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Exergy-based performance analysis of the heavy-duty gas turbine in part-load operating conditions
Exergy, an International Journal 2 (2002) 105–112 www.exergyonline.com
Exergy-based performance analysis of the heavy-duty gas turbine in part-load operating conditions T.W. Song a , J.L. Sohn a,∗ , J.H. Kim b , T.S. Kim c , S.T. Ro a a School of Mechanical and Aerospace Engineering and Institute of Advanced Machinery and Design, Seoul National University,
Shinlim-Dong, Kwanak-Gu, Seoul, 151-742, South Korea b Turbo and Power Machinery Research Center, Seoul National University, Shinlim-Dong, Kwanak-Gu, Seoul, 151-742, South Korea c Department of Mechanical Engineering, Inha University, Yonghyun-Dong, Nam-Gu, Inchon, 402-751, South Korea
Received 7 July 2001; accepted 30 September 2001
Abstract The present study describes details of exergy-based performance characteristics of a heavy-duty gas turbine, 150MW-class GE 7F model. Results have shown that a chemical reaction in the combustor of which the exergy destruction ratio is 28.3% at full-load is one of the major sources of exergy destructions in the gas turbine. It was found that, in spite of its usefulness to the performance enhancement of the combined cycle plant in part-load operations, the variable inlet guide vane located in front of the multi-stage compressor caused the increase of exergy destruction in the first stage (about 10 times lager than that of other stages below 80% load) and decreased the overall compressor efficiency. Also, it was discovered that the magnitude of exergy destruction by the cooling air in turbine stages is large enough to influence the overall turbine efficiency. The exergy destruction by the cooling air is more than half of the total exergy destruction of each cooled turbine stage. 2002 Éditions scientifiques et médicales Elsevier SAS. All rights reserved.
1. Introduction An exergy-based performance analysis is the performance analysis of a system based on the second law of thermodynamics that overcomes the limit of an energy-based analysis. Exergy is defined as the maximum theoretical useful work obtained as a system interacts with an equilibrium state. Exergy is generally not conserved as energy but destructed in the system. Exergy destruction is the measure of irreversibility that is the source of performance loss. Therefore, an exergy analysis assessing the magnitude of exergy destruction identifies the location, the magnitude and the source of thermodynamic inefficiencies in a thermal system. This provides useful information for improving the overall efficiency and cost effectiveness of a system and/or comparing the performance of the two systems. The application of an exergy-based performance analysis extends from economic analysis by Tsatsaronis and Pisa [1], and the life cycle assessment of power plants by Bombardi [2] to the understanding of the structure in nature as a form of entropy generation minimization by Bejan [3]. * Correspondence and reprints.
E-mail address: [email protected] (J.L. Sohn).
The exergy analysis in gas turbine based power plants was motivated when Tsatsaronis and Pisa [1] referred to the exergy-based overall performance of the cogeneration system. Exergetic efficiency for the total system defined in their study was the only expression of the overall performance of the cogeneration system, whose products are both electricity and heat. Later, the applicability of an exergy-based performance analysis was extended to the thermoeconomic analysis of gas turbine based combined cycle plants as described in Agazzani and Massardo [4]. Also, comparative studies on performances of latest generation gas turbines using the exergy analysis are done by Facchini et al. [5] and Horlock et al. [6]. They show that exergy is the useful concept to compare performances of different gas turbines. Neto and Pilidis [7] showed that exergy destruction was a valuable tool when comparing performances of compressors, combustors and turbines with different pressure ratios and turbine inlet temperatures. They also assessed the impact of different fuels such as dry wood and biomass fuel on the performance of the whole plant, including gas turbines using the exergy method. Recently, as the gas turbine based combined cycle plants have come into wide usage across the world, requirements for the performance optimizations of the plants have differed from location to location. Because
1164-0235/02/$ – see front matter 2002 Éditions scientifiques et médicales Elsevier SAS. All rights reserved. PII: S 1 1 6 4 - 0 2 3 5 ( 0 1 ) 0 0 0 5 0 - 4
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T.W. Song et al. / Exergy, an International Journal 2 (2002) 105–112
Nomenclature E S T W yD ε
gen total turb 0
exergy rate entropy temperature work exergy destruction ratio exergetic efficiency
Superscripts cv D in out p s
Subscripts cooling comb comp fuel
air-cooling combustor compressor fuel supplied in combustor
of the sensitivity of performance variations with different operating conditions, the gas turbine is the major source to controlling the overall performance of the combined plants. Kim [8] conducted performance analyses of widely used heavy-duty gas turbine models in many combined plants in the world and assessed their performances at various operating conditions, including part-load and transient conditions. The present study is to extend his work to evaluate the impact of part-load operating conditions on the performance of each component of the gas turbine and its whole system, using the exergy-based performance analysis.
2. Exergy balance formulations Exergy is composed of physical and chemical parts neglecting kinetic and potential ones as described in Bejan et al. [9]. The physical exergy is the theoretical maximum useful work obtainable as a system passes from its initial state to the thermo-mechanical equilibrium state. On the other hand, the chemical exergy is associated with the departure of the chemical composition of a system from that of its chemical equilibrium state. The chemical exergy plays an important role in chemically reacting processes such as combustion. In this study, the standard atmospheric condition (15 ◦ C, 101.325 kPa with its chemical mole fraction of O2 , N2 , CO2 and H2 O as 20.74%, 78.22%, 0.03% and 1.01%, respectively) was selected as the thermomechanical and chemical equilibrium condition for the exergy analysis. In any control volume at steady state in an adiabatic process, the exergy balance is described as: E˙ in = E˙ out + W˙ cv + E˙ D
generation total turbine reference
(1)
where E˙ in and E˙ out are exergy streams flowing into, and rejected out of the system, respectively. W˙ cv represents the time rate of energy transfer by work other than flow work.
control volume destruction inlet condition outlet condition production supply
E˙ D accounts for the destruction of exergy of the system that is directly related to the entropy generation such as, (2) E˙ D = T0 S˙gen A gas turbine is an engine that produces power by rotating the turbine with the pressurized hot gas. The three main components of a gas turbine are a compressor, combustor and turbine and a typical schematic is shown in Fig. 1 (Eldrid et al. [10]). The working fluid, generally air, is pressurized in the compressor driven by the turbine and its temperature is raised, burned with fuel in the combustor. Expansion of the hot combustion gas then produces a sufficient power output from the turbine, so that it is able to provide a useful output in addition to the power necessary to drive the compressor. Recently, operating characteristics have become more complicated than mentioned the above, because novel techniques for enhancing gas turbine performances have been employed. The two main novel techniques are the turbine blade cooling and variable inlet guide vane (VIGV) control for the flow rate modulation. The turbine blades are often cooled to ensure acceptable metal temperatures at elevated gas temperatures. For this purpose, the relative cool air extracted from the inter- or last stage of the compressor is fed to internal cooling passages within the turbine blades. The multi-stage axial flow compressor used in heavy-duty gas turbines is usually equipped with VIGV for a stable startup and enhancement of exhaust heat recovery at part-load in the combined cycle plant. Fig. 2 shows exergy flows in a typical gas turbine. An exergy stream flows into the compressor from the atmosphere through the compressor inlet. Also, mechanical work, in the same form as exergy, is supplied to the compressor by the shaft connected to the turbine. A portion of exergy supplied to the compressor is destroyed due to irreversibilities in compressor flow paths such as frictional and thermal losses. The remaining exergy flows out from the compressor through two streams; one as the highpressure air to the combustor and the other as bleeding air for turbine blade cooling. A high-pressure air stream
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107
Fig. 1. Schematic of gas turbine engine (GE 7FB, Eldrid et al. [10]).
Fig. 2. Schematic diagram of the exergy flow in a typical gas turbine.
from the compressor delivers exergy into the combustor. Fuel supplied to the combustor is another source of exergy in the combustor. Irreversibility in the combustor, mainly caused by the mixture of air with supplied fuel, and their chemical reactions, is known as the biggest source of exergy destruction in the gas turbine. High pressure, high temperature combustion gas is an exergy stream flowing out from the combustor and flowing into the turbine. The turbine has another incoming exergy stream related to the cold bleed air from the compressor. Shaft power, generated by the expansion of hot gas in the turbine flow path, is the main exergy product of the turbine. The compressor consumes part of this power and the remainder is the net power produced by the whole gas turbine. The exhaust gas stream is another exergy flowing out from the turbine. Exergy in the exhaust gas stream is wasted, unless it is recovered by the heat recovery system connected to the bottom cycle in cogeneration or combined cycle systems. Losses in flow paths in the turbine are the source of turbine irreversibility and exergy destruction in the turbine. There are two important parameters in the exergy analysis: exergetic efficiency and exergy destruction ratio. Exergetic efficiency, often referred to as rational efficiency or
second-law efficiency of a component or a system, is defined as the ratio of exergy production (E˙ p ) to its supply (E˙ s ). Because of exergy destruction, exergy production is always less than its supply. Exergetic efficiency can be applicable to both components (e.g., compressor, combustor and turbine) and systems (e.g., gas turbine). An important use of exergetic efficiency is the assessment of thermodynamic performance of components or systems relative to the performance of similar components or systems. Exergy destruction ratio, defined as normalized exergy destruction by total exergy supply to the overall system, provides another thermodynamic measure of the component inefficiency. Generally, exergy destruction ratio is used for the comparison of dissimilar components operating under similar conditions in the same or different systems. Exergetic efficiencies, exergy destructions and exergy destruction ratios of each component in the gas turbine can be expressed as follows: Compressor Exergetic efficiency εcomp =
p out + E in ˙ cooling − E˙ comp E˙ comp E˙ comp = s E˙ comp W˙ comp
(3)
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Exergy destruction D in out E˙ comp = E˙ comp + W˙ comp − E˙ comp − E˙ cooling
(4)
Exergy destruction ratio D in out − E ˙ cooling + W˙ comp − E˙ comp E˙ comp E˙ comp D ycomp = s = in E˙ E˙ comp + E˙ fuel
(5)
Fuel
(6)
(8)
total
Turbine Exergetic efficiency (9)
Exergy destruction D E˙ turb
in out = E˙ turb + E˙ cooling − E˙ turb − W˙ turb
(10)
Exergy destruction ratio D yturb =
out D E˙ turb E˙ in + E˙ cooling − E˙ turb − W˙ turb = turb s in E˙ E˙ comp + E˙ fuel
3600 150 34.5
13.5 Reverse flow type Methane
419 1260 600
(7)
Exergy destruction ratio
p E˙ turb W˙ turb εturb = s = in out E˙ turb E˙ turb + E˙ cooling − E˙ turb
GE 7F
Turbine (3 stages) Exhaust air flow, kg·s−1 Firing temperature, ◦ C Exit temperature , ◦ C
Exergy destruction
out in E˙ D E˙ comb + E˙ fuel − E˙ comb D ycomb = comb = in E˙ s E˙ comp + E˙ fuel
Speed, rpm Electrical power, MW Cycle efficiency, %
Pressure ratio Combustor
Combustor Exergetic efficiency
D in out E˙ comb = E˙ comb + E˙ fuel − E˙ comb
System
Compressor (18 stages)
total
p out E˙ E˙ comb = εcomb = comb s in E˙ comb + E˙ fuel E˙ comb
Table 1 Design specifications of the GE 7F model
(11)
total
where E˙ cooling and E˙ fuel represent a exergy stream of cooling air and fuel supplied to the combustor, respectively. E˙ total denotes a total exergy stream supplied to a component (or an engine).
with decreased loads, special control strategies must be adopted to minimize performance deterioration during partload operations. In case of the heavy-duty gas turbine in the combined cycle and/or cogeneration plants, turbine exhaust temperature (also, with turbine inlet temperature) is normally controlled to maintain its allowable maximum value to enhance exhaust heat recovery for the bottom cycle. This can be done by controlling compressor inlet airflow using VIGV modulation. If the temperature control is not carried out, turbine inlet and exhaust temperatures gradually decrease with a reduction of fuel-air ratio during the partload operations. With the VIGV modulation, however, the airflow rate can be varied during part-load operation, which avoids the reduction of turbine inlet or exhaust temperature. Prior to the exergy-based performance analysis of the gas turbine, computation of thermodynamic variables such as temperature, enthalpy, pressure and entropy at various stations in the gas turbine is necessary. Such computation can be done by the conventional performance analysis based on energy balance. Energy-based performance analyses of the
3. Exergy-based performance analysis of the heavy-duty gas turbine 3.1. Operational characteristics of a selected heavy-duty gas turbine model A 150MW-class heavy-duty gas turbine, GE 7F model, was selected for the exergy-based performance analysis in this study. This model consists of an 18 stages axial compressor, a reverse flow type combustor, and a 4 stage axial turbine. Detailed performance indices at the design point of this model are described in Table 1. In most gas turbines, in addition to the optimal performance at the design point, the best operating characteristics at various part-load conditions are also important. Since the offdesign performance of the gas turbine decreases rapidly
Fig. 3. Predicted part-load performances of the GE 7FA model by Kim et al. [11].
T.W. Song et al. / Exergy, an International Journal 2 (2002) 105–112
GE 7F model at both on-design and part-load conditions were conducted by Kim [8]. He described that his computational results are 99% accurate compared with specifications in Table 1. Reliability of part-load performance analysis was also checked by Kim et al. [11] compared with experimental data of 61.5 MW-class Siemens V64.3 model at part-load conditions. Fig. 3 shows part-load performances of the GE 7F model predicted by Kim et al. [11]. The GE 7F model adopts VIGV control based on a firing temperature (TRIT: Turbine Rotor Inlet Temperature), instead of a turbine exhaust temperature (TET), maintain its maximum value up to 80% load. Thus, TET increases while the load decreases from the design point up to the 80% load. This is for maximum heat recovery during part-load operation from the design point, to 80% load in the combined cycle plant. Therefore, the part-load operating zone between 100% to 80% loads is referred to as “temperature control zone” in this study. After 80% loads, the variable inlet guide vane is fixed and the temperature is not controlled. Because of the fixed VIGV and constant RPM in load-operating conditions, the air mass flow rate is fixed and the air-fuel ratio is increased. As a result, both TRIT and TET are dropped linearly. This zone has been referred to as “fixed VIGV zone” in this study.
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temperature control zone can also be observed from the increase of the exergy destruction in the same zone in Fig. 5. The exergy destruction of each stage in the compressor in different load conditions is shown in Fig. 6. As expected, due to the increase of irreversibility in the first stage of the compressor by distorted inlet flow angle with VIGV control at the compressor inlet, the amount of exergy destruction in the first stage is significantly larger than that of other stages. Also, the increase of exergy destruction in the first stage of the temperature control zone is much higher than that in the fixed VIGV zone. In conclusion, in spite of the usefulness of VIGV in the heavy-duty gas turbine to maintain maximum TET to enhance total performance of the combined cycle plant, there is a negative influence on the compressor efficiency and, consequently, on the gas turbine efficiency.
3.2. Compressor Computed exergetic and isentropic efficiencies of the compressor are shown in Fig. 4. Exergetic and isentropic efficiencies are 88.0%, 94.4% at full-load, and 81.2%, 91.0% at 80% load, respectively. Both efficiencies show similar behaviors with the change of loads but have a difference of magnitude. Control of VIGV angle in the temperature control zone reduces mass flow rate of the compressor intake air and distorts the inlet flow angle of the first stage rotor of the compressor. This causes the rapid decrease of compressor efficiencies in the temperature control zone. Compressor efficiencies monotonically decrease below 80% load conditions but with a lower slope than above 80% load conditions. Rapid decline of compressor performance in the
Fig. 4. Compressor efficiencies for various load conditions.
Fig. 5. Values of exergy streams and exergy destruction in compressor for various load conditions.
Fig. 6. Exergy destruction in each compressor stage for various load conditions.
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3.3. Combustor The source of irreversibility in both the compressor and turbine is mainly frictional and thermal losses in the flow path and is related to the destruction of physical exergy. On the other hand, the irreversibility and the amount of exergy destruction in the combustor are mainly attributed to a chemical reaction during the combustion process. Since the combustion process in an ideal gas turbine cycle is not an isentropic but isobaric process, isentropic efficiency that can be defined in the compressor and turbine, cannot be used in the combustor. Therefore, exergetic efficiency, exergy destruction, and exergy destruction ratio can be good alternatives to express the combustor performance. Exergetic efficiency of the combustor becomes 77.6% at full-load and its variation during part-load is within less than 2% as shown in Fig. 7. The increase of the exergetic efficiency of the combustor in low load conditions is due to an increase of relative differences between exergy values at the combustor exit and of fuel supplied as shown in Fig. 8. Fig. 9 represents exergy destruction ratio of the combustor.
Exergy destruction ratio is 28.3% at full-load and 41.6% at 0% load and remains its full load value in the temperature control zone. However, it increases with the decrease of load in the fixed VIGV zone because of the deviation of air-fuel ratio from its design point value. It is shown that the exergy destruction ratio is a more reasonable representation for the combustor performance than exergetic efficiency. 3.4. Turbine Both exergetic and the 1st law efficiencies show the same trends with the change of load except for the difference of magnitude as shown in Fig. 10. Exergetic and 1st law efficiencies are 93.3%, 88.9% at full-load, and 86.9%, 81.1% at 0% load, respectively. Here, the terminology of the 1st law efficiency is used instead of isentropic efficiency because it cannot be defined in the air-cooled turbine. Supply of bleed-air from the compressor to the turbine blade rows contributes to the increase of entropy and, therefore, there is no reference to isentropic process in the air-cooled turbine, which is necessary to define its isentropic efficiency. The 1st law efficiency in the air-cooled turbine is defined based on
Fig. 7. Exergetic efficiency of combustor for various load conditions. Fig. 9. Exergy destruction ratio of combustor for various load conditions.
Fig. 8. Values of exergy streams and exergy destruction in combustor for various load conditions.
Fig. 10. Turbine efficiencies for various load conditions.
T.W. Song et al. / Exergy, an International Journal 2 (2002) 105–112
the isentropic enthalpy difference in uncooled blade rows, as discussed in Kim et al. [12]. Both exergetic and the 1st law efficiencies decrease rapidly in low-load operating conditions as expected. One important issue in the performance analysis of the turbine is related to the cooling air bled from the compressor. It contributes to the enhancement of gas turbine performance by the increase of the turbine inlet temperature. On the other hand, mixing of the cooling air with the hot stream around air-cooled turbine blades has a negative impact to the turbine efficiency. As described in Kim [8], 16.8% of compressor intake air is used to cool turbine blades in the GE 7F model at the design point condition. And, 58%, 39% and 3% of the total turbine cooling air is supplied to the first, second and third turbine stages, respectively. The mixture of cooling air with hot stream in the turbine stage can be one important source of irreversibility and, as a result, the generation of exergy destruction as shown in Fig. 11. For example, exergy destructions by cooling air in the first two stages are more than 50% of the total exergy destruction of each stage. Relative amounts of the exergy
Fig. 11. Relative exergy destruction by cooling air in each turbine stage.
Fig. 12. Exergy destruction ratio of each turbine stage for various load conditions.
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destruction of cooling air of the first stage are larger than other stages in high-load operating conditions. However, in low-load operating conditions, that of the second stage is larger than other stages. This may be caused by less amount of cooling air due to the decrease of turbine inlet temperature in low-load conditions. Fig. 12 shows exergy destruction ratio in each turbine stages. Exergy destruction ratios of the first, second and third stages become 2.0%, 1.8% and 0.96% at full-load, respectively. Exergy destruction ratios increase with the decrease of loads. In low-load operating conditions, exergy destruction ratio of the first turbine stage is smaller than other turbine stages. This is caused by the decrease of required cooling air for the first turbine stage with the decrease of turbine inlet temperature in low-load conditions. In conclusion, in spite of its contribution to the increase of turbine inlet temperature, cooling air in the turbine is an important source of exergy destruction in the turbine. 3.5. Gas turbine Fig. 13 shows distributions of exergy destruction ratios of the whole GE 7F gas turbine model along with load change. Exergy destruction ratio of the whole engine becomes 65.2% at full-load. As expected, exergy destruction ratio of the gas turbine increases with a decreased load, which results in a decrease of gas turbine efficiency. Exergy destruction ratio of the combustor is the largest among the three major components of gas turbine and increases in low-load conditions. The chemical reaction between air and fuel in the combustion process is the main source of exergy destruction in the combustor. This is referred to as “unavoidable exergy destruction” by Tsatsaronis [13] in any combustion power plant, which limits the increase of their thermal efficiencies. Exergy destruction ratio in stack has its maximum value in the temperature control zone and is decreased in low-load conditions in the fixed VIGV zone. A decrease of exergy destruction ratio in stack results in the decrease of available energy in the bottom cycle of combined cycle plants.
Fig. 13. Exergy destruction ratio of the GE 7F gas turbine model for various load conditions.
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4. Results and conclusions Exergy-based performance analysis for the gas turbine, GE 7F model, in part-load conditions has been carried out in this study. It is known that exergy is an excellent tool to analyze the cause of performance deterioration in gas turbine components, by investigating behaviors of the exergy-related parameters, such as exergetic efficiency, exergy destruction and exergy destruction ratio in part-load conditions. The performance deterioration of the compressor during part-load operations is related to the increase of exergy destruction caused by VIGV control. In spite of its positive contribution to the performance enhancement of the whole gas turbine, the blade cooling air in the turbine plays an important role in exergy destruction. It is known that the inherently limited thermal efficiency and part-load performance degradation of a gas turbine is mainly attributed to the combustion process from the exergy-based analysis’ point of view. The exergy destruction ratio of the combustor ranges from 28.3% to 41.6% at part-load conditions, which is the largest one among those of the three main components. Acknowledgements This work was supported by the Brain Korea 21 Project. References [1] G. Tsatsaronis, J. Pisa, Exergoeconomic evaluation and optimization of energy systems—application to the CGAM problem, Energy 19 (1944) 287–321.
[2] L. Lombardi, Life cycle assessment and exergetic life cycle assessment of a semi-closed gas turbine cycle with CO2 chemical absorption, Energy Conversion and Management 42 (2001) 101–114. [3] A. Bejan, Shape and Structure, From Engineering to Nature, Cambridge University Press, Cambridge, 2000. [4] A. Agazzani, A.F. Massardo, A tool for thermoeconomic analysis and optimization of gas, steam and combined plants, ASME J. Engrg. Gas Turbines Power 119 (1997) 885–892. [5] B. Facchini, D. Fiaschi, G. Manfrida, Exergy analysis of combined cycles using latest generation gas turbines, ASME J. Engrg. Gas Turbines Power 122 (2000) 233–238. [6] J.H. Horlock, J.B. Young, G. Manfrida, Exergy analysis of modern fossil-fuel power plant, ASME J. Engrg. Gas Turbines Power 122 (2000) 1–7. [7] A.C. Neto, P. Pilidis, On-design and off-design performance analysis of a gas turbine combined cycle using the exergy method, ASME Paper 2000-GT-155 (2000). [8] J.H. Kim, Analysis on transient behavior of gas turbines for power generation, Ph.D. thesis, Seoul National University, Korea, 2000. [9] A. Bejan, G. Tsatsaronis, M. Moran, Thermal Design & Optimization, Wiley, New York, 1996. [10] R. Eldrid, L. Kaufman, P. Marks, The 7FB: The next evolution of the F gas turbine, GER-4194, GE Power Systems (2001). [11] J.H. Kim, T.W. Song, T.S. Kim, S.T. Ro, Model development and simulation of transient behavior of heavy duty gas turbines, ASME J. Engrg. Gas Turbines, Power 123 (2001) 589–594. [12] T.S. Kim, S.T. Ro, The effect of gas turbine coolant modulation on the part load performance of combined cycle plants—Part 1: Gas turbines, in: Proceedings of Institution of Mechanical Engineers (IMechE), Part A, Journal of Power and Energy, Vol. 211, 1997, pp. 443–451. [13] G. Tsatsaronis, Strengths and limitations of exergy analysis, in: A. Bejan, E. Mamut (Eds.), Thermodynamic Optimization of Complex Energy System, Kluwer Academic, Dordrecht, 1999, pp. 93–100.
Exergy-based performance analysis of the heavy-duty gas turbine in part-load operating conditions T.W. Song a , J.L. Sohn a,∗ , J.H. Kim b , T.S. Kim c , S.T. Ro a a School of Mechanical and Aerospace Engineering and Institute of Advanced Machinery and Design, Seoul National University,
Shinlim-Dong, Kwanak-Gu, Seoul, 151-742, South Korea b Turbo and Power Machinery Research Center, Seoul National University, Shinlim-Dong, Kwanak-Gu, Seoul, 151-742, South Korea c Department of Mechanical Engineering, Inha University, Yonghyun-Dong, Nam-Gu, Inchon, 402-751, South Korea
Received 7 July 2001; accepted 30 September 2001
Abstract The present study describes details of exergy-based performance characteristics of a heavy-duty gas turbine, 150MW-class GE 7F model. Results have shown that a chemical reaction in the combustor of which the exergy destruction ratio is 28.3% at full-load is one of the major sources of exergy destructions in the gas turbine. It was found that, in spite of its usefulness to the performance enhancement of the combined cycle plant in part-load operations, the variable inlet guide vane located in front of the multi-stage compressor caused the increase of exergy destruction in the first stage (about 10 times lager than that of other stages below 80% load) and decreased the overall compressor efficiency. Also, it was discovered that the magnitude of exergy destruction by the cooling air in turbine stages is large enough to influence the overall turbine efficiency. The exergy destruction by the cooling air is more than half of the total exergy destruction of each cooled turbine stage. 2002 Éditions scientifiques et médicales Elsevier SAS. All rights reserved.
1. Introduction An exergy-based performance analysis is the performance analysis of a system based on the second law of thermodynamics that overcomes the limit of an energy-based analysis. Exergy is defined as the maximum theoretical useful work obtained as a system interacts with an equilibrium state. Exergy is generally not conserved as energy but destructed in the system. Exergy destruction is the measure of irreversibility that is the source of performance loss. Therefore, an exergy analysis assessing the magnitude of exergy destruction identifies the location, the magnitude and the source of thermodynamic inefficiencies in a thermal system. This provides useful information for improving the overall efficiency and cost effectiveness of a system and/or comparing the performance of the two systems. The application of an exergy-based performance analysis extends from economic analysis by Tsatsaronis and Pisa [1], and the life cycle assessment of power plants by Bombardi [2] to the understanding of the structure in nature as a form of entropy generation minimization by Bejan [3]. * Correspondence and reprints.
E-mail address: [email protected] (J.L. Sohn).
The exergy analysis in gas turbine based power plants was motivated when Tsatsaronis and Pisa [1] referred to the exergy-based overall performance of the cogeneration system. Exergetic efficiency for the total system defined in their study was the only expression of the overall performance of the cogeneration system, whose products are both electricity and heat. Later, the applicability of an exergy-based performance analysis was extended to the thermoeconomic analysis of gas turbine based combined cycle plants as described in Agazzani and Massardo [4]. Also, comparative studies on performances of latest generation gas turbines using the exergy analysis are done by Facchini et al. [5] and Horlock et al. [6]. They show that exergy is the useful concept to compare performances of different gas turbines. Neto and Pilidis [7] showed that exergy destruction was a valuable tool when comparing performances of compressors, combustors and turbines with different pressure ratios and turbine inlet temperatures. They also assessed the impact of different fuels such as dry wood and biomass fuel on the performance of the whole plant, including gas turbines using the exergy method. Recently, as the gas turbine based combined cycle plants have come into wide usage across the world, requirements for the performance optimizations of the plants have differed from location to location. Because
1164-0235/02/$ – see front matter 2002 Éditions scientifiques et médicales Elsevier SAS. All rights reserved. PII: S 1 1 6 4 - 0 2 3 5 ( 0 1 ) 0 0 0 5 0 - 4
106
T.W. Song et al. / Exergy, an International Journal 2 (2002) 105–112
Nomenclature E S T W yD ε
gen total turb 0
exergy rate entropy temperature work exergy destruction ratio exergetic efficiency
Superscripts cv D in out p s
Subscripts cooling comb comp fuel
air-cooling combustor compressor fuel supplied in combustor
of the sensitivity of performance variations with different operating conditions, the gas turbine is the major source to controlling the overall performance of the combined plants. Kim [8] conducted performance analyses of widely used heavy-duty gas turbine models in many combined plants in the world and assessed their performances at various operating conditions, including part-load and transient conditions. The present study is to extend his work to evaluate the impact of part-load operating conditions on the performance of each component of the gas turbine and its whole system, using the exergy-based performance analysis.
2. Exergy balance formulations Exergy is composed of physical and chemical parts neglecting kinetic and potential ones as described in Bejan et al. [9]. The physical exergy is the theoretical maximum useful work obtainable as a system passes from its initial state to the thermo-mechanical equilibrium state. On the other hand, the chemical exergy is associated with the departure of the chemical composition of a system from that of its chemical equilibrium state. The chemical exergy plays an important role in chemically reacting processes such as combustion. In this study, the standard atmospheric condition (15 ◦ C, 101.325 kPa with its chemical mole fraction of O2 , N2 , CO2 and H2 O as 20.74%, 78.22%, 0.03% and 1.01%, respectively) was selected as the thermomechanical and chemical equilibrium condition for the exergy analysis. In any control volume at steady state in an adiabatic process, the exergy balance is described as: E˙ in = E˙ out + W˙ cv + E˙ D
generation total turbine reference
(1)
where E˙ in and E˙ out are exergy streams flowing into, and rejected out of the system, respectively. W˙ cv represents the time rate of energy transfer by work other than flow work.
control volume destruction inlet condition outlet condition production supply
E˙ D accounts for the destruction of exergy of the system that is directly related to the entropy generation such as, (2) E˙ D = T0 S˙gen A gas turbine is an engine that produces power by rotating the turbine with the pressurized hot gas. The three main components of a gas turbine are a compressor, combustor and turbine and a typical schematic is shown in Fig. 1 (Eldrid et al. [10]). The working fluid, generally air, is pressurized in the compressor driven by the turbine and its temperature is raised, burned with fuel in the combustor. Expansion of the hot combustion gas then produces a sufficient power output from the turbine, so that it is able to provide a useful output in addition to the power necessary to drive the compressor. Recently, operating characteristics have become more complicated than mentioned the above, because novel techniques for enhancing gas turbine performances have been employed. The two main novel techniques are the turbine blade cooling and variable inlet guide vane (VIGV) control for the flow rate modulation. The turbine blades are often cooled to ensure acceptable metal temperatures at elevated gas temperatures. For this purpose, the relative cool air extracted from the inter- or last stage of the compressor is fed to internal cooling passages within the turbine blades. The multi-stage axial flow compressor used in heavy-duty gas turbines is usually equipped with VIGV for a stable startup and enhancement of exhaust heat recovery at part-load in the combined cycle plant. Fig. 2 shows exergy flows in a typical gas turbine. An exergy stream flows into the compressor from the atmosphere through the compressor inlet. Also, mechanical work, in the same form as exergy, is supplied to the compressor by the shaft connected to the turbine. A portion of exergy supplied to the compressor is destroyed due to irreversibilities in compressor flow paths such as frictional and thermal losses. The remaining exergy flows out from the compressor through two streams; one as the highpressure air to the combustor and the other as bleeding air for turbine blade cooling. A high-pressure air stream
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Fig. 1. Schematic of gas turbine engine (GE 7FB, Eldrid et al. [10]).
Fig. 2. Schematic diagram of the exergy flow in a typical gas turbine.
from the compressor delivers exergy into the combustor. Fuel supplied to the combustor is another source of exergy in the combustor. Irreversibility in the combustor, mainly caused by the mixture of air with supplied fuel, and their chemical reactions, is known as the biggest source of exergy destruction in the gas turbine. High pressure, high temperature combustion gas is an exergy stream flowing out from the combustor and flowing into the turbine. The turbine has another incoming exergy stream related to the cold bleed air from the compressor. Shaft power, generated by the expansion of hot gas in the turbine flow path, is the main exergy product of the turbine. The compressor consumes part of this power and the remainder is the net power produced by the whole gas turbine. The exhaust gas stream is another exergy flowing out from the turbine. Exergy in the exhaust gas stream is wasted, unless it is recovered by the heat recovery system connected to the bottom cycle in cogeneration or combined cycle systems. Losses in flow paths in the turbine are the source of turbine irreversibility and exergy destruction in the turbine. There are two important parameters in the exergy analysis: exergetic efficiency and exergy destruction ratio. Exergetic efficiency, often referred to as rational efficiency or
second-law efficiency of a component or a system, is defined as the ratio of exergy production (E˙ p ) to its supply (E˙ s ). Because of exergy destruction, exergy production is always less than its supply. Exergetic efficiency can be applicable to both components (e.g., compressor, combustor and turbine) and systems (e.g., gas turbine). An important use of exergetic efficiency is the assessment of thermodynamic performance of components or systems relative to the performance of similar components or systems. Exergy destruction ratio, defined as normalized exergy destruction by total exergy supply to the overall system, provides another thermodynamic measure of the component inefficiency. Generally, exergy destruction ratio is used for the comparison of dissimilar components operating under similar conditions in the same or different systems. Exergetic efficiencies, exergy destructions and exergy destruction ratios of each component in the gas turbine can be expressed as follows: Compressor Exergetic efficiency εcomp =
p out + E in ˙ cooling − E˙ comp E˙ comp E˙ comp = s E˙ comp W˙ comp
(3)
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Exergy destruction D in out E˙ comp = E˙ comp + W˙ comp − E˙ comp − E˙ cooling
(4)
Exergy destruction ratio D in out − E ˙ cooling + W˙ comp − E˙ comp E˙ comp E˙ comp D ycomp = s = in E˙ E˙ comp + E˙ fuel
(5)
Fuel
(6)
(8)
total
Turbine Exergetic efficiency (9)
Exergy destruction D E˙ turb
in out = E˙ turb + E˙ cooling − E˙ turb − W˙ turb
(10)
Exergy destruction ratio D yturb =
out D E˙ turb E˙ in + E˙ cooling − E˙ turb − W˙ turb = turb s in E˙ E˙ comp + E˙ fuel
3600 150 34.5
13.5 Reverse flow type Methane
419 1260 600
(7)
Exergy destruction ratio
p E˙ turb W˙ turb εturb = s = in out E˙ turb E˙ turb + E˙ cooling − E˙ turb
GE 7F
Turbine (3 stages) Exhaust air flow, kg·s−1 Firing temperature, ◦ C Exit temperature , ◦ C
Exergy destruction
out in E˙ D E˙ comb + E˙ fuel − E˙ comb D ycomb = comb = in E˙ s E˙ comp + E˙ fuel
Speed, rpm Electrical power, MW Cycle efficiency, %
Pressure ratio Combustor
Combustor Exergetic efficiency
D in out E˙ comb = E˙ comb + E˙ fuel − E˙ comb
System
Compressor (18 stages)
total
p out E˙ E˙ comb = εcomb = comb s in E˙ comb + E˙ fuel E˙ comb
Table 1 Design specifications of the GE 7F model
(11)
total
where E˙ cooling and E˙ fuel represent a exergy stream of cooling air and fuel supplied to the combustor, respectively. E˙ total denotes a total exergy stream supplied to a component (or an engine).
with decreased loads, special control strategies must be adopted to minimize performance deterioration during partload operations. In case of the heavy-duty gas turbine in the combined cycle and/or cogeneration plants, turbine exhaust temperature (also, with turbine inlet temperature) is normally controlled to maintain its allowable maximum value to enhance exhaust heat recovery for the bottom cycle. This can be done by controlling compressor inlet airflow using VIGV modulation. If the temperature control is not carried out, turbine inlet and exhaust temperatures gradually decrease with a reduction of fuel-air ratio during the partload operations. With the VIGV modulation, however, the airflow rate can be varied during part-load operation, which avoids the reduction of turbine inlet or exhaust temperature. Prior to the exergy-based performance analysis of the gas turbine, computation of thermodynamic variables such as temperature, enthalpy, pressure and entropy at various stations in the gas turbine is necessary. Such computation can be done by the conventional performance analysis based on energy balance. Energy-based performance analyses of the
3. Exergy-based performance analysis of the heavy-duty gas turbine 3.1. Operational characteristics of a selected heavy-duty gas turbine model A 150MW-class heavy-duty gas turbine, GE 7F model, was selected for the exergy-based performance analysis in this study. This model consists of an 18 stages axial compressor, a reverse flow type combustor, and a 4 stage axial turbine. Detailed performance indices at the design point of this model are described in Table 1. In most gas turbines, in addition to the optimal performance at the design point, the best operating characteristics at various part-load conditions are also important. Since the offdesign performance of the gas turbine decreases rapidly
Fig. 3. Predicted part-load performances of the GE 7FA model by Kim et al. [11].
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GE 7F model at both on-design and part-load conditions were conducted by Kim [8]. He described that his computational results are 99% accurate compared with specifications in Table 1. Reliability of part-load performance analysis was also checked by Kim et al. [11] compared with experimental data of 61.5 MW-class Siemens V64.3 model at part-load conditions. Fig. 3 shows part-load performances of the GE 7F model predicted by Kim et al. [11]. The GE 7F model adopts VIGV control based on a firing temperature (TRIT: Turbine Rotor Inlet Temperature), instead of a turbine exhaust temperature (TET), maintain its maximum value up to 80% load. Thus, TET increases while the load decreases from the design point up to the 80% load. This is for maximum heat recovery during part-load operation from the design point, to 80% load in the combined cycle plant. Therefore, the part-load operating zone between 100% to 80% loads is referred to as “temperature control zone” in this study. After 80% loads, the variable inlet guide vane is fixed and the temperature is not controlled. Because of the fixed VIGV and constant RPM in load-operating conditions, the air mass flow rate is fixed and the air-fuel ratio is increased. As a result, both TRIT and TET are dropped linearly. This zone has been referred to as “fixed VIGV zone” in this study.
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temperature control zone can also be observed from the increase of the exergy destruction in the same zone in Fig. 5. The exergy destruction of each stage in the compressor in different load conditions is shown in Fig. 6. As expected, due to the increase of irreversibility in the first stage of the compressor by distorted inlet flow angle with VIGV control at the compressor inlet, the amount of exergy destruction in the first stage is significantly larger than that of other stages. Also, the increase of exergy destruction in the first stage of the temperature control zone is much higher than that in the fixed VIGV zone. In conclusion, in spite of the usefulness of VIGV in the heavy-duty gas turbine to maintain maximum TET to enhance total performance of the combined cycle plant, there is a negative influence on the compressor efficiency and, consequently, on the gas turbine efficiency.
3.2. Compressor Computed exergetic and isentropic efficiencies of the compressor are shown in Fig. 4. Exergetic and isentropic efficiencies are 88.0%, 94.4% at full-load, and 81.2%, 91.0% at 80% load, respectively. Both efficiencies show similar behaviors with the change of loads but have a difference of magnitude. Control of VIGV angle in the temperature control zone reduces mass flow rate of the compressor intake air and distorts the inlet flow angle of the first stage rotor of the compressor. This causes the rapid decrease of compressor efficiencies in the temperature control zone. Compressor efficiencies monotonically decrease below 80% load conditions but with a lower slope than above 80% load conditions. Rapid decline of compressor performance in the
Fig. 4. Compressor efficiencies for various load conditions.
Fig. 5. Values of exergy streams and exergy destruction in compressor for various load conditions.
Fig. 6. Exergy destruction in each compressor stage for various load conditions.
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3.3. Combustor The source of irreversibility in both the compressor and turbine is mainly frictional and thermal losses in the flow path and is related to the destruction of physical exergy. On the other hand, the irreversibility and the amount of exergy destruction in the combustor are mainly attributed to a chemical reaction during the combustion process. Since the combustion process in an ideal gas turbine cycle is not an isentropic but isobaric process, isentropic efficiency that can be defined in the compressor and turbine, cannot be used in the combustor. Therefore, exergetic efficiency, exergy destruction, and exergy destruction ratio can be good alternatives to express the combustor performance. Exergetic efficiency of the combustor becomes 77.6% at full-load and its variation during part-load is within less than 2% as shown in Fig. 7. The increase of the exergetic efficiency of the combustor in low load conditions is due to an increase of relative differences between exergy values at the combustor exit and of fuel supplied as shown in Fig. 8. Fig. 9 represents exergy destruction ratio of the combustor.
Exergy destruction ratio is 28.3% at full-load and 41.6% at 0% load and remains its full load value in the temperature control zone. However, it increases with the decrease of load in the fixed VIGV zone because of the deviation of air-fuel ratio from its design point value. It is shown that the exergy destruction ratio is a more reasonable representation for the combustor performance than exergetic efficiency. 3.4. Turbine Both exergetic and the 1st law efficiencies show the same trends with the change of load except for the difference of magnitude as shown in Fig. 10. Exergetic and 1st law efficiencies are 93.3%, 88.9% at full-load, and 86.9%, 81.1% at 0% load, respectively. Here, the terminology of the 1st law efficiency is used instead of isentropic efficiency because it cannot be defined in the air-cooled turbine. Supply of bleed-air from the compressor to the turbine blade rows contributes to the increase of entropy and, therefore, there is no reference to isentropic process in the air-cooled turbine, which is necessary to define its isentropic efficiency. The 1st law efficiency in the air-cooled turbine is defined based on
Fig. 7. Exergetic efficiency of combustor for various load conditions. Fig. 9. Exergy destruction ratio of combustor for various load conditions.
Fig. 8. Values of exergy streams and exergy destruction in combustor for various load conditions.
Fig. 10. Turbine efficiencies for various load conditions.
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the isentropic enthalpy difference in uncooled blade rows, as discussed in Kim et al. [12]. Both exergetic and the 1st law efficiencies decrease rapidly in low-load operating conditions as expected. One important issue in the performance analysis of the turbine is related to the cooling air bled from the compressor. It contributes to the enhancement of gas turbine performance by the increase of the turbine inlet temperature. On the other hand, mixing of the cooling air with the hot stream around air-cooled turbine blades has a negative impact to the turbine efficiency. As described in Kim [8], 16.8% of compressor intake air is used to cool turbine blades in the GE 7F model at the design point condition. And, 58%, 39% and 3% of the total turbine cooling air is supplied to the first, second and third turbine stages, respectively. The mixture of cooling air with hot stream in the turbine stage can be one important source of irreversibility and, as a result, the generation of exergy destruction as shown in Fig. 11. For example, exergy destructions by cooling air in the first two stages are more than 50% of the total exergy destruction of each stage. Relative amounts of the exergy
Fig. 11. Relative exergy destruction by cooling air in each turbine stage.
Fig. 12. Exergy destruction ratio of each turbine stage for various load conditions.
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destruction of cooling air of the first stage are larger than other stages in high-load operating conditions. However, in low-load operating conditions, that of the second stage is larger than other stages. This may be caused by less amount of cooling air due to the decrease of turbine inlet temperature in low-load conditions. Fig. 12 shows exergy destruction ratio in each turbine stages. Exergy destruction ratios of the first, second and third stages become 2.0%, 1.8% and 0.96% at full-load, respectively. Exergy destruction ratios increase with the decrease of loads. In low-load operating conditions, exergy destruction ratio of the first turbine stage is smaller than other turbine stages. This is caused by the decrease of required cooling air for the first turbine stage with the decrease of turbine inlet temperature in low-load conditions. In conclusion, in spite of its contribution to the increase of turbine inlet temperature, cooling air in the turbine is an important source of exergy destruction in the turbine. 3.5. Gas turbine Fig. 13 shows distributions of exergy destruction ratios of the whole GE 7F gas turbine model along with load change. Exergy destruction ratio of the whole engine becomes 65.2% at full-load. As expected, exergy destruction ratio of the gas turbine increases with a decreased load, which results in a decrease of gas turbine efficiency. Exergy destruction ratio of the combustor is the largest among the three major components of gas turbine and increases in low-load conditions. The chemical reaction between air and fuel in the combustion process is the main source of exergy destruction in the combustor. This is referred to as “unavoidable exergy destruction” by Tsatsaronis [13] in any combustion power plant, which limits the increase of their thermal efficiencies. Exergy destruction ratio in stack has its maximum value in the temperature control zone and is decreased in low-load conditions in the fixed VIGV zone. A decrease of exergy destruction ratio in stack results in the decrease of available energy in the bottom cycle of combined cycle plants.
Fig. 13. Exergy destruction ratio of the GE 7F gas turbine model for various load conditions.
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4. Results and conclusions Exergy-based performance analysis for the gas turbine, GE 7F model, in part-load conditions has been carried out in this study. It is known that exergy is an excellent tool to analyze the cause of performance deterioration in gas turbine components, by investigating behaviors of the exergy-related parameters, such as exergetic efficiency, exergy destruction and exergy destruction ratio in part-load conditions. The performance deterioration of the compressor during part-load operations is related to the increase of exergy destruction caused by VIGV control. In spite of its positive contribution to the performance enhancement of the whole gas turbine, the blade cooling air in the turbine plays an important role in exergy destruction. It is known that the inherently limited thermal efficiency and part-load performance degradation of a gas turbine is mainly attributed to the combustion process from the exergy-based analysis’ point of view. The exergy destruction ratio of the combustor ranges from 28.3% to 41.6% at part-load conditions, which is the largest one among those of the three main components. Acknowledgements This work was supported by the Brain Korea 21 Project. References [1] G. Tsatsaronis, J. Pisa, Exergoeconomic evaluation and optimization of energy systems—application to the CGAM problem, Energy 19 (1944) 287–321.
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