Modelling of a Coil Steam Generator for Concentrated Solar Power Applications

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To my family. To whom I owe everything.

You have to learn the rules of the game. And then you have to play better than anyone else.

Albert Einstein

Science knows no country, because knowledge belongs to humanity, and is the torch which illuminates the world. Science is the highest personication of the nation because that

nation will remain the rst which carries the furthest the works of thought and intelligence.

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Modelling of a Coil Steam

Generator for CSP applications

Master's Thesis

-Leonardo Pelagotti

Thermal Energy and Process Engineering Energy, School of Engineering and Science 3. February - 18. July 2014

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Title: Modelling of a Coil Steam Generator for CSP applications

Semester theme: Master's Thesis

Semester: 4th _M.Sc.

Project period: 03.02.14 to 02.06.14

Supervisors: Thomas Condra and Kim Sørensen

In collaboration with Company: Aalborg CSP Company contact person: Jan Kragbæk

This project won the InnoAward Contest

at AAU during thee-DAYS Eventthe 15th

of May 2014, for its innovative content in the eld of energy eciency, energy technology and intelligent energy systems.

Leonardo Pelagotti

Synopsis:

The technology at the basis of the Concentrated Solar Power is quite complex and despite the incredible amount of energy from the Sun, the development of the CSP has to overcome signicant challenges. One of these is to start-up the power plant as fast as possible in the morning in order to harvest as much energy as possible on a daily basis. Unfortunately there are limits on how fast a thermal power plant can be started-up. The focus of this Project is to study a new design of Evaporator in the Coil Steam Generator (CGS), specially designed for solar applications by Aalborg CSP and Dan Boiler. This system allows faster start-ups and therefore higher daily energy production. An analytical thermodynamic simulation model of the evaporator and a mechanical analysis are developed to optimize the behavior of the system in dierent start-up scenarios. Sensitivity analysis carried out to understand the importance of start-up time, oil circuit pressure in the CSP plant and header thickness, show that the these variables are important to determine the total state of stress in the headers, and therefore their eective lifetime (ELT). Applying the results of the optimization analysis means that the oil headers are not critical anymore regarding the start-up process and can easily resist faster start-ups. With the overall optimization the ELT of the CSG can be improved from 13 to more than 100 years, meaning that warm start-ups time can be reduced of more than 15 minutes.

Pages: 174

Copies: 2

Appendices: A-H Supplements: CD

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Executive Summary

The author studied a new design of Evaporator in the Coil Steam Generator, specially designed for concentrated solar power applications and developed by Aalborg CSP and Dan Boiler. This system allows a faster start-up and therefore higher energy production on a daily basis, compared to previous technologies.

An Analytical Thermodynamic model and a Mechanical analysis of the system were developed, in order to understand and optimize the behavior of the system in dierent solar radiation conditions and start-up scenarios. The results obtained in the project include optimization of design parameters in order to improve the eective lifetime of the steam generator, the thermal exibility of the overall CSP plant and faster start-ups. These results are of extreme importance because, they not only lead to higher renewable energy production, but they can improve the penetration of the solar renewable energy into the electricity grid, thanks to a higher exibility. This is signicant also from an energy planning point of view, and leads to more renewable energy and fewer fossil fuels in the next future.

Having a 10 minutes faster start-up of a CSP plants of 75 MW in the morning, leads to an energy production higher of 12.5 MWh every day and more than 4500 MWh a year. This means that, if there are 6 CSP plants of 75 MW each run by a Company, the annual income would be approximately 1 Million dollars higher 1_{. With the study developed}

it was indeed possible to nd the right design value for several parameters in order to increase the eective lifetime of the system and therefore to be able to start-up the system several minutes faster, to produce more energy and to increase the economic value of one day of Sun for the CSP plant.

Moreover, the results of this analysis can be applied not only to CSP plants, but they can also be implemented in other thermal power plants, in order to increase their exibility and use, implying a higher possibility to follow closely the electricity demand curve with the production curve and avoid a damaging black-out.

Thanks to the Thermodynamic model developed in MATLAB for the evaporator in the Coil Steam Generator, it was possible to accurately predict the behavior of the evaporation process inside the tube bundle of the evaporator for dierent load conditions. The 3-D spatial model gives a description of the Temperature and Enthalpy of the water/steam ow in every point of the evaporator shell, and thanks to these data, it was possible to derive also signicant parameters that describe the functioning of the entire Coil Steam

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Generator and the CSP plant such as heat transfer coecients, steam quality and void fraction of the steam produced. These are indicators of eciency of the evaporation process, but also give an important feedback on design safety issues.

Knowing the temperature in the evaporator, and using a semi-dynamic stress analysis it was possible to investigate the critical components and understand how they react to dierent cases. In particular the cylindrical oil headers in the evaporator were studied. The temperature prole in the thickness was estimated with MATLAB simulations, leading to an extensive analysis on the thermal and pressure stresses due to the start-up process for dierent load scenarios.

When the stresses were calculated, using a fatigue life calculation method it was possible to study the eect on the two critical components (oil headers), of dierent start-up procedures. The results showed that the outlet header is more critical than the inlet header, and that plastic deformation often occurs at the inner surface of the inlet header in the proximity to the holes.

Several sensitivity analyses were carried out in order to understand the importance of : start-up time of the CSP plant, oil circuit pressure and header thickness. The results are signicant, and show the importance of a right choice of several design variables value in order to improve the eective lifetime of critical components and to allow a faster start-up. For example, it was found that the value of the oil circuit pressure is extremely important in determining the total state of tension in the headers, and therefore their ELT. Regarding the right value of the pressure used in the CSP plant, it was found for instance that changing the pressure from 10 bar to 100 bar, the eective fatigue life can be increased by a factor of ve. This means that the headers would no longer be critical for the plant, regarding the start-up procedure, leading to possible faster start-ups.

Also the value of the thickness of the header is very important and can lead to signicant improvement of the ELT. If the thickness is increased to the optimum calculated value (approx. 150% the design value), the lifetime is increased up to more than double. Applying a combination of the results of the optimization analysis to the CSP plant and the two critical components in the evaporator, the oil headers are no longer critical regarding the start-up process and can more easily be capable of resisting faster start-ups. In fact from an eective lifetime of 13 years without optimization, the eective lifetime of the header can reach 100 years with the optimized conguration.

If the same analysis is carried out in a similar way for the oil headers in the rest of the heat exchangers in the CSP plant, specially the re-heater and the super-heater an overall optimization can be found, leading to the solution of the problems of having faster start-up in CSP plants.

This is an important result for solar power plants, when considering the limited amount of time to operate a CSP plant (the sun hours in the day), that will hopefully help the future development of the CSP technology all over the world.

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Preface

This Master's Thesis is a collaborative eort between Pisa University and Aalborg University. Moreover the author of this project has been in cooperation with the engineering company Aalborg CSP A/S, which manufactures heat exchangers for solar applications and develops and supplies steam generators for utility size CSP plants. The author signed a NDA with the Company and some of the information in the report have to be considered as condential.

The authors would like to thank the Company and Jan Kragbæk for being a source of inspiration, for the information provided and for the time they spent.

Additionally, a thanks to the supervisors Thomas Condra and Kim Sørensen, from Aalborg University, and Alessandro Franco, from Pisa University, for their precious help.

Reading Instructions

All the references are listed at the end of the report. The Harvard Method is used for references, where the source will be written as [Author, Year] in the text. If the reference is placed before the full stop in a sentence, the reference is stated for only this sentence. If the reference is placed after the full stop, the reference is stated for the whole text piece. Figures, tables and equations are numbered in accordance with the appendix number. This means that the rst gure in Appendix B is numbered B.1 and the next gure numbered B.2. The explanatory text to these will be attached to the given gure or table in a caption.

Please note that in the entire report when referring to pressure, the absolute pressure is intended and not the gauge pressure.

Please note also the the text size of some gure might be small for an easy reading. This is a compromise necessary for a better understanding of some 3-D gures, where a small title was the consequence of choosing to have a clearer and bigger gure. In order to help the reader to understand the gure, a caption substituting the title is present under every gure in the report. Please be aware of dierent scales also in similar gures.

Please note also that the quality is intended in the following way : negative when the water is sub cooled, in the range [0,1] when the water/steam is in the two phase region, and bigger than 1 when the steam is super heated. The author is aware that there is no physical meaning of a quality outside the range[0, 1], but it is only used to indicate some results from the MATLAB model that are outside that range.

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Problem Statement

1

Fast start-ups and higher plant exibility are necessary to extract as much power as possible from the Sun in CSP plants on the limited amount of hours of solar radiation in a day and overcome short unpredictable solar radiation uctuations during the day. Unfortunately faster start-ups mean higher thermal loads on some critical components of CSP plants, that if not controlled, can cause serious and permanent damages and lead to the plant shut-down.

This project wants to investigate in detail how the cross ow evaporator of the Coil Steam Generator, specially designed by Aalborg CSP A/S and DanBoiler A/S for concentrated solar power applications, can be thermodynamically modeled in order to be able to evaluate the fatigue life and damage of the heavier thermally loaded components of the plant during daily start-up routines.

The fatigue damage is due to daily start-up routines typical of CSP plants, and a possible improvement in the design of critical components, in order to have higher exibility and therefore faster daily start-up, is also investigated. A faster start-up means more energy produced during the day and therefore a consistent economic income.

The primary goal of this project was to develop in MATLAB a detailed 3-D thermodynamic model of the cross ow evaporator, able to describe several fundamental parameters in the evaporator, and from them investigate the inuence of the choice of these parameters on the eective life of critical components, such as the cylindrical oil headers.

The thermodynamic model is based on the rst law of thermodynamic and includes several heat transfer correlations, necessary to describe the evaporation process on the tube bundle of the cross ow evaporator. The data are based on heat balances and plant measurements provided by Aalborg CSP and the model is solved analytically in MATLAB.1

For the models a specic and detailed 3-D discretization has been developed.

The specic design of the Coil Steam Generator brings new challenges in developing a model able to describe it, because it is unique in its genre and there are no previous studies in the literature for this kind of steam boiler to which the author could refer

1_{A dynamic model has also been developed in MATLAB, based on a theoretical approach of applying}

transient conservation equations to the tubes of the tube bundle in the cross ow evaporator, solving systems of dierential and algebraic equations with numerical methods.

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to. Therefore the presented study is interesting and leads to several answers and new questions.

1.1 Limitations

All the uids are treated as Newtonian uids. The pressure eld is always considered as isotropic, and the material properties are also considered as isotropic. A semi-dynamic approach has been used to simulate the dynamic behavior of the system. The model is related to the specic dimension of the system. The model is based on several hypotheses, explicitly stated in their respective chapter.

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Project Description

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The main goal of this project is to analyze the steam generator system of a concentrated solar power plant during daily start-up procedures.

This analysis wants to provide a deeper insight into what happens to certain critical components concerning evolution of temperature distributions and gradients during the start-up, and wants to analyze the pressure and thermal stresses during a warm daily basis start-up procedure. Once the pressure-thermal stress analysis is carried out the fatigue life analysis comes straightforward.

After the fatigue analysis is carried out some design changes can be proposed in order to increase the eective lifetime of the critical components. This will allow the plant to be able to have faster start-ups and be more exible.

This gives enormous economical advantages and helps the transition to a renewable based power production concerning the electrical grid problems as well.

In this project, the component of focus is the cross ow evaporator in the Coil Steam Generator, see Chapter 6. In the cross ow evaporator the inlet and outlet oil headers are analyzed, because they are identied as critical components, from previous experience on CSP plants. One of the great advantage of the innovative Coil Steam Generator, is in fact a new design of the oil collectors as cylindrical headers in the cross ow evaporators, in order to lower the thermal stresses that were aecting their lifetime seriously. See Chapters 5 and 6 for a better understanding of the system.

2.1 Structure of the Project Report

First, in Chapter 3 the conceptual scheme of the work is explained in a block diagram showing the steps solved to reach the project goal and how each steps was solved. In the same chapter also the hierarchical explanation of the work is presented. An introduction about the energy scenario and the CSP technology follows in Chapter 4, respectively in Section 4.1 and 4.2. In Chapter 5, the CSP Plant conguration is presented; the operational principle is explained in Section 5.1, and the Coil Steam Generator is presented and explained in Section 5.2. In Chapter 6, the focus is on the design of the evaporator component of the steam generator and its working principle. In Chapter 7, the 3-D discretization used for the thermodynamic model developed in Chapter 8, is explained in order to better understand the presentation of the results in Sections 8.2.1 and 8.3. In Chapter 8, the thermodynamic model of the cross ow evaporator is developed and its

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results are presented, while in Chapter 9, a dynamic model for a tube in the bundle of the evaporator is explained. In Chapter 10, rst the temperature prole in the oil headers is calculated in Section 10.1, and then the pressure-thermal stress calculation for the oil headers is carried out in Sections 10.2 and 10.3. The results are then used in Chapter 11, where the fatigue life estimation of the oil headers is developed. Then in Chapter 12, the main results of the stress-fatigue analysis are explained. In Chapter 13, sensitivity analysis and optimizations are carried out, suggesting possible changing and improvements for the oil headers design and CSP plant settings. Finally in Chapter 14, a short summary of the main results is presented for a fast reading through of the project report.

In the Appendixes, Appendix A is a review and explanation of the heat transfer correlations interesting for the case of this project, while Appendix B is about the investigation of the inuence of using dierent heat transfer correlations in the results of the developed Model. In Appendixes C and D, the pressure drop calculations are investigated for both the oil side and the evaporation side and in Appendix E a fast explanation of the critical heat ux is presented, followed by Appendix F where the explanation of creep according to ASME PVC is shortly presented.

What was expected from this project was a detailed analysis of the evaporator behavior during a warm start-up of the CSP plant. This is why it was necessary to develop at rst, an analytical thermodynamic model able to describe the evaporation process in the tube bundle of the evaporator. From that it was possible to derive the behavior of the oil headers in the shell of the evaporator and understand the inuence of dierent scenarios of start-up, plant setting, and design variables on their ELT. In fact, from the thermodynamic model it was possible to calculate numerically, the consequent temperature prole in the thickness of the headers, and then calculate analytically the headers response in terms of stresses originated from the start-up. Finally, once the stresses were calculated for the start-up scenario, the fatigue life of the headers was estimated using an analytical method. Once the ELT, as a function of dierent investigated variables is known, the engineer in the design phase, or in the production phase, is able to predict the outcome of his choices and the deriving results, concerning the life of the CSP plant.

Moreover several numerical optimizations were carried out in order to improve the ELT of the oil headers also in more severe conditions, such as faster start-up. Additionally if the fatigue life of the oil headers is known, a comparison with the fatigue life of other critical component can be done1_{, in order to understand where the most strict limits regarding}

the start-up time are.

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Conceptual Scheme of the

Project

3

In this chapter the conceptual scheme of the work is presented in Figure 3.1 and the main hierarchical structure of the project is explained.

First of all the main objective of this work is studying the evaporator of the CSG with a focus on the new design of the oil headers. The eective lifetime of these components wants to be estimated accordingly to the start-up scenarios adopted in the CSP plant. How to optimize the eective lifetime of the oil headers with an approach leading to simple and inexpensive modications is then investigated.

As shown in Figure 3.1 the project can be better understood starting from the main goal that was sought and then proceeding backward step by step to the main data available as in input, a process necessarily involving general assumptions and simplications. The column on the left expresses which are the main steps involved in the work from the starting point to the project goal and following optimization. The column on the right in the gure, expresses the approach used to solve each step.

Explaining the scheme of Figure 3.1 In order to calculate the ELT of the oil headers in the evaporator, the damage caused by cycling stresses applied to the components has to be estimated. This damage is caused mainly by alternating thermal and pressure stresses at high temperature and pressure. Fatigue is the main cause of life consumption and also Creep plays an important roles at high temperatures. To estimate the damage, the stresses acting on the headers have to be calculated, and therefore knowing the Temperature and Pressure acting on the oil headers during the start-up is necessary. In order to calculate the pressure, a start-up scenario has to be considered. To calculate the Temperature in the cylindrical headers in the evaporator, a thermodynamic model for the evaporator tube bundle is needed in order to calculate the temperature of the uids in the 3D space in the evaporator shell. Once the uid temperatures are known during a start-up scenario in the 3D space, the heat conduction equation in the oil header's wall can be solved with a PDE initial-boundary conditions problem. Therefore a model for the evaporator is created accordingly with a spatial discretization, solving steady-state equations for a cross ow heat exchanger. The model is then amplied with further equations, as explained in Chapter 8, for accounting of evaporation on the outside of a tube bundle with several layers and 3 tube passes per layer, see Chapter 7. Several correlations are used to describe the

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Figure 3.1: Conceptual scheme of the work

heat transfer process and the pressure drop across the bundle and in the oil circuit. The model is then made quasi-dynamic solving steady state problems for several time steps during the start-up and approximating continuous functions with discrete data. Therefore the very rst step is reconstructing a continuous prole during time of the inputs to the evaporator for a desired start-up scenario. The inputs are taken from plants measurements and data provided by Aalborg CSP.

As shown in Figure 3.1, the damage due to alternate stresses is calculated with the Fatigue Analysis, and Creep is neglected for the reason explained in Appendix F. For calculating the thermal stresses the Plane Strain equations are developed, as explained in

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Chapter 10. For pressure stresses the Lame's equations are used, see Section 10.3. Then a linear superposition is made to take into account both the stresses. For calculating the temperature in the headers wall a PDE heat conduction equation in 1D transient condition is solved in MATLAB, see Section 10.1. The boundary conditions are derived from the solution of the evaporator model for the entire start-up time. The model for the tube bundle is developed in MATLAB and involves various steady state sub-routines solved for various load scenarios during a start-up. The main part of the MATLAB program is based on a cross ow heat exchanger thermodynamic model. All the data provided by the CSP plant are used to reconstruct the inputs time evolution and transform steady state data into tted continuous functions.

Hierarchical structure of the work It can be said that the main eort has been made in order to develop the semi-dynamic model for the cross ow evaporator, that resulted in a structured code, with several sub-routines and a total number of code lines above 500000. An eort to explain the Model in a concise and eective way has been spent in Chapter 8.

What follows was a relatively smaller part of coding regarding the temperature calculations in the headers wall and the following stresses calculations in time and radius. This part of the project was more straightforward thanks to the fact that already developed equations were available in the literature for thermal and pressure stresses in hollow cylinders, while for the tube bundle model, only a small part of it was taken from the literature, and the rest was specially made for this solar application.

For what concerns the fatigue analysis, the theoretical approach used was available in the literature, despite the fact that this approach does not consider the fatigue conditions in the welds.

After the main results were obtained, an optimization followed thanks to an analytical approach of using sensitivity analysis that was eective and productive.

The author would like to emphasize the fact that the whole project was developed with the use of only one program, MATLAB. This was possible thanks to the theoretical analytical approach used. More advanced software developed specially for each applications are available, but this would mean a higher expenses for licensees compared to using only one program. Moreover the academic level of the project would have been lower, relying basically on numerical methods and pre-installed routines or equations in the specic software.

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Introduction

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This Chapter is a short introduction to the World Energy Scenario and the Concentrated Solar Power (CSP) technology.

4.1 Energy Scenario

The technology progress has been growing exponentially since the 19th _{century, and with}

that problems have been rising too. Pollution, higher resources demand and consumption, higher energy need; CO2and GHG concentration in the atmosphere is several times higher

than the concentration back at the beginning of the industrial revolution (see Figure 4.1) and Climate Change and Global Warming (see Figure 4.2) have become serious issues to face in the XXI century.

Figure 4.1: CO2 concentration over the last 1000 years, and in the last decades, registered

in Mauna Loa Observatory, NOAA-Research [2014]

One important way to succeed in the future, avoiding environmental problems, is switching from a fossil fuel basis to a renewable energies basis. Despite the challenging circumstances in the global economy and politics, growth continues especially in the developing world. Meeting the energy needs of the developing countries all over the world will require substantial growth in the global energy sector. Renewable energy can play an essential role in improving the livelihoods of millions while contributing to energy security and climate change mitigation.

Dealing with renewables has several complications compared to burning fossil fuels, especially concerning the electricity grid. Our entire society nowadays relies totally on

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Figure 4.2: Temperature anomaly in 2012 compared to the last 30 years

electricity and the electricity grid is a complex and delicate system that has to be controlled and kept safe at every time, in order to avoid collapses and black-outs. Unfortunately, renewables are intermittent forms of energy and the Sun is an example. It rises in the morning and during the day until the sunset, the heat ux from the Sun that reaches the ground encounters several changes due to clouds and atmospheric conditions. The necessary eort is therefore to be able to integrate the renewable energy sources into the energy production sector and electricity grid. What is required from any power plant is to have a high degree of exibility in order to be regulated according to the balancing between the energy demand and the production at every moment. If not, a possible consequence is what happened in some of the famous electricity crises, including New York and Italy in 2003, that were not caused by inadequate generation capacity but rather by a cascading network collapse.

This project deals with start-ups and dynamic operation of Concentrated Solar Power plants, in other words with a high level transient problem on renewable power plants. Being able to have faster start-ups means also having a higher utilization of CSP plants. The understanding of the methodology for having more exible plants is applicable to all the classical thermal power plant. So an improvement in one type of plant can be also obtained in a similar way in other plants. This can lead to an overall more exible power generation system, that is exactly what is needed in order to be able to switch from fossil fuel to intermittent renewable energy sources. Another important step is having a spread energy storage system, but this issue is not analyzed in this report.

From IAE World Energy Outlook 2010 :

Traditional hydro power is expected to contribute half the share of renewables generation by 2035 in New Policies Scenario, and 16% of global electricity, wind 8%, solar photo-voltaic 2%, and concentrating solar power plants (CSP) slightly more than 1%, and the rest from biomass, geothermal and marine. If these trends are realized one-third of global electricity will be contributed by renewables (half of that new renewables), and with nuclear contributing 14%, correspondingly by mid century around half global

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electricity will be available from non-fossil fuels. This, if accomplished, will be a remarkable achievement but it also carries risks in investments, cost of supply and serious problems in dispatching with possible increasing costs to consumers.

A message stands out clearly: the shift to renewables is absolutely a need in the third millennium, even if the economy is facing a temporary worldwide crises.

4.2 Energy from the Sun

It is therefore clear that the real challenge is a shift to renewables.

But why is Solar Energy so interesting among the other renewable energy sources? ""More energy from the sunlight strikes the earth in 1 hour than all of the energy consumed by humans in an entire year. In fact, solar energy dwarfs all other renewable and fossil-based energy resources combined"", from the article Concentrated solar power plants: Review and design methodology in the Renewable and Sustainable Energy Reviews. Among the dierent renewable energy sources the Sun is the one on which there is the highest possibility to rely on in the future, since from the Sun comes an enormous amount of energy to our planet. The total solar energy absorbed by Earth's atmosphere, oceans and land masses is approximately 3 850 000 exajoules (EJ) per year. In 2002, this was more energy in one hour than the world used in one year. The amount of solar energy reaching the surface of the planet is so vast that in one year it is about twice as much as will ever be obtained from all of the Earth's non-renewable resources of coal, oil, natural gas, and mined uranium combined, [Joint-Research-Centre, 2014].

Figure 4.3: Annual worldwide sum of solar irradiation on horizontal surfaces, from [SOLARGIS, 2014]

Depending on the underlying assumptions for the CSP development, an installed capacity of 120 GWel, 405 GWel or even 1,000 GWel could be reached globally in 2050. In the latter case, CSP would then meet 13-15% of global electricity demand, [Viebhan et al.,

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December 2010]. Great potential of development of the CSP technology is for example, in the Mediterranean African countries, where not only a high amount of solar energy is available, see Figures 4.3 and 4.4, but this potential is linked with the possibility of connecting the CSP plants with the European electrical grid. In this scenario, Italy plays an important role, as well as Spain and France.

Figure 4.4: Annual sum of solar irradiation in Europe, from [SOLARGIS, 2014] From the European Commission website the free tool PVGIS can be used to calculate interactive maps of the solar radiation on horizontal surfaces or surfaces with an optimum angle of inclination during the day as shown in Figure 4.5. In the case of CSP plants, electrical drivers move the heliostats during the entire day to have the optimal inclination for collecting the highest amount of energy.

"Apart from rapid technological improvement, the strength of renewables lies in the diversity and the richness of their technology options and applications, as well as their widespread availability. Every country in the world has at least one renewable energy source that is signicant. Some have many." , from the Energy agenda 2012. For CSP, many square kilometers of desert are available in many regions of the world. But solar power's lower energy density and inferior transportability are two clear disadvantages compared with fossil fuels. That is why a well connected and ramicated electrical grid has a key role in the future of this source.

Concentrating solar power is a complementary technology to the solar photovoltaic process. It uses concentrating collectors to provide high temperature heat to a conventional power cycle. Ecient and low-cost thermal energy storage technologies can be integrated into CSP systems, allowing electricity production according to the demand prole. CSP

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Figure 4.5: Irradiation on horizontal and optimum angle surfaces in Europe

systems can also avoid shadow plant capacity needed to secure generation capacity in periods without sunshine, can provide grid services, and if desired even black start capabilities. It thus supports the penetration of a high share of intermittent renewable sources like wind or PV and avoids a high share of expensive electric storage technology in the grid systems.

The rst commercial implementation of CSP technology began in 2007 in Spain and the United States. Today, a capacity of 3 GW is in operation and another 2 GW is under construction worldwide and is expected to reach 11 GW by the end of 2017 ( [Vallentin and Viebhan, 2013] ). Further developments, in particular in the Middle East and North Africa but also in South Africa, India and China, are under consideration. Figure 4.6 shows the CSP world-wide.

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CSP plants bundle solar radiation using concentrating mirrors. The concentrated radiation is then transformed into thermal energy and used to power conventional steam and gas turbines or Stirling engines. CSP makes it possible to oer power on demand via heat storage and will be of particular interest for generation units between 200 and 400 MWe. It works as a regenerative alternative to conventional power generation technologies both for base load and peak load as well as for balancing varying power supply from wind and photovoltaic. Apart from producing electricity, the process heat emitted by CSP may be used to cool buildings and industrial processes, production of hydrogen or operation of facilities for the desalination of sea water, [SBC, Energy Institute 2010].

The global market spread of CSP technologies is fostered by several initiatives : DESERTEC Foundation, DESERTEC Industrial Initiative, Mediterranean Solar Plan, European Union's legislation.

At present, the international discussion on CSP focuses on two technology options: parabolic trough technologies and solar tower technologies. Other technology paths, such as dish Stirling systems or Fresnel collector systems, are less mature and, therefore, currently not at the center of the debate, [SBC, Energy Institute 2010].

Parabolic trough technology is the most mature and ecient solar thermal power generation technology today. Solar radiation is concentrated by parabolically curved, trough-shaped reectors onto a receiver pipe running along the inside of the curved surface. Within the pipe, the solar energy heats up a heat transfer medium (e.g. oils, molten salt) to approximately 400◦_C_{. The medium transfers the heat to a power block where it is used}

to generate electricity in a conventional steam generator.

Figure 4.7: Solar Trough technology

Solar tower technology utilizes numerous large sun-tracking mirrors (heliostats) to focus sunlight on a receiver at the top of a tower. A heat transfer uid heated in the re-ceiver, which is heated up to temperatures of 500/1000◦_C_{, is used for steam generation.}

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molten salt or air may be used as heat transfer media. Since heat transfer is limited to one point of the process, solar tower systems are less energy intensive than parabolic trough technologies.

Figure 4.8: Solar Tower technology

The solar operation time of all types of CSP technology can be expanded to run on a power on demand mode using thermal energy storage combined with larger collector elds. Solar heat collected during daytime can be stored in storage systems based on concrete, molten salt, ceramics or phase change materials. At night (or during the day, if needed), the heat is extracted from the storage to run the power block continuously (base load) or on demand (balancing power).

But solar energy is of unsteady nature, both within the day (day/night, clouds) and within the year (winter/summer). The capture and storage of solar energy is critical if a signicant portion of the total energy demand needs to be provided by solar energy. This is why a study on the thermal exibility of a CSP plant is of an enormous importance to guarantee to account on solar energy for an increasing percentage in the nearest future. The predictability of the power produced by these sources is most of the time unreliable. It requires the thermal plants to be as fast as the grid requires to supply the dierence between power produced and requirements. A system which is capable of providing exibility to the grid could be a CSP power plant with a daily heat storage system based on molten salts but also a CSP plant with a steam generator unit where the steam is accumulated in the steam drum.

This project deals with the solar trough technology and focuses on the steam generator part of the CSP plant.

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System Specifications

5

In this chapter the analyzed system is described with the main data in order to be able to comprehend the plant conguration and size.

The steam generator system analyzed is in a CSP Plant of 50MW and is designed by Aalborg CSP and Dan Boiler. Aalborg CSP is a world leader in developing and supplying steam generators for utility size CSP plants and delivering module CSP systems for industrial size, see [AalborgCSP-A/S, 2014]. DanBoiler is an engineering company specialized in design of boiler plants and energy systems, see [DanBoiler, 2014].

Figure 5.1: Coil type evaporator of Aalborg CSP, [AalborgCSP-A/S, 2014]

5.1 Steam Generator and Plant Congurations

The following description is taken from Aalborg CSP web site, [AalborgCSP-A/S, 2014]. The parabolic trough solar power plant operates with a heat transfer uid (HTF) that is heated by the sun in linear concentrators. In the specic case of this plant, the HTF is a diathermic oil Dowtherm A (later oil). The HTF is heated to maximum 393◦_C _{by the sun}

and cooled to a temperature just below 300◦_C _{in the steam generator, while exchanging}

its heat to the water/steam ow. From the steam generator, the HTF is heated again to 393◦C in the parabolic trough collectors, forming a closed cycle.

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The HTF is cooled in heat exchangers for generation of high pressure steam that expands in a high pressure steam turbine generator for generation of electrical power. The steam cycle is a Hirn steam cycle, where the steam from the super heater expands in the high pressure section of the steam turbine, and then is led to a re-heater and then expands again in the low pressure section of the steam turbine until reaching the condenser pressure. The high pressure (HP) steam generator consists of one super heater, one evaporator unit and one economizer. The reheater is composed of two separate heat exchangers operated in parallel, respectively with the economizer and the super heater.

The steam ow is around 28.5 kg/s per a unit of 25MWe. The HP steam is generated at

around 105 bar at 380◦_C _{for the HP turbine. The reheater heats the outlet steam from}

the HP steam turbine to 380◦_C_{again before it enters the low pressure (LP) steam turbine.}

The inlet steam to the reheater is typically 15 to 20 bar with a water content of around 1%.

The plant can be congured with several parallel steam generator lines. A 50MWe power plant has 2 steam generator lines generating 28.5kg/s each in parallel.

Figure 5.2: Conguration of the steam generation unit in the CSP plant, [AalborgCSP-A/S, 2014]

Following the T-S diagram for the steam cycle is briey presented, see Figure 5.3.

The water starts at point 0 indicated in the gure after the exit of the condenser, then a pump rises its pressure at the design pressure of the steam cycle. That pressure is also the pressure in the drum and it is regulated by a pressure controller. After point 1 the water enters a regenerator where some steam spilled from the low pressure section of the steam turbine heats it up to point 2 in the diagram. From 2 to 3 the water enters the economizer and is heated up by the oil ow. It arrives then into the drum slightly sub cooled depending on the value of the approach point, that is usually a few degrees. After entering the drum, the water follows the evaporating circuit into the evaporator, going from the drum into the downcomer, reaching the cross ow evaporator at the bottom of the drum, and evaporating on the tube bundle, while moving upwards, thanks to natural circulation through the bundle to the riser and into the drum again. After the evaporation circuit only a small percentage of the total water ow is evaporated, depending on the

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quality at the outlet of the riser and the circulation number. A typical value of the quality is in the range of 0.05-0.2. then the water/steam is separated into saturated steam and saturated water into the drum. Point 4 represents the saturated steam that is led to the superheater. For further explanation on the principle of steam/water separation and the drum inlet components see [Pelagotti et al., 2013]. The saturated steam enters the superheater and becomes superheated, point 5. From point 5 the superheated steam expands into the high pressure section of the steam turbine and reaches the re-heaters low pressure. The steam is then led to the re-heater in parallel, on the HTF side, to the economizer, point 6a and following to the re heater in parallel with the super heater, reaching point 7. Then the superheated steam is expanded in the low pressure section of the steam turbine reaching the condenser pressure at point 8. From 8 to 0 the steam condenses completely and the cycle repeats.

Figure 5.3: T-S diagram for the steam cycle

For the value of pressure and temperature refer to gure 5.4.

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The gure above shows the steam generator conguration where all HTF passes through the evaporator. This plant has two reheaters, RHe and RHs, respectively in parallel with the economizer and the super heater. This conguration will result in a lower HTF ow for the same steam output, or in having a higher amount of electricity at the output for the same heat ux from the sun at the inlet of the parabolic trough collectors.

5.2 Aalborg CSP Coil Steam Generator

The evaporator is the main component of the steam generator plant with respect to weight and cost.

The coil-type evaporator analyzed in this project has been specially developed for solar energy applications, where high steam capacity and high steam pressures are required because of frequent starts/stops and load changes, due to the intermittent nature of the Sun. Moreover the coil-type steam generator has several characteristics, (see later in this section), that guarantee special exibility for frequent and fast start-ups.

The coil evaporator, consists of two evaporators in parallel, that are two cross ow heat exchangers with horizontal plain tube bundle and one separate steam drum. Evaporation occurs on the shell side of the tube bundle. The steam drum is connected to the evaporators with external downcomers and risers. The tube bank has three passes on the oil side which results in a thermally exible tube bank relative to the shell. These three passes guarantee in fact, little dierence in temperature between oil and water/steam ow after the heat exchange process in the evaporator, resulting in a small temperature dierence across the wall thickness of the outlet header. This means, lower thermal stresses, that are for most applications, the most critical limit for faster start-ups.

Figure 5.5: Coil type evaporator of Aalborg CSP, [AalborgCSP-A/S, 2014]

In the coil-type evaporator the steam drum is connected to the evaporators with external downcomers and risers. The circulation in this type of evaporator is natural circulation caused by the dierence in density between the saturated liquid in the downcomer and the lower density of the vapor/liquid mixture in the evaporator and riser. The tube bank has an eective cross ow of boiler water at all times. Downcomers and risers are designed for a circulation ratio from 5 to 15. The circulation ratio is the ratio of total ow, liquid plus

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vapor, to the vapor ow generated and therefore correspond actually to the inverse of the steam quality. This implies that the mean steam quality at the outlet of the evaporator is always lower than 0.2 at design condition.

In solar HTF steam generation plants, the operation steam pressure is typically 100 bar or more. Solar steam generators are subject to start and stop every day and also frequent and rapid load changes during the day due to passage of clouds and meteorological conditions. This will cause variations in temperature of the heating medium creating thermal stress in the tube plates. High material thickness is undesirable with respect to thermal stress, and fatigue cracking is a risk. The coil-type evaporator has no thick tube plates. The hot oil ows are distributed to the heat transfer tube bank via a circular manifold, also called a header. The round shape of the header results in a relative small material thickness and therefore low thermal stress. By splitting the evaporator unit into two heat exchangers and a steam drum, the diameters of the individual pressure vessels are small compared to a shell and tube evaporator, and the wall thickness required to sustain the pressure is smaller too.

This means that the evaporator is less sensitive to fast temperature gradients and therefore is more exible, that is exactly why the coil-type steam generator is specially interesting for solar applications that require faster start-ups. As it can be understood from the following equation, the thermal stress is proportional to the square of the thickness. [Sørensen, 2004] :

σth∝ s2

dT dt (5.1)

Also from the following formulation, see the Appendixes in the Project Report [Pelagotti et al., 2013], the inuence of the material thickness on the thermal stresses can be seen. The integral in fact goes from Ri to Re that is actually the thickness of the wall of the

header; the higher is the thickness and the higher is the value of the integral and therefore of the equivalent thermal stress. See Equation 10.29 and 10.30.

σeq,th = σθ,th(Ri)− σr,th(Ri) = Eα 1_{− ν} · 2· Z Re Ri T (r)· rdr − T (r) [M P a] (5.2)

Aalborg CSP uses large and widely spaced tubes in the evaporator. Operation is therefore well below the critical heat ux, so operation is stable and safe. See the calculation of the critical heat ux in Appendix E.

Other Components

The other heat exchangers in the system are the super heater, the economizer and the reheaters.

When using TEMA-type shell and tube heat exchangers, a high material thickness will be needed for all components, even for the reheater. This is due to bending stresses in the tube plates from internal pressure.

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All the heat exchangers designed at Aalborg CSP are unique coil-types without tube plates. However the other heat exchange surfaces consists of a tube bank with high pressure inside the tubes and the lower pressure HTF owing in counter-ow outside in cross ow which is the opposite of the one in the evaporator. The tube bank is contained in a cylindrical pressure vessel containing the HTF. The tube banks are welded to inlet and outlet manifolds (headers) that pass through the shell into thermo-sleeves for low thermal stress; see Figure A.2.

Figure 5.6: Evaporator drum nozzle detail and thermo sleeve in yellow, [AalborgCSP, 2014]

The tube bank has a high degree of exibility because of the many bends.

The HTF passes through the tube bank in the evaporator in cross ow with the water/steam mixture ow without change of direction in one pass. The pressure drop for the HTF is very low for this conguration while the heat transfer coecient is high. A low pressure loss is very important for the total plant eciency, because less power is used for the auxiliary oil circulating pump.

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Design of the Evaporator

6

In this chapter the geometrical conguration and working principle of the Coil Steam Generator is presented.

Figure 6.1: Steam generation system of the CSP plant,[AalborgCSP, 2014]

The following gures represents the steam generation system of the CSP plant, the two units in parallel of the cross ow evaporator with their respective risers, a common downcomer and common drum.

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Figure 6.2: Evaporator and steam drum from the side,[AalborgCSP, 2014]

Figure 6.3: Evaporator and steam drum from the front and sections,[AalborgCSP, 2014]

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Figure 6.4: Table with the list of the components. [AalborgCSP, 2014]

The following gure shows the structure of one horizontal layer of the cross ow evaporator. There are 20 layers in the tube bundle, and each of them has six parallel tubes starting from the oil inlet header, going through three passes and arriving to the oil outlet header.

Figure 6.5: The six tubes and three passes on a layer for the oil side. [AalborgCSP, 2014]

In the next gure a detail of the evaporator drum inlet header is presented.

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6.1 Working Principle

The steam generation system is basically a steam boiler of the water tube boiler concept. But this specic design of Aalborg CSP and DanBoiler has some dierences from a classical water tube boiler.

The boiler is composed of a steam drum, one common downcomer for two parallel units consisting of two cross ow evaporators with their two independent risers.

The heat ux comes from the oil ow inside the tubes in the cross ow evaporators that have plane horizontal tubes. This is a dierence to that in a heat recovery boiler for combined cycle, where the heat ux comes from ue gases and therefore the evaporator consists of nned riser vertical tubes.

There is one riser for unit that collects the entire water/steam mixture from the tube bundle. There is instead only one common downcomer for boiler that brings all the water ow from the drum to both the parallel units.

In the drum, water and steam are in equilibrium in a two phase state, and Pressure and Temperature are the same variable: the drum pressure and the saturation temperature at the pressure in the drum for water.

The feed water from the economizer comes slightly sub cooled to the drum, with a ∆Tapproach that depends on the load case, and the economizer functioning. From the

bottom of the drum, water at saturation temperature enters the downcomer and then splits into the two cross ow evaporators. For the head pressure of the downcomer the water encounters the rst layer of the tube bundle in a slightly sub cooled condition (approx 1 K under saturation temperature). Then the water starts exchanging heat ux with the tubes of the bundle for every layer and it starts evaporating as soon as the saturation temperature, corresponding to the pressure at the layer in the bundle, is reached.

At the exit of the bundle the water/steam mixture with a mean quality in the range of 0.05-0.2 goes into the riser and rises to the drum, where several internal components of the drum, separate the water from the steam (steam separators: baes and cyclones, see the project report [Pelagotti et al., 2013] at chapter 4). The wet steam in the drum is sent through steam dryers at the top of the drum, called scrubbers and then to the super heater, after which the steam will expand into the steam turbine and then into the condenser.

The evaporator circuit, intended as the circuit from the drum, downcomer, evaporator to the riser, is subjected to natural circulation with a circulation number in the range from 5 to 15. The circulation number expresses the number of times that water has to be circulated through the circulation circuit before all the water will be evaporated, and therefore is the inverse of the mean quality in the riser. The natural circulation is due to the geometrical conguration of the boiler plus the heat supply into the evaporator, and is regulated by the pressure drop all along the circulation circuit and the heat ux supplied to the water/steam.

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Spatial Discretization of

the Evaporator

7

The discretization of the cross ow evaporator is one of the most important initial steps in the understanding of the system.

An appropriate dimension of the sections in which the system is discretized, is important for avoiding accuracy errors but also for maintaining a certain degree of simplicity. In this chapter the discretization used in thermodynamic model is described.

Figure 7.1: Four layers of the tube bundle, with SolidWork

7.1 Thermodynamic Model Discretization

A very accurate and ne mesh has been used. It is composed of around 21 million sections, each with the following dimension: y = 4 mm z = 1 mm x = 70 mm. A very high number of sections is possible, because their number does not aect the computational time when an explicit calculation is carried out, because the equations that are solved are analytical and there is no iterative method applied.

A sensitivity analysis has been carried out about the number of sections, in order to see how the accuracy of the solutions is aected by the spatial discretization. The minimum

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number of sections along z-coordinate has been found to be around 100 in order to avoid boundary jumps between one pass and the following pass. Fewer sections in z can be anyway used if the passes junctions are not taken into considerations. Even 10 sections along z can be used, since the analytical formulation of the problem is exact along z, no matter how big a section along z is, if only a pass is calculated. It is at the junctions between the passes that errors occurs. Therefore the solution in a section of the equation is exact, and is not aected by the mesh renement in z-coordinate. As for the y-coordinate discretization the same conceptual analysis can be developed, resulting in a minimum number of section of 2 on the outside of a single tube, from the 10 used in the Model. Regarding the dimension of one section in the x-coordinate, this dimension is the smallest possible if only one tube has to be included in one section. Therefore the dimension of the section on the x-coordinate cannot be bigger than 70 mm and it has to be big enough to include one tube diameter and enough space in the surroundings. The dimension used is the optimal one, that considers the conguration of the staggered tube bundle.

Each tube in the bundle is approximately 11.1 m long and has an external diameter of 38.1 mm. The tube bundle has a staggered arrangement with a transverse pitch of 30 mm and a longitudinal pith of 80 mm.

There are 6 pipes for every layer, leading from the oil inlet header to the exit manifold, and these six tubes have three passes each, for a total of 18 tubes for layer (each layer is also called row of the tube bundle). There are in total 20 layers, or rows of the tube bundle, in the vertical direction, that are crossed from the inlet (down comer exit) to the outlet (riser inlet). The following pictures can help for understanding the discretization in the volume of the tube bank.

Figure 7.2: One volume unit of one tube on a layer. In the inside ows oil and outside ows water/steam

Figure 7.3: One volume unit with SolidWorks

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The gures above show a section of a tube where oil ows in the inside and water/steam in the outside of the tube. The following gure shows instead the layout of a layer.

Figure 7.4: One tube layer layout with the three passes.

One layer is composed of 6 tubes starting from the oil inlet header, with three passes to the oil outlet header on the same level. Each tube in Figure 7.4 has its color, for the three passes. Each tube is discretized as shown in gure 7.2. There are 20 layers in the y-direction.

Figure 7.5: Space 3D discretization from the outside ow point of view

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Figure 7.6: The three passes of a tube

Figure 7.6 shows how the oil ows in two passes and how these two passes can be treated as a longer single pass in the z-direction on a layer as shown in Figure 7.7

Figure 7.7: How the three passes are put in a row in order to solve the temperature eld, using boundary conditions at the junctions.

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Figure 7.8: Cross sectional volume discretization principle of the entire tube bundle.

7.2 Dynamic Model Discretization

It is a 2-D model and it uses the exponential law founded in the thermodynamic model expressed with Equation 8.15 instead of a classical linear one that uses a linear mean value between the inlet and outlet value.

It models a section of 0.5 m of a tube in the cross ow evaporator. The geometry is the one shown in Figure 7.3, with the only dierence that the length of the section in the axial dimension is 0.5 m and that on the y dimension only one volume section around the tube has been used.

A complete dynamic model has been developed only for the mentioned section of a tube in the cross ow evaporator. Seen the complexity of modeling in dynamic condition the two-phase phenomenon of evaporation on a tube bundle, a semi-dynamic approach has been preferred in order to describe dierent load conditions, instead of developing a complete dynamic model for the entire tube bundle for the entire range of P and T that occurs in a start-up. The concept of the semi-dynamic approach is expressed simply by discretizing the time and considering a nite amount of time steps, and approximate the innitesimal analysis with a discrete analysis. It is the same principle of approximating an integral with a summation. The accuracy depends on the size of the time step used to approximate the integral1_.

A complete dynamic model has not been developed. This has been done for reasons of time, since developing a dynamic model that adapts to dierent range of T and P during a start-up for a two phase evaporation phenomenon in a cross ow tube bundle is

1_{In the time span of this Master's Thesis, this part of the project was not able to be developed with}

the opportune accuracy and therefore a semi-dynamic approach was preferred to a non accurate dynamic model.

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highly complex and time consuming. The author understood a way of doing it, combining small part of codes for discretized sections of the tube bundle, and combining them with appropriate boundary conditions for reconstructing the entire geometry. Moreover dierent correlations have to be used accordingly to the range of P and T during the start-up time as explained in Chapter 9.

The author, after the work already done on this issue, is convinced that this is an interesting part to develop in the future if more time is considered worth spending. See Chapter 15.

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Thermodynamic Model for

the Cross Flow Evaporator

8

In this chapter, a thermodynamic model is developed for the cross ow evaporator of the Coil Steam Generator of the CSP plant analyzed. The purpose of this model is to calculate the temperature distributions in the tube bundle of the evaporator, in every point of the 3-D space in the shell. When the temperature of the two uids is known in every point, it is possible to derive also the temperature in some component inside the shell of the evaporator. For instance it is interesting to nd the temperature prole in the inlet and outlet oil headers, since these two components are believed to be critical from a thermal-stress point of view. See Chapter 10 for the thermal stress analysis deriving from the results of the model explained in this chapter.

A model based on the rst principle of thermodynamic for steady state cross ow heat exchanger has been used. On top of that, a model describing the heat transfer process on a tube bundle is used, and is therefore possible to calculate several important variables in the evaporator, like enthalpy, quality and heat transfer coecients. The input data necessary for the model have been given by Aalborgs CSP from plant measurements. Once these parameters are know it is possible to derive and conduct a series of analyses of interest on the evaporator oil headers, and understand how critical these components are for the plant, and how they respond to dierent load conditions and start-up routines. These analyses are presented in Chapter 10, 11 and 12 arriving with the optimisation of Chapter 13, to signicant conclusions in Chapter 14.

8.1 The Cross Flow Evaporator Model

The temperature and enthalpy distributions are calculated in the tube bundle of the cross ow evaporator, using a 3-D model from Shah and Sekulic (2003) based on the First law of Thermodynamics.

The model is based on the following assumptions for the heat transfer analysis: Steady state conditions

No heat losses

No thermal energy sources or sinks Wall thermal resistance is uniform

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Phase change occurs at constant temperature and pressure (single phase component) Negligible longitudinal heat transfer in both wall and uid

The model uses the − NT U method and solves an analytical system of partial-ordinary dierential equations as shown in Equation 8.1, that when solved leads to the uid two-dimensional temperature elds. The heat balance equations for both the uids are written on control volumes in the 2D discretization used for cross ow arrangements.

The conguration for the cross ow heat exchanger is supposed to be unmixed on the water/steam side and mixed in the thermal oil side. This is due to the used discretization for the evaporator, see Chapater 7. For instance the oil ow inside a tube is considered having a turbulent completely developed ow, where no temperature prole is expected on a direction perpendicular to the ow thanks to the mixing of the turbulence. Dierently for the water/steam ow on the tube bundle, a temperature/enthalpy prole is expected to vary both along the tube length and the bundle height. This can be understood thinking that the water/steam ow has a main vertical component through the tube bundle from the bottom (down comer) to the top (riser) thanks to the natural circulation in the steam generator circuit. This results in a 2D dimensional temperature eld for the water/steam ow along the tube bundle length and height and a 1-D temperature eld for the oil ow along the tube length.

As shown in Shah and Sekulic [2003] (from page 749−753) the model that has to be solved for nding the temperature distributions for the uids with the above mixing conditions is the following system of dierential equations, one partial and one ordinary:

       ∂θ2 ∂ξ + θ2= θ1 dθ1 dχ + θ1= 1 C∗_{N T U} · Z C∗_{N T U} 0 θ2dξ. (8.1)

The system above is made non dimensional and the symbols used represent:

θ1 = T1− T2,i T1,in− T2,in (8.2) θ2 = T2− T2,in T1,in− T2,in (8.3) χ = z L1N T U (8.4) ξ = y L2C ∗_{N T U} (8.5)

where the domain is 0 ≤ χ ≤ NT U and 0 ≤ ξ ≤ C∗_{N T U} _{and 1 refers to the oil ow and}

2 to the water/steam ow, and the boundary conditions areθ1(0) = 1and θ2(χ, 0) = 0.

The solution of the above system of equations is carried out analytically and implemented and solved in MATLAB, applying the Laplace Transform technique to the partial

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dierential equation, in order to replace the non dimensional coordinate ξ = y

L2C∗N T U

with the complex variable s for the space domain of Laplace Transform:

L ∂θ2 ∂ξ + θ2 ξ→s =L {θ1}_ξ→s (8.6) sθ2(χ, s)− θ2(χ, 0) + θ2(χ, s) = θ1(χ) s (8.7)

Rearranging and considering that θ2(χ, 0) = 0:

θ2(χ, s) =

θ1(χ, s)

s (s + 1) (8.8)

Applying an inverse Laplace Transform it gives:

L−1 θ1(χ, s) s (s + 1) s→ξ = θ2(χ, ξ) = θ1(χ) 1− e−χ (8.9)

obtaining therefore an algebraic equation in θ1 and θ2 as function of χ and ξ:

θ2(χ, ξ) = θ1(χ)·

1− e−ξ (8.10)

Replacing the above expression for θ2 in the ordinary dierential equation in χ for θ1, the

following equation can be solved to nd the explicit formulation for θ1(χ):

dθ1 dχ + θ1 = 1 C∗_{N T U} · Z C∗_{N T U} 0 θ1(χ)· 1_{− e}−ξ dξ (8.11)

After determining the integral on the right hand side of the previous equation, the dierential equation can be written as:

dθ1(χ) dχ + Kθ1(χ) = 0 (8.12) K = 1− exp −C∗_{N T U} C∗_{N T U} (8.13)

Where K is a parameter related to the NTU method. The solution of the following system is then straightforward    dθ1(χ) dχ + Kθ1(χ) = 0 θ1(0) = 1 (8.14)

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θ1(χ) = e−Kχ (8.15) θ2(χ, ξ) = 1− e−ξ· e−(Kχ) (8.16)

As expressed from the above equations, it results in a 1-D temperature eld along the χ coordinate for the oil and a 2D temperature eld for the water/steam along χ and ξ, that correspond to the z-coordinate (the tube length) and the y-coordinate (the bundle height).

The system 8.15 is derived from a 2-D energy balance of the heat exchange process in a cross ow heat exchanger and is then made 3-D by the author, invoking the assumption of axial symmetry of a tube in the tube bundle of the cross ow evaporator and considering that every layer of the tube bundle is composed of 6 tubes each with three passes from the inlet to the outlet oil header. In other words, the system 8.15 is solved for each one of the 3 passes of a tube, using appropriate boundary conditions between the passes, see Chapter 7. Moreover when each tube of the rst layer of the tube bundle is solved, the same model is solved for the second layer using boundary conditions from the rst layer outlet as the inlet conditions for the second layer inlet. The same is repeated for the 20 layer of the evaporator bundle.

The temperature proles for the uids are exponential along the tube length and are strictly related to both NTU and C∗_{. Recalling the denition of NT U:}

N T U = U A Cmin

(8.17)

Cmin = ( ˙mcp)_min

(8.18)

This implies that the temperature outlet distributions are depending on the heat transfer coecient of both uid and also the conduction in the tube wall. It is crucial to understand which is actually the bottle-neck for the heat transfer process. From the model calculation it emerges that the conduction in the wall can be, together with the heat transfer on the oil side, the bottle-neck for the heat transfer process. In fact from the MATLAB program it can be calculated that the thermal resistances are: (using a thermal-circuit analogy)

Rh,oil= 1.05· 10−4 [K/W]

Rk= 9· 10−5 [K/W]

Rh,ws= 1.27· 10−5 [K/W]

The thermal resistance network can be seen in 8.1, where Rh,oil = Rconv,1 and Rk= Rcyl

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Figure 8.1: Thermal resistance analogy for a cylinder, from [Cengel and Ghajar, 2011], neglecting the fouling thermal resistances

It can be seen that the oil convection heat transfer thermal resistance is approximately of the same order of the one for the heat conduction in the wall, because the ow inside the tube is highly turbulent with high velocity and that implies a high heat transfer coecient. As for the external thermal resistance for convection and boiling on the outside of a tube, it is on order of amplitude smaller and therefore it does not aect the heat transfer process from the oil to the water/steam.

It was also understood that using a dierent heat transfer correlation for the oil side, as it has been done for a comparison, see Appendix B, aects the value of the oil convective thermal resistance and therefore it has an impact on which one is the bottle-neck for the heat transfer process. Using the Dittus-Boelter correlation gives smaller heat transfer coecient and therefore higher thermal resistance, leading to the convection on the oil side to be the highest thermal resistance in the process and therefore the bottle-neck parameter.

Rh,oil= 1.6· 10−4 [K/W]

Rk= 9· 10−5 [K/W]

Rh,ws= 2.8· 10−5 [K/W]

In this case the wall thermal resistance is half the value of the convective thermal resistance on the oil side, while before the dierence was only 10%. Moreover the mass ow of oil it is relevant, because it is the uid with the Cmin that therefore directly aects the NTU

value as well.

Going back to the model, the extension of the model along the third coordinate x is straightforward considering the design of the cross ow heat exchanger. In fact there are 20 layers on the y coordinate and 6 tubes with 3 passes for each layer along the x coordinate. See Figures 7.1 and 7.8.

Implementing this geometry in the MATLAB program, and solving the equations for the temperature elds for each section of each tube for the three passes on each layer, and for all the 20 layers, an overall temperature eld is calculated in the shell. See next Section 8.2.

Modelling of a Coil Steam Generator for Concentrated Solar Power Applications

Modelling of a Coil Steam

Generator for CSP applications

Master's Thesis

Contents

Executive Summary

Preface

Reading Instructions

Problem Statement

1

1.1 Limitations

Project Description

2

2.1 Structure of the Project Report

Conceptual Scheme of the

Project

3

Introduction

4

4.1 Energy Scenario

4.2 Energy from the Sun

System Specifications

5

5.1 Steam Generator and Plant Congurations

5.2 Aalborg CSP Coil Steam Generator

Design of the Evaporator

6

6.1 Working Principle

Spatial Discretization of

the Evaporator

7

7.1 Thermodynamic Model Discretization

7.2 Dynamic Model Discretization

Thermodynamic Model for

the Cross Flow Evaporator

8

8.1 The Cross Flow Evaporator Model

5.1 Steam Generator and Plant Congurations