Evaporative gas turbine cycles. A thermodynamic evaluation ...
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Department of Heat and Power Engineering Evaporative gas turbine cycles- A thermodynamic evaluation of their potential by Per Rosin MASTER ismm#N if ms bocmmt is wmnts FWBH SALES PltlUfTEI
Transcript of Evaporative gas turbine cycles. A thermodynamic evaluation ...
Department of Heat and Power Engineering
Evaporative gas turbine cycles-
A thermodynamic evaluation of their potential
by Per Rosin
MASTERismm#N if ms bocmmt is wmnts
FWBH SALES PltlUfTEI
DO
KU
MEN
TOA
TAB
LAO
enlig
t SIS
62 1
0 12
Dokumentutgivere HJ/LTH
Inst f6r Varme- och kraftteknikHendliggare
FOriettere
Rosdn, Per M.
Dokumentnamn Ookumentbeteckning
Rapport ISRN LUTMDN/TMVK-7010-SEUtgivnlngsdatum Arendebetecknlng
Mars 1993
Dokumenxtitel och undertitolEvaporative gas turbine cycles- A thermodynamic evaluation of their potetial
Relerat (semmandrag)The report presents a systematic method of thermodynamically evaluating different gas turbine cycles, treating the working fluids as ideal gases (cp = cp(T)). All models used to simulate different components in the cycles are presented in the report in detail and then connected in a computer program fully developed by the author.
The report focuses on the theme of evaporative gas turbine cycles, in which low level heat is used to evaporate water into the compressed air stream between the compressor and recuperator. This leads to efficiency levels close to a comparable combined cycle but without the steam bottoming cycle!
A parametric analysis has been conducted with the aim of deciding the best configuration of an evaporative cycle both for an uncooled expander and for a cooled expander. The model proposed to simulate the cooled expander is a combination between two existing models.
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evaporation, humidification, gas turbine, intercooler, aftercooler, recuperator, economiser, air-cooled expander, humid air turbine cycle, HAT, steam injection
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Department of Heat and Power Engineering Summary
Summary
This thesis presents a systematic method of thermodynamically evaluating different gas turbine cycles, treating the working fluids as ideal gases (c= c_(D). To decide the thermodynamic properties of all constituents of the working fluids polynomials, a description of the thermodynamic of each constituent is made. The polynomials have their origin in works done by NASA.
The report focuses on the theme of evaporative gas turbine cycles, in which low level heat is used to evaporate water into the compressed air stream between the compressor and recuperator. Water is brought into contact with the compressed air stream in a counter flow act, in a humidification tower, causing water to be evaporated into the air. The outlet humidified air temperature of the tower will decrease drastically. At the same time the gas flow will increase due to the water addition. As the mass flow through the expander will be 20-30% larger than through the compressor, the specific work output from evaporative gas turbine cycles also rises greatly. The low temperature after the humidification tower makes it possible to reuse a large amount of low level heat at the expander outlet, by means of a recuperator. Because the gas temperature after the humidification tower can always be kept low, the recuperator can reuse a very large amount of low level heat from exhaust gas at the expander outlet, causing the thermal efficiency of the cycles to rise drastically.
A parametric analysis has been conducted with the aim of deciding the best configuration of an evaporative gas turbine cycle both for an uncooled expander and an air-cooled expander. The analysis shows that efficiency levels of approximately 55% are reachable, using the best configurations ( Natural gas as fuel), for a cooled expander. More advanced evaporative gas turbine cycles reach their efficiency optima at pressure ratios around 15-20, then flattens out. The specific work output, however, rises with the pressure ratio increase in the whole pressure ratio area investigatedf 5<P2/Pi<35).
The model proposed to simulate the cooled expander is a combination of two existing models. It tries to evaluate the gains due to lower temperature and higher specific heat of the cooling air, when extracting the cooling air after the humidification tower, but before the recuperator.
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Table of contents LUND INSTITUTE OF TECHNOLOGY
Table of contents
Summary......................................................................................................................................................... i
Table of contents............................................................................................................................................ ii
Nomenclature.................................................................................................................................................iv
1. Introduction................................................................................................................................................. 1
1.1. Background................................................................................................................................ 1
1.2. Objectives................................................................................................................................... 4
1.3. Method and resources............................................................................................................... 4
1.4. Limitations................................................................................................................................ 5
1.5. Organisation of the report.............................................................................. .......................... 5
1.6. Acknowledgements.................................................................................................................. 5
2. The compressor system...............................................................................................................................6
2.1. The low pressure compressor.....................................................................................................7
2.2. The intercooler......................................................... ................................................................ 8
2.3. The high pressure compressor.................................................................................................. 9
3. The humidification system......................................................................................................................... 11
3.1. The aftercooler...........................................................................................................................11
3.2. The humidification tower..........................................................................................................12
3.3. The pump for circulating water................................................................................................ 14
4. The combustion chamber............................................................................................................................16
5. The expander...............................................................................................................................................19
5.1. An uncooled expander...............................................................................................................20
5.2. A simple thermodynamic model of an air-cooled expander.....................................................21
5.3. An advanced thermodynamic model of an air-cooled expander.............................................. 24
6. Heat-exchangers in the heat recovery boiler..............................................................................................26
6.1. The recuperator......................................................................................................................... 26
62. The economiser......................................................................................................................... 28
6.3. The heat exchanger for district heating.................................................................................... 29
7. Results of some cycle simulations..............................................................................................................31
7.1. One Heat-Exchanger Water Systems....................................................................................... 32
7.1.1. Uncooled Expander..................................................................................................32
7.1.2. Air-Cooled Expander...............................................................................................33
12. Two Heat-Exchanger Water Systems....................................................................................... 34
7.2.1. Uncooled Expander..................................................................................................35
1.22. Air-Cooled Expander...............................................................................................36
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Department of Heat and Power Engineering Table of contents
73. Three Heat-Exchanger Water Systems...................................................................................... 39
7.3.1. Uncooled Expander...................................................................................................40
7.3.2. Air-Cooled Expander....................................... 41
8. Conclusions................................................................................................................................................. 42
9. References.................................................................. 43
Appendix.........................................................................................................................................................49
Appendix A: Thermodynamic Properties of a mixture of ideal gases....... .,...................................49
Appendix B: Thermodynamically based calculation models of the compressor andthe expander.............................................................................................. 51
Conventional thermodynamic simulation model of a compression and anexpansion............................................................................................................................. 52
Otto Zweifels' thermodynamic simulation model of a compression and anexpansion............................................................................................................................. 53
Appendix C: Inputs for systems with an uncooled expander...........................................................55
Appendix D: Inputs for systems with a cooled expander.................................................................57
m
Nomenclature Lund Institute of technology
Nomenclature
Figure 1. An advanced evaporative gas turbine cycle with all subscripts and flows defined as they are used in the report.
Main variablesA Surface area [m2]
a Specific work or specific surface area [J/kgAir]or[m2/kgEx]
c Specific heat capacity [J/kgK]
h Enthalpy [J/kg]
H Heat Value [J/lcg]
M Molar weight [kg/kmole]
m Mass flow per unit compressed air [kg/kgAir]
m Mass flow (kg/s]
n Poly tropic exponent [-]ills] Mole property of substance sin a gas mixture [kmole sub/kmole mix]
P Pressure [N/m2]
PP "Pinch Point", minimum allowed temperature difference in a heat-exchanger IK]R Gas constant [J/kgK]
s Entropy [J/kgK]
Is) Substance HT Temperature PC]V Specific volume [m3/lcg]
IV
Department of Heat and Power Engineering Nomenclature
W Mass flow of water per unit dry air [kg L^O/kgDryAir]
x Mass flow of water per unit water evaporated [kg HjO/kgEvHjO]
[z] Stage in expander [-]
Greek lettersAh Enthalpy difference P/kg]
Ap Dimensionless pressure drop (-]
As Entropy difference [J/kgK]
k Isentrope coefficient - I'l
T| Efficiency H
4 Relative humidity H
to Absolute humidity [kg HgO/kgDtyAir]
Subscriptsa Dry air or available cooling flow
AC Aftercooler
bl All blades in a stage ( Both rotor and stator)
c Cooling air or compression
oa Available cooling air
CC Combustion Chamber
c.i Injected cooling air
Circ Circulating water
DH District heating
e Expansion
E Expander
Eco Economiser
Ev Evaporator ( Humidification tower)
el Electric
f Fuel
HC High pressure compressor
i Injected or integrated
IC Intercooler
io From inside a control volume to outride
k Condense
LC Low pressure compressor
mec Mechanical
mtrl Material
oi From outside a control volume to inside
p Water circulation pump or an isobaric state of change
r Specific heat of evaporation
s Isentrope state of change
sat Sanitated conditions
T Isothermal state of change
t Theoretical
U Universal
v Vapour or an isoschore state of change
V
Lund Institute of Technology
w Water
0 Ambient conditions
la Condition between surge pipe and low pressure compressor
lb Condition between intercooler and high pressure compressor
2 Condition between humidification tower and recuperator
2a Condition between low pressure condition and intercooler
2b Condition between high pressure compressor and aftercooler
2c Condition between aftercooler and humidification tower
3 Condition between recuperator and combustion chamber
4 Condition between combustion chamber and expander
5 Condition between expander and surge pipe
6 Condition between surge pipe and recuperator
7 Condition between recuperator and economiser
8 Condition between economiser and heat-exchanger for district heating
9 Condition at outlet of the heat-exchanger for district heating
w.O Water inlet condition to cycle
w.l Water outlet condition of the circulation pump
w.lb Water inlet condition of the intercooler
w.2 Water outlet condition of the humidification tower
w.2a Water outlet condition of the intercooler
w.2b Water outlet condition of the aftercooler
w2c Water inlet condition of tire aftercooler
w.3 Water inlet condition of the humidification tower
w.7 Water outlet condition of the economiser
w.8 Water inlet condition of the economiser
Department of Heat and Power Engineering Introduction
1. Introduction
1.1. Background
In the late 15th century, the first gas turbine expander ever described in literature was Leonard! da Vincis' automatic steak turner [53]. It used some of the impulse energy stored in the heated exhaust gas to rotate the steak.
The second notation in literature was in the year 1791, when the inventor John Barber obtained an English patent on an idea of a heat machine which had the three major components ( compressor, combustion chamber and expander). Today this is called an open gas turbine cycle [53].
However, all efforts to construct a gas turbine failed and great progress had still to be made in other areas, such as material science and production methods, before the ground was laid to engineer a functional gas turbine. During the last decades of the 19th century, numerous attempts to build a gas turbine were made by many inventors and engineers.
It took until 1903 before the Norwegian engineer vEgidius Elling managed to build a gas turbine that had a positive work output [51, 52]. The gas turbine produced only pressurised air. The air was diverted from the compressed air stream between the compressor and the combustion chamber. The partly vaporised water that was used to cool the combustion chamber, was then injected into the heated exhaust gas flow to lower the temperature down to the permissible levels of the expander and at the same time increasing the work output of the expander (Fig.2).
Figure 2. The Norwegian engineer /Egidius Elling’s gas turbine from 1903.
After this machine, he focused on the compressor, which functioned poorly and was one of the major problems of the gas turbine cycle. In his struggle to make more efficient compressors, he used injections of water between the compressor stages as intercoolers to decrease the compressed air temperature and thereby reduced the work needed and at the same time raised the mass flow through the compressor with evaporated water. It is noteworthy that he used the same physical phenomena to decrease the work of the compressor as in evaporative gas turbine cycles which is discussed further in this report.
This, and other contemporary pioneer works in the gas turbine field, did not result in a massive introduction of gas turbines as power producers. Up to that time steam engines and steam turbines were superior as prime movers in the early 20th century.
Elling used steam injection to compensate for his poorly functioning compressor, but in year 1939 in Neuchatel, Switzerland, the world’s first industrial gas turbine set was running. It was a simple open gas turbine cycle, consisting of a compressor, a combustion chamber, an expander and a generator which produced a maximum work output of 4 MW at an efficiency of 17.4% ( Air inlet condition 20*C and 1 atm)[59]. It was Aurel Stodola [102], one of the most distinguished engineers in the field of thermal machines who supervised the acceptance tests of the power plant
This event started a rapid development process leading to more and more advanced gas turbine settings to increase the efficiency and work output of industrial gas turbines. Intercoolers,
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Introduction Lund Institute of Technology
recuperators, reheat, steam injection and multi-axial machines were built to reach new heights concerning thermal efficiency, work output and part load performance.
Parallel with the industrial gas turbine development, the air plane industry recognised the potential of the gas turbine for propulsion. The frames and goals which existed in developing gas turbines for propulsion were different from those connected with industrial gas turbine development. As lightness and compactness are extremely vital in air-propulsion, the air plane industry stuck to the simple open gas turbine cycle. This narrow frame submitted the development of gas turbine for the propulsion of air planes when trying to raise pressure ratios, temperature ratios and efficiencies of both compressor and expander aiming to increase thermal efficiency and work output
A great amount of effort was put into the development of gas turbines for propulsion, largely because of the interest submitted from the military industry. This led to such a high standard of efficiency and work output that it was impossible to justify any other solution than the simple open gas turbine cycle, even concerning industrial gas turbine sets. If there is a need to boost the efficiency of an industrial gas turbine today, it is combined with a steam turbine cycle as a bottoming cycle [92]( Fig.3).
tSieom Turbine Cycle
\boiler
Figure 3. Combined cycle consisting of a gas turbine topping cycle connected with a steam bottoming cycle.
The steam bottoming cycle utilises the low level heat at expander outlet in a heat recovery boiler, thus raising the overall efficiency and work output. A steam bottoming cycle is, however, a rather expensive way utilising the waist heat of a gas turbine plant. In a combined cycle power plant, approximately 2/3 of the total work output comes from the gas turbine and only 1/3 from the steam turbine, but the cost of the gas turbine is only approximately 1/3 of the total plant cost The remaining 2/3 comes from the steam bottoming cycle [83]. Therefore, it would be rather interesting to eliminate the steam bottoming cycle and instead try to reuse the waste heat from the gas turbine cycle. This would eliminate the steam turbine with its connecting generator, some of the heat-exchangers in the heat recovery boiler and their large cooling towers or water condensers.
Earlier this was done by means of a surface counter flow heat exchanger - a recuperator or a regenerator which heated the compressed air before entering the combustion chamber with waste heat from the expander outlet ( Fig.4).
Figure 4. An open gas turbine cycle with recuperator.
Pressure ratios were moving upwards, forcing the compressor outlet temperature upwards to a point where the temperature difference between the exhaust gas at outlet of the expander and the
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Department of Heat and Power Engineering Introduction
compressed air at outlet temperature of the compressor is too narrow to exchange any useful heat from the exhaust gas.
A feasible way of utilising the waste heat back into the gas turbine cycle today, is to heat water in a heat recovery boiler and then inject the resulting steam into the combustion chamber (Fig.5).
Heat rec 6oiler
Figure 5. A steam injected open gas turbine cycle.
Steam injection will affect the work output positively but also the NO, formation will be reduced [22, 75, 107, 108, 110] and if the steam is heated with waste heat from the heat recovery boiler, the thermal efficiency will also increase. Today, small gas turbine plants are commercially available which use this principle to utilise waste heat from the gas turbine. The major disadvantages with steam injection are connected to the water consumption and the loss of the latent heat of vaporisation which leaves the gas turbine plant with the exhaust gas. This will reduce the heat utilisation in the heat recovery boiler when a cogeneration alternative is considered. Methods of treating water by means of heat recovered from the heat recovery boiler of the steam injected turbine have also been investigated [13,14,15]. The water treatment cost does not, however, effect the economy of the steam injected gas turbine plant more than marginally [2].
In the 70s and 80s a major effort to develop steam injected gas turbines was made [3, 5, 12, 16, 23, 36, 37, 54,60, 65, 66, 73, 103, 104, 106, 111, 113,115,116] and comparisons were also made both from an economic and a technical point of view [8, 11, 17, 39, 64, 97, 114]. Even biomass fuelled alternatives woe investigated [117,118]. The economy of steam injected gas turbines however seems to limit the size of the plant to less than 50 MW output. If larger units are desired the economy of the combined cycles today is favourable.
Steam injection in small amounts is, however, frequently used in simple open gas turbines and combined cycle power plants to reduce NO, formation in the combustion chamber [55] to permissible levels [94,95].
Another possible way in which to utilise the waste heat from the gas turbine and also the main topic of this report, is by means of water evaporation into the compressed air stream. This reduces the air temperature and at the same time elevates the flow through the latter part of the cycle. It is done by introducing a "new" component, the humidification tower, in which the water is brought into contact with the air in a counter flow act, resulting in a temperature decrease and an elevated humid air flow. This way of evaporating water is thermodynamically favourable because of the vaporisation of water into a gas stream that is connected to the vapour pressure in the gas mixture and not the total pressure. As the partial pressure of vapour through the tower will vary, the vaporisation temperature will vary likewise. At the air inlet of the humidification tower, the boiling temperature of the water will therefore be low and as water is evaporated into the air stream the boiling temperature will increase. The exergetically superior gliding boiling temperature of the water has thus been accomplished in the tower.
The exit compressed air temperature can always be kept low by means of the humidification tower, independently of the exit compressed air temperature after the compressor. This opens up an opportunity to introduce recuperators again after a couple of decade's absence (Fig. 6).
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Introduction Lund Institute of Technology
Figure 6. An open gas turbine cycle with humidification tower and recuperator.
In the heat recovery boiler of evaporative gas turbine cycles, the evaporator is eliminated and the super heater exchanged for a recuperator. This results in a more favourable temperature distribution compared to the temperature distribution predominant in a ordinary heat recovery boiler ( Compare heat recovery boiler in figure 6 with figure 3 and 5).
The principle of reducing the compressed air temperature by means of water injection into the compressed air stream, has been known in theory for quite a while [43,44,45,46,47] and some old patents in the field also exist [35,62,63,74]. However no power plants working in this way have ever been built
Today, a new interest in evaporative cycles has arisen due to the remarkable possibility of reusing low level heat and extracting heat of a certain level from the humidification tower. This is interesting when combined with a coal gasification plant where a great amount of low level heat would otherwise be rejected in the process of producing clean gaseous fuel out of coal. The possibility to reach efficiency levels close to gas fuelled combined cycles seems to be feasible when folly integrating the evaporative cycle with the gasification plant but at a substantially reduced cost compared with the combined cycle [21,40,83, 84,85,87,99]. More advanced evaporative cycles have been proposed and theoretically compared with other cycles [1, 24,25, 39, 50, 77, 79, 88, 89, 90, 98]. Some new patents have also been taken out [86,78].
In Belgium, an old gas turbine cogeneration power plant is planned to be reconstructed to test the evaporation concept to some extent. This, as far as the author knows, comes closest to the realisation of an evaporative cycle [93].
The end of the cold war maybe will lead to large resources being diverted from military to non- military engineering, which can create a renaissance in developing more advanced industrial gas turbine sets.
1.2. Objectives
Build up a knowledge base in the area of advanced evaporative gas turbine cycles and their working fluids. Make an evaluation of their potential and clearly present all models used to simulate components of evaporative cycles thermodynamically.
The scientific contribution lies in the systematic, in which gas properties and different configurations of gas turbine cycles are treated and also in a proposed new cooling model of the expander which can adjust the cooling flow after its real requirements on a comparative basis.
1.3. Method and resources
The investigation is based on studies of the literature and personal consultation with different people. It started with a rather large investigation on how to treat the thermodynamic properties of a gas correctly and based on this investigation simulate different components of evaporative gas turbine cycles. A computer based simulation program for evaluating evaporative gas turbine cycles was then
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Department of Heat and Power Engineering Introduction
developed by the auther. All calculations are based on this PC-based program which was written in Turbo-Pascal.
The work presented in this thesis for the degree of licentiate of engineering has been conducted at the Department of Heat & Power Engineering, Lund Institute of Technology. It has been financed by the Board of Technical Development in Sweden and by the University.
This work was conducted between the summer of 1990 and the beginning of 1993.
1.4. Limitations
All calculations of the gases are idealised with an ideal gas assumption (cp = cp(T)). This means that the calculation error of a gas turbine cycle escalates as pressure ratios rise and as the content of three atomic substances in the gas rises.
Only two sets of gas turbine cycles are evaluated, one set for an uncooled expander (Appendix C) and one set for a cooled expander ( Appendix D). Overall efficiency, specific work output and water evaporation ratio are then plotted as a function of pressure ratio over the compressor which is varied between 5- 35. For the cooled expander, also the air cooling flow requirement is plotted as a function of the pressure ratio.
1.5. Organisation of the report
In chapter 2-6, the complete equation foundation for calculating evaporative cycles is presented with comments on each component. In chapter 7 different evaporative cycles are calculated and compared with each other. In chapter 8 some general conclusions and some conclusions of the calculations done in the preceding chapter are drawn.
In Appendix A the model to simulate the thermodynamic properties of ideal gases is described. In appendix B the difference between the conventional way of simulating the compression and expansion is compared with the method used in this report which has its origin in works carried out by O. Zweifel. In appendix C and D is the input values to the cycle calculations are recorded.
1.6. Acknowledgements
In the working environment that exists at the department, it is easy to find helpful people whose advices on different subjects can be relied upon. Therefore I think it is difficult to list everyone who has been of assistance to me. However, I would like to thank some people specially. Firstly I would like to thank my examiner Prof. Tord Torisson who has been my prime discussion partner and tutor during this work, secondly my work associate Jaana Ronkainen (M.Sc.) who has given me much valuable advice, thirdly Prof. Roland Wimmerstedt ( Department of Chemical Engineering 1, Lund Institute of Technology) who has helped me understand the physics behind the humidification tower and lastly Johan Winberg (Teknlac.) whose vast experience in Windows Software has been my main source of knowledge in this area.
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The compressor system Lund Institute of Technology
2. The compressor system
More advanced evaporative gas turbine cycles will consist of a low and a high pressure compressor and between them a counter flow gas to liquid heat-exchanger - the intercooler is placed.
Breaking the compressor apart, into two or several parts and between each part Cool down the air by means of an intercooler, is a well-known method raising the pressure to a certain level with less work needed than if compression was made in a single step. Causing a temperature decrease at the outlet of the compressors can be compared to an undivided concept. As the work of the compressor decreases, the work output from the gas turbine will correspondingly increase. The efficiency, however, will only be affected marginally, due to the need for an additional fuel injection to compensate for the temperature decrease at the outlet of the compressor.
The major drawbacks of intercooled cycles lie in the additional pressure losses occurring at each inlet and outlet of the compressors and also the pressure drop occurring in each intercooler. All this results in a greater need to compress the working fluid. This, combined with increasing complexity of the gas turbine cycle, makes it normally very hard to get the intercooler concept into rate base. Today, no large gas turbine manufacturers use intercoolers as standard equipment in their gas turbine programs.
However, in evaporative cycles the intercooler has one more important advantage. The heat usually rejected in the intercooler is reused by raising the evaporation rate of water into the compressed air stream. This will affect both the work output and efficiency of the gas turbine in a positive manner.
There are two different ways to model a compressor thermodynamically. The first model, representing the conventional way of calculation, described for instance by W. Traupel [109] and the second model that has its origin in works carries out by O. Zweifel [121] but also described by S. Borglin [7] and G. Lindberg [57, 58]. Both use the same level of idealisation, but the former model has an implicit solution and the latter an explicit one. The models are described in detail in Appendix B but in this investigation the explicit model of O. Zweifel is used.
In an intercooled open gas turbine cycle, it can be theoretically shown that the minimum compression work is reached when the pressure rise over the low pressure and the high pressure compressor is exactly the same. This is on condition that the temperature of the air after the intercooler can be cooled down to the initial air temperature before the low pressure compressor.
However, in evaporative gas turbine cycles the temperature condition given above cannot be satisfied because both the cooling water flow and its initial temperature are variables limited by the capacity to evaporate water in the humidification tower and its circulating flow of water. To decrease the number of variables, the pressure ratios over the low, respectively the high pressure compressors, are chosen so that both compressors utilise the same work output The assumption gives a solution that lies rather close to the thermodynamic optimum of cycle.
Both the described models of compression (Appendix B) are based on the polylropic efficiency defined as
(eq.l)
6
Assumptions made for the compressor calculations - summarised:
I. Stationary flow
II. Ideal gas
III. Adiabatic system
IV. The compression represents a poly tropic state of change
V. No leakage occurs
Department of Heat and Power Engineering The compressor system
2.1. The low pressure compressor
The low pressure compressor model is divided into two sub models, one modelling the compressor inlet throttling inlet and another modelling the compression. It is placed as the first component of the gas turbine cycle (Fig. 7).
boiler
Figure 7. The position of the low pressure compressor in an evaporative cycle and the nomenclature used in calculations.
At the inlet and outlet of the compressor pressure losses will occur. The inlet pressure drop is taken into consideration by introducing a dimensionless pressure drop, defined as
aPlc =Po' Pla
PoBy connecting the energy equation for a throttling
=o ci2aho + Y=hi. + T
(eq.2)
(eq.3)
, the impulse equation for a throttling
coPo + V()-Pia +
4vla
(eq.4)
, rewriting v0 and vla with the ideal gas law
RU'Tx Bo'Tx
Vx"P,-Mo" (eq.5)
and assuming the velocity of the ambient air to zero (c0 = 0), it is possible to solve the end state implicitly as
hia ~ ho * 2' *0 * Tla ' (eq.6)
It is only at the inlet of the low pressure compressor and the outlet of the expander that the difference between total and absolute states are taken into consideration. Other pressure drops between the low
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The compressor system Lund Institute of technology
pressure compressor and the expander are assumed only to affect the cycle by narrowing the pressure ratio over the expander or by broadening the pressure ratios over each compressor.
The compression of an ideal gas through a compressor represents a polytropic state of change defined as
p • v” = constant (eq.7)
The calculation of the polytropic state of change representing the compression of a compressor is executed in two steps. First an isobaric state of change followed by an isothermal state of change reaching the actual end state of the compression ( Fig.8).
Figure 8. The difference between the "actual" and the calculated state of change for a compression.
In Appendix B it is shown that eq.l can be rewritten as
Asr slap - s%,1^:-As, =
where the entropy growth of the isobaric state of change can be written asla.p
sl,.p-sl, = Asp= jcpCD'Y
la
(eq.8)
(eq.9)
and the entropy growth of the isothermal state of change can be written as
Sla.p-S2a = AsT=R0‘1 (eq.10)
When the polytropic efficiency (nLC) and the pressure ratio p%/Pi, are considered to be known, the isothermal entropy growth (AsT) is easily calculated with eq.10 and then the isobaric entropy growth (ASp) can be deduced from eq.8 without the need to resolve eq.9. By this calculation procedure it is possible to reach the end state of the compression explicitly!
The specific work per unit compressed air of the low pressure compressor can then be calculated as
aLC = h2a - hla <«1.11)
2.2. The intercooler
The counter flow surface heat-exchanger model used for the calculation of the intercooler, placed between the low and high pressure compressor (Fig. 9), is defined by means of a "pinch-point" concept and pressure drops on the heated and cooled side respectively.
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Department of Heat and Power Engineering THE COMPRESSOR SYSTEM
(Gen)— LC— HCE K
e
Figure 9. The position of the intercooler in an evaporative cycle and the nomenclature used in equations.
The "pinch point" concept introduced is defined as the smallest temperature difference between inlets and outlets of the counter flow heat-exchanger. In calculations, the "pinch point" is first assumed as the temperature difference between the inlet air and the outlet water temperature.
(eq.12)PPlC-T2a - Tw.2a
There are, however, thermodynamic limitations of the intercooler that have to be considered. Firstly, the inlet air temperature minus the "pinch point" must be larger than the inlet water temperature, otherwise the air would be heated instead of cooled. Secondly, the upper limit of the water exit temperature is the saturation temperature determined at the outlet water pressure of the intercooler. Thirdly, a problem that can arise when the water flow through the intercooler is large combined with high water pressures, is that the temperature difference between the outlet air and the inlet water is unrealistically low. The smallest allowed exit air temperature is then assumed to be the inlet water temperature plus the "pinch point".
(eq.13)Tib - Tw.ib + PPlC
The pressure drops are introduced with two further dimensionless quantities, the pressure drop over the water side
and the pressure drop over the air side, which also consists of outiet losses of the low pressure compressor and inlet losses of the high pressure compressor
(eq.15)
The heat balance over the intercooler is written as
b&i * hlb = mw " XIC " ( hw.2a ’ hw.lb )
where mw is the evaporated water flow per unit mass of compressed air, defined as
(eq.16)
(eq.17)
xIC is defined from the expression
XIC + XAC + xEco = 1 + xCirc (eq.18)
where
The compressor system Lund Institute of Technology
m,‘a(eq.19)
w m.'w
m,lawhere subscript j stands for IC, AC, Eco or Circ.
2.3. The high pressure compressor
The high pressure compressor is placed between the intercooler and the aftercooler ( Fig. 10) and its calculation is executed corresponding to the low pressure compressor.
Hc*^Pc
1 2blb 1
Figure 10. The position of the high pressure compressor in an evaporative cycle and nomenclature used in equations.
The polytropic efficiency of the high pressure compressor is rewritten as
where the entropy growth of the isobaric state of change can be written aslb.p
(eq.21)
lb
and the entropy growth of the isothermal state of change can be written as
(eq.22)
Analogous with the low pressure compressor, when the polytropic efficiency CnHC) and the pressure ratio p2b/plb are considered as being known, the isothermal entropy growth (AsT) is easily calculated with eq.22 and then the isobaric entropy growth (ASp) can be deduced from eq.20 without the need of resolving eq.21. By this calculation procedure it is possible to reach the end state of the compression explicitly!
The specific work per unit compressed air of the high pressure compressor can then be calculated as
aHC = ^2b' **ib (eq.23)
Department of Heat and Power Engineering The humidification system
3. The humidification system
The humidification system consists of three closely connected components: a counter flow gas to liquid heat-exchanger - the aftercooler, a humidification tower and a pump for raising the pressure of the circulating water.
In the aftercooler, water is heated by the hot compressed air that is later on injected at the top of the humidification tower, together with heated water from the intercooler and the economiser. In the humidification tower, the heated water meets the compressed air stream counter flow wise, causing water to evaporate. The advantage of evaporating water in a gas lies in the gliding boiling temperature of the water, because water evaporation will take place down to temperatures, not decided by the total pressure in the humidification tower, but decided by the partial pressure of the vapour in the humidified air. As the humidity of the air at the bottom of the humidification tower, where the dry air is injected, is low, the evaporation temperature also will be low and rise steadily through the tower as water is evaporated into the air stream.
There are basically three different driving mechanisms of vaporisation thinkable in a humidification tower
I. Flashing caused by higher temperature and higher total pressure of the water injected at the top compared with the states prevailing in the tower.
n. Vaporisation through cooling of the air.
III. Enthalpy change between the cross flowing water and air caused by the temperature drop between the water inlet and outlet of the tower.
It is the third mechanism that is the most important one if you are interested in evaporating a large amount of water into a compressed stream of air. A favourable humidification tower in this application should therefore have the lowest possible outlet temperature connected with the highest flow of circulating water. This ought to give the highest energy exchange between the air stream and the counter flowing water stream and thereby also reaching the highest evaporation ratios.
Since the outlet temperature of the water is connected to the inlet temperature of the compressed air, it is also vital to keep this temperature down. It is done by implementing an aftercooler between the outlet of the high pressure compressor and the inlet of the humidification tower, causing the air temperature to fall. All energy exchange in the aftercooler is reused in the cycle in the same manner as for the intercooler. The advantage of using an aftercooler diminishes if the pressure ratio over the compressor system is too low.
The pressure of the circulating water is lower than the water pressure prevailing in the water circuit and this is why a water pump is used to raise the pressure back to the initial level.
3.1. The aftercooler
The aftercooler is placed between the high pressure compressor and the humidification tower (Fig. 11). Its implementation depends greatly on the outlet temperature of the compressor and accordingly also on the pressure ratio. If the temperature is too low the advantages of an aftercooler in the evaporative cycle will diminish.
11
The humidification system Lund Institute of Technology
Figure 11. The position of the after cooler in an evaporative cycle and the nomenclature used in equations.
The "pinch point" conception is introduced, which is defined as the smallest temperature differencebetween the inlets and outlets of the counter flow heat-exchanger. In the aftercooler the "pinch point"is first assumed as the temperature difference between the inlet compressed air and the outlet water temperature.
(eq.24)T2b“ Tw.2b + PPac
The aftercooler has thermodynamic limitations which has to be considered. Firstly, the inlet air temperature minus the "pinch point" must be larger than the inlet water temperature, otherwise heat will be exchanged in the wrong direction. Secondly, the upper limit of the water exit temperature is the saturation temperature determined at the outlet water pressure of the aftercooler. Thirdly, a problem can arise when the water flow through the aftercooler is large combined with high water pressures. This can cause the temperature difference between the outlet air and the inlet water to be below the allowed levels defined below. The smallest allowed exit air temperature is assumed to be the inlet water temperature plus the earlier defined "pinch point" or rewritten as
(eq.25)PPaC~T2c"Tw.2c
The aftercooler is not yet thermodynamically defined. The pressure drops over precisely both sidesalso need to be considered. This is done by further introducing two dimensionless quantities, the pressure drop over the water side as
Pw.2c * Pw,2b(eq.26)
and the pressure drop over the air side as
P&'PzcApa.AC= Pa (eq.27)
The heat balance over the aftercooler will be
h2b* h2c = XAC "mw"( h*.2b * hw.2c ) (eq.28)
3.2. The humidification tower
The humidification tower, also called the humidifier or evaporator, is the main feature of evaporative cycles. It is placed between the aftercooler and the recuperator (Fig. 12) adding a couple of important features to the gas turbine cycle:
1. Low level heat, usually rejected from the cycle or from gasification of solid fuels is made possible to reuse in the cycle.
2. The heat is utilised by evaporation of water causing the gas flow to escalate. In doing so, thework of the expander is increased without effecting the work of the compressor. "Expensive" woik of compression of a gas has been exchanged for "cheap" work of an incompressible fluid.
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DEPARTMENT OF HEAT AND POWER ENGINEERING The humidification system
3. The outlet temperature of the humidification tower has decreased to a level that always makesit interesting to reuse heat from the exhaust gas at outlet of the expander to the cycle by means of a recuperator.
Figure 12. The position of the humidification tower in an evaporative cycle and the nomenclature used in equations.
In the humidification tower both heat and mass transfer take place simultaneously. This makes it harder to modulate this component compared to ordinary heat-exchangers. The model used to simulate the tower thermodynamically consists of three different ground assumptions. More detailed investigations of the humidification process have been conducted by Benton [4], Chow [18. 19. 20] and Yoshida [120].
Firstly, an assumption concerning the relative humidity of the outlet humidified air, is defined as
However in large humidification towers the relative humidity at the outlet is close to 100%.
Secondly, you need an assumption connecting the outlet temperature of the water with the inlet temperature of the compressed air. The lowest possible temperature of the exiting water is the saturation temperature of the incoming compressed air ( Point sat,2c in Fig. 13). Theoretically, this state is reached for an infinite tower without any pressure drops or other losses.
>PPev Temperature [E]
Figure 13. Model of the humidification tower with nomenclature and schematically drawn working lines.
A type of "Pinch point" concept is introduced to compensate for inefficiencies connected with thelimitations of its physical properties. It is defined as the actual temperature of the circulating water(Tw>2) minus the lowest possible temperature of the circulating water (T?„«„) or written with symbols as
PPev - Tw.2 • T2c.sat
Thirdly a dimensionless pressure drop is introduced defined as
(eq.30)
(eq.31)
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The humidification system Lund Institute of Technology
Eq.29, eq.30 and eq.31 together fully define the humidification tower thermodynamically.
The absolute humidity at inlet and outlet is calculated as
n2c[H2Q] M,(°2c- 1 - n^IH^O]' Ma (eq.32)
and at outlet as
to2 = ti)2c + mw-(l + fl)2C) (eq.33)
The energy balance over the humidifier can then be written as
ha.2c + "2c hv.2c + W3 ' hw.3 = \.2 + <°2 ’ hy.2 + W2 ' hw.2 (eq.34)
where the mass flow of supplied water per unit dry air is
W3 = mw-(l + to2c)-(l + xCirc) (eq.35)
and the mass flow of circulating water per unit dry air is
w2= mw • (1 + ®2c) • *Circ (eq.36)
All enthalpies of dry air are derived from polynomials that have their origin in NASA [41] further customised for power plant calculations by F. Brandt [10], who derived the thermal properties from the original polynomials and changed the zero level to 0*C (Appendix A). All enthalpies of water in the humidification tower are derived from an ordinary steam table [48], which has its zero level at 0.0VC and 0.006112 bar.
The properties of vapour at outlet of the humidification tower will be
M,
n2[H2°] =----------(eq.37)
1+^xFor all other substances the properties after the humidification tower will be
n^Mn2[sl = l-n2c[H20]'(1 - W) («l-38)
3.3. The pump for circulating water
After the humidification tower it is necessary to raise the pressure of the circulating water to the highest water pressure level existing in the cycle. This is done by a circulation pump that is placed directly after the outlet of water from the tower (Fig. 14).
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Department of Heat and Power Engineering The humidification system
>very boiler
w,2(^^)mwXCirc
w,l
Figure 14. The position of the water circulating pump in an evaporative cycle and the nomenclature used in equations.
The calculation of the circulation pump is performed by introducing the isentropic efficiency of the pump
%.s~"^W.1.5 ~ ^W.2^w.l ' ^w.2 (eq.39)
The pressure level after the pump is decided by the highest inlet water pressures of the intercooler, aftercooler or the economiser. As pressure levels of the inlet water of the heat-exchangers are of the same magnitude, no efforts have been made to consider the need for the extra strangulation of the two heat-exchangers that work at lower pressure levels.
The total pump work, considering mechanical losses and losses due to inefficiencies of the electric engine driving the pump, can be written as
%.oim.., ‘ XQre ( b«.l * ^w.2 )
ipjnec " ^p-el(eq.40)
15
The combustion chamber Lund Institute of Technology
4. The combustion chamber
The combustion chamber can vary both in shape and numbers, largely depending on the aim of the building companies. If the company only develops industrial gas turbines for heavy duty purposes the number of combustion chambers is minimised, often only one or two. However, if the company primarily makes gas turbines for propulsion the number of combustion chambers can be between 6-12, thus making the construction very compact and light. The compactness of the latter construction can make it difficult to implement these aeroderatives in evaporative cycles where there is a need to divert the compressed air flow to the humidification system and the heat recovery boiler, before it enters the combustion chamber.
Today, great efforts are made to understand and suppress thermal NO,-formation in the combustion chamber [38, 42, 94, 95, 96]. The suppressing can be done by injecting water or steam into the primary burning zone, thereby lowering the maximal temperature of the diffusion flame [12, 22, 55, 75, 107, 108, 110]. Alternatively, newly developed so called Tow NO, burners" or "premixed burners" are used in which the flame temperature is kept low by under stoichiometric burning of the fuel in the primary zone followed by after burning with a highly swirled secondary flow of air.
As no evaporative gas turbine cycles have been built yet, there are no reliable data concerning NO,- formation from these types of cycles. However the similarity to usual steam injected gas turbine cycles is apparent It is probably a reasonable assumption to estimate the same magnitude of NO, -formation from evaporative cycles compared with steam injected cycles or with cycles equipped with Tow NO, burners" [34].
Another potential problem concerning a large amount of water evaporation into the air stream before entering the combustion chamber is flame stability. Normally, steam injected gas turbine cycles have maximal injection ratios of about 10% of the total compressed air flow [106]. In evaporative cycles, injection ratios up to 20%-40% of the total compressed air flow are feasible and this may cause problems in the combustion chamber especially, where flame stability is concerned.
The combustion chamber is placed between the recuperator and the inlet of the expander (Fig. 15)
(<5e^— LC — HC ■■ "I E
cc1 ! 9*c ; 1+ mw-rn'cl------------+
Figure 15. The position of the combustion chamber in an evaporative cycle and the nomenclature used in equations.
Tire combustion of the fuel in the combustion chamber is not complete or perfecL In the calculation,this imperfection is taken into consideration by introducing a dimensionless efficiency concept calledthe combustion efficiency. This is defined as the actual heating value of the fuel when burned in the combustion chamber, divided by the "theoretical" heating value of the fuel when fully oxidised. In symbols the combustion efficiency is written as
(eq.41)
The dimensionless pressure drop over the combustion chamber is defined as
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Department of Heat and Power Engineering The combustion chamber
Apcc =P3 ~P4
P3The heat balance over the combustion chamber is written as
(eq.42)
(1+ mw + mf - mj • h4 = ( 1+ mw - m,,) • h3 + mf • (hf + ncc' %) (eq.43)
In the combustion chamber two gas flows are mixed. A chemical reaction takes place between the gases forming a new gas - the exhaust gas leaving the combustion chamber. The properties of the exhaust gas famed can be calculated from the two initial gases, when assuming full oxidation of all hydrogen and coal compounds present in the fuel. The theoretical need of oxygen from the air stream is calculated by means of three different figures tabulated for every substance present in the fuel. The first figure relates to the amount of carbon dioxide formed per unit flow of fuel, the second relates to the amount of water formed per unit flow of fuel and the third relates to the total oxygen content in the fuel available fa oxidation. The oxygen need from the air to folly oxidise the fuel can then be calculated as
Ozneed = CO%f + 2 ' H2Of - Ou
The new properties of the exhaust gas can be calculated as:
I. The properties of water in the exhaust gas:
n2[H20] nf[H20] + H2Of( 1+ mw - mj +------------------Mo Mf m,
x4[H2oi- l+mw+mf-mc
II. The properties of carbon dioxide in the exhaust gas:
n2[co2] nffccy + COZf-M^“'(l+mw-mc) + -
x4IC02] ~ 1+ mw+mf - mc
HI. The properties of oxygen in the exhaust gas:
Mf m.
W °2needMo ( 1+ mw ' mc) * Mf mf
- 1+ mw+mf- mc
IV. Properties of inert substances present in both the humid air and the fuel:
n2[c] fif{c]i • ( 1+ m„ - m„) 4
x4[c] =-------
Mrd+mw-ng+Mpmf
l+mw+mf-mc
V. Properties of inert substances only present in the humid air:
(eq.44)
(eq.45)
(eq.46)
(eq.47)
(eq.48)
n2[cl . ,^-•(l+mw-mc)
x4[c]- i+ mw + mf - n,c
VI. Properties of inert substances only present in the fuel:
n;MMf ‘mf
XJC1~ 1+ mw+mf- mc
(eq.49)
(eq.50)
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The combustion chamber Lund Institute of Technology
Then the molar weight can be calculated as:
.M-=X*,fcl<=0
The new composition of the combustion gas, when fully oxidised, will be:
n4[c] = x4[c] • M4
(eq.51)
(eq.52)
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Department of Heat and Power Engineering The expander
5. The expander
If the fuel used has a high degree of impurity, the inlet temperature of the expander has to be kept low ( 800 - 900 *C) to satisfy demands concerning the safety and lifetime of the gas turbine. In this temperature range there is no need for cooling the first stages of the expander. However, by using a cleaner fuel, for instance natural gas, or by transforming dirty fuels to higher quality, the allowed inlet temperature of the expander can be raised up to 1200 - 1300 "C. No materials today can withstand these temperatures, but by using more sophisticated building techniques, such as coatings and cooling methods of the blades exposed to these high temperatures, it is possible to make expanders that satisfy the demands concerning safety and lifetime. The new building techniques and coatings of the blades do not effect the thermodynamics of the expander more than by the increased inlet temperature of the expander, but blade cooling does. The usual way of blade cooling is by by-passing a part of the compressed air flow passed the combustion chamber and injecting it during the first stages of the expander. This by-passing will effect the thermodynamics of the gas turbine, and the injection of cooling air into the first stage of the expander exhaust flow will disturb the flow depending on cooling method used. The stage efficiencies of the expander will thereby be decreased.
The expander is placed between the combustion chamber and the recuperator (Fig. 16).
boiler
Figure 16. The position of the expander in an evaporative cycle and the nomenclature used in equations.
The assumptions and the calculation of the expander correspond to those of the compressor and the assumptions and derivations are similar.
Assumptions made for the expander calculations - summarised:
I. Stationary flow
II. Ideal gas
III. Adiabatic system
IV. The expansion represents a poly tropic state of change
V. No leakage occurs
VI. Repeating stages
The efficiency concept used in calculations of the expander is the polytropic efficiency for an expansion defined as
dh= (eq.53)
19
THEEXPANDER LUND INSTITUTE OF TECHNOLOGY
The dimensionless pressure drop at outlet is defined as
P5-P6Ape = -
P5By connecting the energy equation for a throttling
c5 c6h5 + Y=h6 + Y
with the impulse equation for a throttling
C52
c6
(eq.54)
(eq.55)
(eq.56)P5 + V5 = P6 + "o
, rewrite v5 and v6 with the ideal gas law as eq. 5 suggests and
assume the velocity of the exhaust gas after the throttle to zero (c6 ~ 0 because Cg » c^) it is possible to solve the end state explicitly as
1h6 = h5 + 2R4‘T5‘ 6") (eq.57)
5.1. An uncooled expander
The calculation of the polytropic state of change representing the expansion of an expander is executed in two steps. First, an isothermal state of change followed by an isobaric state of change and thereby reaching the end state of the expansion ( Fig. 17).
"Actual" way ,Xr' '
Figure 17. The difference between the "actual" and the calculated suae of change for an expansion.
The efficiency concept used in the explicit method for an expansion is the polytropic efficiency that is defined as
n --6- Me-y-dp
In Appendix B it is shown that eq.53 can be rewritten as
Where the entropy growth of the isothermal state of change can be written as
s5p - s4 = As? = R4 • In,P5>
(eq.58)
(eq.59)
(eq.60)
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Department of Heat and Power Engineering THE EXPANDER
and the entropy growth of the isobaric state of change can be written as
5ps5p-s5 = Asp=/cpm-Y (eq.61)
5
When the polylropic efficiency (Tig) and the pressure ratio P4/P5 are considered to be known, the isothermal entropy growth (As?) is easily calculated with eq. 60 and then the isobaric entropy growth (ASp) can be deduced from eq. 53 without the need of resolving eq.61. By this calculation procedure it is possible to reach the end state of the expansion explicitly!
The specific work of the uncooled expander (mc = 0) is defined as
aE = (1 + mw + mf) • (h4 - h5) (eq.62)
5.2. A SIMPLE THERMODYNAMIC MODEL OF AN AIR-COOLED EXPANDER
The implementation of an air cooled expander into thermodynamic calculations has been conducted over the past years and the importance of this implementation has risen as the exhaust gas temperatures into the expander increased and thereby forced the cooling flows of the gas turbines upwards. An introduction to cooled expanders can be read in references [56,119]. Different analytic methods to calculate air-cooled expanders have been proposed and in the references [6, 30,31,32,61, 81, 82,100, 101] some of them are described. They have one thing in common, namely the need for introducing fluid dynamic quantities into the thermodynamic shell of calculations. This also creates a need to implement absolute quantities into the calculations, which leads to loss of the generality of the thermodynamic model, but hopefully the accuracy of the models is higher than for the simplified models discussed below.
The easiest way of taking air cooling into consideration, is by lowering the efficiency of the expander to a point where the work output of the uncooled expander model corresponds to the correct value ( Fig. 18, Cooling model A). The model will always give an elevated exit temperature of the expander, but the efficiency and work output of the gas turbine can be well represented by this model.
21
The EXPANDER Lund Institute of Technology
Uncooled model
Cooling model A Cooling model B
Calculated
Uncooled model
Cooling model C Cooling model DFigure 18. Different air-cooling models of the expander.
Another model for handling air-cooled expanders, is by letting the by-passed cooling air be mixed directly with the exhaust gas from the combustion chamber before the expander inlet and then treating the expander as an uncooled one (Fig. 18, Cooling model B). This method has also great advantages concerning simplicity and generality, though the results must be considered as speculative. The flow change through the expander is not taken into account due to the fact that the cooling-air in reality is mixed with the exhaust gas in a number of places in the first stages of the expander. The different stage efficiency losses due the disturbances of the main flow through the expander are caused by the injected cooling air.
W. Traupel [109] proposed a model that is a combination of the two simple models mentioned above ( Fig. 18, Cooling model C). He introduced two base assumptions, the first regulated how the cooling air flow was distributed into the expander (eq.63) and the second how the stage efficiency over each stage was affected due to the cooling flow, compared with an uncooled expander of the same kind (eq.59). With these two assumptions is it possible to calculate the expander stage by stage. However, Traupel wanted to make a model that reached the end state of the whole expansion in one step. This forced him to build up rather complicated efficiency correlation assumptions from his simple base assumptions resulting in rather decisive calculations [91]. Instead, by combining Traupel's basic assumption concerning air-cooling with Zweifel's method of dealing with the expansion, the calculations are greatly simplified (Fig. 18, Cooling model D).
Traupel's first assumption of an air-cooled expander concerns how the cooling air is distributed into the different stages of the expander. He assumes that all cooling air injected both in the blading of the stator and the blading of the rotor of each stage, is properly mixed with the exhaust gas flow before ottering the stage. The available flow of cooling air before each stage is a linear approximation and is defined as
m„mc,[z] = l+mw+mf
P4.jlzJ' P5P4-P5
(eq.63)
where p4i[l] = p4.
The injected flow of cooling air into the expander before each stage can then be written as
mci[z] = mu[z] - m^lz+i] (eq.64)
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Department of heat and Power Engineering The expander
where m^jz^+l] = 0.
His second assumption adjusts how the stage efficiency is affected as a function of the inlet pressure of the stages
mc P4.iMl+mw+mf'p4-p5 (eq.65)ile.iM = Tle-K-
where
(eq.66)
S in the equation above, is a constant dependent on the fluid dynamic characteristics and building techniques of the expander and varies from 0.5 for a good expander to 1 for a rather bad one [109]. The 0.5 term in eq.59 is introduced to compensate for the error occurring due to the assumption thatall injected cooling air in a stage is assumed to be injected and perfectly mixed before entering thestage.
I have chosen to calculate the expansion stage by stage of the expander as O. Zweifel proposes, only using the two base assumptions made by Traupel (eq. 63 and eq. 59).
To simplify matters, the pressure ratio over each stage is assumed equal and is written as
(eq.67)
The assumption given above is merged into the method of calculating the expander stage described previously.
Before each stage, the new composition of the mixture between exhaust gas and cooling air injected has to be calculated. The total flow through the current stage in mass per unity mass compressed air will be
(eq.68)nWz] = mtot[z-i] + md[z] • (l+mw+mf)
where m^jO] = l+mw+mf - mc.
If component c is present in both the exhaust gas and the cooling air before stage z, the property of the component in the new gas mixture will be
( nyz] \Mp(l+mw+mf)
mc.ilzl ..-(l+mw+mf)
(eq.69)
or else if the component only is present in the exhaust gas then
(eq.70)
where n5 i[o,c] = n4[c] and M^iO] = M4 .
When the properties of the mixture between the injected cooling air and the exhaust gas from the proceeding stage are decided, a heat balance at the injection point before the next stage is completed, assuming total mixing immediately after injection of cooling air into the exhaust gas, as
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The EXPANDER Lund Institute of Technology
niiotiW • h4 i[z] = m^jiz-i] • h5 i[z-i] + mci[z] • (1 + mw + mf) • h2 (eq.71)
where h5i[0] = h4.
The inlet condition before each stage can now be calculated. As the pressure ratio over each stage is known, it is possible to calculate the expansion through each stage of the expander, as described in previously for the uncooled expander. However, this is now used on each stage instead.
Looking at the cooled expander as a whole the assumption of an adiabatic system used for an uncooled one is not correct But if the cooled expander is treated stage by stage, according to Traupel's assumptions concerning the injection of the cooling air, the assumption of an adiabatic system over each stage is still correct
The total specific work per unit compressed air for the cooled expander can finally be calculated as
Z!Ot Sot8e = 5Xj[z] = Xm^Jz] • ( h4i[z] - h5i[z]) (eq.72)
Z=1 Z=1
Traupel’s model does not consider different thermal stresses on the cooled blades when using different forms of cooling techniques and different temperature of the cooling air. However, it would be possible to connect the model with a model describing, for instance, the surface temperature of the blades as a function of the cooling flow for different cooling methods.
5.3. An advanced thermodynamic model of an aircooled EXPANDER
In evaporative cycles, where the cooling air is diverted from the outlet of the humidification tower, the temperature of the cooling medium and its thermal quantities have been changed drastically. The temperature has been lowered to levels around 100'C and the moisture content has been elevated to around 20% making it a rather good cooling medium, if compared with a simple open gas turbine cycle. The cooling flow requirement of compressed air is adjusted to limit thermal stresses on the blades of the expander to permissible levels and as the cooling effect of the cooling medium varies, it leads to a different cooling flow requirement In Traupel's model, variations in cooling flow requirements cannot be taken into consideration, because in one of the base assumptions concerning the cooling flow distribution (eq.63) the total flow of cooling air needs to be known.
Normally in thermodynamic comparisons between gas turbines, the difference between states and properties of the cooling air and combustion gas are so small that one can assume the total flow of cooling air is constant when the pressure ratios and combustion chamber outlet temperatures are of the same magnitude. This is, however, not the case when comparisons are made with evaporative cycles because of the completely different thermodynamic composition of the cooling air. The cooling flow instead has to be calculated from the actual thermal stresses that a specific stage is exposed to.
I have chosen to exchange Traupel's assumption of the cooling flow distribution and its limitations (eq.63) with a cooling flow prediction model developed at Rolls Royce in the late 60s and early 70s that now seems to be a generally excepted prediction model of the cooling flow requirements [33,49, 56,76].
The model introduces a blade-cooling effectiveness concept written as
yzi = T4 ilz] - T2 (eq.73)
Where T4 i[z] - T^[z] represents the achieved temperature difference and T4 i[z] - T2 the maximal theoretical achievable temperature difference between the exhaust gas and the mean surface temperature of a stage in the expander.
It has been found that the blade-cooling effectiveness is a function of a dimensionless parameter called B, given by
24
Department of Heat and Power Engineering Theexpander
*c.;M ‘ cp.2
Sylz] * Ay[z]
<iW:—:—T’viiia + mw + mf
AblMCtyM •
ma + mw + mf
l + mw + mf cP-2
• ay[z](eq.74)
Where otylz] • Ay[z] represents the difficulty to cool stage z of the expander when consuming
mci[z] • cp 2 amount of cooling air.
The blade-cooling effectiveness can then be drawn as a function of the dimensionless factor B (Fig. 19) made for four different air-cooling methods.
Figure 19. Left: Different blade cooling techniques (1) Convective cooling, (2) Impingement cooling, (3) Film cooling and (4) Transpiration cooling. Right: Blade-cooling effectiveness tc (In the figure symbolised T^)as a function of the dimensionless factor B for the different cooling techniques. [49]
The curves in figure 19 are then translated into four coefficient polynomials, one for each cooling method, as:
ec(Convective) = 3.0000-10-3+ 0.63777 • B - 0.25554 • B2 + 3.1808-10'2 • B3 (eq.75)
tflmpingement) = 73333-10"2+ 0.55859 • B - 0.17045 -B2+ 12626-10"2 -B3 (eq.76)
efFilm) =0.15984 + 0.39620 B-4.869-10"3 • B2-2.9461-lO*2 -B3 (eq.77)
^(Transpiration) =0.16032 + 0.56770 • B - 0.15693 • B2 + 1.4730-10"2 • B3 (eq.78)
With the above given equations the air-cooled expander can be simulated considering different cooling flow requirements and methods. The cooling flow requirement can be calculated implicitly.
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Heat-exchangers in the heat recovery boiler Lund Institute of Technology
6. Heat-exchangers in the heatRECOVERY BOILER
The heat recovery boiler consists of three counter flow surface heat-exchangers, first closest to the expander outlet a gas to gas heat-exchanger - the recuperator or the regenerator, second a gas to liquid heat-exchanger - the economiser and third a gas to liquid heat-exchanger for district heating.
6.1. The recuperator
The use of the recuperator is an old well-known method of raising the thermodynamic efficiency of a gas turbine cycle with rather low pressure ratios or with an intercooler. It exchanges the heat in the exhaust gas from the expander outlet to the compressed air, decreasing the amount of heat added by the injection of fuel to reach the allowed exit temperature from the burning chamber. The progresses in gas turbine building, especially in more efficient compressors made it possible to raise the pressure ratios dramatically. This forced the outlet compressor temperature upward and even if progress in material science leads to higher expander inlet temperatures, the outlet expander temperature did not rise in any conclusive manner due to more efficient expanders. Thus, the temperature difference between the outlet exhaust gas and the outlet compressed air is too small for an implementation of a recuperator.
The humid air turbine cycle changes the trend of smaller and smaller temperature differences between expander outlet and compressor outlet. Here the heat in the compressed air is used to heat and evaporate water causing the mass flow through the expander to rise. Most important in this case, it causes the temperature of the compressed humid air mixture to drop to approximately 80-150 *C depending on the pressure ratios and size of the humidification tower. Now there are excellent possibilities to use a recuperator to restore large amounts of heat back into the gas turbine cycle and thereby increasing the cycle efficiency. With the humid air turbine cycle, the development towards higher pressure ratios can continue without any risk that the development of new recuperators would be in vain.
Today the development of recuperators is restricted to rather extreme areas, for instance, military applications and other less cost sensitive areas, though some work of industrial recuperators has more recent beat published [67,68,69,70,71,72,80,112].
Recuperators also have some disadvantages. Heat exchanged between gases is rather bad especially if no large pressure drops on any side of the heat exchanger can be tolerated, which is the case in the Brayton cycle. Firstly, the recuperator will cause a pressure drop on the air side lowering the pressure before the expander, secondly, the pressure drop on the exhaust gas side will cause the back pressure of the expander to rise. As a result of this, the pressure ratio over the expander will narrow and render an efficiency penalty. To minimise flow disturbances in the recuperator it has to become rather large and heavy and thus expensive.
The high temperatures at the end of the expander also lead to high thermal stresses in the recuperator, which easily can lead to failures and leakages from the pressurised air side directly out into the exhaust gas stream, which results in large efficiency penalties. An environmental disadvantage is that the escalated air temperature will normally cause the thermal NOx -production to rise. However, the humidification of the air will tend to press the thermal NOx -production in the combustion chamber downward. This disadvantage can be avoided by by-passing the primary air (Approximately 10% of the total compressed airflow) directly into the combustion chamber and only allowing the remaining 90% of the flow to be heated in the recuperator. This is because the secondary air into the combustion chamber is proven not to effect the thermal NOx -production in any conclusive manner, but a smaller efficiency penalty will occur because of the by-passing. Now two mechanisms work to depress the thermal NOx-production in evaporative gas turbine cycles.26
Department of heat and Power Engineering Heat-exchangers in the heat recovery boiler
The recuperator is placed between the outlet of the humidification tower and the inlet of the combustion chamber on the compressed air side, and between the outlet of the expander and the inlet of the economiser on the exhaust gas side (Fig.20).
rSHHSh + m f6eFigure 20. The position of the recuperator in an evaporative cycle and the nomenclature used in equations.
The thermodynamic analysis of the recuperator is generally made by introducing an efficiency conception called the recuperator efficiency, symbolised by an e. It is defined as the actual amount of heat exchanged, divided by the maximal theoretical amount of heat that can be exchanged when the temperature difference between the exhaust gas inlet and the humidified compressed air outlet of the recuperator is zero.
QR.oi(eq.79)
where q&.i = ( 1 +mw - mc) • ( h3(T3) - hjCTj)) and q^^« = (1 + mw - mc) • ( h3m„(T6) - h2<J$)
The recuperator efficiency rewritten with enthalpy quantities thus is
(eq.80)
The expression given above is used in the calculation with the efficiency as an input parameter.
In some literature the recuperator efficiency is defined in temperature quantities as
(eq.81)
and can be deduced from the previous expression by assuming a perfect gas (cp = constant).
The recuperator is yet as not exactly defined, the pressure drops over both sides needs also to be considered. It is done by introducing two further dimensionless quantities, the pressure drop over the air side
(eq.82)
and the pressure drop over the exhaust gas side
APr-“ = ""£P6-P7
(eq.83)
The heat balance used over the recuperator with proposed quantities can be written as
(1 + mw - mj • ( h3 - h^ = (I + mw + mf) • (1^ - h7) (eq.84)
27
Heat-exchangers in the heat recovery boiler Lund Institute of Technology
6.2. The economiser
After the recuperator in the heat recovery boiler is the economiser. Hoe even more waste heat from the exhaust gas is recovered to heat some of the water and that later on will be injected into the air stream. It will affect both the thermal efficiency and the specific power output. The thermal efficiency will be affected by lowering the level of heat rejected and the specific power output by the possibility of injecting a larger amount of water into the cycle, which causes the power output of the expander to increase. To avoid boiling in the economiser, the pressure level and the water flow through it is matched with the exit exhaust gas temperature from the recuperator.
The pressure drops in the economiser, is only concerned with minimising the pressure drop on the exhaust gas side. Because an escalated back pressure in the heat recovery boiler will always strike harder on efficiency and power output than die extra woik needed for the water pump to raise its pressure ratio and thereby compensate for larger pressure drops on the water side.
The economiser is placed between the outlet of the recuperator and the inlet of the heat-exchanger for district heating, circulating water before being injected into the humidification tower (Fig.21).
fry boiler
Figure 21. The position of the economiser in an evaporative cycle and the nomenclature used in equations.
Instead of using an efficiency concept like the one used in a gas to gas heat exchanger, in gas to liquid heat exchangers a "pinch point" concept is commonly introduced. The "pinch point" is defined as the smallest temperature difference between inlets and outlets of the counter flow heat exchanger. In an economiser die "pinch point" is first assumed as the temperature difference between the inlet air and the outlet water temperature.
PPego = T?- Tw.7 (eq.85)
The calculation, however, is conducted from the expander outiet throughout the heat recovery boiler, which renders a number of control measurements in the economiser. Firstiy, the inlet exhaust gas temperature minus the "pinch point" must be larger than the inlet water temperature, otherwise the economiser will be disconnected. Secondly, the upper limit of the water exit temperature is the saturation temperature determined at the outiet water pressure. Thirdly, a problem that can arise when the water flow through the economiser is large, combined with high water pressure, the exit exhaust gas temperature from the economiser is not allowed to sink below a certain level. The lowest exit exhaust gas temperature allowed is then assumed to be the inlet water temperature plus the "pinch point".
Tg - Tw g + PPeco (eq.86)
The economiser is yet not precisely defined, the pressure drops over both sides also need to be considered. This is done by introducing two further dimensionless quantities, the pressure drop over the water side
Pw.8 * Pw.7*w.=-£7~
and the pressure drop over the exhaust gas side
(eq.87)
28
Department of heat and Power Engineering Heat-exchangers in the heat recovery boiler
^PEco.cx p?P? "Pg
(eq.88)
The heat balance over the economiser will be
(1+ mw + mf) • ( h7 - h8) = mw • x^ • (hw7 - hw8) (eq.89)
6.3. The heat exchanger for district heating
The last heat exchanger in the heat recovery boiler is the heat exchanger for district heating. The only demand on this heat exchanger is a minimal pressure drop on the exhaust gas side at the highest possible heat exchange.
If the inlet temperature of the fluid which is meant to be heated by the exhaust gases is low, there is a possibility of condensation of the vapour in the exhaust gas. The main parameters governing condensation are, of course, the amount of water injected into the cycle, the content of hydrogen rich constituents and the moisture of the fuel used.
The heat-exchanger for district heating is placed as the last heat-exchanger in the heat recovery boiler (Fig.22).
(Genl-lLcI—IhCI -I E
Figure 22. The position of the heat-exchanger for district heating in an evaporative cycle and the nomenclature used in equations.
The calculation of the heat-exchanger starts with checking to see if the exhaust gas temperature, which is an input parameter, is lower or higher than the saturation temperature of the exhaust gas at outlet pressure. If the saturation temperature is lower, condensation will occur, otherwise not.
The condensing flow will then be
(eq.90)
The water flow is calculated so that the equation given above fulfils the assumption that the relative humidity, if condensing, when leaving the heat exchanger is 100%.
Only the pressure drop over the exhaust gas side needs to be considered when evaluating the power cycle. It is defined as
Ps ~ Po(eq.91)
The heat balance over the heat exchanger will be
9dhjo = ( 1+ mw + mf) • h8 - (1 + mw - mwk + mf mwJci' ( rwi + ^wi " hw.9) dT
(eq.92)
29
Heat-exchangers in the heat recovery boiler Lund Institute of Technology
But the integral J mwJci * ( rwi + - hw 9) • dT is approximately equal to mwk • r,
*0all the condensed water leaves the heat exchanger at outlet exhaust gas conditions.
The simplified heat balance will be
9dh.1o “ ( ^ mw )" hg ■ ( 1 + mw - mwJ[ + mf) hg - mwjc *rw
,(T9) assuming that
(eq.93)
30
Department of heat and Power Engineering Results of some cycle simulations
7. Results of some cycleSIMULATIONS
In the simulations below, different evaporative cycle configurations are executed, compared with each other and with a simple open gas turbine cycle ( = System 0) that has the same thermodynamic performance capability as the gas turbine used in the evaporative cycles. The simulations have been classified after the number of heat-exchangers used to heat water, later injected into the cycle and followed then by a comparison made within each group. For each simulation, evaporation ratios of water are calculated with the aim to give the highest possible thermal efficiency within the thermodynamic frames given in Appendix C and D.
The overall electric efficiencies, specific work outputs and evaporation ratios are drawn as a function of the pressure ratio over the compressor, which is varied between 5 and 35.
When a cooled expander is simulated, the compressed air used to cool the expander is drawn as a function of the pressure ratio.
The expander inlet temperature of the uncooled one is set at 850*C and the air-cooled one is set at 1250*C. However, the blade surface temperature of the air-cooled expander are set to the same value ( 850*C) as for the uncooled expander, which means that the thermal stress on the blading is of the same magnitude, when compared with each other
Natural gas is the fuel used in all simulations, but the model can be fed with any coal-hydrogen substance to be oxidised and any inert substance whatsoever, just as long as the substance has been properly thermodynamically examined by NASA [41].
In all the following simulations below the water circulation ratio is set to five times the amount of water evaporated into the compressed air stream and the water flow is evenly shared between the heat exchangers for every system. At this high circulation ratio, most heat exchanging in the different heat exchangers has taken place and a further increase would only marginally effect the thermal efficiency of the system. To decide the thermodynamically best configuration of an evaporative gas turbine cycle, there is therefore no need to optimise the flow composition between the heat exchangers or the circulation ratios. This is possible just as long as the water flows are so large that one is confident that no further heat exchanging will take place, even if the flow through a certain exchanger increases.
31
Results of some cycle simulations Lund Institute of Technology
7.1. One Heat-Exchanger Water Systems
There are three different one heat-exchanger water system configurations simulated, named system 1 to 3 (Fig.23).
System 2System 1 System 3(//
Figure 23. One heat-exchanger water systems. System 1: xJC =6.0, System 2: xAC =6.0, System 3:xEco =60-
7.1.1. Uncooled ExpanderSystem 0 System 1 System 2 —— System 3
.9 20-•
Pressure rat io over compressor
[kJ/kgAir]
Pressure ratio aier compressor Pressure ratio over compressor
Figure 24. Results from simulation of one heat-exchanger water systems with an uncooled expander.
The one heat-exchanger water sytem that is thermodynamically best, using an uncooled expander, is System 1 which reaches an electric efficiency level of approximately 41%. The efficiency optima for all three systems are reached at low pressure ratios compared to the optima for the simple open gas turbine ( System 0).
32
Department of Heat and Power Engineering Results of some cycle simulations
7.1.2. Air-Cooled ExpanderSystem 0 System 1 System 2 —— System 3
[kgCoolAir/IOOkgExhaustGas]
•S 20
Pressure ratio over compressor Pressure ratio over compressor
W 200-•
Pressure ratio over compressorPressure ratio over compressor
Figure 25. Results from simulation of one heat-exchanger water systems with a cooled expander
The one heat-exchanger water system that is thermodynaimically best using a cooled expander, is System 3 in the lower pressure ratio interval but as the pressure ratio increases System 1 becomes the most favourable configuration due to lower cooling flow requirements compared with the other two systems. Both systems reach an electric efficiency of approximately 475%. The efficiency optima for system 1 have now been moved further up in pressure ratios and the optima have become rather flat compared with the systems of the uncooled expander.
33
Results of some cycle simulations Lund Institute of Technology
7.2. Two Heat-Exchanger Water Systems
There are nine different two heat-exchanger water system configurations simulated, named system 4 to 12 (Fig.26).
System 5System 4 System 6
System 8System 7 System 9
System 11 Systeml2System 10
Figure 26. Two heat-exchanger water systems. System 4-6: xIC =3.0, xAC =3.0, System 7-9:xIC =3.0 xEco -3-0, System 10-12: xAC =3.0, =3.0
34
DEPARTMENT OF HEAT AND POWER ENGINEERING Results of some cycle simulations
7.2.1. Uncooled ExpanderSystem 0 System 4 System S — System 6
Pressure ratio over compressor
700- - [kJ/kgAir]
■§• 600 ■.« 600 1 400
^ 300- »—
4-2001^—*----100-
•S 36
j 30
Pressure ratio over compressor Pressure ratio over compressor
Figure 27. Results from simulation of two heat-exchanger Intercooler-Aftercooler water systems with cm uncooled expander.
System 0 System 7 System 8 — System 9
& 5
Pressure ratio over compressor
700--fkJ/kgAir]
#-600-
•g 600- -1 400--
300 ______ •------
J- 200; —----100
I 40-
^ 30 -
Pressure ratio over compressor Pressure ratio over compressor
Figure 28. Results from simulation of two heat-exchanger Intercooler-Economiser water systems with an uncooled expander.
35
Results of some cycle simulations Lund Institute of Technology
System 0 System 10 System 11 -**— System 12
[kgWater/lOOkgAir]
•9 20-•
Pressure ratio over compressor
600-
400-
Pressure ratio over compressorPressure ratio over compressor
Figure 29. Results from simulation of two heat-exchanger Aftercooler-Economiser water systems with an uncooled expander.
The thermodynamical behaviour of the two heat-exchanger water systems using an uncooled expander is similar. However, system 8 reaches the higest efficincy level. It reaches an electric efficiency level of approximately 43%. The efficiency optima for all nine systems are reached at low pressure ratios compared to the optima for the simple open gas turbine ( System 0). System 6 has a discontinuity somewhere between pressure ratio 15 and 20 in the evaporation ratio due to a shift in the pinch-point assumption in the economiser.
36
Department of Heat and Power Engineering Results of some cycle simulations
7.2.2. Air-Cooled Expander
System 0 System 4 System S —— System 6
[kgCoolAir/lOOkgExhaustGas]
6 10 16 20 26 30 36 5 10 16 20 25 80 35
Pressure ratio ooer compressor Pressure ratio over compressor
700- [kJ/kgAir]
600-
600--400- • yS'
•§ 40
§• 300!
200--
Pressure ratio over compressor Pressure ratio over compressor
Figure 30. Results from simulation of two heat-exchanger Intercooler-Aftercooler water systems with a cooled expander.
System 0 —System 7 System 8 —— System 9
[kgWatei/lOOkgAir] [kgCoolAir/lOOkgExhaustGas]
Pressure ratio aver compressor Pressure ratio ooer compressor
Pressure ratio ooer compressor Pressure ratio ooer compressor
Figure 31. Results from simulation of two heat-exchanger Intercooler-Economiser water systems with a cooled expander.
37
RESULTS OF SOME CYCLE SIMULATIONS Lund institute of Technology
Syetem 0 System 10 System 11 —— System 12
IkgCoolAir/lOOkgExhaustGas]
Pressure ratio over compressorPressure ratio over compressor
Pressure ratio over compressorPressure ratio over compressor
Figure 32. Results from simulation of two heat-exchanger Aftercooler-Economiser water systems with a cooled expander.
The thermodynamically behaviour of the two heat-exchanger water systems using a cooled expander are similar. However, system 8 is still the best one. It reaches an electric efficiency level of approximately 51%. The efficiency optima for all nine systems have moved up to the upper region of the simulated pressure ratio interval. System 6 still has a discontinuity somewhere between pressure ratio 15 and 20 in the evaporation ratio due to a shift in the pinch-point assumption in the economiser.
38
Department of Heat and Power Engineering Results of some cycle simulations
7.3. Three Heat-Exchanger Water Systems
There are three different three heat-exchanger water system configurations simulated, named system 13 to 19 (Fig.33).
System 13Hcaa(cc^a lc
jmF|iLC
Systeml4HCI
n>- “t Ei
c------------- 0=3
o—o-
Ln
ftc™■ /«V 1
Figure 33. Three heat-exchanger water systems. System 13-19: xIC -2.0, xAC -2.0, x^ -2.0
39
Results of some cycle simulations Lund institute of Technology
7.3.1. Uncooled Expander
System 0 ♦ System 14 -1— System 16 —*— System 18
System 13 —— System 15 ~H~ System 17 System 19
[kgWater/lOOkgAir]
Be 10--
Pressure ratio over compressor
~ 700-•
600- ■
400- -
300--
Pressure ratio ever compressor Pressure ratio ooer compressor
Figure 34. Results from simulation of three heat-exchanger water systems with an uncooled expander.
The three heat-exchanger system that is thermodynamically best, using an uncooled expander, is System 18 in the examined pressure ratio interval, but beyond this interval it seems as if systems 14 and 16 still gain efficiency at the end of the simulated pressure ratio interval. System 18 reaches an electric efficiency of approximately 46%. The efficiency optima for nearly all three heat-exchanger systems have been reached except for system 14 and 16 due to thermodynamically favourable shifts in the economiser.
40
Department of Heat and Power Engineering Results of some cycle simulations
7.3.2. Air-Cooled Expander
-A- System 0 System 14 System 16 System 18
System 13 System IS System 17 —System 19
[kgWater/lOOkgAir] [kgCooIAir/lOOkgExhauslGas]12.5-
Presstire ratio over compressorPressure ratio over compressor
700-'
1 40--
.5 30-%- 200 -
Pressure ratio over compressor Pressure ratio over compressor
Figure 35. Results from simulation of three heat-exchanger water systems with a cooled expander.
The three heat-exchanger system that is thermodynamically best, using a cooled expander, is System 18 in the examined pressure ratio interval but, beyond this interval it seems as if systems 14 and 16 have a favourable potential due to thermodynamically favourable shifts in the economiser. System 18 reached an electric efficiency of approximately 55% still gaining efficiency. The efficiency optima for all three heat-exchanger systems have not yet been reached.
41
Conclusions Lund Institute of Technology
8. Conclusions
8.1. General conclusions
Evaporative gas turbine cycles have extraordinary possibilities of being integrated with a gasification plant ( biomass or coal) due to possibility of utilising low level heat from/into the gasification plant into/fttxn the humidification tower of the power cycle.
The water consumption is of the same magnitude as the water consumption in a comparable combined cycle with wet cooling towers (About 1 ton of water per hour and MW), but the demands on the water quality in evaporative cycles are higher [2],
The potential of reaching low emission levels of NOx must be considered as good, due to the high amount of vapour in the working media combined with lower ratio of excess air than an ordinary gas turbine.
Evaporative gas turbine cycles in a cogeneration application give many interesting opportunities. The work-heat ratio would be possible to vary from approximately 1 up to 50 or more just by by-passing humidified air over the recuperator and thereby reuse less heat in the power cycle and more in the heat exchanger for district heating. It would then be possible to follow the yearly variation in heat consumption. In winter time the plant would run at lower electric efficiency but at a higher total efficiency than in summer when the plant would run at optimal electric efficiency. The work output, would however, only vary marginally. As only one expander is used in an evaporative cycle the possibility for small scale cogeneration must be considered as good.
8.2. Conclusions drawn from the simulations
In the label below is the results of the systems with the highest electric efficiencies tabulated:
Number of water heat-
exchangers
One Two Three Open simpel gas turbine cycle
Type of expander Uncooled Cooled Uncooled Cooled Uncooled Coded Uncoded Coded
System with highest i) l 3 8 8 18 18 - -Electric efficiency % 41 48 43 51 46 55 34 37
Specific work kJ/kgAir 270 580 290 650 390 740 160 320Evap.ratio kgH2OlkgAir 0.08 0.12 0.10 0.17 0.14 0.21 0 0
Cooling air kgAir/kgEx 0 0.08 0 0.06 0 0.05 0 0.11
Pressure ratio at opt.r\ 10 15 10 20 20 25 20 25Caracleristic of opt. Distinct Distinct Flat Flat Flat Flat Distinct Distinct
Evaporative gas turbine cycles will always benefit from any advances and development made in fields connected with its main components. There is today, no imaginable pressure ratio, maximal expander inlet temperature or pinch-point minimum of the heat exchangers that the most advanced evaporative cycles cannot benefit from.
42
Department of Heat and Power Engineering Conclusions
The water flow distribution through the intercooler, aftercooler and economiser does not have any major impact on the thermal efficiency, just as long as the circulation flow is kept at a high level to insure maximal evaporation ratio in the humidification tower.
More advanced evaporative cycles present a rather flat optima of the thermal efficiency, as a function of the pressure ratio, which gives the power plant builder a free choice concerning the pressure levels used in the cycle.
The air cooling flow requirement of evaporative gas turbine cycles is lower than an ordinary aircooled gas turbine due to lower cool-air temperature and high vapour content of the cooling media which makes it a thermodynamically better cooling media compared to dry air. In. fact, in most evaporative cycles the air cooling flow requirement does not even change when the pressure ratio is elevated as it normally would do in an ordinary air-cooled gas turbine.
43
References Lund Institute of Technology
9. References
[1] Annerwall K., Svedberg G.; A study on modified gas turbine systems with steam injection or evaporative regeneration ; 1991 ASME COGEN-TURBO IGTI-Vol.6, ppl-24
[2] Ayala RE., Thames JM.; Advanced gas turbine steam-injection program water treatment for steam-injected gas turbine systems - Topical report; 1989. Gas Research Institute, Illinois, GRI-89/0048
[3] Baken JAM., van den Haspen B.; Optimised operation of steam-injected gas turbine cogeneration units; 1988 ASME COGEN-TURBO IGH-Vol.3, pp259-265
[4] Benton DJ., Waldrop WE.’, Computer simulation of transport phenomena in evaporative cooling towers; 1988, ASME Journal of engineering for gas turbine and power, Vol.l 10, ppl91-196
[5] Berta GL., Durelli E„ Prato A.P.; A special arrangement of hybrid gas turbines ; 1990, Proceedings of the 25th Intersociety Energy Conversion Engineering Conference, Vol.5, pp495-501
[6] Bolland O.; Analysis of combined and integrated gas turbine cycles ; 1990. Thesis, Thermal Energy Division, N-7034 Trondheim - NTH Norway
[7] Borglin S.H.; A contribution to the thermodynamic calculation of open gas turbine processes ; 1991 ASME COGEN-TURBO IGTI-Vol.6, ppl 15-129
[8] Boyce M.P., Vyas Y.K., Trevillion WE.; The external combustion steam injected gas turbine for cogeneration ; 1978. Proceedings of the 13th intersociety energy conversion engineering conference, IEE 78-CH1372-2, pp860-865
[9] Brandt F.; Brennstoffe und Verbrennungsrechnung; 1981. Vulkan-Verlag, Essen
[10] Brandt F.; Warmeubertragung in Dampferzeugem und Warme- austauschern ; 1985. Volkan-Verlag, Essen, ISBN 3-8027-2274-4
[11] Brown DM., Cohn A.; An evaluation of steam injected combustion turbine systems; 1981. ASME Journal of engineering for power, Vol.103, pp 13-19
[12] Burnham JE„ Giuliani MM., Moeller DJ.; Development, installation and operating results of a steam injection system ( STIG) in a General Electric LM5000 gas generator ; 1987. ASME Journal of engineering for gas turbine and power, Vol.109, pp257-262
[13] Cerri G„ Arsuffi G.; Steam-injected gas turbine integrated with a self-production demineralized water thermal plant; 1987. ASME Journal of engineering for gas turbine and power, Vol.l 10, pp8-16
[14] Cerri G., Arsuffi G.; Calculation procedure for steam injected gas turbine cycles with autonomous distiled water production; 1986. ASME paper 86-GT-297
[15] Cerri G„ Arsuffi G.; Steam injected gas turbine integrated with self-production demineralized water thermal plant; 1986. ASME paper 86-GT-49
[16] Cerri G., Arsuffi G.; Steam injected gas generators in power plants; 1987 ASME COGEN-TURBO IGTI-Vol.1, pp45-54
[17] Cerri G.; Parametric analysis of combined gas-steam cycles ; 1987. ASME Journal of engineering for gas turbines and power, Vol.109, pp46-54
[18] Chow L.C., Chung JM.; Evaporation of water into a laminar stream of air and superheated steam ; 1983. ASME Int. Journal of heat and mass transfer, Vol.26, No.3, pp373-380
44
Department of Heat and Power Engineering References
[19] Chow L.C., Haji M.; Experimental Measurement of water evaporation rates into air and superheated steam ; 1988, ASME Journal of heat transfer, Vol.l 10, pp237-242
[20] Chow L.C., Chung JH.; Water evaporation into a turbulent stream of air, humid air or superheated steam; 1983. ASME Paper 83-HT-2
[21] Cohn A., Louks B.; Nakhamkin M.; The application of humidification to integrated coal gasification/ compressed air storage power plants ; 1991.10th annual EPRI coal gasification conference, ppl-8
[22] Dibelius NJi., Hilt MB., Johnson R.H.; Reduction of nitrogen oxides from gas turbines by steam injection ; 1971. ASME Paper 71-GT-58
[23] Digumarthi R., Chung-Nan Chang; Cheng cycle implementation on a small gas turbine engine; 1984. ASME Journal of engineering for gas turbine and power, Vol.106, pp699-702
[24] El-Masri MA.; A modified, high efficiency, recuperated gas turbine cycle ; 1988. ASME Journal of engineering for gas turbine and power, Vol.l 10, pp233-242
[25] El-Masri MA.; A flexible, efficient gas turbine cogeneration cycle with a novel dualmode heat recovery system ; 1988 ASME COGEN-TURBO IGTI-Vol.3, pp229-237
[26] El-Masri MA.; Exergy analysis of combined cycles: Part 1 - Air-Cooled Brayton-cycle gas turbine ; 1987. ASME Journal of engineering for gas turbine and power, Vol.109, pp228-236
[27] El-Masri MA., Chin W.W.; Exergy analysis of combined cycles: Part 2 - Analysis and optimisation of two-pressure steam bottoming cycles; 1987. ASME Journal of engineering for gas turbine and power, Vol.l 10, pp237-243
[28] El-Masri MA.; On thermodynamics of gas-turbine cycles: Part 1 - Second law analysis of combined cycles; 1985. ASME Journal of engineering for gas turbine and power, Vol.107, pp880-889
[29] El-Masri MA., Chin W.W.; Exergy analysis of combined cycles: Part 2 - Analysis and optimisation of two-pressure steam bottoming cycles; 1987. ASME Journal of engineering for gas turbine and power, Vol.109, pp237-243
[30] El-Masri MA., Pourkey F.; Prediction of cooling flow requirements for advanced utility gas turbines Part 1: Analysis and scaling of the effectiveness curve; 1986. ASME Paper 86-WA/HT-43
[31] El-Masri MA.; Prediction of cooling flow requirements for advanced utility gas turbines Part 2: Influence of ceramic thermal barrier coatings ; 1986. ASME Paper 86-WA/HT- 44
[32] El-Masri MA., Louis J.F., Hiraoka K.; A comparative study of the influence of different means of turbine cooling on gas turbine performance ; 1983. ASME Paper
[33] El-Wakil M.M.; Power plant Technology; 1984. McGraw-Hill Inc.
[34] Eriksson J.; HAT (Humid Air Turbine) - cykelns potential for mycket l&ga kvaveoxidniv&er ; 1991. Vattenfall, VU-S-91:28
[35] Foote WJt., Lake B.; Gas turbine power plant cycle with water evaporation ; 1959. US Pat 2,869324
[36] Foster-Pegg /?.W; TURBO-STIG - The turbo charged steam injected gas turbine cycle ; 1989. ASME Paper 89-GT-100
[37] Fraize W.E., Kinney C.; Effect of steam injection on the performance of gas turbine power cycles ; 1979. ASME Journal of engineering for power, Vol.101, pp217-227
[38] FreimarkM.; NOx reduction in large gas turbines by firing an oil/water emulsion ; 1990. VGB KRAFTWERKSTECHNIK 70, Num.10, pp742-74
45
References Lund Institute of Technology
[39] Frutchi H.U., Wettstein H£.; A thermodynamic comparison of steam injection gas turbines and combined cycle plants for cogeneration applications; 1991 ASME COGEN- TURBO IGTI-Vol.6, pp25-30
[40] Frutchi H.U., Plancherel A.; Comparison of combined cycles with steam injection and evaporation cycles ; 1988 ASME COGEN-TURBO IGTI-Vol.3, ppl37-146
[41] Gardiner Jr. W. C.; Combustion Chemistry; 1984. Springer-Verlag, New York Inc., ISBN 0-387-90963-X
[42] Gasparovic M; Stickoxide in den Gasturbinen: Bildung und Gegenmassnahme ; 1973. BWK, Brennst.-WSrme-Kraft 25, Nr.l, ppl-6
[43] Gasparovic N.; Kiihlung der verdichteten Luft bei Gasturbinen ; 1961. MTZ Jahrg.22, Heft 1, Jan, pp23-25
[44] Gasparovic N., Stapersma £>.; Gas turbines with heat exchanger and water injection in the compressed air ; 1973. Combustion, Dec., pp6-16
[45] Gasparovic N., Hellemans J.G.; Gas turbines with heat exchanger and water injection in the compressed air ; 1971. Proceedings/Institution of mechanical engineers, Vol.185, pp953-961
[46] Gasparovic N.; Efficiencies of cogeneration thermal power plants: A comparison ; 1987 ASME COGEN-TURBO IGTI-VoU, pp337-340
[47] Gasparovic N.; On the theory of the Brayton cycles ;
[48] Grigull U.; Properties of Water and Steam in Si-Units; 1982. Springer-Verlag, Berlin
[49] Hasselbacher H.; Gas Turbines ; 1989. Standard handbook of power plant engineering, Thomas C. Elliot, ISBN 0-07-019106-9, pp2.141-2.143
[50] Higdon CJl., Louks BM., Lynn S.; A novel heat-recovery process for improving the thermal efficiency of gas turbines in electric power generation ; 1990. Proceedings of the American power conference, Chicago, pp216-221
[51] Johnson D.; ASgidius Elling; 1961. Tekniskt Ukeblad, Nr.47
[52] Johnson D.; Zur Geschichte der Gasturbine; 1972. VGB KRFTWERKSTECHNIK 52, Heft 2, Apr, pp93-98
[53] Jung /.; Gasturbinen, dess utveckling, nuvarande anvandning och framtidsutsikter;1940. Teknisk Tidskrift Mekanik, H8fte 5, pp49-66
[54] Keller D., BynumD„ Kosla L.\ Cheng cycle brings flexibility to steam plant; 1986. Power engineering; Nov.; pp45-48
[55] Krugov V£., Shestakov N.S., Shvedkov VH., Fiveiskii V.Yu.; The results of an experimental investigation into lowering the emission of nitrogen oxides by spraying steam or water into the combustion zone; 1979. Thermal engineering, 26 (11), pp662-663
[56] IAess C.; Introduction to cooling of gas turbine blades ; 1969. Lecture series 15 of von Kami an Institute for fluid dynamics
[57] Undberg G.; A method of calculating actual open cycle gas turbine ; 1973. Svenska Tekniska Vetenskapsakademien, Helsinki ( Finland), In: Festschrift for P.-H. Sahlberg on his 60th birthday, Dec.26, pp23-52
[58] Lindberg G.; Accurate determination of gas turbine performance under different operational conditions; 1975. Thesis, Department of Heat and Power Engineering, Lunds Institute of Technology, Lund( Sweden)
[59] van der Linden S.; International Historic Mechanical Engineering Landmark 4MW Gas Turbine, Municipal Power Station Neuchatel, Switzerland ; 1988, ASME, New York
[60] Lorgere M., Carasse J.; Gas-steam cycle with water injection ; 1969. Conference on peakload coverage, Budapest, 18-20th Nov, D-ll ppl-7
46
Department of Heat and Power Engineering References
[61] Louis JJ7., Chuan shoo Wu; A comparative study of the influence of different means of cooling on the performance of the combined (Gas and steam turbines) cycle ; 1984. ASME Journal of engineering for gas turbines and power, Vol.106, pp750-755
[62] LysholmA.; Gas turbine system ; 1938. US Pat. 2,115,112
[63] Lysholm A.; Gas turbine system ; 1938. US Pat 2,115,338
[64] Manfrida G., Bosio A.; Comparative exergy analysis of STIG and combined-cycle gas turbines; 1988. Proceedings of the 23rd intersociety energy conversion engineering conference, 1988IECEC, pp391-397
[65] Maslennikov V.M., Shterenberg V.Y.; Power generation steam turbine - gas turbine plant for covering peak loads; 1974. Teploenergetika, 21 (4), pp59-64
[66] McCormack TJl., Guha P.K.; Matching the LM1600 gas turbine power and efficiency to a 10-13 MW cogeneration system ;Proceedings of the American power conference, pp895- 900
[67] McDonald C.F.; Recuperator utilisation for gas turbine plant performance enhancement - applications and technology ; 1990 ASME COGEN-TURBO IGTI-Vol.5, ppl51-163
[68] McDonald CJF.; Gas turbine recuperator renaissance ; 1990. Heat recovery systems & CHP, Vol.10, ppl-30
[69] McDonald CJ7.; The increasing role of heat exchangers in gas turbine plants ; 1989. ASME Paper 89-GT-103
[70] McDonald CJ7.; Gas turbine recuperator technology advancement; 1972. ASME Paper 72-GT-32
[71] McDonald CJ7.; The role of the recuperator in high performance gas turbine applications ; 1978. ASME Paper 78-GT-46
[72] McDonald CJ7., Van Hagen H., Creek R£.; Heat exchanger design for gas turbine HTGR power plant; 1979. ASME Paper 79-WA/GT-2
[73] Messerlie RL., Adelbert O.T.; Test results of a steam injected gas turbine to increase power and thermal efficiency ; 1983.18th intersociety energy conversion engineering conference, pp615-625
[74] Miller B„ Park O.; Gas turbine using 2 heat sources ; 1954. US Pat. 2,678,532
[75] Mori /., Miyauchi T., Yamagushi T.; Effect of steam addition on NO formation; 1981.18th Int. symposium on combustion, pp43-51
[76] Mukherjee D.K.; Zur Schaufelkuhlung der Gasturbine; 1977. Borwn Boveri Mit. 64:1, pp47-51
[77] Nakamura H., Mori Y., Takashashi T., Yamamoto K.; A highly efficient regenerative gas turbine system by new method of heat recovery with water injection ; 1983 Tokyo int. gas turbine congress, 83-Tokyo-IGTC-38, pp297-303
[78] Nakamura H. et al.; Regenerative gas turbine cycle; 1985. US Pat. 4,537,023
[79] Parsons Jr. EL., Bechtel TJ7.; Performance gain derived from water injection in regenerative, indirect-fired, coal-fuelled gas turbines; 1991. ASME-Paper, 91-GT-288
[80] Parsons EL.; Development, fabrication and application of a primary surface gas turbine recuperators; 1985. SEA Technical paper series 851254
[81] Rice I.G.; The reheat gas turbine with steam-blade cooling - A mean of increasing reheat pressure output, and combined cycle efficiency; 1982. ASME Journal of engineering for power, Vol.104, pp9-22
[82] Rice I.G., Jenkins PL.; Blading heat transfer considerations in reheat-gas-turbine combined cycle ; 1981. ASME Paper 81-GT-155
47
References Lund Institute of Technology
[83] Rao AD., Morton TR.; Perspective for advanced high efficiency cycles using gas turbines; 1989. Flour Daniel Inc., Michelson Drive, Irvine, California 92730
[84] Rao AD., Joiner JR.; A technical and economic evaluation of the humid air turbine ; 1990.7th annual int. Pittsburgh coal conference, pp 437-446, Report no: CONF-900958
[85] Rao AD., William HD.', FT4000 HAT: A 250 MW class aeroderivative gas turbine;1991.10th annual EPRI coal gasification conference
[86] Rao AD.', Process for producing power; 1989. US Pat. 4,829,763
[87] Rao AD., Francuz VJ„ Shen J.C., West E.W.; A comparison of humid air turbine (HAT) cycle and combined-cycle power plants ; 1991. Final report, EPRI IE-7300
[88] Rao AD., Cook D.T., McDaniel J.E.; HAT cycle simplifies coal gasification power ;1991. MPS REVIEW, May, ppl9-25
[89] Rao AD., William HD.; FT4000 Hat with natural gas fuel; 1992. ASME COGEN- TURBO, IGTI-Vol.7, pp239-245
[90] Rao AD. ; Closed cycle gas turbine with humidification of the working fluid ; 1991. Proceedings of the 26th Intersociety Energy Conversion Engineering Conference/La Grange Park, Amarican Nuc cop., pp493-498
[91] Rufli P.; A systematic analysis of combined gas/steam cycle ; 1987 ASME COGEN- TURBO IGTI-Vol.1, ppl 35-146
[92] Rufli P.; Systematische Berechnungen uber kombinierte Gas-Dampf Kraftwerke ; 1990. Diss ETH Nr. 9178, Ztirich
[93] De RuyckJ., Maniatas K., Baron G., Pottie K.; A biomass fuelled cogeneration plant based on an evaporative gas turbine cycle at the university of Brussels; 1991 ASME COGEN-TURBO IGTI-Vol.6, pp443452
[94] Schorr MM.; NOx emission control for gas turbines: A 1991 update on regulations and technology; 1991. Turbomachinery International, Sept/Oct, pp25-30
[95] Schorr MM.; NOx emission control for gas turbines: A1991 update on regulations and technology (Part H); 1991. Turbomachinery International, Nov/Dec, pp29-36
[96] Singh PR., Yuong WE., Ambrose MJ.; Formation and control of oxides of nitrogen emissions from gas turbine combustion systems; 1972. ASME 72-GT-22
[97] Soroka G., Kamali K.; Modular remotely operated, fully steam-injected plant for utility application ; 1987 ASME COGEN-TURBO IGTI-Vol.l, pp55-60
[98] Soroka G., WestsikJJJ.; Steam-injected gas turbines for moderate size power generation ; 1987. Proceedings of the 14th energy technology conference, ppl 185-1197
[99] Stambler I.; Predict $600/kW for HAT cycle compressed air storage plants ; 1992. Gas Turbine World, July-August, pp27-31
[100] Stecco S.S., Facchini B.; A simplified thermodynamic analysis of blade cooling effects in combined gas-steam power plants; 1988 ASME COGEN-TURBO IGH-Vol.3, pp299-304
[101] Stecco S.S., Facchini B.; A computer model for cooled expansion in gas turbines; 1989. ASME COGEN-TURBO IGTI-Vol.4, pp201-209
[102] Stodola A.; Dampf- und Gasturbinen; 1986. VDI-Verlag Diisseldorf, ISBN 3-18-400727-8
[103] Strasser A.; The Cheng cycle cogeneration system: technology and typical applications ; 1991 ASME COGEN-TURBO IGTI-Vol.6, pp419-428
[104] Takeya K„ Akifumi Hori; Outline of plant for advanced reheat gas turbine ; 1981. ASME Journal of engineering for power, Vol.103, pp772-775
48
Department of Heat and Power Engineering References
[105] Takeya K., Yasui H.; Performance of the integrated gas and steam cycle (IGSC) for reheat gas turbines; 1988. AS ME Journal of engineering for gas turbine and power, Vol.110, pp220-232
[106] Thames JM.; Advanced gas turbine steam injection ; 1989. Gas research inst., Chicago,IL, Repeat No. GRI-89/0179
[107] Touchton G.L.; Influence of gas turbine combuster design and operating parameters on effectiveness of NOx suppression by injected steam and water ; 1985. ASME Journal of engineering for gas turbine and power, Vol.107, pp706-703
[108] Touchton GL.; An experimentally verified NO* prediction algorithm incorporating the effects of steam injection ; 1984. ASME Journal of engineering for gas turbine and power, Vol.106, pp833-840
[109] Traupel VP.; Thermische Turbomaschinen ; 1977.3rd Edition, Vol.I, Springer-Verlag, Berlin
[110] Tumanovskii A.G., Tul 'skii VI'.; Influence of water injection on the formation of nitrogen oxides at the outlet of the combustion chamber with series introduction of air into the combustion ; 1982. Thermal engineering, 29 (6), pp319-321
[111] Tuzson Status of steam-injected gas turbines ; 1991 ASME COGEN-TURBO IGTI- Vol.6, pp 19-24
[112] Valentino SJDesigning reliability into high-effectiveness industrial gas turbine regenerators ; 1979. ASME Paper 79-GT-199
[113] Williams R.H., Larson EJD.; Steam-injected gas turbines ; 1987. ASME Journal of engineering for gas turbine and power, Vol.I09, pp55-63
[114] Williams R.H., Larson ED.; Technical and economic analysis of steam-injected gas- turbine cogeneration ; 1985. AIP conference proceedings-Energy sources: Conservation and renewables, No. 135, pp402-425
[115] Williams R.H., Larson ED.; Steam-injected gas turbines and electric utility planning; 1986. Proceedings of the 13th energy technology conference
[116] Williams R.H, Larson ED.; Steam-injected gas turbine and electric utility planning ;1986. IEEE technology and society magazine, mar.1986, pp29-38
[117] Williams R.H., Larson ED.; Biomass-fired steam-injected gas turbine cogeneration ;1988 ASME COGEN-TURBO IGTI-Vol.3, pp57-66
[118] Williams R.H., Larson ED.; Biomass-gasifier steam-injected gas turbine cogeneration ; 1990. ASME Journal of engineering for gas turbine and power, Vol.l 12, ppl57-163
[119] Wilson D.G.; The design of high-efficiency turbomachinery and gas turbines ; 1984. Fifth printing 1991, The Massachusetts Institute of Technology( USA)
[120] Yoshida T., Hyodo T.; Evaporation of water in air, humid air and superheated steam ; 1970. Ind. Eng. Chem. Process Des. Develop., Vol.9, No.2, pp207-214
[121] Zweifel O.; Die Bestimmung des Zustandsverlaufes in Turbomaschinen mit Hilfe der Entropiezunahme ; 1941. Borwn Boveri Mit. 28:8/9, pp232-236
49
Appendix Lund Institute of Technology
Appendix
Appendix A: Thermodynamic Properties of a mixture
OF IDEAL GASES.
The calculation of the thermodynamic properties of an ideal gas is based on an investigation made by NASA, described in [41] where a vast number of gaseous substances have been thoroughly examined.
NASA chose to model the thermochemical behaviour of a substance by using two sets of polynomials. The first set is valid in the temperature range from 300 K to 1000 K and the second set guilty from 1000 K to 5000 K. Both sets have the form:
Cp = R - ( 3] + a2*T + a3-T2 + a4-T3 + a5-T4) (eq.l)
(eq.2)
( t2 T3S = R • I a^ lnT+ a2T + a3-y + a4-g- + a5 (eq.3)
These base formulas have then been customised for thermodynamic calculations by changing A* and A7 and by adding a pressure term in the entropy relation [9]. From Ag and A7 the chemical potential of the substance is redrawn and the enthalpy (eq.5) and entropy relations (eq.6) are adjusted to zero at 0"C ( T0 = 273.15 K and p0 = 1.01325 bar) for all substances. All investigations made by NASA were conducted at a constant pressure level ( p0 = 1.01325 bar) which were the formula of the entropy (eq.6) only is valid at this level, it is however easy, when assuming an ideal gas, to extend the validity by adding a pressure dependent term to the entropy relation. When the unity base kmole substance is also exchanged to kg substance, the three relations given above can be written as:
(eq.4)
(eq.5)
(eq.6)
where (eq.7)
and
(eq.8)
for the lowo: temperature range 300<T<1000 K. This means that h(Tg) = 0 and sCTq) = 0 for the reference state ( T0 = 273.15 K, p0 = 1.0325 bar).
Department of Heat and Power Engineering Appendix
For the higher temperature range 1000<T<5000 K the constants will be
T02 T03 T04 VHh ~ (alL ' al//)'V (a2L ' a2//) 2 + (a3L ■ a3//)‘~3~ + * a4tf) 4 + (a5L ' a5«) 5 + &6L
(eq.9)
and
T02 T03 T04a7ff = * (alL * al//)'lnTo+ (a2L - a2tf)'T0 + (a3t * a3//> 2 + (a4i ' aw)'~3~ + (a5L " a5«) 4 + a7L
(eq.10)
A program package has been developed by the author which predicts any thermodynamic quantity ( Temperature, specific heat capacity, enthalpy, entropy) when one of them is known and the properties of the gas mixture are also known. From the properties of the gas mixture the program calculates two new sets of polynomial coefficients representing the mixture's thermodynamic behaviour within the temperature range.
51
Appendix Lund Institute of Technology
Appendix B: Thermodynamically based calculation
MODELS OF THE COMPRESSOR AND THE EXPANDER.
The state of change prevailing in a compressor or in an expander are examples of polytropic state of change defined as:
Pi*vl” = P2v2nwhere n is the polytropic coefficient
When assuming an ideal gas, the relation can be rewritten by means of eq.3 as
For an ideal gas four base relations can be deduced:
p • v = R • T
R = cp(T)-cv(T)
K =Cp(T)
cv(Ddh = cp(T) • dT
. _ dT „ dpds = cp(D ' ~ * R ‘ p
The polytropic efficiency for a compression is defined as:
T|_v_LiE
dh
(eq.l)
(eq.2)
(eq.3)
(eq.4)
(eq.5)
(eq.6)
(eq.7)
(eq.8)
and for an expansion the polytropic efficiency is defined as:
dh~ v • dp (eq.9)
Assuming an ideal gas, eq.9 and 9 can be rewritten by means of eq.3 and eq.6 as
Rf^c= df (eq.10)
CpfD'Y
for a compression and as
dTcpW —
"He- dp (eq.ll)P
for an expansion.
A state of change from state 1 to state 2 representing a compression can then be written by integrating eq.lOas
R • InTlc = l-----
f dT JcpOVY
1
(eq.12)
52
Department of Heat and Power Engineering Appendix
and a state of change from state 4 to state 5 representing an expansion can be written by integrating eq.ll as
(eq.13)
Conventional thermodynamic simulation model of a compression and an expansion.
In conventional thermodynamic simulations of a compression and an expansion a perfect gas assumption (cp = const.) has to be made. Then eq.12 and eq. 13 can be rewritten as
(eq.14)
(eq.15)
From eq.14 and eq.15 the well known models for a compression l R
and for an expansionR
, valid for a perfect gas can be deduced.
(eq.16)
(eq.17)
Eq. 4 and eq. 5 gives
R k- 1(eq.18)
The relation between the polytropic coefficient and the isentrqpic coefficient for a compression can be written as
n-1 1 k-1n ~qc k
and for an expansion it can be written as
(eq.19)
(eq.20)
Resuming the ideal gas assumption is usually done by using a mean value approximation of the heat capacity. Approximated as
ho - hi" t2-Tj (eq-21)
or more roughly as
53
Appendix Lund institute of Technology
cp(D = c
for a compression and approximated as
(eq.22)
■ hjCpfO = 't4_t5 (eq.23)
or more roughly as
Cp(D = Cp^Y^) (eq.24)
for an expansion.
Both for the compression and for the expansion, the mean value of the heat capacity cannot be decided before the end states are known, which render the iterative solutions of eq.14 and of eq.15 when solved for an ideal gas.
Otto Zweifels' thermodynamic simulation model of a compression and an expansion.
O. Zweifel proposed to simulate the compression and expansion by dividing the polytropic state of change into two state of change, one isothermal state of change and one isobaric state of change ( Fig-1)-
"Actual* way iXr " '
Calculated vay
Expansion
Victual" way& Cajci hied way
Compression
Figure 1. The principle of dividing a compression or an expansion representing a polytropic state of change into one isobaric and one isothermal state of change.
The compression representing a state of change from state 1 to 2, eq.10 can then be rewritten as
(eq-25)
and the expansion representing a state of change from state 4 to 5, eq. 11 can then be rewritten as 5p 5 5p
Tie4 5p
V 5p
5
R* In(eq-26)
54
Department of Heat and Power Engineering Appendix
Using eq.7 on the isobanc state of change from state 1 to Ip, the entropy growth can be written as
ipC dT
Sjp - sj = ASp = J cp(T) • .p (eq.27)
l
and then making an isothermal state of change from state Ip to 2, the entropy growth can be written as
s,p.s2 = AsT = R-ln^ (eq.28)
reaching the end state of the compression.
By identifying the terms in eq.25 with eq.27 and eq.28, eq.25 can be rewritten as
Similar to compression for expansion, the entropy growth for an isothermal state of change from state
(eq.29)
4to5p can be rewritten as
S5p-s4= A*r = R-ln^
and then an isobaric state of change from state 5p to 5 can be rewritten as 5
. r dT s5p - s5 = ASp = JCpfO'Y
5pBy identifying the tarns in eq.26 with eq.30 and eq.31, eq. 26 can be rewritten as
(eq.30)
(eq.31)
Ie S5p-S4 ASt(eq.32)
The isothermal state of change is easy to calculate according to eq.28 for the compression and eq.30 for the expansion. Resolving ASp from eq.29 for the compression and eq.32 for the expansion, it is possible to calculate the isobaric state of change without solving the integrals of eq.27 and eq.31. This results in compression and expansion being solved explicitly, without any idealisation losses in the model as in the conventional calculation under an ideal gas assumption.
55
Appendix Lund Institute of Technology
Appendix C: Inputs for systems with an uncooled
EXPANDER
Relative humidity inlet air = 60%
Ambient temperature = 15 *C
Ambient pressure = 1.01325 bar
Inlet water temperature = 8 *C
Inlet fuel temperature = 15 *CExit exhaust gas temperature from district heater = 65 ‘C
Turbine inlet gas temperature = 850 *C
Compressor pressure ratio p2/Pi = var. 5 - 35
Pressure loss at compressor inlet = 0.7 %Pressure loss at turbine outlet = 3%Pressure loss through combustion chamber = 4%
Pressure loss through intercooler- Air side = 1 %
Pressure loss through intercooler- Water side = 5%
Pressure loss through aftercooler- Air side = 1 %
Pressure loss through aftercooler- Water side = 5%Pressure loss through economiser- Exhaust gas side = 1 %Pressure loss through economiser - Water side = 5%Pressure loss through humidification tower = 2%Water pressure before injection into the humidification tower = 60 barPressure loss through recuperator- Air side = 2%Pressure loss through recuperator - Exhaust gas side = 2%
Pressure loss through district heater- Exhaust gas side = 1%Poly tropic compressor efficiency = 89%Polytropic expander efficiency = 90%Isentropic circulating water pump efficiency = 85%Combustion efficiency = 99%Mechanical efficiency = 99%Generator efficiency = 98.5%Electric efficiency of the circulating water pump = 95%Recuperator efficiency = 85%Relative humidity after humidification tower = 100%Minimum temperature difference between inlet air temperature
of the humidification tower and its exit water temperature Pinch-Point - inlet air intercooler temperature
= 8 "C
and its outlet water temperature = 10 *C
56
Department of Heat and Power Engineering APPENDIX
Pinch-Point - inlet air aftercooler temperature
and its outlet water temperature
Pinch-Point - inlet air economiser temperature
and its outlet water temperature
Properties of dry air substances by volume parts:
N2o2
Ar
C02Ne
0.78084
020948
0.00934
0.00032
0.00002
Properties of fuel substances by volume parts:
CH4c2h6c3h8
Cflion2co2
Heat value of the fuel
0.90982
0.04730
0.01732
0.01456
0.00598
0.00502
= 48 000 kJ/kg
= 10 *C
= 10'C
57
Appendix Lund Institute of Technology
Appendix D: Inputs for systems wit
EXPANDER
Relative humidity inlet air = 60%
Ambient temperature = 15 *C
Ambient pressure = 1.01325 bar
Inlet water temperature = 8‘C
Inlet fuel temperature = 15 "C
Exit exhaust gas temperature from district heater = 65 *C
Turbine inlet gas temperature = 1250 C
Compressor pressure ratio p2/pj = var. 5-35
Pressure loss at compressor inlet = 0.7 %Pressure loss at turbine outlet = 3%
Pressure loss through combustion chamber = 4%
Pressure loss through intercooler- Air side = 1 %
Pressure loss through intercooler- Water side = 5%
Pressure loss through aftercooler- Air side = 1 %
Pressure loss through aftercooler- Water side = 5%
Pressure loss through economiser- Exhaust gas side = 1 %Pressure loss through economiser - Water side = 5%
Pressure loss through humidification tower = 2%
Water pressure before injection into the humidification tower = 60 bar
Pressure loss through recuperator- Air side = 2%
Pressure loss through recuperator - Exhaust gas side = 2%
Pressure loss through district heater- Exhaust gas side = 1 %Polytropic compressor efficiency = 89%
Polytropic expander efficiency = 90%
Isentropic circulating water pump efficiency = 85%
Combustion efficiency = 99%
Mechanical efficiency = 99%
Generator efficiency = 98.5 %Electric efficiency of the circulating water pump = 95%
Recuperator efficiency = 85%
Relative humidity after humidification tower = 100%
Minimum temperature difference between inlet air temperature
of the humidification tower and its exit water temperature
Pinch-Point - inlet air intercooler temperature
= 8 "C
and its outlet water temperature = 10‘C
COOLED
58
Department of Heat and Power Engineering Appendix
Pinch-Point - inlet air aftercooler temperature
and its outlet water temperature = 10 *C
Pinch-Point - inlet air economiser temperature
and its outlet water temperature = 10 *C
Air cooling method alt. 1-4 =3
1) Convective cooling
2) Impingement cooling
3) Film cooling
4) Transpiration cooling
Number of stages in expander = 4
Number of cooled stages in expander = 2
Turbine stage loss coefficient = 0.7
Maximal allowed mean surface temperature of blades:
First cooled stage = 850 *C
Second cooled stage = 850 "C
Mean heat transfer coefficients in :
First cooled stage = 2000 W/m2K
Second cooled stage = 2000 W/m2K
Stage surface area in per mass flow of compressed air
First cooled stage = 0.040 m2/(kg Total Exhaust Gas/s)
Second cooled stage = 0.050 m2/(kg Total Exhaust Gas/s)
Properties of dry air substances by volume parts:
n2 0.78084
02 020948
Ar 0.00934
co2 0.00032
Ne 0.00002
Properties of fuel substances by volume parts:
ch4 0.90982
c2h6 0.04730
c3h8 0.01732
Cflio 0.01456
N2 0.00598
C02 0.00502
Heat value of the fuel = 48 000 kJ/kg
59
