Gas turbine cooling modeling - Thermodynamic analysis and ...

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INSTITUTIONEN FOR VARME- OCH KRAFTTEKNIKKRAFTVERKSTEKNIKLUNDS TEKNISKA HOGSKOLA

Gas Turbine Cooling Modeling - Thermodynamic Analysis and Cycle

Simulations

by

Kristin Uf*oFOREIGN SALES PROHIBITED oJ^

Thesis for the Degree of Licentiate in Engineering

ISRN LUTMDN/TMVK—7034—SE

DIVISION OF THERMAL POWER ENGINEERINGDEPARTMENT OF HEAT AND POWER ENGINEERING LUND INSTITUTE OF TECHNOLOGY P.O. BOX 118, S-221 00 LUND SWEDEN1999

DISCLAIMER

Portions of this document may be illegible in electronic image products. Images are produced from the best available original document.

Abstract

Considering that blade and vane cooling are a vital point in the studies of modern gas turbines, there are many ways to include cooling in gas turbine models. Thermodynamic methods for doing this are reviewed in this report, and, based on some of these methods, a number of model requirements are set up and a Cooled Gas Turbine Model (CGTM) for design-point calculations of cooled turbines is established. Thereafter, it is shown that it is possible to model existing gas turbines with the CGTM. Knowledge of at least one temperature in the hot part of the gas turbine (TET, TRIT or possibly TIT) is found to be vital for a complete heat balance over the turbine.

The losses, which are caused by the mixing of coolant and main flow, are in the CGTM considered through a polytropic efficiency reduction factor S. Through the study of S, it can be demonstrated that there is more to gain from coolant reduction in a small and/or old turbine with poor aerodynamics, than there is to gain in a large, modern turbine where the losses due to interaction between coolant and main flow are, relatively speaking, small.

In most of the calculations, all of the coolant is extracted from the compressor outlet, but it is also shown how bleeding off cooling air at an intermediate point in the compressor, decreases the coolant flow requirements.

It is demonstrated, at the design point (TET=1360°C, tt=20) for the simple-cycle gas turbine, that heat exchanging between coolant and fuel proves to have a large positive impact on cycle efficiency, with an increase of 0.9 percentage points if all of the coolant passes through the heat exchanger. The corresponding improvement for humidified coolant is 0.8 percentage points.

In a design-point study for the HAT cycle, if all of the coolant is extracted after the humidification tower instead of after the compressor, there is a decrease in coolant requirements of 7.16 percentage points, from 19.58% to 12.42% of the compressed air, and an increase in thermal efficiency of 0.46 percentage points, from 53.46% to 53.92%.

It is demonstrated with a TET-parameter variation, that the cooling of a simple-cycle gas turbine with humid air can have a positive effect on the thermal efficiency over a wide temperature range. The higher the temperature of the exhaust gases, the more water can be evaporated into the cooling air. This means that with the current trend of increasing temperature levels in gas turbines, cooling with humid air is a very interesting concept.

A TET-parameter variation for the HAT cycle showed that it is more interesting to maintain the amount of compressed air expended for cooling and try to increase TET rather than to decrease the coolant flow requirements, as different coolant extraction points are examined for varying TET. In this way, it should be possible to obtain a cycle efficiency increase of 0.7-1.0 percentage points or perhaps even more.

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Contents

1 Introduction 11.1 The need for gas turbine cooling modeling............................................................ 11.2 Objective....................................................................................................................... 21.3 Method.......................................................................................................................... 31.4 Definitions....................................................................................................................... 31.5 Report outline ....................................................................................................... 31.6 Acknowledgements....................................................................................................... 4

2 Gas turbine cooling 52.1 History .......................................................................................................................... 52.2 Current technologies and development trends..................................................... 62.3 High-temperature materials...................................................................................... 72.4 Cooling technologies................................................................................................... 82.5 Problems associated with turbine cooling ............................................................ 92.6 The use of compressed air..............................................................................................10

3 Modeling of cooled gas turbines in literature 123.1 Early models, derived for design purposes............................................................ 12

3.1.1 Studies on gas turbine performance............................................................ 123.1.2 Blade heat transfer......................................................................................... 13

3.2 Models for thermodynamic cycle studies............................................................... 133.2.1 Simple models .................................................................................................... 143.2.2 Expansion models that include losses.......................................................... 15

3.3 Cooling modeling.......................................................................................................... 173.4 Some observations on cooled gas turbine modeling........................................... 19

4 A suggestion for a Cooled Gas Turbine Model 204.1 Model requirements ....................................................................................................... 214.2 The Model .................................................................................................................... 21

4.2.1 Cooling models.................................................................................................... 224.2.2 Choice of cooling method................................................................................ 234.2.3 Expansion model.................................................................................................23

4.3 Model parameters ...........................................................................................................234.4 Implementation in IPSEpro.......................................................................................... 24

4.4.1 The units.............................................................................................................. 244.4.2 The turbine stage ..............................................................................................254.4.3 Other features .................................................................................................... 26

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5 Design-point model validation 275.1 TIT and other ISO standards................................................................................... 275.2 Parameter settings...................................................................................................... 285.3 Modeling of existing gas turbines................................................................................ 295.4 Comparison with GATECycle.......................................................................................315.5 Mixing of coolant and hot gases before the expansion............................................325.6 Experiences from the validation calculations............................................................ 33

6 Design-point gas turbine studies 356.1 Reference gas turbines................................................................................................ 356.2 The impact of S and T)p............................................................................................ 366.3 The uncooled gas turbine......................................................................................... 376.4 Cooling air bleed-off................................................................................................... 376.5 Coolant treatment...................................................................................................... 38

6.5.1 Impact of Cp9/cpC on coolant flow requirements........................................ 406.5.2 Fuel pre-heating................................................................................................ 416.5.3 External water heat exchanger...................................................................... 416.5.4 Humidifying the coolant................................................................................... 426.5.5 Synthesis of coolant treatment.................................................... 44

6.6 The HAT cycle - a brief presentation......................................................................... 456.7 Humidification tower....................................................................................................... 46

6.7.1 Simple model....................................................................................................... 466.7.2 More detailed model..........................................................................................466.7.3 Comparison with experiments......................................................................... 48

6.8 HAT Cycle configuration................................................................................................ 496.9 HAT cycle performance at the design point............................................................ 506.10 Combined cycle performance at the design point...................................................51

7 Parameter variations 537.1 The uncooled gas turbine......................................................................................... 537.2 The cooled simple-cycle gas turbine.............................................................................53

7.2.1 The role of S................................................................................................... 537.2.2 Dry-air coolant................................................................................................ 557.2.3 Humid-air coolant......................................................................................... 58

7.3 HAT cycle parameter variation............................................................................... 607.4 Combined cycle parameter variation..........................................................................627.5 Synthesis ....................................................................................................................... 62

8 Concluding remarks 658.1 Conclusions................................................................................................................... 658.2 Discussion and suggestions for future work................................................................66

A Presentation of the software package IPSEpro 73

B Humid air 75B.l Thermodynamics review............................................................................................ 75B.2 Humid air in IPSEpro................................................................................................ 76B.3 Cooling modeling for humid and dry air...................................................................77

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C Input for cycle simulations in chapters 6 and 7 79C.l Miscellaneous input ...................................................................................................... 79C.2 Reference gas turbine input.........................................................................................80C.3 HAT cycle input.............................................................................................................81C.4 Combined cycle input ................................................................................................... 82

D Blade cooling models: Comparison and thermo dynamic analysis 83

Presented at the 5th ASME/JSME joing thermal engineering conference March 14-19, 1999 San Diego, CA (AJTE99-6117)

IV

List of Figures

2.1 The development over time of gas-turbine materials and hot gases temperature levels, and the impact of cooling on this development [18]...................... 6

2.2 Principles of the four different cooling methods.................................................... 82.3 Convection cooled blade (Courtesy of ABB STAL).............................................. 102.4 Principle of vane impingement cooling (Courtesy of ABB STAL)........................ 11

3.1 Method for considering the expansion over one cooled turbine stage according to ref [35]................................................................................................................... 17

3.2 e&m as a function of m*.................................................................................................... 19

4.1 Black-box model of the cooled turbine.........................................................................204.2 cooLrumix (left) and Turbine (right) units created in IPSEpro............................. 254.3 The graphical representation of a cooled turbine stage in IPSEpro..................... 254.4 TS-diagram for expansion over a stage with the CGTM.........................................264.5 Turbine-inlet (left) and Turbine-outlet (right) units in IPSEpro........................... 26

5.1 Flowsheet for IPSEpro calculations with the Cooled Gas Turbine Model . . 305.2 Flowsheet for IPSEpro calculations with a simple cooling model......................... 32

6.1 Impact of S on r\VT and ip with model for expansion losses derived fromTraupel [57]..........................................................................................................................36

6.2 Ts-diagram for calculations with uncooled turbine...................................................386.3 Change in simple-cycle efficiency (upper left), coolant flow requirements

(upper right) and compressor specific work (lower diagram) for changing pressure of coolant extraction for second vane....................................................... 39

6.4 (p[ as a function of m*.......................................................................................................406.5 Impact on simple cycle efficiency from heat exchanging between cooling air

and fuel.................................................................................................................................426.6 Impact on simple cycle efficiency from heat exchanging between cooling air

and an external water source (left) and heat removed from the coolant asa function of cooling flow (right)....................................................................................43

6.7 Flowsheet for gas turbine cycle with evaporatively cooled coolant.......................436.8 Principle for calculating the pinch point of the humidification tower.................. 476.9 HAT cycle configuration with coolant extraction points......................................... 49

7.1 Variation of specific power with thermal efficiency for the uncooled gasturbine, tt = 5 — 40 and TET=900 — 1500° C.........................................................54

7.2 The impact of varying S on simple-cycle efficiency................................................ 55

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7.3 Variation of specific power with thermal efficiency for the reference gasturbines............................................................................................................................. 56

7.4 Simple cycle efficiency % as a function of ip for the three reference gasturbines............................................................................................................................. 57

7.5 Specific work a; as a function of <p for RefGT2......................................................587.6 Results for simple cycle cooled with humid air, tt=20, TET=1200 — 1520°C. 597.7 Variation of Cp9/cpC for simple cycle cooled with humid air as a function of

the temperature right before the cooling point...................................................... 607.8 Results of TET-parameter variation for HATcycles 1-7.......................................617.9 HATcycles 1 and 6 and the relation between changes in and TET, and

their impact on thermal efficiency. .............................................................................627.10 Comparison of simple gas turbine cycles, combined cycle and HAT cycles

for various TET. All calculations made with RefGT2............................................... 64

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List of Tables

1.1 The effect of adding gas turbine cooling. TET= 1360° C, ir = 30..................... 2

5.1 Deviation from standard case for the different cases of parameter settingsfor GTS.............................................................................................................................28

5.2 Manufacturers’ data for seven existing gas turbines................................................. 295.3 Calculated results with the CGTM................................................................. -. . . 305.4 Primary input parameters for gas turbine simulations.............................................315.5 Data and results for GT4 with GATECycle and with the CGTM................... 325.6 Results from simulation when all of the coolant is entered before the ex

pansion begins................................................................................................................ 33

6.1 Performance and vital input data for the three reference gas turbines. Turbine polytropic efficiency rjp in the uncooled part=0.91...................................... 35

6.2 Results from simulations with Brayton cycle..............................................................376.3 Performance of the three reference gas turbines cooled with evaporatively

cooled coolant..................................................................................................................... 446.4 Change in percentage points for RefGT2, in thermal efficiency for the dif

ferent cases of coolant treatment................................................................................... 456.5 Comparison between calculated and measured values for the humidification

tower......................................................................................................................................486.6 Cases considered in HAT cycle study, coolant for 2nd vane extracted at

intermediate point in the compressor for case 1A................................................. 506.7 Performance of HAT cases at design point for RefGTl, RefGT2 and RefGT3. 516.8 Performance, reference combined cycle.................................................................. 52

B.l Comparison between data for humid air with water as water vapor and forhumid air with water as an ideal gas. u> — 0.2....................................................... 77

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N omenclat ure

A area, m2 7T pressure ratio, -P power, W P density, kg/m3Ft Prandtl number, - w specific humidity,

R specific gas constant, kJ/(kgK) kg HgO/kg dry air

Re Reynolds number, - SubscriptsS polytropic efficency reduction

factor, - 0 reference condition4 turbine inletSt Stanton number, -5 turbine outlet

T temperature, °C or Kctix

TET ISO turbine entry temperature, °G 6TIT ISO turbine inlet temperature, °C c coolant, coolingTRIT ISO turbine rotor inlet cmp compressor

temperature, Ccr critical

U velocity, m/s da dry airCLi specific work, kJ/kg e exitCp specific heat, kJ/(kgK) el electricalh enthalpy, kJ/kg evap evaporatedk slope, - exh exhaustm mass flow, kg/s 9 gasm* dimensionless coolant i inlet

mass flow ratio, - l localP pressure, Pa m mechanicalg heat, kJ/kg mix mixtures enthropy, kJ/(kgK) P polytropicV specific volume, m3/kg PP pinch point

Greek symbols r reduceds standard

a heat transfer coefficent, W/(m2K) t turbineA arithmetic difference, - th thermal£bm cooling effectiveness, - V vaporY> coolant to compressor inlet w water

mass-flow ratio, % X arbitrary point<Ph relative humidity, %

V efficiency, % Superscript

K specific heat ratio - averageV viscosity, m2/s

Vlll

Chapter 1

Introduction

For both environmental and economical reasons, there is an interest in and a need for power plants with increased efficiency and power output. Power plant cycles that include gas turbines are interesting from these points of view, since the gas turbine combines rapid and easy installation with low cost and low emissions. The most common gas turbine cycle for efficient electrical power production, as of today, is the combined cycle, but extensive research is currently going on to find new, competitive gas turbine cycles, e.g. the HAT and STIG cycles. These kinds of gas turbine cycles are often referred to as advanced cycles in literature.

Development of new cycles is only one of the many domains in gas-turbine related research. Much effort is put into improving the gas turbine itself. Increasing the efficiency of the gas turbine can be done through the increase of component efficiencies and through the increase of cycle pressure ratio and/or the temperature of the gases leaving the combustion chamber. Here, industrial gas turbines can benefit from the developments in cooling methods, materials and computer-based design methods that come from the development of aircraft engines.

1.1 The need for gets turbine cooling modeling

The addition of cooling to the gas turbine means that it will be much more complicated to design and manufacture. From a thermodynamic point of view, it can no longer be treated as a Brayton cycle in the simple, straightforward way that is described in several places in literature [10, 12, 24]. Still, it must be possible to calculate the impact of cooling on gas turbine efficiency and outlet temperature, in order to enable calculations on power plant cycles and concept studies for new power generation solutions. Since the thermodynamics and fluid dynamics of the expansion in a cooled turbine are extremely complicated, and thus, time-consuming to calculate, this means that a simplified thermodynamic model that can be incorporated into power plant cycle calculations, is required.

The following example illustrates the importance of gas turbine cooling modeling in thermodynamic cycle calculations: intercooled aeroderivative gas turbines (ICAD) have high pressure ratios and high combustor exit temperatures, and are mentioned in literature as a possible solution for electric power generation, since they in simple cycle have higher efficiency than common industrial gas turbines [26]. Intercooling in itself lowers the efficiency of the Brayton cycle [24], but the fact that cooling air can be supplied at a lower temperature, helps in reducing the cooling air requirements enough actually to increase

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Table 1.1: The effect of adding gas turbine cooling. TET= 1360°C, tt = 30.

No cooling Cooled GTVth Vth y

Simple cycle ICAD

44.6%42.5%

39.0%39.7%

20.8%15.7%

the efficiency of the gas turbine. This is shown in table 1.1 where results for a simple uncooled Brayton cycle with component losses, but without any cooling, axe compared to an engine with the same component losses, but where cooling is considered according to the method presented in chapters 4 and 5 in this work.

It can be seen in table 1.1 that omitting the cooling in cycle calculations leads to an error in cycle efficiency estimation by several percentage points. The ICAD shows a considerable decrease in cooling air requirements compared to the simple cycle and, hence, more of the compressed air can be used to extract power from the turbine. Without a cooling model incorporated in the cycle calculations, the estimation of the impact of the intercooling would be completely wrong. For the ICAD cycle, these facts are already known, but this example illustrates the importance of considering cooling for completely new power plant concepts that include gas turbines. If cooling is not considered properly, there might be severe errors that will not be discovered until more detailed studies are made, and much time and money have been wasted.

1.2 Objective

It is the objective of the present work to derive and evaluate a design-point model for expansion in cooled gas turbines, and to apply it to cycle calculations, in order to gain more knowledge about the connection between coolant flow requirements and cycle performance. In particular, the following questions are to be answered:

What is the impact on cycle efficiency if we

• bleed off cooling air at an intermediate point in the compressor?

• pre-cool the cooling air of the simple-cycle gas turbine?

• humidify the cooling air in the simple-cycle gas turbine?

• cool the gas turbine of the Humid Air Turbine (HAT) cycle with cooled or humidified air?

It must be emphasized that the work has been limited to thermodynamic studies, i.e. turbine geometries and required volume flows have not been considered, although this is a most important issue in gas turbine design.

It was determined that a model for the cooled gas turbine was required that can handle

• calculation of coolant mass flow requirements with consideration taken regarding temperature and specific heat;

• losses caused by the mixing of the main flow with the coolant;

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• cooling air bleed-off from the compressor.

Since knowledge about different kinds of software for heat balance calculations is a fundamental research area at the division of Thermal Power Engineering at the Department of Heat and Power Engineering, an additional goal has been to learn more about the software employed. IPSEpro has been used for most of the calculations, but also GATECycle 4.3 has been of use.

1.3 Method

In order to reach the goal described above, an extensive literature study was made, both to learn more about gas turbine cooling and to see how this cooling has been accounted for in previous thermodynamic studies. Based on the results from the literature study and on experiences from calculations, a model for open-loop gas turbine cooling calculations was derived, and some rules of thumb were established to facilitate methodical use of it. The model was validated against gas turbine manufacturers’ data and a previous parameter study, and thereafter, applied in parametric studies of the simple gas turbine cycle and the HAT cycle. Also, a combined cycle was established in order to quantify the results from the HAT-cycle calculations.

During the work, contact was kept with the industry, notably, ABB STAL in Finspong. Also, contacts were made with the Dipartimento di Energetica of the University of Perugia in Italy. These contacts resulted in the article in appendix D.

1.4 Definitions

The word modeling has many different meanings in scientific literature. In the present work, modeling means to put together sets of equations in an appropriate way, so that the phenomenon that is studied can be described. Simulation in this context means to perform calculations with the sets of equations that make up the models.

The word turbine is, in this context, used for the device where the actual expansion takes place; whereas, gas turbine is used for the entire engine, with compressor and combustion chamber.

Turbine cooling is used to define the cooling of blades, vanes and disks in the hot part of the turbine. Of course, other parts of the gas turbine are also cooled, in particular the combustion chamber and the transition piece from the combustion chamber to the inlet guide vanes; but this has not been studied in the present work.

1.5 Report outline

The main body of the report consists of three parts: literature review, model establishment and simulations. Chapters 2 and 3 are pure literature reviews. In chapter 2, the concept of gas turbine cooling is presented, and in chapter 3, different aspects of gas turbine cooling modeling are presented, with the restriction that no numerical studies have been reviewed.

Based on some of the works presented in chapter 3, chapter 4 contains a synthesis model (referred to as Cooled Gas Turbine Model, CGTM) for thermo dynamic calculations of the expansion in a cooled gas turbine. The design-point behavior of this model is evaluated in chapter 5, as it is used to simulate some industrial gas turbines.

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Using the results from chapter 5 as guidelines, three reference gas turbines are established in chapter 6 and used for design-point simulations, where the items listed in section 1.2 are studied. In chapter 7, parameter variations are made for some of the cycles discussed in chapter 6. Based on parameter variations of the simple-cycle gas turbine, the differences among the three reference gas turbines are discussed. At the end of chapter 7, a synthesis is made of the parameter variations, where the different kinds of cycles studied are compared to each other.

In chapter 8, a discussion of some of the assumptions made in the CGTM is provided, followed by a conclusion of the results. In appendices A and B reviews of the software employed and of humid air thermodynamics are given - information that is not vital to the understanding of the report, but that might be of interest to some readers. Input data for the simulations are given in appendix C, and an article written in connection with the report is enclosed in appendix D.

1.6 Acknowledgements

First of all, I’d like to thank my supervisor, Professor Tord Torisson, for giving me the opportunity to become a Ph.Dstudent, and also for good advice and pertinent comments throughout the progress of this work.

There are many others at the Department of Heat and Power Engineering, whom I wish to thank in one way or another: first of all, thanks to Fredrik Olsson, for his patience with a messy roommate during the past years, then thanks to Mikael Naslund and Johan Revstedt for helping me with D-T^X, and thanks to everybody else, with whom I’ve ever spent a nice lunch or coffee-break during the past two and a half years, for easing the burden of long and sometimes perhaps not-so-ffuitful research.

Furthermore, I wish to thank Ulf Linder at ABB STAL, for teaching me something about the realities of gas turbine cooling, and Umberto Desideri and Francesco Di Maria, for a good and instructive time in Perugia, Italy.

I also wish to thank my parents for their support, as well as all my friends for being there.

This work was made possible thanks to financial support by the Swedish National Energy Administration.

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Chapter 2

Gas turbine cooling

Increasing the turbine rotor inlet temperature (TRIT) of the gas turbine leads to higher thermal efficiency, since the average high temperature of the cycle increases (see e.g. Haywood [24]). Increased temperature levels, however, require materials that are resistant to these temperatures. Although substantial development has been made in the domain of high temperature materials, the materials are still not sufficient to withstand the high temperatures that are used in present gas turbines. To compensate for this, and also to make better use of the material improvements that are made, technologies have been developed to cool the hot parts of the gas turbine, i.e. combustion chamber, rotor discs, and turbine blades and vanes. This chapter presents a literature study of the concept of gas turbine cooling, with the focus on blade and vane cooling. Of course, cooling of other parts, e.g. the combustion chamber liners, is also an important issue in gas turbine technology, but it will not be addressed here; since for a thermodynamic study of the gas turbine cycle, only the temperature after the combustion chamber matters and not how it was obtained.

2.1 History

Several authors have included in their work a chapter with a more or less brief history of the development of the gas turbine, e.g. [3, 12, 58, 61]. The reader who is interested in the general history of gas turbines should refer to these works, since the presentation below will be a review of what has been found in the literature on the history of gas-turbine cooling.

In 1929, Brown Boveri Corporation is reported to have manufactured turbine blades intended for air cooling [3]. The first turbo jet engine that had cooled blades and that actually was in service, was the German Junker Jumo 004> which flew shortly before the end of World War II. The cooled blades were simply made from a bent metal sheet, and thus, were hollow inside.

The purpose of applying cooling to the Junker Jumo was not to raise the turbineinlet temperature, but instead to allow the use of non-heat-resistant materials. After World War II, however, research and development in the domain of gas turbine cooling and materials was performed in order to raise cycle efficiency. According to Rohsenow [47], National Advisory Comittee for Aeronautics (NACA)1 published several unclassified reports on experimental work with blade cooling already in 1947.

1 Predecessor of National Aeronautics and Space Administration (NASA)

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During the 1950s and 1960s, extensive effort was made in the domain of gas turbine cooling, and, depending on the source, it appears that from the 1960s or the 1970s onward, cooling has been an integrated part of commercially available gas turbines [3, 18]. As a rule of thumb, the turbine-inlet temperature of modern gas turbines has, on average, been increasing at a rate of 20° C per year since the 1960s. Approximately half of the increase is due to improved cooling methods, and the other half is due to improved high- temperature materials. An illustration of previous and expected future development is given in figure 2.1.

Compressor discharge air is still the coolant most commonly used. In the early 1960s, however, General Electric initiated development on a water cooled gas turbine, and the first laboratory model was tested in 1973 [3]. The system was reported to be still under development in 1982 by Wilson [61], but appears to have come to an end without being launched on the market.

2000

hot gases temperature (IS 0)

coolingceramics

metal

1960 1970 1980 1990 2000 2010

Year

Figure 2.1: The development over time of gas-turbine materials and hot gases temperature levels, and the impact of cooling on this development [18].

2.2 Current technologies and development trends

Gas turbine cooling is a field in engineering that evolves continuously. The modeling and simulations in the rest of the present work focus on open-loop air cooled gas turbines, film-cooling being the state-of-the art cooling of gas turbines currently available on the market. This section, however, presents some of the development trends that can be found in recent literature, where closed-loop cooling with steam or air seem to be the most interesting trends, as well as uncooled ceramic blades and vanes.

In what is reported to be the current fine of advanced gas turbines, General Electric[41] reports a temperature drop of 155° C over the first stage air-cooled nozzle. This means that, before the air reaches the first rotational stage, much of the work potential in the hot

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gases leaving the combustion chamber is lost due to the cooling. If the first stage nozzle could be cooled with a closed-loop steam coolant without film cooling, the temperature drop would be less than 44° C, and hence, the work extraction from the turbine would increase. In ref. [41], it is claimed that by replacing all of the present cooling, that is of the open-loop type, with closed-loop cooling, an improvement of two percentage points in efficiency can be obtained. General Electric, therefore, suggests a combined cycle with a closed-loop steam cooled gas turbine, where the cooling steam comes from and returns to the steam cycle. This concept is claimed to reach a cycle efficiency of 60%.

Within the Advanced Turbine Systems (ATS) program sponsored by the US Department of Energy (refer to [33]), Westinghouse is working on a new 200 MW gas turbine called the 501 ATS [16]. This turbine employs closed-loop steam cooling in the combustion chamber transition piece and stationary vanes, and closed-loop air cooling in rotor blades. The steam cooling will also have the function of steam reheat between the HP and IP turbines in a combined cycle, and the rotor coolant will be cooled ” after being removed from the combustor shell”, which is said to result in a very small cooling air requirement. The net efficiency of the triple pressure combined cycle with the 501ATS will be larger than 60%.

Japan plays a leading role in the development of high-temperature gas turbines andcooling technologies. Mitsubishi employs steam cooling for the cooling of the combustion chambers in their 501G/701G [2]. Toshiba and Tohoku Electric Power Inc. report on a joint project where steam-cooled blades and air-cooled vanes have been investigated for a future combined cycle gas turbine with temperatures up to 1500° C [40].

A cooling concept recently presented by MIT is that of vaporization cooling, where the advantage is claimed to be that the blades should be maintained at a nearly uniform temperature. Results of laboratory experiments have been published to confirm the concept [29].

Small ceramic gas turbines for automotive purposes are under development by, among others, Solar [45]. Here, the first stage blades and vanes are made of ceramic materials and completely uncooled.

2.3 High-temperature materials

The development of high-efficiency gas turbines has to a great extent taken place due to the development of high-temperature materials. Higher melting points and higher operating stress levels have been made possible through tremendous research in both processing techniques and in inventing new alloys, so-called superalloys, that are in general based on nickel.

As gas turbine temperatures continue to increase, the melting points of these alloys are likely to be surpassed, and emerging techniques to overcome this are the development of ceramics, refractory metals, composites and intermetallic compounds. Also, to protect the alloys from oxidation and corrosion in the hot parts of the turbine, thermal barrier coatings (TBC) can be applied to the blade or vane, i.e. a thin layer of metal and/or ceramic. TBCs reduce the level of heat transfer to the metal; but a problem is that they, in general, have lower thermal expansion coefficients than the materials that they are applied on, which calls for manufacturing process research.

Casting is the main manufacturing method for superalloy blades and vanes, and over the past few years, the fabrication of single crystal components has been made possible.

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The advantage of single-crystal blades is that they are more resistant to creep and fatigue than poly-crystalline blades [51].

In the recently developed GTX100 from ABB [39], the first stage film-cooled blade is made of single-crystal material. This is also the case for the first stage blades and vanes for the Westinghouse 501 ATS [16]. Westinghouse also reports that the closed-loop cooled blades and vanes are made of very thin material (nickel alloy) to reduce thermal gradients and are covered with TBCs. Reliable TBCs are reported to be vital to the realization of closed-loop cooling [60].

2.4 Cooling technologies

Cooling technologies can be divided into two groups: open-loop and closed-loop cooling.- Open-loop cooling is when the coolant, after having absorbed heat, is injected into and

mixed with the main flow, which means that the heat absorbed by the coolant is returned to the hot gases. In closed-loop cooling, the coolant passes through the blade or vane, absorbs heat and rejects it outside of the expansion process. Open-loop air cooling is the most common way to cool a gas turbine, although much research and development is presently being made on closed-loop steam and air cooling as mentioned in section 2.2.

There are (currently) four ways of cooling blades and vanes that are described in the literature [3, 20]: convection, impingement, film and transpiration cooling. The principles of the four methods are illustrated in figure 2.2. In air cooled gas turbines, a combination of film, convection and impingement cooling is usually applied. For closed-loop cooling, only convection and impingement cooling can be applied.

Figure 2.2: Principles of the four different cooling methods: 1= convection cooling, 2=impingement cooling, 3=film cooling, 4=transpiration cooling [20].

Convection cooling was the earliest method to be applied. The coolant flows in channels within the blade and is heated as it cools the blade. High velocity is required when air is employed as the coolant, and to increase the heat transfer, turbulence can be enhanced with different kinds of fins and ribs in the channels, but at the cost of more difficult

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manufacturing. The coolant is usually discharged at the trailing edge and mixed with the main flow, but can also be discharged outside of the blade or vane. Convection cooling technology has developed so that today, the coolant can be directed inside the blade to where it is most needed, i.e. at the leading and trailing edges.

Impingement cooling is a very efficient way to cool locally, usually on the blade leading edge. The air is directed radially through a central core in the blade, and then turned to the axial direction and made to impinge through small holes onto the inside of the blade. Impingement cooling is usually employed on stator vanes, but the method can be adapted to rotor blades as well.

Film cooling is an efficient way to protect the blade surfaces from the surrounding hot gases. The cooling air passes through holes in the blade surface and forms a protective film of relatively low temperature. The technology has enabled the development of today’s high-temperature gas turbines, but nevertheless, it has some drawbacks. The film increases the boundary layer thickness, which results in higher blade profile losses and, worse, if the coolant is injected with too high a velocity, it penetrates the boundary layer and decreases the protection of the blade. Film cooling is typically applied on the hottest parts of the gas turbine, e.g. the first stage blades and vanes.

Transpiration cooling is sometimes claimed to be the most efficient cooling method. The coolant is forced through the porous blade surface and creates a continuous film that protects the surface, at the cost of a rough surface that might decrease turbine efficiency. Manufacturing and materials problems have lead to the fact that transpiration cooling still remains a hypothetical cooling method. However, it is sometimes argued that the development of the ” shower-head” film cooling design at the leading edge of certain blades and vanes, is very close to local transpiration cooling.

Figures 2.3 and 2.4 show in more detail, the design of a convection cooled blade (figure 2.3) and the principle of impingement cooling (figure 2.4).

2.5 Problems associated with turbine cooling

The advantage of turbine cooling is that it allows the use of higher turbine inlet temperature, which should result in higher cycle efficiency. There are, however, disadvantages with blade cooling that cannot be neglected. Some of the disadvantages connected to each cooling method were discussed in section 2.4 above. Other disadvantages with turbinecooling follow:

• Turbine work is lost due to the compressed cooling air bypassing one or more of the turbine stages;

• Turbine work is lost due to the colder cooling air being mixed with the hot gases of the main stream, meaning that enthalpy and total pressure are reduced;

• The extraction of air from the compressor outlet might disturb the flow field into the combustion chamber;

• There is less heat to recover in applications where the exhaust gases are used, since the temperature of the gases leaving the turbine is lowered;

• The cost of producing the blades is increased.

9

Figure 2.3: Convection cooled blade (Courtesy of ABB STAL).

Attention must be given to these points so that any gain in increased turbine inlet temperature will not be counteracted by these disadvantages, and so that the result will not be a decrease in overall efficiency and/or economic drawbacks.

If closed-loop steam cooling is employed, the first three points are avoided.

2.6 The use of compressed air

In air-cooled gas turbines, the coolant employed is compressed air. Since lower coolant pressure is required for cooling as the hot gases expand through the turbine, only a minimum of air is discharged from the compressor outlet. The rest is extracted from between the stages. It should be pointed out, however, that all of the air that is discharged from the compressor, that does not go to the combustion chamber, is not used for blade and vane cooling. Compressed air is also used or expended for [59]:

• turbine disc cooling and sealing;

10

Figure 2.4: Principle of vane impingement cooling (Courtesy of ABB STAL).

• bearing chamber sealing, so that no oil escapes from the bearings into the engine;

• thrust balancing to reduce axial loads;

• customer bleed extractions; such as, cooling plant systems or aircraft cabin pressurization;

• leakage from high-pressure air systems to low-pressure air systems.

From a gas turbine cooling point of view, turbine disc cooling is the most interesting point of the above-mentioned. According to ref. [59], depending on the pressure level and sealing technology, 0.25-0.5% of the compressor mass flow is expended for cooling of each disk face.

11

Chapter 3

Modeling of cooled gas turbines in literature

Thermodynamic modeling of the expansion in a cooled gas turbine is not a new field in the domain of gas turbine calculations. The early models that can be found in literature were derived for gas turbine design, a task that is today mainly performed with 3D computer codes. More or less detailed thermodynamic models for the expansion in a cooled gas turbine, derived with the purpose of studying power plant cycles, can be found in literature from the early 1980s onwards.

In this chapter various models found in literature, which consider the expansion in a cooled gas turbine, will be presented. If not relevant to the present work, the nomenclature given by the author of each model has been kept, and it will be explained in connection with the model description and not with the nomenclature on page viii. (The specific heat ratio, Cp/cv, is in the reviewed works denoted as either 7 or k.)

3.1 Early models, derived for design purposes

The earliest references in the domain of gas turbine cooling modeling, found by the present author, are by Rohsenow [47] and Hawthorne [21, 22]. These articles are now and then in more recent papers cited as the beginning of the gas turbine cooling modeling. Also, two early works on heat transfer in gas turbine blades are reviewed. The first one [34] is included mainly for its historical interest; whereas, the second by Halls [19] gives the prerequisite of the work presented by Holland [25] that, in turn, constitutes the basis for the cooling model developed and used in the following chapters.

3.1.1 Studies on gas turbine performance

The work of Rohsenow [47] is an investigation of the effects of blade cooling on the performance of a simple gas turbine plant. It does not claim to show the actual situation in the cooled turbine, but trends; i.e. the results should be regarded as qualitative rather thanquantitative.

The turbine is divided into two parts, a cooled part and an uncooled part. The investigations were carried out for both varying turbine inlet temperature (firing temperature) and varying temperature of the point where the expansion changed from cooled to uncooled. The most important cooling parameter is the ratio of heat removed through the cooled blades to the work extracted from the turbine, i.e. Q/Wt. The Q/Wt is said to be

12

a measure of the required amount of cooling. It is set to values between 0.1 and 0.3, and is found to have a high impact on cycle efficiency. However, Rohsenow appears to have omitted the fact that if the coolant is added to the main flow, then the heat extracted from the gases is added to the cycle again.

The object of the analysis seems to be to develop design criteria, or rather to evaluate whether or not blade cooling is an interesting solution for gas turbine design, and the conclusion is that the real value of cooling lies in the possibility of using less expensive materials at the cost of losing perhaps 1-2 percentage points of efficiency. This is the opposite conclusion of virtually all other works on gas turbine cooling, where cooling is studied in order to enable a rise in temperature levels, and thus, improved efficiency for gas turbine power plants.

In two papers, Hawthorne [21, 22] first derives a theory for the cooled gas turbine stage, and then applies this theory to a multi-stage turbine. The model developed is based on profile loss coefficients, velocity triangles and knowledge of the amount of heat transferred in the blading, and the Mach number is an important parameter. The purpose of the work is clearly to facilitate the design of cooled gas turbines, and the need for experimental work in the area is pointed out. In contrast to Rohsenow, Hawthorne talks about blade cooling as a way of increasing turbine inlet temperature and thermal efficiency output.

3.1.2 Blade heat transfer

A description of the status of blade cooling at the end of the 1960s is given by Liess [34]. Common one-dimensional heat transfer theory is developed to cover blade cooling with the objective to enable better blade design. The work presented by Liess has been of little interest for the present work from a modeling point of view.

Halls [19] uses a simple approach to identify the factors that lead to good blade cooling. Halls reports that one of the first to lay the foundation for a logical and systematic design procedure was Ainley1, who made two simplifying assumptions, namely, that the influence of spanwise blade conduction on blade temperature is negligible, and that the blade metal temperature in chordwise direction is uniform. The second assumption is far from being realized in practice, but it greatly simplifies the analysis. Thereafter, Halls presents the standard blade approach, developed by Rolls Royce. The standard blade is the basis for the work done by Holland [25] that is reviewed in section 3.3.

3.2 Models for thermodynamic cycle studies

The main objective of the works reviewed so far was to develop design tools for gas turbine engines. There is also in literature a plethora of works describing cycle calculations where a model for the impact of gas turbine cooling has had to be incorporated. The complexity and perhaps also the accuracy of the models vary depending upon what importance turbine cooling has for the author’s purpose, and to a certain extent, also upon when the models were first published, since computer capacity never ceases to improve, and it has always been possible to handle more and more complex models with reasonable effort. Starting with the most simple methods, some of this literature is reviewed in the following sections.

'Ainley, D.G. ’’The High Temperature Turbo-Jet Engine” J.R. Aero.Soc., Vol 60, No 549, Sept. 1956.

13

3.2.1 Simple models

A simple way to take into account the impact of the turbine cooling is presented by De Ruyck et al. [14]. The coolant is supposed to be injected at one single point along the expansion line, where the hot gases have the temperature T that is given by the equation

T = (3.1)

A maximum material temperature is assumed, and the heat balance over the mixing point is described, without further references, as

'ffl'coolCp,cool (Tfjiade Tc00l) — h .' (T Tbla.d.e\

P\JlRT(3.2)

It appears from the article that the cooling method is taken into account by the parameter h, and that A" is a proportional constant for the engine cross section, which seems to be calculated with the equation of continuity, assuming speed of sound at mixing temperature T. Kh is calibrated to a certain value for a given pressure and coolant flow. The model results in that the cooling flow is mainly affected by the changes in the gas mass flow and density, and the temperature T.

Another simple method is described by Horlock [27]. Unlike most thermodynamic power plant studies, Horlock’s calculations are made per unit mole flow in the compressor (instead of per unit mass flow). The coolant mass flow requirement is assumed to be 0.1 moles of air per mole of air leaving the compressor, and hence, the model is just a mixing model for heat and mole balances, where all of the cooling air is assumed to be mixed into the flue gases before the expansion.

Also, Korakianitis and Wilson [31] present a model where all of the cooling air is extracted from the compressor outlet and mixed with the hot gases before the expansion starts. But instead of just assuming a mass flow fraction of cooling air, a cooling flow parameter w is calculated:

To4 — Tfrmw =Tq 4 — Tq2

(3.3)

where T04 is the total temperature after the combustion chamber, T02 is the total temperature after the compressor and T^m is the blade surface temperature. With help from a diagram derived from Livingood et al.2, the coolant mass flow fraction is obtained.

Brown, Jubran and Martin [9] present a method of calculating the cooled gas turbine, where all of the coolant is mixed into the main stream at a temperature that is assumed to be the arithmetic mean value of inlet and outlet temperatures in the compressor turbine (i.e. the part of the expander that is used to power the compressor). It is interesting to note the fact that the coolant is considered to be preheated before entering the blades and vanes. An explanation to this can possibly be found in Hay and Taylor [23]: if the temperature difference between blade and coolant is too large, there is a risk of overcooling,i.e. the temperature gradients in the material will be too steep, with shortened blade life as a consequence. The concept of overcooling has not been encountered elsewhere during this literature study and will not be further considered in the following chapters.

The coolant mass flow in [9] is used as a parameter that is varied in order to find the optimum coolant mass flow requirement; i.e. the coolant mass flow that gives the

2J. N. B. Livingood, H. H. Ellerbrock and A. Kaufman: ’’NASA Turbine Cooling Research”, NASA TM-X2384, 1971.

14

optimum efficiency. The analysis also considers the bleeding off (also referred to as prebleeding) of some of the coolant at an intermediate point in the compressor. According to the results presented, there is, in general, a slight advantage in using pre-bled air up to the optimum coolant flow. Thereafter the pre-bleeding seems to have a large negative effect on cycle efficiency. Approximately 10% of the compressor inlet flow is said to be an optimum coolant flow. An important parameter for the calculations is the heat extraction parameter A, defined as

t7 - r6 t7-t2

(3.4)

where T7 is the temperature of the coolant air leaving the tip of the blade after cooling, T& is the temperature of the coolant at the root of the blade (before cooling the blade) and T2 is the temperature of the air leaving the compressor. The difference between Tg and T2 is due to the preheating of the coolant and/or the pre-bleeding of the coolant before the final compressor stage.

The work in ref. [9] on finding the optimum coolant mass flow is continued in ref. [36]. In ref. [9], the optimum combination of coolant mass flow fraction and cycle efficiency in a point is found iteratively, but in the model presented in chapter 4, it is found on the first calculation.

3.2.2 Expansion models that include losses

As mentioned in section 2.5, gas turbine cooling has its disadvantages. One of the major disadvantages is the loss in stagnation pressure (also referred to as mixing losses) that occur when coolant and main flow are mixed. These losses must be accounted for in an accurate model for expansion in a cooled gas turbine.

Traupel [57] presents a model for the expansion in the cooled turbine that is based on the linear assumption

ip = (pi-------- (3.5)1 — 7T2

where tt is the pressure ratio, ip is the amount of cooling air still available for cooling at an arbitrary point along the expansion line, and <p\ is the amount of cooling available at the beginning of the expansion. Index 2 represents the end of the expansion. The assumption in equation 3.5 makes sense from a physical point of view, since much of the cooling air is mixed into the main flow at the beginning of the expansion and little at the end. Although the assumption is linear, this method makes it complicated to calculate analytically the temperature at the end of the expansion, and hence, to determine the specific work. There is no way of calculating the total required coolant mass flow <pi, but this has to be set to an appropriate value.

The losses due to the mixing of the coolant with the main flow are taken into account by Traupel through a reduction of the polytropic efficiency of the turbine. Let rjp denote the efficiency of the uncooled turbine and rjpr the reduced polytropic efficiency of the cooled turbine. Traupel states that tjp and r]pr are related through the assumption

Vpr = Vp~ = Vp- (3.6)air 1 — 7T2

where K is an empirically found constant that is specific for every turbine. Since the expression for the reduced polytropic efficiency varies only with the pressure ratio tt, the deviation from rjp is larger at the beginning of the expansion than at the end, which is

15

usually the case also in a real turbine. With z being the number of turbine stages K isderived as

K= -In f—) (S + 0.5) (3.7)Z \7T2/

where the mixing of 1% of coohng air to a stage leads to S% decrease of the stage efficiency. According to Traupel, the theory presented assumes that the coohng air participates in the work extraction from the moment that it is added to the expansion path. Actually, this is not the case, since it does not contribute to the work until the stage following that where it was added. This error is compensated for by decreasing the stage efficiency by an additional 0.5% for each percent of cooling air added (the term 0.5 in equation 3.7). The value of S depends on the turbine configuration and has, according to Traupel, the value of 0.5-1. Examples of the use of Traupel’s expansion model can be found in Rosen [48] and Rufli [50].

Louis et al. [35] make a comparative study of the influence of different means of turbine cooling. The purpose is to give some design guidelines for five different coohng means: internal coohng by air, internal and film cooling with air, internal coohng by steam, internal and film cooling with steam, and finally, closed-loop and film coohng with steam. One of the main features of the article, though, is that it presents a concise way of dealing with the expansion line for cooled turbines. The method has been been frequently used in different ways by a large number of authors [6, 17, 30, 52, 55]. The expansion over one cooled turbine stage is divided into the parts

1. coohng

2. mixing with isothermal pressure loss

3. expansion

4. cooling

5. mixing with isothermal pressure loss

where the first cooling and mixing process represents the vanes, and the second represents the blades. The principle for the expansion over one stage is represented in figure 3.1.

The mixing losses are calculated as stagnation pressure losses at constant temperature from

dpoPo

■ —jM2 dmcm

7 M2 f dho dW dj2 + (7 - 1) M2 ~ ~W + V (3.8)

with indices 0 and c representing stagnation conditions and coolant, respectively. As an explanation to the equation, it is said that dho = {hoc — ho) drhc/m. V'c is the component of the coolant injection velocity that is parallel to the main flow. Using equation 3.8 means that the pressure losses are considered to be a function of the Mach number M and that they also depend on the angle between the main flow and the injected stream.

Equation 3.8 reappears in a work by Holland and Stadaas [7], but in a simplified version:

dpo _ dmc po ihguM2

(3.9)

The origins of the entire cooling calculation method can be derived from Louis et al. [35] via El Masri [17]. One of the most interesting features of the coohng modeling in ref [7] is that in the implementation (made with an in-house code), the expansion is divided into

16

T

isothermalpressureloss

SFigure 3.1: Method for considering the expansion over one cooled turbine stage according to ref [35].

”a large number of steps” with the sequence cooling, mixing, expansion instead of onedetermined sequence for each turbine stage (c.f. ref [35] and fig 3.1).

3.3 Cooling modeling

The advanced expansion models in the previous section need to be completed with a cooling model in order to calculate the coolant mass flow requirement. Such models are presented in many of the works cited in section 3.2.2. This section will concentrate on reviewing the cooling model presented by Holland [25], that is based on the standard blade assumption presented by Halls [19]. A standard blade has an infinite thermal conductivity, a uniform temperature and the same geometry as the actual blade. Also, the gas temperature surrounding the blade is uniform, and the cooling air is warmed up to the temperature of the blade before leaving it.

Of course, the standard blade does not exist in reality. Nevertheless, the description of the deviation between the behaviour of the standard blade and of a real blade in a gas turbine is a very convenient way to deal with gas turbine cooling. The heat transfer from the gas through the standard blade leads to an enthalpy rise for the coolant. For an ideal gas and relatively small temperature changes, the enthalpy difference Ah can be expressed as CpAT, and consequently, negliecting thermal radiation, the enthalpy rise can be expressed as

digAi (Tg — Tft) — rncsCpC (Tb — T&) (3.10)

where A& is the wetted surface of the blade. The temperature rise for the coolant in a real blade is somewhat lower, which means that a larger coolant mass flow is required to cool the blade. Assuming that the average specific heat for the coolant is the same for the standard blade and a real blade we can write

rilcsCpc (T& Tci) — rilcCpC (Tee Tcj) (3.11)

17

With the obvious interest in minimising the coolant flow, the cooling efficiency r)c can be defined as

Now we define the dimensionless coolant mass flow m* and insert the first expression for cooling effectiveness given in equation 3.12

1 ffics^pc* 77lcCpc . 77lc Cpc m — A — mcs- ~ 7~ — - 1&gAb T7lCs Oig-n-b Tjc CtgAb

(3.13)

The use of the dimensionless coolant mass flow can also be found in Haselbacher [20] and Mukherjee [37], but under the name of B. Haselbacher describes the factor mcCpC as an indicator of the cooling effort and agAb as an indicator of the difficulty of the cooling problem.

We rewrite equation 3.10 and insert 3.13:

T3 Tb _ ThcsCpC _

Equation 3.14 can be rewritten as

Tg-TbTg Tci

= m*T]c 1Tb

Now we define the cooling effectiveness ebm as

£bm —T0-TbTg — Tci

Equations 3.15 and 3.16 can be put together to form

m*rjc£bm — 1 + m*ric

(3.14)

(3.15)

(3.16)

(3.17)

The cooling effectiveness is a widely used variable in gas turbine cooling. Much experimental research has been carried out where the cooling effectiveness is evaluated for different cooling methods. Diagrams of as a function of m* can be found in publications by Haselbacher [20], Mukherjee [37] and Holland [25]. These three diagrams were scanned and digitized. Thereafter, the data from the three different diagrams were plotted in one single diagram (Fig 3.2). It can be seen that the data from the different sources coincide rather well, and it should, therefore, be of little importance which diagram is used in calculations.

The local coolant to flue gases mass-flow ratio is defined as

mcVl = — (3.18)

mg

The Stanton number is defined as

Si- (3.19)pgUgOpg

This means that equations 3.13, 3.18 and 3.19 can the very useful equation

be put together and rewritten as

m* = (3.20)

18

Convection + film

Impingement

' Convection

Figure 3.2: e&m as a function of m*. Reproduced with data from digitized diagrams in Haselbacher [20] (dotted lines), Holland [25] (dash-dotted lines) and Mukherjee [37] (solid lines).

3.4 Some observations on cooled gas turbine modeling

In this chapter, some of the methods found in the literature that deal with the complicated problem of the expansion in a cooled gas turbine were reviewed. Either one can use a more simple model and give an estimate of the coolant mass flow requirements, or one can calculate these requirements with a cooling model.

One of the important things to retain from section 3.2.2 is the convenient division of the expansion path into three separate phenomena: cooling, losses and expansion [17]. In a cooled turbine, these phenomena occur more or less simultaneously, but dealing with them separately enables a more structured thermodynamic analysis.

There are many parameters involved in the modeling process. Since thermo dynamic calculations of the expansion in a cooled gas turbine must, by their nature, be greatly simplified, it is the author’s opinion that the number of parameters should be kept as few as possible.

Many, if not all authors talk about in-house codes, i.e. codes that were created at the institute where the work was done. (c.f. IPSEpro in appendix A.)

19

Chapter 4

A suggestion for a Cooled Gas Turbine Model (CGTM)

The open-loop cooled turbine of a gas turbine engine can be schematically illustrated as a ” black box” according to figure 4.1, with a number of streams entering the box, and with one stream and a shaft work that exit the box.

hci hc2 ha et.c.mci mc2 *^*C3

Figure 4.1: Black-box model of the cooled turbine.

The goal of a model for a cooled turbine is to describe what happens inside the box so that heat and mass balances can be satisfied. The black box is assumed to be adiabatic, which means that for n streams of coolant, the energy balance over it will be:

nP — Tflghg + ^ ) (rrichc) j inexh^exh (4.1)

1=1

Here it should be emphasized that although the entire turbine is assumed to be adiabatic, the expansion in the cooled part of the turbine is not adiabatic, since there is heat transfer from the hot gas, through the blades, to the coolant. This heat, however, is added to the gases again, as the coolant leaves the blade. Hence, as long as the turbine is well-insulated there will be no heat loss to the environment, and hence, the entire turbine can be regarded as being adiabatic.

20

4.1 Model requirements

As described in the previous chapter, there is a multitude of approximate ways to calculate the thermodynamics of a cooled gas turbine. The features of a model depend on the purpose of its author and also on the software used. Nevertheless, there are some requirements for a model for the cooled gas turbine to be good:

1. To predict gas turbine efficiency and turbine exhaust temperature with acceptable accuracy;

2. To give a correct indication of the coolant mass flow requirements;

3. To be easily implemented with the software tool employed;

4. To contain as few model parameters as possible.

The meaning of ’’acceptable accuracy” in point 1 is, of course, not clearly defined, butmust be determined by the user. Possibly a compromise has to be made between points1 and 2 on the one side and points 3 and 4 on the other, i.e. an accurate model mightrequire a more advanced software solution and/or more model parameters.

Due to the aims of the present work, an additional requirement was that the model should be applicable for gas turbine processes where humidified air is used as the coolant.

4.2 The Model

The model presented in this chapter and used in the rest of this work, is a design-point model based on a synthesis of works presented in chapter 3. It is mainly influenced by Holland [25], Louis et al. [35], Rosen [48] and Traupel [57]. The part of the turbine where cooling is applied (i.e. where the gas temperature is superior to the average blade temperature) is divided into a number of sequences, where first cooling and then expansion is calculated. As explained in section 4.4, the implementation of the model has been strongly influenced by the features of the IPSEpro software (refer to appendix A). In the rest of the work the model will be referred to as the CGTM (=Cooled Gas Turbine Model).

The difference between the local coolant flow requirement <pi and total coolant flow requirement ip must be emphasized. <pi is the ratio between the coolant mass flow and the hot gases mass flow at a specific point in the turbine and is defined as

mc (4.2)

whereas ip is the ratio between the mass flow of compressed air that is extracted for cooling purposes, m, and the mass flow that enters the compressor, i.e.

mc-----mcmp

(4.3)

Here it must be emphasized that in the studies with humidified cooling air it is always the mass flow of compressed air, which is expended for cooling, that is considered in the value given for ip, and not the total coolant mass flow; i.e. the water added is not included in ip.

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4.2.1 Cooling models

In the following, values of specific heats, flue gas and coolant inlet temperatures are assumed to be known from elsewhere in the calculation procedure. The cooling method can be accounted for in two different ways, either by employing the diagrams shown in figure 3.2 or by setting an appropriate value of the cooling efficiency t?c. The differences between these two methods are evaluated in the article in appendix D and are briefly mentioned in chapter 5.

Using the diagrams in figure 3.2, we set the algorithm

1. Determine from equation 3.16

2. Choose the cooling method and get a value of m* from figure 3.2

3. Determine <pi from equation 3.20

4. Determine coolant mass flow requirements mc from equation 3.18

5. Determine rjc from equation 3.17

6. Determine Tce from equation 3.12

7. Determine the temperature of the flue gases after the cooling process by a heat balance, where the heat added to the coolant is extracted from the flue gases

Points 5 to 7 are only necessary if closed-loop cooling is considered. For open-loop cooling, they need not be considered, since the heat extracted from the flue gases is added again when the coolant and flue gases are mixed. The enthalpy hmiX before the expansion is obtained through the energy balance:

(?71c + 771 <7) hmix — 77lchd -f- Tflghgi (4.4)

The second algorithm has the feature that a value of r]c is set:

1. Set a value of %, depending on the cooling method

2. Determine from equation 3.16

3. Determine m* from equation 3.17

4. Determine (pi from equation 3.20

5. Determine coolant mass flow requirements mc from equation 3.18

Again the enthalpy after the mixing of coolant and hot gases is determined from equation 4.4.

A comment to the second algorithm is that it is possible to rewrite m* as

= (T.-Ij,) = (T,-Tb)(Tce-Ta) ScPt-iy

It then becomes possible to reduce the entire algorithm to

(4.5)

Tftr — TTtf%-Tb)

7?c (2fc I'd) Cpc -^g(4.6)

Using equation 4.6 might reduce the understanding of the problem, but ought to be convenient when traditional (sequential) programming languages are used. Equation 4.6 is also used when the impact of Cpg/Cpc on ipi is studied in section 6.5.

22

4.2.2 Choice of cooling method

As is described in section 4.2.1 above, the cooling method employed must be chosen. In the first algorithm, depending on temperature levels in each turbine stage and if possible, on manufacturers’ data, the adequate method (film, impingement or convection) is set, i.e. the appropriate curve in figure 3.2 is chosen. This method was used for the simulations with ’’Model 1” in the article in appendix D and for GT5-1 in section 5.3.

It is possible to implement the first algorithm in a very elegant way in IPSEpro, so that the user can choose the cooling method for each cooling unit (refer to figure 4.2) separately. This was done, and some practical drawbacks were found. First of all, since the curves in figure 3.2 rely on some kind of semi-empirical basis, they do not emanate from the origin of the diagram. This leads to difficulties for parameter studies, since small values of £bm may not correspond to a value of m*, and vice versa. Also, the curves in figure 3.2 are not really just curves, but they are the limits of an area. Within this area, the point that gives the adequate value of y>z could lie anywhere, so that if the user skips, from say, the lower limit of convection cooling to the upper limit, the point that gives the correct value will not be found.

Due to this, the second algorithm has been used for most of the calculations in this report, in particular, for all of the parameter variations. Here, r}c is set to an appropriate value using diagrams in the article in appendix D as guidelines together with manufacturers’ information about how the turbine is cooled. Information about the number of cooled stages and the cooling method employed can also be found in e.g. Gas Turbine World1.

4.2.3 Expansion model

The expansion in an uncooled turbine is determined from the well-known equation

n W

The stagnation property losses that occur in the turbine due to the mixing between coolant and flue gases are accounted for through the replacement of r)p with the reduced poly tropic efficiency 7]pr, which is determined with equations 3.6 and 3.7 rewritten as:

<4-8)

The equation differs from Traupel’s model in that all losses are put into the factor S, i.e. the additional 0.5 has been removed. Since the result of this is that the losses become a function of S over the number of turbine stages z, z has simply been removed, in order to reduce the number of parameters.

The conditions at inlet and outlet for each turbine stage can be determined either by using an assumption of equal pressure ratio for each stage, as is done in [48], or by assuming equal enthalpy drop over each stage, i.e. that the blade loading coefficient described in e.g. [12] is equal over each stage. Both methods are evaluated in ch. 5.3.

4.3 Model parameters

As discussed above, it is desirable to have a model with as few parameters as possible. The parameters used in the simulations in the following chapters are:

1 Published by Pequot Publishing Inc.

23

• average blade temperature (T&)

• cooling method employed (t?c or curve in fig. 3.2)

• Stanton number (St)

• geometry factor (Ab/Ag)

• polytropic efficiency reduction factor (S)

The average blade (or vane) temperature T& is set to the same value over each stage, and is a compromise parameter, meaning that all blades and vanes in a gas turbine have varying temperatures in all directions, and also the average blade temperature changes from one stage to another. Hence, one single exact value cannot possibly be set for the entire turbine, nor is it reasonable to try to set different values for different stages, since they probably are going to be wrong anyway. For the simulation of real gas turbines, T& should be regarded as one of the primary parameters to vary in order to get close to the manufacturers’ performance data.

For air cooled blades, a typical value of the Stanton number that can be found in literature is 0.005 [7, 25]. For the discussion of the Stanton number in humid air, refer to appendix B.3.

The geometry parameter Ab/Ag changes with each turbine step and for each turbine, and for someone who wishes to study a specific gas turbine and who does not have access to geometries, it is, of course, impossible to enter a correct value of this parameter. El- Masri [17] points out that a typical value for an entire stage is 8, i.e. one row of blades or vanes would have the value 4. It should be noted, though, that not only blades and vanes, but also rotor disks and the transition piece from the combustion chamber to the first stage nozzles, are subject to cooling, i.e. an average value should perhaps be slightly higher, e.g. 5 or 6.

It can be seen in equation 3.20 that Ab/Ag is directly proportional to <p/. Also, with an increasing value of Tb, cpi decreases. Hence, for one specific value of <pi, there are many combinations of Ab/Ag and T&. A conclusion from this is that in order to reduce the number of parameters to vary, Ab/Ag should be kept constant and Tb should vary in order to match the turbine model with vendors’ data. Then for parameter studies, Tb becomes an interesting parameter to vary, in order to study how materials development affects improvements in gas turbine cycle efficiency.

4.4 Implementation in IPSEpro

The Process Simulation Environment (PSE) part of IPSEpro is in a way basically a graphic representation of an equation system. Small equation systems represented by icons are linked together by the connections to form larger equation systems. The use of discrete components with connections between them means that it is easy to adopt the cooling- expansion sequence where each physical turbine stage is represented by a defined number of components. It would have been more difficult to implement other models, e.g. the model used by Holland et al. [6], since it requires a large number of steps.

4.4.1 The units

The two most important units created with IPSEpro for this project are cooLnjmix, where the cooling and mixing occurs, and Turbine, where the expansion occurs (figure 4.2)

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coolant inlet hot gases inlet hot gases outlet

hot gases inlet J hot gases outlet shaft in shaft out

Figure 4.2: cooLrumix (left) and Turbine (right) units created in IPSEpro.

To each graphic unit in IPSEpro, several sets of equations can be connected. This means that cooLn-mix contains the two cooling algorithms in section 4.2.1 and that Turbine contains both the equations for an ’’ordinary” turbine and for the turbine with reduced polytropic efficiency according to equation 4.8. The cooLnjmix also contains a by-pass condition, so that if Tg < T&, then mc is set to 0.

4.4.2 The turbine stage

As mentioned above, there are two ways of calculating the turbine stage: either by assuming equal pressure ratio or by assuming equal enthalpy drop over each stage. When the principle of equal pressure ratio is applied each cooled stage is divided into two steps, also of equal pressure ratio. The stator cooling air is mixed into the turbine before the expansion.The rotor cooling air enters the turbine after the first of these two steps. When the principle of equal blade loading coefficient is applied, the rotor cooling air is mixed into the turbine after half of the enthalpy drop over the stage. In both cases this means that graphically the turbine stage will look as in figure 4.3. The numbers in the figure refer to the numbers in the TS-diagram in fig. 4.4.

blade coolantvane coolant

Figure 4.3: The graphical representation of a cooled turbine stage in IPSEpro.

The expansion over the stage is represented in a TS-diagram in figure 4.4. The points plotted in the diagram are calculated values from the first turbine stage of the reference gas turbine in chapter 5. The three dashed lines in the diagram represent curves of constant pressure.

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Figure 4.4: TS-diagram for expansion over a stage with the CGTM.

Between points 1 and 2 in the diagram, the flue gases give off heat to the stator coolant at a constant pressure. Thereafter, the gases and stator coolant are mixed in point 3, at a pressure that is equal to that at points 1 and 2. The composition of the gases changes, however, which leads to the fact that point 3 is offset from the constant-pressure line shown in the figure. The expansion with reduced polytropic efficiency takes place between points 3 and 4, and thereafter, the rotor coolant is added to the stage, and the rest of the expansion takes place.

4.4.3 Other features

Several flowsheets of the entire gas turbine model can be found in this work. Two units that can be seen on these flowsheets are the Turbine-inlet and Turbine-outlet (refer to figure 4.5). These units were created to enable the reduction of the polytropic efficiency according to equation 4.8 and have no physical meaning.

m fro

Figure 4.5: Turbine-inlet (left) and Turbine-outlet (right) units in IPSEpro.

Two compressor models were created, one wit one inlet and one outlet, that can be seen in the flowsheets in the following chapters, and one with one inlet and two outlets, that was employed for the studies on coolant extraction at a pressure lower than the compressor outlet pressure.

In the equations that make up the model, an enthalpy difference sometimes is described as h.2 — hi and sometimes as Cp (Tg — Ti). What is used depends on what is the most suitable in each equation. With IPSEpro, no extra work is required when considering this, since all the information needed is available in each connection in the IPSPpro flowsheet. For further description of IPSEpro, refer to appendix A.

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Chapter 5

Design-point model validation

In this chapter, the design-point behavior of the CGTM described in chapter 4 will be validated, through a comparison between gas turbine vendors’ data and calculated results. This is done, in order to verify that it is actually possible to simulate cooled gas turbines with the model, and also in order to get sufficient background for the setting of themodel parameters for the reference gas turbines in section 6.1. The results for one of the existing gas turbines are compared with data from the GATECycle gas turbine library. Furthermore, in section 5.5, calculations are done with a very simple model for the cooled gas turbine.

5.1 TIT and other ISO standards

For competitive reasons, gas turbine manufacturers are rather reluctant to publish data about their products, and it is not always easy to interpret the few data that are available. For instance, power output and thermal efficiency can be given with reference either to shaft or to generator terminals. Often, but not always, gas turbine data are given according to ISO1 standards. Definitions of ISO standards for gas turbines are mainly found in ref. [1]. It is very important for gas turbine calculations how the temperatures in the hot part of the gas turbine are defined:

TIT - Turbine inlet temperature is defined as the temperature that would occur before the nozzle guide vanes, if all cooling air was mixed into the flue gases at that point.

TRIT - Turbine rotor inlet temperature is the temperature before the first rotor stage, i.e. right before the work extraction begins.

TET - Turbine entry temperature is the actual temperature before the nozzle guide vanes.

In manufacturers’ data, the temperature(s) in the hot section of the turbine can be given according to different definitions and with different names (e.g. firing temperature can be employed for TRIT). However, the ISO definitions have been strictly followed in all the following calculations. Also, the ambient conditions (design-point data) axe set according

1 International Organization for Standardization

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to ISO standards, i.e. 15°C, 60% relative humidity and a barometric pressure of 1.013 bar. The standard gas fuel is methane (CH4), with a specific energy (LHV) of 50 000 kJ/kg.

For sources of external fluids, used for e.g. intercooling, the ISO temperature is 15°C.

5.2 Parameter settings

Although an effort has been made to keep as low as possible the number of parameters that must be set, there axe still many degrees of freedom left, when it comes to the parameter settings for the cooled gas turbine with the model suggested in the previous chapter. In order to give a more structured treatment of the simulations, a standard case was established after some introductory calculations. In this standard case,

• all cooling units, in a particular turbine, use the same value of T&;

• all cooling air is extracted from the compressor outlet;

• the Stanton number is set to 0.005 (refer to appendix B.3);

• the geometry parameter Af,/Ag is set to 10 for the first cooling unit, and to 5 for the other cooling units (giving a good estimate of TRIT after the first cooling unit);

• cooling model 2 is employed;

• auxiliary losses are neglected;

• the same value of t/p is applied in the cooled and in the uncooled part of the turbine;

• either pressure ratio 7r, or enthalpy drop Ah is equal over each cooled turbine step.

The last point is discussed further in section 4.2.3. It should be added, though, that when a gas turbine has a free, uncooled power turbine, the pressure ratio and enthalpy drop for the uncooled part are obtained directly, since the shaft between the compressor turbine and the power turbine is removed. For all turbines that were simulated, except GTS, the above-mentioned principles for parameter settings were applied. For GTS, six different cases were evaluated, as listed in table 5.1.

Table 5.1: Deviation from standard case for the different cases of parameter settings for GTS.

GT5-1 Cooling model 1 employedGT5-2 Standard case, as described aboveGT5-3 Cooling air for second vane bled off at intermediate point in

compressorGT5-4 Tb set to 850° C over the first stage, resulting temperature

over the second stage calculatedGT5-5 7/p reduced in the cooled part of the turbine, which results

in a reduced value of SGT5-6 S set to 0.0, r/p reduced further than for GTS-5

Except for GT5-1, the adjusting of the cooling effectiveness r/c is part of the modeling process. With help from manufacturers’ data and articles describing the different

28

turbines, the cooling technology employed is often more or less well-known, and if not, it can be estimated with experience from the modeling of other turbines, and from general information that can be found in the literature. Thereafter, an approximate value of r)c can be set, with help from figure 4 in the article in appendix D. Some approximate values of T)c are:

• convection cooling: 0.45-0.65;

• impingement cooling: 0.8;

• film cooling: 0.9-1.0.

5.3 Modeling of existing gas turbines

Seven gas turbines of varying size, inlet temperature and pressure ratio were selected from the available literature, mainly Turbomachinery Handbook and Gas Turbine World. Manufacturers’ data for these gas turbines are put together in table 5.2. The IPSEpro flowsheet for the simulation of each turbine differs, depending on the number of cooled stages. As an example, the flowsheet for a three-stage gas turbine with the first two stages fully cooled, is represented in figure 5.1

Table 5.2: Manufacturers’ data for seven existing gas turbines.

Turbine P [MW] Vth [%] TET [°C] TRIT [°C] TIT [°C] Texh [°C] 7TGT1 25.3 35.0 — — 1112 534 14.0:1GT2 12.9 33.4 — 1250 — 560 16.7:1GT3 10.0 35+ 1300 — — 516 21.0:1GT4 152.0 36.1 — 1288 — 550 16.0:1GTS 43.0 37.0 — — 1207 546 20.0:1GT6 27.9 36.1 — =1230 — 526 23.3:1GT7 226.5 35.7 — 1288 — 589 15.0:1

In all calculations, the manufacturer’s value of Texh was used as an input parameter, allowing Tf, to vary. Regardless of whether ir or Ah was kept constant over the turbine stage, identical values of % and P (and TIT) were obtained, but for some of the turbines, there was a difference in the value of <p. The results from the calculations are given in table 5.3.

The primary parameters for the simulations are given in table 5.4. The typical ranges of the secondary parameters are given in appendix C.

For GT5-3, a flowsheet was established, where the coolant for the second stator was extracted after half of the total pressure rise in the compressor. Here, r)c was kept at the same values as for GT5-2, and the only secondary parameter that was changed, to match the cycle efficiency, was the compressor polytropic efficiency, that was decreased with 0.4 percentage points; i.e. since less work is lost due to the earlier extraction of cooling air, and since the cycle efficiency is to be maintained constant, the compressor component had to be made less efficient in the calculations. The error in power output remains the same; the efficiency is the same as for GT5-2, but ip decreases with 0.3 percentage points. A conclusion to be drawn from this, is that the value of which is calculated with all of

29

ExhaustCoolant

CombustionchamberCompressor

Figure 5.1: Flowsheet for IPSEpro calculations with the Cooled Gas Turbine Model (CGTM).

Table 5.3: Calculated results with the CGTM.

Turbine P [MW] Vth [%] y [%], tt ip [%] AhGT1 25.3 35.0 17.9 17.9GT2 12.9 33.5 16.9 16.7GT3 10.1 35.0 18.5 18.5GT4 152.0 36.2 21.5 22.4GT5-1 43.7 37.0 19.8 19.9GT5-2 43.7 37.0 19.9 19.9GT5-3 43.7 37.0 19.6 19.6GT5-4 43.7 37.0 19.8 19.8GT5-5 43.7 37.0 19.8 19.8GT5-6 43.7 37.0 19.8 19.8GT6 27.9 36.1 17.0 17.0GT7 226.5 35.7 20.0 19.0

the compressed air extracted from the compressor outlet, is probably overestimated with some tenths of a percentage point.

A possible interpretation, when comparing the results for GT5-2 and GT5-3 in tables 5.2 and 5.3, is that, for a given thermal efficiency, the use of pre-bled air is a way to decrease the blade temperature to more acceptable levels. The slight decrease in average temperature for GT5-3 should be understood as a larger decrease in temperature for the second vane row. The bleeding off of cooling air before the compressor outlet is further studied in section 6.4.

For GT5-4 and GT5-5, the polytropic efficiency in the uncooled part was maintained at 0.91; whereas, it was set to 0.87 in the cooled part for GT5-4 and to 0.84 in the cooled part for GT5-5. The temperature given for GT5-6 in table 5.4 is the temperature for the second stage.

During the model evaluation, it became evident that results of rjth and P, which are identical to each other, can be obtained, regardless of method employed to divide the

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Table 5.4: Primary input parameters for gas turbine simulations.

7r const. Ah const.Turbine Vc Tb S Tb SGT1 0.95;0.65;0.65;0.5 733 0.150 736 0.153GT2 0.95;0.7;0.7;0.55 785 0.198 789 0.203GT3 0.9;0.55;0.55;0.35 795 0.287 798 0.288GT4 0.95;0.75;0.7;0.5;0.5;0.3;0.3 795 0.048 770 0.051GT5-1 0.98;0.74;0.54;0.54 774 0.199 — —

GT5-1 0.97;0.74;0.74;0.57 — — 754 0.189GT5-2 0.9;0.65;0.65;0.5 761 0.181 776 0.197GT5-3 0.9;0.65;0.65;0.5 758 0.189 772 0.206GT5-4 0.9;0.65;0.65;0.5 761 0.083 777 0.105GT5-5 0.9;0.65;0.65;0.5 759 0.0 769 0.0GT5-6 0.9;0.65;0.65;0.5 684 0.150 713 0.178GT6 0.9;0.8;0.7;0.6 794 0.442 794 0.440GT7 1.0;0.75;0.75;0.5;0.5 734 0.065 759 0.080

expansion path into segments. Most of the results are identical to manufacturers’ data. For large gas turbines, there is a larger difference in between the two methods than for small gas turbines.

The agreement between calculated and given data, is good enough to judge that the CGTM in chapter 4 is validated, i.e. it can be employed to model existing gas turbines at the design point. When it comes to the crucial point, i.e. the amount of coolant extracted from the compressor, there are no (public) data available for comparison. All cooling flows are within reasonable ranges, however.

5.4 Comparison with GATECycle

GATECycle2 is a commercially available heat balance program, which was originally developed for detailed gas turbine cooling calculations. Thereafter, the program has been developed as a heat balance program, with the possibility of performing calculations with very detailed input data. This enables calculations close to reality, but also requires extensive knowledge about power plant components. Version 4.3 of GATECycle is available at the Department of Heat and Power Engineering in Lund.

For gas turbine calculations, it is possible to set up user-defined models or to use data from the GATECycle gas turbine library. In this library, data for GT4 are available. A comparison between data from this library and results from the simulations above is shown in table 5.5. The results from the case, where tt is equal over each stage, are shown for the CGTM. The same source for input data that was employed in GATECycle, was employed in the calculations made here with GT4.

It is obvious that the simulation of GT4 with the CGTM gives better results than those obtained with GATECycle. Note that GATECycle is also adapted for off-design and partload calculations; whereas, the present work only deals with design-point calculations; i.e.

2developed and purchased by Enter Software Ltd.

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Table 5.5: Data and results for GT4 with GATECycle and with the CGTM.

Turbine Vth P TET TRIT Texh H%]GATECycle 35.9 151.1 1362 1267 554 20.5CGTM 36.2 152.0 1364 1288 550 21.5Manuf. data 36.1 152.0 — 1288 550 —

there might be other considerations involved in the GATECycle library, which lead to a deviation between the manufacturer’s data and the calculated data.

5.5 Mixing of coolant and hot gases before the expansion

In order to evaluate the use and usefulness of a really simple cooling model, the results from section 5.3 were compared to the results for the case where all of the cooling air is mixed into the flue gases before the expansion (c.f. Horlock [27] and Korakianitis and Wilson [31]). The flowsheet for these calculations in IPSEpro is shown in figure 5.2. The values of <p, which were calculated with the CGTM with equal pressure ratio over each stage, were used as input in these calculations.

Coolant Exhaust

Mixer

Figure 5.2: Flowsheet for IPSEpro calculations with a simple cooling model.

First, the polytropic efficiency was set to the values used in section 5.3. Not very surprisingly, this gives an underestimation of the turbine exhaust temperature and an overestimation of the cycle thermal efficiency, since the mixing losses are not considered in any way.

Thereafter, the polytropic efficiency was reduced using the same method as for the CGTM. It was found that, for the same amount of coolant flow, exactly the same values of turbine exhaust temperature and power output could be obtained as were obtained with the CGTM, but for a lower value of S. This is not very surprising, when one considers that the difference between the CGTM and this simple model is that, for the simple model, all of the mass flow passes through the entire turbine, which means that the polytropic efficiency need not be that much reduced. Hence, the real use of a cooling model is to determine a value of the cooling flow ip\ or, referring back to the black-box concept in figure 4.1, the task of the cooling model is to determine what happens inside the black box so that rhc can be calculated. Once is known, the turbine can be simulated. The

32

results for the simple method are given in table 5.6. It is obvious that using such a simple model, without reducing the polytropic efficiency, leads to an overestimation of gas turbine efficiency and an underestimation of Texh.

Table 5.6: Results from simulation when all of the coolant is entered before the expansion begins.

r)p unchanged j]p changedTurbine Vth Texh Vth S VprGT1 37.5 513 35.0 0.067 0.870GT2 36.5 534 33.5 0.080 0.853GT3 40.7 471 35.0 0.111 0.832GT4 37.9 535 36.2 0.035 0.888GTS 41.4 508 37.0 0.086 0.845GT6 44.0 464 36.1 0.160 0.807GT7 37.7 570 35.7 0.050 0.876

Mixing all of the coolant with the hot gases before the expansion, in combination with the use of a reduced polytropic efficiency, should be a comprehensive way of dealing with gas turbine cooling, e.g. in undergraduate teaching. But when studying, e.g. coolant treatment as in section 6.5, the model cannot be employed, since it is too simple.

5.6 Experiences from the validation calculations

Some of the experiences from and reflections over the validation calculations are judged to be of common interest, and are thus briefly described here. Knowledge of TIT proved to be very useful, when adjusting temperature levels and blade temperature, in order to obtain an agreement between Texh and %/,. Also knowledge of TET or TRIT is useful, and without any of this information, simulation of existing gas turbines is a very difficult task, although public data for power output, Texh and %, together with tt and inlet or outlet mass flow ratio, help to restrict the possible ranges of parameter settings.

Knowledge of whether the gas turbine has a single-shaft turbine or a free turbine also proved to be vital, in order to establish pressure or enthalpy drops over the stages. This information, together with information about the number of cooled stages, can usually be obtained from magazines, such as, Gas Turbine World.

No major difference was found between the two methods for defining the conditions over a stage in the turbine model. The general conclusion is that when Ah is constant, the blade temperature must be set to a slightly higher value than when 7r is constant over a stage. There is a tendency that the larger the turbine, the larger the difference in blade temperature between the two expansion models.

There is also a tendency, although it is not quite unambiguous, that the value of S is lower for large gas turbines than for smaller ones.

In real gas turbines, all of the cooling air is not extracted from the compressor outlet. Some of the air is extracted at an intermediate point, which results in a lower coolant pressure and temperature, and also that less work is lost. Not considering this in the model, however, appears to have no significant impact on the results. The concept of bleeding off air for cooling is further evaluated in section 6.4. The fact that the blade

33

temperature is set equal over the entire turbine does not prevent the model from giving satisfactory results.

It is not obvious how to simulate a gas turbine only with help from unclassified manufacturers’ data. There are many parameters that can be varied, as is shown for GTS, and different sets of parameters can give acceptable results for the same turbine. Nevertheless, the calculated value of <p remains rather constant although different parameters are varied.

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Chapter 6

Design point gas turbine studies

A first illustration of the impact of cooling on gas turbine efficiency is given for the ICAD cycle in section 1.1. In this chapter, studies are made on the design-point performance of the simple-cycle gas turbine, the Humid Air Turbine (HAT) cycle and briefly on the combined cycle, with focus on turbine cooling and its impact on cycle efficiency. Also, the impact of coolant cooling and/or humidification is studied.

In all calculations in this and in the next chapters, the thermal efficiency and specific work are calculated from the electrical output of the cycles studied. This means that in order to obtain the values of rjth and a; from shaft power output, the values given mustbe divided with the assumed mechanical and electrical efficiencies of the generator, i.e.0.99*0.98=0.9702 (refer to appendix C).

6.1 Reference gas turbines

Based on the results from the simulations of real gas turbines in chapter 5, three reference gas turbines were established. All three reference gas turbines are used as the basis for most of the calculations in this chapter. The exceptions are the studies on the uncooled gas turbine in section 6.3, where calculations were made with RefGTl, and on coolant pre-cooling in sections 6.5.2 and 6.5.3, where calculations were made with RefGT2. The performance and vital input data for the reference gas turbines are given in table 6.1. Other input data are given in appendix C.2.

Table 6.1: Performance and vital input data for the three reference gas turbines. Turbine polytropic efficiency r)p in the uncooled part=0.91.

RefGTl RefGT2 RefGT3nth 37.0 % 37.0% 37.1%Oi 364.3 kJ/kg 363.2 kJ/kg 364.7 kJ/kg

TIT 1201°C 1202°C 1203°CTexh 541°C 542° C 542° C

V 19.5 % 19.4% 19.3%S 0.18 0.08 0.00

nP, cooled part 0.91 0.87 0.84

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The three reference gas turbines have an identical flowsheet, which represents a three- stage one-shaft model, and the principle of equal pressure ratio over each turbine stage has been adopted. The two first stages are fully cooled. The flowsheet of the reference gas turbines is identical to that represented in figure 5.1.

6.2 The impact of S and r)p

The three reference gas turbines were established in order to enable a more thorough examination of the role of equation 4.8, i.e. the reduction of turbine polytropic efficiency due to the mixing of coolant and main flow. Hence, the only difference in input for the reference gas turbines is that S and r)p for the cooled part of the turbine have been changed.

It can be seen in equation 4.8 that the value of the reduced turbine polytropic efficiency T]pr depends on the non-reduced polytropic efficiency tjPi the pressure at turbine inlet and outlet (p4 and ps, respectively), the pressure pxi at the beginning of the cooled stage under consideration, the total coolant mass flow p that is mixed with the main gas stream, and finally, the polytropic efficiency reduction factor S.

Since the pressure pXi decreases along the expansion fine, the work reduction due to the decreased polytropic efficiency, i.e. due to the losses caused by the injection of coolant into the main flow, is larger at the beginning than at the end of the turbine model, which is also the case in a real open-loop cooled turbine. If S is set to 0, as is the case for RefGT3, the polytropic efficiency will be equal over each stage, which is less realistic.

Also, for a given turbine, the value of p will increase slightly with increasing S, since the temperature decrease over a stage is smaller if the polytropic efficiency is lower. Hence, the temperature at the inlet of the following stage will be slightly higher, which leads to an increased value of p for a given T&. The impact of S on r]pr and p is further illustrated in figure 6.1.

—o— 1sl expansion

—B— 2nd expansion

—A— 3rt expansion

—x— 4th expansion

Figure 6.1: Impact of S on r}pr and p with model for expansion losses derived from Traupel [57].

36

The discussion on what is an appropriate value of S is continued in connection with the parameter variations in chapter 7.

6.3 The uncooled gas turbine

To illustrate the impact of cooling on gas turbines (without intercooling), three cases, with input from the calculation of RefGTl, were investigated for the simple-cycle gas turbine,i.e. the Brayton cycle:

1. Texh is input

2. TIT is input and set equal to temperature after combustion chamber

3. TET is input

Component efficiencies, and other input data, were taken from appendix C.2. Since there is no cooling in the Brayton cycle, TIT, TRIT and TET occur at the same point, that is the point in the cycle with the highest temperature. The results of the calculations are shown in table 6.2 and should be compared with the data for RefGTl in table 6.1.

Table 6.2: Results from simulations with Brayton cycle.

Input temp. Vth TIT/TET Texh1. TET 41.8 1360 6032. Texh 41.5 1261 5413. TIT 41.2 1201 504

The physical meaning of the results in table 6.2 is illustrated in figure 6.2. A turbine without cooling, with an expansion that starts from TET, and that has no mixing losses and reduction of the polytropic efficiency, has a higher thermal efficiency than the cooled turbine, although Texh is considerably higher. The expansion that ends at the real value of Texh also has a higher thermal efficiency, although the expansion starts from a lower temperature than for the cooled gas turbine. This illustrates the impact of the losses, which occur in a cooled gas turbine, due to wasted compressor work and due to the mixing losses that reduce the polytropic efficiency of the turbine.

It is also evident from figure 6.2, that TIT has no physical meaning for the work extraction and efficiency of the gas turbine. On the other hand, TIT gives an estimation of the technology level of the gas turbine, meaning that the higher the value of TIT, the lower the value of <p and/or the higher the value of TET. But with only TIT known as a ’’hot” temperature, it is difficult to estimate the exact values of each of these two important parameters. To sum up this section, it is interesting to note that even a Brayton cycle with that low maximum temperature, still has a thermal efficiency that is considerably higher than that of the real, cooled gas turbine.

6.4 Cooling air bleed-off

In section 5.3, all versions of GTS, except for GT5-3, are simulated with all of the cooling air taken from the compressor outlet. In the case of GT5-3, some of the cooling air is

37

approximate expansion line in cooled gas turbine

Figure 6.2: Ts-diagram for calculations with uncooled turbine.

bled off from an intermediate point in the compressor, which resulted in slightly lowered coolant mass flow requirements, for a given thermal efficiency.

A gas turbine model with some of the coolant bled off at lower pressures, of course, means that the model is closer to reality, but in consequence with the goal that the model should be easy to use, most calculations were made with all of the coolant taken from the compressor outlet. To further illustrate the potential of coolant pre-bleeding, however, some calculations were made with RefGT2, where the coolant for the second vane was bled off at an intermediate pressure in the compressor.

Bleeding off the air at an intermediate point in the turbine means that the cooling air is colder and has a lower pressure, i.e. turbine stages of low pressure can be cooled with a smaller mass flow, and at the same time, less work is required to compress the air. A parameter variation was made where the second stator vane is cooled with air bled off at the intermediate pressure, pextr■ The changes in coolant flow requirements and efficiency are shown in the upper two diagrams in figure 6.3. TET and tt were kept constant at the design point, 1360°C and 20, respectively. Coolant extraction pressures, which are lower than the pressure of the main flow at the point where the coolant is to be injected, are not realistic, which is illustrated by the hatched area in the figures.

The decrease of compressor work per unit mass flow at compressor inlet a^)C7np with decreasing coolant extraction pressure is shown in the lower diagram in figure 6.3.

6.5 Coolant treatment

The cooling model in chapter 4 can be summarized in the equation

(6.1)

This equation shows that (pi depends on temperatures and on the ratio Cp9/cpC. Hence, two of the possible ways of reducing (and, in addition, hopefully increasing %&) are to reduce Td and/or reduce Cpg/cpC. Cooling the air, which is extracted from the compressor,

_ _ \Tg Tb) Cpg-^—Ab

•nig 77c (Tb - Td) OpC Ag

38

37.7 t 19.4 T

19.2 -X/.X37.6 -/-.A

37.5 ■ ■■'■

XXXX18.837.4-XX)'X:\XXXX

XXXX

AAAXxxxxx AAA

439 f,

437 t;Y

15 20

Figure 6.3: Change in simple-cycle efficiency (upper left), coolant flow requirements (upper right) and compressor specific work (lower diagram) for changing pressure of coolant extraction for second vane.

before it enters the blades and vanes, leads to an increase in cooling effectiveness, and thus, a decrease in the coolant flow requirements. Three possible ways of doing this are studied below, the first two deal with dry air and the third with humid air as the coolant. For all three examples, three cases of cooling air treatment will be studied:

1. only first stage vane coolant is affected by the coolant treatment;

2. coolant for first and second vanes is affected by the coolant treatment;

3. all of the coolant, i.e. blades and vanes for the first two stages, is affected by the coolant treatment.

To take out the stator cooling air from the gas turbine, cool it and put it back again appears, from what can be found in literature, to be quite feasible in the near future [16], (if it does not exist already), which explains the investigation of cases 1 and 2.

In general, the cooling air for blades and disks is directed from the compressor, through the gas turbine shaft, to the hot part of the turbine. It might, in practice, be difficult to take out the rotor cooling air and put it back again, at least without any major pressure losses occurring. Anyway, the extraction of rotor coolant, where it is pre-cooled and put

39

back into the rotating part of the gas turbine, is presented in studies for closed-loop cooling (refer e.g. to [16, 28, 60]), and hence, case 3 was judged to be an interesting concept to study.

6.5.1 Impact of Cpg/cpC on coolant flow requirements

The ratio of specific heat for hot gases to cooling air, Cp9/cpC, is vital to the coolant flow requirements. This is illustrated in figure 6.4, where, based on equation 4.6, coolant flow requirements as a function of m* are plotted for various Cp-ratios. Since St and A^/Ag may change with different gas turbines, the parameter on the y-axis was set to ip[ where

V[ s$t (6.2)

For reasons of simplicity, we here regard Cpg/cpC=l as an approximate value for cooling with humid air in dry-air gas turbines (or perhaps an approximate value for closed gas turbine cycles). A good average for a ’’dry”1 gas turbine cycle is cpg/cvc=1.2, and an average value for the hot part of a humid air cycle is Cpg/cpC=lA, where both coolant and flue gases contain a large amount of water vapor. Some calculated values of Cpg/cpC are shown in figure 7.7.

Example 1

Example 2

Figure 6.4: ip\ as a function of m*.

Humid cooling air has, due to the humidification process, a higher Cp-value and a lower temperature than the cooling air that is extracted from the compressor. Benefit could be taken from this in two ways : either to reduce the coolant mass flow or to increase the temperature in the turbine, or a combination of both, which is shown in the following examples, and illustrated in figure 6.4.

1Note that in a directly fired gas turbine, there is always a certain humidity in the exhaust gases, due to combustion of hydrogen.

40

The following data are assumed for an arbitrary point in the cooled part of a turbine: Tci=400°C (dry air)TCi=150°C (humid air)T9=1200°CT6=800°C77c=0.9

Example 1 - Increasing TET

With the data above m* is 1.1 for dry air, and with Cpg/cpC=1.2 figure 6.4 gives ip\ as approximately 1.33. If ip\, i.e. the coolant mass flow, is to be kept unchanged, the value of 77i* can be decreased to about 0.95 for a HAT cycle, and increased to 1.33 for a dry-air gas turbine cooled with humid air. Since the temperature of the humid coolant is 150°C, this means that, using equation 4.5, this corresponds to an increase of Tg to 1357°C for the HAT, and to 1580° C for the simple gas turbine. Hence, the decrease in temperature, which is obtained through the humidification of the coolant, can be used to raise the temperature levels even for the HAT cycle, although Cp9/cpC increases.

Example 2 - Decreasing ipi

On the other hand, if Tg is kept at 1200°C, then m* has the value 0.68 for 2^=150° C, and ip[ can be reduced to 0.95 for the HAT cycle, and to 0.68 for the dry-air gas turbine cooled with humid air.

Of course, an unlimited number of combinations of decrease in <pi and increase in Tg are possible, within the ranges calculated in examples 1 and 2. The impact on cycle efficiency, from the decrease of ip and/or increase of TET, is further discussed for the HAT cycle in section 7.3.

6.5.2 Fuel pre-heating

Pre-heating the fuel, before it enters the combustion chamber, means that less heat, i.e. less fuel, needs to be added. Exchanging heat between the coolant and the fuel, so that the cooling air is cooled and the fuel is pre-heated, is used in the ABB GT13E.

The parameter varied in this study is the fuel temperature after the heat exchanger. The impact on cycle efficiency from coolant temperature decrease is shown in the right diagram in figure 6.5. It can be seen that an efficiency increase can definitely be obtained with this concept. The increase in fuel temperature and decrease in coolant temperature are shown in the right diagram in figure 6.5. The fuel temperature increase is the critical parameter. As long as the fuel is not mixed with any air, the temperature remains well below the self-ignition limit [56]. In modern gas turbine combustors with a pressurized pre-mix of air and natural gas, however, the explosion limit of the mixture must be taken into consideration.

The calculations were made with RefGT2 at the design point TET=1360°C and tt=20.

6.5.3 External water heat exchanger

Removing heat from the cooling air, with an external heat exchanger, means that less coolant will be required; but, at the same time, heat will be removed from the gas turbine cycle, which reduces the work potential. As will be shown below, this might reduce

41

AT,fu0 50 100 150 200 250 300 350 400 450

0

-50

-100

-150

-200

-250

-300

36.9

14 16 18 <p 20 -350

Figure 6.5: Impact on simple cycle efficiency from heat exchanging between cooling air and fuel.

or obstruct the gain in efficiency that should be obtained from the decrease in coolant temperature.

In the simulations, the water temperature at the inlet is 15°C, i.e. the ISO temperature for any external source. The calculations were made with RefGT2 at the design point. The results for coolant cooling with an external water heat exchanger are shown in the left diagram in figure 6.6. It can be seen in the left diagram that there is a slight decrease in thermal efficiency, except for the case where all of the coolant passes through the heat exchanger. In this case, there is a (very small) increase in although heat is removed from the process. If the heat removed can be of use elewhere in the process, there will mostprobably be an increase in thermal efficiency for all cases. This is possible, for instance, in a combined cycle, where it can be added to the heat recovery steam generator. The concept, where water in the steam generator is heated through heat exchanging with cooling air, is suggested, e.g. by Westinghouse, for the rotor coolant in the ATS combined cycle [16].

In the right diagram in figure 6.6, it is shown how the heat, which is transferred from the coolant to the water, is proportional to the coolant mass flow.

6.5.4 Humidifying the coolant

As illustrated with the examples connected to figure 6.4, it is possible to reduce ip if humid air can be used as coolant. The possible efficiency increase, that can be obtained through cooling with humid air in a simple gas turbine cycle, is investigated for the reference gas turbines in this section, and for varying TET in section 7.2.3. Some or all of the cooling air is passed through a humidification tower (refer to section 6.7.2) before it is used for cooling, and as in all HAT cycle calculations, it is assumed that the air leaving the humidification tower is saturated.

In order to obtain a sufficiently high temperature of the water that enters the tower, a cycle configuration was set up according to figure 6.7. (The case where the coolant for first and second vanes is humidified is shown in the figure.) Water of 15°C from an external source passes through a heat exchanger, where it is heated by the flue gases leaving the turbine. The water that leaves the tower is recirculated, and mixed with the feedwater

42

600 --

q[kJ/kg]37.05 -r

500 --1st vane

•B—1st, 2nd vanes

-£t— blades and vanes400 --

36.9 --

300 -■36.85 -

36.8 --200 --

36.75 -

100 --

36.7 --

36.65

Figure 6.6: Impact on simple cycle efficiency from heat exchanging between cooling air and an external water source (left) and heat removed from the coolant as a function of cooling flow (right).

before the heat exchanger. Since some of the heat in the gases leaving the turbine is recovered, the gas-turbine cycle studied is not, strictly speaking, a simple cycle, but a kind of recuperative cycle. The cycle differs from a recuperative cycle in that here the heat recovered is used to evaporate water and cool the hot parts more efficiently; whereas, in the recuperative gas turbine, the heat recovered is used to preheat the air before it enters the combustion chamber, thus decreasing the amount of fuel that is needed.

A pinch point of 2°C is assumed throughout the calculations (refer to section 6.7.2).The theory of humid air and how it was implemented in IPSEpro is presented in

appendix B.2.

Exhaust

FeedwaterHumidificationtower Water recirculation

Figure 6.7: Flowsheet for gas turbine cycle with evaporatively cooled coolant.

The results at the design point, for the simple cycle with evaporatively cooled coolant,

43

axe given in table 6.3. The value of ip is (according to the definition) the ratio of the air extracted for cooling to the total mass flow of air entering the compressor, i.e. the evaporated water is not included in ip.

Table 6.3: Performance of the three reference gas turbines cooled with evaporatively cooled coolant.

Vth Texh CLi wFirst vane coolant humidified RefGTl 37.35 14.59 540.9 390.6 0.209

RefGT2 36.88 14.55 544.7 385.8 0.215RefGT3 36.59 14.50 547.1 383.0 0.221

All of vane coolant humidified RefGTl 37.82 12.88 538.6 403.4 0.205RefGT2 37.20 12.88 543.3 396.8 0.213RefGT3 36.80 12.90 546.3 392.6 0.219

All coolant humidified RefGTl 38.68 9.02 534.7 430.8 0.200RefGT2 37.78 9.00 541.1 420.9 0.209RefGTS 37.15 8.97 545.4 414.1 0.217

Already at this point, it should be stated that RefGT3 is not a very realistic gas turbine model. Since 5=0.0, any decrease in ip has no impact on the turbine polytropic efficiency. This is definitely not the case in a real, open-loop cooled gas turbine. Hence, it can be stated that for any gas turbine where ip has been reduced, the calculated value of the thermal efficiency of RefGT3 is definitely lower than any expected real value. This means that for the simple gas turbine where all of the coolant is humidified, there will definitely be an increase in thermal efficiency. The other two cases are more uncertain; in the case where just the first vane coolant is humidified, there is even an decrease in for RefGT2. This decrease is caused by the increased fuel consumption, in turn caused by the larger mass flow of air that passes through the combustion chamber, and is not compensated for by the increased specific work.

The results for ip are rather unanimous for the different reference gas turbines in each case, but the impact on cycle efficiency and specific work, from this reduction in coolant flow requirements, differs. There is definitely an increase in turbine specific work, due to the water contents of the evaporatively cooled coolant, which increases the mass flow through the turbine.

There is a correlation between the exhaust temperature and the specific humidity u of the coolant; the higher the value of Texh, the higher the value of u. This is caused through the interaction of a number of parameter settings in the heat exchanger and the humidification tower. (Among others, there is a limit so that the water that enters the tower is 10°C below the saturation temperature.) The reader should know that the higher the value of Texh, the more of the heat has been extracted from the exhaust gases that leave the turbine, thus enabling more water to be heated to the required temperature and, hence, more water to be evaporated into the cooling air.

6.5.5 Synthesis of coolant treatment

Three different ways of lowering the temperature have been reviewed above, one of them, the coolant humidification, in combination with an increase in coolant Cp-value. The hu

44

midified cooling air that leaves the tower has an approximate temperature of 152°C, and in order to make a comparison between the reference gas turbine and the different coolant treatment concepts, the increase in efficiency for all cases is compiled into table 6.4. The one case that does not have a coolant temperature of 152° C is the case where all of the coolant passes through a heat exchanger where it heats the fuel. Here, it is thermodynamically impossible to obtain a coolant temperature lower than 281°C. (The minimum pinch point in the heat exchanger is set to 10°C.) It can be seen that exchanging heat between the fuel and the coolant is the superior method coolant cooling, from a thermodynamic point of view. Technical aspects of the design of different solutions will not be addressed here.

Table 6.4: Change in percentage points for RefGT2, in thermal efficiency for the different cases of coolant treatment.

1st vane vanes blades and vanesFuel heat exchanging +0.4 +0.7 +0.9Water heat exchanger -0.3 -0.2 ±0.0Humidification -0.1 +0.2 +0.8

6.6 The HAT cycle - a brief presentation

The exhaust gases from a simple-cycle gas turbine have a high temperature and, thus, a high energy content, which means that much potential work is lost. Instead of ejecting the exhaust gases directly to the environment, more advanced power plant cycles have been suggested, where the heat from the exhaust gases is used for further power generation. The most successful of these cycles is the combined cycle, where heat from the gas-turbine exhaust gases is used to generate steam in a steam cycle. Most power plants built today are of the combined cycle type, and have a thermal efficiency that largely exceeds 50%. Recent concept studies have even presented combined cycles with thermal efficiency over 60% [8,41]. However, the adding of a steam bottoming cycle to the gas turbine is relatively expensive; roughly estimated, the steam cycle represents 2/3 of the investment cost for a combined cycle, but it only produces 1/3 of the electric power.

As demonstrated in section 6.5.4, an alternative way of recovering heat from the gas- turbine exhaust gases is to evaporate water into the air that exits the compressor. In section 6.5.4, the heat recovery is mainly done with one single heat exchanger (corresponding to the economiser in the HAT cycle) and the humidification tower, but the process can be thermodynamically improved if more heat exchangers (recuperator, intercooler and aftercooler) are incorporated. For further discussion on the use of these different heat exchangers, refer to [48]. Additionally, an external cooler can be used, as mentioned in [53].

Cycles using the concept of evaporated water in compressed air are usually called HAT (Humid Air Turbine) or EvGT (Evaporative Gas Turbine) cycles. Depending on the configuration, other designations, such as CHAT, IGHAT, REVAP or EGT, are also in use. HAT cycle is used throughout the present work. The HAT cycle has been widely discussed in literature over the past few years. Some studies intended to evaluate commercial operation [13, 38], and more ”academic” concept studies [11, 46, 48, 53, 54] have been

45

published. The academic studies also include some works on humid air cycles without a humidification tower [14, 27].

The HAT cycle should be cheaper to construct than the combined cycle, since it needs no steam turbine nor condenser or cooling tower [13]. The efficiency of a HAT power plant in operation is still unknown, since the first commercial plant is still to be built2; but studies have made claim of thermal efficiencies of up to 58% [32].

The aim of the design-point study in section 6.9 is to investigate the impact of the coolant extraction point on thermal efficiency for a potential HAT cycle operating at the design point of the three reference gas turbines. Studies of the impact of varying turbine inlet temperature are presented in chapter 7. Before any studies axe reported, however, the key component of the HAT cycle, the humidification tower, is presented.

6.7 Humidification tower

The humidification tower is the key component in most evaporative processes, although some processes have been suggested without a tower [14, 27]. This section presents a simple way to model the tower with heat and mass balances, and a more advanced method, where a minimum distance between saturation line and working line (pinch point) can be set.

6.7.1 Simple modelSix equations are needed to describe the humidification tower in a simple way with MDL3. First of all, the total pressure of the humid air is set to be the same at inlet and outlet. Secondly, the outlet pressure of the water is equal to the total pressure of the air (although the inlet water pressure is higher). The mass balance for dry air simply states that the dry air mass at the inlet is equal to the dry air mass at the outlet.

The mass balance for the water in and out of the tower is given by

ffi'da (k^e ~ rhttfi (6.3)

The energy balance over the entire tower is described by

(hoe hai) = ‘^we^'we '^wi^'wi (6-4)

The temperature of the humidified air at the outlet of the tower is given by the approximation that the relative humidity of the air is 100%.

6.7.2 More detailed model

Using the model described above means that there is no possibility to check whether the working line of the tower crosses the saturation line of the humid air or not. It is physically impossible to build a humidification tower where the working line is to the left of the saturation line. There must, in fact, be a minimum distance (driving temperature difference) between the working line and the saturation line. One recommended minimum value for this difference is 5°C [46]. This means that the difference between the temperature of the air that is in contact with the water and the temperature of the saturated air at the same

2 A demonstration plant is currently in operation at the Department of Heat and Power Engineering, Lund Institute of Technology

3Model Description Language in IPSEpro

46

enthalpy must be at least 5°C. (Actually, it is not the temperature difference, but the enthalpy difference that is the driving force, but to use the temperature difference is a good approximation.) Results from the demonstration plant at Heat and Power Engineering at the Lund Institute of Technology, however, indicate that in a pressurized tower, the pinch point is smaller, about 2°C, and this value has been used in the simulations in the present work.

The method used by Agren [46] is to divide the humidification process into a large number of segments, take a heat and mass balance over each segment, and then check whether or not the calculated point on the working line is on the right side of the saturation line and at a distance equal to or larger than the required pinch point.

An alternative to this method is to use the fact that the minimum distance between a straight line and a curve is at the point where the derivative of the curve is identical to the slope of the line (refer to figure 6.8). When the slope of the working line is known, together with the coordinates at water inlet/air outlet, and also the enthalpy at the air inlet is known, this means that the water temperature at the bottom of the tower can be determined, and hence, the simple heat and mass balances from section 6.7.1 can be applied.

saturation line. working line

Figure 6.8: Principle for calculating the pinch point of the humidification tower.

The working line of the humidification tower is not really a straight line, due to the mass transfer from water to air. However, according to ref [46], the curvature of the line is so small that the approximation with a straight fine gives an error that can be neglected.

The derivative of the saturation line was approximated with enthalpy difference over temperature difference for two adjacent calculated points on the saturation line. The derivative is supposed to be valid at the point in the middle of the two temperatures for which the enthalpy was calculated, i.e.

where

h2 — h\ t2-tx

Tpp —Ti+T2

2

(6.5)

(6.6)

47

The slope k of the working line is determined from

Ah _ hae haiAT Twi — Twe

(6.7)

At the pinch point, the derivative of the saturation line equals the slope of the workingline

& = %,)„. (6.8)

where Tvv is the temperature at the pinch point on the saturation line. The enthalpy at the pinch point on the saturation line (that equals the enthalpy on the working line) is given by

hpp — hsat {Tpp)Pa (6 9)

The temperature on the working line at the pinch point can be found through the equation for a straight line, and thereafter, the pinch point can be calculated or set to the desired value.

6.7.3 Comparison with experiments

The humidification tower model was compared with measured values from the demonstration plant in operation at the Department of Heat and Power Engineering. Since IPSEpro is an equation-solving program, it is arbitrary what measured data should be used as input and what data should be compared to calculated results. In this study, the following values were used as input:

• mass flows: air into tower, water into tower

• temperatures: air into tower, water into and out of tower

• pressures: air into tower, water into tower

In the model presented in section 6.7.2, there is no air pressure loss, and the experiments have proven that this is also the case in the real tower. Also, the condition that there is 100% relative humidity in the air at the tower outlet was maintained, since nothing in the experiments justify that a lower value should be set. The results of the comparison are given in table 6.5.

Table 6.5: Comparison between calculated and measured values for the humidification tower.

20% load 40% load 60% load 70% load 80% loadmeas. calc. meas. calc. meas. calc. meas. calc. meas. calc.0.307 0.306 0.324 0.324 0.346 0.347 0.358 0.356 0.370 0.367

Toe 107.8 111.2 110.6 113.6 113.6 116.2 115.2 117.5 116.9 119.0PP — 1.9 — 2.1 — 2.2 — 2.2 — 2.1

— 15.2 — 16.1 — 17.3 — 18.0 — 18.7

48

It can be seen in table 6.5 that there is not much difference between calculated and measured values of evaporated water; which is due to the fact that the mass flow of air into the tower, which was used as an input parameter in this case, is in reality calculated from the measured value of rhw>evap. Hence, the calculated values of rnw>evap merely show that the calculations made within the data acquisition program for the humidification tower are close to those of the model developed in the present project. The difference in temperature at the tower outlet between calculated and measured values was obtained also with the data acquisition program, and is thought to depend on the fact that the mixture of water and air does not, in reality, behave as a mixture of ideal gases. The conclusion of the calculations in this section is, thus, that the tower model is validated. The pinch point in the tower is always located at the bottom of the tower in the five cases represented above. There is (currently) no means of measuring the specific humidity ue at the tower outlet.

More experimental and analytical work must be done in the area of humidification tower modeling. Among other things, the behavior of the working line must be better known; can it be approximated with a straight line regardless of pressure, or is it (as some experimental results tend to indicate) a more strongly curved fine? If it is possible to determine an expression for the working line, where pressure is a parameter, it should be possible to implement the principle of equal derivatives at the pinch point also for a curved working line and, hence, obtain a model of the humidification tower that is moreclosely adapted to reality.

6.8 HAT Cycle configuration

A HAT cycle was set up, similar to what is referred to as ” cycle 18” in Rosen [48]. This cycle configuration is also the base for studies by Stecco, Desideri, Di Maria and others [4, 15, 53, 54]. The cycle configuration can be seen in figure 6.9.

2nd vane

1st vane

Recuperator

Economiser

d£> Exhaust

Feedwater

Figure 6.9: HAT cycle configuration with coolant extraction points.

49

The three different coolant extraction points that are used in this study are marked in the figure: CMP represents extraction after the compressor, AC extraction after the aftercooler and HT extraction after the humidification tower. For each reference gas turbine, eight different cases are studied, where the coolant is added to the turbine as listed in table 6.6. For the case 1A, the coolant for the second vane is extracted from an intermediate point in the compressor, at a pressure slightly above the pressure where it is injected into the main flow in the turbine.

Input data for the HAT cycle are given in appendix C.3.

Table 6.6: Cases considered in HAT cycle study, coolant for 2nd vane extracted at intermediate point in the compressor for case 1A.

Case No 1st vane 2nd vane rotor1 CMP CMP CMP

1A CMP CMP CMP2 AC CMP CMP3 AC AC CMP4 AC AC AC5 HT CMP CMP6 HT HT CMP7 HT HT HT

6.9 HAT cycle performance at the design point

The performances of the eight HAT cycle cases that are listed in table 6.6, are given in table 6.7. The coolant requirements ip are calculated as the percentage of the compressor inlet mass flow that is extracted for cooling; i.e. the actual coolant mass flow that enters the turbine in cases 5-7 is larger than the value given in table 6.7, since a certain amount of water is added to the air. It can be seen in table 6.7 that the difference between the case with the lowest (case 1) and that with the highest % (case 7) occurs for RefGTl and is 0.72 percentage points.

When comparing the simplified case 1 with the more realistic case 1A, it is clear that, regardless of what reference gas turbine is employed, the difference in efficiency is 0.2 percentage points, and the decrease in coolant mass flow requirements is 0.5-0.6 percentage points.

In case 2, there is an efficiency increase only for RefGTl, i.e. it is uncertain whetherthe HAT cycle efficiency will increase, due to the reduction in coolant mass flow that is obtained if the coolant for the first vane is extracted after the aftercooler. In cases 3 and 4, the efficiency increase is more certain since it is obtained for both RefGTl and RefGT2. It should be remembered here that RefGT3 is a worst case, where the impact on cycle efficiency from a reduction in coolant requirements is definitely underestimated.

The thermal efficiency of the HAT cycle increases, for all cases and for all reference gas turbines, when some or all of the coolant is extracted after the humidification tower. In the best case, case 7, the increase when compared to case 1 is 0.72, 0.46 and 0.27 percentage points, respectively, for the three different gas turbine models.

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Table 6.7: Performance of HAT cases at design point for RefGTl, RefGT2 and RefGT3.

Case No RefGT nth V Texh a,i w1 1 53.69 19.66 90.6 648.9 0.2141 2 53.46 19.58 90.7 644.7 0.2141 3 53.34 19.53 90.7 642.6 0.214

1A 1 53.88 19.04 89.8 651.6 0.2121A 2 53.66 19.01 89.9 646.7 0.2121A 3 53.54 18.98 89.9 664.0 0.2122 1 53.78 17.44 90.7 664.3 0.2132 2 53.43 17.55 90.7 657.1 0.2142 3 53.24 17.54 90.8 652.7 0.2143 1 53.88 16.70 90.6 671.0 0.2133 2 53.50 16.71 90.7 662.8 0.2133 3 53.27 16.75 90.8 657.6 0.2144 1 54.07 15.04 90.5 685.3 0.2124 2 53.60 15.12 90.7 675.1 0.2134 3 53.31 15.14 90.8 668.2 0.2135 1 54.00 16.01 87.5 664.5 0.1965 2 53.63 15.94 87.6 656.9 0.1975 3 53.42 15.94 87.6 652.1 0.1976 1 54.14 14.86 86.5 670.6 0.1916 2 53.73 14.82 86.8 661.9 0.1916 3 53.49 14.84 86.7 660.2 0.1927 1 54.41 12.37 84.6 683.1 0.1817 2 53.92 12.42 84.7 672.3 0.1817 3 53.61 12.45 84.8 665.0 0.182

6.10 Combined cycle performance at the design point

HAT cycles do not (presently) exist on the power plant market, but combined cycles do. In order to enable an evaluation of the results for the HAT cycle design-point calculations and parameter variations with combined cycles, a reference dual pressure combined cycle was created with input data according to appendix C.4. The performance data of this cycle at the gas turbine design point are given in table 6.8 for the three reference gas turbines.

Input data for the combined cycle can be found in appendix C.4. The efficiency of the reference combined cycle is not extremely high (c.f. a combined cycle based on ABB GT24/GT26 that has a thermal efficiency of 58%) but high enough to picture the performance of a modern combined cycle. It can also be noticed that the performance of the combined cycle hardly varies depending on the reference gas turbine employed.

51

Table 6.8: Performance, reference combined cycle

RefGTl RefGT2 RefGT3VthOiTITSteam turbine inlet temperature Texh

53.3% 520.0 kJ/kg

1199°C 536° C 126°C 19.8%

53.3% 521.4 kJ/kg

1200°C 537° C126° C 19.6%

53.4%522.9 kJ/kg

1201°C 537° C 126°C 19.5%

Chapter 7

Parameter variations

The previous chapter dealt with the design-point performance of various gas turbine cycles, and the impact of cooling and coolant modification on cycle efficiency at the design point. In this chapter, the study on the cooled gas turbine will be completed with parameter variations, where mainly TET, but in some cases, also 7r or T&, is varied. Comparisons are made with material previously published in the literature, in order to verify the calculations. Some of these comparisons also serve as a reference for the determining of the polytropic efficiency reduction factor S.

7.1 The uncooled gas turbine

Some aspects of the uncooled gas turbine (i.e. the Brayton cycle engine) were illustrated already in section 6.3. The behavior of the uncooled gas turbine with varying TET and 7r was calculated, and is shown in the upper two diagrams in figure 7.1. These diagrams are well in agreement with what can be found in the literature on uncooled gas turbines, in e.g. [3, 10, 12]. The data, which are used to plot the upper two diagrams, are also put together in the lower diagram in figure 7.1. This type of diagram is well-known from the literature, and shows very good agreement with that reproduced in [3]. Thus, without any coolant mass flow, and with S set to 0.0, the gas turbine model in figure 5.1 behaves as an uncooled gas turbine. The basis for the calculations of the uncooled gas turbine was RefGTl, i.e. t?p=0.91 in the entire turbine.

7.2 The cooled simple-cycle gas turbine

7.2.1 The role of SAs discussed in section 6.2, the impact of the change in gas turbine efficiency with decreased coolant mass flow strongly depends on S and %. The change in simple cycle efficiency with varying S is shown in figure 7.2. (The figure is based on RefGTl, i.e. the turbine polytropic efficiency ijp was kept at 0.91 in all stages.) For comparison, the curve for the uncooled turbine has also been drawn in the figure. This diagram comfirms the conclusion that can be drawn from equation 4.8, i.e. that the optimum thermal efficiency decreases with increasing S. Also, the value of TET, for which the optimum r}th occurs, is significantly lower than for the uncooled turbine.

To further investigate the role of S and %&, the diagrams that correspond to the lower diagram in figure 7.1 are shown in figure 7.3 for the three cooled reference gas turbines.

53

-1100°C-1000°C

1300°C

1200°C

1100°C

1000°C

900°C

,700°C800°C

i700°C

Figure 7.1: Variation of specific power with thermal efficiency for the uncooled gas turbine. 7T = 5 - 40 and TET=900 - 1500° C.

Since T& is kept constant during the parameter variations that constitute the base for figure 7.3, the dip in thermal efficiency for high temperatures (i.e. much heat must be removed from the blading) and high pressures (i.e. the cooling air is relatively hot), is perhaps not quite realistic. This is, however, difficult to judge since the equivalent diagrams, whicht have been found in the literature by the present author, do not cover pressure ratios above 30 and turbine entry temperatures above approximately 1400° C [5, 6, 49]. The diagram for RefGTl is similar to the plot for a simple gas turbine cycle of ’’Level 1”, which can be found in Bolland [6]. ’’Level 1” is a gas turbine where all of the cooling air is extracted from the compressor outlet, as is the case for all three reference gas turbines in this work. Therefore, it is interesting to note that the gas turbine model of ’’Level 2” shows a behavior for varying pressure and temperature that is very similar to that of RefGT3, except that the thermal efficiencies for the Level 2-turbine consequently are higher. (Recall that the polytropic efficiency in the cooled part of RefGT3 is very low). The Level 2-turbine in the work by Bolland is an advanced turbine with ”a large

54

e----- e- -6-----------6- o43

29 -I----------------- 1----------------- 1----------------- 1----------------- i----------------- i----------------- 1700 900 1100 1300 1500 1700 1900

TET

Figure 7.2: The impact of varying S on simple-cycle efficiency.

number” of bleeding points, for turbine cooling air, in the compressor, and is said to be a representation of the extremum of the design trend with more and more bleeding points for cooling air in the compressor.

The diagram with RefGT2 data is the one that shows the most agreement with the other two references mentioned above. The diagram published by Bdhm [5] has a connection to Siemens, and hence, to real gas turbines; whereas, the diagram published by Rufli [49] is based on more theoretical parameter variations. Anyway, these two references, and RefGT2 show similar results and a behavior that lies well inbetween the ’’old” Level 1-gas turbine and the hypothetical, ’’futuristic” Level 2-gas turbine of Bolland.

One conclusion that can be drawn from table 5.4, with the input parameters for the modeling of real gas turbines, is that the larger the gas turbine, the lower the value of S. With help from the discussion above, this conclusion can be completed. Hence, the trend is that for a large and modern gas turbine, the value of S is lower than for a smaller and/or older one. This is logical, since gas turbine designers continuously work on decreasing the losses in the flow field of the gas turbine, and also since there is less fluid friction in a large gas turbine than in a small one.

7.2.2 Dry-air coolant

For the three reference gas turbines with coolant extracted from the compressor outlet, variations of TET and T;, were made in order to illustrate the relation between these two parameters, and the thermal efficiency and coolant flow requirements. An additional purpose with these calculations is to further illustrate the impact of S on the cycle behavior.

TET was varied from 1040°C to 1520°C, in steps of 80°C, and T& was varied from 680°G to 880°C, in steps of 40°C. For T&=880°C, the calculations were made for TET down to 880 °C, i.e where the cycle takes on the behavior of the uncooled Brayton cycle.

In figure 7.4, % as a function of cp is represented for the three turbines. In order to facilitate the interpretation of the diagrams, the lines that intersect with the design point

55

RefGT2RefGTI

RefGTS

100 200 300 400 a.

Figure 7.3: Variation of specific power with thermal efficiency for the reference gas turbines.

of the reference gas turbines has been made thicker than the others. In common for the three diagrams is the trend that the thermal efficiency increases with increasing average material temperature T&. Also, there is a trend that the higher the value of T^, the higher the temperature TET at which the optimum rjth occurs. The large difference between the turbines is that, for a certain T&, the temperature at which the thermal efficiency optimum occurs is different. For RefGTI, the optimum has already been surpassed for the lower values of T& shown in the diagram; for RefGT2, the optimum is visible for all values of TET, and for Ref GTS, the optimum occurs at higher values of TET. These tendencies can also be seen in figure 7.3.

It was mentioned in chapter 2 that, over the past decades, approximately half of the hot gas temperature increase that has been made possible is due to improved cooling technologies, and the other half is due to improved materials. An example of a trendline for this development of TET and T&, where TET increases twice as much as T&, has been drawn with a gray fine in the diagrams in figure 7.4. It can be seen that for any point situated to the right of the optimum thermal efficiency on a line for constant TET, there is less benefit in increasing TET than there is in just increasing T&. Such a development trend for a gas turbine model is not very likely, and hence, it can be concluded once again that RefGTI is not a probable model for a modern gas turbine.

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Tb~880° approximatedevelopmenttrend Inconstant

------------Inconstant

-[.=880-0 trend

approximatedevelopment - Inconstant

- Inconstant

RefGT2

10 15 20 25 30 35 40

approximate development

.trend-e-~. _... T^r-. ------------Tg=constant

RefGTS

5 10 15 20 25 30 35 40<P

7.4: Simple cycle efficiency jjth as a function of ip for the three reference gas turbines.

57

500 - approximate development trend A -------Tb=constant

— T =constant450 -

400 --

300 --

250 --RefGT2

Figure 7.5: Specific work «2- as a function of <p for RefGT2.

If just optimum thermal efficiency was the design goal for an industrial gas turbine, the desirable development trend would be to climb from one optimum TET to the next, as Tb increases. In industrial gas turbine design, however, the specific work of the turbine is also important. The specific work as a function of cp is plotted in figure 7.5. Since the three reference gas turbines turned out to have very similar behavior, only the results for RefGT2 are shown. It can be seen that, for any increase in TET and/or Tb, there is an increase in specific work. Hence, a compromise must be made between specific work and thermal efficiency, which in turn means that a probable trendline for the development of the temperature levels in a gas turbine should be drawn somewhat to the left of the optimum thermal efficiencies in the diagrams in figure 7.4. If one follows the trendline that would cut through the design point of RefGT2, it can be seen that such a line follows this criterion rather well; i.e. RefGT2 is probably a good turbine model for parameter variations, and definitely the best choice among the three reference gas turbines studied in the present work. Hence, RefGT2 will be used as a base for the parameter variations in the following sections.

7.2.3 Humid-air coolant

The ’’simple cycle” cooled with humid air is described in section 6.5.4. For this cycle, a parameter variation was made with RefGT2, where TET varied from 1200 — 1520°C. To make it possible for the calculations to converge with the same settings over the entire parameter range, an equation setting, which governs Tw{, is required. The one condition that was chosen was to set Twi to a temperature AT less than the boiling temperature. In this case, AT was set to 10°C, and the pressure of the water that enters the tower was set to be 1 bar above air pressure in the tower. This solution also made it possible to vary the compressor pressure ratio, but such calculations were never performed within the frame of the present work. Since the pressure out of the turbine remained constant during the calculations presented here, the temperature of the water that enters the tower is constant (205° C), and the temperature of the exhaust gases decides the mass flow of water that can be heated to this temperature.

58

36.81200 1300 1400 1500 1600

0.6 •"

-6— 1st vane

■B— vanes-a— blades and vanes

0.4 -■

0.2 --

Figure 7.6: Results for simple cycle cooled with humid air, tt=20, TET=1200 — 1520° C.

The results from the calculations are shown in figure 7.6. The thermal efficiency as a function of both cp and TET is shown in the upper two diagrams. For the case where all of the coolant is humidified, it can be seen that there is a definite increase in % with increasing TET, and that the coolant mass flow requirements are very low. The shapes of the curves for the two other cases might seem rather peculiar at a first look, but can be explained by figure 7.4, by the lower two diagrams in figure 7.6 and by figure 7.7. Inthe diagram for RefGT2 in figure 7.4, regarding the line that represents the behavior of RefGT2 at the design-point value of T& (triangular symbols), it can be seen that the point for optimum thermal efficiency lies in the lower limit of the parameter variation range; i.e. as TET increases, there is a decrease in the thermal efficiency, due to the increased coolant mass flow requirement. Up to values of TET of approximately 1400°C, this effect can also be seen for the case where only the first vane coolant is humidified, but it is less pronounced, since the increase in cp is lower. For the case where all of the vane coolant is humidified, the decrease in cp is so large that there is no decrease in

For TET=1400°C and above, it can be seen in the lower right diagram in figure 7.6

59

that the increase in exhaust gas temperature, TeXh, is slower. This is explained by the lower left diagram in the same figure, where it can be seen that the higher the exhaust gas temperature, the higher the specific humidity of the cooling air. This is due to the fact that the warmer the exhaust gases, the more heat can be recovered by the water in the heat exchanger, and the more water can be evaporated in the humidification tower.

It was discussed in section 6.5.1 how the ratio of Cpff/cpC affects the coolant flow requirements: the lower the ratio, the lower the coolant mass flow required. The value of Cpg/cpC for each cooling unit is shown in figure 6.7. It can be seen that Cpg/cpC is definitely lower for the humidified air than for the dry cooling air, and that with increasing temperature levels, this difference increases. The conclusion is that the higher the temperature level in the turbine, the larger the benefit of humid air cooling in the gas turbine.

Figure 7.7: Variation of Cp9/cpC for simple cycle cooled with humid air as a function of the temperature right before the cooling point.

7.3 HAT cycle parameter variation

The possible benefit of extracting some or all of the turbine cooling air after the aftercooler or after the humidification tower in the HAT cycle was evaluated in section 6.9 for the design point TET=1360°C. In this section, the evaluation is continued for RefGT2 with a parameter variation, where TET is varied from 1040 — 1520°C.

The results for all cases (refer to table 6.6) are shown in figure 7.8. In the figure, it can be seen that, compared to cycle 1, the efficiency is improved for all other cycles. It is evident that cycle 7, where all of the cooling air is extracted after the humidification tower, is the best cycle with the lowest coolant requirements for all values of TET.

The higher the value of TET, the larger the difference in thermal efficiency for the different cycles. Also, % increases with increasing TET. For cases 1, 2 and 3, though, it can be estimated, from the shape of the curves, that an optimum thermal efficiency occurs at a value close to the upper limit of the parameter range studied.

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54.5--

53.5 ••

case no52.5 --

■H— 1A

51.5 -■

■*—4

-e—5

1000 1400 TET 1600

Figure 7.8: Results of TET-parameter variation for HATcycles 1-7.

The curves for cases 1 and 6 are reproduced in figure 7.9 in order to illustrate the topic discussed in section 6.5: if cooling air with lower temperature and/or higher Cp is available, should it be employed to reduce (p or to increase TET?

The design point of case 1 is marked with the line with small dashes in figure 7.9. The thermal efficiency for this case is 53.5% and <p is 19.6% (Refer to table 6.7). The design point of case 6 has been marked with dash-dotted lines. It can be seen that, compared to the design point of case 1, there is both a decrease in <p, to 14.8%, and an increase in to 53.7%, for the design point of case 6. Hence, at the design point, a reduction of coolant flow requirements leads to an increase in thermal efficiency. However, if <p for case 6 is kept at the same value as for case 1 (lines with long dashes in figure 7.9), it can be seen that this results in an even higher thermal efficiency, approximately 54.2%, at a TET-value of 1490° C. Hence, if it is technically feasible, it should be better to expend the same amount of compressed air for the modified HAT cycle, and try to use the increased specific heat and decreased temperature of the coolant to increase the turbine entry temperature.

Case 7, where all of the coolant is humidified, was not used in the example, merely because the maximum coolant flow for this case is inferior to the design-point coolant flow of case 1. Of course, the increase in thermal efficiency is even larger for case 7 than for case 6, if the coolant flow is maintained at 19.6%. It can be seen in figure 7.9 that for TET=1520°, r)th is 54.5%, i.e. one percentage point larger than at the reference point of case 1, and that for a coolant flow of 19.6%, the difference would be even larger.

For all results concerning cooling with humid air, recall that ip is defined as the percentage of the compressed air that is extracted for cooling, i.e. the evaporated water is not included. Hence, with a coolant flow of 19.6% as mentioned above, the total coolant mass flow will be larger in the HAT cycle cooled with humid air than in the HAT cycle cooled with air extracted after the compressor or aftercooler. When it comes to the volume flows, though, nothing can be said with certainty, except that the volume flow of the coolant extracted after the aftercooler will be lower, since the air is colder. Also, the humid air is colder than the air extracted after the compressor, and it is uncertain whether the increase

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54.5 T

53.5 --

52.5 --

51.5 -case no

50.5 -

Figure 7.9: HATcycles 1 and 6 and the relation between changes in and TET, and their impact on thermal efficiency.

in mass flow will compensate for this enough so that there will be a sufficient amount of coolant available to cover the blades and vanes that require film cooling. This, of course, also depends on how much the coolant is heated within the blade before it passes through the material and is used for film cooling.

7.4 Combined cycle parameter variation

For the combined cycle described in section 6.10, one single parameter variation was made: for tt=20, TET was varied from 1120 — 1520° C in order to provide data for the synthesis diagrams in the following section. As in the other parameter variations with cooled cycles, RefGT2 was used in the calculations.

7.5 Synthesis

To round off the parameter-studies chapter, some of the results from the different TET- variations have been put together in three diagrams in figure 7.10. Here, the relationship among the thermal efficiency, %, the proportion of the compressed air that is extracted for cooling, <p, and the turbine entry temperature, TET, are made visible for the different categories of cycles that have been studied previously in this chapter.

The most obvious feature in the upper diagram in figure 7.10 is the significant decrease in ip when the simple cycle is cooled with humid air. This diagram also gives the impression that the thermal efficiency of the simple gas turbine cooled with humid air is inferior to that of the dry-air cooled gas turbine. This is not quite correct, as can be seen in the middle diagram: for low values of TET, the dry-air cooled cycle is indeed better than the one cooled with humid air, but the advantage in thermal efficiency for the humid-air cooled cycle increases as TET increases.

A look at the middle diagram in figure 7.10 gives the impression that there is not much difference in thermal efficiency among the combined cycles and the different HAT cycles

62

as TET varies. A closer look at the scale, however, reveals that there is a difference of up to perhaps slightly less than a percentage point at some temperatures. A comparison between the results in tables 6.7 and 6.8 gives the difference between HAT case 7 and the combined cycle, 0.6 percentage point at 1360° C for RefGT2.

The results for the combined cycle and HAT case 1 follow each other rather closely in all three diagrams, although the HAT cycle results have a more curved shape and the combined cycle results follow a straight line. Hence, the humidity of the hot gases in the HAT cycle seem to have no major negative impact on HAT cycle efficiency with the cooling air extracted directly from the compressor. The compressor of the HAT cycle is intercooled, and it appears that the lower temperature of the cooling air compensates for the higher Cp-value of the combustion gases.

In the diagram at the bottom of figure 7.10, it can be seen that y as a function of TET is almost identical for the combined cycle, HAT case 1 and the simple cycle cooled with dry air. Furthermore, in this diagram, it can be seen how the coolant flow requirements decrease, as all of the cooling air is extracted after the aftercooler, and decrease even more for HAT case 7, where all of the cooling air is extracted after the humidification tower. The lowest increase in (p is obtained for the simple cycle cooled with humid air.

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—£r— combined cycle

—x— HAT, case 1

—x— HAT, case 4

—6— HAT, case 7

o- -e-

1100---1----------------------- 1-----------------------i----------------------- !---1200 1300 1400 1500

simple GT—B— simple GT, humid vane and blade coolant

■a— combined cycle —x HAT, case 1

—X— HAT, case 4

® HAT, case 7

TET

—i

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------------------- i-------------------------- :----------------------- 1-------------------------- i----------------------- i----------------------- 1

1100 1200 1300 1400 1500 TET 1600

7.10: Comparison of simple gas turbine cycles, combined cycle and HAT cycles for: TET. All calculations made with RefGT2.

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Chapter 8

Concluding remarks

8.1 Conclusions

Blade and vane cooling are vital to the high performance of modern gas turbines. There are many ways to include cooling in gas turbine studies. Thermodynamic methods for doing this were reviewed in this report, and, based on some of these methods, a number of model requirements were set up and a Cooled Gas Turbine Model (GCTM) for design- point calculations of cooled turbines was established.

It was shown that it is possible to model existing gas turbines with the CGTM. Since there are many degrees of freedom left, even after listing the public information that is available for any existing gas turbine, some rules of thumb were established in a standard case, in order to facilitate the use of the CGTM. For one of the existing gas turbines, different deviations from the standard case were investigated, and it was found that the calculated coolant requirements, <p, was hardly affected by these deviations, i.e. the prediction of y? is rather stable. In the standard case, all of the coolant is extracted from the compressor outlet, but it was also shown how bleeding off cooling air at an intermediate point in the compressor decreases the coolant flow requirements with some tenths of a percentage point. Knowledge of at least one temperature in the hot part of the gas turbine (TET, TRIT or possibly TIT) was found to be vital for a complete heat balance over the turbine.

The losses that are caused by the mixing of coolant and main flow were considered through a polytropic efficiency reduction factor S, which was found to be an important model parameter. The reduction of the polytropic efficiency % as a function of S was illustrated, and three different reference gas turbines (RefGTl, RefGT2 and RefGTS) with almost identical output data, but with different values of S and polytropic efficiency in the cooled part of the turbine, were established.

A number of studies were made on the simple-cycle gas turbine (cooled with dry or humid air), the HAT cycle and the combined cycle. The calculations can be divided into design-point studies, where TET=1360°C and tt=20 are kept constant, and parameter variations, where mainly TET was varied.

As a part of the design-point studies, it was demonstrated that the thermal efficiency of the simple gas turbine can be improved if heat exchanging between fuel and coolant is incorporated in the cycle. Also, coolant cooling with an external heat exchanger with water on the cold side was investigated. Here, it appears that no thermal efficiency increase can be obtained for the simple cycle, but this concept should be very interesting in combined cycles. The possibility of increasing the thermal efficiency of the simple gas turbine through

65

humidification of the cooling air was also demonstrated. Among these three ways of modifying the thermodynamic properties of the coolant, heat exchanging between coolant and fuel proved to have the largest positive impact on cycle efficiency, with an increase of 0.9 percentage points if all of the coolant passes through the heat exchanger. The corresponding improvement for humidified coolant was almost just as large, 0.8 percentage points.

Eight different cases of coolant extraction points were investigated for the HAT cycle at the design point. The calculations were made with all three reference gas turbines, and it is believed that the results for RefGT2 are the most likely for a modern gas turbine. It was found that if all of the coolant is extracted after the humidification tower instead of after the compressor, there is a decrease in coolant requirements of 4.76 percentage points and an increase in thermal efficiency of 0.46 percentage points, from 53.46% to 53.92%. In connection to the HAT calculations, a model for calculating the humidification tower was presented. The principle of the model is that at the pinch point, the slope of the working line must equal the derivative of the saturation line.

Introductory parameter variations were made in order to further verify the behavior of the CGTM. First, it was shown that with the cooling turned off, the model had the same behavior as an uncooled Brayton cycle as TET and ix varied. The role of the polytropic efficiency reduction factor S was studied in detail, and it was found that a model of a modern and/or large gas turbine has a lower value of S than an old and/or small one. A low value of S means that any decrease in coolant flow will have only a small impact on the turbine polytropic efficiency; i.e. there is more to gain from coolant reduction in an old turbine with poor aerodynamics, than there is to gain in a modern turbine where the losses due to interaction between coolant and main flow are relatively smaller.

For the three reference gas turbines with cooling, two different parameter variations were made, first, a combination of varying TET and tt, and then, a combination of varying TET and average materials temperature T&. Based on results from the literature, both cases showed that RefGT2 was the most probable model of a modern gas turbine, and, hence, the rest of the parameter variations were made with this model.

It was demonstrated that the cooling of a simple-cycle gas turbine with humid air can have a positive effect on the thermal efficiency. The higher the temperature of the exhaust gases, the more water can be evaporated into the cooling air. This means that with the current trend of increasing temperature levels, cooling with humid air is a very interesting concept.

For the HAT cycle, it was shown that it is more interesting to maintain the amount of compressed air expended for cooling and try to increase TET rather than to decrease the coolant flow requirements, as different kinds of coolant were examined for varying TET. In this way, it should be possible to obtain an efficiency increase of 0.7-1.0 percentage points or perhaps even more.

8.2 Discussion and suggestions for future work

In order to simplify the present work, many assumptions were made. One of those that might affect the calculations is that T& is set equal over each stage in the gas turbine. This is, of course, a very coarse assumption. Different materials are used in different stages, which means that in a real gas turbine the allowed value of T& varies from stage to stage. Furthermore, varies over the blade surface. An idea, which arose during the progress of this work, is that it ought to be possible to let T& decrease linearly with decreasing Tg

66

along the expansion line. Possibly, such a correlation between 2& and Tg could be derived with help from the diagram in figure 2.1. This would perhaps also resolve the problem with the possibly unrealistic dip in thermal efficiency, which occurs for high values of TET in the parameter variations.

Also, instead of just assuming a value of r)c, it should be possible to derive an expression for the cooling efficiency rjc as a function of Tw-, Tg and T&. This idea was never implemented, since the assumptions made in chapter 5.3 proved to give a model with sufficient accuracy.

Integrating the modular gas turbine model with a more detailed blade cooling model, perhaps with ideas borrowed from numerical simulation codes, could be another possible continuation of the work presented in the present report.

The model for calculating cooling flow requirements, which has been presented in this work, is based on the assumption that all heat transfer from gas to blade is convective heat transfer. According to Holland [25], the radiant heat flux is relatively small, even in the hot part of the turbine (approximately 5-10% of the convective heat flux). Hence, thermal radiation has been left out in the model, since the radiation is negligible compared to the uncertainties in the cooling model. However, for high temperature gas turbines with a high water content in the flue gases this might not be quite correct, since the heat transfer by radiation from water vapour at high temperatures is rather important. This issue ought perhaps to be further investigated.

For RefGT2 and RefGT3, the polytropic efficiency was set to different values in the cooled and the uncooled part of the turbine. Although it was shown that RefGT2 was the best model for parameter variations, different settings of rjp in different parts of the turbine, is perhaps not quite satisfactory, when one considers that one of the requirements for a good turbine model is to contain as few model parameters as possible (refer to section 4.1), and also that the reason for using the polytropic efficiency instead of the isentropic efficiency, is that it is the same in every part of the turbine or compressor.

Cooled dry air and saturated humidified air tend to have a relatively low temperature, which increases the risk of large thermal gradients in the cooled blades. This issue has not been studied in the present work, but cannot be neglected in gas turbine design. Modern blades are, in general, highly alloyed and, in general, poor conductors [25]; i.e. there is definitely an increasing risk of thermal stresses with increasing temperature differences.

In all calculations, it is the coolant mass flow that has been studied. It must be remembered, though, that for a given existing gas turbine, the volume flow is important, since the geometries are fixed. Taking constant geometries into consideration, however, would have complicated the thermodynamic analysis considerably. (Also, recall that, in the present work, the geometry parameter Ai/Ag is kept constant, which guarantees some consistency when considering the geometries.)

In the HAT cycle, the humidified air that enters the combustion chamber cannot contain too much water, since this will lead to difficulties with ignition and combustion stability. For humid cooling air, there is no such limit, and it might be interesting to investigate the possibilities of further humidifying the cooling air in the HAT cycle, and study both further humidification of already humidified cooling air extracted after the humidification tower, and humidification of air extracted after the compressor or after the aftercooler.

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Bibliography

[1] Gas Turbines - Vocabulary. International Organization for Standardization. Reference number ISO 11086:1996(E/F).

[2] Anon. Gas Turbine 501G/701G. Mitsubishi Data blade, 1997.

[3] W. W. Bathie. Fundamentals of Gas Turbines. John Wiley & Sons, Inc., 1996.

[4] G. Bidini, U. Desideri, and F. Di Maria. Thermodynamic Analysis of Injected Water Recovery Systems for the Humid Air Turbine (HAT) Cycle. In Proceedings of the ASME Advanced Energy Systems Division, 1996.

[5] H. Bohm. Fossil-Fuelled Power Plants. VGB Kraftwerkstechnik, 74, 1994.

[6] O. Holland. Analysis of Combined and Integrated Gas Turbine Cycles. PhD thesis, Norwegian Institute of Technology, 1990.

[7] 0. Holland and J. F. Stadaas. Comparative Evaluation of Combined Cycles and Gas Turbine Systems with Water Injection, Steam Injection and Recuperation. Journal of Engineering for Gas Turbines and Power, 117, 1995.

[8] M. S. Briesch, R. L. Bannister, I. S. Diakunchak, and D. J. Huber. A Combined Cycle Designed to Achieve greater than 60 percent Efficiency. Journal of Engineering for Gas Turbines and Power, 117, 1995.

[9] A. Brown, B. A. Jubran, and B. W. Martin. Coolant Optimization of a Gas Turbine Engine. Proceedings of the Institution of Mechanical Engineers, 207, 1993.

[10] Y. A. Cengel and M. A. Boles. Thermodynamics, An Engineering Approach. McGraw- Hill, 3rd edition, 1998.

[11] P. Chiesa and G. Lozza. Intercooled Advanced Gas Turbines in Coal Gasification Plants, with Combined or HAT Power Cycle. In ASME International Gas Turbine and Aeroengine Congress & Exhibition, 1997. Paper No 97-GT-39.

[12] H. Cohen, G. F. C. Rogers, and H. I. H. Saravanamuttoo. Gas Turbine Theory. Longman Group Ltd, 4th edition, 1996.

[13] W. H. Day and A. D. Rao. FT400 HAT with Natural Gas Fuel. Turbomachinery International, 1993.

[14] J. De Ruyck, S. Bram, and G. Allard. Humid Air Cycle Development based on Exergy Analysis and Composite Curve Theory. In ASME Cogen-Turbo Power Conference, 1995. Paper No 95-CTP-39.

68

[15] U. Desideri and F. Di Maria. Water Recovery from HAT Cycle Exhaust Gas: A Possible Solution for Reducing Stack Temperature Problems. International Journal of Energy Research, 21, 1997.

[16] I. S. Diakrunchak, M. P. Krush, G. McQuiggan, and L. R. Southall. Status of West- inghouse’s Advanced Turbine Systems Program. In ASME International Gas Turbine & Aeroengine Congress & Exhibition, 1998. Paper No 98-GT-77.

[17] M. A. El-Masri. On Thermodynamics of Gas-Turbine Cycles: Part 2 - A Model for Expansion in Cooled Turbines. Journal of Engineering for Gas Turbines and Power, 108, 1986.

[18] H. Geipel, W. Keppel, and H. B. Weyer. Verbundforschung zur Hochtemperatur- Gasturbine. In VGB-Konferenz Forschung fur die Kraftwerkstechnik, 1998.

[19] G. A. Halls. Air Cooling of Turbine Blades and Vanes. In Supersonic Turbo-Jet Propulsion Systems and Components. Technivision Services, 1969. AGARDograph No 120.

[20] H. Haselbacher. Gas turbines. In Thomas C. Elliott, editor, Standard Handbook of Power Plant Engineering, chapter 2.5. McGraw-Hill, 1989.

[21] W. R. Hawthorne. The Thermodynamics of Cooled Turbines Part 1 - the Turbine Stage. In ASME Diamond Jubilee Annual Meeting, 1955. Paper No 55-A-186.

[22] W. R. Hawthorne. The Thermodynamics of Cooled Turbines Part 2 - the Multistage Turbine. In ASME Diamond Jubilee Annual Meeting, 1955. Paper No 55-A-191.

[23] N. Hay and J. H. Taylor. Effect of Reducing the Blade Cooling air Temperature and Mass Flow on Blade Life and Cycle Efficiency. Proceedings of the Institution of Mechanical Engineers, 198A, 1984.

[24] R. W. Haywood. Analysis of Engineering Cycles. Pergamon Press, 4th edition, 1991.

[25] M. J. Holland. Cranfield lecture notes - Rotor Blade Cooling in HP Turbines. Technical report, Rolls Royce pic, 1992.

[26] J. H. Horlock. Aero-Engine Derivative Gas Turbines for Power Generation: Thermodynamic and Economic Perspectives. Journal of Engineering for Gas Turbines and Power, 119, 1997.

[27] J. H. Horlock. The Evaporative Gas Turbine (EGT) Cycle. In ASME International Gas Turbine and Aeroengine Congress & Exhibition, 1997. Paper No 97-GT-408.

[28] T. Ikeguchi and K. Kawaike. Effects of Closed-Circuit Gas Turbine Cooling Systems on Combined Cycle Performance. In ASME Joint International Power Generation Conference, 1994. Paper No 94-JPGC-GT-8.

[29] J. L. Kerrebrock and D. B. Stickler. Vaporization Cooling for Gas Turbines, the Return-Flow Cascade. In ASME International Gas Turbine & Aeroengine Congress & Exhibition, 1998. Paper No 98-GT-177.

69

[30] T. S. Kim and S. T. Ro. Comparative Evaluation of the Effect of Turbine Configuration on the Performance of Heavy-Duty Gas Turbines. In ASME International Gas Turbine and Aeroengine Congress and Exposition, 1995. Paper No 95-GT-334.

[31] T. Korakianitis and D. G. Wilson. Models for Predicting the Performance of Brayton- Cycle Engines. Journal of Engineering for Gas Turbines and Power, 116, 1994.

[32] C. Laier. Parameterstudie eines mit einer Stufenverbrennungsgasturbine aus- geriisteten Humid-Air-Turbine-(HAT-)Prozesses und dessen Vergleich mit einem GUD-Prozess. Technical Report ITS-Nr. 326, Institut fur Thermische Stromungs- maschinen, 1995.

[33] A. W. Layne and P. A. Hoffman. The U.S. Department of Energy’s Advanced Turbine Systems Program. In ASME International Gas Turbine & Aeroengine Congress & Exhibition, 1998. Paper No 98-GT-141.

[34] C. Liess. Introduction to Cooling of Gas Turbine Blades. Technical report, von Karman Institute for Fluid Dynamics, 1969. Lecture series 15.

[35] J. F. Louis, K. Hiraoka, and M. A. El-Masri. A Comparative Study of the Influence of Different Means of Turbine Cooling on Gas Turbine Performance. 1983. ASME Paper No 83-GT-180.

[36] B. W. Martin, A. Brown, and M. Finnis. The Influences of Turbine Blade Mean Temperature and Component Efficiencies on Coolant Optimization in the Gas Turbine. Proceedings of the Institution of Mechanical Engineers, 211A, 1997.

[37] D. K. Mukherjee. Ziir Schaufelkiihlung der Gasturbine. Brown Boveri Mitteilungen, 1977.

[38] M. Nakhamkin, G. Touchton, and M. Polsky. CHAT Technology: An Alternative Approach to Achieve Advanced Turbine Systems Efficiencies with Present Combustion Turbine Technology. In ASME International Gas Turbine and Aeroengine Congress & Exhibition, 1997. Paper No 97-GT-142.

[39] B. Nilsson. GTX100 - A new High-Performance Gas Turbine. ABB Review 6/97, 1997.

[40] H. Nomoto, A. Koga, S. Ito, Y. Fukuyama, F. Otomo, S. Shibuya, M. Sato, Y. Kobayashi, and M. Matsuzaki. The Advanced Cooling Technology for the 1500° C Class Gas Turbines: Steam-Cooled Vanes and Air-Cooled Blades. Journal of Engineering for Gas Turbines and Power, 119, 1997.

[41] T. C. Paul, R. W. Schonewald, and P. J. Marolda. Power Systems for the 21st Century - ” H” Gas Turbine Combined Cycles. Technical Report GER-3935A, GE Power Generation, 1996.

[42] E. Perz. A Computer Method for Thermal Power Cycle Calculation. Journal of Engineering for Gas Turbines and Power, 113, 1991.

[43] E. W. Perz. Computer Aided Analysis of Thermal Power Processes. In ASME Cogen Turbo, 1993.

70

[44] E. W. Perz, U. Riesel, and H. A. Schinagl. A new Approach for Modelling Energy- Systems. In ASME Cogen Turbo, 1995.

[45] J. R. Price, O. Jimenez, L. Faulder, B. Edwards, and V. Parthasarathy. Ceramic Stationary Gas Turbine Development Program - Fifth Annual Summary. In ASME International Gas Turbine & Aeroengine Congress & Exhibition, 1998. Paper No 98-GT-181.

[46] N. Agren. Simulation and Design of Advanced Air-Water Mixture Gas Turbine Cycles. Technical Report ISRN/KET/R-74-SE, Department of Chemical Engineering and Technology, Energy Processes, Royal Institute of Technology, 1997.

[47] W. M. Rohsenow. Effect of Turbine Blade Cooling on Efficiency of a Simple Gas Turbine Power Plant. In ASME Diamond Jubilee Annual Meeting, 1955. Paper No 55-A-120.

[48] P. M. Rosen. Evaporative Gas Turbines - A Thermodynamic Evaluation of their Potential. Technical Report ISRN/LUTMDN/TMVK-7010-SE, Department of Heat and Power Engineering, Lund Institute of Technology, 1993.

[49] P. Rufli. A Systematic Analysis of the Combined Gas/Steam Cycle. In ASME COGEN-TURBO, 1987.

[50] P. Rufli. Systematische Berechnungen uber kombinierte Gas-Dampf-Kraftwerke. PhD thesis, ETH, Zurich, 1990.

[51] C. T. Sims, N. S. Stoloff, and W. C. Hagel, editors. Superalloys II. John Wiley & Sons, 1987.

[52] O. Singh and R. Yadav. Performance Analysis with Different Means of Cooling in a Combined Cycle. In ASME International Gas Turbine and Aeroengine Congress and Exposition, 1995. Paper No 95-GT-451.

[53] S. S. Stecco, U. Desideri, and N. Bettagli. Humid Air Turbine Cycle: A Possible Optimization. In ASME International Gas Turbine and Aeroengine Congress and Exposition, 1993. Paper No 93-GT-178.

[54] S. S. Stecco, U. Desideri, B. Facchini, and N. Bettagli. The Humid Air Cycle: Some Thermodynamic Considerations. In ASME International Gas Turbine and Aeroengine Congress and Exposition, 1993. Paper No 93-GT-77.

[55] S. S. Stecco and B. Facchini. A Computer Model for Cooled Expansion in Gas Turbines. In ASME Cogen Turbo, 1989.

[56] Sydgas AB. Naturgashandbok, 1981.

[57] W. Traupel. Termische Turbomaschinen. Springer Verlag, 1977.

[58] H. von Chain. Elements of Gas Turbine Propulsion (by J. D. Mattingly), pages XV-LIV. McGraw-Hill, 1996.

[59] P. P. Walsh and P. Fletcher. Gas Turbine Performance. Blackwell Science, 1998.

71

[60] D. T. Watson and I. Ritchey. Thermodynamic Analysis of Closed Loop Cooled Cycles. In ASME International Gas Turbine and Aeroengine Congress & Exhibition, 1997.

Paper No 97-GT-288.

[61] D. G. Wilson. The Design of High-Efficiency Turbomachinery and Gas Turbines.

MIT Press, 1984.

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Appendix A

Presentation of the software package IPSEpro

The heat balance program used in this project is IPSEpro, a software package developed and sold by SimTech Thermodynamic Simulations in Austria. IPSEpro is delivered with APP-Lib (Advanced Power Plant Library), which consists of components for creatingpower plant simulation projects. Unlike many other heat balance programs (e.g. GATE- Cycle and ASPEN), in IPSEpro, the user has full access to the component equations, since it is not the mathematical models of power plant components that are the main feature of the program. Instead the semiparallel solution method and the language for creating new components are the features of IPSEpro. However, the user does not have access to the source code of the thermodynamic data for gases, steam and water that are provided with IPSEpro.

A description of the semiparallel solution method is given by Perz [42]. The development of IPSE, the predecessor of IPSEpro, is described by Perz [43], and the architecture and features of IPSEpro are described by Perz et al. [44]. It is clear from these references that two of the main goals during development have been that the software should be flexible and should be easy to use.

IPSEpro consists of two separate modules, the Process Simulation Environment (PSE) and the Model Development Kit (MDK). PSE has a graphic interface that is similar to other heat balance programs: the user chooses icons, puts them on a flowsheet and draws connections between the icons. Unlike e.g. GATECycle 4.3, IPSEpro has a Windows interface, which means that it is rather easy for a user who is familiar with Windows to learn how to work with PSE. Through the help function, the user has full access to the equations that make up the mathematical model connected to each icon in APP-lib, and it is possible to create the same help function also for user-made libraries.

In MDK, the user can create new models with the Model Description Language MDL and design the icon that will represent the model graphically in PSE. The major restriction of MDL is that it is (currently) not possible to create loops of the kind ’’for i=l to n do”. The advantage is that since IPSEpro is an equation-solving package, the user need not think of which variable should stand to the left of the =-sign, nor of the order in which to enter the equations. Additionally, there is the possibility of dynamically linking code written in a traditional programming language, such as, C or Fortran.

One of the major simplifications that was achieved through the use of IPSEpro was the easy implementation of the advanced humidification tower model (refer to section 6.7.2).

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With a sequential programming language, it would have been necessary to iterate to find the slope of the working line that gives the desired pinch point. With IPSEpro, it was sufficient to set up the equations for the tower and give enough input data.

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Appendix B

Humid air

Doing power plant cycle simulations is basically setting up appropriate intensive properties (p, T, h et.c.) and applying thermodynamic principles. Humid air is an important factor in the calculations, and therefore, the thermodynamics of humid air will be reviewed in this chapter, and it will be discussed whether or not the ideal-gas equation of state can be applied to humid air.

B.l Thermo dynamics review

When performing thermodynamic calculations for a gas turbine cycle with dry air or air at the ISO reference state (60% relative humidity at 15° C), the assumption that the working medium is an ideal gas can be adopted without too much worry. When dealing with humid air, this is no longer obvious, but it is desirable, since dealing with ideal gases is much easier than dealing with water vapor. Assuming a gas to behave like an ideal gas means that the ideal-gas equation of state is valid, i.e.

pv = RT (B.l)

The assumption also implies that the enthalpy and specific heat of a gas are functions of temperature alone, and not of pressure. The ideal gas assumption is valid if at least one of the following two conditions is satisfied [10]:

• Pr « 1

• Tr >2

Where the reduced pressure pr and the reduced temperature Tr are defined as

Pr = (B.2)Per

Tr = ^~ (B.3)J-cr

The critical pressure and temperature, p,^ and T^, describe the state at the critical point, above which there are no distinct phase-changes. Most substances that occur in thermodynamic calculations are gases that have critical temperatures that are so high that the critical pressures need not even be considered, but equation B.l can be applied directly. This is, however, not the case for water. The critical point for water is at 647.3 K and 220.9

75

bar; i.e. fortunately, the critical pressure is so high that the ideal gas assumption probably should be valid, unless we deal with high partial pressure for water in combination with low temperatures.

Humid air is in general considered as an ideal-gas mixture where the total pressure p is the sum of the partial pressure for dry air, pda and that for water vapor pv. The relative humidity of the air is described by

Pg(B.4)

where pg is the saturation pressure of water at a given temperature. When <p&=l, the air is referred to as saturated; i.e. it cannot contain any more water at that temperature, and if the temperature is lowered, water will condense from the air. Another useful way of specifying the amount of water in humid air is to use the specific humidity w

^ mv PvV/ {Ry'P) Pv/Ry zg g\‘OT.da PdaV/ (Rda'P) Pda/Rda

Since the amount of water in humid air may change due to condensation or evaporation, it is common to calculate properties with respect to the amount of dry air involved; e.g. enthalpy is calculated as

h = hda + ajhv (B.6)

where the unit is kJ/kg dry air.

B.2 Humid air in IPSEpro

The Advanced Power Plant Library (APPJLib) that is shipped with IPSEpro includes both a ’’steam table”, i.e. physical properties data for liquid water and steam, and a ”gas table”, i.e. a database with physical properties for several gases, treated as ideal gases. The data in the steam table come from the IFC Formulations for Industrial Use1 and are valid from 0.01°C to 800°C and from 0.1E-6 bar to 1000 bar. The steam table has been extended to 850°C in APPJLib, but it is pointed out in the IPSEpro manual that it is the user’s responsibility to verify the validity of the results in the temperature range of 800 — 850°C. The steam table can be accessed through the variable WATER in the global composition in APPJLib. The physical properties for the other components are in APPJLib calculated with polynomials derived from the JANAF* 2 Thermochemical tables. Data for steam as an ideal gas can be accessed through the variable H20 in the global composition.

Since the connection stream in APP_Lib deals with only either the steam table or mixtures of ideal gases, a new connection had to be created to deal with humid air. Using data for water vapor would mean that the results would be more exact, but the number of equations (and hence the calculation time) would be considerably reduced if the properties for H20 could be employed. Besides the existing global composition, two new global units were created, G-H20 and GJ WATER, which were specified to get data only from H20 and WATER, respectively. The results of the calculations with Humidstream with data for water, either from WATER or from H20, are shown in table B.l. It was found that the zero level for enthalpy was defined differently in the two databases, and in order to

'Schmidt, E.: Properties of Water and Steam in Si-Units, Springer-Verlag Heidelberg New York, 1969.2Joint Army Navy Air Force

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Table B.l: Comparison between data for humid air with water as water vapor and for humid air with water as an ideal gas. w = 0.2.

vapor ideal gasP [bar], T[°C] h [kJ/kJ] h [kJ/kJ] diff. [%]1.01325, 100 673.8 638.1 0.471.01325, 200 778.1 778.1 020, 200 773.5 778.1 0.5930, 200 770.8 778.1 0.9540, 200 768.0 778.1 1.32

get comparable results, equation B.6 above had to be modified when data was taken from H20 into [46]:

h = hda + (cv/i„ + 2500) (B.7)

where 2500 is the heat of vaporization for water at 0°C and 0 bar.It can be seen in table B.l that the error increases with increasing pressure. One

must remember, though, that for thermodynamic cycle calculations it is always the enthalpy dijererzce that matters in the end; i.e. the resulting error over e.g. a turbine stepwill be smaller than the absolute errors at each point. The conclusion is that no significant error will occur for pressures and temperatures that are relevant for the HAT cycle if water vapor is considered as an ideal gas. It should be emphasized, though, that there is a lack of available experimental data on pressurized humidified air that can confirm the real error that occurs when treating humid air as a mixture of ideal gases.

The only exception for this is made in the humidification tower, where data for water must be taken from the steam table, due to the evaporation. At the inlet of the tower, H20 (from the humidity in the air) is converted to WATER and at the outlet of the tower, all WATER is converted back to H20.

B.3 Differences between cooling modeling for humid and dry air

Since cooling with humid air is considered in the present work, the impact of the humidity of the air on the equations and parameters used for cooling modeling needed to be considered. When modeling the cooling according to the method described in section 4.2.1, the Stanton number needs to be set to an appropriate value. According to Bolland and Stadaas [7], a typical value is 0.005. This is also fairly well supported by diagrams in Holland [25]. Due to the lack of experimental data for heat transfer in pressurized humid air and in flue gases with high moisture contents, a general discussion is attempted below, in order to justify the use of St=0.005 also for the turbine in the HAT cycle.

According to Holland [25], the Reynolds’ number for a turbine airfoil is well within the range of 105 — 107. For turbulent flow along a flat plate, it is possible to write (Sunden, 1988)

St = 0.0296Re-^Pr-2!* (B.8)

which will give the following expression for the ratio of the Stanton number for an arbitrary

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degree of humidity to the reference state (index 0 for reference state):

(St\_( Rex \ 1/5(Pr_\~2/3 \Sto) \(Rex)0J \Pro) (B.9)

Except for at high pressures and low temperatures, Pr/Pro is very close to 1. Since the partial pressure of water does not attain very high values, the assumption is therefore made that the addition of more water to the flue gases does not change the Prandtl number substantially.

The Reynolds’ number over a flat plate is written as:

UtRe == (B.10)

The characteristic length x does not change, and the velocity U is assumed not to change. This means that changes in the Reynolds’ number due to changes in humidity depends onthe ratio uq/u.

Numerical calculations were made for various temperatures and various water content, and the conclusion was drawn that vq/u could be approximated with 1.

The estimations made in this chapter are very coarse, and the author welcomes more detailed information about heat transfer in HAT cycles. In the present work, 0.005 will be used for the Stanton number regardless of the degree of humidity in the cooling air and flue gases. This approximation is supported by El-Masri [17].

The curves representing the cooling effectiveness as a function of the dimensionless coolant mass flow m* (refer to figure 3.2) are assumed to be valid also for humid air. The cooling effectiveness £bm depends only on temperatures and not on any other changes in physical properties; whereas, m* will change with changing values for the specific heats for flue gases and coolant. Consequently, when the cooling effeciveness rjc is used as input, it is assumed that it is not affected by increased coolant humidity.

The conclusion of the discussion in this chapter is that the only variable in equation 3.20 that will vary with varying humidity in the simulations is the specific heat ratio Cpff/cpC; i.e. if the coolant mass flow is to vary with humidity, it will vary due to changes in specific heat.

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Appendix C

Input for cycle simulations in chapters 6 and 7

C.l Miscellaneous input

For all simulations, dry air is assumed to have the following composition in mass fractions:

Ng 0.75518o2 0.23142co2 0.00049Ar 0.01291

For the gas turbines in section 5.3, the following parameters were judged to be of secondary interest to adjust, as the general model was tuned to fit vendors’ data. The exceptions are, of course, GT5-5 and GT5-6, where the polytropic efficiency r/p was reduced in the cooled part of the turbine.

Vp 0.90-0.92Vcmp 0.89-0.915Vcomb 0.99APcomb 0.04Api 0.01^■Pexh 0.01

Vm 0.99Vel 0.98

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C.2 Reference gas turbine input

Ambient conditionsT

P

15°C60%1.013 bar

CompressorAPi

Pp,cmp

7r

0.01 bar0.9120

CombustionLHVApcomfcVcomb

50000 kJ/kg4%0.99

Cooling and expansion TETVptsSt

Tb■A-b/Ag

1360°C0.91/0.87/0.840.18/0.08/0.00.005760° CFirst stage: 10Other stages: 5

Vc First stage: 0.952nd, 3rd stages 0.65 4th stage 0.5

A-Pexh 0.01 barOther parametersVm

Pel

0.990.98

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C.3 HAT cycle input

In addition to the input data for the reference gas turbines in section C.2, the following data were used as input for the HAT cycle:

IntercoolerAT, hot side 15°CAT, cold side 5°CApa 2%Apto 1%AftercoolerATevap, hot side 10°CAT, cold side 5°CApa 2%Apur 1%Humidification towerpinch point 2°CAp, top of tower 1 barRecuperatorAT, hot side 15°CApa 2%AP„ 2%EconomiserAT hot side 30° CATevap hot side 10°CAT cold side 5°CApa 2%APQ 2%

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C.4 Combined cycle input

In addition to the input data for the reference gas turbine in section C.2, the following data were used as input for the combined cycle:

Low pressure circuit, HRSGapproach point 4°Cpinch point, boiler 6°Cpinch point, superheater 8°CHigh pressure circuit, HRSGpinch point, 1st eco 18°Capproach point 4°Cpinch point, boiler 6°Cpinch point, superheater 16°CPressure losses, HRSGwater side, per heat exchanger 0.09gas side, eco 0.01gas side, boiler 0.03gas side, superheater 0.003Steam turbineinlet pressure, HP turbine 80 barinlet pressure, LP turbine 4 barpressure, feed water heater 1.3 barpressure, condenser 0.045 barisentropic efficiency 0.89

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Appendix D

Blade cooling models: Comparison and t her mo dynamic analysis

Presented at the 5th ASME/JSME joint thermal engineering conference, March 14-19, 1999.

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