POLITECNICO DI MILANO Facoltà di Ingegneria Industriale Corso di Laurea Magistrale in Ingegneria Energetica Numerical modelling of molten-salt thermocline storage systems: feasibility and criteria for performance improvement Relatore: Prof. Giampaolo Manzolini Correlatori: Prof. Andrea Lucchini Prof. Michaël Kummert Tesi di Laurea di: Giovanni Angelini 770990 Anno Accademico 2011 - 2012 “Within 6 hours deserts receive more energy from the sun than humankind consumes within a year” Dr. Gerhard Knies Index Figures index ...................................................................................................... vii Tables index ........................................................................................................ xi Abstract ............................................................................................................ xiii Sommario .................................................. Errore. Il segnalibro non è definito. Estratto in lingua italiana .............................................................................. xvii Introduction ..................................................................................................... xxv Background.................................................................................................... xxv Objectives ................................................................................................... xxvii 1 Electric supply form solar energy .............................................................. 1 1.1 Photovoltaic ............................................................................................ 2 1.2 Thermoelectric conversion ..................................................................... 5 1.3 Not concentrated solar power plants ...................................................... 8 1.3.1 Solar pond ....................................................................................... 8 1.3.2 Solar updraft tower .......................................................................... 8 1.4 Concentrated solar power plant ............................................................ 10 1.4.1 Parabolic trough ............................................................................ 10 1.4.2 Linear Fresnel collectors ............................................................... 12 1.4.3 Central receiver ............................................................................. 13 1.4.4 Solar dish ....................................................................................... 15 1.5 History of CSP plants ........................................................................... 16 2 Thermal energy storage ............................................................................. 19 2.1 Thermal energy storage media ............................................................. 21 2.1.1 Steam ............................................................................................. 22 2.1.2 Mineral/synthetic oil ..................................................................... 22 2.1.3 Molten salt ..................................................................................... 23 iii 2.2 Indirect Two-Tank TES system ........................................................... 24 2.3 Direct Two-Tank TES system ............................................................. 26 2.4 Direct Thermocline TES system .......................................................... 28 2.5 Passive storage ..................................................................................... 30 2.6 Latent TES system ............................................................................... 32 2.7 Chemical thermal energy storage ......................................................... 33 2.8 Thermal energy storage cost assessment ............................................. 34 2.8.1 Choice of the filler material for molten salt thermocline TES ..... 38 3 Previous studies on molten salt thermocline TES systems .................... 39 3.1 Previous thermocline TES models ....................................................... 40 3.1.1 Schumann equation set ................................................................. 40 3.1.2 Schumann-Darcy-Brinkman-Forchheimer equation set ............... 41 3.1.3 Hypothesis and assumptions ......................................................... 42 3.2 Model implementation ......................................................................... 44 3.2.1 Pacheco ......................................................................................... 44 3.2.2 Yang .............................................................................................. 45 3.2.3 Garimella ...................................................................................... 45 3.2.4 Xu ................................................................................................. 46 3.3 Validation of the model – Pacheco’s experimental data ...................... 46 3.4 Previous findings on Thermocline Performances ................................ 47 3.4.1 Inlet fluid velocity......................................................................... 49 3.4.2 Porosity ......................................................................................... 50 3.4.3 Particle diameter ........................................................................... 50 3.4.4 Tank height ................................................................................... 50 3.4.5 Inlet temperature ........................................................................... 51 3.4.6 Thermal conductivity .................................................................... 51 3.4.7 Interstitial heat transfer coefficient ............................................... 51 3.4.8 Insulation of the tank .................................................................... 52 3.4.9 External air velocity ...................................................................... 52 iv 4 Development of the thermocline model ................................................... 53 4.1 Fundamental equations ......................................................................... 53 4.2 Discretization ........................................................................................ 54 4.2.1 Discretization of mass balance equation ....................................... 56 4.2.2 Discretization of energy equations ................................................ 58 4.2.3 Flow chart of the thermocline model ............................................ 59 4.3 Comparison with analytical solutions .................................................. 61 4.3.1 Transient radial diffusion .............................................................. 62 4.3.2 Transient axial thermal diffusion .................................................. 64 4.3.3 Heat transfer between molten salt and packed bed ....................... 66 4.3.4 Axial advective transport and axial diffusion ............................... 69 4.4 Molten salt physical properties – Sensitivity analysis .......................... 71 4.5 Comparison with Pacheco experimental results ................................... 75 4.6 Order of convergence of the numerical model ..................................... 76 4.6.1 Order of convergence - mesh dimension ...................................... 76 4.6.2 Time step length ............................................................................ 77 5 Thermocline TES issues ............................................................................ 79 5.1 Thermal ratcheting................................................................................ 79 5.1.1 Thermal ratcheting safety factor - Analytical method .................. 82 5.1.2 Thermal ratcheting factor of safety - Numerical method .............. 83 5.1.3 Proposed wall structures ............................................................... 86 5.2 Thermal Stability of the thermocline - Fingering ................................. 86 5.2.1 Hydrostatical criterion ................................................................... 87 5.2.2 Hydrodynamic criterion ................................................................ 87 5.3 Standby behavior of thermocline TES system ..................................... 90 5.3.1 Thermocline expansion during standby mode .............................. 90 5.3.2 Heat loss to the environment ......................................................... 92 6 Optimal design of the thermocline ........................................................... 97 6.1 Simulation on a typical summer week .................................................. 98 6.1.1 Optimal tank size ......................................................................... 103 v 6.2 Simulation on a early-spring week .................................................... 106 6.2.1 Optimal size of the tank – spring season .................................... 109 6.2.2 Comparison of thermocline TES performancek ......................... 109 6.3 Improvement of thermocline TES performance ................................ 110 6.3.1 Discharge efficiency and threshold temperature ........................ 110 6.3.2 Molten salt choice ....................................................................... 113 6.3.3 Molten salt and packed bed thermal conductivity ...................... 115 6.3.4 Tank height ................................................................................. 116 Conclusions .....................................................................................................