슬라이드 1

Transcription

1 . Fundamentals of Gas Turbines Combined Cycle Power Plants. Fundamentals of Gas Turbines /5

2 Fundamentals for Gas Turbines Thermodynamics 53 Combined Cycle Power Plants. Fundamentals of Gas Turbines /5

3 Efficiency Availability Operating Flexibility Power Generation Requirement Variety of Fuels Coal Gas Oil Water Nuclear Wind Solar Geothermal Biomass Competitive Machine Costs Emissions Combined Cycle Power Plants. Fundamentals of Gas Turbines 3 /5

4 A Typical Gas Turbine for Power Generation 7FA, GE VIGV Air extraction ports Transition piece Diffuser Starter & gear box Air inlet Compressor Turbine Combustor Exhaust Cold section Hot section Combined Cycle Power Plants. Fundamentals of Gas Turbines 4 /5

5 Gas Turbine 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 937. It was a standby unit with a thermal efficiency of 7%. 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. Combined Cycle Power Plants. Fundamentals of Gas Turbines 5 /5

6 Idealized Brayton Cycle [/3] Air Fuel Combustor 3 Exhaust gas 4 Power Compressor Turbine p q in 3 T (h) 3 q in w in w out w out 4 w in q out 4 q out s Combined Cycle Power Plants. Fundamentals of Gas Turbines 6 /5

7 Idealized Brayton Cycle [/3] Compression Process ( ) 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. Combustion Process ( 3) 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. Combined Cycle Power Plants. Fundamentals of Gas Turbines 7 /5

8 Idealized Brayton Cycle [3/3] Expansion Process (3 4) 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. Exhaust Process (4 ) 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. Combined Cycle Power Plants. Fundamentals of Gas Turbines 8 /5

9 Variation of Major Parameters m/s bar C Pressure (p o ) Temperature (T o ) Velocity Combined Cycle Power Plants. Fundamentals of Gas Turbines 9 /5

10 Terminology Terminology Combined cycle Simple cycle Heavy duty gas turbines Aeroderivative gas turbines Mechanical drive gas turbines Meaning 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. 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. 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. The aero-engines transformed into land based gas turbines successfully. P&W JT8/FT8, GE J79/LM500, GE CF6/LM500, CF6/LM5000, CF6/LM6000 The LM500 has been the most commercially successful one. 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 MW up to 50 MW. Combined Cycle Power Plants. Fundamentals of Gas Turbines 0 /5

11 Combined Cycle Power Plants [/] 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. Fuel Combustor HP drum LP drum Exhaust gas Steam turbine G G Turbine HRSG Condenser Inlet air Compressor HP superheater HP evaporator HP economizer LP superheater LP evaporator LP economizer LP boiler feed pump HP boiler feed pump Deaerator Condensate pump Combined Cycle Power Plants. Fundamentals of Gas Turbines /5

12 Combined Cycle Power Plants [/] Cycle Diagram for a 3 Pressure Reheat Cycle (F-Class Gas Turbine) Fuel G Gas turbine Heat recovery steam generator Air Hot reheat steam Main steam Cold reheat steam IP steam LP steam G Steam turbine Condenser Condensate pump Steam Water Fuel Air Combined Cycle Power Plants. Fundamentals of Gas Turbines /5

13 Combined Cycle Power Plants [3/] T-s Diagram for a Typical CCPPs Combined cycle power plants have a higher thermal efficiency because of the application of two complementary thermodynamic cycles T Combustion (heat In) Topping cycle Bottoming cycle Stack (heat out) Condenser (heat out) s Combined Cycle Power Plants. Fundamentals of Gas Turbines 3 /5

14 Combined Cycle Power Plants [4/] The Second Law of Thermodynamics T H Q H Gas turbine W T H Q H HRSG Steam turbine W Steam turbine W Q L Q L T L T L [ Fossil / Nuclear ] [ Combined cycle] Combined Cycle Power Plants. Fundamentals of Gas Turbines 4 /5

15 Combined Cycle Power Plants [5/] Cycle Characteristics 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 Combined Cycle Power Plants. Fundamentals of Gas Turbines 5 /5

16 Combined Cycle Power Plants [6/] Generals [/] 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. Combined Cycle Power Plants. Fundamentals of Gas Turbines 6 /5

17 Combined Cycle Power Plants [7/] Generals [/] 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 970s, 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. Combined Cycle Power Plants. Fundamentals of Gas Turbines 7 /5

18 Combined Cycle Power Plants [8/] GT vs. ST Gas turbine Steam turbine Combustion Internal External Thermodynamic cycle Brayton Rankine Cycle type Open Closed Working fluid Air Water/Steam Max. pressure, bar 3 (40 for Aviation) 350 (5050 psig) Max. temperature, C(F) 350 (46) 630 (66) Blade cooling Yes No Shaft cooling No Yes (USC only) Max. cycle efficiency, % (USC only) Max. number of reheat Power density High Low Steam conditions of the steam turbines for combined cycle applications are lower than those for USC steam turbines. Combined Cycle Power Plants. Fundamentals of Gas Turbines 8 /5

19 Improved Condenser Combined Cycle Power Plants [9/] Heat Balance of CCPPs Three pressure reheat cycle Fuel energy 00% Loss in HRSG 0.3% Loss 0.5% GT 37.6% ST.7% 8.6% Stack Loss 0.3% 3.0% Combined Cycle Power Plants. Fundamentals of Gas Turbines 9 /5

20 Combined Cycle Power Plants [0/] Flow Diagram of a Typical CCPP Three Pressure Reheat Cycle Dual HP superheater/reheater,4,6 HP,IP,LP evaporators 3 HP economizer/ip superheater 5,7 Dual HP/IP economizer 8,9,0 HP,IP,LP drums HP steam turbine IP/LP steam turbine 3,4,5 HP,IP,LP steam bypasses 6 Condenser 7 Condensate pump 8 Deaerator 9,0 IP,HP feedwater pumps LP 0 IP 9 HP Natural gas 3 G G Combined Cycle Power Plants. Fundamentals of Gas Turbines 0 /5

21 Combined Cycle Power Plants [/] Heat Balance Diagram of a Typical CCPP Three Pressure Reheat Cycle P.03 T 03 M P 33.7 T 40 P 0. T 60 M.3 M 59. M 0 M 3.5 P 33.7 T 40 P 5.0 T 5 M 5.4 P 33.7 T 40 P 3. T 369 M 5.9 P 4.6 T 50 M 5.4 M 0 M MW Natural gas T 647 M P 0 T 568 P 30.0 T 568 P 5. T 565 M 59. M 0 P 8.5 T 565 M MW 78 MW G Air P.03 T 5 X 60 % Gross output = 80.5 MW Gross effi. (LHV) = 59.3% P bar T C M kg/s X Rel. humidity G P T 3 M 67 Combined Cycle Power Plants. Fundamentals of Gas Turbines /5

22 Simple Cycle 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,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. [ with Bypass Stack ] [ without Bypass Stack ] Combined Cycle Power Plants. Fundamentals of Gas Turbines /5

23 Heavy Duty vs. Aeroderivative GT [/3] MS700F, GE Heavy duty gas turbines LM6000, GE 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 00 MW due to the maximum size of aircraft Combined Cycle Power Plants. Fundamentals of Gas Turbines 3 /5

24 Heavy Duty vs. Aeroderivative GT [/3] Aero Trent MT30 Aero Trent New LP compressor replaces fan LP bleed added for low speed operation DLN combustor replaces annular aero combustor Last two stages of LPT and exhaust redesigned Rear drive added Trent 60 Gas Turbine (Mechanical Drive) Combined Cycle Power Plants. Fundamentals of Gas Turbines 4 /5

25 Heavy Duty vs. Aeroderivative GT [3/3] 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. Combined Cycle Power Plants. Fundamentals of Gas Turbines 5 /5

26 Hot-End Drive vs. Cold-End Drive MS700E, GE Hot-end drive MS700F, GE 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. Combined Cycle Power Plants. Fundamentals of Gas Turbines 6 /5

27 Single-Shaft vs. Multi-Shaft [/] 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 Combined Cycle Power Plants. Fundamentals of Gas Turbines 7 /5

28 Single-Shaft vs. Multi-Shaft [/] Two-Shaft GT Fuel Combustor Exhaust gas Air Compressor HP turbine LP turbine (power turbine) Power 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. Combined Cycle Power Plants. Fundamentals of Gas Turbines 8 /5

29 Type of Plants Base load Intermediate load Peak load Operating hours [hr/a] to 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 Characteristics 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 Combined Cycle Power Plants. Fundamentals of Gas Turbines 9 /5

30 Billions of dollars (007) Gas Turbine Production by Sector Source: Davis Franus, Forecast International 8 5 Commercial aviation 9 Electrical generation 6 3 Mechanical drive Military aviation Marine propulsion Combined Cycle Power Plants. Fundamentals of Gas Turbines 30 /5

31 발전설비성능향상 열역학적성능향상 유체역학적성능향상 기타 온도향상 차유동손실최소화 대형화 압력향상 누설손실최소화배기손실최소화 Options for Power Enhancement H-Gas Turbine USC Steam Turbine Combined Cycle Power Plants. Fundamentals of Gas Turbines 3 /5

32 Thermodynamic Improvement Gas Turbine E-class F-class H-class J-class TIT, C = PR = th (SC/CC) = 37/55 39/58 --/60 40/6 Steam Turbine SC (Subcritical) SC (Supercritical) USC A-USC T, F(C) = 000(538) 00(593) 30(60) 9(700) P, psig = th = ? Combined Cycle Power Plants. Fundamentals of Gas Turbines 3 /5

33 Evolution of GE Gas Turbine Combined Cycle Power Plants. Fundamentals of Gas Turbines 33 /5

34 Net Efficiency, % (Based on LHV) STAG Product Line Ratings 64 6 Fourth Generation H Gas Turbine Technology Reheat, 3-Pressure Steam Cycle 60 S07H S09H Third Generation F Gas Turbine Technology Reheat, 3-Pressure Steam Cycle S07FA S07FB S09FA S09FB S06FA S06B S07EA S09E Second Generation B & E Gas Turbine Technology Non-Reheat, 3-Pressure Steam Cycle Net Plant Output, MW Combined Cycle Power Plants. Fundamentals of Gas Turbines 34 /5

35 Why Technology Matters? Core Technologies Materials / coatings Cooling / sealing 3D aerodynamic designs Tools and talent Installed base learning Compressor Pressure ratio Combustor Dry low NOx Turbine TIT Superiority Lower cost of electricity Higher market share Plant Performance Higher efficiency Higher output Higher reliability Lower emissions Lower O&M costs Combined Cycle Power Plants. Fundamentals of Gas Turbines 35 /5

36 Required Technologies 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 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. Combined Cycle Power Plants. Fundamentals of Gas Turbines 36 /5

37 Gas Turbine Technologies 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 0 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: in some aerospace applications, and a pressure ratio of 30: 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. Combined Cycle Power Plants. Fundamentals of Gas Turbines 37 /5

38 Users Point of View 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, NO x control, etc. Combined Cycle Power Plants. Fundamentals of Gas Turbines 38 /5

39 Compressor [/7] Developmental Trends 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: 80 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 000 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. Combined Cycle Power Plants. Fundamentals of Gas Turbines 39 /5

40 Compressor [/7] Developmental Trends Previous Designs New Designs Risk D 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 Combined Cycle Power Plants. Fundamentals of Gas Turbines 40 /5

41 Pressure ratio Compressor [3/7] Pressure Ratio GE Siemens Alstom WH/MHI GT4/GT6 50ATS 7H/9H E/9E 7F/9F 7EA/9EC V84./V94. 50F/70F 7FA/9FA GT3E GTN 50G/70G V84.3 V84.3A/ V94.3A 50D5A /70D Combined Cycle Power Plants. Fundamentals of Gas Turbines 4 /5

42 Pressure ratio Compressor [4/7] Pressure Ratio - GE 4 MS900H MS700H MS500M 8 MS700E MS700C MS500N MS500P MS700B MS700A MS900B MS900E MS600B MS700EA MS900F MS700EF MS900FA Combined Cycle Power Plants. Fundamentals of Gas Turbines 4 /5

43 Air flow, lb/sec Compressor [5/7] Air Flow - GE MS900FA MS900H MS700H MS900B MS900E MS700FA MS700EF MS700A MS500A MS500M/R 00 MS500N MS700B MS500B MS500P MS700C MS700E MS600A MS600B MS700EA Combined Cycle Power Plants. Fundamentals of Gas Turbines 43 /5

44 Air mass flow, kg/sec TIT, C Compressor [6/7] Historical Development of Maximum Air Flows and TITs TIT Air mass flow Combined Cycle Power Plants. Fundamentals of Gas Turbines 44 /5

45 Compressor [7/7] 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 Combined Cycle Power Plants. Fundamentals of Gas Turbines 45 /5

46 Turbine [/6] Developmental Trends 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 0 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 5 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 600C to get higher combined cycle efficiency. It seems that the engines have TIT higher than 600C 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. Combined Cycle Power Plants. Fundamentals of Gas Turbines 46 /5

47 Turbine Inlet Temperature, C Turbine [/6] Turbine Inlet Temperature GE Siemens 50ATS 400 Alstom WH/MHI 7H/9H 50G/70G V84.3A/V94.3A 7FA/9FA 50F/70F V84.3 7F/9F GT4/GT6 GT3E 50D5A/70D 00 7E/9E 7EA/9EC V84./V94. GTN EGT increases with TIT. The HRSG efficiency increases with EGT. Combined Cycle Power Plants. Fundamentals of Gas Turbines 47 /5

48 Turbine [3/6] Advanced Vortex Blades Combined Cycle Power Plants. Fundamentals of Gas Turbines 48 /5

49 Turbine [4/6] Production Technologies Precision Casting Equi-axial material Directional solidification Single crystal Coating Oxidation resistance Corrosion resistance Thermal barrier Heat Resistance Alloy Forging Combined Cycle Power Plants. Fundamentals of Gas Turbines 49 /5

50 Temperature, C Turbine [5/6] Cooling Technologies 500 TBC; Thermal Barrier Coating DS; Directional Solidification SX; Single Crystal Closed-loop Cooling Film Cooling Allowable Gas Temperature Benefits of Cooling 000 U700 IN738 IN939 IN9DS Maximum Material Temperature st Gen. SX nd Gen. SX Combined Cycle Power Plants. Fundamentals of Gas Turbines 50 /5

51 Turbine [6/6] Advanced Seal Systems Combined Cycle Power Plants. Fundamentals of Gas Turbines 5 /5

52 Mechanical Improvement Gas Turbine Steam Turbine Remarks 차유동손실 최소화 배기손실최소화 GT: ) Hot-End Drive Cold End Drive ) TBN: 3 4 stages (large exhaust area) ST: ) Advanced LP exhaust hood ) longer LSB 누설손실최소화 작동압력증가에따라누설제어중요 Brush seal 적용 내열소재 Single Crystal Cooling Technology Ni-alloy Creep 특성향상 Combined Cycle Power Plants. Fundamentals of Gas Turbines 5 /5

53 Fundamentals for Gas Turbines Thermodynamics Combined Cycle Power Plants. Fundamentals of Gas Turbines 53 /5

54 Which Subject? Control System Electrical Engineering Fluid Mechanics Thermodynamics Numerical Analysis Mathematics Manufacturing Engineering Turbomachinery Research Development Design Manufacturing Maintenance Heat Transfer Solid Mechanics Vibration Acoustics Rotor Dynamics Material Science 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. Combined Cycle Power Plants. Fundamentals of Gas Turbines 54 /5

55 . Change of State Heat Engines A Typical Gas Turbine for Power Generation A Typical Steam Turbine for Power Generation 발전설비는가장대표적인열기관 열기관은열에너지를기계적인에너지로변환시키는기계장치 열기관에서의에너지변환은열역학및유체역학을이용분석 ( 발전설비는가장대표적인열유체기계 ) 발전설비의효율극대화를위해극단적인열및유동조건적용 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 Combined Cycle Power Plants. Fundamentals of Gas Turbines 55 /5

56 . Change of State 열역학은일 (work) 과열 (heat) 을다루는과학 일 : 어떤물체를힘을가해서이동시켰을때, 힘과변위의곱으로주어지는물리량 열 : 온도차가존재하는경우에계의경계를넘어서이동하는에너지 일과열은열역학적상태량이아니라물질의에너지상태및열역학적상태량을달라지게하는열역학적인양 (thermodynamic quantities) 으로서일과열은에너지전달이다 일은쉽게열로변환가능 열또한일로변환가능. 그러나열을일로바꾸는것은쉽지않음. 이는일을하기위해서는힘이필요한데열속에는힘의요소가없기때문에열을직접적으로일로바꾸기힘들며, 열을일로변환시키기위해서는반드시열기관필요 열기관은열에너지를이용해서동력을얻는장치로서공기또는증기와같은물질의압력및온도가쉽게변하는성질을이용하여열을일로변환시키는기계적장치 공기나증기와같은물질을작동유체 (working fluid) 라함 즉, 작동유체는계내부를채우고있거나계를통과하여흘러가는유체로서열에너지를저장 ( 보관 ) 할수있는능력을가지고있으며, 이는작동유체의열역학적상태변화를통해서확인가능 따라서열기관을해석하기위해서작동유체의상태변화를이해하는것이매우중요 열기관에서작동유체의상태변화는여러가지과정 (process) 으로나타남 대표적인열역학적상태량 : 온도, 압력, 비체적, 내부에너지, 엔탈피, 엔트로피등 Combined Cycle Power Plants. Fundamentals of Gas Turbines 56 /5

57 . Change of State 작동유체종류에따른터빈분류 Working Fluids Water Steam Combustion Gas Air Hydraulic Turbine Steam Turbine Gas Turbine Wind Turbine Combined Cycle Power Plants. Fundamentals of Gas Turbines 57 /5

58 . Change of State 상 (phase): 기체, 액체, 고체처럼화학적성질과분자식은같지만분자가모여있는구조가다르며, 상질도약간다른모습이존재하는것을말한다. 얼음, 물, 증기의경우분자식은 H O 로같지만얼음의경우분자는가깝게모여있고, 액체인물의경우조금더떨어져있고, 증기의경우에는훨씬더떨어져있다. 상태 (state): 계를구성하는작동유체 (working fluid) 의물리적 화학적특성 상태량 : 물질의존재방식을나타내는양 대표적상태량 : 온도, 압력, 체적, 질량, 밀도등 추상적상태량 : 내부에너지, 엔트로피등 거시적상태량 : 물질이다수의분자로이루어짐에따라이들양의조합에의해물질의상태를나타낼수있을때이들양을거시적상태량이라함 ( 밀도, 온도, 압력등 ) 미시적상태량 : 분자수준의상태로나타낼수있는양 ( 질량, 운동량, 에너지등 ) 상태변화 : 계를구성하는작동유체가열 (heat) 이나일 (work) 에의하여한상태에서다른상태로변화되는것 ( 예 : 계의온도나압력의변화 ) p Combined Cycle Power Plants. Fundamentals of Gas Turbines 58 /5

59 . Change of State 상태량 [Properties] 열역학은에너지 (energy) 와평형 (equilibrium) 을다루는과학 어떤한물질 (substance) 의열역학적상태는에너지를나타낼수있는상태량 (properties) 과평형상태에이르게하는에너지전달에의하여기술 강도성상태량 물질의질량과관계없음 압력, 온도, 밀도, 비체적, 비엔탈피, 비엔트로피, 비내부에너지 열역학에서주로사용하며, 소문자로표시 종량성상태량 물질의질량에정비례하여변함 질량, 체적, 엔탈피, 엔트로피, 내부에너지 대문자로표시 B A C 비체적 (specific volume): 단위질량당체적 ( 종량성상태량인체적을강도성상태량으로나타내기위함 ) = V /m [m 3 /kg] 밀도 (density): 단위체적당질량 = m /V [kg/m 3 ] ( = / ) Combined Cycle Power Plants. Fundamentals of Gas Turbines 59 /5

60 . Change of State 과정 [Process] 과정 (process): 상태가변해가는연속적인경로 (path) 과정종류 : 정압과정, 정적과정, 등온과정, 단열과정, 등엔트로피과정, 폴리트로픽과정 가역과정 (reversible process): 어떤진행된과정을거꾸로진행시켰을경우계및주위가최초상태로되돌려질수있는과정. 마찰손실을수반하지않는과정 ( 유체마찰과열전달이없는경우가역과정이가능하지만유체가흘러가는동안마찰과열전달이필수적으로수반되기때문에가역과정은실질적으로불가능 ) 비가역과정 (irreversible process): 과정이진행되는동안마찰손실을수반하는과정 p p T T s s [ 정압과정 ] [ 정적과정 ] [ 등온과정 ] [ 단열과정 ] Combined Cycle Power Plants. Fundamentals of Gas Turbines 60 /5

61 . Heat and Work Heat Work Work Heat 피스톤운동 p 온도계 W W dx m pa 낙하추 액체 d 교반기 [ 줄의실험장치 ] w w F dx pd [ 밀폐계에서의절대일 ] 줄 (Joule) 은단열용기에물을채운상태에서낙하추를떨어뜨리는실험을통하여다음사항을확인함. kcal = 47 kg f m ( 낙하추일 마찰열 + 유체교란 ) 일 (work) = 힘 거리 일은경로함수 (path function) 불완전미분 ( 미분기호 사용 ) Combined Cycle Power Plants. Fundamentals of Gas Turbines 6 /5

62 . Heat and Work Path Function vs. Point Function 열역학적상태량은상태변화가일어난경로 (path) 에좌우되어그변화량이결정되는상태량이있는반면에경로에는무관하게최초상태와최종상태에의해서만상태변화량이결정되는상태량이있다. 예를들면, 열과일은상태변화가일어난경로에따라상태변화량크기가달라지는경로함수 (path function) 이며, 상태변화량은수학적으로불완전미분을이용해서구해진다. dh h h w w 이에반해서내부에너지의상태변화량크기는상태변화가일어난경로에무관하고최초상태와최종상태에의해서만상태변화량이결정되는점함수 (point function) 이며, 상태변화량은수학적으로완전미분을이용해서구해진다. p a b 열역학에서완전미분에대해서는미분기호 d, 불완전미분에대한미분기호는 를사용한다. 완전미분과불완전미분을통해서구해진상태변화량크기를서로구분하기위하여각각다음과같이표현한다. d Combined Cycle Power Plants. Fundamentals of Gas Turbines 6 /5

63 . Heat and Work 일의방향 There are two types of fluid machines, powerproducing 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. Q in (+) W in () W out (+) System Q out () [ 열과일에대한방향성 ] 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. Combined Cycle Power Plants. Fundamentals of Gas Turbines 63 /5

64 . Heat and Work Heat 열역학적으로평형에도달하는과정에서열은고온체로부터저온체로흘러가며, 열평형에도달한후에열은더이상전달되지않는다. 즉, 열 (heat) 은계와주위또는다른계와의온도차에의하여이동하는에너지로서 Q 로표시. 열에의한에너지전달은다음식으로표현한다. Q mct (or Q mcdt ) 비열 (c) 은단위질량을가지는물질의온도를 상승시키는데필요한열량을의미한다. 한편, 단위질량당전달된열량을나타내기위하여소문자 q' 를사용한다. 열역학적계에서전달된열이없는경우단열 (adiabatic) 이라한다. 열은부호를가지며, 계로유입되는열을양 (+) 의열, 계를빠져나가는열을음 (-) 의열이라한다. 일과마찬가지로열도에너지전달이다. 그러나일이거시적으로조직화된에너지전달인반면에열은미시적으로비조직화된에너지전달이다. 이에대한이해를돕기위하여기체로채워진밀봉된용기를가열하는경우를살펴보기로한다. 이경우열역학적상태량인온도와압력을조사하면비록가해진일이없더라도기체의에너지상태가바뀌었다는것을알수있다. 열역학적개념에서열은이런에너지전달을나타내는것이다. 그러나계가일단평형상태에도달하면에너지가열에의해서전달되었는지아니면일에의해서전달되었는지확인하기어렵다. Combined Cycle Power Plants. Fundamentals of Gas Turbines 64 /5

65 . Heat and Work 열의방향 Fuel in = q in (+) Exhaust gas = q out () Exhaust gas = q out () Fuel in = q in (+) Exhaust gas = q out () Fuel in = q in (+) Combined Cycle Power Plants. Fundamentals of Gas Turbines 65 /5

66 . Heat and Work 열과일의단위 kcal = 물 kg 의온도를 ( ) 상승시키는데필요한열량 Btu = 물 lb m 의온도를 (63 64 ) 상승시키는데필요한열량 kcal = 4.85 kj Btu = 0.5 kcal =.055 kj 일의단위 : J(Joule) = N m ( 일 = 힘 거리 ) 열의단위 : ) 국제단위계 : J ) 공학단위계 : kcal or Btu, 일과열의관계 : kcal = 47 kg f m = 4.85 kj (Joule experiment) Combined Cycle Power Plants. Fundamentals of Gas Turbines 66 /5

67 . Heat and Work 단위계 단위계국제단위계공학단위계단위환산 기본단위 길이 (m) 질량 (kg) 시간 (sec) 길이 (m) 힘 (kg f ) 시간 (sec) 질량 kg kg f s /m 힘 N (Newton) kg f kg f = 9.8 N 압력 Pa (=N/m ) kg f /m kg f /cm = 98,069 Pa 일 ( 에너지 ) J (Joule) kg f m kg f m = 9.8 J 열량 J (Joule) kcal or Btu kcal = 47 kg f m = 4.85 kj Btu = 778 lb f ft =.055 kj 동력 W (Watt) PS PS = 75 kg f m/s = W 대부분의국가에서국제단위계사용 Combined Cycle Power Plants. Fundamentals of Gas Turbines 67 /5

68 3. The First Law of Thermodynamics 열역학제 법칙 = 에너지보존법칙 국제단위계 : Q = W [kj] 공학단위계 : Q = AW [kcal], JQ = W [kg f m] ( kcal = 47 kg f m or Btu = 778 lb f ft) A: 일의열당량 (A = /47 kcal/kg f m) J: 열의일당량 (J = 47 kg f m/kcal) 열역학제법칙에대한표현 : ) 열은에너지의한형태로서일을열로변환시키는것과역으로열을일로변환시키는것이가능 ) 열을일로변환시킬때혹은일을열로변환시킬때에너지총량은변화하지않고일정 3) 에너지를소비하지않고계속해서일을발생시키는기계인제종영구기관을만드는것은불가능 가스터빈에서열과일의변화 ( 국제단위계 ) 754 MJ/s (00%) 7 MJ/s (36.%) 05 MW (7.%) MW = 48 MW (63.9%) 77 MW (Net Output = 36.7%) Combined Cycle Power Plants. Fundamentals of Gas Turbines 68 /5

69 Combined Cycle Power Plants. Fundamentals of Gas Turbines 69 /5 3. The First Law of Thermodynamics c c q w z z q w [ Closed system ] [ Open system ] w de q 계에가해진열량은일부가일로변화되고나머지일부는에너지변환으로나타남 기계공학 ( 열유체기계 ) 계에관계된에너지는내부에너지, 유동에너지, 운동에너지, 위치에너지 PE KE FE u e w z z g c c p p u u q w z z g c c h h q 일반식 : 밀폐계 : 개방계 : w u u q W z z g c c p p u u m Q w PE d KE d FE d du q ) ( ) ( ) ( w c h c h q w h h q w dh q,, w h h q o o (h o : stagnation enthalpy) (If KE is small)

70 3. The First Law of Thermodynamics Flow Energy [ 유동에너지 ] Flow energy (flow work) is the work associated with the masses crossing the control surface. The term p 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, p 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. FE p Adl pdv pmd m pd q c c z z w [ Open system ] Combined Cycle Power Plants. Fundamentals of Gas Turbines 70 /5

71 3. The First Law of Thermodynamics Enthalpy 밀폐계에대한열역학제 법칙 : q du w 밀폐계정압과정에대한일의크기는, w pd p w p 따라서다음과같은관계식성립 q u p u p 피스톤운동 pa W W dx q h h h u p 결론적으로, 밀폐계정압과정에서가열한열량의크기는최종상태와초기상태사이의 (u + p) 상태량변화와같아졌으며, 이를특별한열역학적상태량인엔탈피라한다. 여기서 p 를유동에너지 ( 또는유동일 ) 라고한다. 그러므로엔탈피는내부에너지와유동에너지의합이다. [ 정압가열과정 ] [Exercise.] ) 발전설비에서정압가열이중요한이유를설명하시오. ) 발전설비에서정압가열후가장중요하게취급되는열역학적상태량은무엇인가? Combined Cycle Power Plants. Fundamentals of Gas Turbines 7 /5

72 3. The First Law of Thermodynamics Cycle Cycle: 계를구성하는작동유체가일련의과정을거쳐서최초의상태로다시돌아왔을경우사이클 (cycle) 을이루었다고함 흡입압축연소배기 p 3 p Otto Cycle - Closed System Brayton Cycle - Open System Combined Cycle Power Plants. Fundamentals of Gas Turbines 7 /5

73 3. The First Law of Thermodynamics Cycle Integration 열역학제 법칙은사이클을겪는계에대해서도성립 p 3 Q W 4 q cycle q q q q q q3 q34 q q 4 [ Otto Cycle ] w cycle w w w w w w3 w34 w w 4 p [ Sabathe Cycle ] Combined Cycle Power Plants. Fundamentals of Gas Turbines 73 /5

74 4. 공업일 (Technical Work) 개방계에서의열역학제 법칙과열역학제 기초식을비교하면, q q dh w dh dp p p 다음과같은공업일을구할수있다. w dp 펌프 ( 비압축성유체 ) 인경우 : dp p w p p Combined Cycle Power Plants. Fundamentals of Gas Turbines 74 /5

75 4. 공업일 (Technical Work) 과정 : 흡입과정 일의크기 = p p 과정 : 팽창과정 일의크기 = 면적 ---- 과정 : 배기과정 일의크기 = -p 과정 : 공급압력상승 일의크기 = 0 dp 0 유동가스가한공업일의크기 = dp p p Combined Cycle Power Plants. Fundamentals of Gas Turbines 75 /5

76 4. 공업일 (Technical Work) 절대일 vs. 공업일 p b p p a dp p d 절대일 (absolute work) 공업일 (technical work) 밀폐계에서의일 개방계에서의일 Combined Cycle Power Plants. Fundamentals of Gas Turbines 76 /5

77 4. 공업일 (Technical Work) Brayton Cycle p 3 p 3 p 3 w in w out w sys (a) (b) (c) Combined Cycle Power Plants. Fundamentals of Gas Turbines 77 /5

78 5. Specific Heat [ Exercise. ] Solid materials have one specific heat. However, all gases have two different specific heats. Discuss for this. W W pa dx Q mcdt c q dt q cdt c p q dt p dh dt dh c p dt ( 열역학제 기초식참조 ) c q dt du dt du c dt ( 열역학제 기초식참조 ) c p : Specific heat ratio c 단원자가스 : = 5/3 (=.67) 원자가스 : = 7/5 (=.40) 다원자가스 : = 4/3 (=.33) Combined Cycle Power Plants. Fundamentals of Gas Turbines 78 /5

79 5. Specific Heat Substance J/kgK kcal/kgk Aluminium Beryllium, Cadmium Copper Germanium Gold Iron Lead Silicon Silver Glass Ice (-5C), Wood, Alcohol (ethyl), Mercury Water (5C) 4,86.00 Steam (00C), Specific Heats of Some Substances at 5C and Atmospheric Pressure 물 : 지구상에존재하는물질가운데비열이가장크다. 물이풍부한지방이온화 ; 겨울동안공기 (c p =004.7 J/kgK) 온도가내려감에따라물에서공기로열이전달되기때문에공기온도증가. 미국서해안에는겨울동안에동풍이불기때문에동쪽의육지로따뜻한공기가유입. 따라서미국의경우겨울엔기후가온화한서해안선호. 해변에서공기의순환 한여름더운낮에모래위의차가운공기는물위에있는공기보다더빨리가열. 따뜻해진공기가부력에의해상승하면물위의차가운공기가모래사장쪽으로유입. Combined Cycle Power Plants. Fundamentals of Gas Turbines 79 /5

80 5. Specific Heat 기체의비열은각종엔진의성능을계산하는데필수적으로사용되는매우중요한물리량임. 따라서비열은매우정확하게구해야함 가스터빈엔진에있어서통상적으로다음과같은비열값과비열비가사용 Cold end gas properties: c p = J/kg-K, =.4 Hot end gas properties: c p = 56.9 J/kg-K, =.33 이는 Cold end gas 는공기 ( 원자가스 ) 이며, Hot end gas 는 CO, H O, NOx 등과같은다원자가스이기때문임 그러나이렇게일정한값을가진다고가정하여성능을계산하는경우최대 5% 정도의오차를보이는것으로알려져있음 한편, 비열에대한정확한값을계산하기위해서는연료종류및연소생성물등을고려하여계산해야함 Combined Cycle Power Plants. Fundamentals of Gas Turbines 80 /5

81 5. Specific Heat Specific Heat for Ideal Gases c p c (.4 for air) h u p h u RT 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. h u RT dh dt du dt R c p c R From this equation and the ratio of specific heat, we can get c R c p R Combined Cycle Power Plants. Fundamentals of Gas Turbines 8 /5

82 6. Entropy Entropy = Energy + Tropy Tropy = Transformation (in Greek) 엔트로피 물질의열적상태를나타내는물리량 (865 년 Clausius 가제안 ) 전통적으로엔트로피라는물리량은신비에싸여있음 엔트로피가다른물리량들에비해훨씬덜명확함 이는엔트로피는그절대적인값보다는그변화량에관심을두기때문임 압축과정이나팽창과정에서엔트로피가증가된다는것은열에너지 (thermal energy) 가유용한일 (useful work) 로사용할수없는마찰로손실된다는것을의미 T (hot) q Heat transfer q ds T T (cold) 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. Combined Cycle Power Plants. Fundamentals of Gas Turbines 8 /5

83 6. Entropy Gibbs Equation s s u, (for a simple compressible substance) ds A s u s du B u d A B T q Tds u A s A u B s B q q Tds Tds du pd q du pd (Gibb s equation) (The first law of thermodynamics) s ds s s q Tds ds q T rev Combined Cycle Power Plants. Fundamentals of Gas Turbines 83 /5

84 6. Entropy 정량적계산 From Gibbs equation and first law of thermodynamics, Tds dh dp c pdt ds T dp R p and integrating. This gives s dt T T T T, p st, p c T c T dt T p p Rln T T ref ref p p Entropy is assigned the value zero at the reference state, T ref = 0 K and p ref = atm. The value of entropy at temperature T and pressure p is then calculated from s dt, p Rln Tref T T T p c T p p ref Combined Cycle Power Plants. Fundamentals of Gas Turbines 84 /5

85 6. Entropy Why we need T-s diagram? p w pdv T q Tds q=tds d s ds s s 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. Combined Cycle Power Plants. Fundamentals of Gas Turbines 85 /5

86 6. Entropy T-s diagram Rankine Cycle T T T q sys q in 4 q out 4 4 s s (a) (b) (c) s Combined Cycle Power Plants. Fundamentals of Gas Turbines 86 /5

87 6. Entropy T-s diagram Otto Cycle / Diesel Cycle / Brayton Cycle T 3 T 3 T 3 q in 4 4 q sys 4 q out s s (a) (b) (c) s 과정의 s- 축에대한투영면적이계로공급되거나계를빠져나간열량을나타냄 엔트로피가증가하면계내부로열량공급, 엔트로피가감소하면계외부로열량배출의미 Combined Cycle Power Plants. Fundamentals of Gas Turbines 87 /5

88 p s = const. (adiabatic) 6. Entropy p- and T-s Diagrams p = const. T T = const. adiabatic = const. = const. T = const. p = const. s Combined Cycle Power Plants. Fundamentals of Gas Turbines 88 /5

89 Available energy Useful energy 6. Entropy Isentropic Efficiency & Loss h A p i th = Useful energy Available energy AB : Isentropic expansion line AC : Original expansion line AD : New expansion line due to aging p i : Pressure at the inlet of turbine p o : Pressure at the outlet of turbine ds : Increase of entropy due to the loss B C ds D p o Loss Reduction in useful energy (Performance degradation) Increase in entropy due to aging s Combined Cycle Power Plants. Fundamentals of Gas Turbines 89 /5

90 6. Entropy The Second Law of Thermodynamics q ds T d q T d = entropy increase by heat transfer = entropy increase due to internal irreversibility, such as friction d LW T LW = lost work Friction is ignored in thermodynamics, thus this equation is not used generally. However, isentropic process can be expressed very clearly by this equation. Combined Cycle Power Plants. Fundamentals of Gas Turbines 90 /5

91 Combined Cycle Power Plants. Fundamentals of Gas Turbines 9 /5 T T T T h h h h s s C s s T T T T T h h h h Efficiency of compressor (or pump) Efficiency of turbine Efficiency 6. Entropy T s s 3 4s 4 [ Brayton cycle T-s diagram ]

92 7. Heat Rate 복합발전에서 Heat Rate 를사용하는이유 보일러 (HRSG) 급수펌프에서다양한손실발생 펌프자체효율존재 보일러는보일러배관에서발생하는마찰손실, 외벽을통해빠져나가는열손실, 연도가스통로압력손실, 굴뚝으로빠져나가는열손실, 보일러자체의열전달효율이존재 - 보일러자체효율존재 가스터빈 / 증기터빈에서다양한손실발생 가스터빈 / 증기터빈자체효율존재 복수기손실발생 기계적손실발생 가스터빈 / 증기터빈에서생산된동력이발전기에전달되면서베어링에서기계적손실발생 발전기자체효율 ( 대개 98~99%) 존재 전기적손실및기계적손실 발전소보조기기 ( 오일펌프, 팬등 ) 에사용되는전력존재 실질적으로다양한손실을반영하여정확하게효율을계산하기어려움 Heat rate 는열입력을발전기출력으로나눈값 Heat rate 는열효율과역수관계 Combined Cycle Power Plants. Fundamentals of Gas Turbines 9 /5

93 7. Heat Rate 발전설비열효율은각구성품에서발생하는비가역성으로인하여계산하기어렵다. 따라서열효율대신에열입력을발전기출력으로나누어준열율을많이사용 heat rate heat input [Btu/kWh, generator output or kj/kwh] 열율과열효율관계 : th heat 34.4 rate [Btu/kWh] heat 3600 rate [kj/kwh] kcal = 물 (water) kg 의온도를 C 상승시키는데필요한열량 Btu = 물 (water) lb 의온도를 F 상승시키는데필요한열량 kcal = 47 kg f m = 47 kg 9.8 m/s m = 485 N m = 4.85 kj Btu = kcal / /9 = 0.5 kcal =.055 kj 양변을시간 h 로나누면, Btu/h =.055 kj/3600 s =.055/3600 kw kwh = 3600/.055 Btu = 34.4 Btu 따라서이상적인경우 ( 열효율 00%) 에 kwh 의전기를생산하기위해서는 34.4 Btu 의열량이필요. 그러나실제적으로는다양한손실로인하여 kwh 의전기를생산하기위해서는이상적인경우보다더많은열량이요구. Combined Cycle Power Plants. Fundamentals of Gas Turbines 93 /5

94 7. Heat Rate Net Plant Efficiency 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 /00) (00%AP)/00) [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 9%. Combined Cycle Power Plants. Fundamentals of Gas Turbines 94 /5

95 7. Heat Rate Combustion C + O = CO MJ/kg H + /O = H O(water) MJ/kg (HHV) H + /O = H O(vapor) MJ/kg (LHV) S + O = SO MJ/kg Combined Cycle Power Plants. Fundamentals of Gas Turbines 95 /5

96 7. Heat Rate Heating Value [/] 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 H fg (M H )/00 where, M is fuel moisture % by weight, H fg is water latent heat at reference temperature 5C, H is fuel hydrogen % by weight. The lower heating value of the gas is one in which the H O 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. Combined Cycle Power Plants. Fundamentals of Gas Turbines 96 /5

97 7. Heat Rate Heating Value [/] [Exercise.3] 어떤발전소열효율이 HHV 를기준으로 45% 이다. 이발전소의열효율을 LHV 를기준으로계산하시오. 이발전소에사용하는석탄의 HHV 는 540 Btu/lb 이며, 석탄은 5.% 의수분과 4.83% 의수소를포함하고있다. [Solution] Heat rate 를구하면다음과같다. th,hhv = 34.4/HR HHV = 0.45 HR HHV = 7,58.5 Btu/kWh LHV 를계산한다. LHV = HHV H fg (M H )/00 = ( )/00 = 03.5 Btu/lb LHV/HHV 를계산한다. LHV/HHV = 03.5/540 = 따라서 LHV 를기준했을때 heat rate 는다음과같다. HR LHV = HR HHV = Btu/kWh th,lhv = 34.4/HR LHV = 34.4/775.4 = 46.9% Combined Cycle Power Plants. Fundamentals of Gas Turbines 97 /5

98 8. Cycle Analysis Carnot Cycle 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. p T 3 4 T H 3 q in (+) 4 T L q out () s s s q q 3 Isothermal compressor Isentropic compressor Isothermal turbine Isentropic turbine Combined Cycle Power Plants. Fundamentals of Gas Turbines 98 /5

99 8. Cycle Analysis Carnot Cycle q du w q u u w Process Work Heat Compression at constant temp. w = RT ln( / ) (= w in ) q = w = T (s s ) (= q out ) 3 Adiabatic compression w 3 = (u 3 u ) = c (T 3 T ) (= w in ) q 3 = 0 34 Expansion at constant temp. w 34 = RT 3 ln( 4 / 3 ) (= w out ) q 34 = w 34 = T 3 (s 4 s 3 ) (= q in ) 4 Adiabatic expansion w 4 = u 4 u = c (T 4 T ) (= w out ) q 4 = 0 output Output wsys w w w3 w34 w4 w q sys sys in out th input qin qin qin q q q q out in th, Carnot s s T TL s4 s3 T3 TH T T 3 [Exercise.4] 카르노사이클열효율향상방법두가지를제시하시오. ) ) Combined Cycle Power Plants. Fundamentals of Gas Turbines 99 /5

100 8. Cycle Analysis Rankine Cycle T 3 q B q B a q B w T w P q C 4 s q h h c c gz z w Process Component Heat Work Process Pump q = q P = 0 w = w P = (h h ) Power in (adiabatic compression) 3 Boiler q 3 = q B = h 3 h w 3 = w B = 0 Heat addition at constant pressure 34 Turbine q 34 = q T = 0 w 34 = w T = h 3 h 4 Power out (adiabatic expansion) 4 Condenser q 4 = q C = (h 4 h ) w 4 = w C = 0 Heat release at constant temperature Combined Cycle Power Plants. Fundamentals of Gas Turbines 00 /5

101 8. Cycle Analysis Brayton Cycle p q in 3 T (h) 3 w out q in w in w out w in 4 q out 4 q out q h h c c gz z w s Process Component Heat Work Process Compressor q = q C = 0 w = w C = (h h ) Power in (adiabatic compression) 3 Combustor q 3 = q B = h 3 h w 3 = w B = 0 Heat addition at constant pressure 34 Turbine q 34 = q T = 0 w 34 = w T = h 3 h 4 Power out (adiabatic expansion) 4 Exhaust q 4 = q E = (h 4 h ) w 4 = w E = 0 Heat release at constant pressure Combined Cycle Power Plants. Fundamentals of Gas Turbines 0 /5

102 8. Cycle Analysis h-s Diagram [Mollier Diagram] 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 선도는이상기체와다른성질을가지는실재기체의상태변화를실험을통하여확인하여표와선도로나타낸것이다. h-s 선도는 906 년 R. Mollier 가개발 h를종축, s를횡축으로설정하여증기의상태 (p,, T, x) 를나타낸선도. 증기의상태량 (T, p,, x, h, s) 가운데 개를알면, h-s 선도로부터다른상태량을알수있다. 주로연소기체나수증기를대상으로하기때문에가스터빈및증기터빈의사이클해석에이용된다. 압축수의엔탈피는파악하기어렵다. Combined Cycle Power Plants. Fundamentals of Gas Turbines 0 /5

103 8. Cycle Analysis h-s Diagram [Mollier Diagram] Combined Cycle Power Plants. Fundamentals of Gas Turbines 03 /5

104 8. Cycle Analysis h-s Diagram [Mollier Diagram] T (h) 3 q in w out w in 4 q out s Wilson line [Exercise.5] 작동유체가공기 ( 이상기체 ) 인경우 T-s 선도와 h-s 선도가동일한형상을가지는이유에대해서설명하시오. Combined Cycle Power Plants. Fundamentals of Gas Turbines 04 /5

105 8. Cycle Analysis h-s Diagram [Mollier Diagram] h Turbine efficiency decreases as the entropy increases during expansion process. h = h at 0% Turbine Efficiency 0% 5% 50% h at 5% 75% 00% h at 50% h at 75% h at 00% s Combined Cycle Power Plants. Fundamentals of Gas Turbines 05 /5

106 Pressure 9. Throttling Process 유체가노즐이나오리피스와같이갑자기유로가좁아지는곳을통과하면외부와열량이나일의교환없이도압력이감소하는교축과정 (throttling process) 발생 교축과정이발생하면와류가생성되어에너지가손실되면서압력손실발생 작동유체가액체인경우교축과정이일어나서압력이액체의포화압력보다낮아지면액체의일부가증발하며, 증발에필요한열을액체자신으로부터흡수하기때문에액체온도감소 p Combined Cycle Power Plants. Fundamentals of Gas Turbines 06 /5

107 9. Throttling Process 열역학제 법칙 : q h h c c gz z w 단순유동에서교축과정이일어나면, 벽면에서의열전달이없으며, 이루어진일이나공급된일도없으며, 위치에너지변화량도무시할수있으므로, h h c c 0 속도가 40m/s 이하인경우운동에너지는엔탈피크기에비해매우작다. h h ( 교축과정 = 등엔탈피과정 ) 교축과정은발전설비에서자주일어나는과정인데, 특히증기가밸브를통과할때교축과정이발생하며, 이때압력강하가발생한다. Combined Cycle Power Plants. Fundamentals of Gas Turbines 07 /5

108 9. Throttling Process 증기특성 작동유체가이상기체인경우교축과정이발생한후에엔탈피는일정하게유지됨 엔탈피는온도만의함수이므로교축과정발생후에온도변화없음 그러나작동유체가증기인경우에는교축과정이발생하면압력과온도가떨어져서에너지수준이낮아짐. 주울 - 톰슨효과 (Joule-Thomson effect) 증기터빈버켓커버상부에는증기누설을방지하기위해서 seal 을설치하여증기누설방지 Seal 을통해서누설되는증기는 seal strips 을통과하면서교축과정이발생하기때문에실을빠져나온증기는온도와압력이떨어져서엔탈피가낮아짐 따라서누설증기가다음단에서주유동과합류하더라도주유동의에너지수준을높이지못하기때문에손실발생 누설손실 즉누설증기가실을빠져나오면서에너지를잃지않았다면다음단에서사용할수있지만이미잃어버렸기때문에손실발생 Combined Cycle Power Plants. Fundamentals of Gas Turbines 08 /5

109 9. Throttling Process [Exercise.6] Compare the velocity at 그림에서 A 와 B 는동일한규격의도관이다. 도관 B 에오리피스를설치하였다. 그리고도관 B 입구압력은도관 A 와동일하게유지시킨상태에서질량유량을절반으로줄였다. 그리고이때도관 B 의하류 에서압력을측정하였더니입구압력의절반이었다. 이때오리피스하류 에서유속을비교하시오. A B Combined Cycle Power Plants. Fundamentals of Gas Turbines 09 /5

110 9. Throttling Process [Solution] 문제에서주어진조건은다음과같다. 그리고 m p VA VA B, ma, B, A, B, p B, p A, () 교축과정이일어나면온도는변하지않는다. 따라서이상기체라고가정하면다음관계식이성립한다. p B, B, B, B, 그러므로다음관계식이성립한다. p B, B, and B, A, A,, therefore, () A, B, 유동단면적이일정하기때문에식 () 은다음과같이된다. B,VB, A,VA, (3) 식 () 와식 (3) 을결합하면다음과같은식을얻는다. V V B, A, 따라서질량유량이달라지더라도압력을조절하여하류에서일정한속도를얻을수있다. Combined Cycle Power Plants. Fundamentals of Gas Turbines 0 /5

111 Available Energy 9. Throttling Process Nozzle Row h p 0 p p Bucket Row 5% 00% U 5% load 00% load U 75% load 50% load T 0 p 0 : Inlet pressure p : Throttle pressure Design-flow expansion line Partial-flow expansion line [ Velocity Diagram at Various Loads ] A turbine has different expansion lines as the load is decreased. Expansion lines are essentially parallel 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. p c However, the cycle efficiency is reduced under part load conditions. [ Effect of Throttling on Non-Reheat Steam Turbine Expansion Line ] s Combined Cycle Power Plants. Fundamentals of Gas Turbines /5

112 Power, MW Efficiency, % 9. Throttling Process Comparison of Part Load Efficiency Efficiency Power Load, % [ Steam Turbine] Load, % [ Gas Turbine] Combined Cycle Power Plants. Fundamentals of Gas Turbines /5

113 9. Throttling Process 교축과정적용예 Coal Pipe Arrangement Coal Burners Coal Piping Pulverizers Combined Cycle Power Plants. Fundamentals of Gas Turbines 3 /5