피스와 같이 갑자기 유로가 좁아지는 곳을 통과하면 외부와 열량이나 일의 교환 없이
도 압력이 감소하는 교축과정(throttling process) 발생
교축과정이 발생하면 와류가 생성되어 에너지가 손실되면서 압력손실 발생
작동유체가 액체인 경우 교축과정이 일어나서 압력이 액체의 포화압력보다 낮아지면 액체의 일부가 증발하
며, 증발에 필요한 열을 액체 자신으로부터 흡수하기 때문에 액체 온도 감소
Pre
ssu
re
p
1 2
Combined Cycle Power Plants 1. Fundamentals of Gas Turbines 107 /115
HIoPE
열역학 제1법칙:
단순유동에서 교축과정이 일어나면, 벽면에서의 열전달이 없으며, 이루어진 일이나 공급된 일도
없으며, 위치에너지 변화량도 무시할 수 있으므로,
속도가 40m/s 이하인 경우 운동에너지는 엔탈피 크기에 비해 매우 작다.
교축과정은 발전설비에서 자주 일어나는 과정인데, 특히 증기가 밸브를 통과할 때 교축과정이 발
생하며, 이때 압력강하가 발생한다.
12 hh (교축과정 = 등엔탈피 과정)
1212
2
1
2
212122
1wzzgcchhq
02
1 2
1
2
212 cchh
9. Throttling Process
Combined Cycle Power Plants 1. Fundamentals of Gas Turbines 108 /115
HIoPE
작동유체가 이상기체인 경우 교축과정이 발생한 후에 엔탈피는 일정하게 유지됨
엔탈피는 온도만의 함수이므로 교축과정 발생 후에 온도변화 없음
그러나 작동유체가 증기인 경우에는 교축과정이 발생하면 압력과 온도가 떨어져서 에너지 수준이 낮아짐.
주울-톰슨 효과(Joule-Thomson effect)
증기터빈 버켓커버 상부에는 증기누설을 방지하기 위해서 seal을 설치하여 증기누설 방지
Seal을 통해서 누설되는 증기는 seal strips을 통과하면서 교축과정이 발생하기 때문에 실을 빠져나온 증기
는 온도와 압력이 떨어져서 엔탈피가 낮아짐
따라서 누설증기가 다음 단에서 주유동과 합류하더라도 주유동의 에너지 수준을 높이지 못하기 때문에 손실
발생 누설손실
즉 누설증기가 실을 빠져나오면서 에너지를 잃지 않았다면 다음 단에서 사용할 수 있지만 이미 잃어버렸기
때문에 손실 발생
증기 특성
9. Throttling Process
Combined Cycle Power Plants 1. Fundamentals of Gas Turbines 109 /115
HIoPE
[Exercise 1.6] Compare the velocity at 2
그림에서 A와 B는 동일한 규격의 도관이다. 도관 B에 오리피스를 설치하였다. 그리고 도관 B 입구압력은
도관 A와 동일하게 유지시킨 상태에서 질량유량을 절반으로 줄였다. 그리고 이때 도관 B의 하류 2에서
압력을 측정하였더니 입구 압력의 절반이었다. 이때 오리피스 하류 2에서 유속을 비교하시오.
1 2
A
1 2
B
9. Throttling Process
Combined Cycle Power Plants 1. Fundamentals of Gas Turbines 110 /115
HIoPE
[Solution]
문제에서 주어진 조건은 다음과 같다.
(1)
그리고
교축과정이 일어나면 온도는 변하지 않는다. 따라서 이상기체라고 가정하면 다음 관계식이 성립한다.
그러므로 다음 관계식이 성립한다.
and , therefore, (2)
유동 단면적이 일정하기 때문에 식 (1)은 다음과 같이 된다.
(3)
식 (2)와 식 (3)을 결합하면 다음과 같은 식을 얻는다.
따라서 질량유량이 달라지더라도 압력을 조절하여 하류에서 일정한 속도를 얻을 수 있다.
2,2,2,2,
2
1
2
1ABAB VAVAmm
1,1,2,2
1
2
1ABB ppp
2,2,1,1, BBBB pp
2,1,2 BB
2,2,2,2,2
1AABB VV
2,1,1, AAB 2,2,2 BA
2,2, AB VV
9. Throttling Process
Combined Cycle Power Plants 1. Fundamentals of Gas Turbines 111 /115
HIoPE
A turbine has different expansion lines as the load is
decreased.
But the part load expansion lines are generally parallel
to the full load expansion line.
This means that the internal efficiency under part load
conditions is very close to that under full load
conditions. That is, design efficiency of the turbine
blades is maintained during part load operations by
using the control valve.
However, the cycle efficiency is reduced under part
load conditions.
p1
Ava
ilab
le E
ne
rgy
pc
p0
T0
h
s
Partial-flow expansion line
Expansion lines are
essentially parallel
Design-flow expansion line
p1’
p0: Inlet pressure
p1: Throttle pressure 1 1′
2′
2
U 100% load
Nozzle Row
25% load
100%
25%
Bucket Row
U
75% load
50% load
[ Effect of Throttling on Non-Reheat
Steam Turbine Expansion Line ]
[ Velocity Diagram at Various Loads ]
9. Throttling Process
Combined Cycle Power Plants 1. Fundamentals of Gas Turbines 112 /115
HIoPE
Load, % 30 40 50 60 70 80 90 100
65
60
75
70
85
80
95
90
100
49.0
48.3
47.6
46.9
46.2
45.5
44.8
44.1
43.4
42.7
42.0 45 50 55 60 65 70 75 80 85 90 95 100
200
500
470
440
410
380
350
320
290
260
230
Load, %
Eff
icie
ncy,
%
Po
we
r, M
W
Power
Efficiency
9. Throttling Process
Comparison of Part Load Efficiency
[ Gas Turbine] [ Steam Turbine]
Combined Cycle Power Plants 1. Fundamentals of Gas Turbines 113 /115
HIoPE
Pulverizers
Coal Piping
Coal Burners
교축과정 적용 예 – Coal Pipe Arrangement
9. Throttling Process
Combined Cycle Power Plants 1. Fundamentals of Gas Turbines 114 /115
HIoPE
The steam has an initial pressure P1 at the entry to the seal
assembly.
After expanding past the first constriction, the pressure will
have been reduced to condition Xo, with pressure P2.
In the chamber formed between the first and second seal
strips, the kinetic energy of the steam is destroyed and
reconverted at constant pressure P2 to condition X.
From point X, there is then a further expansion of the steam
past the second constriction, with the pressure falling to P3 at
condition Yo.
The kinetic energy is again reconverted in the chamber
between the second and third seal strips, raising the thermal
energy level from Yo to Y at constant pressure P3.
This process of expansion and kinetic energy reconversion is
continued throughout the series of seal strips until the final
expansion takes the steam to condition Qo at pressure P5.
The locus of the points Xo….Qo is called the Fanno curve.
h
s
T1
P1 P2 P3 P4
P5
Xo Yo Zo
Qo
X Y Z
Leakage
Flow
P1 P2 P3 P4 P5
X Y Z
Rotation Side
Principle of Labyrinth Seal
9. Throttling Process
Combined Cycle Power Plants 1. Fundamentals of Gas Turbines 115 /115
HIoPE
질의 및 응답
작성자: 이 병 은 (공학박사) 작성일: 2015.02.11 (Ver.5) 연락처: [email protected]
Mobile: 010-3122-2262 저서: 실무 발전설비 열역학/증기터빈 열유체기술