The second law of thermodynamics and exergy analysis

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Introduction

In this work, a small-scale receiver for a small-scale open solar thermal Brayton cycle is required. The accuracy of the dish and tracking system used is often an important factor in the total cost of the system. Since the development of the solar thermal Brayton cycle in the 1960s, many attempts have been made to improve the efficiency of the cycle and the solar receiver. A high solar receiver efficiency, however, does not necessarily mean that the receiver will perform well in a solar thermal Brayton cycle. A literature study is conducted to identify the different attempts of optimisation, modelling and development of the solar thermal Brayton cycle and its components. Different solar receiver and recuperator designs are investigated in the study. The importance of the optimisation of components for a common goal is emphasised. Optimisation using the method of total entropy generation minimisation is shown to be a holistic optimisation approach.

Solar thermal Brayton cycle

The closed Brayton cycle was developed in the 1930s for power applications, according to Pietsch and Brandes (1989). The technology was adapted to the design and development of solar thermal Brayton cycles for space power in the 1960s, with the success of lightweight and high-performance gas turbines for aircraft. According to Pietsch and Brandes (1989), experimental testing of the solar thermal Brayton cycle proved high reliability and efficiencies above 30% with turbine inlet temperatures of between 1 033 K and 1 144 K. Dickey (2011) also presented experimental test results of a solar thermal Brayton cycle (20-100 kW), an initiative from HelioFocus Ltd. and Capstone Microturbine at the Weizmann Institute. A proprietary pressurised volumetric solar receiver was used in the experiment.

Test set-up of a solar thermal Brayton cycle (Image extracted from Heller et  al., 2006).

A micro-turbine’s air compressor, turbine and generator are usually mounted on a single shaft and all spin at the same rate (Willis and Scott, 2000; Shiraishi and Ono, 2007). It is simple, robust and easy to maintain. According to Willis and Scott (2000), the generator also operates as the starter motor, running off battery power to bring the turbine up to speed to begin operation. This eliminates the need for a separate starter and simplifies design. According to Willis and Scott (2000), micro-turbines use a high-rpm DC generator coupled to a DC-AC power converter with efficiency of 96% to 97% mechanical to electrical DC.

Solar collector

For large-scale systems, a heliostat field is typically used to focus the sun’s rays onto a receiver. For the small-scale solar thermal Brayton cycle, however, a solar dish can be used to track the sun and to reflect the solar radiation onto the receiver. A solar dish is thus considered in this work as it is more practical for a small-scale set-up. A solar dish, however, has its own problems and limitations as discussed in this section.

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ACKNOWLEDGEMENTS
CHAPTER 1: INTRODUCTION
1.1 Background
1.2 Literature
1.3 Problem
1.4 Purpose of the study
1.5 Objectives
1.6 Scope
1.7 Overview of the thesis
CHAPTER 2: LITERATURE STUDY
2.1 Introduction
2.2 Solar thermal Brayton cycle
2.3 Solar collector
2.3.1 Solar tracking error
2.3.2 Reflectance, slope error and specularity error
2.3.3 Modelling the collector
2.3.4 Constructing the collector
2.4 Solar cavity receiver
2.4.1 Solar receiver types
2.4.1.1 Particle receiver
2.4.1.2 Open volumetric receiver
2.4.1.3 Closed volumetric receiver
2.4.1.4 Tubular receiver
2.4.2 Shape and design
2.4.3 Heat loss models
2.5 Recuperator
2.6 Optimisation and the second law of thermodynamics
2.6.1 Background
2.6.1.1 The second law of thermodynamics and exergy analysis
2.6.1.2 The Gouy-Stodola theorem
2.6.1.3 The sun as an exergy source
2.6.1.4 Entropy generation minimisation
2.6.2 Optimisation of the solar thermal Brayton cycle
2.6.2.1 Results from the literature and influencing factors
2.6.2.2 Optimisation using EGM and geometry optimisation
2.6.2.3 Effect of weather conditions
2.7 Summary
CHAPTER 3: MODELLING AND OPTIMISATION
3.1 Introduction
3.2 Structuring the objective function for solar thermal Brayton cycle optimisation
3.3 Solar collector
3.4 Solar receiver
3.4.1 Solar receiver entropy generation
3.4.2 Solar receiver modelling
3.4.2.1 Conduction heat loss from the solar receiver
3.4.2.2 Radiation heat loss from the solar receiver
3.4.2.3 Convection heat loss from the solar receiver
3.4.2.4 Solar receiver pressure drop
3.4.2.5 Method of determining receiver tube surface temperatures
and net heat transfer rates
3.5 Recuperator
3.5.1 Recuperator entropy generation
3.5.2 Recuperator modelling
3.6 Compressor and turbine
3.6.1 Compressor and turbine entropy generation
3.6.2 Compressor and turbine modelling
3.6.2.1 Compressor modelling
3.6.2.2 Turbine modelling
3.7 Other entropy generation mechanisms
3.8 Flownex modelling
3.9 Summary
CHAPTER 4: ANALYTICAL RESULTS
4.1 Introduction
4.2 Analytical results
4.2.1 Receiver performance
4.2.1.1 Preliminary results
4.2.1.2 Receiver solar heat flux profile
4.2.1.3 Temperature profile and net heat transfer rate of receiver tube
4.2.1.4 Effect of wind
4.2.1.5 Entropy generation rate due to the solar receiver
4.2.2 Optimum performance of the open solar thermal Brayton cycle
4.2.2.1 Results
4.2.2.2 Summary
4.3 Flownex results
4.4 Summary
CHAPTER 5: EXPERIMENTAL STUDY
5.1 Introduction
5.2 Experimental set-up
5.2.1 Two-axis solar tracker
5.2.2 Solar dish
5.2.3 Measurement of the solar resource
5.2.4 Solar receiver
5.2.5 Blower
5.3 Experimental procedure
5.3.1 Test A
5.3.2 Test B
5.4 Experimental results
5.4.1 Test A, Blower Test
5.4.1.1 Results
5.4.1.2 Discussion
5.4.1.3 Conclusion
5.4.2 Test B, High-temperature test results
5.4.2.1 Results – Part 1
5.4.2.2 Discussion – Part 1
5.4.2.3 Results and discussion – Part 2
5.4.2.4 Conclusion
5.5 Error analysis
5.6 Summary
CHAPTER 6: SUMMARY, CONCLUSION AND RECOMMENDATIONS
6.1 Summary
6.2 Conclusion
6.3 Recommendations
REFERENCES

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