Numerical modelling of a parabolic trough solar collector Centre Tecnològic de Transferència de Calor Departament de Màquines i Motors Tèrmics Universitat Politècnica de Catalunya Ahmed Amine Hachicha Doctoral Thesis Numerical modelling of a parabolic trough solar collector Ahmed Amine Hachicha TESI DOCTORAL presentada al Departament de Màquines i Motors Tèrmics E.T.S.E.I.A.T. Universitat Politècnica de Catalunya per a l’obtenció del grau de Doctor per la Universitat Politècnica de Catalunya Terrassa, September, 2013 Numerical modelling of a parabolic trough solar collector Ahmed Amine Hachicha Directors de la Tesi Dr. Ivette Rodríguez Pérez Dr. Assensi Oliva Llena Tribunal Qualificador Dr. Carlos David Pérez-Segarra Universitat Politècnica de Catalunya Dr. José Fernández Seara Universidad de Vigo Dr. Cristobal Cortés Garcia Universidad de Zaragoza Dr. Jesús Castro González Universitat Politècnica de Catalunya Dr. Maria Manuela Prieto González Universidad de Oviedo In the name of God, Most Gracious, Most Merciful 7 8 Acknowledgements It would not have been possible to complete this doctoral thesis without the guid- ance of my PhD advisors, help from friends, and support from my family. I would like to express my deepest gratitude to Prof Assensi Oliva the head of the heat and mass transfer technological center CTTC for giving me the opportunity to do my doctoral program under his guidance and to learn from his research expertise. His personal support and great patience provided me with an excellent atmosphere for doing research work. I would like also to thank Dr Ivette Rodríguez for her excellent guidance, pa- tience, motivation, enthusiasm and immense knowledge. Her guidance helped me in all the time of the research and writing of this thesis, as well as, in developing my background in solar energy and fluid dynamics. Moreover, I want to give my gratitude to Dr Roser Capdevila for her guidance and precious advices which resulted in increase of the quality of this thesis. Her ex- pert knowledge in radiative heat transfer area and kind support have been essential for this work. I extend my sincere thanks to all members of the CTTC center for their help and support whenever I was in need. I would thank also all my colleagues and friends for the great time that we have had in particular the CTTC football team. I gratefully acknowledge the funding received towards of my PhD from the Span- ish Agency for International Development Cooperation (AECID). I am also thankful to Prof Chiheb Bouden from the National Engineering School of Tunis for his recom- mendation to pursue my research in CTTC. Finally, my most sincere and very heartfelt thanks to my Parents and Family who have been utmost supportive to me in my life and help me become today what I am. 9 10 Contents Acknowledgements 9 Abstract 15 1 Introduction 17 1.1 Solarconcentratingtechnology . ... 17 1.1.1 Lineconcentrating . 17 1.1.2 Pointconcentrating. 19 1.2 Parabolictroughtechnology . .. 20 1.2.1 Receivertube ............................. 21 1.2.2 Structureandmirrors . 22 1.2.3 Thermalfluid ............................. 23 1.2.4 Thermalstorage............................ 23 1.2.5 Solarpowercycle... .... .... .... ... .... .... 24 1.3 State-of-the-artofmodellingPTC . .... 25 1.4 Objectivesofthisthesis. .. 26 1.5 Background .................................. 27 1.6 Outlineofthethesis.............................. 29 References ...................................... 29 2 RadiativeanalysisandopticalmodelofaPTC 37 2.1 Introduction .................................. 38 2.2 RadiativeTransferEquation(RTE) . ... 38 2.2.1 TheFiniteVolumeMethod(FVM) . 41 2.2.2 Collimatedirradiation . 44 2.3 Casestudies .................................. 45 2.3.1 Isothermal absorbing-emitting medium . .. 45 2.3.2 Purelyscatteringmedium . 46 2.3.3 Absorbing, emitting and isotropically scattering medium. 48 2.3.4 Normalcollimatedincidenceproblem . 49 2.3.5 Oblique collimated incidence problem . .. 52 2.3.6 Oblique collimated with specular reflecting walls . ..... 53 2.3.7 Centralblockageproblem . 55 2.3.8 Normal collimated radiation in a rectangular enclosure con- tainingablacksquare . 56 2.4 Resolution of the RTE for a parabolic trough solar collector using the FVM ...................................... 58 11 Contents 2.5 Newopticalmodel .............................. 61 2.6 Conclusions .................................. 69 References ...................................... 70 3 Heat transfer analysis and numerical simulation of a parabolic trough solar collector 73 3.1 Introduction .................................. 74 3.2 PTCnumericalmodel ............................ 74 3.2.1 Convection heat transfer between the HTF and the absorber . 77 3.2.2 Conduction heat transfer through the absorber wall and the glassenvelope............................. 78 3.2.3 Convection heat transfer between the absorber and the glass envelope................................ 78 3.2.4 Thermal radiation heat transfer between the absorber and the glassenvelope............................. 79 3.2.5 Convection heat transfer from the glass envelope to the envi- ronment ................................ 83 3.2.6 Thermal radiation heat transfer between the glass envelope andthesurrounding . .... .... .... ... .... .... 83 3.2.7 Solarirradiationabsorption . 85 3.3 NumericalSolution.............................. 86 3.4 Computational results and validation . .... 88 3.5 Conclusions .................................. 95 References ...................................... 95 4 Numerical simulation of wind flow around a parabolic trough solar collec- tor 97 4.1 Introduction .................................. 98 4.2 PTCnumericalmodel ............................ 99 4.2.1 Mathematicalmodel . 99 4.2.2 Definition of the case and numerical model . 100 4.3 Validationofthenumericalmodel . 103 4.4 Resultsanddiscussion . 106 4.4.1 Averagedforcesontheparabola . 106 4.4.2 Instantaneousflow . 108 4.4.3 Meanflowconfiguration. 108 4.4.4 HeattransferaroundHCE. 113 4.5 Conclusions ..................................118 References ......................................119 12 Contents 5 Wind speed effect on the flow field and heat transfer around a parabolic trough solar collector 123 5.1 Introduction ..................................124 5.2 PTCnumericalmodel ............................125 5.2.1 Mathematicalmodel . 125 5.2.2 Definition of the case. Geometry and boundary conditions . 125 5.3 Heat transfer from a circular cylinder in cross flow and wind speed effects......................................127 5.4 Resultsanddiscussion . 129 5.4.1 Windspeedeffects . 129 5.4.2 Unsteady-stateflow . 138 5.5 Conclusions ..................................144 References ......................................146 6 Conclusions and further work 151 A First steps in the thesis 155 A.0.1 Definitionoftheproblem . 155 A.0.2 Results.................................157 References ......................................164 B ConvectionbetweentheHTFandtheHCE 165 References ......................................166 C PTCperformancesusingFVMinopticalmodelling 169 References ......................................171 Nomenclature 173 13 14 Abstract Concentrated Solar Power (CSP) technologies are gaining increasing interest in electricity generation due to the good potential for scaling up renewable energy at the utility level. Parabolic trough solar collector (PTC) is economically the most proven and advanced of the various CSP technologies. The modelling of these de- vices is a key aspect in the improvement of their design and performances which can represent a considerable increase of the overall efficiency of solar power plants. In the subject of modelling and improving the performances of PTCs and their heat collector elements (HCEs), the thermal, optical and aerodynamic study of the fluid flow and heat transfer is a powerful tool for optimising the solar field output and increase the solar plant performance. This thesis is focused on the implementation of a general methodology able to simulate the thermal, optical and aerodynamic be- haviour of PTCs. The methodology followed for the thermal modelling of a PTC, taking into account the realistic non-uniform solar heat flux in the azimuthal direc- tion is presented. Although ab initio, the finite volume method (FVM) for solving the radiative transfer equation was considered, it has been later discarded among other reasons due to its high computational cost and the unsuitability of the method for treating the finite angular size of the Sun. To overcome these issues, a new optical model has been proposed. The new model, which is based on both the FVM and ray tracing techniques, uses a numerical-geometrical approach for considering the optic cone. The effect of different factors, such as: incident angle, geometric concentration and rim angle, on the solar heat flux distribution is addressed. The accuracy of the new model is verified and better results than the Monte Carlo Ray Tracing (MCRT) model for the conditions under study are shown. Furthermore, the thermal behaviour of the PTC taking into account the non- uniform distribution of solar flux in the azimuthal direction is analysed. A general performance model based on an energy balance about the HCE is developed. Heat losses and thermal performances are determined and validated with Sandia Labo- ratories tests. The similarity between the temperature profile of both absorber and glass envelope and the solar flux distribution is also shown. In addition, the convection heat losses to the ambient and the effect