Simulation of an Innovative Integrated Solar Receiver/Combustor Unit for Flexible Gas Turbine Based CSP

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Master of Science Thesis

KTH School of Industrial Engineering and Management Energy Technology EGI-TRITA-ITM-EX 2020:452

Division of Heat and Power Technology SE-100 44 STOCKHOLM

Simulation of an Innovative

Integrated Solar Receiver/Combustor Unit for Flexible Gas Turbine Based

CSP

Cristina Blajin

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Master of Science Thesis TRITA-ITM-EX 2020:452

Simulation of an Innovative Integrated Solar Receiver/Combustor Unit for Flexible Gas Turbine Based CSP

Cristina Blajin

Approved Examiner

Anders Malmquist

Supervisor

Jens Fridh

Commissioner Compower

Contact person

2020-10-26

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List of Figures

Figure 1. TULIP solar hybrid MGT plant developed by AORA-Solar [22] ...17

Figure 2. Schematic of the 247Solar low-pressure Brayton system configuration (left) and a photo picturing the tower with the receiver on top, thermal storage next to it and the heliostat field (right). ...18

Figure 3. Schematic of the hybrid gas turbine-receiver unit [26] ...19

Figure 4. Investigated layouts: A-Series arrangement, B-parallel arrangement, C-externally fired gas turbine. ...22

Figure 5. Receiver system boundary ...23

Figure 6. Compower turbocharger ...23

Figure 7. The 16 beta lines superimposed on the original compressor map ...24

Figure 8. Interpolated and extrapolated compressor speed lines (red lines) and extrapolated efficiency lines (green lines) ...25

Figure 9. Turbine map ...26

Figure 10. Compressor operating line for different turbine scaling factors ...28

Figure 11. Recuperator pressure loss as affected by mass flow ...29

Figure 12. Schematic of the impinging receiver: (A) 3D geometrical model; (B) 2D drawing. [33] ...30

Figure 13. Receiver pressure drop as a function of air mass flow and at different air inlet conditions (receiver inlet temperature of 634 ℃) ...31

Figure 14. Receiver outlet temperature as a function of the air mass flow and DNI, at a fixed inlet temperature of 634 °C ...34

Figure 15. Receiver efficiency as a function of the air mass flow and DNI, at a fixed inlet temperature of 634 ℃ ...35

Figure 16. Combustor model AspenPlus...36

Figure 17. Combustor temperature as a function of air inlet temperature to the combustor ...37

Figure 18. Combustor NO emissions as a function of air inlet temperature to the combustor ...37

Figure 19. Combustor NO2 emissions as a function of air inlet temperature to the combustor ...37

Figure 20. Combustor CO emissions as a function of air inlet temperature to the combustor ...37

Figure 21. Combustion chamber ...38

Figure 22: System pressure changes trough the series system arrangement. Pressure losses have been exaggerated for emphasis and are not proportional to the real ones. ...40

Figure 23. Series arrangement flowchart of the design model ...42

Figure 24. Parallel arrangement ...43

Figure 25. Air mass flow through the receiver and the receiver efficiency at varying DNI ...43

Figure 26. Pressure drop in the combustor and receiver with varying DNI ...44

Figure 27. Valve characteristics curve [38] ...45

Figure 28. Pressure drop across the two valves and the respective valve openings at different DNI (design point). ...45

Figure 29. Pressure drops ...46

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Figure 30: T-S diagram of the MGT with series arrangement at 400 DNI ...48

Figure 31. Effects of ambient temperature on load, turbine power, compressor power and air mass flow at constant rotational speed ...50

Figure 32. Effects of air humidity on load, turbine power and compressor power at constant rotational speed ...51

Figure 33. Compressor efficiency sensitivity analysis ...51

Figure 34. DNI Sensitivity analysis ...52

Figure 35. Estimated addressable market for electricity access solutions (2019)[40]. ...54

Figure 36. Market analysis results ...57

Figure 37. Population density of South Africa (left image) and the South Africa map showing the percentage of people using electricity as their main energy sources for lighting (right image). ...58

Figure 38. Annual power generation in South Africa site Nr. 1 ...59

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List of Tables

Table 1. Key companies in the micro turbine industry ...15

Table 2. Receiver input and output parameters obtained from CFD simulations [33] and current model calculations at 800 DNI. ...33

Table 3. Molecular composition of dry air [36] ...38

Table 4. System pressure drops ...40

Table 5. Sensitivity analysis on the opening of the receiver side valve opening ...46

Table 6. Design point simulation results for the three different configurations ...49

Table 7. Factor weights ...55

Table 8. System performance summary for two selected sites in South Africa ...60

Table 9. System performance summary for two selected islands ...61

Table 10. Sustainability analysis ...62

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Nomenclature Abbreviations

CFD Computational Fluid Dynamics

CSP Concentrated Solar Power

PV Photovoltaic

KPI Key performance indicators

NTU Number of transfer units

R&D Research and development

RH Relative humidity

SSA Sub Saharan Africa

TIT Turbine Inlet Temperature

MGT Micro Gas Turbine

DNI Direct Normal Irradiance

Exp exponential

LHV Lower Heating Value

IMP Index of Market Potential

Symbols

Symbol Unit Description

𝐴 𝑚² Area

𝐴 − Access to electricity

𝐵_{𝑝𝑜𝑡.} 𝑘𝑊ℎ/𝑝𝑝/𝑦𝑟 Biogas potential 𝑐 𝐽/(𝑘𝑔 ∙ 𝐾) Specific heat capacity

𝐶 𝐽/𝐾 Heat capacity

𝐶_𝑑 − Discharge coefficient of the nozzle which is dependent on the nozzle configuration

𝐷_{𝑝𝑜𝑡.} 𝐺𝑊ℎ Demand potential

𝑑 𝑚𝑚 Diameter of the nozzle or orifice 𝐸 𝐺𝑊ℎ Total power generation in one year

𝐹 − Factor

𝐾_𝑣 𝑚³/ ℎ𝑟 Flow coefficient

ℎ 𝐽/𝑘𝑔 Enthalpy

𝑄 𝐽 Energy

𝑚̇ 𝑘𝑔/𝑠 Mass flow

𝑀 Molecular mass

𝑛 − Number of nozzle orifices

𝑁 − Rotational speed

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𝑁̇ Molar flowrate

𝑃 𝑃𝑎 Pressure

𝑃 − Population

𝑃𝑒𝑙. $/𝑀𝑊ℎ Electricity price

∆𝑝 − Relative pressure loss

∆𝑃 𝑃𝑎 Absolute pressure loss

𝑟 − Pressure ratio

𝑇 ℃ Temperature

𝑈 𝑊/(𝑚²∙ 𝐾) Heat Transfer coefficient

𝑉 𝑚/𝑠 Velocity

𝑤 − Factor weight

𝑊 𝑊 Power

𝑥 − Molar fraction

𝜎 𝑊/(𝑚²∙ 𝐾⁴) Stefan-Boltzman constant

𝜀 − Effectiveness

𝜀 − Emissivity

𝜂 − Efficiency

𝜌 𝑘𝑔/𝑚³ Density

Subscripts

abs absolute

amb ambient

ap aperture

atm atmospheric

B Biogas

C Compressor

comb combustor

corr corrected

cyc cycle

d discharge

D Demand

elec electrical

F Finance

HEX heat exchanger (recuperator)

I Irradiance

in inlet

max maximum

mec Mechanical

min minimum

N normal conditions

out outlet

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P price

pot. potential

R risk

rad radiative

rec receiver

ref reference

sat saturation

T Turbine

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Abstract

In the wake of climate change, the generation of renewable power is of vital importance to ensure a sustainable development with reduced carbon emissions. Among all renewable energy sources, solar power is the most abundant and has a great potential to move the global energy production away from fossil fuels as well as to bring power into regions that currently lack access to electricity. The hybridization of gas turbines with solar power is a promising way to harness the solar energy while ensuring that the technology can meet the demand at any times.

Currently, the researchers from the Department of Energy Technology at KTH and Compower AB are working on developing an innovative hybrid solar micro-turbine, which allows nominal power output with a solar share between 0% and 100% by integrating a biogas based internal combustor. The current thesis explores different ways in which the hybridization of the micro-turbine can be achieved. Specifically, the thesis examines three different configurations of integrating the receiver with the combustor e.g. serial, parallel or externally fired gas turbine.

The first part of the thesis develops a steady state model to simulate the three different configurations at the design point. The results indicate that the parallel configuration has a slightly better thermodynamic performance. However, given the fact that the series arrangement is still the preferred choice considering its reduced complexity.

The second part of the thesis develops a methodology to evaluate the market potential and identify the most suitable countries where the technology could be deployed. Based on the identified suitable location, annual simulations were run. South Africa is identified as the most suitable country since it has a high solar and biogas availability, as well as a high-power demand.

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Sammanfattning

Till följd av klimatförändringarna är produktionen av förnybar elkraft av avgörande betydelse för att säkerställa en hållbar utveckling med minskade koldioxidutsläpp. Bland alla förnybara energikällor finns solenergi i rikligast mängd och har stor potential att flytta den globala energiproduktionen bort från fossila bränslen samt förse el till de regioner som i dagsläget saknar tillgång. Att kombinera gasturbiner med solenergi är ett lovande sätt att utnyttja solenergi och samtidigt se till att tekniken kan möta efterfrågan när som helst.

För närvarande arbetar forskare på Institutionen för Energiteknik vid KTH och Compower AB med att utveckla en innovativ solhybrid-mikroturbin som tillåter nominell uteffekt där solenergin står för mellan 0%

och 100% genom att integrera en biogasbaserad förbränningsenhet. Detta examensarbete undersöker de olika sätten på vilka hybridiseringen av mikroturbinen kan uppnås. Mer specifikt undersöker examensarbetet tre olika konfigurationer för att integrera mottagaren med förbränningen, en serie-, parallell- eller en externt eldad gasturbin.

I den första delen av examensarbetet utvecklas en steady-state-modell för att simulera de tre olika konfigurationerna vid designpunkten. Resultaten indikerar att den parallella konfigurationen har en något bättre termodynamisk prestanda. Men med tanke på dess mindre komplicerade konfiguration är seriekonfigurationen fortfarande att föredra.

Med tanke på det faktum att seriekonfigurationen fortfarande är det föredragna valet med tanke på dess minskade komplexitet.

I den andra delen av examensarbetet utvecklas en metod för att utvärdera teknikens marknadspotential och identifiera de mest lämpliga länderna för tekniken att användas. Baserat på den identifierade lämpliga platsen körs simuleringar på årsbasis. Sydafrika identifieras som det mest lämpliga landet tack vare dess höga tillgänglighet till solenergi och biogas, samt ett högt effektbehov.

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Acknowledgements

Throughout the course of writing my master thesis, I received support from many people for which I am forever grateful.

First, I would like to thank Jens Fridh, my supervisor, and Dr. Anders Malmquist for giving me the oportunity to write this thesis with the Unit of Heat and Power Technology at KTH. Without their guidance, patience and continuous support this research would not have been possible. The same gratitude is extended to Wujun Wang, Prof. Torsten Strand and Lars Malmrup for their crucial contribution to this work.

Many thanks to my dear friends Anna and Oluchi with whom I shared a gazillion of beautiful moments during my master studies, and who played an essential part in making my Stockholm experience unforgettable. I would also like to thank my friends Camelia, Youssef and Jindan for their support and being there for me when I needed them.

Finally, infinite thanks to my family who always believed in me. Without their unconditional love and encouragement I woudn’t be where I am.

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1 Introduction

Climate change is one of the most pressing challenges the world faces today. According to “The Global Risks Report 2019”, the global environment-related risks account for there of the top five risks by likelihood and four by impact [1]. In order to address climate change and the associated risks, a transition to a low- carbon economy should be on top of the political agenda of every country. Although the global energy market is already undergoing a paradigm shift in the way energy is generated, the pace at which this shift is happening is too slow. According to the IRENA Roadmap 2050, the deployment of renewable energies should be at least six times faster in order to meet the goals set out in the Paris Agreement [2]. In this context, it is of a paramount importance to ensure that the rising global energy demand is met within sustainable boundaries. However, curbing the emissions for newly built energy systems is not enough to tackle the climate change. In next decades, the existing generating facilities that rely on conventional sources should also be replaced by renewables. This dual energy dilemma of keeping up with the increasing demand while at the same time replacing the existing power generation capacities, requires significant efforts and most importantly, it emphasis the need for innovative and low cost technologies.

Concentrated Solar Power market overview

The two prominent technologies that are able to harness the solar energy for electricity generation purposes are PV and Concentrated Solar Power (CSP). These two technologies are fundamentally different; while PV is converting the solar energy directly into electricity, the CSP technology concentrates the solar energy into one focal point where the thermal fluid is heated to a high temperature and later on used to drive a heat engine. In the last decade, the plunging PV prices made this technology very attractive from an economic point of view and thus, along with hydro and wind power, the PV has made a significant contribution in increasing the share of renewables in the power generation sector, overshadowing the CSP developments.

According to the World Energy Outlook 2018, the total electricity generated by PV in 2017 was estimated to be 435 TWh whereas for CSP only to 11 TWh. The same report outlines that the PV are still expected to dominate over the CSP technology with a total estimated electricity generation in 2025 increasing to 1,334 TWh for PV and 30 TWh for CSP under the current policies scenario [3]. Nonetheless, the interest in CSP technology is increasing steadily and the technology is expected to play an important role in the decarbonization of the energy sector. One of the most attractive features of the CSP technology is the possibility to integrate storage and thus ensure a stable and reliable power supply. According to the GlobalData’s CSP market Update 2019, at the end of 2018 the total installed capacity of CSP was 5.6 GW, out of which only 2.6 GW include energy storage. In contrast, 95.8% of the total CSP projects that are currently under development have integrated thermal storage in the range of 6-10 hours [4]. Moreover, the integrated storage also enables the usage of CSP for baseload energy.

The above mentioned CSP market data focuses primarily on big scale plants with MW capacities. However, the development and deployment of small scale CSP is also gaining traction in recent years, especially for providing off-grid energy solutions. The potential growth for small scale CSP is enormous and is estimated that it could potentially reach 63 GW installed capacity by 2050 from only 25 MW in 2012, which corresponds to an increase factor of 2,500 [5]. One advantage of small-scale CSP is that the technology is suitable for meeting other energy needs such as heat for local activities. Because of these additional benefits, small scale solar plants could be deployed as a solution for smart energy and water use in the “agri-food chain”; a sector which currently generates about 21.5 % of the global emissions [6].

Micro Gas turbine market overview

Microturbines are small scale power generators able to produce electrical power by extracting the energy from a working fluid. Usually, the turbines are classified as “micro” if their power output does not exceed 500 kW. However, depending on the literature, this limit varies a lot with some authors setting the limit as low as 250 kW whereas other set a higher limit such as 1 MW. [7]

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The early application of microturbines was mainly limited to the automotive industry and aircraft auxiliary power systems. It was not until 1978, the year when the deregulation of the electricity market in the United States started, that the microturbine gained attention as a mean to generate power. This event was a turning point and led to a significant increase in distributed generation which subsequently intensified the R&D for microturbines [8]. Several advantages such as small number of moving parts, compact size, lightweight and reliable operation made this technology especially attractive for many different sectors. For example, a special interest in microturbines comes from the commercial sector where there is high demand for cost- effective electricity and thermal power. The technology is also successfully used to supply power in remote areas with no access to the grid.

In recent years, the microturbine market has witnessed a continuous grow. The main drivers behind this expansion stem from an increasing need for on-site resilient power generation. The aging infrastructure, which results in a less reliable grid, combined with the urge to transition towards more sustainable energy sources are expected to further increase the demand for decentralized solutions, including microturbines.

According to a recent report released by Fortune Business Insights, the global market for microturbine is currently valued at $ 180 millions and is expected to double by 2026 reaching $ 360 millions. The market is highly dominated by major, well established companies such as Capstone Turbine Corporation, which is currently the leader. Other key companies in the microturbine market are listed in Table 1.

Table 1. Key companies in the micro turbine industry

Company name Product description Fuel used

Capstone Turbine Corporation [9]

With products in the range of 30 kW to 1 MW, the company is well established in the market offering a wide range of solutions. The electrical efficiency for the 30 kW microturbine is 26%.

Wide range of fuels including methane from landfills, wastewater treatment and food processing facilities.

Bladon Micro Turbine [10]

Microturbine design delivering 12 kW power. The peak electrical efficiency is 25%.

The micro turbine is able to operate with kerosene, diesel or kerosene/diesel mix.

Ansaldo Energia [11]

Offers several micro gas turbine models (AE-T100). The microturbine design able to operate with biogas, AE- T100B has a capacity of 105 kW and 30% electrical efficiency.

The company offers three distinct models able to operate with natural gas, biogas and an externally fired micro gas turbine model able to work with a wide range of fuels.

Aurelia Turbines [12]

The company’s microturbine A400 provides 400 kW. The company claims its product to have the highest efficiency in the world, above 40%.

Given the modular construction of the turbine, it is possible to operate it with a wide variety of fuels, including biogas and biodiesel.

MTT

Microturbine [13]

The company develops recuperated micro turbines up to 30 kW with electrical efficiencies between 16% and 25%.

The commercially available products operate with natural gas. Products able to operate with or liquid fuels such as oil or biodiesel are currently under development.

ICR Turbine Engine

Corporation [14]

The company provides an innovative gas turbine with a 350 kW power output, with an efficiency of 40% and above.

The micro turbine can operate with a large variety of fuels such as natural gas, diesel, synthetic gas, wellhead gas, etc.

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Company name Product description Fuel used

Turbo Tech Precision

Engineering [15]

The company provides a 500 kW micro turbine

The turbine has multi-fuel capabilities able to operate with liquid as well as gaseous fuels, including biogas.

Brayton Energy The company offers a large spectrum of products able to generate from as little as 2 kW power up to 1.2 MW. The company also develops brayton cycle based on solar power combined with thermal storage.

Depending on technology, different fuels can be used including biogas.

FlexEnergy The company offers 333 kW micro turbine and a 1.3 MW one. The electrical efficiency of both models is 33%. The Flex Turbine technology was adapted from the Dresser Rand KG2 by Ingersoll Rand in the early 2000's.

The micro turbines can operate with natural gas and LPG.

There are a number of companies in the market that offer micro turbine solutions for specific applications.

For instance, the Bowman Power Group Ltd. offers Electric Turbo Compounding (ETC) technology that can produce electricity by recovering the waste heat energy from the exhaust of reciprocating engines [16].

Hybrid micro gas turbines

The hybridization of gas turbines with solar power has been a research topic for almost four decades [17].

The most prominent projects are presented in the following subsections.

1.3.1 SOLGATE and SOLHYCO

SOLGATE is one of the most successful project in which a helicopter engine was hybridized to enable external solar heating. The project run from 1999 to 2003, and the consortium included the German Aerospace Center DLR which developed and supplied the solar receiver modules and ORMAT which worked on the necessary modifications of the helicopter engine to be able to integrate the solar power. The project was among the first to experimentally demonstrate that the combination of pressurized receiver and gas turbine really works.

For absorbing the solar heat, the hybrid cycle comprised three receiver modules connected in series, which could increase the temperature from 550 °C in the low temperature receiver module to 1,000 °C in the high temperature receiver module. A field of ray tracing heliostats was used to reflect the solar irradiation towards the receivers. The receiver modules were then followed by a combustor connected in series used to provide the necessary heat for reaching the desired turbine inlet temperature (TIT). The combustor was modified in order to allow inlet temperature up to 800 °C. The design power output of the plant was 250 kWe. [18]

SOLHYCO was a follow up of the SOLGATE project and run from 2006 to 2010. The project used the Turbec 100 microturbine, which was modified from the original cogeneration unit to be able to use solar heat as fuel. At the design point, the receiver outlet temperature was 800 °C. After the receiver, the air was further heated in a combustor, which was able to operate with biodiesel as fuel. The system was successfully demonstrated for more than 165 hours, out of which 100 hours were solar operation. [19]

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The first commercially available hybrid solar MGT was provided by AORA-Solar; a company specializing in developing small-scale off-grid solutions. The hybrid system can use both solar and fuel (biogas or diesel) to supply a stable power output. The first two demonstration units were built in Samar, Israel and Almeria, Spain. The plant is able to provide 100 kWe and 170 kWt of heat that can be used for different purposes such as water desalination and cooling.

The AORA’s power plant features a field of heliostats to concentrate the solar irradiation into a focal point on top of the tower where the receiver is located. The exact number of heliostats depends on the location.

The first power plant in Israel had 50 mirrors and the entire area of the plant was 2,500 m². The latitude of the second plant is Spain was higher, and therefore, the heliostats were spaced farther apart to avoid blocking and shading. For the plant in Spain a total number of 52 heliostats were needed to provide the nominal power and the total occupied area of the plant was 2,800 m².[20]

In contrast to the conventional CSP towers that have the power block located on the ground, the AORA- Solar technology has the MGT, combustor and generator located on the top of the tower, inside the so called “tulip”. This compact design allows an increased efficiency by eliminating additional losses between the components. Both plants that were already constructed were equipped with a diesel tank located on the ground to provide backup fuel. The diesel fuel, however, was only used to demonstrate the concept of the hybrid system and the final configuration of the plant will be based on biogas fuel. The company advertises its solutions as suitable for remote areas, and thus being able to operate on biogas allows tapping into the local available renewable resources.

After the second demonstration plant was built back in 2012 in Spain, the technology made it to the headlines and many more plants were expected to be built soon after. However, this did not happen, and since 2012 no more commercial plants were built. In 2015 AORA-Solar has signed a Memorandum of Understanding with the Ethiopian Ministry for Water, Irrigation and Energy to build the first solar-hybrid plant in Ethiopia [21]. The construction was supposed to start by mid-2015, however, as of May 2019 there are no updates regarding the status of the project. The lack of available information about the company and its project coupled with the fact that its website is shut-down might imply that the company went bankrupt.

Figure 1. TULIP solar hybrid MGT plant developed by AORA-Solar [22]

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A more advanced CSP technology was introduced in the market by 247Solar. The company developed a 300kWe system that, similar to AORA Solar technology, features a heliostat field to concentrate the solar irradiation into a focal point on top of the tower where the receiver is located. The 247Solar system, however, introduces several innovative features that differentiate the product from the previously developed small scale CSP systems. The main breakthrough is the introduction of a high-temperature heat exchanger that transfer the heat from the air exiting the solar receiver to the compressed air entering the turbine. The high temperature heat exchanger is a novel technology that was recently released in the market by the Hayens International and relies on a nickel-chromium-iron alloy which is able to withstand temperatures above 955 °C [23]. By integrating the high temperature heat exchanger, it is possible to have a simplified design and subsequently reduced costs for the receiver since it can be placed after the turbine and thus operate at a low pressure.

Figure 2. Schematic of the 247Solar low-pressure Brayton system configuration (left) and a photo picturing the tower with the receiver on top, thermal storage next to it and the heliostat field (right).

Another innovative aspect of the 247Solar system is the integration of a thermal storage with up to 15 hours full load operation capacity. The system is also equipped with a combustor which makes it possible to use conventional fuels or biofuels when no sun or stored energy are available.

In February 2018, the company announced that it has entered into a Collaborative Research and Development agreement with Masdar Institute to build its first pilot plant at the Institute’s Solar Platform in Abu Dhabi [24].

The novelty of the current dish hybrid system

The hybrid-solar technologies described in the above sections have a net electricity output in the range of 100 kWe and more. Power plants with such a capacity are suitable for communities’ micro-grids or small industrial applications and less suitable for single or several household(s) use. Moreover, these hybrid systems rely on small tower systems for harnessing the solar energy which increases the system complexity and the respectively O&M costs.

Currently, the researchers from the Department of Energy Technology at KTH and Compower AB are working on developing an innovative hybrid solar micro-turbine, which allows nominal power output with

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a solar share between 0% and 100% by integrating a biogas based internal combustor. The system integrates an innovative compact solar receiver/combustor unit where the combustion chamber is located directly at the outlet of the high temperature receiver. The receiver was developed in the framework of the OMSOP project [25].

Figure 3. Schematic of the hybrid gas turbine-receiver unit [26]

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2 Objectives and methodology

Objectives

The objectives of the current study are the following:

- Compare the performance of three different system configurations at the design point.

- Perform sensitivity analysis for the series configuration to get a better understanding of system behaviour at different operating conditions.

- Identify suitable locations where the technology could be deployed and perform annual simulations on the identified locations.

Methodology

In order to compare the three system configurations, a steady-state model is developed using the MATLAB- based routines for each configuration. Steady state-model is an optimal choice, in terms of complexity, computational power required and provided accuracy, for calculating the thermodynamic states and different mass flows within the cycle at the design point [27]. Moreover, steady-state model is an important first step when designing and sizing the system for nominal operation [17]. In terms of the tool used for steady-state modelling, MATLAB was deemed appropriate given its versatility and ability to integrate it with other tools for more accurate results.

For calculating the thermodynamic properties of the fluid throughout the system, an integrated function is applied to MATLAB model which uses the NIST REFerence fluid thermodynamic and transport PROPerties database (REFPROP) [28]. For the simulation of the combustion process Aspen Plus is chosen;

a computer-aided software which uses underlaying physical relationship to simulate chemical and other related processes. By defining the process flow, input as well as required output parameters, Aspen Plus calculates the necessary fuel mass flows for different operating conditions as well as the output gas composition. As fuel, a mixture of 65 vol% methane and 35 vol% carbon dioxide is used. The results from Aspen Plus combustion simulation are integrated into the MATLAB modelling environment.

Report structure

The current report is split up in the following chapters:

- The first chapter represents an introduction to concentrated solar energy, literature research on the state of the art of the MGT as well as hybridised MGT with concentrated solar power.

- The second chapter, the current one, presents the objective and methodology of the thesis.

- The third chapter presents the assumptions and equations that were used to build the steady state models used to simulate the three different configurations.

- The fourth chapter presents the modelling approach as well as the simulation results for each configuration.

- The fifth chapter presents the methodology developed to conduct a market analysis in order to identify the most suitable locations to deploy the hybrid MGT technology.

- The sixth chapter presents the annual simulations results for the two chosen locations.

- The seventh chapter summarizes the main conclusions of the thesis.

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3 Steady State Model

A hybrid system that uses solar as well as biofuel resources to drive a microturbine can be designed in different ways by arranging the main components differently. Each configuration will present certain advantages as well as disadvantages, and depending on the final scope of the system, a certain configuration will be preferred. In order to analyse different component arrangements in terms of cycle thermodynamic performance, a steady state model for each individual configuration is developed. The following section will detail the equations used to model different components and the relation between them within each configuration.

Investigated configurations

The following three configurations are investigated in the current thesis:

Configuration A: series arrangement. In this configuration, the compressed air is first preheated in the recuperator before entering the receiver. After leaving the receiver, the air passes through the combustor where the necessary amount of heat is added to increase the temperature of the fluid to the required turbine inlet temperature (TIT). The receiver is also equipped with a bypass pipe. The bypass is necessary in order to avoid a sudden drop in temperature when the DNI suddenly changes. Moreover, during no sun conditions or very low DNI the air will bypass the receiver as well in order to avoid additional heat and pressure losses.

Configuration B: parallel arrangement. In this configuration, the receiver and combustor are arranged in parallel. The split of the mass flow that goes through the receiver is adjusted with varying DNI so that the outlet temperature corresponds to the desired inlet temperature to the turbine.

Configuration C: externally fired gas turbine. In this configuration, the receiver is positioned downstream of the turbine. The outlet air from the turbine is heated in the receiver followed by a combustor.

Part of the energy from hot gases leaving the combustor is transferred to the compressed air by means of two heat exchangers: high temperature and low temperature heat exchangers.

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Figure 4. Investigated layouts: A-Series arrangement, B-parallel arrangement, C-externally fired gas turbine.

A

B

C

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System boundary condition

The overall hybrid system comprises many components, the most important being the compressor, turbine, combustor, recuperator, receiver, bearings, shaft and high-speed generator, control unit, solar collector and pipes. Moreover, the system can be coupled with additional equipment that will extract and valorise the heat from the exhaust gases.

For the series arrangement and the externally fired gas turbine arrangement (Figure 4 A and C), only five components are considered as part of the analysis; namely the compressor, turbine, recuperator(s), combustor and receiver. The system boundary of the parallel arrangement (Figure 4 B) also includes the two valves that regulate the flow split between the combustor and the receiver. The current model does not include the dish concentrating system as well as the generator. The system boundary of the receiver is shown in Figure 5. Moreover, it is not within the scope of the current thesis to model any further application of the exhaust heat.

Figure 5. Receiver system boundary

The five most important components that are within the system boundary investigated in the current thesis are the compressor, turbine, recuperator, combustor and receiver. In the following sections, each component and the respective equations used to model it are presented in details.

Compressor

The compressor and turbine are the two critical components that determine the overall system performance.

As shown in Figure 6, the components are radial turbomachines derived from a turbocharger and modified to fit new system requirements. The compressor and the turbine, together with the generator, are mounted on the same shaft that rotates at a high speed.

Figure 6. Compower turbocharger

3.3.1 Compressor map

The compressor map contains the information about the machine performance in terms of mass flow, pressure ratio and efficiency at different rotational speed. Collecting the data for a specific compressor in

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order to obtain its characteristic map is often a time consuming and costly process requiring specific laboratory settings. One solution to overcome this problem is to use the available maps from compressor with similar geometries but different sizes. For the current model, a compressor map from Garrett Turbocharger GT2259 was used. The map was scaled down with a factor of 0.5 to get the correct mass flow for the Compower AB turbocharger. However, when scaling down the compressor, the speed values have to be corrected with a factor of 0.913.

The compressor used in the current study is able to operate at higher speeds than the maximum speed shown on the Garrett Turbocharger compressor map. Therefore, it is necessary to extrapolate the available compressor map for higher speeds. Usually, the compressor maps are non-linear and thus it can be challenging to achieve an accurate extrapolation.

One way to mathematically represent a map is to introduce auxiliary coordinates, also called beta-lines. The beta-lines have no physical meaning and are used to facilitate the reading of the compressor map [29][30].

For reading the map, sixteen beta lines were plotted on top of the compressor map as shown in Figure 7.

For each beta-line, the five intersection points with the five compressor lines provided in the original map were extracted. Using these points, two second-degree polynomial functions were fitted for the corrected mass flow and compressor pressure ratio for each beta line (𝑚̇𝐶_{𝑐𝑜𝑟𝑟}= 𝑓(𝑁) and 𝑟𝐶 = 𝑓(𝑁)). With the help of this simple mathematical trick, it is possible to obtain the compressor operational line for higher speeds.

In order to extrapolate the compressor efficiencies for higher rotational speeds, a second-degree polynomial was generated for each efficiency line using the known data from the available compressor map (𝑚̇_𝐶_{𝑐𝑜𝑟𝑟} = 𝑓( 𝑟_𝐶)). The polynomial function was then used to extrapolate the efficiency line for higher pressure ratios. The compressor map showing the extrapolated efficiency lines as well as an example of an interpolated and extrapolated speed line is shown in Figure 8.

Figure 7. The 16 beta lines superimposed on the original compressor map

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Figure 8. Interpolated and extrapolated compressor speed lines (red lines) and extrapolated efficiency lines (green lines) The compressor corrected mass flow is defined as follows:

𝑚̇_𝐶_{𝑐𝑜𝑟𝑟}=

𝑚̇_𝐶_𝑎𝑏𝑠∙ √𝑇𝐶_𝑖𝑛

𝑇𝑟𝑒𝑓

√𝑃𝐶_𝑖𝑛

𝑃𝑟𝑒𝑓

Eq. 2. 1

Where the reference values were set at 𝑇𝑟𝑒𝑓= 15 ℃and 𝑃𝑟𝑒𝑓 = 101,325 𝑃𝑎. 3.3.2 Compressor equations

The pressure of the air entering the compressor is slightly below the ambient pressure due to the pressure losses (∆𝑝_{𝑖𝑛𝑙𝑒𝑡}) in the inlet duct. The compressor inlet pressure is calculated as follows:

𝑃_𝐶_𝑖𝑛= 𝑃_𝑎𝑚𝑏∙ (1 − ∆𝑝_{𝑖𝑛𝑙𝑒𝑡}) Eq. 2. 2 The outlet pressure from the compressor is calculated using the equation below where ^𝑟𝐶 is the compressor pressure ratio and is obtained by matching the compressor map with the turbine map.

𝑃_𝐶_𝑜𝑢𝑡 = 𝑟_𝐶∙ 𝑃_𝐶_𝑖𝑛 Eq. 2. 3

The compressor outlet temperature is calculated using the following formula:

𝑇_𝐶_𝑜𝑢𝑡 = 𝑇_𝐶_𝑖𝑛(1 + 1 𝜂𝐶

∙ [(1 𝑟𝐶

)

𝛾_𝑎𝑖𝑟−1 𝛾_𝑎𝑖𝑟

− 1]) Eq. 2. 4

In the above equation, 𝛾𝑎𝑖𝑟 denotes the average heat capacity ratio and the 𝜂𝐶 denotes the compressor efficiency which is extracted from the compressor map at the operation point. The heat capacity ratio is a function of the average air temperature as well as on the air composition. The equations for calculating the air molecular composition taking into consideration the air humidity is detailed in section 3.8.1. Neither the

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average heat capacity ratio nor the air temperature at the end of the compression process are known initially.

Therefore, in order to find the correct heat capacity ratio and outlet temperature, an iterative process was used. The iteration starts by guessing the 𝑇_𝐶_𝑜𝑢𝑡 = 200℃. Then the 𝛾_𝑎𝑖𝑟 was calculated for an average temperature ^(𝑇𝐶_𝑜𝑢𝑡+ 𝑇_𝐶_𝑖𝑛)/2. Having the value for the ^𝛾𝑎𝑖𝑟, the outlet temperature ^𝑇𝐶_𝑜𝑢𝑡 was calculated and compared with the initial value of 200°C. If the difference is bigger than 1°C, the iteration process is repeated.

The compressor power is calculated as follows:

𝑊_𝐶= 𝑚̇_𝑎𝑖𝑟∙ (ℎ_𝐶_𝑜𝑢𝑡− ℎ_𝐶_𝑖𝑛) Eq. 2. 5

The enthalpy of air is calculated with the help of REFPROP tool as a function of the air pressure and temperature as well as the air molecular composition.

Microturbine

3.4.1 Microturbine map

The turbine map used for modelling the system was provided by Compower AB (see Figure 9). The map shows the turbine corrected mass flow over the pressure ratio for eight corrected rotational speeds. The corrected mass flow as well as corrected rotational speed can be expressed as follows:

𝑚̇_𝑇_{𝑐𝑜𝑟𝑟} =𝑚̇_𝑇_𝑎𝑏𝑠∙ √𝑇𝐼𝑇

√𝑃𝑇_𝑖𝑛

Eq. 2. 6

𝑁_{𝑐𝑜𝑟𝑟} = 𝑁𝑎𝑏𝑠

√𝑇𝐼𝑇

Eq. 2. 7

Figure 9. Turbine map

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The turbine outlet pressure is calculated as follows:

𝑃_𝑇_𝑜𝑢𝑡 =𝑃𝑇_𝑖𝑛

𝑟_𝑇 Eq. 2. 8

Where the ^𝑟𝑇 is the turbine pressure ratio obtained from matching the compressor map with the turbine map at specified operating conditions.

The turbine outlet temperature is calculated using the following formula:

𝑇𝑇_𝑜𝑢𝑡= 𝑇𝑇_𝑖𝑛(1 + 𝜂𝑇∙ [(1 𝑟𝑇

)

𝛾_𝑔𝑎𝑠−1 𝛾_𝑔𝑎𝑠

− 1]) Eq. 2. 9

Where the ^𝜂𝑇 is the turbine efficiency and is extracted from the turbine map at the operation point. Similar to the compressor, the outlet temperature is obtained through an iterative process. The iteration starts by guessing the ^𝑇𝑇_𝑜𝑢𝑡= 600℃. The ^𝛾𝑔𝑎𝑠 is then calculated for an average temperature ^(𝑇𝑇_𝑖𝑛+ 𝑇_𝑇_𝑜𝑢𝑡)/2 . Having the value for the 𝛾𝑔𝑎𝑠, the outlet temperature 𝑇𝑇_𝑜𝑢𝑡 is calculated and compared with the initial value of 600°C.

If the difference is bigger than 1°C, the iteration process is repeated.

The turbine power is calculated as follows:

𝑊𝑇 = 𝑚̇𝑔𝑎𝑠∙ (ℎ𝑇_𝑖𝑛− ℎ𝑇_𝑜𝑢𝑡) Eq. 2. 10

3.4.3 Microturbine scaling factor

The compressor and turbine components were originally designed for a turbocharger, which relies only on the combustor to provide the necessary heat. Because a new component has been integrated into the system, namely the receiver, which increases the pressure drop between compressor and turbine, the system’s operational line will shift from the design one. In order for the turbine to operate at the design point, it should be adjusted by the changing the nozzle guide vanes flow area.

Before performing the simulation, the re-scaling factor of the micro-turbine for each configuration was identified. Figure 10 shows how rescaling the turbine changes the compressor operation. From the figure, it can be noticed that, for the series arrangement, the turbine needs to be rescaled by a factor of 1.093 in order to meet the design point.

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Figure 10. Compressor operating line for different turbine scaling factors

Recuperator

The recuperator is a key component that significantly increases the overall system efficiency by recuperating the heat from the exhaust gases and transferring it to compressed air.

3.5.1 Recuperator effectiveness

The recuperator is modelled as a counter-flow heat exchanger. The total heat transfer between the air and gas stream can expressed as follows [17]:

𝑄̇𝐻𝐸𝑋= 𝜀 ∙ 𝑚̇𝑎𝑖𝑟 ∙ 𝑐𝑝,𝑚𝑖𝑛∙ (𝑇𝑇_𝑜𝑢𝑡− 𝑇𝐶_𝑜𝑢𝑡)= 𝜀 ∙ 𝐶𝑚𝑖𝑛∙ (𝑇𝑇_𝑜𝑢𝑡− 𝑇𝐶_𝑜𝑢𝑡) Eq. 2. 11 At the same time, the total heat transfer can be expressed in terms of heat absorbed by the air (Eq. 2. 12) and the heat taken away from the exhaust gas (Eq. 2. 13), assuming no external losses.

𝑄̇_𝐻𝐸𝑋= 𝑚̇_𝑎𝑖𝑟∙ 𝑐_{𝑝,𝑚𝑖𝑛}∙ (𝑇_{𝐻𝐸𝑋,𝑎𝑖𝑟}_𝑜𝑢𝑡− 𝑇_𝐶_𝑜𝑢𝑡)=𝐶𝑚𝑖𝑛∙ (𝑇_{𝐻𝐸𝑋,𝑎𝑖𝑟}_𝑜𝑢𝑡− 𝑇_𝐶_𝑜𝑢𝑡) Eq. 2. 12 𝑄̇𝐻𝐸𝑋= 𝑚̇𝑔𝑎𝑠 ∙ 𝑐𝑝,𝑚𝑎𝑥∙ (𝑇𝑇_𝑜𝑢𝑡− 𝑇𝐻𝐸𝑋,𝑔𝑎𝑠_𝑜𝑢𝑡) = 𝐶𝑚𝑎𝑥∙ (𝑇𝑇_𝑜𝑢𝑡− 𝑇𝐻𝐸𝑋,𝑔𝑎𝑠_𝑜𝑢𝑡) Eq. 2. 13 The effectiveness (^𝜀) of the heat exchanger can be expressed as a function of the number of transfer units (NTU) and capacity ratio (𝐶𝑟= 𝐶𝑚𝑖𝑛/𝐶𝑚𝑎𝑥). The number of transfer units (NTU) is defined as [31, p. 12]:

𝑁𝑇𝑈 =𝑈 ∙ 𝐴

𝐶_𝑚𝑖𝑛 Eq. 2. 14

Where 𝑈 is the heat transfer coefficient and has a value100 W/(m²·K), and 𝐴 is the recuperator heat transfer surface with a value of 9 m².

Having the NTU value and the ^𝐶𝑟, the effectiveness can be calculated according to the following formula:

𝜀 = 1 − exp (−𝑁𝑇𝑈 ∙ (1 − 𝐶𝑟))

1 − 𝐶_𝑟∙ exp (−𝑁𝑇𝑈 ∙ (1 − 𝐶_𝑟)) Eq. 2. 15

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When the capacity ratio ^𝐶𝑟= 1, the effectiveness can be estimated trough the following simplified formula:

𝜀 = 𝑁𝑇𝑈

1 + 𝑁𝑇𝑈 Eq. 2. 16

After calculating the recuperator effectiveness, the temperatures of the recuperator outlet air ^(𝑇𝐻𝐸𝑋,𝑎𝑖𝑟_𝑜𝑢𝑡) can be calculated as follows:

𝑇_{𝐻𝐸𝑋,𝑎𝑖𝑟}_𝑜𝑢𝑡 = 𝜀 ∙ (𝑇_𝑇_𝑜𝑢𝑡− 𝑇_𝐶_𝑜𝑢𝑡) + 𝑇_𝐶_𝑜𝑢𝑡 Eq. 2. 17 The recuperator outlet temperature of the gas (𝑇_{𝐻𝐸𝑋,𝑔𝑎𝑠}_𝑜𝑢𝑡) can be calculated as follows:

𝑇_{𝐻𝐸𝑋,𝑎𝑖𝑟}_𝑜𝑢𝑡= 𝑇_𝑇_𝑜𝑢𝑡− 𝐶_𝑟∙ (𝑇_{𝐻𝐸𝑋,𝑎𝑖𝑟}_𝑜𝑢𝑡− 𝑇_𝐶_𝑜𝑢𝑡) Eq. 2. 18

3.5.2 Recuperator pressure loss

Based on the information provided by Compower AB, the total relative pressure loss in the recuperator at the design point is 4%, with 1.5% loss on the airside and 2.5% on the gas side. According to the manufacturer datasheet, there is a linear dependence between the total relative pressure loss and the air mass flow across the recuperator. However, the recuperator was tested at different air inlet pressure than the one used in the current system and therefore it is not possible to use the pressure loss line directly from the manufacturer datasheet. Therefore, to calculate the actual pressure loss as a function of air mass flow, the line was adjusted to fit the 4% total pressure loss while keeping the same slope of the line as in the datasheet.

The results are shown in Figure 11.

Figure 11. Recuperator pressure loss as affected by mass flow

The linear equations describing the pressure drop of the recuperator as a function of fluid mass flow are as follows:

∆𝑝𝐻𝐸𝑋,𝑎𝑖𝑟 = 9.375 ∙ 𝑚̇𝑎𝑖𝑟 + 0.5625 Eq. 2. 19

∆𝑝_{𝐻𝐸𝑋,𝑔𝑎𝑠}= 15.625 ∙ 𝑚̇_𝑔𝑎𝑠+ 0.9375 Eq. 2. 20

The outlet pressure of the air and gas are calculated as follows:

𝑃𝐻𝐸𝑋,𝑎𝑖𝑟_𝑜𝑢𝑡 = 𝑃𝐻𝐸𝑋,𝑎𝑖𝑟_𝑖𝑛∙ (1 − ∆𝑝𝐻𝐸𝑋,𝑎𝑖𝑟) Eq. 2. 21 𝑃𝐻𝐸𝑋,𝑔𝑎𝑠_𝑜𝑢𝑡 = 𝑃𝐻𝐸𝑋,𝑔𝑎𝑠_𝑖𝑛∙ (1 − ∆𝑝𝐻𝐸𝑋,𝑔𝑎𝑠) Eq. 2. 22

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Receiver

The receiver is one of the key components of the hybrid cycle, which absorbs the solar irradiation and transfers the heat to the working fluid. In the framework of the OMSoP project, a new receiver design was developed specifically for a small-scale solar dish-Brayton system with similar design conditions as the system analysed in this thesis. The new receiver design utilizes an impinging jet cooling technology that uses impinging fluid jets on a surface to enhance the heat transfer rates. The schematic of the receiver is show in Figure 12. The design presents a cylindrical cavity with 12 orifice nozzles distributed evenly around the cylindrical wall. The cylinder ring around which the nozzles are distributed corresponds with the peak flux region and thus, the impinging jets help to control the receiver wall temperature.

Two important parameters that have an impact on the overall system performance are the receiver pressure drop and its total efficiency [32]. The formulas and modelling approach used to estimate these two parameters are presented in the following sections.

Figure 12. Schematic of the impinging receiver: (A) 3D geometrical model; (B) 2D drawing. [33]

3.6.1 Receiver pressure drop

The pressure drop in the receiver depends on several factors such as the temperature and mass flow of the air. Based on previous research on the performance of the impinging receiver conducted at the Energy Department, KTH [33], the pressure drop can be estimated according to the following function:

∆𝑃_𝑟𝑒𝑐 =𝜌𝑎𝑖𝑟_𝑖𝑛∙ 𝑉𝑗𝑒𝑡2

2 ∙ 𝐶_𝑑²

Eq. 2. 23

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Where ^𝜌𝑎𝑖𝑟_𝑖𝑛 is the density of the air at the receiver inlet and ^𝑉𝑗𝑒𝑡 is the air velocity and ^𝐶𝑑 is the is the discharge coefficient of the nozzle and for this specific nozzle configuration has a value of 0.8 [33]. The air velocity can be correlated with the total mass flow of the air (𝑚̇𝑎𝑖𝑟 )as follows:

𝑉_𝑗𝑒𝑡= 𝑚̇𝑎𝑖𝑟 ∙ 4

𝜌_𝑎𝑖𝑟_𝑖𝑛∙ 𝜋 ∙ 𝑑²∙ 𝑛 Eq. 2. 24 Where 𝑑 is the nozzle diameter and equals to 10 mm and 𝑛 is the number of nozzles which equals to 12 [33]. Combining Eq. 2. 23 with Eq. 2. 23, the absolute pressure loss in the receiver can be estimated as follows:

∆𝑃𝑟𝑒𝑐 = 8 ∙ 𝑚̇_𝑎𝑖𝑟^𝟐

𝐶_𝑑²∙ 𝜌_𝑎𝑖𝑟_𝑖𝑛∙ 𝜋²∙ 𝑑⁴∙ 𝑛² Eq. 2. 25

Figure 13 below shows how the absolute pressure loss changes with increasing the air mass flow through the receiver while keeping the air inlet temperature and pressure constant. From the graph it can be seen that at lower inlet air pressure, which will result in lower density of the air, the pressure loss increases.

Figure 13. Receiver pressure drop as a function of air mass flow and at different air inlet conditions (receiver inlet temperature of 634 ℃)

Having the absolute pressure loss, the relative pressure loss can be determined as follows:

∆𝑝_𝑟𝑒𝑐 =∆𝑃𝑎𝑏𝑠

𝑃_𝑟𝑒𝑐_𝑖𝑛 Eq. 2. 26

As seen from the above formula, in order to calculate the pressure drop in the receiver the mass flow of the air needs to be known. The mass flow of the air is, however, is calculated by matching the compressor map with the turbine map which takes into consideration the pressure drops in the receiver. In order to overcome this two-way dependency problem, an iterative process was used. First, an initial value for the pressure drop in the receiver was assumed (2%). Having the first guess for the pressure drop, the air mass flow was calculated. Having a new value for the air mass flow, the pressure drop in the receiver was calculated again and used to recalculate the air mass flow. The process was repeated until the pressure drop converged to a constant value.

After calculating the pressure drop in the receiver, the outlet pressure from the receiver was calculated as follows:

𝑃_𝑟𝑒𝑐_𝑜𝑢𝑡 = 𝑃_𝑟𝑒𝑐_𝑖𝑛∙ (1 − ∆𝑝_𝑟𝑒𝑐) Eq. 2. 27

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3.6.2 Receiver outlet temperature and efficiency

The outlet air temperature from the receiver depends on the following parameters:

- the inlet temperature of the air to the receiver (𝑇𝑟𝑒𝑐_𝑖𝑛) - ambient temperature (𝑇𝑎𝑚𝑏)

- air mass flow through the receiver (𝑚̇_𝑎𝑖𝑟) - incident power to the receiver (^𝑄̇𝑟𝑒𝑐)

A simple model based on energy balance equations was built to calculate the outlet temperature as well as the efficiency of the receiver. The following two hypothesis were used to build the receiver model:

- the receiver heat loss is only due to radiative losses - the absorber is a black body

In reality, the absorber will lose heat to the surroundings not only through radiation but also through natural convection and heat conduction to the insulating layers. At high temperature, however, the natural convection heat losses are significantly lower compared to radiative losses. For this reason, in the study done by Wujun et al. which investigated the thermal performance of the receiver presented herein, the natural convection losses were neglected [33]. Considering that the receiver model in the current thesis relies on the CFD model results obtained by Wujun et al, it was deemed appropriate to neglect the conventional losses as well.

The receiver energy heat balance can be expressed as follows:

𝑄̇_𝑟𝑒𝑐 = 𝑄̇_𝑎𝑏𝑠− 𝑄̇_𝑟𝑎𝑑 Eq. 2. 28

Where 𝑄̇_𝑟𝑒𝑐 is the incident solar power, 𝑄̇_𝑎𝑏𝑠 is the power absorbed by the working fluid and 𝑄̇_𝑟𝑎𝑑 is the radiated power. The absorbed power can be expressed in terms of enthalpy difference of the working fluid across the receiver as follows:

𝑄̇_𝑎𝑏𝑠= 𝑚̇_𝑎𝑖𝑟∙ (ℎ_𝑎𝑖𝑟_𝑜𝑢𝑡− ℎ_𝑎𝑖𝑟_𝑖𝑛) Eq. 2. 29

At the same time, the absorbed power can also be expressed as the conductive heat transfer through the receiver wall:

𝑄̇_𝑎𝑏𝑠= 𝑈_𝑟𝑒𝑐𝐴_𝑟𝑒𝑐∙ (𝑇_{𝑤𝑎𝑙𝑙}− 𝑇_{𝑚𝑒𝑎𝑛,𝑎𝑖𝑟}) Eq. 2. 30 Where ^𝑇𝑚𝑒𝑎𝑛,𝑎𝑖𝑟 is the mean air temperature across the receiver.

𝑇𝑚𝑒𝑎𝑛,𝑎𝑖𝑟=𝑇𝑟𝑒𝑐_𝑖𝑛+ 𝑇𝑟𝑒𝑐_𝑜𝑢𝑡

2

Eq. 2. 31 The 𝑈_𝑟𝑒𝑐𝐴_𝑟𝑒𝑐 is a constant value that depends on the receiver heat transfer coefficient and the area of the receiver cavity. Combining the Eq. 2. 29 and Eq. 2. 30 and using the available receiver parameters obtained from previously conducted CFD simulations (Table 2), the 𝑈𝑟𝑒𝑐𝐴𝑟𝑒𝑐 was calculated to be 100.93 W/K.

The power lost by radiation is calculated as follows:

𝑄̇𝑟𝑎𝑑= 𝜀 ∙ 𝜎 ∙ 𝐴𝑎𝑝∙ (𝑇_{𝑤𝑎𝑙𝑙}⁴ − 𝑇_𝑎𝑚𝑏⁴ ) Eq. 2. 32 For a black body, the receiver emissivity ^(𝜀) equals 1. The diameter of the aperture is 20 cm and the respective area (𝐴𝑎𝑝) is 0.0314 m² (see Figure 12).

The receiver efficiency is calculated as follows:

𝜂𝑟𝑒𝑐=𝑄̇_𝑎𝑏𝑠∙ 100%

𝑄̇_{𝑟𝑒𝑐𝑒𝑖𝑣𝑒𝑟} Eq. 2. 33

Simulation of an Innovative Integrated Solar Receiver/Combustor Unit for Flexible Gas Turbine Based CSP

Simulation of an Innovative

Integrated Solar Receiver/Combustor Unit for Flexible Gas Turbine Based

CSP

Cristina Blajin

Table of Contents

List of Figures

List of Tables

Nomenclature Abbreviations

Symbols

Subscripts

Abstract

Sammanfattning

Acknowledgements

1 Introduction

Concentrated Solar Power market overview

Micro Gas turbine market overview

Hybrid micro gas turbines

The novelty of the current dish hybrid system

2 Objectives and methodology

Objectives

Methodology

Report structure

3 Steady State Model

Investigated configurations

A

B

C

System boundary condition

Compressor

Microturbine

Recuperator

Receiver