thermal efficiency improvement of closed hydrogen and
TRANSCRIPT
Thermal efficiency improvement of closed hydrogen andoxygen fuelled combined cycle power plants with theapplication of solid oxide fuel cells using an exergy
analysis method
Bram Schouten
student number: 4390504
to obtain the degree of Master of Scienceat the Delft University of Technology,
to be defended publicly on Thursday the 9th of April, 2020 at 13:30 PM.
an electronic version of this thesis is available at http://repository.tudelft.nl
Abstract
Today’s renewables, wind and solar power, have a fluctuating nature, making the grid less stable.However, with the increasing share of intermittent sources of renewable power, novel options have tobe created to stabilize the power grid. One of these options is energy storage via the conversion ofexcess power to hydrogen, during periods of high generation from wind and/or solar. In periods ofpower shortages hydrogen is converted back to power.
In the literature fossil fuelled turbine cycles have been studied extensively, furthermore multiple fuelcell turbine cycles have been modelled. However, models with hydrogen and oxygen fuelled turbinecycles and fuel cell turbine cycles are scarce, leaving opportunity for further optimization of modeledhydrogen and oxygen fuelled cycles. The application of pressurized H2/O2 can lead to several improve-ments over conventional thermodynamic cycles and fuel cells.
In this work, a number of high efficiency hydrogen and oxygen fuelled thermodynamic cycles, basedupon the Graz cycle and the Toshiba Reheat Rankine cycle, both a coupled closed Brayton cycle witha Rankine cycle, are investigated. Furthermore, the following thermodynamic improvements are pro-posed to fit the Graz cycle: an increased TIT (turbine inlet temperature), the use of a reheat combustor(the inclusion of a 2nd combustor), condensate preheating and hybrid cooling (a combination of openloop and closed loop cooling) of the high temperature turbine blades. All upgrades together lead to anefficiency of 75% LHV. The rise of efficiency of the individual upgrades summed up is lower than therise off all upgrades together. This is due to the fact that adding reheat and increasing TIT introduceextra high temperature turbine blade cooling needs and losses, which an improved cooling methodcounteracts. For this reason, the cooling method used is rather influential. Therefore, two coolingmethods, open loop cooling and hybrid cooling, used in the Graz and Toshiba cycle respectively, arestudied in this thesis.
Next to the thermodynamic improvements, an electrochemical improvement is studied, by adding fuelcell systems to the turbine cycles. Multiple fuel cells combinations are studied: a single low tempera-ture solid oxide fuel cell (SOFC) and a low temperature, intermediate temperature and high temperatureSOFC in series. Moreover, the type of fuel cell cooling is investigated, both cooling by adding steam tothe cathode and recirculating excess oxygen in the cathode are studied.
The addition, of a triple SOFC cooled by oxygen recirculation, to an upgraded Graz cycle leads toa potential efficiency of 84% LHV. This efficiency is reached at a relatively low fuel cell fuel utilizationof 58%. In this study the turbine cycle is not fully adapted to the fuel cell system or vice versa. Bothsystems are adapted to each other, leading to the unique triple fuel cell system operating in series,which is more easily coupled to a turbine cycle and can operate at an overall higher SOFC utilization,compared to a single fuel cell. However, from the fuel cell side 2 of the 3 fuel cells are less electro-chemically favorable, as only one of the three fuel cells can operate in the best conditions. The overallsystem efficiency of the combined multiple fuel cell in series system with a turbine cycle, however ismost efficient.
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Acknowledgement
First and foremost, I would like to thank Prof.dr.ir. Sikke Klein for giving me the opportunity to workon this topic and for supervising this project. Also, at least as important, was his clear guidance keep-ing me from losing the broader picture. I also extend my sincere gratitude to Ir. T. Woudstra, Jelle Stamand S.A. Saadabadi for helping me out with some fuel cell related questions.
Furthermore, my gratitude goes to my study buddies working with me at the fluids lab for getting coffeewith me whenever I needed to clear my mind. Thanks to my brother, for proof-reading my report andproviding feedback.
Finally, I would like to thank my family, and friends for their support throughout and advice on thingsless technical.
Bram SchoutenDelft, April 2020
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Contents
1 Introduction 11.1 Innovations in this thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.2 Thesis outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2 Thermodynamic and electrochemical power cycle analysis 62.1 Thermodynamics of power cycles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62.2 Hydrogen fueled cycles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.2.1 Toshiba cycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112.2.2 Graz cycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.3 The solid oxide fuel cell (SOFC) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132.3.1 Fuel cell-turbine cycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152.3.2 Fuel cell physics model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
3 Cooling of the high temperature turbine blades 183.1 Closed loop steam cooling (CLSC) physics . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.1.1 Mathematical derivation closed loop steam cooling . . . . . . . . . . . . . . . . . 223.2 Open loop cooling physics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3.2.1 Validation of open loop cooling method, with Thermoflex method . . . . . . . . . 273.3 Open loop cooling implementation into the models of this thesis . . . . . . . . . . . . . . 273.4 Hybrid cooling implementation into the models of this thesis . . . . . . . . . . . . . . . . 29
4 Analysis of the Toshiba-Reheat-Rankine cycle and the Graz cycle 334.1 Comparison of the Graz and Toshiba cycles . . . . . . . . . . . . . . . . . . . . . . . . . 334.2 Making the cycles comparable . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 344.3 Path through the different models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 364.4 Exergy analysis method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 364.5 Exergy analysis equalized (EQ) cycles . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
5 Improvements to the Graz cycle 405.1 Individual cycle improvements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 405.2 Temperature entropy diagrams improved Graz cycles . . . . . . . . . . . . . . . . . . . . 42
6 Fuel cell addition to the Graz cycle 446.1 Fuel cell connection to the Graz cycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . 446.2 Electrochemical performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 486.3 Electrochemical operation and IV curves . . . . . . . . . . . . . . . . . . . . . . . . . . . 506.4 Exergy analysis FC-Graz cycles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
6.4.1 1 fuel cell vs 3 fuel cells (1FC vs 3FC): . . . . . . . . . . . . . . . . . . . . . . . . 536.4.2 Steam vs Oxygen cooled fuel cells (Steam vs OX): . . . . . . . . . . . . . . . . . 536.4.3 The U-Graz-FC cycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
7 Conclusions 57
8 Recommendations for future research 58
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A Mathematical derivation open loop cooling 62A.1 Derivation open loop cooling without TBC coating . . . . . . . . . . . . . . . . . . . . . . 62A.2 Derivation open loop cooling with the TBC coating . . . . . . . . . . . . . . . . . . . . . 65
B Thermoflex models without FC 66B.1 Graz-EQ cycle Thermoflex model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67B.2 Toshiba-EQ cycle Thermoflex model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68B.3 Graz-1700C cycle Thermoflex model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
B.3.1 Graz-1700C cycle Thermoflex stage by stage cooling model (open loop cooling) 70B.4 Graz-HEX cycle Thermoflex model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71B.5 Graz-Hybrid cooled cycle Thermoflex model . . . . . . . . . . . . . . . . . . . . . . . . . 72B.6 Graz-2CC cycle Thermoflex model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73B.7 U-Graz-1500C cycle Thermoflex model . . . . . . . . . . . . . . . . . . . . . . . . . . . 74B.8 U-Graz cycle Thermoflex model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
C Thermoflex models with FC 76C.1 Graz-1FC-Steam cycle Thermoflex model . . . . . . . . . . . . . . . . . . . . . . . . . . 77C.2 Graz-3FC-Steam cycle Thermoflex model . . . . . . . . . . . . . . . . . . . . . . . . . . 78C.3 Graz-1FC-OX cycle Thermoflex model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79C.4 Graz-3FC-OX cycle Thermoflex model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80C.5 U-Graz-3FC-OX cycle Thermoflex model . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
C.5.1 U-Graz-3FC-OX cycle Thermoflex stage by stage cooling model (hybrid cooling) 82
D MATLAB code 83D.1 Scripts for calculating the cooling needs per turbine stage U-Graz-3FC-OX cycle(which
uses hybrid cooling) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83D.1.1 Main script, HTT cooling of stages . . . . . . . . . . . . . . . . . . . . . . . . . . 83D.1.2 Function file, HTT cooling of stages . . . . . . . . . . . . . . . . . . . . . . . . . 87
D.2 Scripts for calculating the FC parameters . . . . . . . . . . . . . . . . . . . . . . . . . . 88D.2.1 Main script set to retrieve 3FC-OX data, needed to calculate the FC parameters 88D.2.2 First function file, needed to calculate the FC parameters . . . . . . . . . . . . . 91D.2.3 Second function file, needed to calculate the FC parameters . . . . . . . . . . . 93
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Nomenclature
Abbreviations
ASR Area specific resistance
BFP Boiler feed pump
CC Combustor
CCGT Combined cycle gas turbine
CIT Combustor inlet temperature
CLS Closed loop steam
CLSC Closed loop steam cooling
Comp. Compressor(s)
Deaer. Deaerator
EQ Equalized cycle
FC Fuel cell
FC-OX Oxygen recirculated fuel cell
FC-Steam Steam cooled fuel cell
HC Hybrid cooling
HEX Heat exchanger
HPT High Pressure turbine
HRSG Heat Recovery steam generator
HTT High temperature turbine
IRES Interruptible renewable energy source
LPT Low Pressure turbine
SOFC Solid oxide fuel cell
TIT Turbine inlet temperature
Variables and physical constants
χmolecule Mol fraction of the relevant molecule
v
εTg−TbTg−Tci
η Efficiency
e Exergy ( Jkg )
E0 Potential voltage (V )
ech Chemical exergy ( Jkg )
em Mechanical exergy ( Jkg )
Enernst Nernst voltage (V )
Ex Exergy (J)
F Faraday Constant ( Cmol )
G0 Gibs free energy of formation (J)
H0 Enthalpy of formation (J)
Ppmolecule Partial pressure molecule (Pa)
R Gas Constant ( Jmol·K )
S0 Entropy of formation ( JK )
A Area (m2)
Bi Biot number
Cp Heat capacity ( JK )
FOB Fraction of the blade
h Heat coefficient ( Wm2K )
HHV Higher heating value (kJkg )
LHV Lower heating value (kJkg )
n Amount of electrons used in the reaction
P Pressure (Pa)
POW Power (W )
Q Heat (J)
s Entropy ( JK )
St Stanton number
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T Temperature (K)
t Thickness (m)
U Internal energy (J)
V Volume (m3)
v Velocity (ms )
W Work (J)
Subscripts
ano Anode
b Metal Blade
cat Cathode
ce Coolant exitting the blade
ci Coolant going into the blade
c Coolant
ex External
g Main gas
in Internal
rxn reaction
w Wall
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1 Introduction
The accumulation of greenhouse gasses (carbon dioxide, methane and nitrous oxide) is one of theworlds most challenging problems, that needs to be tackled. The greenhouse gasses create a layerthat reflects the UV radiation and concentrates the incoming heat from solar radiation into the atmo-sphere of earth. As a consequence, the temperature rises on earth. It has been proven the increasein greenhouse gas concentration is the main reason for this increase in temperature. The OECD [1]predicts that at the 2011 emission rate, the temperature increase from 2011 to 2100 will range between3 and 6 C. Other very likely side effects of the greenhouse gas increase are more drought, more flood-ing, less ice and snow, more extreme weather incidents and a rising sea level [2]. From the greenhousegasses carbon dioxide has the highest share. Without new policies, by 2050, more disruptive climatechange is likely to be locked in, with global greenhouse gas (GHG) emissions projected to increase by50%, primarily due to a 70% growth in energy-related CO2 emissions [1]. Figure 1 shows the accumu-lation of greenhouse gasses and the global combined land and ocean surface temperature rise since1850.
(a) Globally averaged concentrations of carbon dioxide (CO2), methane (CH4) and nitrous oxide (N2O) determined from icecore data (dots) and from direct atmospheric measurements (lines).
(b) Globally averaged combined land and ocean surface temperature anomalies relative to the average over the period 1986 to2005. Colours indicate different data sets.
Figure 1: Observations of a changing global climate system [2]
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More use of renewable energy seems to be the most logical next step. The power system alreadymade significant changes during the last decade due to the large scale introduction of interruptiblerenewable energy sources (IRES) like wind and solar. It is expected that the power supplied from windand solar will increase further at the expense of power from thermal power plants [3]. This change in thepower system is driven by a combination of the increased attention to CO2 emissions and the decreaseof costs of IRES versus conventional plants [3]. When the stated policies are globally executed, theglobal power capacity is expected to look like figure 2. This further increase in interruptible supply fromrenewable sources will place challenges on the stability of the electricity system, with the decrease offossil-fired thermal power plants. Storage of electricity will be required in the future electricity systemsfor stability reasons.
Figure 2: The distribution of generated power is being reshaped by the rise of renewables. In 2040, renewablesaccount for nearly half of total electricity generation [3]
A potential storage option is hydrogen [4] in large scale volumes, such as salt caverns. Excess renew-able power will be used to generate hydrogen and oxygen by electrolysis from water.
The power-to-power efficiency of hydrogen as an energy storage depends on a number of parame-ters, such as power to hydrogen conversion, compression, transport, storage and hydrogen back topower conversion. A full cycle, from excess electricity to the cycles modeled in this thesis, is depictedin figure 3. The most standard way for hydrogen back to power conversion is application in a fuel cell.A state of the art solid oxide fuel cell (SOFC) transforms 65% LHV of the converted fuel’s energy intoelectricity [5]. Nowadays conversion efficiency of power to hydrogen in elektrolyzers is around 70%(ranging from 60-80%) LHV [6], the hydrogen fuelled SOFC fuel to power efficiency is 65%, making themaximum power-to-power efficiency of energy storage by hydrogen 46%, in this case transport losses,storage losses and compression power are neglected. Important improvements in this power-to-powerround trip efficiency can be achieved by increasing the efficiency of the subsystems. In this thesis thefocus will be on the improvement of the fuel (hydrogen) to power efficiency.
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Figure 3: A full cycle from excess renewable energy, to an electrolyser, storing the obtained hydrogen in a storagefacility (salt caverns) and converting this hydrogen back to power via the cycles discussed in this thesis
The utilization of both the hydrogen and the oxygen from the electrolysis, introduces the option to useboth hydrogen and oxygen as a fuel for the turbine cycles. The use of hydrogen and oxygen makespath for common hydrogen and oxygen fuelled cycle principles. Steam can be used as the workingfluid throughout the cycle, moreover the cycle can be used as a closed cycle. The advantages of thesehydrogen and oxygen fuelled cycle principles are explained in the next paragraph. These cycles, resultin electrical efficiencies over 70% LHV [7] [8] [9], while state of the art fossil fuelled CCGT (Combinedcycle gas turbine) cycles have efficiencies around 60% LHV [10]. Two of these hydrogen/oxygen cy-cles, the modified Graz cycle developed by the Graz University [7] and the Toshiba Reheat Rankinecycle [8], will be studied in this thesis and potential optimizations and improvements will be identified.
These high efficiency hydrogen/oxygen cycles have a number of common principles:
1. Cascading of thermal energy. Like in CCGT power plants, the basic input is the combustion offuel. The thermal energy is extracted in two phases: first in a high temperature turbine (HTT) atmoderate pressures, comparable to pressures in a normal gas turbine, secondly the excess heatfrom the flow at the outlet of the HTT is transferred to a steam cycle using a heat recovery steamgenerator at different steam cycle pressure levels.
2. Steam as working fluid for the cycle. In a normal CCGT cycle, air is the working fluid for theBrayton Gas Turbine cycle. In the studied hydrogen/oxygen cycles steam is the working fluidin the combustor and the HTT part of the cycle. Hydrogen and oxygen are combusted at thestoichiometric ratio resulting in pure steam as product. The combustor temperature and the inlettemperature for the HTT are controlled by the addition of steam. Because no nitrogen is present,there is no risk of NOX formation.
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3. Closed cycle. The low temperature steam at the exit of the heat recovery steam generator(HRSG) is fed into the steam cycle making it possible to extract power from the available sen-sible and latent heat in this flow. The studied hydrogen/oxygen cycles therefore do not have astack. The mass of water that is created in the combustor should be removed downstream of thecondenser.
The simplified principle flow scheme of a hydrogen-oxygen cycle is shown in figure 4.
Figure 4: Simplified process flow diagram for the hydrogen and oxygen cycles. CC: combustor, HTT: high temper-ature turbine, HRSG: heat recovery steam generator, HPT: high pressure turbine, LPT: low pressure turbine, BFP:boiler feed pump, Cond.: Condenser, Comp.: Compressor, Deaer.:Deaerator. In the Graz cycle an extra steamcompressor is added upstream of the combustor displayed in yellow. This steam compressor is not included in theToshiba Reheat Rankine cycle.
1.1 Innovations in this thesisIn this thesis the following question will be answered:
How can one improve the configuration of a hydrogen and oxygen fuelled turbine cycle, for efficiency?
To answer the question fully, the following subquestions need to be answered:
1. How can one minimize the exergy losses throughout a hydrogen and oxygen fuelled turbine cy-cle?
2. How can one describe and model the high temperature turbine blade cooling needs in the hydro-gen and oxygen fuelled turbine cycle?
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3. What is the added value of a fuel cell system integrated into a hydrogen and oxygen fuelledturbine cycle?
4. What configuration of a fuel cell system integrated into a hydrogen and oxygen fuelled turbinecycle is most efficient?
1.2 Thesis outlineThe theoretical background necessary is provided in chapter 2 in which both the thermodynamics be-hind power cycles and the physics behind the fuel cell is covered. Moreover, an analysis of existinghydrogen-oxygen cycles is made in this chapter.
The HTT cooling model is discussed in chapter 3. The physics behind CLSC and open loop cool-ing is explained. The implementation of open loop cooling into the open loop cooled models, of thisstudy, is covered. Subsequently, the implementation of hybrid cooling into the hybrid cooled models, ofthis study, is covered (hybrid cooling is a combination of film cooling and closed loop cooling used inthe Toshiba cycle [8]). The resulting hybrid cooling model and open loop cooling model are used in thesucceeding chapters.
In chapter 4, the overall model is described and the existing cycles are validated and made com-parable using an equal set of parameters. An exergy analysis is performed for both the Graz cycle [7]and the Toshiba Reheat Rankine cycle (also called Toshiba cycle) [8].
In chapter 5, a set of thermodynamic improvements are modeled and analyzed, the main objectiveis to quantify, for every upgrade, the reduction (or addition) of exergy losses through the components.The most important elements from both cycles will be included: reheat combustor, hybrid cooling in thehot section of the HTT and the compressor upstream of the combustor. The efficiency of this optimalcycle reaches 74-75% LHV, depending on the choices of the turbine inlet temperature.
The exergy analysis of this optimized cycle shows that the main exergy losses occur in the combustorpart of the cycle. The potential improvement lays in the partial replacement of the combustor with anSOFC. An SOFC fits well with these kind of cycles due to its high operating temperature and efficiency.In chapter 6, the addition of a fuel cell to the turbine cycle is modeled, to further reduce the exergylosses going through the cycle. Two different set-ups with the SOFC are studied: First a single SOFCoperating at 700 C and then a set of three SOFC in series, operating at 700 C, 850 C and 1000C respectively. In the second situation the amount of exergy loss is further reduced. Moreover, theimpact of two different operating philosophies for the cooling of the fuel cells will be discussed: in thefirst operating philosophy the fuel cell is cooled by an excess of oxygen that will be circulated over thecell, in the second approach the hydrogen and oxygen are supplied at the stoichiometric ratio and thefuel cell is cooled by steam addition to the oxygen (cathode side) flow. The electrochemical results ofthe various fuel cells are analyzed. Additionally, the fuel cell turbine cycles are exergetically analyzed.The result of the optimum fuel cell configuration in combination with the optimum thermodynamic cycleresults in an efficiency of up to 83.8% LHV.
In chapter 7, the main conclusions are drawn. Recommendations and possible future research arediscussed in chapter 8.
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2 Thermodynamic and electrochemical power cycle analysis
In this chapter, the thermodynamics behind the power cycles are explained. The Carnot cycle (themost efficient thermodynamic cycle) is explained and will act as a reference cycle for cycles discussedin this thesis. Moreover, hydrogen and oxygen fuelled cycles from literature are covered. The dif-ferences between conventional fossil fuelled and hydrogen and oxygen fuelled cycles are discussed.Additionally, the Graz and Toshiba cycle are identified to illustrate the main aspects of hydrogen-oxygenfired turbine cycles. Thereafter, the SOFC (an electrochemical apparatus) is introduced and comparedto thermodynamic power cycles. Moreover, the combination of a fuel cell and gas turbine is covered.Furthermore, the physics behind the fuel cell is explained in the final section of this chapter.
2.1 Thermodynamics of power cyclesA thermodynamic cycle consists of multiple thermodynamic processes transferring heat and work, whilevarying state variables (temperature, pressure, volume, enthalpy and entropy) and eventually returningto the systems initial state [11]. In this study, the goal is to produce power (mechanical work), for thatreason the thermodynamic cycles, used in this thesis, are called power cycles. Power is obtained in aheat engine, which converts heat into power. The hydrogen combustion converts the chemical energy,of the fuel, into heat.
For thermodynamic cycles the first law of thermodynamic applies:
∆U = Q−W (1)
Here ∆U is the change in internal energy of the system. Q is the net heat transferred to the system.W is the net work done by the system. Therefore, energy cannot be created, nor destroyed. However,energy can be transferred, from heat to work, for example.
The power produced in a cyclic process can be described by the following equation:
W =
∮p dv (2)
Therefore, the net work can be visualized in a PV (pressure and volume) diagram as the enclosed areaof the cycle [11]. The expansion of a pressurized system converts the internal energy into work, asdone in a turbine where high pressures fluids are expanded. However, compression of a fluid needsenergy. This is similar to what is done in a compressor, where fluids are pressurized. However, byadding heat to the cycle after the compression step and disposing less heat after the expansion pro-cess, net heat is added to the cycle. According to the first law of thermodynamics, net work must becreated in this case (there is no internal energy change).
To first compress a liquid at the cost of work and directly expand the fluid to obtain work has no purpose,no net work will be obtained. However, by adding heat to the cycle after the compression step and dis-posing less heat after the expansion process, net heat is added to the cycle. According to the first law ofthermodynamics (equation 1) net work must be created in this case (their is no internal energy change).
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The heat (Q) input and output can be visualized in a Ts (temperature entropy) diagram. The high-est possible theoretical exergy efficiency in a thermodynamic cycle is the Carnot efficiency. It providesan upper limit on the efficiency that any thermodynamic heat engine can achieve during the conversionof heat into work. This upper limit comes from adding heat to the cycle at the highest temperature (Th),without temperature increase (nor decrease) during the heat addition. Moreover, heat is subtractedfrom the cycle at the coldest temperature (Tc), without temperature decrease (nor increase) duringthe heat addition. The use of the 4 ideal stages can be seen in the pressure volume and tempera-ture entropy diagram in figure 5. It is not an actual (physical) thermodynamic cycle, but a theoreticallyconstructed cycle.
(a) Carnot cycle PV diagram (b) Carnot cycle Ts (temperature entropy) diagram
Figure 5: Carnot cycle diagrams with a Th of 673 Kelvin and a Tc of 293 Kelvin [12]. The heat inserted into thecycle is Qadd = Qh and heat removed from the cycle is Qre = Qc. The cycles consists of 4 theoretical stages,first (from point 1 to 2) the adiabatic compression from Tc to Th, secondly the isothermal expansion at Th (heatis added in this process), thirdly adiabatic expansion from Th to Tc and lastly isothermal compression at Tc (heatis rejected during this process). The enclosed area of the process in both the PV and Ts diagram represents theamount of work produced.
The Carnot efficiency is defined as:
ηcarnot =W
Qh=Qh −QcQh
= 1− QcQh
= 1− TcTh
(3)
In which Tc is the coldest temperature to which heat is rejected (ambient temperature) and Th the high-est temperature achieved in the cycle. Increasing the firing temperature Th and decreasing Tc will leadto an increased efficiency. For this reason, one wants to minimize Qc and maximize Qh.
The Carnot process is a theoretical process, in real life there are lots of irreversibilities that lead toentropy production such as friction, leakages and mixing. So this Carnot process can be used as aguideline and if a change in the model gives a quantitative improvement one can look for the qualitativeresemblance in the Carnot cycle.
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Real world thermodynamic cycles do not work in ideal conditions and have losses. A standard CCGTcycle (gas turbine cycle and steam cycle) scheme is depicted in 6 and the Ts diagram can be found infigure 7. This combined cycle contains both a Brayton cycle (gas turbine GT) and a Rankine (steam)cycle. The Brayton part of the cycle contains a compressor (1g-2g), a combustor (2g-3g), a high tem-perature turbine (3g-4g) and heat rejection in the stack (4g-1g). The Rankine part of the cycle containsa pump (1-2), heat addition (2-3-4-5), steam turbine (5-6) and condenser (6-1).
The cycles are coupled to each other, for this reason it is called a combined cycle. The Gas turbine cy-cle’s heat rejection (4g-1g), in the stack, is not solely to the environment (as done in a conventional Gasturbine-only cycle), but most of the heat is passed through a heat recovery steam generator (HRSG) tothe bottoming Rankine cycle. Consequently, the heat addition (2-3-4-5) is not done in a boiler (as donein Rankine-only cycle), but the heat is obtained in the HRSG from the Gas turbine cycle’s otherwisewasted heat.
Figure 6: Fossil fuelled simplified CCGT cycle scheme [13]. The Brayton part of the cycle is numbered from 1g-4gand the Rankine part of the cycle is numbered from 1-6.
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Figure 7: Standard CCGT Ts diagram, the points (numbered) correspond to the numbered components of theCCGT cycle depicted in figure 6. In green is the area depicted that can be incorporated into the cycle to increaseefficiency (to look more like the reference Carnot cycle in figure 5b). The area in red should be reduced to increaseefficiency. This is explained below.
Possible improvements to a standard CCGT cycle, to become more similar to the Carnot process andenhance efficiency are:
1. During the compression of the fluid, 1g-2g and 1-2, entropy is generated as friction occurs, thisshould be minimized. Furthermore, during the expansion process of 3g-4g and 5-6 entropy isgenerated due to friction, this also needs to be minimized.
2. The heat rejected from the gas turbine cycle is rejected from 4g-1g, this heat is used in the HRSGto heat the steam cycle from 2-5. The smaller the temperature difference between 4g to 5 and1g to 2 is, the smaller the work free gap, inbetween the cycles. A smaller gap will fit the Rankinepart to the gas turbine part better and consequently lead to a higher efficiency.
3. Temperature 2g (the combustor inlet temperature, CIT) and 3g (the turbine inlet temperature,TIT)should be maximized to increase the amount of work per unit of heat input. The increase in CITand TIT, resulting in higher thermal efficiencies, is quoted on multiple occasions in this thesis.
4. The heat loss underneath the steam cycle (condensing process 6-1) should be minimized, there-fore the temperature at point 6 and 1 should be minimized. The minimum temperature point 6 canreach is limited by the amount of condense the low pressure turbine can withstand at the chosencondenser pressure. When too much condense forms, the vapor quality is too low in point 6 andundesirable turbine blade erosion can occur.
2.2 Hydrogen fueled cyclesHydrogen-oxygen fueled cycles differ from conventional fossil fuelled cycles in multiple ways. They donot produce CO2, NOx and other harmful emissions. Moreover, the exhaust gas is water, which is theworking fluid as well. For this reason, the hydrogen CCGT cycles are closed and the GT and steampart of the cycle are more closely integrated. Creating a smaller work free gap in between the cyclesas illustrated in figure 7. Moreover having steam as a working fluid throughout the cycle makes way fornew cycle opportunities as used in the Graz cycle [7], discussed in section 2.2.2.
9
Hydrogen-oxygen cycles have first been studied during the late 1990’s. In the recent years therehas been a small revival in the study of these types of cycles. In this thesis a recent cycle, the Grazcycle [7], will be compared to the Toshiba cycle [8]. A number of other cycles have been evaluated.
The most efficient large scale hydrogen-oxygen fired cycles are CCGT cycles. The CCGT cycle ex-tracts work from multiple pressure regimes by cascading energy throughout the cycle, using the wasteheat of the Brayton part of the cycle to heat the Rankine part of the cycle. The most efficient hydrogencycles minimize waste heat (like the most efficient fossil fuelled cycles). For this reason, the CCGT cy-cles are the most efficient hydrogen cycles, since they cascades energy through all pressure regimesof the cycle.
The SOFC also has been investigated. The SOFC can either be a standalone power generator, orcan be coupled to a turbine cycle. Standalone operation cannot compete yet, with the class leading hy-drogen fired turbine cycles. However, a fuel cell in conjunction with a turbine cycle can be competitive.Therefore, the addition of a fuel cell coupled to a turbine cycle is discussed in section 2.3.1.
The Westinghouse company has developed two hydrogen-oxygen fired CCGT cycles, named theBannister-Westinghouse cycles [9], the research was led by Bannister. The cycles use reheat witha TIT of 1700 C. The most promising cycle makes use of hybrid cooling and reaches an efficiency of70.9% LHV.
The Toshiba cycle [8] is an improved Bannister-Westinghouse cycle [9]. The Toshiba cycle has broadlythe same configuration, but includes low pressure turbine condensing heat extraction, for better per-formance. Moreover, the Toshiba [8] is operated at different temperatures, pressures and mass-flowsthan the Bannister-Westinghouse cycle. The Toshiba cycle (explained in detail in the next section) isa CCGT cycle that includes multiple extra performance extraction methods: hybrid cooling, reheat (theuse of a second combustor) and low-pressure turbine condensing. All the performance enhancementslead to a remarkable high thermal efficiency of 72.9% LHV for the Toshiba cycle.
The Graz cycle [7] is a modification (explained in detail in section 2.2.2) to a standard CCGT cycle.The cycle is not enhanced with extra performance extraction methods and it operates at a relatively lowTIT of 1500 C. Nevertheless, the cycle reaches a high thermal efficiency (70.4% LHV).
The high efficiencies of these cycles with high TIT’s (1500-1700C), comes with a cost. The turbineblades can withstand metal temperatures between 750C [7](obtained from table 1 of the respectivepaper) and 788 C [8](obtained from figure 13 of the respective paper). The blades need to be kept atthe right temperature, while the main gas in the first high temperature turbine stage is (1500-1700C).Therefore, a significant amount of high temperature turbine blade cooling is needed. Cooling however,introduces complexity and losses, therefore a good turbine blade cooling solution is very important.The Graz cycle and the Toshiba cycle have been identified as cycles to illustrate the main aspects ofthe hydrogen-oxygen turbine cycles.
10
2.2.1 Toshiba cycle
The Toshiba cycle with reheat and recuperation [8] is stated as a cycle with a potential for very highthermal efficiencies (61.7% HHV, which equals 72.9% LHV) in the literature. The cycle can be consid-ered as a CCGT cycle, with steam as the working fluid for both the Rankine part and Brayton part ofthe cycle. The principle flow scheme is shown in figure 8.
Figure 8: Principle flow scheme of the Toshiba cycle [8]. The temperatures and pressures are from the Toshiba-EQ cycle, this cycle is introduced in section 4.2. The detailed flow scheme of the Toshiba-EQ cycle is depicted inappendix B.2. The part at the left of the HRSG can be considered as a modified Brayton cycle with steam as aworking fluid, the part at the right of the HRSG is a ’conventional’ Rankine cycle
The cycle uses two hydrogen–oxygen combustors for heating and reheating with a turbine inbetween.At two locations steam is generated: (1) The combustors generate high-temperature steam at moder-ate pressures (66 bar in CC-1 and 7.7 bar in CC-2) by combusting hydrogen and oxygen and (2) inthe HRSG at a high-pressure (340 bar) by boiling water. The steam generated in the combustors isexpanded in two turbines (from 66 bar to 8 bar in HTT-1 and from 7.7 bar to 1 bar in HTT-2), the excessheat is transferred to a Rankine cycle via the HRSG after which the steam flow from the combustorsis expanded in a condensing LP turbine. Heat is extracted from the LP turbine for feedwater heating.The high pressure steam flow generated in the HRSG is expanded in the HP turbine and fed into thefirst combustor. The steam flow from both the combustors and the Rankine cycle are fully integrated.The steam that is generated in the combustors has to be removed from the cycle downstream of thecondenser.
11
2.2.2 Graz cycle
The original Graz cycle is a CH4 and oxygen fuelled cycle for CO2 capture which has been developedat Graz University of Technology since 1995 [14]. This cycle is further developed to become the hydro-gen and oxygen fuelled Graz cycle [7], to be used as a reference cycle in this thesis.
The Graz cycle can be seen as a modification to a standard CCGT cycle, working with hydrogenas a fuel and pure oxygen as the oxidant, leaving steam as the combustion product and working fluidin the Brayton part of the cycle. Similar to the Toshiba cycle, the high temperature steam from thecombustor is expanded in a HTT and transfers heat to a Rankine cycle in the HRSG. The steam fromthe ‘stack’ of the HRSG is partly expanded in a condensing LP turbine and partly compressed to 41bar to be used for cooling the combustor. A principle flow scheme of the cycle is shown in figure 9. Theoverall efficiency of the Graz cycle is 70.4% LHV.
Figure 9: Principle flow scheme Graz cycle [7]
The direct compression of the steam downstream of the HRSG introduces an extra degree of freedomcompared to the Toshiba cycle to secure the correct turbine inlet temperature of the HTT. This extraoption enables a better energy balance over the HRSG and thereby a lower temperature difference inthe heat transfer (from Brayton to Rankine part of the cycle) in the HRSG, this results in lower exergylosses. This can be visualized in figure 7 from section 2.1, the red area inbetween the two cycles isreduced.
12
2.3 The solid oxide fuel cell (SOFC)The SOFC is a fuel cell (FC) with a solid oxide or ceramic electrolyte, the working principle of an SOFCis depicted in figure 10. The FC is an electrochemical cell that converts chemical energy directly intoelectricity and heat, whereas heat engines/cycles convert chemical energy into heat and then extractelectricity from this heat. Therefore, the fuel cells efficiency is not limited to the Carnot efficiency, shownin equation 3, in section 2.1.
Figure 10: SOFC working principle [15]. The illustrated SOFC is operated with air as the oxidizer.
The efficiency is however limited by the available Gibbs free energy of formation.
ηmax =∆Grxn∆Hrxn
=∆Hrxn − T ·∆Srxn
∆Hrxn(4)
∆H is the enthalpy of formation and ∆S is the entropy of formation. Contrary to heat engines themaximum obtainable electrical efficiency of electrochemical converters (fuel cells) decreases with anincreasing temperature, as can be seen in equation 4. The efficiency curve of an ideal FC, operated atatmospheric pressure, is compared with a Carnot cycle at 90C exhaust temperature in figure 11.
13
Figure 11: Ideal fuel cell operated at ambient pressure and Carnot efficiencies (using exhaust temperature of90C) as a function of temperature [16].
The reaction is driven by redox reactions as the reducer, the fuel hydrogen, flows through the anode.Oxygen, the oxygizer, flows through the cathode, ions (O2−) are formed and conducted through theelectrolyte into the anode where together with the H2, water and electrons are formed. The cathodeand anode half reactions are:
1
2O2 + 2e− −→ O2− (5)
O2− +H2 −→ H2O + 2e− (6)
Resulting in the following reaction:1
2O2 +H2 −→ H2O (7)
Thus for each mole of hydrogen 2 electrons are used. The stoichiometry is that for every mole of H2
half a mole of O2 is used. The lower the temperature the larger the theoretical maximum efficiency asequation 4 states. However, in practice the efficiencies of LT-SOFC’s (low temperature solid oxide fuelcells) and HT-SOFC’s (high temperature solid oxide fuel cells) do not differ significantly. Lower temper-ature fuel cells have higher resistances, as the resistivity of the materials used is inversely proportionalwith the temperature.
The latest spec high efficient SOFC’s are planar SOFC’s as these can reach higher power densi-ties and efficiencies than their tubular counterparts [17]. The layout of both a tubular and planar FC isillustrated in figure 12. The electrons travel a longer path in the tubular counterpart, for that reason theresistance in tubular FC’s is higher, resulting in a lower electrical efficiency. Generally, in planar SOFCsthe electrolyte is made from yttria-stabilized zirconia (YSZ), a cathode made from lanthanum strontiummanganite (LSM) and an anode consisting of nickel-YSZ (Ni-YSZ) [18].
14
Figure 12: Planar and tubular SOFC [17]
Typically an SOFC is fuelled by gas using air as the oxidizer. The anode needs pure hydrogen for itshalf reaction. For this reason, the gas needs to be reformed. This can either be done in the FC orpreliminary.
Today’s operating SOFC’s can have a working range from 550C to 1000C [17]. A state of the artSOFC transforms 65% of the converted fuel’s energy into electricity [5]. In test conditions even 74%LHV is reached for the NELHI project [19]. The remaining energy is heat, which is absorbed by thegasses passing through the FC, and because of its high temperature, this released heat can easily beused in a bottoming cycle. An FC can be placed in front of the combustor, leading to an increasedcombustor inlet temperature and thus less exergy loss in the combustor.
2.3.1 Fuel cell-turbine cycle
Fuel cells (FC’s) offer an interesting cycle improvement opportunity, to further reduce the exergy lossesin the turbine cycle as the main exergy losses take place in the combustor. (Partial) replacement ofthe combustor by an FC can lead to a further reduction in exergy losses. The most promising FC forthis application is the SOFC, having a high and broad operating temperature window. Turbine-SOFCcycles with air as a working fluid have been studied extensively and some units have been built, forexample the Siemens-Westinghouse cycle [20]. This turbine cycle is coupled to a tubular SOFC, thecycle’s priciple flow scheme is depicted in figure 13.
When an FC is directly fuelled with hydrogen and oxygen, no reforming of the fuels is required,which leads to better performance [18]. The efficiency, lifetime and power density are all higher withoutthe reforming process [18]. Another compelling reason for combining the FC with a turbine cycle isthat the driving force, the Nernst voltage, will increase with an increased pressure in the FC, as can beseen in equation 8 [18]. An increase in the Nernst voltage leads to a higher FC efficiency and a higherpower density. Additionally, the use of pure hydrogen as fuel and pure oxygen as oxidizer increasesthe driving force of a fuel cell, as can be seen in equation 8.
Enernst = E0 +RT
2Fln
(PpH2Pp
12
O2
PpH2O
)(8)
Pp indicates the partial pressure, while F indicates the Faraday constant, R indicates the gas constantand E0 indicates the potential voltage.
15
Figure 13: Principle flow scheme of the Siemens-Westinghouse cycle [20]. The cycle is fed with air and naturalgas, for this reason the cycle needs a desulphurizer and the SOFC needs to reform the natural gas. The SOFCis placed in donwstream of the compressor and upstream of the turbine (in conventional cycles this is the place ofthe combustor).
2.3.2 Fuel cell physics model
The Gibbs free energy of formation (∆G) indicates how favorable the chemical reaction is (if the reactioncan take place spontaneously) [21]. The potential voltage is calculated as follows:
E0 =∆GrxnnF
(9)
In which n equals the electrons released per mole of hydrogen which is 2 in our case.
∆Grxn,T = ∆Hrxn,T − T ·∆Srxn,T (10)
∆Grxn,T is lowered with an increasing temperature, for this reason the potential and Nernst voltage arelowered (see equation 9 and 8). Also, the FC efficiency decreases with an increasing temperature ascan be seen in figure 11. The stoichiometry of the reaction needs to be taken into account.
∆Hrxn,T = ∆Hf,H2O,T −∆Hf,H2,T −1
2∆Hf,O2,T (11)
∆Srxn,T = ∆Sf,H2O,T −∆Sf,H2,T −1
2∆Sf,O2,T (12)
In high temperature FC’s the activation overpotential can be neglected as it is really small. Further-more the concentration overpotential only becomes significant when the limiting current density is ap-proached [18]. In this study efficiency is key and the high temperature SOFC is operated far away from
16
the limiting current density. Therefore, the ohmic resistance is the only significant resistance we aredealing with. For the planar (this study) case the resistance of the anode (component 1, c=1), elec-trolyte (c=2), cathode (c=3) and interconnect (c=4) are in series and the sum of these resistances isthe total resistance.
R =
4∑c=1
ρctcAcrosssection
(13)
Icell =Enernst − E0
R(14)
CH2 = −Icell2F
(15)
CH2 is the consumption rate of H2 in mole per second.
POWcell = Ecell · Icell (16)
η =POWcell
∆Hrxn,T(17)
The FC operates at unique operating conditions (high pressure ∼40 MPa, with hydrogen and oxygenas fuel). A conventional FC layout [22] is used. The design of an FC layout, tuned to these uniqueoperating conditions, is not in the scope of this thesis. In table 1, the resistivity equations (from [23]) ofthe individual components of the FC stack are depicted.
Table 1: Geometry and resistances for the SOFC used in this thesis
Components thickness t Resistivity equations
Cathode (LSM-YSZ) 0.2 cm 8.114 ∗ 10−3e600T Ωcm
Electrolyte (YSZ) 0.004 cm 2.94 ∗ 10−3e10350T Ωcm
Anode (Ni-YSZ) 0.015 cm 2.98 ∗ 10−3e−1392T Ωcm
Interconnect (metal) 0.01 cm 100/( 9.3∗105
T · e−1100T )Ωcm
17
3 Cooling of the high temperature turbine blades
In this chapter, in section 3.1 the physics behind closed loop cooling of the high temperature turbineblades is covered. Subsequently, in section 3.2 the physics behind open loop cooling of the high tem-perature turbine blades is discussed. In subsection 3.2.1 the result of the open loop cooling is validatedwith the build in Thermoflex open loop cooling method. In section 3.3 the implementation of open loopcooling into the open loop cooled models of this study is treated. Finally, in section 3.4 the implemen-tation of hybrid cooling into the hybrid cooled models of this study is discussed. The different coolingmethods are depicted in figure 14.
The different turbine cycle configurations, covered in this study, have different cooling needs, whichis discussed in chapter 5. Additional cooling leads to more exergy losses in the cooled turbines. Thetwo cooling methods discussed in this study are very different, especially in the cooling losses induced.No new blades are designed in this study, based on existing designs and the parameters associatedwith this, the required cooling mass flows are calculated. For this reason, a good cooling model isessential for a good performance/exergy analyses of the cycles.
Open loop cooling is the conventional method to cool down HTT blades in gas turbines [24]. Openloop cooling means a liquid is delivered to the blade and passes through (convecting heat away fromthe blade in the process) and then quenches into the main stream of the cycle. Both air and steamcan be used to go through the blade. The open loop cooling method used in this thesis combinesinternal convection with film cooling. Internal convection cooling means the coolant convects the heataway via internal channels in the blade, going past cooling fins and impingements inside the blade.Subsequently, the coolant reaches the surface of the blade and reaches the film cooling holes. Thefluid exits the blade through film cooling holes to form an active fluid film layer, that acts as an activethermal barrier. An open loop cooled blade is illustrated in figure 14a.
Closed loop steam cooling (CLSC) is a cooling method in which steam passes through the bladeand is retrieved (it does not quench into the main stream of the cycle). The heat is convected awaythrough fins and impingements inside the blade. The retrieved coolant can be used somewhere elsein the cycle. The exergy losses are reduced because no steam is quenched into the main stream,however CLSC will lead to local high metal temperatures. For this reason, CLSC is not used in HTT’s.A CLSC blade is shown in figure 14b.
Hybrid cooling is a combination of both CLSC and open loop cooling. This solution combines theexergetic advantage of CLSC (less quenching of steam into the main flow), with a flat metal temper-ature throughout the blade, made possible by the film cooling holes. In this cooling method part ofthe coolant is quenched via film cooling holes into the stream, however a fraction of the coolant is notquenched and retrieved. The Original Toshiba cycle [8] uses this cooling method. A hybrid cooledblade is depicted in figure 14c.
18
(a) Open loop cooling as used in the Original Graz cycle [7].State of the art fossil fuelled CCGT cycles make use of this tech-nology, making use of air as the coolant [24].
(b) CLSC (not used as a cooling solution in this thesis)
(c) Hybrid cooling as used in the Original Toshiba cycle [8]. The hybrid cooled blade differs from the conventional open loopcooled blade, as part of the coolant is retrieved.
Figure 14: Different cooling methods
19
The heat coefficients depend on the internal blade geometries (which are unknown). The amount offilm cooling holes and impingements inside the blade are unknown. The temperatures Taw,Tw, Tbe andTbi are unknown, only Tg and Tb are known. Thus, a detailed cooling mass calculation, based on ge-ometry data, will not be possible. For that reason, empirical relations are used to calculate the amountof coolant mass needed. The amount of stages per turbine are known. Therefore, an estimation ofthe amount of cooling must be based on the thermodynamic layout (the mass streams, their respectiveenthalpies, temperatures and pressures). For that reason, the cooling mass streams and the main gasstreams are the given parameters.
The Original Toshiba cycle is a hybrid cooled cycle. Cycles designed in this thesis, that include hy-brid cooling, are modeled to have the same cooling performance as the Original Toshiba cycle. Thecooling performance parameters (tuning parameters, C1 and C2) together with the operating conditionsdictate the amount of coolant necessary to keep the turbine blades from overheating. For this reason,(tuning parameters, C1 and C2) from the Original Toshiba cycle will be clarified and retrieved in section3.4.
The Original Graz cycle is a open loop cooled cycle. Cycles designed in this thesis, that includeopen loop cooling, are modeled to have the same cooling performance as the Original Graz cycle.The cooling performance parameters (tuning parameter, Ctune) together with the operating conditionsdictate the amount of coolant necessary to keep the turbine blades from overheating. For this reason,(tuning parameter, Ctune) from the Original Graz cycle will be clarified and retrieved in section3.3. Theparameters used to tune the cooling methods and their resulting tuning parameters are depicted intable 2.
Table 2: Cooling parameters used for modeling hybrid and open loop cooled high temperature turbine blades
hybrid cooling open loop coolingReference cycle for obtaining tuningparameter
Replicated Graz cycle values Replicated Toshiba cycle values
Physics used a combination of CLSC andopen loop cooling
open loop cooling
Bulk blade temperature 787.85 C from figure 13 [8] 750C from table 1 [7]Enthalpy increase coolant CLSC ** 342 KJ/Kg there is no CLSC (part) usedNumber of blade rows in HTT-1 5 2Number of blade rows in HTT-2 4 4Number of blade rows in HTT-3 non existent 2Calculated tuning parameter(s)(Cooling performance parameters)
C1=0.0021, C2=0.0026 Ctune=0.0183
Cycles modeled with this methodand the corresponding tuning pa-rameter(s)
Toshiba-EQ, Graz-HC,U-Graz, U-Graz-1500C,U-Graz-3FC-OX
Graz-EQ, Graz-1700C, Graz-HEX, Graz-2CC, Graz-1FC-OX,Graz-3FC-OX, Graz-1FC-Steam, Graz-1FC-Steam
* Temperatures, mass flows and specific heats of the coolant individual streams can be retrieved from the principleflow schemes [7] and [8].** The enthalpy rise equals the enthalpy of the CLSC coolant going out of the turbine blades minus the enthalpyof the CLSC coolant going into the blades.
20
3.1 Closed loop steam cooling (CLSC) physicsIn this section the physics behind closed loop steam cooling is derived. CLSC is implemented as partof the hybrid cooling method used in this thesis. The heat resistance scheme through the CLSC andTBC coated blade is depicted in figure 15.
Figure 15: Temperature profile across a CLSC high temperature turbine blade with a TBC
CLSC is a closed cycle, thus the cooling steam will not enter the main flow contrary to open loop cool-ing. This is beneficial from an exergetic point of view, as the steam is not quenched into the cycle thusless losses occur. However, closed loop cooling will lead to certain hot points in the system, where filmcooling can lead to a flat metal temperature profile throughout the blade. Moreover, film cooling is moreeffective (in bringing the turbine blade temperature down) per kg of coolant used.
Rtotal =1
hg+LTBCkTBC
+Lbkb
+1
hc(18)
The heat resistance scheme is solved in the next section, the following equation is the result:
mc =1
BiTBC + 1mg
CpgCpc
· St · AgAw· Tg − TbTce − Tci
(19)
In which mc equals the coolant going through one turbine stage, mg equals the main gas mass flowgoing through the turbine stage. A turbine stage consist of one rotor row and one stator row. Aw is thearea available for the main gas to flow through the blade wall. Ag is the surface area of the hot gas sideon the blade.
21
3.1.1 Mathematical derivation closed loop steam cooling
The heat transfer is in steady state. Therefore, the heat flux is constant across the thickness of theblade. The heat flux through all parts of the blade is given in equation 20 and 21.
q = hg(Tg − Tw) =Tw − Tb,ex
tTBCkTBCAg
=Tb,ex − Tb,in
tbkbAg
= mc(hci − hce) (20)
Q
Ag= q =
Tg − TcRtotal
(21)
The heat convected from the hot gas to the blade outer wall equals the heat conducted through theTBC coating. This heat equals the heat conducted through the metal blade, which in turn equals theheat that is removed by the coolant.
An approximation is made in equation 23 as Tb,ex ≈ Tb,in. The metal blade conducts heat very well, forthis reason there is very little temperature variation through the blade. The bulk temperature (Tb) willbe very close to both the external blade and internal blade temperature, thus the following is assumedTb,ex ≈ Tb.
Q = hgAg(Tg − Tw) (22)
Q =kTBCtTBC
Ag(Tw − Tb,ex) ≈ kTBCtTBC
Ag(Tw − Tb) (23)
Q =kbtbAg(Tb,ex − Tb,in) (24)
Q = mc(hci − hce) ≈ mcCpc(Tci − Tce) (25)
The standard approach to calculate the cooling needs from these governing equations is from [25].This approach does not contain a TBC coating. Therefore, the approach is adjusted later on in thisstudy, to fit a turbine with TBC coating. The heat resistance scheme of a CLSC blade without a TBCis depicted in figure 16. The external metal blade is now in contact with the hot gas, thus the externalmetal blade is the wall. Therefore, Tw is used for this approach. Equation 22, 24 and 25 still hold forthe uncoated blade.
22
Figure 16: Temperature profile across CLSC turbine blade(without TBC coating)
Stg =hg
ρg · vg · Cpg(26)
The Stanton number (St) is a dimensionless number that measures the ratio of heat transferred into afluid to the thermal capacity of the fluid, where vg is the main gas velocity.
The total heat flow (Q) equation 27 can be found by combining equation 26 and 22:
Q = Stg · ρg · vg · Cpg ·Ag(Tg − Tw) (27)
mg = ρg · vg ·Aw (28)
Q = Stg · mgAgAw· Cpg ·Ag(Tg − Tw) (29)
Combining equation 29 with equation 25 gives:
mc
mg=CpgCpc
· Stg ·AgAw· Tg − TwTce − Tci
(30)
This is the final result in the Masi [25] approach. This equation is the basic CLSC function in Thermoflex[26]. However, for our case, which includes a TBC coating, the wall temperature is not equal to the metal
23
blade temperature, as one can see in figure 15. The metal blade temperature Tb is known and the TBCoutside temperature Tw is not. Therefore, one prefers a solution where Tb is a variable.To achieve this, equation 22 and 23 are combined to:
BiTBC =hgtTBCkTBC
≈ Tw − TbTg − Tw
(31)
The Biot number of the TBC coating (BiTBC) displays the ratio between the transport by flow (convec-tion) outside the TBC coating and the conduction of heat within the TBC coating.
The wall temperature (Tw) is eliminated out of the governing equation using the following algebraictrick:
Tg − TwTce − Tci
·(Tw − TbTg − Tw
+ 1
)=
Tg − TwTce − Tci
·(Tw − TbTg − Tw
+Tg − TwTg − Tw
)=
Tg − TbTce − Tci
(32)
Tg − TwTce − Tci
· (BiTBC + 1) =Tg − TbTce − Tci
(33)
Tg − TwTce − Tci
=1
BiTBC + 1
Tg − TbTce − Tci
(34)
Therefore, equation 30, for a CLSC blade with a TBC coating included, can be written as:
mc =1
BiTBC + 1mg
CpgCpc
· St · AgAw· Tg − TbTce − Tci
(35)
24
3.2 Open loop cooling physicsIn this section the physics behind open loop cooling is derived. Open loop cooling is implemented aspart of the hybrid cooling method and as a standalone open loop cooling solution. Open loop coolingis a combination of film, impingement and convection cooling. For the open loop case the heat networkdepicted in figure 17 is used. Equation 36 and 37 govern the heat network.
Figure 17: Temperature profile across open loop cooled and TBC coated turbine blade
The resistance scheme is:
Rtotal =1
hg+
1
hfilm+LTBCkTBC
+Lbkb
+1
hc(36)
Q =Tg − TcRtotal
= hg(Tg − Taw) = hfilm(Taw − Tw) =Tw − Tb,ex
LTBCkTBCA
=Tb,ex − Tb,in
LbkbA
= hc(Tb,in − Tc) (37)
The derivation done by [27] and better explained in [24] is done for a blade without a TBC coating. Forthat reason, the mathematical derivation of the system is done as if there is no TBC coating at first.
For the open loop case without TBC coating, the heat network depicted in figure 18 is used whereequation 38 and 39 govern the heat network. Leading to the following resistance scheme and heatnetwork:
25
Figure 18: Temperature profile across film cooled and TBC coated turbine blade
Rtotal =1
hg+
1
hfilm+Lbkb
+1
hc(38)
Q =Tg − TcRtotal
= hg(Tg − Taw) = hfilm(Taw − Tb,ex) =Tb,ex − Tb,in
LbkbA
= hc(Tb,in − Tc) (39)
The heat resistance scheme of the open loop cooled blade without TBC is solved in appendix subsec-tion A (Derivation open loop cooling), equation 40 is the result.
mc = mgStgCpgCpc
AgAw
ε
1− ε(40)
ε =Tg − TbTg − Tci
(41)
For an open loop cooled turbine blade with TBC coating the result is:
mc = mg1
1 +BiTBCStg
CpgCpc
AgAw
ε
1− ε(42)
This equation will be used for calculating the coolant flow in the open loop cooled cycles. The param-eters are tuned to correspond to cooling solution used in the original Graz cycle. The tuning is done insubsection 3.3.
26
3.2.1 Validation of open loop cooling method, with Thermoflex method
In this section the open loop cooling physics result is compared to the Masi [25] approach (the methodused in the Thermoflex program [26]). The calculated result is very similar to an empirically foundequation by Masi [25]. In his study, Masi researched the significance of all the influencing parametersand came to the following equation:
mc = mgCpgCpc
ARC · CF(
ε
1− ε
)n(43)
For pure film cooling n=0.9, for pure convection cooling n=1.25. Pure film cooling is not achievableand there will always be a fraction of convection. Therefore, n is often assumed to be 1 for film cooledblades [24]. CF is the cooling correction factor and equals 1
1+BiTBC. ARC is the tuning parameter (area
ratio coefficient), this parameter can be tuned to fit the cooling performance. When this equation iscompared to equation 42, using n=1, it is exactly the same with:
ARC = StgAgAw
(44)
3.3 Open loop cooling implementation into the models of this thesisOpen loop cooling is used in a number of cycles modeled in the subsequent chapters. In this section,the tuning process is covered as the open loop cooling method is tuned to the open loop cooling usedin the original Graz cycle [7]. Furthermore, the interaction between the stage by stage cooling model(Thermoflex) and the cooling script (MATLAB) is covered.
The blade temperature that the Graz cycle’s cooling method can withstand is 750C. The tempera-ture of the coolant, the main gas stream mass and the specific heat of the streams are known percycle, leaving the Biot number and Stanton number as unknowns. The Biot and Stanton number canbe assumed constant throughout (all stages of) the turbine [24]. In this study, the same cooling perfor-mance for every turbine is assumed. Therefore, the Biot and Stanton number, are assumed constantthrough all turbine stages also in between the different turbines.
Ctune =1
1 +BiTBCStg ·
AgAw
(45)
The total coolant mass flow Mc for the original Graz cycle is given. Mc is the summation of all the bladerows (of all turbines) their mc, as depicted in figure 19. Therefore, Ctune (the cooling performanceparameter) can be retrieved in an iterative manner, as the Biot number, Stanton number and the Ag
Aware assumed constant through all blade rows of all cycles using this cooling method.
27
Figure 19: Simplified general open loop cooling, stage by stage cooling scheme. A detailed Thermoflex stage bystage cooling scheme is plotted in appendix B.3.1. Mc is the summation of all the blade rows (of all turbines) theirmc. The individual stages have different temperatures and pressures leading to different individual cooling needsof mc per stage, the needs are calculated in a MATLAB script using the tuned open loop cooling parameter.
An estimation of the coolant going into every blade row is made. The corresponding temperatures, spe-cific heats and main gas flows can then be retrieved from the Thermoflex stage by stage cooling model.Ctune is tuned until its calculated Mc matches the Mc from the original cycle. The individual blade rowscalculated mc will be different from the initial estimation of mc through every blade row. Therefore,the newly calculated mc will act as the begin value of the new loop. These values are looped untilmc is within 0.5% of the previous iterations mc. The corresponding Ctune is used in all other cycles tocalculate their coolant needs. In a nutshell, the tuning parameter is calculated as illustrated in figure 20.
This tuning parameter (combined Biot and Stanton number for film cooling) can be used to calculatethe cooling needs of all designed open loop cooled cycles, using equation 46.
mc = mgCtuneCpgCpc
ε
1− ε(46)
28
Figure 20: Retrieving the cooling Tuning parameter
3.4 Hybrid cooling implementation into the models of this thesisHybrid cooling is used in a number of cycles that are modeled in the subsequent chapters. In this sec-tion, the tuning process is covered as the hybrid cooling method is tuned to the hybrid cooling solutionused in the original Toshiba cycle [8]. Furthermore, the results from the physical derivation of openloop cooled blade and the physical derivation of CLSC blade are assimilated into an approach to modela hybrid cooled blade (a partially CLSC and open loop cooled blade).
In the Toshiba cycle a combination of open loop and closed loop cooling is used. Closed loop coolingis beneficial as the steam is not quenched into the cycle and the film cooling (an open loop coolingmethod) will make sure a flat temperature profile is reached throughout the blade. For this reason, acombination of both is used where a fraction x (in the Original Toshiba cycle this part is 2
3 ) of the coolingsteam used is recovered (CLSC). The remaining 1-x part (in the original Toshiba cycle this fraction is13 ) of the used cooling steam used is discharged to the main stream through film cooling holes, so thispart is open loop cooled.
As there are no equations for the combination of cooling, a combination of both equations is used.So the cooling needs for a hybrid cooled stage are calculated as if a part of the blade is solely filmcooled and the rest is solely CLSC. In real life the full hybrid cooled blade is both CLSC and open loopcooled and there is interaction between the CLSC and open loop cooling. In real life a hybrid blade willhave a thinner active film layer then a purely film cooled blade. A hybrid cooled blade is depicted infigure 14c.
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To be able to model a hybrid cooled blade the CLSC part and open loop cooled part are separated. Itis assumed and modeled as if part of the blade is solely CLSC and the other part is solely open loopcooled. The parts of the blade do not influence each other. This assumption can be visualized in figure21. The open loop cooled part has all the film cooling holes and will have an active film layer, while theCLSC part will not have a film layer.
Figure 21: Modeling assumption visualized for hybrid cooling. The separation of the CLSC and open loop coolingpart is a simplification, to be able to model the closed loop coolant mass flow and film cooled mass flow, goingthrough, separately. In real life the blade will be CLSC and open loop cooled throughout the whole blade.
Aext,blade = Aext,film +Aext,clsc (47)
The fraction of the blade that is CLSC is called FOBclsc.
FOBclsc =Aext,clscAext,blade
(48)
FOBfilm =Aext,filmAext,blade
(49)
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Equation 19 still holds for a fully CLSC blade, however for a partially CLSC blade the introduced pa-rameter FOBclsc is added to the equation:
mc,clsc =1
BiTBC + 1mg
CpgCpc
· Stclsc ·AgAw· Tg − TbTce − Tci
· FOBclsc (50)
The tuning parameter to calculate the cooling needs of the CLSC part of the blade becomes:
C1 = Stclsc ·AgAw· FOBclsc ·
1
BiTBC + 1=mc,clsc
mg
CpcCpg
Tce − TciTg − Tb
(51)
The open loop cooled part of the blade is done in the same manner.
mc,film = FOBfilm · mg1
1 +BiTBCStfilm
CpgCpc
AgAw
ε
1− ε(52)
C2 = FOBfilm · Stfilm ·AgAw
1
BiTBC + 1=mc,film
mg
CpcCpg
1− εε
(53)
Using the Toshiba cycles parameter with a blade temperature of 787.85 C [8] (figure 13 in the arti-cle). The tuning parameters C1 and C2 can be retrieved using equation 51 and 53, making use of thetemperatures, mass flows and specific heats of the Original Toshiba cycle. This is done in the sameiterative manner as the open loop only cooling tuning parameter (Ctune) is retrieved. For hybrid coolingthis is solved simultaneously for both tuning parameters, as both Mc,clsc and Mc,film are given for theOriginal Toshiba cycle. The cooling parameters (C1 and C2) are retrieved as illustrated in figure 20 fromsection 3.3.
With the obtained hybrid cooling tuning parameters, the coolant going into one hybrid cooled HTTstage can be retrieved using equation 54.
mc
mg=mc,clsc
mg+mc,film
mg=CpgCpc
· C1 ·Tg − TwTce − Tci
+CpgCpc
· C2 ·CpgCpc
ε
1− ε(54)
The temperature/enthalpy increase of the steam in the closed loop cooling is limited by the thermalstresses. Therefore, the 342 kJ/kg enthalpy increase is used for all closed loop cooling cases (thecoolant enthalpy retrieved is 342 kJ/kg higher than the enthalpy of the coolant going in). A simplifiedgeneral hybrid cooling, stage by stage cooling scheme is depicted in figure 22.
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Figure 22: Simplified general hybrid cooling, stage by stage cooling scheme. A detailed Thermoflex stage by stagecooling scheme is plotted in appendix C.5.1. Mc,clsc is the summation of all the blade rows (of all turbines) theirmc,clsc. The total film coolant mass Mc,film is the summation of all the blade rows (of all turbines) their mc,film.The individual stages have different temperatures and pressures leading to different individual cooling needs ofmc per stage, the needs are calculated in a MATLAB script using the tuned open loop cooling parameter, a scriptusing hybrid cooling is depicted in appendix D.1.
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4 Analysis of the Toshiba-Reheat-Rankine cycle and the Graz cy-cle
In order to find the optimal hydrogen-oxygen cycle, the Graz and Toshiba cycles are reproduced (withThermoflex modelling software [26]) and validated to their original counterparts. The way the coolingmodel is integrated into the main model is described. Furthermore, the way the exergy analysis is madeis covered. After the exergy analysis is explained, the main performance parameters of the Graz andToshiba cycle are set to identical values and an exergy analysis is performed between the two cycles,resulting in the Graz-EQ and Toshiba-EQ cycle.
4.1 Comparison of the Graz and Toshiba cyclesTo exactly rebuild the same cycle, all thermodynamic properties (mass flow, pressure, temperatureand composition) must be known for validation. Furthermore, the component parameters (heat loss,pressure loss, efficiency, etc.) are required. There are some limitations in the available data from theliterature as not all specifics are given in the papers, e.g. sometimes the turbine efficiency is given, butnot the type of turbine efficiency (isentropic, polytropic, dry step).
The parameters used to build the cycles are depicted in table 3. The pressures and pressure lossesoff all streams and components throughout the system are depicted in the original flow diagrams in [7]and [8].
Table 3: Component efficiencies and important parameters used in the thermodynamic simulation of the replicatedToshiba and replicated Graz cycles
Replicated Toshibacycle values *
Replicated Grazcycle values *
Turbine inlet temperature 1700C 1500 CFuel and oxygen supply temperature 15 C 15 CAmbient temperature 15 C 15 CProperty calculations IF-97 Formulation IF-97 FormulationExcess oxygen 0% 0%HPT inlet pressure 340 bar 170.4 barHTT inlet pressure 66 bar 40 barCondenser pressure 0.05 bar 0.025 barTurbine isentropic efficiency 93% HTT 92% ,HPT,LPT: 90%Compressor isentropic efficiency ** 88%Pump isentropic efficiency 70% 70%Combustor heat loss as % 0.3% 0.25%Cooling flow as % of mass-stream after CC-1
32.4% 21.8%
Oxygen available and pressurized for free freeHydrogen pressurized for free free
* For detailed cycle parameters the original detailed flow diagrams can be seen in [7] and [8].** No such component in the cycle.
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With the available information the cycles are recreated using the Thermoflex [26] software and validatedwith all the given performance parameters from table 4 and table 5. The replicated cycles representtheir original counterparts very well. All main parameters of both cycles are within 1.1% of the literaturevalues. The resulting efficiencies are within 0.2% of the literature values.
Table 4: Validation of the Toshiba Reheat Rankine cycle versus data from literature [8]
Original Toshibacycle values
Replicated Toshibacycle values Percentage off
Hydrogen Input 5.7 kg/s 5.685 kg/s -0.3%HPT Power 52.5 MW 52.2 MW -0.5%HTT-1 Power 183.8 MW 185.9 MW +1.1%HTT-2 Power 204.7 MW 206.7 MW +1.0%LPT Power 59 MW 59.2 MW +0.3%Gross output power 500 MW 498.3 MW -0.3%Gross thermal η 61.7 % HHV 61.8% HHV +0.1%
Table 5: Validation of the Graz cycle versus data from literature [7]
Original Grazcycle values
Replicated Grazcycle values Percentage off
Power HTT turbine 231.8 MW 233 MW +0.5%Total Turbine Power 284 MW 285.2 MW +0.4%Compression Power 72.7 MW 73.2 MW +0.7%Thermal η 70.4% LHV 70.6% LHV +0.2%
4.2 Making the cycles comparableThe main parameters from both the Graz cycle and the Toshiba cycle are made comparable to facili-tate the analysis of both cycles. The most relevant changes from a thermodynamic point of view aredepicted in table 6.
Only the thermodynamic properties of the cycles are of interest in this research. The new equal-ized cycles are called the Graz-EQ (equal parameters) cycle and Toshiba-EQ cycle.
All cycles designed in this study (except the replicated original cycles) are made in accordance withthe rule-set of table 6.
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Table 6: Equal comparison rule-set
Components ValueCycles conform rule-set All cycles modelled except the Replicated Graz cycle and
the Replicated Toshiba cycle.Ambient temperature and pressure 15 C, 1.01324 barLHV hydrogen 120.0 kJ
kg
Chemical exergy hydrogen 116.4 kJkg
Chemical exergy oxygen 0.25 kJkg
Chemical exergy water 0.07 kJkg
Property calculations IF-97 Formulation, to get entropy and enthalpy for mechan-ical exergy calculation
Fuel and oxygen supply tempera-ture
15 C
Excess oxygen used in CC 0%Turbine (uncooled) isentropic effi-ciency
HPT,LPT: 90%,HTT:92%
Pump and compressor efficiency 70%, 88%HRSG or HEX minimum tempera-ture difference
Superheater = 15K, Other heat exchange equipment = 5K
Heat exchanger heat loss 0Oxygen and Hydrogen Freely available and pressurizedCondenser subcooling 2KCondenser pressure 0.025 barDeaerator and condenser pressurelosses
0
Combustor pressure loss ∆PP =0.0425
Combustor Heat loss QCC,loss =0.25% of the fuels energy burned in this combus-tor (LHV)
Coolant mass-flow HTT blade cooling is altered as described in the chap-ter:’Cooling of the cycles’. The closed-loop cooling pres-sure loss is ∆P
P =0.0606Other components pressure ratio’sand losses
Are kept the same as their original cycle counterpart, ex-cept for*
Mechanical losses DC-AC con-verter and generator losses
Are not considered. As the thermal efficiency is of interestin this study
Single FC pressure loss ∆PP =0.02
Single FC Heat loss 2% of the heat converted in this FC (LHV)* In the original Toshiba cycle a stream gains pressure in the HRSG this is deemed unlikely. Therefore, in the
Toshiba-EQ cycle, the HTT-2 turbine expands to 1.1 bar (instead of the 1 bar in the original Toshiba cycle).Upstream of the LPT the pressure is 1.05 bar (instead of the original 1.3 bar) meaning a 5% HRSG hot-side
pressure drop.
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4.3 Path through the different models
Figure 23: Path through the different models* If an FC is included in the model
Using the cooling parameters (C1 C2 and Ctune), obtained in chapter 3, the cooling needs can becalculated and the different models can be modeled as done in figure 23. The main model simulatesthe cooling going into each turbine. A stage by stage modelling approach in the main model made themodel too complex and buggy. For this reason, the main model models full turbines (not the stages inthe turbines). Therefore, two separate Thermoflex models are used: the Main model and the Stage bystage cooling model.
4.4 Exergy analysis methodExergy is the combination of the first and second law of thermodynamics and is defined as the maxi-mum amount of work-potential a material or an energy stream contains, in relation to the surroundingenvironment. More loosely it is defined as the quality of different forms of energy in relation to a givenenvironment. The loss of exergy generally provides an applicable quantitative measure of process in-efficiency. Therefore, analyzing a cycle exergetically indicates the total plant irreversibility distributionamong its components, identifying the components contributing most to overall plant inefficiency. Thetotal exergy a stream contains is the combination of the mechanical and chemical exergy a stream
36
contains. The chemical exergy of the used substances is stated in table 6.
em = (h− h0)− T0(s− s0) (55)
e = em + ech (56)
The value of e expresses the ability of the maximum work the working fluid (water/steam/hydrogen/oxy-gen) holds, until the external environmental state is reached. This is based on the second law ofthermodynamics.
The available energy a subsystem generates (Wgenerated) or is inserted in the subsystem (-Wgenerated)is calculated in Thermoflex, moreover the streams (stream properties) are known. For this reason, thelost exergy (Exlost) per component can be calculated using equation 57.
Exlost = m(∆ein −∆eout) +Wgenerated = ∆Exin −∆Exout +Wgenerated (57)
The enthalpy h is obtained from the Thermoflex model (Thermoflex is set to use IF97 steam tables).The entropy s cannot be retrieved directly from Thermoflex. The temperature, pressure and enthalpyis known for each stream in Thermoflex, inserting these in the fluid prop (which also uses IF97 steamtables) calculator the entropy is retrieved. The IF 97 steam tables contain steam/water data, there isno database for hydrogen and oxygen, thus for the hydrogen and oxygen flows the entropy is obtainedfrom the NIST (National Institute of standards and technology) web application [28].
To go through a whole cycle, the exergy losses of all components and stream mixers are combinedto a total exergy loss. The percentage loss of a system, is the exergy loss divided by the exergy sup-plied to the cycle. The supply of exergy per kg of fuel used, differs from cycle to cycle as the suppliedpressure of the fuels differ. Cycles that have 2 combustors have 2 supplies of fuel at different pressures.
The fuel energy supply of all cycles is the same. The hydrogen LHV is a given and is independentof the pressure. The statement stated earlier, the hydrogen is pressurized for free, is only relevant forthe energy calculation. The exergy calculation takes the supplied pressure of the fuels into account.
4.5 Exergy analysis equalized (EQ) cyclesWith the data set formulated in the previous section, the cycles are adjusted and can now be compared.The performance per component of the EQ-cycles is depicted in table 7. The performance of Toshiba-EQ cycle (fired at a TIT of 1500C) is lower compared to the original Toshiba cycle, due to the originalcycle’s higher TIT of 1700 C. The principle Toshibe-EQ cycle scheme shown is illustrated in section2.2.1 in figure 8. The difference between the Graz-EQ cycle and the replicated Graz cycle efficiency isless than 0.2%.
37
Figure 24: Principle flow scheme of the Graz-EQ cycle. The detailed flow scheme of the Graz-EQ cycle is depictedin appendix B.1.
Table 7: Exergy analysis equalized cycles
Exergy losses Toshiba-EQ (TIT=1500C) Graz-EQCombustor 1 14.52% *23.18% 21.27%Combustor 2 6.85% *18.33% **HRSG 4.63% 1.93%Turbines 3.33% 5.49%HTT’s 1.56% 3.92%HPT 0.29% 0.33%LPT 1.48% 1.24%Compressors ** 1.17%Pumps 0.20% 0.11%Condenser 0.96% 0.97%Deaerator 0.27% 0.48%Drainage 0.52% 0.52%mixing 0% 0.11%Exergy η 68.74% 68.06%Thermal ηLHV 70.98% 70.43%Principle flow scheme in figure 8 section 2.2.1 figure 24 this section
* Relative combustor loss (loss if it was the only combustor)** No such component in the cycle
38
The exergy losses in the different components of the cycle are calculated and compared. Both theindividual performance of the components and the main cycle performance can be analyzed this way.From table 7, with the comparison of both cycles with identical main parameters, one can observe thefollowing advantages:
Advantages of the Graz cycle:• The Graz-EQ cycle HRSG exergy losses are significantly lower because of the small temperaturedifference in the HRSG (the heated steam downstream of the HRSG temperature is only 15C lowerthan the exhaust HTT steam). The main reason is the direct compression of the steam downstreamof the HRSG. This opens the options to optimize the mass flow over the HRSG. Additionally, in theToshiba-EQ cycle the temperature differences in the HRSG are higher due to the higher exit tempera-ture of the second High Temperature Turbine.• The cycle combustor losses are the lowest (Toshiba’s combined CC losses are 21.37%). The temper-ature of the entry steam in the first combustor is higher in the Graz cycle. The rise in entry temperaturefor the combustion chamber reduces the combustor exergy losses [11].• The cycle works at lower pressure ratios. Both the HPT and HTT have a lower entry pressure, reduc-ing the amount of turbine stages and thus reducing complexity and costs.
Advantages of the Toshiba Rankine Reheat cycle (1500C) :• Overall cycle efficiency is slightly higher than the Graz cycle.• The relative exergy loss in the second combustor is very low (taking the fuel amount going in rela-tively), mainly due to the higher entry temperature.• The deaerator losses are very low due to extraction of the heat from the LPT to preheat the conden-sate with a preheating HEX network.• HTT exergy losses are lower as hybrid cooling of the turbine blades reduces cooling losses.• Pressurization is only done in the water phase (pumping water instead of compressing steam) leadingto lower overall pump and compressor losses.
The main advantages of the Graz EQ cycle are due to the extra degree of freedom by feeding the com-bustor with both steam from the HP turbine and the compression of the exhaust low pressure steam ofthe HRSG. In the Toshiba EQ cycle a larger part of the steam is condensated and has to be evaporatedin the HRSG in order to function as cooling steam for the combustor.
The cycle efficiencies of the Toshiba-EQ cycle and Graz-EQ cycle are within 0.6% of each other. Thestrong points from the Toshiba-EQ cycle are: a second combustor, closed loop cooling in the HTTand extraction of heat from the LPT to preheat the condensate. These additions increase the cycleefficiency by more than 0.6%, this is confirmed in the next chapter (chapter 6) as the U-Graz-1500Ccycle is 3.2% more efficient than the (basic) Graz cycle. The inherent advantage of the Graz cycle isthe inclusion of the steam compressor. Therefore, the Graz-EQ cycle is used as basis for the optimumhydrogen/oxygen cycle and is extended with a second combustor, hybrid cooling of the HTT and ex-traction of heat from the LPT to preheat the condensate.
39
5 Improvements to the Graz cycle
In this chapter, the improvements proposed in the previous chapter (hybrid cooling, the inclusion of asecond combustor, condensate preheating and increased turbine inlet temperature) are implementedinto the Graz cycle. Furthermore, all improvements together will be implemented as the U-Graz (up-graded Graz cycle), the cycle is depicted in figure 25. The resulting cycles will be analyzed based onexergy. Additionally, the temperature entropy diagrams of the cycles are plotted to compare the cyclesfrom another angle.
Figure 25: Principle flow scheme U-Graz cycle, a detailed flow scheme is depicted in appendix B.8. The flowscheme differs from the Graz and Graz-EQ cycle configuration, as depicted in figure 24, due to the following cycleadjustments. A second combustor (depicted as CC-2) is included. Hybrid cooling is used, now part of the HTTcoolant is retrieved and is send into the first combustor (CC-1). Condensate preheating is applied, thus multiplestreams are extracted from the low pressure turbine (LPT) to enter the heat exchangers (HEX). The turbine inlettemperature is increased from 1500C to 1700C (the stream between the combustor and HTT).
5.1 Individual cycle improvementsHybrid cooling (Graz-HC): Hybrid cooling is a combination of film cooling and closed loop coolingused in the Toshiba cycle [8]. Hybrid cooling will lead to a reduction in turbine exergy losses as lesscooling steam is quenched into the turbine main gas flow. The steam that is used in the closed loopcooling is fed back into the combustor. This results in a higher average steam inlet temperature enteringthe combustor. Due to the higher combustor inlet temperature and the fixed turbine inlet temperature,the increase of steam inlet temperature leads to a reduction of exergy losses. Closed loop coolingalone will lead to local hot-points in the metal. To enable the right metal temperatures throughout theblade, the closed loop cooling is combined with film cooling, this combination is called hybrid cooling.
40
Reheat (Graz 2-CC): The addition of a second combustor will decrease the relative combustor exergydestruction further. The steam entering the second combustor will be hotter than with a single com-bustor, leading to an overall higher average steam inlet temperature, resulting in lower exergy losses.The turbine loss is increased due to the addition of a second HTT as more cooling steam is requiredin the HTT turbines. The flue gas (steam) at the exit of the second HTT is hotter than in the referencecase (the Graz cycle) leading to more heat transfer in the HRSG, but also to a higher temperaturedifference in the HRSG, therefore higher exergy losses. However, the reduction in combustor exergyloss is greater than the the increase in HRSG exergy loss. Furthermore, the increase of heat transferin the HRSG reduces the amount of steam to be compressed for the combustor.
Condensate preheating (Graz-HEX): The bottoming cycle (Rankine part of the cycle) of the Toshibacycle is copied completely. Steam extracted from the LPT is used to preheat the condensate beforedeaerator entry. This results in a smaller temperature difference over the deaerator, therefore the ex-ergy loss is reduced.
Increasing the TIT (Graz-1700C): Increasing the turbine inlet temperature to 1700C improves theCarnot efficiency of the cycle. It will reduce the combustor exergy losses. The higher turbine inlettemperature will require increased cooling in the HTT, therefore the HTT exergy loss is increased.
Upgraded Graz cycle (U-Graz): All these upgrades together make the U-Graz cycle. The resultsof all these upgrades on the exergy losses are shown in table 8. As can be seen in table 8 the rise inefficiency of all the upgrades together (4.4%) is larger than the rises in efficiency from all the individualupgrades added up. The main contributions in the reduction of exergy losses are from the hybrid cool-ing and the increase of the TIT. The changes in the exergy losses for the combustor, HTT and HRSGdominate the differences between the other options. The main exergy losses in the U-Graz cycle arestill in the combustor (17.7% of the total loss of 27.6%). The U-Graz cycle principle flow scheme canbe seen in figure 25.
41
Table 8: Exergy analysis of improved Graz cycles.
Exergylosses in %
GrazEQ
Graz-1700C
Graz-HEX
Graz-2-CC
Graz-HC
U-Graz-1500 C U-Graz
CC 1 21.27 19.67 21.24 12.73* 20.85 21.12 14.51
* 20.3412.87* 18.42
CC 2 ** ** ** 6.57* 16.88 ** 4.96
* 17.324.85* 16.09
HRSG 1.93 1.88 1.94 2.45 1.81 2.86 3.40HTT 3.92 4.71 3.94 5.08 2.07 2.35 2.57HPT 0.33 0.36 0.33 0.46 0.27 0.29 0.27LPT 1.24 1.31 1.32 1.45 1.35 1.40 1.36Compressors 1.17 1.02 1.17 0.87 0.88 0.61 0.44Pumps 0.11 0.11 0.11 0.12 0.10 0.10 0.10Condenser 0.97 0.95 0.96 0.98 0.92 0.90 0.88Dearator 0.48 0.47 0.23 0.50 0.45 0.21 0.20Drainage 0.52 0.52 0.52 0.52 0.52 0.52 0.52Mixing 0.11 0.04 0.11 0.00 0.12 0.05 0.10Exergy efficiency 68.06 69.01 68.24 68.27 70.50 71.24 72.44Efficiency LHV 70.43 71.47 70.60 70.43 72.96 73.63 74.86Principle flowscheme in figure 24 figure 24
*** none none none figure 25*** figure 25
* Relative combustor loss(loss if it was the only combustor)** There is no second combustor
***Only the flow scheme fits the cycle. The displayed pressures and temperatures in the figure do not belong tothis cycle.
5.2 Temperature entropy diagrams improved Graz cyclesThe reference Graz cycle Ts (temperature entropy diagram) can be seen below in figure 26a next tothe U-Graz cycle’s Ts diagram in figure 26b. The figures are plotted with a clear differentiation betweenthe Brayton and Rankine part of the cycle.
The following can be retrieved from the Ts diagrams. There is more Rankine and Brayton cycle areain the U-Graz cycle Ts diagram as the Rankine part goes into the higher temperatures (leading to thehigher efficiencies) as it increases the Qh without increasing the Qc. Meanwhile, the theoretical maxi-mum efficiency η of a Carnot cycle is η = 1 − Qh/Qc. The Brayton part of the cycle is wider (leadingto more specific work) as more entropy is used and created and Qh is higher. However, the amountof mass going though the different parts of the cycles differs from cycle to cycle, therefore no directconclusion can be made solely from the Ts diagrams. For instance, the ratio of steam going throughthe first HTT and LPT is 1.13 for the U-Graz cycle and 1.84 for the Graz-EQ cycle. Thus, the Rankinebottoming cycle influences the efficiency of the U-Graz-cycle more. The plots are there to visualize thecycle in another way.
42
Noteworthy is the entropy reduction in the first high temperature turbine of the Graz-EQ cycle. Entropyis created during (non-reversible) turbine expansion. This can be explained by a significant amount ofopen loop cooling that is quenched into the HTT-1. The U-Graz cycle uses hybrid cooling, thereforeless steam is quenched into the HTT-1 and the reduction in entropy is absent.
(a) Ts diagram Graz-EQ cycle (b) Ts diagram U-Graz cycle
Figure 26: TS diagrams
43
6 Fuel cell addition to the Graz cycle
As discussed in section 2.3, the fuel cell is a very promising addition to a hydrogen and oxygen firedturbine cycle. As the pressurization of the fuel, the use of hydrogen and pure oxygen increases thedriving force of the electrochemical reaction (the Nernst voltage equation 8). For instance, the U-Grazcycle transforms the heat (from the combusted fuel) into electricity with a LHV efficiency of approxi-mately 75%. A state of the art SOFC transforms 65% of the converted fuel’s energy into electricityLHV [5], thus 35% of this converted fuel LHV energy becomes heat. Thus if both cycles would fit toeach other perfectly and the fuel utilization of the FC is 100% (no downstream combustor is requiredfor complete fuel utilization) a combination of the two could lead to a 65 + 35·75
100 = 91.2% LHV efficiency.To come as close as possible to this perfect combination one would need an FC which can be fed withthe fuel temperatures as given and exit the FC at TIT (1700C) with 100% fuel consumption in the FC.Unfortunately, no such FC exist. The U-Graz cycle needs to be modified significantly to accommodatethe FC.
For this reason, in this chapter the connection of FC system to a turbine cycle is investigated, fur-thermore the modifications that need to be made to the cycle are covered. This will be done for a singlelow temperature SOFC and a triple SOFC system containing low, intermediate and high temperatureSOFCs. Moreover, the different cooling methods used to keep the SOFCs cool are covered, both theaddition of steam and the use of excess oxygen is covered. The electrochemical operation and per-formance for the different SOFCs is investigated. Current density voltage (IV) curves are investigated.And finally, the different FC-Turbine cycles are exergatically analyzed.
6.1 Fuel cell connection to the Graz cycleThe FC is placed upstream of the combustor and the unutilized heated fuel, leaving the FC, is burnedin the combustor. The combustor acts as an afterburner in this case. The full SOFC temperature rangewill be used in the system and the gasses are fed to the FC system at a temperature of 550 C andexits at 1000 C (the minimum and maximum operating temperatures for state of the art SOFCs). Thebroader this range the less thermodynamic adjustments that need to be made to fit the FCs. Today’sFCs can have temperature deltas of 150 C [17] per FC, therefore 3 FCs in series are required toachieve the 450 C temperature delta. The fuel and oxidizer enter the first low temperature SOFC(LT-SOFC) at 550 C and exit at 700 C. For the intermediate temperature SOFC (IT-SOFC) entry isat 700 C, while it exits at 850 C. The high temperature SOFC (HT-SOFC) entry is at 850 C, while itexits at 1000 C.
An important aspect of the FC is the cooling. The waste heat must be extracted from the FC. Twooptions have been studied: (1) cooling via excess pure oxygen circulation at the cathode (cycles withFC-OX-abbreviation) and (2) cooling by dilution of the oxygen flow with steam (cycles abbreviated withFC-Steam). Both options will be compared.
Adding steam to the FC cathode for cooling, decreases the partial pressure of the oxygen resultingin a decrease in the electrochemical driving force (Nernst voltage) as can be seen in equation 8. Theexcess oxygen cooling has a higher Nernst voltage, but it requires an additional compressor (at hightemperatures) for the oxygen recirculation. The addition of cooling steam to the anode side (hydrogenside) has also been evaluated. However, this has a very negative impact on the Nernst voltage as can
44
Figure 27: Principle flow scheme 3FC-OX-Graz cycle. A detailed flow scheme is depicted in appendix C.4. TheFC is cooled using oxygen recirculation.
be seen in equation 8: the partial pressure of steam increases and the partial pressure of hydrogendecreases.
In the steam cooled FC, the hydrogen, steam and oxygen are preheated to SOFC inlet conditions.The HTT downstream steam preheats the flows. In the oxidant recirculated FC, the hydrogen andoxygen are preheated to SOFC inlet conditions. This heat is extracted from the excessive oxygen thatexits the FC.
Moreover, the use of a single FC operating at a single temperature is compared to the use of threeFCs. For the single FC configuration the LT-FC is chosen as it needs the same 550 C feed as the 3FCconfiguration.
The steam cycles fuel utilization is limited by the amount of heated steam it can extract from the maincycle. The higher the fuel utilization in the SOFC, the less heat goes into the cycle. Therefore, lesssteam is needed in the combustor to get to the same TIT. Less steam in the combustor results in lesssteam through all parts of the cycle. Consequently, the compressors cannot feed enough steam to theFC entry. The 3FC-steam cycle is operated at this limit (at maximum fuel utilization in the FC) as thebest efficiency is extracted at maximum FC usage. For a fair comparison the 3FC-OX cycle is operatedat the same fuel utilization level as the 3FC-steam cycle. The 1FC-OX cycle uses the same amount ofoxygen re-circulation as the 3FC-OX cycle. The 1FC-Steam cycle uses the same amount of fuel as the1FC-OX cycle for a fair comparison.
45
Table 9: Fuel cell operating parameters
1FC-OX 1FC-Steam 3FC-OX 3FC-SteamTemperature out (C) 700 700 1000 1000Fuel used FC1(kg/s) 0.483 0.483 0.483 0.480Fuel used FC2(kg/s) * * 0.483 0.482Fuel used FC3(kg/s) * * 0.484 0.489Fuel used total(kg/s) 0.483 0.483 1.450 1.450Oxygen inlet (kg/s) 93.13 19.84 93.13 19.84Oxygen utilization (kg/kg)** 0.041 0.193 0.124 0.580Water inlet (kg/s) 0 34.19 0 33.80
* No such component in the cycle** Oxygen utilization in kg oxygen reacted in FC’s per amount of oxygen going into the first FC.
Figure 28: Fuel cell flow scheme 3FC-OX-Graz cycle. The FC is cooled using oxygen recirculation. A moredetailed flow scheme is depicted in appendix C.4.
All these input values can be seen in table 9, the difference in the amount of oxygen utilization be-tween the systems is particularly striking. A heat balance (equation 58) is calculated for each FC,which shows that the 3FC cycles are able to use 3 times the amount of fuel in the FCs for the sameamount of coolant going in. The 3FC-OX principle flow scheme can be seen in figure 27. The recir-culated oxygen preheats the fuels and heats the flow upstream of the compressor. A more detailedpicture of the FC part of the cycle can be seen in figure 28. The 1FC-OX cycle flow scheme, as canbe seen in figure 29, is different than its 3FC counterpart. One FC is not able to insert sufficient heat
46
Figure 29: Principle flow scheme 1FC-OX-Graz cycle. A more detailed flow scheme is depicted in appendix C.3.The FC is cooled using oxygen recirculation.
in the recirculated oxygen (the oxygen exits this FC at 700C), to preheat the fuel and oxygen to FCinlet conditions. Therefore, in the 1FC-Ox cycle the recirculated oxygen together with the steam down-stream of the HTT preheats the fuels.
The 3FC-steam principle flow scheme can be seen in figure 30. This cycle uses the downstreamgas from the HTT to preheat the gasses before FC entry.
The FC Steam cycles need to be fed a certain amount of steam (dependant on the FC operatedfuel utilization) at 550C and 40 MPa. This steam is needed to cool the FC (the OX-FC cycles userecirculated oxygen). The more fuel is utilized in the FC the more heat is generated in the FC (andmore steam cooling is needed). The steam is extracted from the turbine cycle (the amount of steamavailable is however limited). The requirement to be fed an amount of 550C and 40 MPa steam in-creases complexity. Therefore, the Steam-FC cycles are more difficult to design and regulate.
Increasing TIT or adding an extra combustor leads to less working fluid through the cycle, thus less(high temperature) steam is available to use elsewhere. The Steam-FC cycles need to be fed a certainamount of 40 MPa 550C steam (the amount is dependant of the amount of fuel utilization in the FC).Therefore, not all cycle additions (operated configurations) are possible for steam cooled FC.
47
Figure 30: Principle flow scheme 1FC/3FC-Steam-Graz cycle, with the pressures and temperatures of the 3FC-Steam-Graz cycle. A more detailed flow scheme is depicted in appendix C.2. The FC is cooled by the addition ofsteam.
6.2 Electrochemical performanceTo analyse the addition of FCs to the U-Graz cycle, all FCs are operated at 65% efficient LHV. Astandard anode supported SOFC geometry as found in [22] is used with the materials and their re-spective resistivities from [23]. The resistivities and thicknesses of the components used in the FCstack are displayed in table 1. Losses occur due to electrical resistance (overpotential) in the FC. Inhigh temperature FCs (all SOFCs are in this category) the activation overpotential is negligibly small[18]. Furthermore, the concentration overpotential only becomes significant when the limiting currentdensity is approached [18]. In this study, efficiency is key and the SOFC is operated far away from thelimiting current density. Therefore, the ohmic resistance is the only significant resistance in this study.The FC LHV efficiency is fixed at 65% and the inlet conditions are fixed, therefore the cell voltage isfixed as well. The FC model is used to estimate the power densities one can expect. Furthermore,the FC operates in steady state conditions, thus the following heat balance is valid, as can be seen inequation 58.
mcat,inhcat,in + mano,inhano,in = WFC + QLoss + mcat,outhcat,out + mano,outhano,out (58)
The subscript cat represents the cathode and ano represents the anode. The heat balance and theelectrochemical operation both depend on the flows going in. Therefore, the equations are solvedsimultaneously. The heat loss (QLoss) to the environment is assummed to be 2% LHV of the fuelreacting in the FC. Furthermore, the pressure loss per FC is assumed to be 2% (The 3FC pressureloss, therefore equals 6% in total).
48
A lumped parameter approach is assumed, meaning:
1. The FC temperature is constant in all directions.
2. The current density is constant.
3. The potential is constant, and therefore determined by the outlet compositions of the fuel andflow, since at this point the Nernst voltage is at its minimum.
The results for both the 3FC-OX and 3FC-steam cycle are shown in table 10. The resistivities of theSOFC materials are very temperature dependent as one can see from the reduction in the area specificresistance (ASR: the total FC electrical resistance divided by the total FC stack active area) when theFC temperature increases. The potential voltage E0 decreases slightly with an increase in tempera-ture. The driving force (the Nernst voltage) decreases even more in the downstream FCs as both E0
decreases due to the increase in temperature and more steam is formed decreasing χH2 and χO2 (onlyin the steam cooled FCs). In the oxygen cooled cycle χO2
is always 1.
The power density of the 1FC-OX system is 0.324 Wcm2 , while the power density of the 1FC-Steam
system is merely 0.290 Wcm2 . The power density of the 3FC-OX system is 0.409 W
cm2 , while the powerdensity of the 3FC-Steam system is merely 0.329 W
cm2 .
Based on the difference in power density the required cell area for the 3FC-OX system is 24% smallerthan the area for the 3FC-steam system, resulting in significant lower cost per kW [18]. Therefore, therecirculation of oxygen is superior to steam cooling, from an electrochemical point of view.
The 3FC-OX system has a 26% higher power density compared to the 1FC-OX system. Therefore,the use of multiple FCs is superior to the use of a single FC, from an electrochemical point of view.
Table 10: Elechtrochemical results 3FC-Steam and 3FC-OX configuration
FC-1OX
FC-2OX
FC-3OX
FC-1Steam
FC-2Steam
FC-3Steam
TemperatureFC exit (C) 700 850 1000 700 850 1000
Pressure FC exit (bar) 39.9 39.2 38.4 39.9 39.2 38.4Cathode χO2
1 1 1 0.211 0.169 0.122Anode χH2 0.807 0.614 0.420 0.808 0.615 0.420E0 (V) 1.006 0.963 0.919 1.006 0.963 0.919Nernst voltage (V) 1.143 1.074 1.001 1.111 1.031 0.952Cell voltage (V) 0.834 0.838 0.840 0.834 0.838 0.840ASR ( ohmcm2 ) 0.794 0.398 0.303 0.794 0.398 0.303Power density ( W
cm2 ) 0.324 0.496 0.445 0.290 0.407 0.310Current density ( A
cm2 ) 0.389 0.593 0.530 0.348 0.485 0.369Power (MW) 37.69 37.70 37.77 37.44 37.62 38.10
49
6.3 Electrochemical operation and IV curvesThe IV curves and efficiency voltage curves, for the 3FC-OX and 3FC-Steam cycle are plotted in figure31 and 32 respectively. The electrochemical results of table 10 are from the chosen operation at 65%efficiency. This is a choice taking efficiency and power density into consideration. The power densityvoltage curves are parabolas. A certain power density (except for the maximum power density) of a FCcorresponds to 2 operational voltages, of which the higher voltage has the higher efficiency. For exam-ple, this can be seen from figure 31b as one can operate this FC at a 0.83 V (cell voltage) correspondingto a power density of 0.32 W/cm2 with 65% efficiency or one operates it at 0.31 V corresponding to apower density of 0.32 W/cm2 with 24% efficiency. Therefore, in general the logical operational voltageof a FC is at a voltage higher than the voltage corresponding to maximum power density.
For the LT-SOFC of the 3FC-OX system maximum power density occurs at 0.57 V, at 0.41 W/cm2
power density, 0.72 W/cm2 current density and 44% efficiency, as depicted in figure 31a and 31b .At the highest operatable voltage the efficiency is highest, but the power density is 0. Therefore, onewants to operate between these points, somewhere at a high efficiency with an acceptable power den-sity. The operation at 65% seems to be very reasonable.
All three FC’s operate at the same efficiency. This is however not the most optimal configuration.The fuel cells behave differently and for that reason have a different optimum operation point for a cer-tain use case. The system can be optimized by operating all 3 FC’s at a different efficiency, but reachthe same overall system efficiency at a higher power density. However, this will be an optimizationstudy on its own.
The 3 steam fed FC’s operate at a lower power density compared to the oxygen recirculated FC’s.For the HT-SOFC this difference is largest. The driving force of this fuel cell the Nernst voltage is low-est as depicted in table 10 and the difference in Nernst voltage compared to the oxygen recirculatedFC’s is largest. This can be explained by the low cathode oxygen mol fraction (0.122) as depicted intable 10. The low cathode oxygen mole fraction results in a lower PpO2
(partial oxygen pressure), thusthe Nernst voltage is lower according to equation 8.
50
(a) LT-SOFC IV curve (b) LT-SOFC Efficiency to power-density
(c) IT-SOFC IV-curve (d) IT-SOFC Efficiency to power-density
(e) HT-SOFC IV-curve (f) HT-SOFC Efficiency to power-density
Figure 31: 3FC-OX IV-curves and efficiency power-density plots
51
(a) LT-SOFC IV curve (b) LT-SOFC Efficiency to power-density
(c) IT-SOFC IV-curve (d) IT-SOFC Efficiency to power-density
(e) HT-SOFC IV-curve (f) HT-SOFC Efficiency to power-density
Figure 32: 3FC-Steam IV-curves and efficiency power-density plots
52
6.4 Exergy analysis FC-Graz cycles
6.4.1 1 fuel cell vs 3 fuel cells (1FC vs 3FC):
The FC acts as a preheating device for the combustor, heating the inlet flow to the combustor to 700 Cand 1000 C for the 1FC and 3FC case respectively. The higher the inlet temperature of the combustor,the lower the combustor exergy losses. For that reason, the relative (and absolute) combustor lossesdrop due to the use of multiple FCs compared to a single FC. The absolute combustor losses drop evenfurther, as the multiple FC cycles burn less fuel in the combustor, due to their higher overall FC fuelutilization. The 3FC combination has a clear efficiency advantage not only due to the higher conversionin the FC, but also due to the reduction of relative exergy losses in the combustor.
6.4.2 Steam vs Oxygen cooled fuel cells (Steam vs OX):
Both cooling options need different amounts of FC preheat at different utilizations of fuel in the FC. TheFC-OX cycles are partly or fully preheated by the excess oxygen of the FC itself. The 1FC-OX cycleneeds some extra heat from the HTT turbine, while the 3FC-OX cycle excess oxygen is too hot afterpreheat and needs to be cooled by streams after the HPT and compressors. The HPT and compressorstreams differ in temperature from cycle to cycle. Therefore, the U-Graz-3FC-Ox cycle, Graz-3FC-Oxand Graz-1FC-OX have different HEX-Preheat FC exergy losses, as stated in table 11. Furthermore,the cycles introduce a very small compressor loss as the oxygen needs to be recirculated.
The Steam FC cycles preheat the fuel streams using only the main cycles heat (the HTT downstream).Therefore, the HEX-Preheat FC exergy losses are almost the same for the steam FC cycles, as statedin table 11. Furthermore, upstream of the HRSG there is less heat and thus less heat to be carried tothe HPT. This results in lower temperature cooling water going into the combustor and HTT’s, leadingto reduced cooling mass needs (less HTT turbine exergy losses) and higher combustor losses.
In a nutshell, the steam cooled FC cycles extract more heat from the HTT downstream, leading toless heat upstream of the HRSG and therefore less heat downstream and upstream of the HPT. Lessheat upstream of the HPT leads to less cooling mass required for the HTT turbine, thus less HTTexergy losses, but a cooler combustor inlet means more combustor exergy losses. The addition of acompressor to recirculate the oxygen adds a small compressor loss to the recirculated oxygen cycles.Overall, the oxygen cycle and steam cycles operate around the same efficiency, at some FC utilizationrates the oxygen circulation efficiency is more efficient and at other fuel utilization the steam FC cycleis more efficient. Moreover, another advantage of the FC-OX cycles is their ability to operate at higherfuel utilization compared to the Steam-FC cycles, as they do not need a certain amount of steam feedat 550C. For that reason, the FC-OX cycles have the prospect of becoming even more efficient, whenoperated at higher fuel utilization (than is done in this study).
6.4.3 The U-Graz-FC cycle
The best performing thermodynamic cycle the, U-Graz-1700C, cannot be coupled to an FC cycle (withthe same 0.58 fuel utilization in triple FC configuration). The system could not provide sufficient heatinto the cycle, without huge adjustments (introducing multiple new heat exchangers and changing theinherent cycle design) and supplying the right amount of cooling to the HTT’s.
53
Table 11: Exergy analysis FC enhanced cycles compared to Graz-EQ and U-Graz cycle
ExergyLosses in % Graz-EQ Graz-
1FC-OxGraz-1FC-Steam
Graz-3FC-Ox
Graz-3FC-Steam U-Graz U-Graz-
3FC-Ox
Fuel cell stack ** 1.56*8.10
1.55*8.00
3.78*6.51
3.75*6.46 ** 3.78
*6.51HEX-Preheat FC ** 2.52 2.03 3.16 2.00 ** 3.33FC Comp. ** 0.01 ** 0.02 ** ** 0.02
Combustors 21.27 14.77*18.31
15.65*19.39
7.10*16.91
7.87*19.83 19.47 6.63
*15.79HRSG 1.93 1.69 1.71 1.18 1.21 2.86 1.55Turbines 5.49 4.84 4.79 3.39 3.51 4.04 2.49Pumps & Comp.excluding FC Comp. 1.28 1.10 1.10 0.59 0.70 0.71 0.22
Condenser 0.97 0.87 0.88 0.70 0.69 0.90 0.67Deaerator 0.48 0.41 0.42 0.28 0.27 0.21 0.13Energy ηLHV 70.43 74.49 74.21 82.48 82.65 73.63 83.79Principle flow-scheme in figure 24 figure 29 figure 30
***figure 27*** figure 30 figure 25 figure 33
* Relative FC/combustor loss (loss if it was the only fuel using device)**Non existent
***Only the flow-scheme fits the cycle. The displayed pressures and temperatures in the figure do not belong tothis cycle.
Figure 33: Principle flow scheme U-Graz-3FC-OX cycle. A detailed flow scheme is depicted in appendix C.5.
54
The 3FC-Steam cycle cannot be coupled to either the U-Graz-1700C nor the U-Graz cycle (TIT of1500C). Due to the addition of FCs less heat is supplied to the cycles, therefore less working fluid isused throughout the cycle to be able to provide the same TIT. As a result, an insufficient amount ofsteam can be provided to the FC. The 3FC-OX cycle is therefore coupled to the U-Graz cycle as its TITof 1500C is reachable. The result is the U-Graz-3FC-OX cycle and is shown in figure 33. This combi-nation is 1.3% more efficient as the Graz-3FC-OX cycle, as can be seen in table 11. This difference isless than half of the difference of the thermodynamic only Graz and U-Graz cycle (3.2% more efficient).This smaller effect can be explained by the fact that only 61% of the fuel energy is released as heatto the working fluid (41.9% of this heat is from the combustor and 19.1% from the FCs). Moreover,to incorporate the FCs, extra components (the FC itself and heat exchangers) are included, resultingin extra heat and pressure losses. A Sankey power diagram of the U-Graz-3FC-OX cycle is shown infigure 34, in which the energy (thus not the exergy) streams of the components are plotted.
Figure 34: Sankey power (in LHV) diagram U-Graz-3FC-OX cycle.
55
The following can be noticed from figure 34: the power produced by the LPT and HPT falls short incomparison to the power produced by the HTT. This is a property of Graz cycles. In a Graz cycle,part of the steam, downstream of the HTT, skips the LPT and HPT and is compressed directly to enterthe combustor. For this reason, the HTT power is more significant in Graz cycles than in conventionalCCGT cycles.
56
7 Conclusions
This work presents the thermodynamic analysis of multiple very high efficiency hydrogen and oxygenfuelled electricity generating power cycles. The thermodynamic cycles are closed loop combinationsof a Brayton and a Rankine cycle. Both a turbine-only-cycle and a cycle with the addition of FCs havebeen designed, followed by an analysis of all possible plant configurations.
The thermodynamic cycle (U-Graz-1700C cycle) constructed is an adjusted Graz cycle, with addedreheat combustor, hybrid cooling, extra heat exchangers to preheat the condensate and an increasedTIT. These improvements result in a 74.9% LHV thermal efficiency, a 4.4% increase in efficiency overthe Graz-EQ cycle. The main efficiency increase is generated by a lower overall combustor loss. How-ever, the combustor loss is still the biggest exergy loss. Therefore, the integration of FCs before thecombustor is investigated for further efficiency gains.
The addition of a turbine cycle to a FC is well known to extract performance from the otherwise wastedheat from a FC. This thesis examines the concept from the other side, a very efficient turbine cycleis developed and multiple FCs are placed there where they are most desired (from an exergetic pointof view). The FCs are designed to fit the cycle. Furthermore, the cycle is adjusted to accommodatethe FCs in the most efficient way. This leads to a turbine cycle with multiple FCs in series operatingin different temperature regimes. FCs have not been modulated in series before, but the studied cyclehas shown that it leads to the highest overall efficiency. Using oxygen recirculation as cooling methodfor the FC yields the best results, moreover the integration of the oxygen cooled FC into the cycle isless complex.
Moreover, the FC combination with 3 FCs in series combined with oxygen recirculation (3FC-OX) ismost electrochemical favorable and results in the highest FC power density. The resulting efficiencyis 82.5% LHV for the Graz-3FC-OX cycle and 83.8% LHV for the U-Graz-3FC-OX cycle. The FC de-creases the role of the combustor and its exergy losses in the cycle. Therefore, all the methods usedin the U-Graz cycle to decrease the combustor losses, which gave it a 3.2% efficiency benefit, havebecome less influential in the cycles with FCs. The U-Graz-3FC-OX cycle is only 1.3% more efficientthan the Graz-3FC-OX cycle. Finally, the FC reduces the overall heat input in the cycle. Therefore,compromises need to be made to get to the same turbine inlet temperature. Both the thermodynamic(U) upgrades and FC addition mainly reduce the combustor exergy losses.
57
8 Recommendations for future research
The hybrid cooling model used for the hybrid cooled HTT blades is a new approach. In the approachit is assumed the blade can be modeled as if a fraction of the blade is solely CLSC and the rest ofthe blade is solely open loop cooled. In real life the full hybrid cooled blade is both CLSC and openloop cooled and there will be interaction between the CLSC and open loop cooling. Therefore, theapproximation used is rather simplistic and should be improved in a future study.
An existing FC layout is used in this thesis. However, the operating conditions (a pressure of ≈ 40MPa) fuelled with pure hydrogen and oxygen is unique. The SOFC design should be adapted to theunique operating conditions, to estimate the FC parameters (power density, operating voltage) corre-sponding to a chosen efficiency more accurately. The design of an SOFC layout that fits these uniqueoperating conditions should be investigated in a future study.
Further efficiency improvements can be achieved by operating the SOFCs at higher fuel utilization,higher voltages or by an increase in operational temperature. Operation at higher voltages or higherfuel utilization will lead to lower power densities, resulting in a larger and costlier fuel cell. Moreover, inthe 3FC cycles all three FCs are operated at the same efficiency, this is not the most ideal type of op-eration. The different FCs can be optimized to operate at different efficiencies each, but operate at thesame overall efficiency with a lower total FC stack area. This can be done in a future optimization study.
An increase in the working temperature window of the fuel cells (now 550 to 1000C) would leadto lower heat exchanger losses, resulting in an increased efficiency. Moreover, the inclusion of othertypes of fuel cells can be investigated, for example the proton exchange membrane (PEM) FC. PEMFCs operate around 100C, the inclusion of a PEM FC would further increase the working temperaturewindow of the FCs used.
The most efficient cycle, the 3FC-U-Graz cycle, is far too complex and expensive for near future use.It is in the earliest design phase, making an accurate estimation of the costs impossible at this pointin time. A potential direction for further research is to develop a less complex cycle, based upon the3FC-U-Graz cycle, incorporating the most important elements. A first step could be the coupling of aseries of lab scale FCs to a simplified Graz cycle. The Graz cycle can be simplified by lowering theTIT to eliminate cooling needs. Additionally, one can reduce the turbines respective pressure ratios(reducing the amount of turbines stages/blade rows), or even remove the complete HPT.
Another research and development direction is to use the knowledge and insights from the 3FC-U-Graz cycle to study the option of modifying an existing CCGT cycle to a higher efficiency semi-closedH2/O2 cycle.
58
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61
A Mathematical derivation open loop cooling
A.1 Derivation open loop cooling without TBC coatingThe derivation continues on the earlier made derivation of section 3.2. For the open loop case withouta TBC coating the heat network depicted in figure 35 is used.
Figure 35: Temperature profile across film cooled and TBC coated turbine blade
The following parameters are introduced, to simplify the calculation:
ηc =Tce − TciTb − Tci
(59)
ε =Tg − TbTg − Tci
(60)
The the metal blade conducts heat very well Tb,ex − Tb,in is assumed to be negligible, therefore thebulk value will be used Tb for the interior and exterior wall. Moreover, Due to the assumptions made thegoverning equations become:
Q = hgAg(Taw − Tw) ≈ hgAg(Tg − Tb) (61)
62
Q = mc(hce − hci) ≈ mcCpc(Tce − Tci) (62)
Together they form:mcCpchgAg
=Tg − TbTce − Tci
= m∗ (63)
Which can be rewritten to:m∗ =
Tg − TbTg − Tci
Tg − TciTce − Tci
(64)
Which can be further rewritten to:
Tce − TciTb − Tci
+Tg − TbTce − Tci
− Tce − TciTb − Tci
+Tg − TbTce − Tci
· Tg − TbTg − Tci
=Tg − TbTg − Tci
(65)
Which can be rewritten to:ηc ·m∗ =
ε
1− ε(66)
At this point the following figures 36 and 37 illustrates the concept:
Figure 36: Simplified cross section of a single convection cooled blade[24]
63
Figure 37: Simplified cross section of blade film cooling[24]
The heat balance of an elementary strip dy out of figure 36 is:
mcCpcdTc = hcSc(Tb − Tc)dy (67)
The left part is integrated from Tce to Tci and the right part of the equation is integrated from y = 0 toy = L. This leads to:
Tb − TceTb − Tci
= e−hcScmcCpc
L (68)
ηc = 1− e−hcAc
m∗hgAg (69)
Ac is the area of the cooled wall (including the fins inside). Combining equation 69 with equation 66gives:
(1− e−hcAc
m∗hgAg ) ·m∗ =ε
1− ε(70)
(1− e− αm∗ ) ·m∗ =
ε
1− ε(71)
If α m∗ thenm∗ ≈ ε1−ε . For modern turbines this is the case as the cooling technology has increased
a lot over time.Using equation 63 one gets:
mc =hgAgCpc
ε
1− ε(72)
mg = ρg · vg ·Aw (73)
mc =mg
mg· mc =
mg
ρg ∗ vg ∗Aw· mc =
mg
ρg ∗ vg ∗Aw· hgAgCpc
ε
1− ε(74)
Combining this equation with the Stanton number leads to:
mc = mgStgCpgCpc
AgAw
ε
1− ε(75)
64
A.2 Derivation open loop cooling with the TBC coatingThe derivation of the previous subsection is for a blade without the TBC coating. As the blades of ourstudy use a TBC coating this extra conducting part needs to taken into account in the heat transferequation. This addition is done in the same way as in the CLSC case. Therefore, the resulting equationfor the film cooling mass flow with a TBC becomes:
mc = mg1
1 +BiTBCStg
CpgCpc
AgAw
ε
1− ε(76)
mc
mg(BiTBC + 1)
CpcCpg
AwAg· 1− ε
ε= St (77)
65
B Thermoflex models without FC
The Thermoflex models are depicted in this part of the appendix. Fuel sources are depicted as an or-ange rectangle, the oxygen source is depicted as a red rectangle. The other components are explainedon the Thermoflex website [26]. The full Thermoflex models include the operational parameters of theindividual components. For those who want the full models please contact me (the author) via email.
The Exergatic analysis is done in MATLAB scripts. However, the stream and components power data isfirst copied to an Excel file, the MATLAB script reads the data out of the Excel file. The MATLAB scriptretrieves data from online fluid prop libraries. This fluid data is retrieved using certain function files.The right libraries need to be downloaded and one needs the right MATLAB files in the right folders.For this reason, contact me (the author) to access the MATLAB file folders, with an explanation.The main Thermoflex models are depicted in subsection B.1-B.8. The stage by stage Thermoflexcooling model of the Graz-1700C cycle, is displayed in B.3.1. This cycle is open loop cooled.
66
TH
ER
MO
FLE
X V
ersi
on 2
7.0
Rev
isio
n: M
arch
11,
201
9
bram
T
U D
elft
She
et 1
2614
02-
19-2
020
17:2
6:02
fil
e= C
:\U
sers
\bra
m\D
eskt
op\M
atla
b sc
ript
s\A
fstu
dere
n\be
ste\
Alle
_mod
elle
n_m
et_S
TAN
TO
Nco
olin
g\G
raz_
EQ
_Sta
nton
.tfx
bar
kJ
/kg
C
kg/s
Gro
ss p
ower
2113
86 k
WG
ross
ele
ctric
effi
cien
cy(L
HV
)70
,43
%N
et f
uel i
nput
(LH
V)
3001
54 k
W
10
41
,73
419
48
9,1
88
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12
41
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9,8
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519
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16
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15
312
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43
44
40
45
41
27
B.1 Graz-EQ cycle Thermoflex model
67
TH
ER
MO
FLE
X V
ersi
on 2
7.0
Rev
isio
n: M
arch
11,
201
9
bram
T
U D
elft
She
et 1
2614
02-
19-2
020
15:5
9:34
fil
e= C
:\U
sers
\bra
m\D
eskt
op\M
atla
b sc
ript
s\A
fstu
dere
n\be
ste\
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kJ
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C
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Gro
ss p
ower
4760
59 k
WG
ross
ele
ctric
eff
icie
ncy(
LHV
)70
,98
%N
et f
uel i
nput
(LH
V)
6706
48 k
W
468
,81
1199
2415
3,46
3
666
3399
1500
135,
317
0,02
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6
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1995
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2
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7
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7
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9
23
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a
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a
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65
66
64
B.2 Toshiba-EQ cycle Thermoflex model
68
TH
ER
MO
FLE
X V
ersi
on 2
7.0
Rev
isio
n: M
arch
11,
201
9
bram
T
U D
elft
She
et 1
2614
02-
19-2
020
15:5
2:38
fil
e= C
:\U
sers
\bra
m\D
eskt
op\M
atla
b sc
ript
s\A
fstu
dere
n\be
ste\
Alle
_mod
elle
n_m
et_S
TAN
TO
Nco
olin
g\17
00\G
raz_
1700
_Sta
nton
_750
C_m
etal
.tfx
bar
kJ
/kg
C
kg/s
Gro
ss p
ower
2145
25 k
WG
ross
ele
ctric
effi
cien
cy(L
HV
)71
,47
%N
et f
uel i
nput
(LH
V)
3001
54 k
W
10
41
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469
51
0,9
69
,14
12
41
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9,8
11
519
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13
41
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24
15
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254
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16
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00
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38
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43
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40
45
41
27
46
47
B.3 Graz-1700C cycle Thermoflex model
69
TH
ER
MO
FLE
X V
ersi
on 2
7.0
Rev
isio
n: M
arch
11,
201
9
bram
T
U D
elft
She
et 1
2614
03-
03-2
020
17:3
5:04
fil
e= C
:\U
sers
\bra
m\D
eskt
op\M
atla
b sc
ript
s\A
fstu
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AL_
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RC
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3.tf
x
bar
kJ
/kg
C
kg/s
Gro
ss p
ower
2228
24 k
WN
et p
ower
2205
96 k
WG
ross
ele
ctric
eff
icie
ncy(
LHV
)0
%
1741
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B.3.1 Graz-1700C cycle Thermoflex stage by stage cooling model (open loop cooling)
70
TH
ER
MO
FLE
X V
ersi
on 2
7.0
Rev
isio
n: M
arch
11,
201
9
bram
T
U D
elft
She
et 1
2614
02-
19-2
020
15:5
6:19
fil
e= C
:\U
sers
\bra
m\D
eskt
op\M
atla
b sc
ript
s\A
fstu
dere
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ste\
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elle
n_m
et_S
TAN
TO
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olin
g\LP
T H
RS
G\G
raz_
HE
X_S
tant
on.t
fx
bar
kJ
/kg
C
kg/s
Gro
ss p
ower
2119
05 k
WG
ross
ele
ctric
effi
cien
cy(L
HV
)70
,6 %
Net
fuel
inpu
t(LH
V)
3001
54 k
W
10
41,7
3419
489,
188
,07
12
41,7
-19,
8115
19,8
4
13
41,7
1199
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6
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263
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35
1,11
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2,9
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7
38
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39
193,
755
5,2
129
48,4
3
40
41,7
574,
736
2,5
7,99
1
19
176
2918
,540
3,9
48,4
3
7
1,14
656,
136
2,8
134,
7
46
1,11
429,
910
2,5
48,4
3
47
1,08
161,
411
6,7
63,9
5
11
187,
617
30,3
357,
848
,43
44
181,
725
02,8
357,
848
,43
14
4034
0014
99,9
110,
4
50
1524
23,7
1132
,812
6,7
52
1,17
933,
849
6,1
134,
7
53
1,2
1146
,459
4,4
134,
7
42
4031
2136
116
,32
54
1531
2133
7,4
8,16
1
37
1534
0,6
235,
67,
991
49
2,86
314
9174
8,5
134,
7
56
2,86
334
0,6
210,
73,
996
3
0,02
522
90,2
21,0
864
,24
4 298
,56
23,4
867
,55
20
1,11
2781
,215
2,7
1,23
1
21
0,02
588
,43
21,0
864
,24
22 231
7,5
75,8
245
,21
24
0,5
340,
581
,32
1
25
1,22
134
0,6
81,3
31
57
0,3
2580
,869
,167
,55
58
1,11
2781
,215
2,7
69,5
4
64
0,3
2580
,869
,164
,24
65
0,5
2653
,485
,39
1
66 298
,56
23,4
845
,21
67
0,3
2580
,869
,13,
31
68
0,8
2726
123,
70,
9895
69
0,8
319,
676
,33
47,2
70
0,5
2653
,485
,39
1
71 226
6,3
63,6
45,2
1
73
0,3
289,
269
,13,
31
23
0,8
391,
693
,49
0,98
95
60
0,8
368,
587
,98
47,2
2
11
14
HPT
19
17
4
HT
T-1
23
2425
12
HT
T-2
18
26
28
15
C1
31
C2
33
HP
T m
ini
3
34
36
16
35
29
30
38
39
42
HT
T-3
43
44
40
45
41
27
5
67
LPT
b
8
10
13
LPT
a
19
20
21
22
3237
46
47
48
LPT
a
4950
LPT
a
5152
53 54
55
57
5856
B.4 Graz-HEX cycle Thermoflex model
71
TH
ER
MO
FLE
X V
ersi
on 2
7.0
Rev
isio
n: M
arch
11,
201
9
bram
T
U D
elft
She
et 1
2614
02-
19-2
020
15:5
4:45
fil
e= C
:\U
sers
\bra
m\D
eskt
op\M
atla
b sc
ript
s\A
fstu
dere
n\be
ste\
Alle
_mod
elle
n_m
et_S
TAN
TO
Nco
olin
g\cl
osed
loop
coo
ling\
Gra
z_H
ybri
dcoo
l_S
tant
on_a
fblij
ven.
tfx
bar
kJ
/kg
C
kg/s
Gro
ss p
ower
2189
83 k
WG
ross
ele
ctric
effi
cien
cy(L
HV
)72
,96
%N
et f
uel i
nput
(LH
V)
3001
54 k
W
10
41
,73
45
95
06
,58
9,5
12
41
,7-1
9,8
11
51
9,8
4
13
41
,71
19
92
41
52
,5
84
4,2
33
30
24
40
,24
6,3
7
31
,11
80
,22
19
,11
62
,52
62
00
45
9,7
10
6,1
46
,37
10
,02
52
23
5,8
21
,08
62
,52
24
32
1,3
25
,00
23
21
2
25
36
3,2
81
5,0
23
21
2
22
1,1
18
0,2
21
9,1
14
0,1
8
18
17
93
9,2
50
7,5
47
,77
91
70
,43
73
46
63
,94
6,3
7
33
16
,63
19
43
72
,64
7,7
7
34
41
,73
53
15
38
,14
7,7
7
35
1,1
11
52
,21
12
,31
16
,5
36
1,1
11
52
,21
12
,36
8,7
38
1,1
11
52
,21
12
,34
7,7
7
39
19
3,7
46
2,3
10
6,8
46
,37
20
1,1
12
69
9,7
11
2,3
62
,52
23
1,1
18
0,2
21
9,1
12
2,3
4
21
1,1
12
69
9,7
11
2,3
6,1
89
27
1,1
12
69
9,7
11
2,3
68
,7
19
17
62
80
4,1
38
3,2
46
,37
71
,14
65
6,1
36
2,8
11
6,5
45
0,0
25
80
,06
19
,16
2,5
2
46
1,0
74
29
,91
01
,54
6,3
7
47
1,0
81
49
,71
11
47
,77
11
18
7,6
17
28
,33
57
,64
6,3
7
44
18
1,7
25
02
,83
57
,84
6,3
7
52
1,1
79
64
,45
10
,41
16
,5
40
44
,23
33
02
44
0,2
32
,73
15
41
,73
64
45
87
,38
,99
7
14
40
34
00
14
99
,81
11
,8
16
44
,23
33
02
44
0,2
4,7
85
41
44
,23
33
02
44
0,2
2,3
93
42
44
,23
33
02
44
0,2
2,3
93
62
41
,73
64
45
87
,24
,21
2
63
41
,73
64
45
87
,24
,78
5
57
41
,73
64
45
87
,22
,39
3
58
41
,73
64
45
87
,22
,39
3
37
40
33
02
43
7,5
2,5
08
64
40
33
02
43
7,5
1,2
54
66
40
33
02
43
7,5
1,2
54
29
44
,23
33
02
44
0,2
13
,64
68
44
,23
33
02
44
0,2
6,0
79
70
44
,23
33
02
44
0,2
2,0
17
71
44
,23
33
02
44
0,2
2,0
17
61
41
,73
64
45
87
,21
,00
86
04
1,7
36
44
58
7,2
1,0
08
76
41
,73
64
45
87
,22
,19
5
53
1,2
13
34
,46
78
,91
16
,5
81
44
,23
33
02
44
0,2
0,2
69
82
44
,23
33
02
44
0,2
0,0
89
28
34
4,2
33
30
24
40
,20
,08
92
79
2,8
64
33
02
41
2,7
0,0
90
5
80
2,8
64
33
02
41
2,7
0,0
45
3
84
2,8
64
33
02
41
2,7
0,0
45
3
85
44
,23
33
02
44
0,2
0,1
78
5
69
44
,23
33
02
44
0,2
4,0
33
74
41
,73
64
45
87
,21
,00
8
75
41
,73
64
45
87
,21
,00
8
86
41
,73
64
45
87
,20
,08
92
87
41
,73
64
45
87
,20
,08
92
88
41
,73
64
45
87
,20
,17
85
65
15
26
57
,71
22
3,3
11
4,3
67
2,8
64
17
21
,88
47
11
5,4
77
6,5
55
21
48
,51
02
3,2
11
5,4
30
15
33
02
42
1,1
2,0
46
89
15
33
02
42
1,1
1,0
23
59
15
33
02
42
1,1
1,0
23
90
2,8
64
17
13
,38
43
,51
16
,4
2
5
LP
T
7
14
HPT
19
17
13
19
20
21
22
23
24
25
6
26
28
15
C1
31
C2
3
34
35
10
29
32
37
30
38
39
8
43
44
12
18
48
11
16
4
36
46
45
47
27
49
33
50
40
51
52
53
54
42
5556
57
58
59
60
61
62
B.5 Graz-Hybrid cooled cycle Thermoflex model
72
TH
ER
MO
FLE
X V
ersi
on 2
7.0
Rev
isio
n: M
arch
11,
201
9
bram
T
U D
elft
She
et 1
2614
02-
19-2
020
15:3
5:19
fil
e= C
:\U
sers
\bra
m\D
eskt
op\M
atla
b sc
ript
s\A
fstu
dere
n\be
ste\
Alle
_mod
elle
n_m
et_S
TAN
TO
Nco
olin
g\2
Com
bust
ors\
Gra
z_2C
C_S
tant
on_7
50C
_met
alT
_2.t
fx
bar
kJ
/kg
C
kg/s
Gro
ss p
ower
3476
12 k
WG
ross
ele
ctric
effi
cien
cy(L
HV
)70
,44
%N
et f
uel i
nput
(LH
V)
4935
03 k
W
10
41
,68
351
45
30,
79
1,5
3
12
41
,68
-19,
81
519
,84
13
41
,71
199
24
15
2,5
8
41
,68
342
64
92,
18
3,0
5
16
41
,68
342
64
92,
11
4,6
8
31
,11
80
,31
9,1
31
08,7
62
00
45
9,7
10
6,1
83
,05
1
0,0
25
223
4,3
21
,08
108
,7
24
32
1,3
25
,00
25
579
25
36
3,2
81
5,0
25
579
28
41
,71
342
64
92,
14
2,5
9
22
1,1
180
,31
9,1
37
1,9
5
18
17
940
,65
08,
17
6,8
5
9
17
0,4
39
137
33,
78
3,0
5
33
16
,63
194
37
2,6
76
,85
34
41
,68
353
15
38
76
,85
35
1,1
11
49,
71
11,
11
96,
6
36
1,1
11
49,
71
11,
11
19,
8
38
1,1
114
9,7
11
1,1
76,
85
39
19
3,7
45
9,3
10
6,1
83
,05
20
1,1
12
697
,21
11,
11
08,
7
23
1,1
18
0,3
19
,13
36,
73
21
1,1
12
697
,21
11,
11
1,0
9
27
1,1
12
697
,21
11,
11
19,
8
19
17
62
77
4,6
37
8,8
83
,05
7
1,1
46
56,
13
62,
81
96,
6
45
0,0
25
80,
06
19
,11
08,
7
46
1,0
742
9,9
10
1,5
83,
05
47
1,0
81
50,
21
11,
27
6,8
5
11
18
7,6
16
58,2
35
0,5
83
,05
44
18
1,7
25
02,8
35
7,8
83
,05
14
39
,98
340
01
499
,91
13,9
52
1,1
71
012
,85
33
19
6,6
42
39
,98
342
64
91,
22
5,7
85
41
5,6
43
426
47
8,4
12
,89
56
2,8
64
594
,93
35,
61
8,7
4
50
41
,21
199
24
15
1,6
15
71
5,6
4-1
3,1
51
512
,78
59
15
,64
237
2,2
11
12,7
139
,66
01
534
00
14
99,8
154
40
41
,71
877
,34
92,
14
2,5
9
61
15
594
,93
47,
23
7,4
8
53
2,8
64
193
3,2
93
51
91
,5
62
7,3
27
594
,93
39,
95
,11
2
63
1,2
15
08,
27
55
19
4,1
64
1,2
14
93,
57
48,
71
96,
6
66
2,8
64
380
,92
30,
52
,55
6
67
1,2
38
0,9
22
6,1
2,5
56
2
5
LPT
7
11
14
HPT
19
17
13
19
20
2122
4
HT
T-1
23
2425
6
12
HT
T-2
18
26
28
15
C1
31
C2
33
HP
T m
ini
3
34
36
16
35
10
29
3237
30
38
39
8
42
HT
T-3
43
44
40
45
41
27
46
47
48
49
50
5152
HP
T m
ini
53
54
B.6 Graz-2CC cycle Thermoflex model
73
TH
ER
MO
FLE
X V
ersi
on 2
7.0
Rev
isio
n: M
arch
11,
201
9
bram
T
U D
elft
She
et 1
2614
02-
19-2
020
17:3
6:23
fil
e= C
:\U
sers
\bra
m\D
eskt
op\M
atla
b sc
ript
s\A
fstu
dere
n\be
ste\
Alle
_mod
elle
n_m
et_S
TAN
TO
Nco
olin
g\U
_GR
AZ
ALL
UP
GR
AD
ES
150
0C\U
GR
AZ
1500
_afb
lijve
n.tf
x
bar
kJ
/kg
C
kg/s
Gro
ss p
ower
3107
65 k
WG
ross
ele
ctri
c ef
ficie
ncy(
LHV
)73
,63
%N
et f
uel i
nput
(LH
V)
4220
73 k
W
10
41
,73
66
75
97
97
,66
12
41
,7-1
9,8
11
51
9,8
4
13
41
,71
19
92
41
52
,5
6
20
04
59
,71
06
,16
4,1
9
18
17
94
0,6
50
8,1
45
,68
33
16
,63
19
43
72
,64
5,6
8
35
1,1
11
49
,81
11
,21
41
,3
38
1,1
11
49
,81
11
,24
5,6
8
39
19
3,7
45
9,4
10
6,2
64
,19
21
1,1
12
69
7,3
11
1,1
1,6
89
27
1,1
12
69
7,3
11
1,1
95
,58
19
17
62
71
23
70
,56
4,1
8
7
1,1
46
56
,13
62
,81
41
,3
4
1,1
14
29
,91
02
,56
4,1
9
46
1,0
74
29
,91
01
,56
4,1
9
47
1,0
81
50
,31
11
,24
5,6
8
11
18
7,6
15
74
,33
39
,86
4,1
9
52
1,1
71
07
8,2
56
3,2
14
1,3
40
44
,23
35
55
54
9,6
16
,68
15
41
,73
89
76
96
,61
6,7
9
14
40
34
00
14
99
,91
20
62
41
,73
89
76
96
,61
1,5
3
63
41
,73
89
76
96
,65
,26
5
57
41
,73
89
76
96
,62
,63
3
58
41
,73
89
76
96
,62
,63
3
64
40
35
55
54
7,9
1,9
7
37
41
,21
19
92
41
51
,01
5
43
15
,64
-13
,15
15
8,0
6
53
17
0,4
40
82
80
06
4,1
8
66
15
34
00
14
99
,91
33
71
15
35
55
53
7,2
3,4
77
3
0,0
25
22
36
21
,08
86
,66 2
0
29
8,6
52
3,5
91
,17
23
0,0
25
88
,43
21
,08
86
,66
24
23
17
,57
5,8
25
9,7
8
25
0,8
39
1,6
93
,49
1,3
53
45
0,5
34
0,5
81
,32
1,3
66
72
1,2
21
34
0,6
81
,33
1,3
66
75
0,3
25
11
69
,19
1,1
7
76
1,1
12
69
7,3
11
1,1
93
,89
82
0,3
25
11
69
,18
6,6
6
83
0,5
25
79
,38
1,3
21
,36
6
84
29
8,6
52
3,5
59
,78
85
0,3
25
11
69
,14
,51
86
0,8
26
47
,49
3,4
91
,35
3
87
0,8
31
9,6
76
,34
62
,5
88
0,5
25
79
,38
1,3
21
,36
6
89
22
66
,36
3,6
59
,78
91
0,3
28
9,2
69
,14
,51
92
1,1
13
68
,68
7,9
96
2,5
49
41
,73
89
76
96
,60
,91
67
95
41
,73
89
76
96
,60
,91
67
50
44
,23
35
55
54
9,6
16
,65
98
2,8
64
22
11
,81
04
7,7
13
9,9
99
15
35
55
53
7,2
3,4
77
68
1,2
17
50
,18
58
,21
41
,3
10
3
44
,23
35
55
54
9,6
1,8
33
10
4
2,8
64
35
55
53
1,9
0,6
55
71
05
2,8
64
35
55
53
1,9
0,6
55
71
06
44
,23
35
55
54
9,6
3,1
45
60
41
,73
89
76
96
,62
,42
461
41
,73
89
76
96
,62
,42
4
10
0
44
,23
35
55
54
9,6
9,6
95
10
8
44
,23
35
55
54
9,6
4,8
48
11
1
44
,23
35
55
54
9,6
4,8
48
96
41
,73
89
76
96
,62
,42
4
11
2
41
,73
89
76
96
,62
,42
4
11
3
41
,73
89
76
96
,66
,68
1
11
4
41
,73
89
76
96
,61
,83
3
67
15
,64
26
70
12
28
12
3,9
11
5
15
,64
26
96
,71
23
8,2
12
1,9 16
44
,23
35
55
54
9,6
1,9
7
11
6
44
,23
35
55
54
9,6
9,2
05
30
44
,23
35
55
54
9,6
3,9
41
17
44
,23
35
55
54
9,6
5,2
65
8
44
,23
35
55
54
9,6
45
,68
29
44
,23
35
55
54
9,6
29
69
44
,23
35
55
54
9,6
29
44
18
1,7
25
02
,83
57
,86
4,1
9
11
8
18
1,7
25
02
,83
57
,86
4,1
8
11
9
18
1,7
25
02
,83
57
,80
,00
8
12
0
18
1,7
25
02
,83
57
,80
,00
8
12
1
18
1,7
25
02
,83
57
,80
,00
41
22
17
0,4
41
91
84
3,2
64
,18
12
3
41
,73
63
55
83
,36
4,1
9
12
4
18
1,7
25
02
,83
57
,80
,00
4
2
7
14
HPT
19
17
13
23
2425
26
28
15
C1
31
C2
3
34
35
10
29
37
30
38
39
43
44
12 HTT
2
18
48 HTT
111
16
436
46
45
4727
4950
51
52 A B
53
40
5
8
LPT
b
19
20
21
LPT
a
22
32
54
55
5657
59
60
LPT
a
6162
LPT
a
6364
65 66
67
6869
6
HTT
3
3358
42
70
71
7273
74
75
76
HTT
2
77
78
79
80
81
41
82
83 84
85
86
B.7 U-Graz-1500C cycle Thermoflex model
74
TH
ER
MO
FLE
X V
ersi
on 2
7.0
Rev
isio
n: M
arch
11,
201
9
bram
T
U D
elft
She
et 1
2614
02-
19-2
020
17:3
7:42
fil
e= C
:\U
sers
\bra
m\D
eskt
op\M
atla
b sc
ript
s\A
fstu
dere
n\be
ste\
Alle
_mod
elle
n_m
et_S
TAN
TO
Nco
olin
g\U
_GR
AZ
ALL
UP
GR
170
0C\U
GR
AZ
1700
_5.t
fx
bar
kJ
/kg
C
kg/s
Gro
ss p
ower
3226
73 k
WG
ross
ele
ctri
c ef
ficie
ncy(
LHV
)74
,86
%N
et f
uel i
nput
(LH
V)
4310
22 k
W
10
41
,73
90
97
01
,48
0,8
4
12
41
,7-1
9,8
11
51
9,8
4
13
41
,71
19
92
41
52
,5
6
20
04
59
,71
06
,16
2,6
6
18
17
94
0,8
50
8,2
33
,51
33
16
,63
19
43
72
,63
3,5
1
35
1,1
11
49
,81
11
,21
28
,2
38
1,1
11
49
,81
11
,23
3,5
1
39
19
3,7
45
9,4
10
6,2
62
,66
21
1,1
12
69
7,3
11
1,1
1,6
5
27
1,1
12
69
7,3
11
1,1
94
,74
19
17
62
66
0,1
36
4,9
62
,63
7
1,1
46
56
,13
62
,81
28
,2
4
1,1
14
29
,91
02
,56
2,6
6
46
1,0
74
29
,91
01
,56
2,6
6
47
1,0
81
50
,41
11
,33
3,5
1
11
18
7,6
14
95
,83
28
62
,66
52
1,1
71
14
8,2
59
5,2
12
8,2
14
40
39
61
16
99
,91
03
,2
62
41
,73
92
57
08
,41
4,9
5
63
41
,73
92
57
08
,56
,15
7
57
41
,73
92
57
08
,53
,07
8
58
41
,73
92
57
08
,53
,07
8
64
40
35
83
56
02
,30
6
37
41
,21
19
92
41
51
,09
43
15
,64
-13
,15
15
8,6
5
53
17
0,4
40
82
80
06
2,6
3
66
15
39
60
16
99
,91
17
,5
71
15
35
83
54
9,9
4,3
22
3
0,0
25
22
36
21
,08
86
,02 2
0
29
8,5
23
,46
90
,43
23
0,0
25
88
,43
21
,08
86
,02
24
23
17
,57
5,8
25
8,3
5
25
0,8
39
1,6
93
,49
1,3
22
45
0,5
34
0,5
81
,32
1,3
34
72
1,2
21
34
0,6
81
,33
1,3
34
75
0,3
25
11
69
,19
0,4
3
76
1,1
12
69
7,3
11
1,1
93
,09
82
0,3
25
11
69
,18
6,0
2
83
0,5
25
79
,38
1,3
21
,33
4
84
29
8,5
23
,46
58
,35
85
0,3
25
11
69
,14
,40
8
86
0,8
26
47
,49
3,4
91
,32
2
87
0,8
31
9,6
76
,34
61
,01
88
0,5
25
79
,38
1,3
21
,33
4
89
22
66
,36
3,6
58
,35
91
0,3
28
9,2
69
,14
,40
8
92
1,1
13
68
,68
7,9
96
1,0
1
49
41
,73
92
57
08
,51
,44
8
95
41
,73
92
57
08
,51
,44
8
50
44
,23
35
83
56
1,7
20
,7
98
2,8
64
25
77
,21
19
11
26
,2
99
15
35
83
54
9,9
4,3
22
68
1,2
20
51
,29
82
,51
28
,2
10
3
44
,23
35
83
56
1,7
2,8
95
10
4
2,8
64
35
83
54
4,7
1,0
35
10
5
2,8
64
35
83
54
4,7
1,0
35
10
6
44
,23
35
83
56
1,7
4,9
66
60
41
,73
92
57
08
,53
,01
361
41
,73
92
57
08
,53
,01
3
10
0
44
,23
35
83
56
1,7
12
,05
10
8
44
,23
35
83
56
1,7
6,0
26
11
1
44
,23
35
83
56
1,7
6,0
26
96
41
,73
92
57
08
,53
,01
3
11
2
41
,73
92
57
08
,53
,01
3
11
3
41
,73
92
57
08
,48
,92
1
11
4
41
,73
92
57
08
,52
,89
5
67
15
,64
31
09
13
93
,21
07
,8
11
5
15
,64
31
55
14
09
,91
05
,5 16
44
,23
35
83
56
1,7
2,3
06
11
6
44
,23
35
83
56
1,7
10
,77
30
44
,23
35
83
56
1,7
4,6
12
11
7
44
,23
35
83
56
1,7
6,1
57
84
4,2
33
55
55
49
,63
3,5
1
69
44
,23
35
83
56
1,7
36
,43
44
18
1,7
25
02
,83
57
,86
2,6
6
11
8
18
1,7
25
02
,83
57
,86
2,6
3
11
9
18
1,7
25
02
,83
57
,80
,02
8
12
0
18
1,7
25
02
,83
57
,80
,02
8
12
1
18
1,7
25
02
,83
57
,80
,01
41
22
17
0,4
45
09
96
7,5
62
,63
12
4
18
1,7
25
02
,83
57
,80
,01
4
12
3
44
,23
39
03
69
9,6
2,9
17
12
5
44
,23
39
03
69
9,6
59
,74
2
7
14
HPT
19
13
23
2425
26
28
15
C1
31
C2
3
34
35
10
29
37
30
38
39
43
44
12 HTT
2
18
48 HTT
1
11
16
436
46
45
4727
4950
51
52 A B
53
40
5
8
LPT
b
19
20
21
LPT
a
22
32
54
55
5657
59
60
LPT
a
6162
LPT
a
6364
65 66
67
6869
6
HTT
3
3358
42
70
71
7273
74
75
76
HTT
2
77
78
79
80
81
41
82
83 84
85
86
17
87
B.8 U-Graz cycle Thermoflex model
75
C Thermoflex models with FC
The schemes with the FC’s operate with a ”blackbox” around the FC part, this part is calculated inMATLAB, therefore only the turbine cycle power is displayed. Some trickery is applied to calculatedto model the streams going through this part. The first combustor of the cycle acts as a FC, howeveronly 35% of the energy is transferred to heat in the gasses going through. Therefore, the heat adderdevices (displayed as Q+) subtract the surplus of added heat from the working fluids. Therefore thefirst combustor and the heat adder devices can be seen as ”blackbox” items calculated in separateMATLAB script. The amount of oxygen recirculation, steam addition for an amount of fuel utilization iscalculated per FC in MATLAB. For a detailed explanation of this integration and for the code email theauthor.
The main Thermoflex models are depicted in subsection C.1-C.5. The stage by stage Thermoflexcooling model of the U-Graz-3FC-OX cycle, is displayed in C.5.1. This cycle is hybrid cooled. The MAT-LAB code accompanied to calculate the stage by stage model cooling mass is displayed in appendixD.
76
TH
ER
MO
FLE
X V
ersi
on 2
7.0
Rev
isio
n: M
arch
11,
201
9
bram
T
U D
elft
She
et 1
2614
02-
19-2
020
16:2
7:58
fil
e= C
:\U
sers
\bra
m\D
eskt
op\M
atla
b sc
ript
s\A
fstu
dere
n\be
ste\
Alle
_mod
elle
n_m
et_S
TAN
TO
Nco
olin
g\Z
_FU
ELC
ELL
_Gra
zcyc
le\1
FC
_Ste
am\F
C_1
_Gra
z_w
ater
_Sta
nton
_750
C.t
fx
bar
kJ
/kg
C
kg/s
Gro
ss p
ower
with
out
FC
po
wer
18
506
2 kW
839
,89
305
833
5,8
41,7
2
31,
1180
,22
19,1
158
,68
620
045
9,7
106,
141
,72
10,
025
2295
,721
,08
58,6
8
24 321
,32
5,00
230
99
25 363
,28
15,0
230
99
221,
1180
,22
19,1
136
,34
1817
988
,452
9,9
55,7
2
917
0,4
3444
555,
541
,72
3316
,631
9437
2,6
55,7
2
351,
1124
6,9
159,
611
9,8
361,
1124
6,9
159,
664
,06
381,
1124
6,9
159,
655
,72
3919
3,7
555,
212
941
,72
201,
1127
94,4
159,
358
,68
231,
1180
,22
19,1
122
,34
211,
1127
94,
415
9,3
5,37
4
4039
,89
511,
733
5,8
7,36
2
271,
1127
94,
415
9,3
64,0
6
1917
629
59,2
412,
541
,72
71,
1465
6,1
362,
811
9,8
450,
025
80,0
619
,158
,68
461,
0742
9,9
101,
541
,72
471,
0817
5,4
123,
755
,72
3217
646,
737
2,8
55,7
2
1118
7,6
173
0,3
357,
841
,72
4418
1,7
250
2,8
357,
841
,72
1438
,27
3400
1500
99,7
4
5015
2479
,411
54,5
112,
4
521,
1792
5,2
492
119,
8
4238
,27
3058
334,
212
,68
5415
3058
308,
86,
342
492,
862
1524
,876
3,1
119,
8
5615
291
,921
6,5
3,68
1
3442
,12
3535
540,
155
,72
1639
,89
2881
,727
3,1
43,2
158
41,7
119
924
152,
5
6239
,89
3058
335,
821
,67
6542
,12
3535
540,
121
,54
6640
,69
2704
,425
1,4
21,5
4
6840
,68
1276
86
550
0,48
29
6939
,89
1955
,310
88,2
54,5
1
7039
,89
1161
,470
054
,51
5740
,68
1276
86
550
2,01
7
6039
,89
1299
16
700
2,01
7
1341
,71
-19,
8115
19,8
4
6741
,712
708
350
92,
512
40,6
935
6055
034
,19
531,
293
120
362
0,1
119
,8
101,
210
9457
0,5
119
,8
591,
2311
83,5
611,
311
9,8
611,
261
119
6,1
617
119,
8
6342
,12
3535
540,
134
,19
6440
,68
1276
86
550
2,5
7140
,69
520,
355
019
,84
2
5
LPT
7
11
14
HPT
1
17
13
19
20
2122
4
HT
T-1
23
2425
6
12
HT
T-2
18
26
28
15
C1
31
C2
33
HP
T m
ini
3
34
36
16
35
10
29
3237
30
38
39
8
42
HT
T-3
43
44
40
45
41
27
46
62
53 A B
48Q
+
51
52
54Q
-47 A B
55 A B
56 A B
C.1 Graz-1FC-Steam cycle Thermoflex model
77
TH
ER
MO
FLE
X V
ersi
on 2
7.0
Rev
isio
n: M
arch
11,
201
9
bram
T
U D
elft
She
et 1
2614
02-
19-2
020
16:3
2:16
fil
e= C
:\U
sers
\bra
m\D
eskt
op\M
atla
b sc
ript
s\A
fstu
dere
n\be
ste\
Alle
_mod
elle
n_m
et_S
TAN
TO
Nco
olin
g\Z
_FU
ELC
ELL
_Gra
zcyc
le\3
FC
_Ste
am\O
_GR
AZ
_3F
C_W
AT
ER
_Sta
nton
_750
C3.
tfx
bar
kJ
/kg
C
kg/s
Gro
ss p
ower
with
out F
C p
ower
13
4921
kW
838
,39
2917
,428
2,6
26,8
2
31,
1180
,22
19,1
145
,75
6
200
459,
710
6,1
26,8
2
1
0,02
523
20,4
21,0
845
,75
24 321
,32
5,00
224
42,8
25 363
,28
15,0
224
42,8
221,
1180
,22
19,1
123
,41
18
1710
65,6
564,
836
,08
917
0,4
3265
494,
226
,82
3316
,631
9437
2,6
36,0
8
351,
1128
6,4
179,
585
,24
381,
1128
6,4
179,
536
,08
3919
3,7
555,
212
926
,82
20
1,11
2833
,917
9,3
45,7
5
231,
1180
,22
19,1
122
,34
211,
1128
33,9
179,
33,
405
4038
,39
369,
228
2,6
5,50
7
27
1,11
2833
,917
9,3
49,1
6
1917
630
6643
8,4
26,8
2
71,
1465
6,1
362,
885
,24
450,
025
80,0
619
,145
,75
461,
0742
9,9
101,
526
,82
47
1,08
215,
414
3,7
36,0
8
3217
646,
737
2,8
36,0
8
11
187,
617
30,3
357,
826
,82
4418
1,7
2502
,835
7,8
26,8
2
1436
,83
3400
1499
,972
,54
5015
2544
,311
79,6
79,7
3
521,
1789
9,1
479,
885
,24
4236
,83
2917
,428
0,5
7,18
854
1529
17,4
247,
23,
594
492,
862
1564
,378
0,1
85,2
4
562,
862
267,
717
5,5
2,75
4
3442
,12
3535
540,
136
,08
16
38,3
925
48,8
247,
916
,41
58
41,7
1199
2415
2,5
62
38,3
929
17,4
282,
614
,12
6542
,12
3535
540,
12,
289
6640
,727
4,9
64,8
82,
289
68
40,6
812
7686
550
1,45
6938
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4170
1902
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70
38,3
919
20,8
1000
55,0
8
5740
,68
1276
8655
01,
05
6038
,38
1344
9110
001,
05
13
41,7
1-1
9,81
1519
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67
41,7
1229
1022
2,3
2,5
1240
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6055
033
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53
1,29
312
37,1
635,
485
,24
10
1,2
961,
750
9,2
85,2
4
59
1,23
1087
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7,4
85,2
4
611,
261
1227
,563
1,1
85,2
4
63
42,1
235
3554
0,1
33,7
9
6440
,68
1276
8655
02,
5
7140
,752
0,3
550
19,8
4
2
5
LPT
7
11
14
HPT
1
17
13
19
20
2122
4
HT
T-1
23
2425
6
12
HT
T-2
18
26
28
15
C1
31
C2
33
HP
T m
ini
3
34
36
16
35
10
29
3237
30
38
39
8
42
HT
T-3
43
44
40
45
41
27
46
62
53 A B
48Q
+
51
52
54Q
-47 A B
55 A B
56 A B
C.2 Graz-3FC-Steam cycle Thermoflex model
78
TH
ER
MO
FLE
X V
ersi
on 2
7.0
Rev
isio
n: M
arch
11,
201
9
bram
T
U D
elft
She
et 1
2614
02-
19-2
020
17:3
4:26
fil
e= C
:\U
sers
\bra
m\D
eskt
op\M
atla
b sc
ript
s\A
fstu
dere
n\be
ste\
Alle
_mod
elle
n_m
et_S
TAN
TO
Nco
olin
g\Z
_FU
ELC
ELL
_Gra
zcyc
le\1
FC
_OX
_0_4
83\1
FC
_OX
_0_4
83_S
TA
NT
ON
_750
C_m
etal
2.tf
x
bar
kJ
/kg
C
kg/s
Gro
ss p
ower
with
out
FC
pow
er18
5903
kW
13
39,8
912
9916
700
2,01
7
839
,930
22
322,
241
,08
16
39,9
302
232
2,2
21,9
1
3
1,11
80,
2219
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58,
14
6
200
459,
710
6,1
41,0
8
1
0,02
523
00,4
21,0
85
8,14
24 321
,32
5,00
230
76
25 363
,28
15,0
230
76
28
39,9
302
232
2,2
7,00
7
22
1,11
80,
2219
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35,
8
18
171
007,
353
8,5
56,7
3
9
170,
433
9253
7,1
41,0
8
33
16,6
319
437
2,6
56,7
3
35
1,11
254
,416
3,3
120,
1
381,
112
54,4
163,
356
,73
39
193,
755
5,2
129
41,0
8
201,
112
801,
816
3,1
58,1
4
23
1,11
80,
2219
,11
22,
34
21
1,11
280
1,8
163,
15,
277
40
39,9
475
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2,2
7,00
7
27
1,11
280
1,8
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163
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176
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8
7
1,14
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1
45
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4
46
1,07
429
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1,5
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8
47
1,08
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3
1118
7,6
1730
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7,8
41,0
8
44
181,
725
02,8
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841
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14
38,2
73
400
1499
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01
50
152
488,
611
58,1
113
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52
1,17
920
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1
42
38,2
730
2232
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38,2
73
022
320,
46,
081
37
152
65,2
206,
67,
007
49
2,86
315
34,6
767,
412
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56
152
65,2
206,
63,
503
58
40,6
81
2768
655
00,
483
59
40,6
952
0,2
550
3,83
360
40,6
95
20,2
550
3,83
3
61
39,9
332
014
70,8
4,3
16
63
40,6
812
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7
67
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68
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69
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9
71
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72
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39,9
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6
12
39,9
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2
64
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700
16,0
1
74
38,9
253
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673
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6640
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37,9
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9
78
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337
746
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4
10
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452
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56,7
3
34
1,23
119
2,7
615,
412
0,1
53
1,2
1054
552,
112
0,1
2
5
LPT
7
11
14
HPT
17
13
19
20
2122
4
HT
T-1
23
2425
6
12
HT
T-2
18
26
28
15
C1
31
C2
33
HP
T m
ini
3
34
36
16
35
10
29
3237
30
38
39
8
42
HT
T-3
43
44
40
45
41
27
1
9
49Q
+
50Q
+
51
52
53
54
55 A B
56Q
-
57
58 A B
59Q
60
61
62Q
-
46
68
47
A
B
C.3 Graz-1FC-OX cycle Thermoflex model
79
TH
ER
MO
FLE
X V
ersi
on 2
7.0
Rev
isio
n: M
arch
11,
201
9
bram
T
U D
elft
She
et 1
2614
02-
19-2
020
16:3
0:25
fil
e= C
:\U
sers
\bra
m\D
eskt
op\M
atla
b sc
ript
s\A
fstu
dere
n\be
ste\
Alle
_mod
elle
n_m
et_S
TAN
TO
Nco
olin
g\Z
_FU
ELC
ELL
_Gra
zcyc
le\3
FC
_OX
_1_4
5\3F
C_O
X_1
_45_
STA
NT
ON
_750
C_m
etal
T.tf
x
bar
kJ
/kg
C
kg/s
Gro
ss p
ower
with
out
FC
pow
er
1344
21 k
W
13
38,3
813
4491
1000
1,0
5
8
39,7
33
113
357,
627
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1639
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3113
357,
613
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3
1,11
80,
2219
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46,
53
6
200
459,
710
6,1
27,7
8
1
0,02
522
93,8
21,0
84
6,53
24 321
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5,00
224
55
25 363
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15,0
224
55
2839
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3113
357,
65,
375
221,
118
0,22
19,1
12
4,19
18
179
44,5
509,
929
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9
170,
435
1558
1,2
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8
33
16,6
319
437
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4
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4
35
1,11
243
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879
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36
1,11
243
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850
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38
1,11
243
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829
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39
193,
755
5,2
129
27,7
8
20
1,11
279
1,8
158
46,5
3
23
1,11
80,
2219
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22,
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21
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7
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11
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7
58
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81
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2
5
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7
11
14
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17
13
19
20
2122
4
HT
T-1
23
2425
6
12
HT
T-2
18
26
28
15
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3
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52
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54
55 A B
56Q
-
57
58 A B
59Q
60
61
62Q
+
46
68
47
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B
C.4 Graz-3FC-OX cycle Thermoflex model
80
TH
ER
MO
FLE
X V
ersi
on 2
7.0
Rev
isio
n: M
arch
11,
201
9
bram
T
U D
elft
She
et 1
2614
02-
19-2
020
17:3
2:19
fil
e= C
:\U
sers
\bra
m\D
eskt
op\M
atla
b sc
ript
s\A
fstu
dere
n\be
ste\
Alle
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elle
n_m
et_S
TAN
TO
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olin
g\Z
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ELC
ELL
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zcyc
le\U
_Gra
z_3F
C_1
500C
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\UG
RA
Z_3
FC
1500
_2.t
fx
bar
kJ
/kg
C
kg/s
Gro
ss p
ower
1383
33 k
W
10
38
,39
39
01
69
7,3
39
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62
07
46
0,8
10
6,2
27
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18
17
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25
08
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33
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03
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35
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5
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4
38
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50
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11
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7
39
20
0,5
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10
6,3
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51
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11
19
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31
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5
15
38
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53
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22
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6162
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6364
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71
72
73
74
75
76
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77
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79
80
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85
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87
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98
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101
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102
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105
106
107
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90
9
C.5 U-Graz-3FC-OX cycle Thermoflex model
81
TH
ER
MO
FLE
X V
ersi
on 2
7.0
Rev
isio
n: M
arch
11,
201
9
bram
T
U D
elft
She
et 1
2614
02-
28-2
020
16:1
8:51
fil
e= C
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ript
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slag
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bar
kJ
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31
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81
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38
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22
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56
61
72
73
86
88
94
18
96 100
C.5.1 U-Graz-3FC-OX cycle Thermoflex stage by stage cooling model (hybrid cooling)
82
D MATLAB code
D.1 Scripts for calculating the cooling needs per turbine stage U-Graz-3FC-OXcycle(which uses hybrid cooling)
The cooling per turbine stage for the U-Graz-3FC-OX cycle is calculated using 2 scripts: The mainscript and a function file.
The main file calculates the cooling needs per turbine stage, using the temperatures from the de-tailed stage by stage cooling model, which is depicted in subsection C.5.1. The function file retrievesthe heat capacity, from the Fluid-prop database.
D.1.1 Main script, HTT cooling of stages
clcclear all
K=273.15;St=0.00067;%stanton *FOBSt film=0.00082;%stanton *FOB
Bi tbc=0.9;Ag Aw=2*6; %%%%*2 is truukje zodat je alleen stator berkent maar ook rotor meeneenmt
CoefficientFilm=Ag Aw*St film/2*1/(1+Bi tbc);CoefficientCLSC=Ag Aw*St/2*1/(1+Bi tbc); % is in literatuur standaard 0.012
Tw=1061;%1150Twrot=1061; %1150Tce=971.6;Tci=824.1;Pci=40.72;%barCPc=cpverkrijg(Pci,Tci−K);
Tcifilm=822.5;CPcfilm=cpverkrijg(Pci,Tcifilm−K);Tcifilm HTT2=813.3;Tcifilm HTT3=808;TciHPT=630.9;P HPT=181.7;mdotHPT=26.61;CPc HPT=cpverkrijg(P HPT,TciHPT−K);
CF=1/(1+Bi tbc);%% elke ronde aanpassen%% HT1mdotg1ja=45.27;Tg1=1773;Tg2=1640.8;
83
%%%%%%%%%%%%%%%%%%%%%%%% HT2mdotg3ja=54.32;Tg3=1773;Tg4=1645.3;Tg5=1527.9;Tg6=1419.8;%% HT3Tg7=1319.1;Tg8=1220.8;% bar en K
%% stator 1+rotor CLSCmdotg1=mdotg1ja;Tg=Tg1;Pg=36.82;Cpg=cpverkrijg(Pg,Tg−K);
mdotc1 clsc=CF*Cpg/CPc*St*Ag Aw*(Tg−Tw)/(Tce−Tci)*mdotg1;eps1=(Tg−Tw)/(Tg−Tcifilm);mdotc1 film=CF*Cpg/CPcfilm*St film*Ag Aw*(eps1/(1−eps1))*mdotg1;
%% stator 2+rotor CLSCmdotg2=mdotg1+mdotc1 film;Tg=Tg2;Pg=23.5;Cpg=cpverkrijg(Pg,Tg−K);
mdotc2 clsc=CF*Cpg/CPc*St*Ag Aw*(Tg−Tw)/(Tce−Tci)*mdotg2;eps1=(Tg−Tw)/(Tg−Tcifilm);mdotc2 film=CF*Cpg/CPcfilm*St film*Ag Aw*(eps1/(1−eps1))*mdotg2;
mdottotalcoolingCLSC HTT1=mdotc1 clsc+mdotc2 clsc;mdottotalcoolingfilm HTT1=mdotc1 film+mdotc2 film;%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% HTT−2Tcifilm=Tcifilm HTT2;%% stator 3+rotor CLSCmdotg3=mdotg3ja;Tg=Tg3;%Pg=15;Cpg=cpverkrijg(Pg,Tg−K);
mdotc3 clsc=CF*Cpg/CPc*St*Ag Aw*(Tg−Tw)/(Tce−Tci)*mdotg3;eps1=(Tg−Tw)/(Tg−Tcifilm);mdotc3 film=CF*Cpg/CPcfilm*St film*Ag Aw*(eps1/(1−eps1))*mdotg3;
%% stator 4+rotor CLSCmdotg4=mdotg3+mdotc3 film;Tg=Tg4;Pg=9.914;Cpg=cpverkrijg(Pg,Tg−K);
mdotc4 clsc=CF*Cpg/CPc*St*Ag Aw*(Tg−Tw)/(Tce−Tci)*mdotg4;eps1=(Tg−Tw)/(Tg−Tcifilm);
84
mdotc4 film=CF*Cpg/CPcfilm*St film*Ag Aw*(eps1/(1−eps1))*mdotg4;
%% stator 5+rotor CLSCmdotg5=mdotg4+mdotc4 film;Tg=Tg5;Pg=6.553;Cpg=cpverkrijg(Pg,Tg−K);
mdotc5 clsc=CF*Cpg/CPc*St*Ag Aw*(Tg−Tw)/(Tce−Tci)*mdotg5;eps1=(Tg−Tw)/(Tg−Tcifilm);mdotc5 film=CF*Cpg/CPcfilm*St film*Ag Aw*(eps1/(1−eps1))*mdotg5;
%% stator 6+rotor CLSCmdotg6=mdotg5+mdotc5 film;Tg=Tg6;% bar en KPg=4.331;Cpg=cpverkrijg(Pg,Tg−K);
mdotc6 clsc=CF*Cpg/CPc*St*Ag Aw*(Tg−Tw)/(Tce−Tci)*mdotg6;eps1=(Tg−Tw)/(Tg−Tcifilm);mdotc6 film=CF*Cpg/CPcfilm*St film*Ag Aw*(eps1/(1−eps1))*mdotg6;
mdottotalcoolingCLSC HTT2=mdotc3 clsc+mdotc4 clsc+mdotc5 clsc+mdotc6 clsc;mdottotalcoolingfilm HTT2=mdotc3 film+mdotc4 film+mdotc5 film+mdotc6 film;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %% Film part Rankine HTT 2 is the same for this cycle as HTT−1 thus keep commented% Tce=868;% Tci=728;% Tcifilm=648;% Pc=70;% CPc=cpverkrijg(Pc,Tci−K);% Pcfilm=7.5;% CPcfilm=cpverkrijg(Pcfilm,Tci−K);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% HTT−3Tcifilm=Tcifilm HTT3;%% stator 7+rotormdotg7=mdotg6+mdotc6 film;Tg=Tg7;% bar en KPg=2.863;Cpg=cpverkrijg(Pg,Tg−K);
mdotc7 clsc=CF*Cpg/CPc*St*Ag Aw*(Tg−Tw)/(Tce−Tci)*mdotg7;eps1=(Tg−Tw)/(Tg−Tcifilm);mdotc7 film=CF*Cpg/CPcfilm*St film*Ag Aw*(eps1/(1−eps1))*mdotg7;
if mdotc7 clsc <= 0mdotc7 clsc=0endif mdotc7 film <= 0
85
mdotc7 film=0end%% stator 8+rotormdotg8=mdotg7+mdotc7 film;Tg=Tg8;Pg=1.854;Cpg=cpverkrijg(Pg,Tg−K);
mdotc8 clsc=CF*Cpg/CPc*St*Ag Aw*(Tg−Tw)/(Tce−Tci)*mdotg8;eps1=(Tg−Tw)/(Tg−Tcifilm);mdotc8 film=CF*Cpg/CPcfilm*St film*Ag Aw*(eps1/(1−eps1))*mdotg8;if mdotc8 clsc <= 0mdotc8 clsc=0;endif mdotc8 film <= 0mdotc8 film=0;end
mdottotalcoolingCLSC HTT3=mdotc7 clsc+mdotc8 clsc;mdottotalcoolingfilm HTT3=mdotc7 film+mdotc8 film;%% HPT COOLING ENKEL OPENLOOPSt filmHPT=0.00704;%0.8%fictive value for CLSCStantonfHPT=St filmHPT;%real stanton number to be able to calc Bi tbcmdotg=mdotHPT;Tg1=1116;%40barP1=170.4;P2=181.7;Cpg HPT=2.55;%REFPROP P170.4 T1116 %THis is supecritical dus dit kannie cpverkrijg(P2,Tg1−K);eps1=(Tg1−Tw)/(Tg1−TciHPT);mdotcHPT=CF*Cpg HPT/CPc HPT*St film*Ag Aw*(eps1/(1−eps1))*mdotg
%% Results knallen
mdotCLSCTOTAL=mdottotalcoolingCLSC HTT1+mdottotalcoolingCLSC HTT2+mdottotalcoolingCLSC HTT3;mdotfilmTOTAL=mdottotalcoolingfilm HTT1+mdottotalcoolingfilm HTT2+mdottotalcoolingfilm HTT3;coolingtotal=mdotfilmTOTAL+mdotCLSCTOTAL
name cooling='HTT1 CLSC';'HTT2 CLSC';'HTT3 CLSC';'HTT1 FILM';'HTT2 FILM';'HTT3 FILM';'CLSC total';'Film total';
Cooling tabel=[mdottotalcoolingCLSC HTT1;mdottotalcoolingCLSC HTT2;mdottotalcoolingCLSC HTT3;mdottotalcoolingfilm HTT1;mdottotalcoolingfilm HTT2;mdottotalcoolingfilm HTT3;mdotCLSCTOTAL;mdotfilmTOTAL];
Cooling gewild=[0;0;0;0;0;0;0;0];TabUITGFC=table(name cooling,Cooling tabel,Cooling gewild)
%% fraction of valvesFraction Htt1=(mdottotalcoolingCLSC HTT1+mdottotalcoolingfilm HTT1)/coolingtotal;Fraction Htt2=(mdottotalcoolingCLSC HTT2+mdottotalcoolingfilm HTT2)/coolingtotal;
Fraction Htt1 film=mdottotalcoolingfilm HTT1/(mdottotalcoolingCLSC HTT1+mdottotalcoolingfilm HTT1);
Fraction Htt2 film=mdottotalcoolingfilm HTT2/(mdottotalcoolingCLSC HTT2+mdottotalcoolingfilm HTT2);
Fraction Htt3 film=mdottotalcoolingfilm HTT3/(mdottotalcoolingCLSC HTT3+mdottotalcoolingfilm HTT3);
86
name fractions='HTT1';'HTT2';'HTT1film';'HTT2film';'HTT3film';Fractions=[Fraction Htt1;Fraction Htt2;Fraction Htt1 film;Fraction Htt2 film;
Fraction Htt3 film];tablefrac=table(name fractions,Fractions)
D.1.2 Function file, HTT cooling of stages
function [cp] = mywaarde(P,T)Cmp = 'water';FP = actxserver ('FluidProp.FluidProp');Model = 'IF97';ErrorMsg = invoke(FP,'SetFluid M',Model,1,Cmp,[1,0]);
[Enthalpy,ErrorMsg] = invoke(FP,'Enthalpy','PT', P, T);[cp,ErrorMsg] = invoke(FP,'HeatCapP','PT', P, T);% SpecVolumeEnthalpy;cp;end
87
D.2 Scripts for calculating the FC parametersThe FC parameters are calculated using 3 scripts: The main script, the first function file and the secondfunction file.
The FC script calculates the fuel utilisation and other electrochemical results per FC, using a cer-tain amount of oxygen recirculation/steam cathode cooling as input for the calculation. Furthermore, itmakes the fuel cell figures (figure 31 and 32) displayed in section 6.3 of this thesis.
D.2.1 Main script set to retrieve 3FC-OX data, needed to calculate the FC parameters
clear allclcclose all%% welke plot wil je zienFCwanttoplot=1;%FC 1 2 of 3%% TFLEX FUELCELL values afbijvenceffi=0.65;LHV H2=120067.5;%KJ/kgheatloss=0.02;%heatloss of LHVP1=39.9;%bar exit FC1P2=39.2;%bar exit FC 2P3=38.4;%bar
%% cycle kiezen 5 is 3FC−OX 6is 3FC−steamcycle=5;
%% 3FC−OXif cycle==5 % 3 FC−OXfuelin=2.5;%kg/soxin=93.13;%19.84;%kg/sfuelusedtot=1.45;%kg/s eerste schattingsteamin=0;%% 3FC Steamelseif cycle==6 % 3 FC steamfuelin=2.5;%kg/soxin=19.84;fuelusedtot=1.45;steamin=33.8;%% 1FC steamelseif cycle==8 % 1FC steam infuelin=2.5;%kg/soxin=19.84;%19.84;%kg/sfuelusedtot=1.45;%kg/s eerste schattingsteamin=34.19;end%%
MH2=2.0156*10ˆ−3;%kg/mol molar massMO2=2*15.999*10ˆ−3;%kg/mol molar massMH2O=18.01528*10ˆ−3;%kg/mol molar massRatioO2 H2=0.5*MO2/MH2;RatioH2O H2=MH2O/MH2;
88
HHV=0;fuel h550=127686.4+HHV;%−LHV H2;%enthalpy Kj/kg at 550cfuel h700=129916.4+HHV;%−LHV H2;%enthalpy Kj/kg at 700cfuel h850=132183+HHV;%−LHV H2;%enthalpy Kj/kgfuel h1000=134491+HHV;%−LHV H2;%enthalpy Kj/kg% fuel h15=119923.5+HHV;%
ox h550=520.26;%enthalpy Kj/kg at 550cox h700=682.05;%enthalpy Kj/kg at 700cox h850=846.98;%enthalpy Kj/kgox h1000=1014.5;%enthalpy Kj/kgox h15=−9.16;%
hvap=2547;%2547;steam h=3558.61−hvap;%enthalpy Kj/kg at 550csteam h700=3905.4−hvap;%enthalpy Kj/kg at 700csteam h850=4261.7−hvap;%enthalpy Kj/kg at 850csteam h1000=4630.62−hvap;%enthalpy Kj/kg at 850c
%% FC's samenaaerror=2;for k=1:100fuelusedtot=fuelusedtot−aaerror/100000;oxuit=oxin−(fuelusedtot)*RatioO2 H2;oxuitmol=oxuit/MO2;steamuit=steamin+fuelusedtot*RatioH2O H2;steamuitmol=steamuit/MH2O;fueluit=fuelin−fuelusedtot;huit=fueluit*fuel h1000+oxuit*ox h1000+steamuit*steam h1000;hin1=fuelin*fuel h550+oxin*ox h550+steamin*steam h;qinall=LHV H2*fuelusedtot;Wfc=effi*qinall;qintot=LHV H2*(1−effi)*fuelusedtot;% aaerrorq=hin1+qintot−huitqloss=heatloss*LHV H2*fuelusedtot;aaerror=hin1−Wfc−huit−qloss;if abs(aaerror) <= 0.00001
breakendend%% FC 1fuelused1=0.1;%kg/saaerror1=2;for k=1:100fuelused1=fuelused1−aaerror1/100000;oxused1=fuelused1*RatioO2 H2;Wfc1=LHV H2*effi*fuelused1;fuelin2=fuelin−fuelused1;oxin2=oxin−oxused1;steamin2=steamin+fuelused1*RatioH2O H2;hin2=fuelin2*fuel h700+oxin2*ox h700+steamin2*steam h700;qloss1=heatloss*LHV H2*fuelused1;aaerror1=hin1−Wfc1−hin2−qloss1;if abs(aaerror1) <= 0.00001
breakend
89
end
%% Fc 2
fuelused2=0.3462;aaerror2=2;for k=1:100fuelused2=fuelused2−aaerror2/100000;oxused2=fuelused2*RatioO2 H2;Wfc2=LHV H2*effi*fuelused2;fuelin3=fuelin2−fuelused2;oxin3=oxin2−oxused2;steamin3=steamin2+fuelused2*RatioH2O H2;hin3=fuelin3*fuel h850+oxin3*ox h850+steamin3*steam h850;qloss2=heatloss*LHV H2*fuelused2;aaerror2=hin2−Wfc2−hin3−qloss2;if abs(aaerror2) <= 0.00001
breakendend
%% FC3fuelused3=fuelusedtot−fuelused2−fuelused1;oxused3=fuelused3*RatioO2 H2;Wfc3=LHV H2*effi*fuelused3;oxuit=oxin−(fuelusedtot)*RatioO2 H2;steamuit=steamin3+fuelused3*RatioH2O H2;fueluit=fuelin−fuelusedtot;%huit=fueluit*fuel h1000+oxuit*ox h1000+steamuit*steam h1000;qloss3=heatloss*LHV H2*fuelused3;aaerror3=hin3−Wfc3−huit−qloss3;
aaerror123=aaerror1+aaerror2+aaerror3;%% ResultsFu1=fuelused1/fuelin;Fu2=fuelused2/fuelin2;Fu3=fuelused3/fuelin3;
x H2 1=1−Fu1;%mol percentage at end fc1x H2O 1=Fu1;%mol percentage at end fc1
x H2 2=1−(fuelused1+fuelused2)/fuelin;%mol percentage at end fc2x H2O 2=(fuelused1+fuelused2)/fuelin;%mol percentage at end fc2
x H2 3=1−(fuelused1+fuelused2+fuelused3)/fuelin;%mol percentage at end fc3x H2O 3=(fuelused1+fuelused2+fuelused3)/fuelin;%mol percentage at end fc3
Oxi1=(oxin2/MO2)/(oxin2/MO2+steamin/MH2O);Oxi2=(oxin3/MO2)/(oxin3/MO2+steamin/MH2O);Oxi3=(oxuit/MO2)/(oxuit/MO2+steamin/MH2O);
%% Functiefile inknallen%operating voltage moet ook meegenomen worden[efficiency FC1,E0 FC1,Enernst FC1,Ecell FC1,Powdens FC1,q FC1,ASR FC1]=
FC mainmodel efficientie input3(P1,Oxi1,x H2 1,x H2O 1,973);
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[efficiency FC2,E0 FC2,Enernst FC2,Ecell FC2,Powdens FC2,q FC2,ASR FC2]=FC mainmodel efficientie input3(P2,Oxi2,x H2 2,x H2O 2,1123);
[efficiency FC3,E0 FC3,Enernst FC3,Ecell FC3,Powdens FC3,q FC3,ASR FC3]=FC mainmodel efficientie input3(P3,Oxi2,x H2 3,x H2O 3,1273);
%% TablesFuelnames='Fuelused FC1';'Fuelused FC2';'Fuelused FC3';'Fuelused total';Fuelvar=[fuelused1;fuelused2;fuelused3;fuelusedtot];Fueltable=table(Fuelnames,Fuelvar);
FC1names='Fuel utilisation (Fu1)';'Cathode Oxygen molpercent';'Anode H2 molpercent';'AnodeH2O molpercent';'Power in kW FC1';
FC1var=[Fu1;Oxi1;x H2 1;x H2O 1;Wfc1];FC1table=table(FC1names,FC1var);
FC2names='Fuel utilisation (Fu2)';'Cathode Oxygen molpercent';'Anode H2 molpercent';'AnodeH2O molpercent';'Power in kW FC2';
FC2var=[Fu2;Oxi2;x H2 2;x H2O 2;Wfc2];FC2table=table(FC2names,FC2var);
FC3names='Fuel utilisation (Fu3)';'Cathode Oxygen molpercent';'Anode H2 molpercent';'AnodeH2O molpercent';'Power in kW FC3';
FC3var=[Fu3;Oxi3;x H2 3;x H2O 3;Wfc3];FC1table=table(FC3names,FC3var);%% Fuelcells compared to each otherFC parrameters='Cathode Oxygen molpercent';'Anode H2 molpercent';'E0';'Nernst Voltage';'Cell
voltage';'Area specific resistence ohm/cmˆ2';'Power density in w/cmˆ2';'current densityA/cmˆ2';'Power in kW';
FC1 result=[Oxi1;x H2 1;E0 FC1;Enernst FC1;Ecell FC1;ASR FC1;Powdens FC1;q FC1;Wfc1];FC2 result=[Oxi2;x H2 2;E0 FC2;Enernst FC2;Ecell FC2;ASR FC2;Powdens FC2;q FC2;Wfc2];FC3 result=[Oxi3;x H2 3;E0 FC3;Enernst FC3;Ecell FC3;ASR FC3;Powdens FC3;q FC3;Wfc3];FCvergelijktable=table(FC parrameters,FC1 result,FC2 result,FC3 result)FC totalAREA=Wfc1/Powdens FC1+Wfc2/Powdens FC2+Wfc3/Powdens FC3;FC totalPower=(Wfc1+Wfc2+Wfc3);FC totalPowerdensity=FC totalPower/FC totalAREA
D.2.2 First function file, needed to calculate the FC parameters
function [efficiency,E0,Enernst,Ecell,Pload percm2,q,ASR,qfig,Ecellfig] = mywaarde(P,Oxi,x H2,x H2O,T)
%% CalculationF=96485;% Faradays constant in coulombs/moleR=8.314;% Gas constantT ref=298;Acell=5;%in cmˆ2;n=1;%amount of cellsx O2=Oxi; %hier zit dus 70%h2o bijLHV H2mol=242.36;%Mj/mol isLHV H2=LHV H2mol/2.02*10ˆ6;%MJ/kg%% Perfect stuk
dH H2 298K=0;A=3.249;B=.422*10ˆ−3;C=0;D=0.083*10ˆ5;
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dG H2 298K=0;dS H2 298K=−(dG H2 298K−dH H2 298K)/298;dH H2=dH H2 298K+R*(A*T+B/2*Tˆ2+C/3*Tˆ3−D/T)−R*(A*T ref+B/2*T refˆ2+C/3*T refˆ3−D/T ref);dS H2=dS H2 298K+R*(A*log(T)+B*T+C/2*Tˆ2−0.5*D/Tˆ2)−R*(A*log(T ref)+B*T ref+C/2*T refˆ2−0.5*D
/T refˆ2);
dH O2 298K=0;A=3.639;B=0.506*10ˆ−3;C=0;D=−0.227*10ˆ5;dG O2 298K=0;dS O2 298K=−(dG O2 298K−dH O2 298K)/298;dH O2=dH O2 298K+R*(A*T+B/2*Tˆ2+C/3*Tˆ3−D/T)−R*(A*T ref+B/2*T refˆ2+C/3*T refˆ3−D/T ref);dS O2=dS O2 298K+R*(A*log(T)+B*T+C/2*Tˆ2−0.5*D/Tˆ2)−R*(A*log(T ref)+B*T ref+C/2*T refˆ2−0.5*D
/T refˆ2);
% Water vapordH H2O 298K=−241.83*10ˆ3;A=3.470;B=1.45*10ˆ−3;C=0;D=0.121*10ˆ5;dG H2O 298K=−228.6*10ˆ3;dS H2O 298K=−(dG H2O 298K−dH H2O 298K)/298;dH H2O=dH H2O 298K+R*(A*T+B/2*Tˆ2+C/3*Tˆ3−D/T)−R*(A*T ref+B/2*T refˆ2+C/3*T refˆ3−D/T ref);dS H2O=dS H2O 298K+R*(A*log(T)+B*T+C/2*Tˆ2−0.5*D/Tˆ2)−R*(A*log(T ref)+B*T ref+C/2*T refˆ2−0.5
*D/T refˆ2);
dH reactie=dH H2O−dH H2−.5*dH O2;dS reactie=dS H2O−dS H2−.5*dS O2;dG reactie=dH reactie−dS reactie*T;
%% CalculationdG=dG reactie;dGkg=dG reactie*18.02;dH=dH reactie;E0=−dG/(2*F);
%% Standard cell values as Samuelt CAT=0.2;%0.2;%0.2;%cathode thickness in cmt elec=0.004;%40*10ˆ−6*10ˆ2;%electrolydte thickness in cmt ANO=0.015;%150*10ˆ−6*10ˆ2;%Anode thickness in cmt int=0.01;%100*10ˆ−6*10ˆ2;%interconnect thickness 9mm breed
C1 CAT=8.114*10ˆ−3*10ˆ2;C2 CAT=600;%coefficients ressesivityC1 elec=2.94*10ˆ−3;C2 elec=10350;%coefficients ressesivityC1 ANO=2.98*10ˆ−3;C2 ANO=−1392;%coefficients ressesivity% C1 inter=1.256*10ˆ−1;C2 inter=4690;%coefficients ressesivity
Res CAT=C1 CAT*exp(C2 CAT/T);Res elec=C1 elec*exp(C2 elec/T);Res ANO=C1 ANO*exp(C2 ANO/T);Res inter=1/((9.3*10ˆ5/T*exp(−1100/T)))*10ˆ2;% komt uit artikel Effect of Electrolyte
Thickness on Electrochemical Reactions and Thermo−Fluidic Characteristics inside a SOFCUnit Cell Jee Min Park 1 , Dae Yun Kim
R CAT=t CAT*Res CAT/Acell;%Acat is cross sectional area cathodeR elec=t elec*Res elec/Acell;R ANO=t ANO*Res ANO/Acell;R inter=t int*Res inter/Acell;Rint=R CAT+R elec+R ANO+R inter;
ASR=Rint*Acell;%in ohm/cmˆ2ASR SI=ASR*10ˆ−4;%% partial p
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PH2=x H2*P;PO2=x O2*P;PH2O=x H2O*P;
Enernst=E0+R*T/(2*F)*log((PH2*PO2ˆ.5)/PH2O);
%% NOICE plotjes knallenaaerror1=0.1;kend=100;Ecell=0.7;%linspace(0,Enernst,kend);%operating voltage must be lower then E0efficiencywanted=0.65for k=1:kendEcell=Ecell−aaerror1/10;Icellfig=(Enernst−Ecell)/Rint;RH2fig=Icellfig/(2*F);%consumption rate in moles / secondq=Icellfig/Acell;%current density in amperage/cmˆ2Rloadfig=Ecell/Icellfig;Ploadfig=Ecell*Icellfig;Pload percm2=Ploadfig/Acell;%load/cmˆ2 powdensefficiency=Ploadfig/(−dH*RH2fig);aaerror1=efficiency−efficiencywanted;if abs(aaerror1) <= 0.00001
breakendendend
D.2.3 Second function file, needed to calculate the FC parameters
function [qfig,Ecellfig,Pload percm2fig,efficiencyfig,Enernst] = mywaarde(P,Oxi,x H2,x H2O,T,Ecell)
%% CalculationF=96485;% Faradays constant in coulombs/moleR=8.314;% Gas constantT ref=298;
Acell=5;%in cmˆ2;n=1;%amount of cellsx O2=Oxi; %hier zit dus 70%h2o bij
LHV H2mol=242.36;%Mj/mol isLHV H2=LHV H2mol/2.02*10ˆ6;%MJ/kg%% Perfect stuk
dH H2 298K=0;A=3.249;B=.422*10ˆ−3;C=0;D=0.083*10ˆ5;dG H2 298K=0;dS H2 298K=−(dG H2 298K−dH H2 298K)/298;dH H2=dH H2 298K+R*(A*T+B/2*Tˆ2+C/3*Tˆ3−D/T)−R*(A*T ref+B/2*T refˆ2+C/3*T refˆ3−D/T ref);dS H2=dS H2 298K+R*(A*log(T)+B*T+C/2*Tˆ2−0.5*D/Tˆ2)−R*(A*log(T ref)+B*T ref+C/2*T refˆ2−0.5*D
/T refˆ2);
dH O2 298K=0;A=3.639;B=0.506*10ˆ−3;C=0;D=−0.227*10ˆ5;dG O2 298K=0;dS O2 298K=−(dG O2 298K−dH O2 298K)/298;
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dH O2=dH O2 298K+R*(A*T+B/2*Tˆ2+C/3*Tˆ3−D/T)−R*(A*T ref+B/2*T refˆ2+C/3*T refˆ3−D/T ref);dS O2=dS O2 298K+R*(A*log(T)+B*T+C/2*Tˆ2−0.5*D/Tˆ2)−R*(A*log(T ref)+B*T ref+C/2*T refˆ2−0.5*D
/T refˆ2);
% Water vapordH H2O 298K=−241.83*10ˆ3;A=3.470;B=1.45*10ˆ−3;C=0;D=0.121*10ˆ5;dG H2O 298K=−228.6*10ˆ3;dS H2O 298K=−(dG H2O 298K−dH H2O 298K)/298;dH H2O=dH H2O 298K+R*(A*T+B/2*Tˆ2+C/3*Tˆ3−D/T)−R*(A*T ref+B/2*T refˆ2+C/3*T refˆ3−D/T ref);dS H2O=dS H2O 298K+R*(A*log(T)+B*T+C/2*Tˆ2−0.5*D/Tˆ2)−R*(A*log(T ref)+B*T ref+C/2*T refˆ2−0.5
*D/T refˆ2);
dH reactie=dH H2O−dH H2−.5*dH O2;dS reactie=dS H2O−dS H2−.5*dS O2;dG reactie=dH reactie−dS reactie*T;
%% CalculationdG=dG reactie;dGkg=dG reactie*18.02;dH=dH reactie;E0=−dG/(2*F);
%% Standard cell values as Samuelt CAT=0.2;%0.2;%0.2;%cathode thickness in cmt elec=0.004;%40*10ˆ−6*10ˆ2;%electrolydte thickness in cmt ANO=0.015;%150*10ˆ−6*10ˆ2;%Anode thickness in cmt int=0.01;%100*10ˆ−6*10ˆ2;%interconnect thickness 9mm breed
C1 CAT=8.114*10ˆ−3*10ˆ2;C2 CAT=600;%coefficients ressesivityC1 elec=2.94*10ˆ−3;C2 elec=10350;%coefficients ressesivityC1 ANO=2.98*10ˆ−3;C2 ANO=−1392;%coefficients ressesivity% C1 inter=1.256*10ˆ−1;C2 inter=4690;%coefficients ressesivity
Res CAT=C1 CAT*exp(C2 CAT/T);Res elec=C1 elec*exp(C2 elec/T);Res ANO=C1 ANO*exp(C2 ANO/T);Res inter=1/((9.3*10ˆ5/T*exp(−1100/T)))*10ˆ2;% komt uit artikel Effect of Electrolyte
Thickness on Electrochemical Reactions and Thermo−Fluidic Characteristics inside a SOFCUnit Cell Jee Min Park 1 , Dae Yun Kim
R CAT=t CAT*Res CAT/Acell;%Acat is cross sectional area cathodeR elec=t elec*Res elec/Acell;R ANO=t ANO*Res ANO/Acell;R inter=t int*Res inter/Acell;Rint=R CAT+R elec+R ANO+R inter;
ASR=Rint*Acell;%in ohm/cmˆ2ASR SI=ASR*10ˆ−4;%% partial p
PH2=x H2*P;PO2=x O2*P;PH2O=x H2O*P;
Enernst=E0+R*T/(2*F)*log((PH2*PO2ˆ.5)/PH2O);Icell=(Enernst−Ecell)/Rint;% q=...???%
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% Icell=q*Acell;% Ecell=−Icell*Rint+Enernst%% ResultsRH2=Icell/(2*F);%consumption rate in moles / secondRO2=Icell/(4*F);%consumption rate in moles / secondq=Icell/Acell*10ˆ4%current density in amperage/mˆ2Rload=Ecell/Icell;Pload=Ecell*Icell;efficiency=Pload/(−dH*RH2);voltage efficiency=Ecell/Enernst;Powdens=Pload/Acell*10;%in kwatt/mˆ2EFFmax=dG/dH;%max achievable efficiencyTotal Power=Pload*n;q mAcm2=q/10;
RELAname='ASR';'Power density in kwatt/mˆ2';'Power';'Enernst';'Potential V';'Operating V';'efficiency';'efficiencyMAX';'current density amperage/mˆ2';
RELA=[ASR;Powdens;Pload;Enernst;E0;Ecell;efficiency;EFFmax;q];TabRELA=table(RELAname,RELA)
%% NOICE plotjes knallen
kend=100;Ecellfig=linspace(0,Enernst,kend);%operating voltage must be lower then E0
for k=1:kend
Icellfig(k)=(Enernst−Ecellfig(k))/Rint;
%% Results% RH2=Icell/(2*F);%consumption rate in moles / second% RO2=Icell/(4*F);%consumption rate in moles / secondRH2fig(k)=Icellfig(k)/(2*F);%consumption rate in moles / secondqfig(k)=Icellfig(k)/Acell;%current density in amperage/cmˆ2Rloadfig(k)=Ecellfig(k)/Icellfig(k);Ploadfig(k)=Ecellfig(k)*Icellfig(k);Pload percm2fig(k)=Ploadfig(k)/Acell;%load/cmˆ2efficiencyfig(k)=Ploadfig(k)/(−dH*RH2fig(k));end
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