UNIVERSIDAD DE VALLADOLID ESCUELA DE INGENIERÍAS INDUSTRIALES PROYECTO FIN DE CARRERA INGENIERO INDUSTRIAL Numerical-Stochastic Modeling, Simulation and Design Optimization of Small Particle Solar Receivers for Concentrated Solar Power Plants AUTHOR: Pablo Fernández del Campo SUPERVISOR: Prof. Fletcher J. Miller July 2013 © Pablo Fernández del Campo Pablo Fernández del Campo Universidad de Valladolid 2 Pablo Fernández del Campo Universidad de Valladolid Numerical-Stochastic Modeling, Simulation and Design Optimization of Small Particle Solar Receivers for Concentrated Solar Power Plants Pablo Fernández del Campo Escuela de Ingenierías Industriales, Universidad de Valladolid Paseo del Cauce 59, 47011, Valladolid July 17th, 2013 Abstract While most commercial Concentrated Solar Power plants rely on surface absorption of solar irradiation to drive a steam turbine (Rankine cycle), there exist several advantages in employing gas turbines (Brayton cycle). First, it requires less water to generate electricity; second, it leads to higher thermodynamic efficiency (due to the higher temperatures required); and third, the air is a non-problematic heat transfer fluid owing to its inert nature within the temperature range of interest. This Proyecto Fin de Carrera aims to first develop a robust multi-physics numerical model for a Small Particle Solar Receiver, one such receiver to drive a gas turbine in Concentrated Solar Power plants. This concept is based on employing carbon nanoparticles in an air stream to volumetrically absorb highly concentrated solar irradiation and drive a gas turbine at temperatures in excess of 1300 K, with the corresponding three advantages previously mentioned. The thermo-fluid dynamic modeling of the Small Particle Solar Receiver requires solving a system of eight coupled, non-linear integro-partial differential equations in six independent variables (three spatial variables, two directional variables and wavelength). The solution procedure relies on the coupling of the CFD solver ANSYS Fluent to an in-house Monte Carlo Ray Trace software developed in this Proyecto Fin de Carrera. On the one hand, ANSYS Fluent is utilized as the mass-, momentum- and energy- equation solver and requires the divergence of the radiative heat flux, which constitutes a source term of the energy equation. On the other hand, the MCRT solver calculates the radiation heat transfer in the solar receiver and needs the temperature field to do so. By virtue of the coupled nature of the problem, both codes should provide feed-back to each other and iterate until convergence. The coupling between ANSYS Fluent and our in-house MCRT code is done via User-Defined Functions (UDFs). Both the UDFs and the MCRT 3 Pablo Fernández del Campo Universidad de Valladolid were programmed specifically for this Proyecto Final de Carrera and consist of over 12,500 lines of code. Moreover, they can be used interchangeably for either the two-dimensional (axisymmetric) or the three-dimensional version of the CFD solver. After developing the mathematical model, setting up the code, validating the software and optimizing the coupled solution procedure, the receiver was simulated under fifteen different solar irradiation and mass flow rate cross combinations in an effort to assess the potential of this new technology to generate electricity. Among other results, the behavior of the receiver at different times of the day and the optimum mass flow rate as a function of the solar thermal input are presented. On an average day, the thermal efficiency of the receiver is found to be over 89% and the outlet temperature over 1250 K at all times from 7:30 AM to 4:00 PM (Albuquerque, USA) by properly adapting the mass flow rate. The origin of the losses and how to improve the efficiency of the Small Particle Solar Receiver are discussed as well. A multidisciplinary design optimization is finally conducted in order to maximize the efficiency, reduce the initial and operating costs, increase the lifespan of the different components and, in turn, minimize the generation cost of the electricity. The design space consists of the geometry of the receiver, the geometry of the window, the radiative properties of the walls and the direction of the fluid flow with respect to the concentrated solar irradiation. The constraints are based on material limits (stresses and temperatures), the space available on the top of the tower and other technical issues; though some of them are imposed via a penalty method. The design space is explored via parametric study and a multidisciplinary approach is adopted. The cocurrent flow direction, aluminum oxide walls, a 45º spherical-cap window and the so-called Design 2 showed the best compromise between thermal efficiency and wall temperature. Moreover, the particles were proved to be fully oxidized prior to exiting the solar receiver and the outlet air ready to drive a gas turbine at high temperature, which is the ultimate goal of the Small Particle Solar Receiver. Finally, several ideas and considerations to further improve the design are presented and discussed as well. Thesis Supervisor: Dr. Fletcher J. Miller Title: Associate Professor at San Diego State University, Department of Mechanical Engineering Thesis Supervisor: Dr. María Teresa Parra Santos Title: Professor at Universidad de Valladolid, Departamento de Ingeniería Energética y Fluidomecánica 4 Pablo Fernández del Campo Universidad de Valladolid “Do not go where the path may lead; go instead where there is no path and leave a trail”, Ralph Waldo Emerson 5 Pablo Fernández del Campo Universidad de Valladolid Acknowledgements First, I would like to gratefully acknowledge the support by the U.S. Department of Energy through the SunShot Initiative under the Award #DE-EE0005800, without which this research wouldn’t be possible. I would also like to thank Pratt & Whitney Rocketdyne, Solar Turbines and Thermaphase Energy for their support to the project. I wish to recognize in a special way my advisor, Professor Fletcher J. Miller, for his support and guidance throughout the research process. It has been indeed a privilege and pleasure to work with him this year. Dr. Miller’s breadth of knowledge and perfectionism were a constant source of inspiration and encouragement for me. I also owe him a debt of gratitude for taking responsibility of this exchange program after Professor Gustaaf Jacobs left for The Netherlands. I am also appreciative of the opportunity to work with such great professionals as Michael McDowell from Rocketdyne or Dr. Arlon Hunt from Thermaphase Energy, among other examples. I look forward to somehow continuing collaborating with them and with the project itself in the incoming years. Let me also acknowledge my Spanish advisor, Professor Teresa Parra, without whom it wouldn’t have been possible to research for my Proyecto Fin de Carrera in the United States. I would also like to thank my colleagues of the Solar Energy and Combustion Lab for making my time in the lab enjoyable and for some unforgettable moments. I would like to particularly thank Steve Ruther and Adam Crocker for their previous work on the receiver’s modeling, as well as Ahmet Murat Mecit for his work on the window’s optical model. I am also thankful to all my friends, here and there, as they cheered me up and helped me take a step back from my research when necessary. Last but clearly not least, my family. I cannot thank enough my parents for their patience, encouragement and tremendous support during this year, especially when nothing seemed to work out. 6 Pablo Fernández del Campo Universidad de Valladolid Contents List of Figures ...................................................................................................................... 10 List of Tables ........................................................................................................................ 13 Nomenclature ........................................................................................................................ 15 Chapter 1. Introduction ....................................................................................................... 27 1.1. Solar Energy as a solution towards sustainable development ......................................... 27 1.2. Concentrated Solar Power ............................................................................................... 28 1.3. Small Particle Solar Receiver .......................................................................................... 29 1.4. Scope and Objective of this Proyecto Fin de Carrera .................................................... 30 Chapter 2. Problem Statement and Model Overview ....................................................... 33 2.1. Mathematical Formulation of the Problem...................................................................... 33 2.2. Model Overview .............................................................................................................. 36 2.3. Main hypotheses of the model ......................................................................................... 36 2.3.1. Local Thermodynamic Equilibrium ......................................................................... 37 2.3.2. Particles move with the air flow as a unique phase .................................................. 38 Chapter 3. The Monte Carlo Ray Tracing Method for Radiation Heat Transfer ......... 42 3.1. Intuitive Idea of the Monte Carlo Ray Tracing Method .................................................