Parametric Study of High-Temperature Volumetric Solar Absorbers Mechanical Engineering

76 Pages·2015·4.13 MB·English

Parametric Study of High-Temperature Volumetric Solar
Absorbers

José Bruno Pinto da Natividade

Thesis to obtain the Master of Science Degree in
Mechanical Engineering

Supervisor: Prof. Pedro Jorge Martins Coelho

Examination Committee
Chairperson: Prof. Viriato Sérgio de Almeida Semião
Supervisor: Prof. Pedro Jorge Martins Coelho
Member of the Committee: Prof. José Leonel Monteiro Fernandes

June, 2015
Acknowledgements

I would like to thank Professor Pedro Coelho for his dedication while leading this project, for keeping
me focused and motivated during these exciting 8 months, and for all the knowledge shared.
I would also like to thank my family and friends for all the unconditional support and for being the
backbone of my motivation to succeed.
And last, but not the least, I would like to show my gratitude to my teammates from Projecto FST for
always being there to tell me I should work harder, which allowed me to complete this work within the
predicted time range.

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Resumo

Devido ao seu enorme potencial quando comparada com outras fontes de energia, a energia solar
tem sido o principal alvo de investimento nas energias renováveis ao longo dos últimos anos, com o
objectivo de aumentar as eficiências de conversão e torná-la rentável, continuando a explorar novas
maneiras de aproveitar cada vez mais radiação solar.
Este estudo centra-se numa das mais recentes tecnologias relativas à energia solar, a torre de
potência solar, que é uma solução possível para substituir as comuns centrais termoeléctricas a
carvão, mais precisamente no material cerâmico poroso utilizado para absorver a radiação no topo da
torre e transferi-la para um fluido que o atravessa.
Neste trabalho, um modelo computacional utilizando o método das ordenadas discretas num domínio
unidimensional discretizado foi desenvolvido, tendo em conta as transferências de calor por
condução, convecção e radiação, e é usado para prever o desempenho do receptor poroso.
Os parâmetros de funcionamento individuais, como a condutibilidade térmica, a porosidade do
receptor e o caudal mássico de fluido são posteriormente estudados com o objectivo de aumentar a
eficiência da conversão de energia solar incidente em energia térmica, e alguns casos de estudo são
apresentados.
Palavras-chave: energia solar; material cerâmico poroso; receptor volumétrico solar; modelo de
transferência de calor; análise paramétrica

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Abstract

Due to its extraordinary potential when compared to other energy sources, solar energy has been the
main target for renewable energy investment for the past years, with the purpose of increasing the
conversion efficiencies and making it profitable, while exploring new ways of harnessing more solar
radiation.
This study is focused on one of the most recent technologies regarding solar energy, the Solar Power
Tower, which is a prospective solution to replace the common coal power plants, more precisely on
the reticulated porous ceramic (RPC) material used to absorb the reflected radiation intensity at the
top of the tower and transfer that energy to a working fluid.
In this work, a computational model using the discrete ordinates (DO) method on a discretized one-
dimensional domain is developed, taking into account the heat transfers by conduction, convection
and radiation, and is used to predict the performance of the RPC absorber.
The individual working parameters, such as the thermal conductivity, the porosity of the absorber and
the fluid mass flow rate are then studied with the purpose of increasing the solar to thermal conversion
efficiency at the volumetric receiver, and several case studies are presented.
Keywords: solar energy; reticulated porous ceramic; volumetric solar receiver; computational heat
transfer model; parametric analysis.

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Table of Contents

Acknowledgements …………………………………………………………………………………ii
Resumo …………………………………………………………………………………………iii
Abstract …………………………………………………………………………………………iv
Table of Contents …………………………………………………………………………………v
Figure List ………………………………………………………………………………………..vii
Table List …………………………………………………………………………………………x
Nomenclature ………………………………………………………………………………………...xi
1. Introduction ........................................................................................................…...1
1.1. Motivation …..……………………………………………………………………1
1.1.1. Global Energetic Situation ………..…………………………………….1
1.1.2. Solar Energy ……………………………………………………………….4
1.2. Objectives ………………………………………………………………………..5
1.3. Structure ………………………………………………………………………..5
2. Literature Review ………………………………………………………………………..6
2.1. State of the Art ……………………………………………………………….6
2.1.1. Thermal Energy Systems ……………………………………………...6
2.1.2. Photovoltaic Energy Systems ……………………………………..8
2.1.3. Concentrating Solar Power Systems ……………………………………..9
2.2. Porous Ceramic Materials ……………………………………………………..11
3. Heat Transfer Model .................................................................................................13
3.1. System Description ………………………………..........................................13
3.2. Thermal Model ……..............................................................................14
3.2.1. Thermal Equilibrium ……………………………………………….........14
3.2.2. Balance Equations and Discretization ……………………….......15
3.2.3. Thermal Boundary Conditions …………………………………....18
3.2.4. Volumetric Heat Transfer Coefficient …………………………...20
3.3. Radiative Model ……………………………………………………………...21
3.3.1. Discrete Ordinates Method …………………………………………….21
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3.3.2. Balance Equations ……………………………………………………..21
3.3.3. Radiative Boundary Conditions ……………………………………23
3.3.4. Radiative Properties ..........................................................................25
3.4. Absorber Performance ……………………………………………………..26
3.5. Convergence ………………………………………………………………………27
3.6. Algorithm ………………………………………………………………………28
3.7. Validation ………………………………………………………………………32
4. Results and Discussion ……………………………………………………………...36
4.1. Reference Values ……………………………………………………………...36
4.2. Parametric Sensitivity Analysis …………………………………………….38
4.2.1. Absorber Thickness ……………………………………………………..38
4.2.2. Mass flow rate per unit area …………………………………………….39
4.2.3. Absorber thermal conductivity ……………………………………41
4.2.4. Incident Solar Flux ……………………………………………………..42
4.2.5. Porosity ……………………………………………………………...44
4.3. Case Studies ………………………………………………………………………45
4.4. Variable Thermal Conductivity …………………………………………….49
5. Conclusion ……………………………………………………………………………….52
5.1. Final Conclusions ……………………………………………………………...52
5.2. Future Work ………………………………………………………………………53
5.2.1. 2D and 3D analysis ……………………………………………………..54
5.2.2. Transient analysis ……………………………………………………..54
5.2.3. Experimental setup ……………………………………………………..54
5.2.4. Energetic and cost analysis of power tower system …………………..54
References ……………………………………………………………………………………….55
Appendix ……………………………………………………………………………………….57
Appendix A ………………………………………………………………………………57
Appendix B ………………………………………………………………………………61
Appendix C ………………………………………………………………………………62

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Figure List

Chapter 1
Fig. 1.1 – World energy consumption per source, based on Vaclav Smil estimates from Energy
Transitions: History, Requirements and Prospects together with BP Statistical Data for 1965 and
subsequent. …………………………………………………………………………………………………2
Fig. 1.2 – Comparison between global energy potentials and world energetic consumption (2012).
Figure adapted from [21] ………………………………………………………………………………4

Chapter 2
Fig. 2.1 – Flat plate collector (left) and evacuated tube collector (right). Images adapted from
http://www.gogreenheatsolutions.co.za and http://www.completesolars.com websites respectively. …7
Fig. 2.2 – Global installed capacity of solar thermal energy since 2000. Data from [1]. ...…………...8
Fig. 2.3 – Global installed capacity of solar photovoltaic energy since 2000. Data from [1]. ……9
Fig. 2.4 – Concentrating solar power technologies. a) Trough System; b) Dish/engine System; c)
Power Tower System. Images adapted from [4]. …………………………………………………10
Fig. 2.5 - Geometry used in the study of Wu et al. [12] (a) Unit tetrakaidecahedron cell, (b) bulk foams
formed by packed tetrakaidecahedrons and (c) computational domain and boundary conditions. …..12

Chapter 3
Fig. 3.1 – porous ceramic material used as solar receiver on power tower solar systems. Image
adapted from http://www.gigaom.com and [19]. …..………………………………………….……………13
Fig. 3.2 – Thermal influences: (a) pure diffusion, Pe = 0; (b) diffusion and advection. Image adapted
from [5] .………………………………………………………………………………………………..16
Fig. 3.3 – Mesh control volume. Image adapted from [5]. ..……………………………………….17
Fig. 3.4 – values and weights of the discrete ordinates for the S4 and S6 approximations; spatial
representation of the SN discretization. Image adapted from [6]. ………...………………………………21
Fig. 3.5 – Solid angle of cone with half angle θ. ………….………………………………………………..24
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Fig. 3.6 – Volumetric receiver back wall boundary: 1 solid absorber phase; 2 fluid phase; 3 back wall;
dashed line is the radiative enclosure. Image adapted from [19]. ……………………………….24
Fig. 3.7 – influence of the number of mesh elements in the final efficiency result for one case study.
Absorber length L=20mm. …………………………………………………………………………......27
Fig. 3.8 – Iterative profiles of the divergence of radiative heat flux across the receiver for a case where
convergence is not obtained. …………………………………………………………………..………….31
Fig. 3.9 - Iterative profiles of the divergence of radiative heat flux across the receiver for a case where
convergence is obtained. ………………………………………………………………………….….31
Fig. 3.10 – Total irradiance results for the cold simulation, published in A. Kribus et al. (2014) [19] for
Two-Flux, Discrete Ordinates, Monte Carlo and P1 methods. ……………………………………......32
Fig. 3.11 – Total irradiance results for the cold simulation, obtained in this work for the Discrete
Ordinates method. ……………………………………………………………………………………....33
Fig. 3.12 – Temperature distribution for the validation case 1, results published in A. Kribus et al.
(2014) [19]. ………………………………………………………………………………………………...34
Fig. 3.13 – Temperature distribution for the validation case 1, results obtained in this work. …..34
Fig. 3.14 – Temperature distribution for the validation case 2 (with x5 convection enhancement factor),
results published in A. Kribus et al. (2014) [19]. …………………………………………………………..35
Fig. 3.15 – Temperature distribution for the validation case 1 (with x5 convection enhancement factor),
results obtained in this work. ……………………………………………………………………………..35

Chapter 4
Fig. 4.1 – Temperature distribution of solid and fluid phases using the reference parameters listed in
table 3.1. ………………………………………………………………………………………………...37
Fig. 4.2 – Radiative heat flux throughout the absorber in both directions for the reference parameter
values. ……………………………………………………………………………………………………….....37
Fig. 4.3 – Efficiency results as function of absorber thickness. ……………………………………..…38
Fig. 4.4 – efficiency and air exit temperature as function of the air mass flow rate per unit area. …..39
Fig. 4.5 – solid and air temperature distributions for ̇ ⁄ . ……………...……...40
Fig. 4.6 – Temperature distribution of the solid absorber for different solid thermal conductivities.…..41
Fig. 4.7 – Efficiency results for different solid thermal conductivities. ………………………………42
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Fig. 4.8 – Influence of the incident solar flux on the solid and fluid temperature distributions along the
absorber. …………………………………………………………………………………………………43
Fig. 4.9 – Efficiency results for different values of incident solar flux. ……………………………….43
Fig. 4.10 – Efficiency and front surface solid temperature variations for different absorber porosity
values. ……………………………………………………………………………………………………….…44
Fig. 4.11 – Temperature distribution of solid and fluid phases for the case with 0.92 porosity value. ..45
Fig.4.12 – Temperature distribution of solid and fluid phases for the first updated parameters case
study. ……………………………………………………………………………………………………….…46
Fig. 4.13 – Temperature distribution of solid and fluid phases for the second updated parameters case
study. ……………………………………………………………………………………………………….…47
Fig. 4.14 – Temperature distribution of solid and fluid phases for the third updated parameters case
study. ……………………………………………………………………………………………………….…48
Fig. 4.15 – Temperature distributions for the first case study with variable thermal conductivity …..49
Fig. 4.16 – Temperature distributions for the second case study with variable thermal conductivity. ..50
Fig. 4.17 – Temperature distributions for the high solar irradiation study with variable thermal
conductivity. ………………………………………………………………………………………………..51

Appendix
Fig. A.1 – Angular distribution of the scattering phase function used in this work. …………….61
Fig. A.2 – Specific heat correlation fitted to tabulated data for air from http://engineeringtoolbox.com 62
Fig. A.3 – Kinematic viscosity correlation fitted to tabulated data for air from
http://engineeringtoolbox.com ………………………………………………………………………………62
Fig. A.4 – Thermal conductivity correlation fitted to tabulated data for air from
http://www.engineeringtoolbox.com …………………………………………………………...…….....63
Fig. A.5 – Density correlation fitted to tabulated data for air from http://engineeringtoolbox.com …..63

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Table List

Chapter 1
Tab. 1.1 – Renewables’ worldwide installed capacity evolution since 2004. Table adapted from [1]. …3
Tab. 1.2 – Renewables worldwide investment since 2004. Table adapted from [1]. ……………...3

Chapter 2
Tab. 2.1 – Nusselt number vs. Reynolds number correlations developed for five cellular ceramics:
PPC = 4-26 and L = 6-12 mm. Table adapted from Fu et al. [7]. ………………………………………..11

Chapter 3
Table 3.1 – Absorber properties for cold medium validation case. ………………………………32
Table 3.2 – Absorber properties for complete simulation validation cases 1 and 2. ……………33

Chapter 4
Table 4.1 – Reference values for simulation parameters. ……………………………………….37
Table 4.2 – Data used for the first case study. ………………………………………………………….46
Table 4.3 – Data used for the second case study. ………………………………………………...47
Table 4.4 - Data used for the third case study. ………………………………………………………….48
Table 4.5 – Data used for the variable thermal conductivity experiment, correspondent to the first case
study. ………………………………………………………………………………………………................49
Table 4.6 – Data used for the variable thermal conductivity experiment, correspondent to the second
case study. .……………………………………………………………………………………................50
Table 4.7 – Data used for the variable thermal conductivity experiment for high solar irradiation. …..51

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