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Thermal Stress Analysis for Ciritical Components of a Solar Thermo-Chemical Reactor

Permanent Link: http://ufdc.ufl.edu/UFE0045543/00001

Material Information

Title: Thermal Stress Analysis for Ciritical Components of a Solar Thermo-Chemical Reactor
Physical Description: 1 online resource (82 p.)
Language: english
Creator: Sehgal, Nikhil
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2013

Subjects

Subjects / Keywords: solar -- stress -- thermochemical
Mechanical and Aerospace Engineering -- Dissertations, Academic -- UF
Genre: Mechanical Engineering thesis, M.S.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: Two major components, namely the absorber tube and the back plate, of a high flux solar thermo-chemical reactor (STCR) has been analyzed for thermal stresses which arise due to high amount of variation in temperature field over the component during the operation of the reactor. The commercially available FEA code ABAQUS is used for this purpose. Experiments were also conducted in the solar simulator facility at UF to test the response of the proposed design of a STCR to thermal shock. Using a Monte-Carlo ray tracing software flux mapping for various designs of a STCR was simulated. Based on the flux maps a multi horizontal tube arrangement was chosen for analysis. Temperature distribution over the absorber tubes were obtained from a radiation-conduction heat transfer code. Using this data as the input for thermal stress analysis (TSA) simulations were run for 3 different tube diameter and two different ceramic materials. Currently, the analysis uses published standard material properties. Effects of creep, viscoelasticity and pre-existing flaws have been neglected. The simulations presented in this thesis focus on that phase of operation of the STCR when redox reactions take place. Simulations predicted that alumina tubes of 25.4  mm 14 diameter do not exceed critical stress values when the temperatures were cycled at a low rate. However, alumina tubes of 50.8mm and 76.2 mm diameter are predicted to exceed the critical stress values. For SiC tubes of 25.4 m and 50.8mm O.D stresses predicted were under critical stresses while the 76.2mm tube is predicted to exceed the critical stress. Finally, an alumina back plate is predicted to have large stress concentration in some areas. When experiments were conducted at solar simulator with one alumina absorber tube of 25.4 mm O.D/19.0 mm I.D the tube did not appear to have cracked after inspection. The back plate developed several cracks. Moreover, the data for the temperature at the inside of the tubes is acquired which can be used to further refine simulation results.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Nikhil Sehgal.
Thesis: Thesis (M.S.)--University of Florida, 2013.
Local: Adviser: Klausner, James F.
Local: Co-adviser: Mei, Renwei.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2013
System ID: UFE0045543:00001

Permanent Link: http://ufdc.ufl.edu/UFE0045543/00001

Material Information

Title: Thermal Stress Analysis for Ciritical Components of a Solar Thermo-Chemical Reactor
Physical Description: 1 online resource (82 p.)
Language: english
Creator: Sehgal, Nikhil
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2013

Subjects

Subjects / Keywords: solar -- stress -- thermochemical
Mechanical and Aerospace Engineering -- Dissertations, Academic -- UF
Genre: Mechanical Engineering thesis, M.S.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: Two major components, namely the absorber tube and the back plate, of a high flux solar thermo-chemical reactor (STCR) has been analyzed for thermal stresses which arise due to high amount of variation in temperature field over the component during the operation of the reactor. The commercially available FEA code ABAQUS is used for this purpose. Experiments were also conducted in the solar simulator facility at UF to test the response of the proposed design of a STCR to thermal shock. Using a Monte-Carlo ray tracing software flux mapping for various designs of a STCR was simulated. Based on the flux maps a multi horizontal tube arrangement was chosen for analysis. Temperature distribution over the absorber tubes were obtained from a radiation-conduction heat transfer code. Using this data as the input for thermal stress analysis (TSA) simulations were run for 3 different tube diameter and two different ceramic materials. Currently, the analysis uses published standard material properties. Effects of creep, viscoelasticity and pre-existing flaws have been neglected. The simulations presented in this thesis focus on that phase of operation of the STCR when redox reactions take place. Simulations predicted that alumina tubes of 25.4  mm 14 diameter do not exceed critical stress values when the temperatures were cycled at a low rate. However, alumina tubes of 50.8mm and 76.2 mm diameter are predicted to exceed the critical stress values. For SiC tubes of 25.4 m and 50.8mm O.D stresses predicted were under critical stresses while the 76.2mm tube is predicted to exceed the critical stress. Finally, an alumina back plate is predicted to have large stress concentration in some areas. When experiments were conducted at solar simulator with one alumina absorber tube of 25.4 mm O.D/19.0 mm I.D the tube did not appear to have cracked after inspection. The back plate developed several cracks. Moreover, the data for the temperature at the inside of the tubes is acquired which can be used to further refine simulation results.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Nikhil Sehgal.
Thesis: Thesis (M.S.)--University of Florida, 2013.
Local: Adviser: Klausner, James F.
Local: Co-adviser: Mei, Renwei.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2013
System ID: UFE0045543:00001


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1 THERMAL STRESS ANALYSIS FOR CIRITICAL COMPONENTS OF A SOLAR THERMO CHEMICAL REACTOR By NIKHIL SEHGAL A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR TH E DEGREE OF MASTER OF SCIENCE UNIVERSITY OF FLORIDA 2013

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2 2013 Nikhil Sehgal

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3 To my parents, thank you both for supporting me in every possible way to help me achieve my goals and fulfill my dreams

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4 ACKNOWLEDGMENTS Firstly, I would like to thank my parents for their encouragement, blessings and never ending support which has helped me achieve one of the most cherished dreams of my life to study in USA and participate in cutting edge research. I would like to thank Dr. James Klausner for taking me on as a m work on this wonderful project. I would also like to thank Dr. Renwei Mei for providing valuable guidance at all stages of this work. Very special thanks to Nick Au Yeung for being ever so patient, helpful and concerned over my progress in this project. Without his support I would not have accomplished whatever little results that I have managed to produce. Finally, thanks to all the members of the solar fuel team. I had taken guidance and advice from each one of them at some stage of this project. It has been wonderful working with everyone.

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5 TABLE OF CONTENTS page ACKNOWLEDGMENTS ................................ ................................ ................................ .. 4 LIST OF TABLES ................................ ................................ ................................ ............ 7 LIST OF FIGURES ................................ ................................ ................................ .......... 8 LIST OF ABBREVIATIONS ................................ ................................ ........................... 11 ABSTRACT ................................ ................................ ................................ ................... 13 CHAPTER INTRODUCTION ................................ ................................ ................................ ........... 15 Motivation ................................ ................................ ................................ ............... 15 Literature Review ................................ ................................ ................................ .... 16 Solar Thermal Technology ................................ ................................ ............... 16 Solar Thermochemical Technology ................................ ................................ .. 17 Solar Thermochemical Reactors (STCR) ................................ ................................ 22 Monte Carlo Ray Tracing Method and the Vegas Code ................................ ... 25 Thermal Shock in Solar Thermochemical Reactors ................................ ......... 26 Outline ................................ ................................ ................................ .................... 29 MONTE CARLO SIMULATIONS ................................ ................................ ................... 30 The Vegas Code ................................ ................................ ................................ ..... 30 Monte Carlo Simulations for STCR ................................ ................................ ......... 32 THERMAL STRESSES IN REACTOR COMPONENTS ................................ ............... 39 Theory of Linear Thermoelasticity ................................ ................................ ........... 39 Constitutive Laws of Linear Thermoelasticity ................................ ................... 39 Displacement Formulation of Thermoelasticity ................................ ................. 40 Linear Thermoelasticity Reduced to Two Dimensional ................................ .... 41 Fully Coupled Thermoelastic Equations ................................ ................................ .. 41 Ty pes of Thermal Stress Analysis ................................ ................................ .......... 42 Thermal Stress Analysis ( TSA ) using Finite Element Analysis ( FEA ) ..................... 44 Sequential Thermal Stress Analysis ( STSA ) in ABAQUS ................................ ....... 44 STSA in ABAQUS for Reactor Tubes ................................ ................................ ..... 49 Material Properties ................................ ................................ ........................... 50 Tube Dimensions ................................ ................................ ............................. 50 Assumptions Made in STSA ................................ ................................ ............. 51 Heat Transfer Analysis ................................ ................................ ..................... 53 TSA on Other Components of the Reactor ................................ ....................... 61

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6 Assumptions for TSA in Back Plates ................................ ................................ 61 THERMAL TESTS WITH SOLAR SIMULATOR ................................ ........................... 67 Experimental Setup ................................ ................................ ................................ 67 Solar Thermochemcial Reactor ................................ ................................ .............. 68 Construction ................................ ................................ ................................ ..... 68 STCR on the XY Table ................................ ................................ ..................... 69 Experiments ................................ ................................ ................................ ............ 71 Experiment 1 ................................ ................................ ................................ .... 71 Results ................................ ................................ ................................ ............. 71 Experiment 2 ................................ ................................ ................................ .... 73 Results ................................ ................................ ................................ ............. 74 Effectiveness of the Shutter to Prevent TS ................................ ............................. 75 CONCLUSIONS ................................ ................................ ................................ ............ 76 Summary ................................ ................................ ................................ ................ 76 Future Work ................................ ................................ ................................ ............ 77 LIST OF REFERENCES ................................ ................................ ............................... 79 BIOGRAPHICAL SKETCH ................................ ................................ ............................ 82

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7 LIST OF TABLES Table page 2 1 Input parameter for a four tube vertical (solar thermochemical reactor) STCR .. 33 2 2 O utput results for a four tube vertical STCR ................................ ....................... 33 2 3 Power distribution in four tube STCR with deflector tubes ................................ .. 35 3 1 Determination of A/M ratio for alumina ................................ ............................... 43 3 2 Determination of A/M ratio for SiC ................................ ................................ ...... 43 3 3 List of non dimension al parameters ................................ ................................ .... 46 3 4 Properties of alumina and SiC at different temperatures ................................ .... 50 3 5 Different tube dimensions considered in simu lations ................................ .......... 51 3 6 Values of coefficient for the polynomial surface fit ................................ .............. 52 3 7 Temperature dependence of flexural strength of alumin a and SiC ..................... 55

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8 LIST OF FIGURES Figure page 2 1 Vegas Code sample contour plots ................................ ................................ ...... 31 2 2 A four tube vertical (solar thermochemical reactor) STCR modelled in Vegas Code ................................ ................................ ................................ ................... 32 2 3 Flux distribution for a four tube vertical STCR modelled in Vegas Code ............ 34 2 4 Flux distribution as a function of angle for side tube ................................ ........... 34 2 5 Flux distribution as a function of angle for side tube ................................ ........... 35 2 6 Addition of deflector tubes inside the cavity ................................ ........................ 36 2 7 Horizo ntal tube arrangment for STCR ................................ ................................ 37 2 8 Multiple vertical tube arrangment for STCR ................................ ........................ 37 2 9 Flux distribution on tubes for a multiple vertical tube arrangment for STCR ....... 38 3 1 Axisymmetric cylinder with radial heat transfer model in ABAQUS .................... 46 3 2 Quarter cylinder heat transfer result for two different mesh sizes ....................... 47 3 3 Comparison of heat transfer analysis between ABAQUS and published results for boundary condition 1 ................................ ................................ .......... 47 3 4 Comparison of (thermal stress analysis) TSA between ABAQUS and published results for boundary condition 1 ................................ ......................... 48 3 5 Comparison of heat transfer analysis between ABAQUS and published results for boundary condition 2 ................................ ................................ .......... 48 3 6 Comparison of TSA between ABAQUS and published results for boundary condition 1 ................................ ................................ ................................ .......... 49 3 7 Polynomial surface fit through the data of nodal values of temperature obtai ned from the in house code ................................ ................................ ........ 51 3 8 Temperature distribution on the surface of absorber tubes as calculated by the polynomial function ................................ ................................ ....................... 53 3 9 Normalized temperature for absorber tubes outer surface Heating phase ......... 54 3 10 Normalized temperature for absorber tubes outer surface Cooling phase ......... 54

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9 3 11 Stress distribution on the surface of alumina absorber tubes at the end of heating phase ................................ ................................ ................................ ..... 56 3 12 Comparison of stress developed for 25.4mm tubes Coolin g Phase ................. 57 3 13 Comparison of stress developed for 50.8mm tubes Cooling Phase ................. 58 3 14 Comparison of stress developed for 76.2mm tubes Cooling Phase ................. 58 3 15 Comparison of stress developed for 3 different sizes of alumina tubes Cooling Phase ................................ ................................ ................................ .... 59 3 16 Comparison of stress developed for 3 different sizes of SiC tubes Cooling Phase ................................ ................................ ................................ ................. 59 3 17 Comparison of stress developed for 3 different sizes of alumina tubes Heating Phase ................................ ................................ ................................ .... 60 3 18 Comparison of stress developed for 3 different sizes of SiC tubes Heating Phase ................................ ................................ ................................ ................. 60 3 19 Temperature distribution on back plate made of fully dense alumina Heating Phase ................................ ................................ ................................ ................. 62 3 20 Temperature distribution on back plate made of fully dense alumina Cooling Phase ................................ ................................ ................................ ................. 62 3 21 Stress distribution on back plate made of fully dense alumina Heating Phase ... 63 3 22 Stress distribution on back plate made of fully dense alumina Cooling Phase ... 63 3 23 Temperature distribution on back plate with 76.2 mm diameter tube holes made of fully dense alumina Heating Phase ................................ ...................... 64 3 24 Temperature distribution o n back plate with 76.2 mm diameter tube holes made of fully dense alumina Cooling Phase ................................ ...................... 65 3 25 Stress distribution on back plate with 76.2 mm diameter tube holes made of fully dense alumina H eating Phase ................................ ................................ .... 65 3 26 Stress distribution on back plate with 76.2 mm diameter tube holes made of fully dense alumina Cooling Phase ................................ ................................ .... 66 4 1 Ellipsoidal lamps at the solar simulator facility at UF. ................................ ......... 67 4 2 CCD camera at the solar simulator facility at UF ................................ ................ 68 4 3 Different components of a STCR ................................ ................................ ........ 68

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10 4 4 STCR kept on fire bricks ................................ ................................ ..................... 69 4 5 Assembly of STCR insulated with glass wool ................................ ..................... 70 4 6 Complete assembly of the STCR framework mounted on XY table ................... 70 4 7 STCR with the shutter on the left ................................ ................................ ........ 72 4 8 STCR with ceramic plugs on the back plate ................................ ....................... 72 4 9 Crack at the periphery of the back plate of STCR ................................ .............. 73 4 10 ............................... 74

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11 LIST OF ABBREVIATIONS FCTSA Fully coupled thermal stress analysis FEA Finite element analysis RT Room temperature STCR Solar thermo chemical re actor STSA Sequentially coupled thermal stress analysis TSA Thermal stress analysis Total strain in the ij direction Strain due to mechanical forces in the ij th direction Strain due t o thermal forces in the ij th direction G Shear Modulus Total stress in the ij th direction Krone cke r delta E Temperature differen ce with respect to the stress free temperature Thermal coefficient Body force in the i th direction Displ acement in the i th direction Thermal conductivity Density

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12 Specific heat at constant volume Gas constant Initial temperature Normalized time Normalized stress

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13 Abstract of Thesis Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Master of Science THERMAL STRESS ANALYSIS FOR CRITICAL COMPONENTS OF A SOLAR THERMO CHEMICAL REACTOR By Nikhil Sehgal May 2013 Chair: James Klausner Cochair: Renwei Mei Major: Mechanical Engineering T wo major components, namely the absorber tube and the back plate, of a high flux sola r thermo chemical reactor (STCR) has been analyzed for thermal stresses which arise due to high amount of variation in temperature field over the component during the operation of the reactor. The commercially available finite element analysis ( FEA ) code A BAQUS is used for this purpose. Experiments were also conducted in the solar simulator facility at UF to test the response of the proposed design of a STCR to thermal shock. Using a Monte Carlo ray tracing software flux mapping for various designs of a STC R was simulated. Based on the flux maps a multi horizontal tube arrangement was chosen for analysis. Temperature distribution over the absor ber tubes were obtained from a radiation conduction heat transfer code. Using this data as the input for thermal str ess analysis (TSA) simulations were run for 3 different tube diameter and two different ceramic materials. Currently, the analysis uses published standard material properties. Effects of creep, viscoelasticity and pre existing flaws have been neglected. Th e simulations presented in this thesis focus on that phase of operation of the STCR

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14 when redox reactions take place. Simulations predicted that alumina tubes of 25.4 mm diameter do not exceed critical stress values when the temperatures were cycled at a lo w rate. However, alumina tubes of 50.8mm and 76.2 mm diameter are predicted to exceed the critical stress values. For SiC tubes of 25.4 m and 50.8mm O.D stresses predicted were under critical stresses while the 76.2mm tube is predicted to exceed the critic al stress Finally, an alumina back plate is predicted to have large stress concentration in some areas. When experiments were conducted at solar simulator with one alumina absorber tube of 25.4 mm O.D /19.0 mm I.D the tube did not appear to have cracked af ter inspection. The back plate developed several cracks. Moreover, the data for the temperature at the inside of the tubes is acquired which can be used to further refine simulation results.

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15 CHAPTER 1 INTRODUCTION M otivation Today, t he technology for u sing concentrated solar radiation to drive redox reactions for producing compounds which can either be used directly as a gaseous fuel or further converted into liquid fuel has been the subject of extensive research in the past few years. An important part of this research has been the design of high heat flux solar thermochemcial reactors (STCR). Various designs STCR have been proposed by different research groups. The designs are driven by two primary considerations: (i) favorable temperature for chemical reactions and (ii) robustness of the design against thermal shock. Since the reactors operate at temperatures as high as 1600 C failure o f material due to thermal shock and thermal fatigue becomes a concern. The ability of the reactor material to withstand thermal shock also directly impacts the production of fuel since the extent to which a material is resistant to thermal sh ock limits the rate of cycling of temperature for the two parts of a redox reaction Therefore, it is essential to study the response of some critical components of a STCR to thermal shock. One can explore different material of construction or different si zes of the same geometry can be tested for thermal shock resistance. Another parameter of investigation is the rate at which temperatures can be cycled over the reactor components. To study the effect of these parameters on reactor design finite element a nalysis ( FEA ) simulations for predicting thermal stresses have been carried out for different sizes and material of some components of the reactor. It is also desired to study the effect of thermal stresses on these components by conducting experiments usi ng a solar simulator. Having the ability to the nature of thermal stresses allows improvement in the overall design of the STCR.

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16 Literature Review Solar Thermal Technology Solar thermal technology, as the name suggests, converts the energy of solar irradi stored in a medium which may further be utilized to produce electricity or supply energy to a chemical reaction or stored in a thermal storage system. Solar thermal technolo gy is one of the most promising technologies for producing clean fuel. It has several advantages over the other convention al solar photovoltaic technology The primary advantages ([1], [2]) over photovoltaic technology are ease of large scale setup and eco nomics. Another major advantage over photovoltaic is the option of storing thermal energy. For instance thermal energy can be stored in molten salts which can later be used to generate steam which in turn generates electricity. The heat produced can also b e directly used to drive mechanical systems like Stirling s team e ngine s which convert thermal energy into mechanical energy. For large scale systems solar thermal is more cost effective [3] than PV and fossil fuels such as natural gas. Other key advantage of solar thermal technology is to store the converted thermal energy to in the form of fuels to source takes place. S olar thermochemical technology is one such met ho [ 4] Concentrated energy is used to drive endothermic reactions which produce compounds which can be directly used as fuels, like bio fuels, or can be used to produce intermediate products, like syngas (CO+H 2 ), which are furthe r processed to produce fuels.

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17 There are several technological challenges in the field of solar thermal technology that are the focus of wide spread research around the world. Capturing the maximum amount of solar energy is one such challenge. For large sc ale production there are essentially two ways of collecting solar radiation [5]: line focus and point focus. While line focus requires lesser efforts in terms of design and maintenance, point focus can achieve higher temperatures [6] The line focus approa ch is capable of achieving about half of the maximum theoretical concentration. The losses occur because of errors in parabolic shape, thermal expansion and shifting of parts etc. On the other hand point focus can achieve at least twice the concentration a s that of line focus. For solar fuel production the research is two pronged [4] One side of the research focuses on the chemistry of the endothermic reactions and the other aspect of research is the design of the reactors in which the solar energy is conc entrated to produce fuel. Solar Thermochemical Technology Steinfield et al [7] discuss the different applications of solar thermochemical technology. Of these, the most notable is the production of solar fuels like hydrogen. The earliest work in producing solar hydrogen was using the solar energy to split the H 2 O molecule. Solar t hermolysis requires temperatures of the order of 2500K and the products separation at high temperature to avoid an explosive recombination. In the process of separating these gase s the operation loses a considerable amount of efficiency and working at such high temperatures induces serious material constraints. Other sources of solar hydrogen have also been explored. Noring et al [8] describe the research conducted towards producti on of H 2 by splitting the H 2 S molecule. H 2 S is a highly toxic gas which is produced as a byproduct in the process of removal of sulphur from petroleum or coal. Utilizing a toxic waste to produce fuel by using a renewable

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18 source of energy like hydrogen is a highly lucrative option. The endothermic reaction can be carried out at 1800 K and successful separation of gases has been achieved using water cooled heat exchangers. Noring et al [8 ] have also explored the H 2 S splitting via three different mechanisms; ( i) pure solar (ii) a hybrid process of solar and natural gas and (iii) the Clauss process. The results of their study indicate that the pure solar process has the potential of lowering the disposal cost of H 2 S when compared to the conventional Clauss Proce ss. The hybrid technology can further lower the cost of production of hydrogen but at the expense of increased complexity of hybrid reactor design and production of CO 2 as a byproduct. Pop ular method of hydrogen production is the use of solar energy in pro ducing solar hydrogen from reduction of metal oxides [7]. The extraction of metals from their oxides from carbothermic and electrolytic process consumes a high amount of energy which typically comes from combustion of fossil fuels which in turn produces l arge amount of greenhouse emissions. Therefore using concentrated solar energy to achieve the same is an appealing option. Typically the reduction of metal oxides in the absence of any reducing agent requires very high temperatures for the thermodynamics t o be feasible. Alternatively, electrical work or other forms of supplementary heat, like the waste heat from process gases, can be used along with solar heat to achieve the same results. While it is possible to achieve stagnation temperatures as high as 35 00K, material restrictions and efficiency requirements suggest operating the solar thermal reactors at much lower temperatures. Thus, use of reducing agent is widespread. Coke or natural gas is a popular choice as reducing agent. Steinfield et al [9] discu ss the thermodynamic feasibility of reduction of metal oxides in presence of reducing agents.

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19 Detailed calculations performed by the authors reveal that Fe 2 O 3 ZnO and MgO are the only metal oxides that will yield a significant amount of free metal below 2 000K. The reduction of ZnO has been one of the more widely researched chemical reactions. The two step cycle of CeO 2 /Ce 2 O 3 for water splitting has been shown to have fast kinetics in a lab scale solar reactor at 2000 C [10, 11]. Mehdizade et al [12] have conducted research on the chemical kinetics of the reduction of ferrous oxides. Serpone et al [13] discuss the advantages of this process in that H 2 and O 2 are produced in two different steps and thus the issue of separation of gases at high temperature does not arise. In the first step the metal oxide is thermally dissociated into corresponding metal and oxygen. In the subsequent step the hydrolysis of metal produces metal oxide and hydrogen. Although this process requires high temperature, but, with the use of heat recuperation systems and highly concentrated solar heat efficiency of upto 30% can be achieved. Since syngas is one of the chief components of synthetic fuels, including Fischer Tropsch chemicals, ammonia etc, a lot of importance has been give n to production of syngas through this technology. Biomass can be converted into biofuels or syngas using different solar thermochemical approaches [14] Experiments show that nearly all carbon in biomass can be converted into syngas which drastically impr oves the ability of biomass to produce clean energy economically. Perkins et al [15] have tested the gasification of corn stover, a common agricultural by product, for production of syngas. Although they did not use a solar furnace to test the samples, an electric furnace in a controlled environment was used. The effects of water concentration, temperature, particle size were explored. Their ongoing work involves the verification of the results of

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20 this experiment with experiments conducted in an actual so lar furnace. Lichty [1 6 ] et al. have tested the gasification of biomass in a reflective cavity multitude prototype reactor. They achieved biomass conversion as high as 68%. Stamatiou et al [1 7 ] have conducted experiment on the solar production of syngas fr om H 2 O and CO 2 via two step thermochemical cycles based on Zn/ZnO and FeO/Fe 3 O 4 redox reactions. The first, endothermic step is the thermal dissociation of the metal oxide using concentrated solar radiation as the energy source of high temperature process heat. The second, nonsolar, exothermic step is the reaction of the metal or reduced metal oxide with a mixture of H 2 O andCO 2 yielding syngas (H 2 and CO), together with the initial form of the metal oxide that is recycled to the first step. While productio n of solar fuels is one of the more popular applications in solar thermochemical field it is not the only one. Steinberg [1 8 ] describes the use of concentrated solar energy for upgrading the fossil fuels. Since the research in the area of producing solar f uels economically still requires considerable efforts researchers have started focusing on the interim solution. Concentrated solar energy can be used to upgrade the quality/calorific value of the fossil fuels by providing energy equal to the enthalpy of t he reaction. This results in longer fuel life and hence the upgraded fossil thermochemical process is the decarbonization of fossil fuels. The underlying idea is to remove carbo n from fossil fuels so that no CO 2 is released. Two methods have been proposed [17] ; (i) Solar thermal decomposition of fossil fuels and (ii) gasification of fossil fuels. The thermal decomposition results in products which are easily phase separated. Ther e is a carbon rich condensed phase and a hydrogen rich gaseous phase. The

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21 hydrogen in the gaseous phase may be further processed to yield high purity hydrogen or high quality syngas. Since methane has the highest H C ratio, it is a widely studied compound for thermal decomposition using solar energy. Maag et al [1 9 ] present results of decomposing methane a solar thermal reactor. They are able to achieve 99% of methane conversion and 98% of h ydrogen yield. The solar to chemical efficiency of their reactor i s reported to be an average of 9.1 % with peak efficiency reaching the values of 16%. These values can be considered as highly promising since the typical design efficiency target for solar thermal reactors is 20 %. Further studies by Mier et al.[20] have e xplored the nano structure of the carbon produced when different catalysts are used in thermal decomposition of methane. Both of the methods have their advantages [17]. The biggest advantage of thermal decomposition is that it is able to achieve a complete separation of carbon from gaseous product in a single step whereas gasification requires additional step of converting CO into CO 2 and subsequent removal of CO 2 On the other hand thermal decomposition has a large energy penalty associated with carbon seq uestration. This in turn is primarily dependent on the type of feedstock used. For solid carbonaceous materials like coal the residual energy after decarbonization may not be sufficient for an industrial application. But with hydrocarbons with high H 2 /C ra tio this method may be preferred. Additionally, gasification of solid fuels like coal into liquid fuels can improve the efficiency (of generating electricity in steam turbine) by 20%. Synthesis of chemical commodities by using solar energy in endothermic r eactions has also been explored.

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22 At the heart of a solar thermochemical process is a solar thermal reactor the furnace where chemical reactions take place. Much research has gone into the design and development of different types of solar thermal reactors Solar Thermochemical Reactors S olar thermochemical reactor can be thought of as a device in which the solar energy is concentrated and retained for long enough time to produce the desired energy conversion. The type and characteristics of a reactor depe nds upon various factors such as, the material of construction chosen, the size and type, the kinetics of the chemical reaction to be performed and other such important parameters. Steinfield et al[2] have classified the reactors into two broad categories, namely, (i) Indirectly I rradiated reactor (IRR) and (ii) Directly irradiated reactor (DIR). The chief difference, as the name suggests, is the way the solar irradiation is directed towards the reactants. In the Indirectly I rradiated reactor the reactants are in a tube or other similar cavity and the irradiation hits the opaque walls of the reactor tubes. Heat is transferred through conduction into the opaque wall to the reactants. The Directly I rradiated (DIR) reactor in contrast allows the solar irradiat ion to fall directly on the reactants. The biggest disadvantage of this type of arrangement is the presence of a transparent window which imposes serious design constraints. A few prototypes have been developed around the world. A description of a select f ew is as follows: Palumbo et al [21] discuss one type of DIR called ROCA (short for R eactor C losed to A ir). The reactor kinetics involves the thermal dissociation of the ZnO(s) into Zn(g) and O 2 at temperatures above 2000K. It consists of a conical rotati ng vortex cavity and a transparent window which allows the irradiation to hit the reactants directly. The reactor aims at concentrating enough solar irradiation to achieve a temperature of

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23 2000K and higher. Hirsch et al [22] report a decomposition of metha ne in the same vortex reactor while reaching a nominal temperature of 1600K. The Sandia National Laboratory [23] has developed another type of DIR called the CR 5 (Counter Rotating Ring Receiver Recuperator Reactor) The reactor consists of counter rotatin g rings with the reactive metal oxide filled between them. One side of the reactor is undergoing reduction and is exposed to the concentrated radiation and has significantly higher temperature. The material in the other set of rings is turned away from the solar radiation and is at a lower temperature for undergoing oxidation Although this type of reactor achieves high temperature, it does require a separate cooling mechanism to cool the reactor area around the window. Additionally, the authors report that frequent cleaning of the window was required. Another attractive design for the reactor is that of a cavity type reactor. This type of design aims at capturing a solar irradiation, coming through a small aperture, in the cavity. The idea is to simulate a black body type geometrical arrangement in which a high percentage of solar radiation are reflected within the cavity and result in raising the temperature of the absorber tubes. There have been a few designs proposed for the Indirectly I rradiated reactor s. On e type of indirectly irradiated 10kW solar reactor for thermal decomposition of methane has been proposed at CNRS France [24]. It is a double cavity reactor with the inner cavity completely covered with insulation. Within the inner cavity there are gr aphite tubes in which process gases enter and the reaction takes place. However, the reactor still consists of a window to capture radiation. This window and the associated cooling mechanism can perhaps be avoided by choosing the appropriate cavity to aper ture ratio. The appropriate ratio will bring the whole system

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24 closer to approximating a perfect black body. This ratio is discussed by Piatowski et al [25] for a single cavity type reactor. They concluded that a value of 0.6 for the ratio resulted in least amount of re radiation losses through the aperture. Melchoir et al [26] discuss the design and of one such reactor. The reactor consists of a tubular cavity with an aperture to capture the solar irradiation as well as a compound parabolic concentrator pla ced at the aperture to help further concentrate the solar irradiation. Once again, the thermal decomposition of ZnO is c hosen as the chemical reaction o f interest. The reactants are placed inside smaller cylindrical tubes placed inside the cavity. Using Mo nte Carlo ray tracing methods the authors experimented with the number of reactor tubes, the ratio of cavity size to aperture size, the distance of the reactor tubes from cavity. It was found that there is an optimum ratio of the aperture size to that of t he cavity. While increasing cavity size increases loses via conduction/convection, decreasing the aperture size relative to the cavity size tends to is an optimum di stance from the aperture where the reactor tubes should be placed so as to have maximum temperature on the surface of the absorber tubes. Thus, for a design of a small scale prototype reactor a windowless approach may be considered as advantageous form the point of view of minimalistic design considerations and ease of maintenance. In fact, these issues may be compounded in a larger size reactor and may offset the energy efficiency benefits of directly irradiated reaction. Yet another type of small windowle ss reactor design is discussed by Meier et al [26a] for the endothermic calcinations at above 1300 K. The cavity is placed horizontally and the absorber tubes are laid along the periphery of the cavity wall. With the simplified design for a prototype

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25 the a uthors foresee no major technical difficulties in scaling up the reactor to power levels of 0.5 1 MW. L iterature on the detailed design procedure for respective reactors is largely missing. Most literature focuses on the performance of different designs. P alumbo et al [21] discuss the general methodology for designing a solar thermal reactor. They lay out a three step approach to optimize the design of the reactor. These are, (i) establishing the kinetics of the chemical reaction; (ii) develop a reactor co ncept that meets the mechanical boundary condition of being scalable. That is the reactor must have a minimal start up time when the sun is available and secondly, owing to the transitory nature of the solar energy, it must withstand thermal shock Finally (iii) model the reactor concept in order to evaluate the potential performance of the scaled up project. The output from this step is temperature and gas production rate, preferably as a function of solar energy input. If these results are unacceptable o ne returns back to step (ii). Otherwise a test reactor model is built ad experiments are conducted. In the discussion of a cavity type reactor Melchoir et al [27] discuss about the effects basic parameters like cavity diameter, tube diameter and tube arran gement have on the radiative flux distribution and temperature distribution on the tubes. Monte Carlo Ray Tracing Method and the Vegas Code Monte Carlo Ray Tracing Method [28] is widely used to predict the radiative transfer for complex geometries. In this method large numbers of ray energy packages are used to approximate the radiative transfer. Each package carries the same amount of energy. These rays are emitted from the source in a direction as defined in the input file. The rays are traced to the nea rest surface and on the surface it may be absorbed,

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26 transmitted or reflected. If absorbed, it adds to the total flux on the surface otherwise it is traced again to the nearest surface. Vegas Code developed by Jorg Petra s ch [29] is a software tool which uti lizes the Monte Carlo ray tracing code to model concentrating optical devices. It has been extensively used in this project to optimize the preliminary design of the solar thermal reactor based on the power incident on the reactor tubes. More precisely, in the words and convection heat transfer effects but the results can predict radia tive flux distribution. Most importantly it does not include re radiation from a target on account of high temperatures of the target geometries. The sources and the targets are defined in an input file. The various pre defined geometry targets can be used in different combinations to create a complex geometry. Other parameters that are requ ired by t he Vegas Code is the target position, surface reflection type and emissivity. The output is the total flux distribution on the target geometries and a visual re presentation of the same. Thermal Shock in Solar Thermochemical Reactors One of the primary concerns in design of a solar thermochemical reactor is its ability to withstand thermal shock Since a solar thermochemical reactor undergoes drastic temperature changes, thermal shock can be a severe deterrent in the selection of material for the reactor components. This in turn can affect the whole dynamics of the heat transfer exchange in the reactor. Ceramics materials which are best suited for high temperature applications are brittle in nature and can crack easily under large thermal fluctuation. Not much literature is available on the study of the nature of thermal shock

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27 in basic components of a solar thermochemical reactor. The d ata available mostly concerns the thermal shock in test specimen of different materials and the application of finite element methods to numerically estimate thermal stresses in simple geometries like a cylinder. A nalysis for estimation of thermal stress can have two approaches [30]. First is the sequential thermal stress analysis where temperature and stresses are calculated independently. The temperature field is calculated first as a function of time and position. Next, the stresses are calculated because of this temporal and spatia l variation of the temperature field. The second approach involves solving the fully coupled thermoelastic equation. In this type of analysis stresses and temperature both are simultaneously solved. The FEA software ABAQUS used in this project for estimati ng the thermal stresses in absorber tubes, for a given the temperature distribution, is capable of performing both the analysis. Carter et al [31] compares the two approaches for estimating thermal stresses in a given system and establish a set of paramete rs whose values can help a designer to decide as to which approach is best suited for the given application. These parameters are solely dependent on the material properties. However for high temperature applications such as the solar thermochemical react or the material properties itself are dependent on the temperature. Numerous data have been published [ 31a ] to estimate the changes in properties (thermal conductivity, of temperature Kandil et al [32] used FEM to simul ate a sequential thermal stress problem in thick cylinders. The method solved for radial heat transfer in a cylinder when the inner wall of the cylinder was subjected to different type of temperature boundary conditions.

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28 Once the temperature profile throug hout the cylinder was calculated, based on the boundary condition, the thermal stress values were estimated. The results of this paper were used to calibrate the results of the thermal stress simulation obtained from the FEA software ABAQUS. Akiyama et al. [33] established a test procedure for determining thermal shock in solid cylinders using laser beams. This test assumed that the compressive hoop stress is the primary cause of fracture. Further Finite Element Method was used to develop a numerical model which closely agreed with the results of the experimentation. This methodology was later used to estimate the thermal shock strength of Al 2 O 3 Although the results of this study give an insight into the nature of thermal stresses the results cannot be con sidered as a reference for calibration. This is so because unlike Kandil et al the study assumes that compressive hoop stress as the only cause of fracture in the cylinder. In contrast, Kandil estimates the effective stress and all the individual component s of thermal stress. One of t he most relevant study of this nature on a solar reactor type temperature distribution on specimen was carried out by Lichty et al [34] who studied the effects of high temperature induced tensile stresses in super alloys at th e High Flux Solar Furnace at the National Renewable Energy Laboratory. However, the study did not include testing of ceramics which are the prime candidates for solar thermochemical reactors. The study concluded that the largest temperature does affect the ultimate strength of the material. For cylindrical shapes (unpublished results) the failure occurred primarily due to compressive hoop stress. This might seem to suggest that the results from Akiyama et al [33] accurately predict the nature of stresses in cylindrical objects but Lichty et al d id not comment a bout the temperature distribution on the cylindrical

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29 specimen under stress and hence an accurate comparison cannot be made. Lichty et al also attempted to perform a life cycle fatigue analysis of the super alloy. However, the alloy being highly ductile did not yield in the HFSF and thus the study could not comment anything on the life cycle of the material. Finally, additional considerations in the prediction of thermal stress and thermal fatigue in ceramics are discussed by Hasselman [3 5 ] The material properties governing the thermal stresses in a ceramic are dependent on the microstructure, impurities and geometry of the specimen. Hence, it is advised to test the specimens to evaluate these propert ies before carrying out any suitable analysis. The paper also recommends taking into account any pre existing flaws that might exist in the specimen. Finally, the paper recommends considering the phenomenon of creep for very high temperature (greater than 1200 C) applications. However, once again the author cautions against using handbook data or empirical relationship for creep data since the creep properties are specimen. Outline This thesis will present the result of simulations for thermal stresses on reactor components. The preliminary design consideration of flux distribution using Vegas Code is presented. The constitutive equations for thermal stresses are discussed. Further, the two theories of TSA are discussed and analysis is provided to choose one over the other. Results of FEA simulations using ABAQUS are presented and compared for different material and tube sizes. Finally, the thermal tests conducted at the UF s olar simulator facility are detailed.

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30 CHAPTER 2 MONTE CARLO SIMULATIONS The Vegas Code S olar simulator at University of Florida is a research facility used to create controllable experiments which mimic the actual operation of a STCR in a solar therma l plant. The use of a statistical Monte Carlo ray tracing method to predict the behavior of such reactors or receivers is common. In such a method every variable included in the simulation is defined by an individual probability distribution function (PD F) Using the PDF, a cumulative distribution function is created and then inverted. Generating a random number to be substituted into the inverted cumulative distribution function produces a value for the desired variable [ 3 6 ]. For instance, consider the application to STCR. A ray from a parabolic surface is traced to target geometry. Based on the known properties of the target geometry it is decided whether the ray is reflected, absorbed or transmitted. More details of this method can be found in book by Modest [ 28 ]. The Vegas code is an in house Monte Carlo ray tracing program that is used to predict the flux distribution on target geometries in solar simulator. The Vegas Code has a complete model of the solar simulator facility at UF. It can model the seven ellipsoidal mirrors at the facility and is capable of ray tracing from these lamps. The Vegas code has an extensive library of different geometries. Complex geometries can be created by combination of these predefined geometries in the library. Figur e 2 1 shows sample diagrams for ellipsoidal mirror modeling and sample geometry of a disc.

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31 ( A) ( B ) ( C ) Figure 2 1. Vegas Code sample contour plots A ) 3D plots of ellipsoidal m irror B ) S imple disk geometry C ) A ll seven mirrors with the disc geometry Capabilities of Vegas Cod e : The Vegas Code is capable of predicting the incident flux distribution on target geometry. The primary purpose of Vegas Code is to track the path of th e rays as it hits the target geometry. The resulting plots can help the user predict the spots where the maximum flux intensity lies. The sources and targets are defined in an input file. Target position, surface reflection type and emissivity are the

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32 para meters that the user can define. The Vegas code does not calculate temperatures for the target geometries. It also does not take into account the conduction and convection heat transfer. Monte Carlo Simulations for STCR With respect to thermal stresses it is desirable that the flux distribution on the absorber tubes be as uniform as possible. This will prevent large temperature gradient and hence significantly reduce the stresses arising due to thermal fluctuations. Since Vegas Code can give a good idea ab out the relative flux distribution these simulations are used as the starting point in analysis for predicting the nature of thermal stresses in reactor components. The basis of the first design of STCR is the vertical tube reactor at ETH [ 27 ]. This geome try was modeled in Vegas Code (Figure 2 2.) to study the relative flux distribution on the absorber tubes. Absorber tubes were placed 60% of the maximum distance from the aperture. Melchior et al. [27] have estimated this to be the optimal distribution for attaining maximum temperature on the tubes. ( A) ( B ) Figure 2 2. A four tube vertical STCR modelled in Vegas Code A )Isometric View B )Top view

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33 Table 2 1 Input parameter for a four tube verti cal STCR Diameter of absorber tubes (m) 0.08 Diameter of cavity (m) 0.5 Diameter of aperture (m) 0.05 Material of absorber tubes Alumina/Silica Material of cavity Alumina Table 2 2 O utput results for a four tube vertical STCR Absorber Tube Material > Alumina SiC Power incident on the aperture 0.599 0.599 Power absorbed by the cavity 0.3584 0.162 Tube 1 0.061 0.105 Tube 2 0.058 0.095 Tube 3 0.058 0.095 Tube 4 0.061 0.106 Total power on the tubes 0.565 0.589

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34 Figure 2 3. Flux distribution for a four tube vertical STCR modelled in Vegas Code P ercentage of power absorbed by individual tubes is shown in table 2 2. Also, the flux distribution on the tubes is shown in Figure 2 3. As is evident from the diagram the tubes have a poor distribution of flux with some evident hot spots. Figure 2 4. Flux distribution as a function of angle for side tube

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35 Figure 2 5. Flux distribution as a function of angle for side tube Moreover, the cavity received a high amount of radiation which is undesirable because that heat is lost to the surrounding and reduces the efficiency of the process. Therefore, modifications in design are made with aim of improving the uniformity of flux distribution on the tubes and reducing the flux on the cavity. One way of doing that is to Various arrangements of deflector tubes were tried. Figure 2 6 shows the various arrangements of deflector tubes and the absorber tubes that were tried. All these trials did not produce any significant change in the flux distribution on the tubes. In fact, in some cases the power absorbed by individual tubes dropped significantly (Table 2 3). Table 2 3 Power distribution in four tube STCR with deflector t ubes Absorber Tube Material > Alumina Power incident on the aperture 0.599 Tube 1 0.032 Tube 2 0.0348 Tube 3 0.0311 Tube 4 0.0351

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36 Figure 2 6. Addition of deflector tubes inside the cavity Further trials of different tube and cavity arrangement revealed that the hot spots on the tubes cannot be eliminated completely. There are essentially seven hot spots, within any STCR design, each corresponding to one lamp in the solar simulator. However, with a horizontal type reactor, shown in Figure 2 7, th e hot spot can be spread over multiple tubes. This might lead to less severe temperature gradient on the reactor tubes and thereby lead to less severe thermal shock Another advantage of this design is that no radiation is lost to the cavity. The disadvant age of this design is that the total flux on each tube is not as high as in some of the previous cases ( Table 2 3 ). However, experimental validation is required to check whether this arrangement can still result in favorable heat flux for chemical kinetics Early results of the experiments in the

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37 solar simulator (chapter 4) showed that relatively high temperature can be achieved over the surface of absorber tubes in this arrangement. A) B ) Figure 2 7. Horizontal tube arrangment for STCR A ) B ack view B ) I sometric view As seen above there is not much of a difference in the total power absorbed by the two tube sizes. In such scenario a smaller tube size will be favorable because a smal ler specimen of a given material will develop lower thermal stresses than a bigger one given that they are of the same geometric shape. A variation of this design is the vertical arrangement of tube and cavity with deflector tubes at the back (Figure 2 8) Figure 2 8 Multiple vertical tube arrangment for STCR

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38 This design was not pursued because of predicted the tubes near the aperture of the cavity had lowest power absorption than any of the previous case (0.0269) [Figure 2 9]. Also, this design was pr edicted to pose greater challenges for experimental setups. Thus, a horizontal multi tube cylinder design is pursued. A) B) Figure 2 9 Flux distribution on tubes for a multiple vertical tube arran gment for STCR

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39 CHAPTER 3 THERMAL STRESSES IN REACTOR COMPONENTS Theory of Linear Thermoelasticity V ariation of temperature field within an elastic continuum produces thermal stresses. The theory of linear thermoelasticity is based on the addition of t hermal strains to mechanical strains. There is also a different class of thermoelasticity problems where the temperature and displacement appear in a coupled form in the equation. This class of problem will also be discussed However, the main focus of thi s section will be the discussion of the basic theory of linear thermoelasticity. Constitutive Laws of Linear Thermoelasticity C lassical theory of thermoelasticity states that the total strain in a component is a linear addition of strain tensor due produce d by mechanical loading and that of strain tensor produced due to temperature change. (3 1) Also, by (3 2) Therefore, we get (3 3)

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40 Solving the system of equation for stress tensor we get (3 4 ) constant respectively The relationship between these constants are given as (3 5) Displacement F ormulation of T hermoelasticity D thermoelasticity. The equilibrium equations may be expressed in terms of displacement as (3 6) The equations of thermoelasticity are usually solved for displacement based under the given boundary condition and the corresponding stresses and strains are then obtained from the solution of displacement at each point in the system.

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41 Linear T hermoela sticity R educed to T wo D imensional Some problems in the classical theory of elasticity may be reduced to two dimensional form for ease of solution. These solutions can be classified in two categories: plane stress or plane strain state. The following equa tions represent simple plane stress state (3 7) For simple plane strain rate (3 8) Fully C oupl ed T hermoelastic E quations Most problems in thermoelasticity are based on semi coupled assumption. This means that it is assumed that the stresses developed in the component depend on the changes in the temperature field. However, the converse effect is no t considered significant. That is, the temperature field in a body is independent of the changes in stress tensor. The later situation occurs when the rate of change of thermal boundary

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42 conditions is large enough so as to cause thermal stress wave propagat ion. The general governing equations of coupled thermoelasticity are: (3 9) Types of Thermal Stress Analysis Based on the two theories of thermal stresses discussed in the preceding section there are two types of thermal stress analysis that can be performed. These are: (i) Sequential Thermal Stress Analysis (STSA) and (ii) Fully coupled thermal stress analysis (FCTSA). In STSA heat transfer analysis is first carried out to calculate the temperature fi eld in the component. In the second step the temperature field is used to estimate the residual stress values caused due to changes in the temperature field. The STSA problem only assumes a transient nature in the heat transfer part of the problem. Stresse s are calculated based on the results of the transient heat transfer step. In FCTSA, temperature and displacements are calculated simultaneously based on the constitutive laws of fully coupled thermal stress analysis discussed in the preceding section. Th e choice of analysis procedure is a significant one. Since in STSA the temperature and stresses are uncoupled a designer can directly use the pre calculated temperature field history to estimate the stresses in the body. This is particularly important in t he case of STCR because an accurate solution of the estimation of the temperature field on the reactor tubes may not be possible using ABAQUS CAE. Therefore, choosing STSA allows the freedom to input the temperature calculated from

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43 an external code. The ra tio A/M is a deciding factor in the decision to choose either of the two methods. Here, A and M are constrained moduli corresponding to adiabatic and isothermal conditions respectively. (3 10) and (3 11) Both M and A are material properties and does not depend on the geometry of the body under consideration. It is estimated that in general that STSA is suitable for A/M< 1.5 and FCTSA otherwise. The following table shows the variation of the ratio A/M for alumina and SiC at different temperatures. For alumina: Table 3 1 Determination of A/M ratio for alumina Temp M (dimensionless) A(dimensionless) A/M 293 4.66E+11 4.66E+11 1 573 4.66E+11 4.66E+11 1.01 1273 4.59E+11 4.59E+11 1.01 1473 4.57E+11 4.57E+11 1.01 1673 3.50E+11 3.50E+11 1.01 For SiC Table 3 2 Determination of A/M ratio for SiC Temp M(dimensionless) A(dimensionless) A/M 293 4.42E+11 4.4 2E+11 1.01 573 4.30E+11 4.31E+11 1.01 1273 4.16E+11 4.18E+11 1.01 1473 4.11E+11 4.14E+11 1.01 1673 4.06E+11 4.09E+11 1.01

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44 The value of A/M = 1 corresponds to an uncoupled behavior. Thus from the above table it is evident for silicon carbide and alumi na the thermal stresses are uncoupled in nature and hence STSA is chosen. TSA using FEA Most FEA formulation of thermal stress problems uses the Body Force Analogy (BFA). This method reduces the problems of thermal gradient to that of elasticity problems with body force acting on the given system. Considering the constitutive equation for a static condition in absence of mechanical body forces (3 12) (3 13) Now, this problem can be considered as an isothermal problem in elasticity if the terms ( 3 14) are considered as equivalent components of body force and t he terms (3 15) are considered as equivalent components of surface traction. Therefore, one can use the commonly available FEA method to solve the thermal stress problems. A STSA in ABAQUS is solved by this methodolo gy. STSA in ABAQUS ABAQUS is commercially available FEA software which has the ability to analyze thermal stress problems. It can conduct both STSA and FCTSA analysis. A STSA in ABAQUS is carried out in two steps. First a heat transfer problem is set up an d nodal

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45 temperature is calculated for the body. Next, a stress problem is set up and the time history of temperature at the node is imported from the previous analysis. Mechanical boundary conditions are applied and the problem is solved for residual stres ses. It is advisable to keep the mesh ( the number of elements and the nodes) unchanged for both the analyses. However, the type of elements used in the mesh must be changed. ABAQUS uses different type of elements for stress and heat transfer analysis. In t he event that the number of nodes in the two analyses is unequal ABAQUS interpolates the results for the missing nodes. Validation of results of ABAQUS STSA : To verify the results of STSA method in ABAQUS a comparison was made between the results of ABAQU S and an external FEA code for a simple plane strain problem. The problem consists of a 2D hollow cylindrical body where temperature boundary conditions are varied at the interior surface. The external code solves a transient heat transfer problem and cal culates the resulting stress as a function of radius and time. The temperature of the cylinder is considered to vary only in the radial direction. The longitudinal strain is uniform and constant. That is this is a plane strain condition. Where z =0. The material properties of the cylinder material are assumed to be constant and do not vary with temperature. For simulation in ABAQUS a quarter of the geometry was chosen since the geometry is axisymmetrical. Since the heat flow is only in the radial directi on, the ends of the quarter cylinder were assumed to be insulated. The appropriate boundary condition was applied at the inner radius.

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46 Figure 3 1. Axisymmetric cylinder with radial heat transfer model in ABAQUS The plots for normalized temperature var iation w.r.t to the normalized time for different normalized radii are shown for the external code (EC) and ABAQUS for two different types of boundary conditions. Further more the plots for corresponding normalized stress are shown and the results are compa red for the innermost radius of the cylindrical body. In the plots shown: Table 3 3 List of non dimensional parameters normalized radius normalized temperature normalized time normalized stress

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47 T 0 calculated for stress analysis. In the current simulations T 0 =300K. Figure 3 2. Quarter cylinder heat transfer result for two different mesh sizes Figure 3 3. Comparison of heat transfer analysis between ABAQUS and published results for boundary condition 1

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48 Figure 3 4. Comparison of TSA between ABAQUS and published results for boundary condition 1 Figure 3 5 Comparison of heat transfer analysis between ABAQUS and published results for boundary condition 2

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49 Figure 3 6. Comparison of TSA between ABAQUS and published results for boundary condition 1 There is a good degree of agreement between the two results and thus it is henceforth assumed that the STSA results from ABAQUS are accurate. STSA in ABAQUS for R eactor T ubes The procedure discussed above is now carried out for the reactor tubes of STCR. C urrent ly, STSA is divided into three parts: Stage 1: Heating up to the cycling temperature: This stage is the rise of temperature from RT to the stress free temperatures. Stage 1 can be considered as an event which happens once every day when the STCR is started. Stage 2: This is the cycling process between 1200 C to 1600 C. Stage 2 is the main focus of the study since the reactor will operate on this mode for most of the time. Although the minimum and maximum stress values may not change substantially at each cycle, this stage is the most important when consider ing the thermal fatigue in the reactor tubes. Stage 3: This is the stage where the reactor tubes are cooled from 1200 C to RT. At present, since the nature of surface temperature at the start of cycling process is known, reasonable assumptions can be mad e for stage 2 to carry out TSA. Thus, this study covers thermal stresses and fatigue calculated only for stage 2.

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50 Material Properties Two ceramics are considered al umina and s ilicon c arbide. The material temperature. The variation of these properties as a function of temperature is listed in the table below for sintered alumina and si ntered silica carbide: Table 3 4 Properties of alumina and SiC at different temperatures Property [unit] 20 C 500 C 1000 C 1200 C 1400 C 1500 C Al 2 O 3 Density [g/cm3] 3.984 3.943 3.891 3.868 3.845 3.834 Elastic Modulus [GPa] 416 390 364 354 343 3 38 Poisson's Ratio [] 0.231 0.237 0.244 0.247 0.25 0.252 Specific Heat [J/kgK] 755 1165 1255 1285 1315 1330 Thermal Conductivity [W/mK] 33 11.4 7.22 6.67 6.34 6.23 Thermal Expansion (m/m) 4.6 7.1 8.1 8.3 8.5 8.6 SiC Density [g/cm3] 3.16 3.14 3.11 3 .1 3.09 3.08 Elastic Modulus [GPa] 415 404 392 387 383 380 Poisson's Ratio [] 0.16 0.159 0.157 0.157 0.156 0.156 Specific Heat [J/kgK] 715 1086 1240 1282 1318 1336 Thermal Conductivity [W/mK] 114 55.1 35.7 31.3 27.8 26.3 Thermal expansion (m/m) 1.1 4.4 5 5.2 5.4 5.5 Tube Dimensions One of t he significant parameter for a tube is its outer diameter. To facilitate heat transfer via conduction a thin tube is desirable. Therefore, the significant parameter under consideration in this study is the outer d iameter of the tube. Three tube diameters

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51 are considered as shown in the table below. Based on the results of Vegas Code simulation we are interested in finding out how larger diameter tubes perform with respect to thermal stresses. Table 3 5 Different tube dimensions considered in simulations Sr. No. Parameter Values 1 Thickness ( m m) 6 3 2 Outer radius( m m) 25.4,50.8,76.2 3 Material of construction Alumina, Silicon Carbide Assumptions M ade in STSA Through an in house FORTRAN code simulations the tem perature on the surface of the absorber tubes is known for a steady state at the end of reduction temperature field serves as the initial starting point for stage 2. It is assum ed that during stage 2 there is no further change in the spatial distribution of the temperature. It is only the magnitude of the temperature at each point that rises and falls during the cycling procedure. A polynomial surface is fit through the given dat a of temperature to obtain an shown in Figure 3 7 below. The polynomial has a 95% goodness of fit. Figure 3 7. Polynomial surface fit through the data of nodal values of temperature obtained from the in house code

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52 The polynomial is of the form (3 16) where, the coefficients are Table 3 6 Values of coefficient for the polynomial surface fit p 00 = 1356 p 40 = 4.547 p 10 = 13.84 p 31 = 42.16 p 01 = 159.3 p 22 = 1448 p 20 = 31.05 p 13 = 1 468e+004 p 11 = 981.9 p 04 = 3.517e+005 p 02 = 5275 p 50 = 0.3785 p 30 = 18.7 p 41 = 0.10 35 p 21 = 378.7 p 32 =138.4 p 12 =6077 p 23 =846.3 p 03 =7.591e+004 p 14 = 1.442e+004 p 05 = 5.319e+005 Temperatures are assumed to be cycled between 1200 C to 1600 C. It has been observed during experiments in the solar simulator that a temperature rise of 10 15 C can be achieved during the heating phase while in the cooling phase the temperature drop is faster. Hence, an average temperature change of 15 C /min and 20 C /min are considered du ring the heating and cooling part of the cycling stage respectively. However, it is important to note that much higher temperature changes 30 C /min 40 C /min ) are desirable. The stress free temperature of sintered ceramics is assumed to be the average sin tering temperat ure of that ceramic. This is because in the manufacturing of the ceramic tubes the ceramic material is sintered at high temperature. At this temperature the ceramic powder becomes viscous and by chemical processes bonds together to give a fi nal form. Hence, at this temperature the body is free of

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53 any thermal stresses. For alumina and silicon carbide these temperatures are assumed to be 1700 C and 2000 C respectively. Heat Transfer Analysis As discussed, the first step in STSA is heat transfe r based on the boundary condition of assumed surface temperature. Temperature at the surface of absorber tubes are increased linearly such that the rate of rise of temperature is 15 C /min and 20 C /min for heating and cooling part of the cycle respectively The contour plots for three different sizes of Alumina tubes are shown below. ( A ) ( B ) ( C ) Figure 3 8. Temperature distribution on the surface of absorber tubes as calculated by the polynomial function ( A ) 25.4mm ( B ) 50.8mm ( C ) 76.2mm

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54 T ransient he at transfer analysis gives the following results for the innermo st radius in and silicon carbide tubes for heating and cooling phase for 25mm O.D tubes. Here, normalized temperature is the ratio of actual temperature at the node to the assumed stress free temperature of the material. Figure 3 9. Normalized temperature for absorber tubes outer surface Heating phase Similarly, the temperature profile, for the same tube, du ring the cooling phase is shown Figure 3 10. Normalized temper ature for absorber tubes outer surface Cooling phase

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55 Stress Analysis Based on the temperature history obtained in the heat transfer analysis the next step is to estimate the stresses in the tube. The flexural strength of alumina and silicon carbide as a fu nction of temperature is shown in the table below. Flexural strength is the ability of material to resist deformation under an applied load. For ceramics usually the tensile strength is the low and that is considered as the safest measure of design to prev ent failure. However, the advantage of using flexural strength data is that a typical flexural strength test captures different loads (compression, bending, tension and so on) acting on a test specimen at the same time. This captures the way individual com ponent of stresses interact with each other to produce net stress on a body. A noteworthy point for SiC is that it exhibits an unusual behavior of increasing flexural strength at increasing temperatures. One reason given for this behavior is that the flexu ral tests are conducted in an air environment. In an air environment SiC at high temperature forms an oxide SiO 2 Table 3 7 Temperature dependence of flexural strength of alumina and SiC Propert y [unit] 20 C 500 C 1000 C 1200 C 1400 C 1500 C Flexural Strength [MPa] SiC 359 359 397 437 446 446 Flexural Strength [MPa] Al 2 O 3 380 375 345 300 210 130 The normalized stresses in the three tubes for the two materials are plotted. The normalize d stress is the ratio of maximum actual von misses stress at a node to that of the flexural strength of the material at that temperature. To estimate the flexural strength at different temperatures following interpolations are used for the two materials ar e:

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56 For Al 2 O 3 (3 17) For SiC (3 18) (A ) ( B ) ( C ) Figure 3 11. Stress distribution on the surface of alumina absorber tubes at the end of h eating phase ( A ) 25.4mm ( B ) 50.4mm ( C ) 76.2mm

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57 M aximum stresses in the tubes occur at the end of the cooling period. The contours of the stress distribution, for Al 2 O 3 tubes, at the end of the cooling phase are also shown. The maximum stresses occur on th e inside of the tube. As expected the stresses increase with increasing size of the tube. As seen from the contour plot, for 25.4 mm alumina tubes the stresses are well below the critical stresses and hence it should be expected that the tubes do not crac k during the operation. This trend was also observed during the actual experimentation at the solar simulator. Further, plots for cooling phase of SiC tubes are shown and the performances of the two materials are compared. As can be seen from the plots the stresses in S iC are well below the critical stress for all three sizes of the tubes. This suggests that bigger tubes can be used if the material of construction is SiC. Figure 3 12. Compa rison of s tress developed for 25.4mm tubes Cooling Phase

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58 Figur e 3 13. Comparison of stress developed for 50.8mm tubes Cooling Phase Figure 3 14. Comparison of stress developed for 76.2mm tubes Cooling Phase

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59 Figure 3 1 5 Comparison of stress developed for 3 different sizes of alumina tubes Cooling Phase Figure 3 16. Comparison of stress developed for 3 different sizes of SiC tubes Cooling Phase The plots below show the stresses in heating phase of the cycle. Since the stress free temperatures are assumed to 1700 C and 2000 C, it is expected that the st resses will fall down during the heating phase.

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60 Figure 3 17. Comparison of stress developed for 3 different sizes of alumina tubes Heating Phase Figure 3 18. Comparison of stress developed for 3 different sizes of SiC tubes Heating Phase

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61 TSA on O ther C omponents of the R eactor O ther component analyzed for thermal stress is the back plate of the reactor. Since the geometry of the back and front plate of the reactor is dependent on the tube size it is interesting to note how the stresses vary in the plates for different tube sizes. A TSA procedure similar to the tube was carried out for different back plate geometry. The idea is to check that for a given outer diameter of a back plate what will be the stresses in the geometry considering we fit the m aximum number (as possible geometrically and ease of manufacturing)of tubes in the plate. Assumptions for TSA in B ack P lates Since the back plate always will receive direct radiation a constant flux of 7kW is assumed to hit a circular area with diameter o f 5cm for the entire heating operation. It is assumed that the remaining area receives 1.5kW of uniform constant flux on account of diffuse radiation from other components within the cavity. During the heating phase the heat fluxes on the two different ar eas of the back plate are responsible for the temperature rise. During the cooling phase no heat flux acts on the back plate and it cools down primarily because of re radiation to other cavity parts. The tube holes in the plate are assumed to be insulated. The tube holes are also assumed to be constrained for translational and rotational degree of freedom. Following contour plots show the temperature profile in an Al 2 O 3 back plate at the end of heating and cooling operations.

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62 Figure 3 19. Temperature dis tribution on back plate made of fully dense alumina Heating Phase Figure 3 20. Temperature distribution on back plate made of fully dense alumina Cooling Phase

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63 Corresponding to the above temperature profile the stresses in the back plate are shown in the following contour plots. Figure 3 21. Stress distribution on back plate made of fully dense alumina Heating Phase Figure 3 2 2 Stress distribution on back plate made of fully dense alumina Cooling Phase

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64 As seen from the above contour plots the critical stress limit of 130 MPA is exceeded during the heating phase itself indicating that the material could fail during heating. As expected the stresses are greater during the cooling phase. Experiments with similar geometry of a lumina plates have sho wn that the cracks do occur at the places marked with highest stresses in the contour plots. This will be discussed in a later chapter again. Now, if we consider a similar plate which will house 76.2mm tubes following are the results that we get for Al 2 O 3 plates. Figure 3 2 3 Temperature distribution on back plate with 76.2 mm diameter tube holes made of fully dense alumina Heating Phase

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65 Figure 3 2 4 Temperature distribution on back plate with 76.2 mm diameter tube holes made of fully dense alumina Cooling Phase The related stresses developed in an Al 2 O 3 plate are: Figure 3 2 5 Stress distribution on back plate with 76.2 mm diameter tube holes made of fully dense alumina Heating Phase

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66 Figure 3 2 6 Stress distribution on back plate with 76.2 mm diameter tube holes made of fully dense alumina Cooling Phase In the above contours one can see that the critical stress for alumina is still well exceeded during the cooling stage and is almost equal to the failure value at 1500 C. Thus, as the tube size increases the stresses in the back plate will decrease.

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67 CHAPTER 4 THERMAL TESTS WITH SOLAR SIMULATOR Experimental Setup The solar simulator at University of Florida consists of seven identical 3D ellips oidal lamps that are ali gned to have a common focal point. Each lamp has the ability to focus 7kW of thermal energy at a predetermined focal plane. The focal point lies in the Z plane of an XY table. The reactor or a flux target can be mounted on this table and the table can be c ontrolled externally through a L abview program. On the XY table a flux target is mounted which can be used to create flux maps before or after the experiments. To capture the flux incident on the flux target there is an industrial grade CCD camera. The out put of the camera, with post processing, can be viewed with the help of a MATLAB program. (A) ( B ) Fig ure 4 1 Ellipsoidal lamps at the solar simulator facility at UF A ) Front view B ) B ack view

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68 Fig ure 4 2 CCD camera at the solar simulator facility at UF Solar Thermochemical Reactor Construction The reactor is constructed in 4 different parts: the front plate, back plate and two halves of a cylindrical body. As seen from Figure 4 4 below the two end plates have 29 tube holes for the tubes. Currently STCR is built for 29 25 .4 mm O.D tubes. The material for the STCR is Buster M 35 from Zircar Zirconia composed of 80% alumina and 20% silica tes The front plate has a 5 cm aperture which is aligned with the focal plane. Fig ure 4 3 Different components of a STCR

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69 STCR on the XY Table To mount STCR on the XY table a separate frame was built off the XY table. This allowed the flexibility to move the focal plane of the reactor with the XY table. Whole of STCR was wrapped in 3 layers of 3cm thick glass wool insulation. The aperture of STCR was held fixed in the focal plane of the mirrors. This was done by gently pressing the STCR together with the help of metal strips pressed against the insulation cove r. The STCR was mounted next to the flux target in such a way that during flux mapping operation STCR can be completely removed from the path of the light coming from the mirrors. A base of fire bricks was mounted on the metal base of the frame to prevent any damage to the frame due to excessive heat transfer. Fig ure 4 4 STCR kept on fire bricks

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70 Fig ure 4 5 Assembly of STCR insulated with glass wool Fig ure 4 6 Complete assembly of the STCR framework mounted on XY table

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71 Finally, a shutter mechani sm was created to prevent rapid cooling of the reactor during the shutdown stage. The shutter mechanism consists of a moving cam base (mounted on the reactor frame), a vertical structure and a fire brick covered with insulation ( Figure 4 7 ). The idea behin d the shutter is to cover the aperture of the reactor during the shutdown stage. Since, the reactor loses heat primarily by reradiating a shutter at the cavity can arrest the drastic drop of temperature within the cavity. Experiments Experiment 1 The first experiment was carried out without any tubes. In this experiment all the tube holes were closed with ceramic plugs ( Figure 4 8 ). The basic idea behind this test was to test the ability of the structure to withstand thermal shock It was pre decided that t he rate of change of temperature will be controlled to 10 C/min as closely as possible at least until working temperatures of 800 C were attained. Thermocouples were placed at different locations to log the temperature change. Of particular importance is the temperature history of the thermocouple which was placed at the center of the back plate. Since, TSA showed that the back plate will crack at the wedges between the holes, data from this particular thermocouple can be used to recalibrate the simulation model. Results After the test when the reactor was dissembled the back plate was found to have cracked on every wedge between any two tube holes. Also there was a major crack on the top of the back plate ( Figure 4 9 ). The result of TSA also predicted str esses greater than the critical stresses at these on the wedges. However, it did not predict a major crack on the periphery of the back plate Also, as stated before in Chapter 4 the stress

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72 values predicted by TSA are probably over predicted. Hence, altho ugh TSA predicts a fracture of tubes at these locations in the actual experiments one can only observe cracks at the surface of the back plate and not a complete fracture of the component. Fig ure 4 7 STCR with the shutter on the left Fig ure 4 8 STCR with ceramic plugs on the back plate

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73 Fig ure 4 9 Crack at the periphery of the back plate of STCR Experiment 2 The second experiment was carried out with one tube in the reactor. The basic idea behind this test was to determine the thermal robust ness of the tube during a complete cycle of temperature. The tube is made of fully dense alumina. It was placed in one of the bottom holes of the reactor. The average rate of heating and cooling was maintained at 10 C/ min at least till cycling temperature was attained It is to be noted that much higher cycling temperatures (3 0 C 4 0 C / min ) are desired in future. Since this was the first experiment with a tube in cavity a rate of 10 C/ min was chosen because it has been observed in other experiments(not r elated to solar simulator) that the alumina tubes, with similar properties, do not crack at this cycling rate.

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74 Fig ure 4 10 Results During the experiment an average temperature change of 8.5 C /min was achieved in the heating phase. The graph ( Figure 4 10 ) above shows the reading of the thermocouple which was placed inside the tube. As can be seen the temperatures do not increase linearly. This has to be taken into account in TSA simulations. A t the end of the experiment there appeared be no visible cracks on the surface of the tubes although a much detailed inspection of the tube surface is pending. The TSA also predicted stress values lower than the critical values for 25 .4 mm alumina tubes. Th erefore, faster temperature gradients can be tried during the cycling period while running the experiments. Similarly, appropriate changes can be made in the TSA to recalculate the stresses in the simulations.

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75 Effectiveness of the Shutter to Prevent TS Whi le running the experiments in a solar simulator relatively good control was achieved over the temperature change during the heating phase by adjusting the lamps current and selecting the time when different lamps would turn on. As mentioned above, during t he shutdown phase the shutter covers the aperture of the cavity and prevents drastic fall in temperature. The shutter was deployed after the last lamp was switched off. At this point the temperature of the tube was 720 C and the experiment had been running for approximately 320 minutes. What was observed was that the average temperature drop rate after the deployment of shutter, was as low as of 5 C /min as compared to an average rate of 11 C /min before the shutter was deployed. As was seen in TSA for 25m m O.D diameter alumina tubes a cooling rate of 20 C /min was acceptable because it did not cause critical stress values in the tube. The critical rate of cooling can hence be assumed to be at least greater than 20 C /min Therefore, by using a shutter the te mperature drop was kept well below the critical rate for cooling.

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76 CHAPTER 5 CONCLUSIONS Summary An analysis to predict thermal stresses on two components of a STCR assembly has been presented. The analysis starts with preliminary investigation of flux ma pping on different STCR design s using the Vegas Code. For the solar simulator facility available at UF the flux mapping results indicate the occurrence of hot spots for all designs and a heat loss through the cavity body. As a result, a design which consis ts of horizontal tubes arranged circumferentially on the inside surface of cavity body is chosen. By the results of an in house code the temperature distribution on an absorber tube for this particular design is obtained. Using this data a TSA is carried o ut, for the cycling period of a STCR, based on some crucial assumptions. The most important of these are The spatial distribution of temperatures is assumed to be fixed and only the amplitude of the temperatures changes. The material properties considered are those provided in published results of standard test specimen. The current simulations are run for three different tube sizes for O.D. For each size two material of construction are considered: alumina and SiC. It is seen that alumina tubes of sizes 50.8mm and 76.2mm O.D the stresses developed are greater than the critical stresses at that temperature. For SiC stresses developed for 76.2 mm O.D exceed the critical stress values. It is also seen that SiC has the property of increasing flexural strength with increase in temperature which makes it an excellent candidate for high temperature application. Similar simulations were run for the back plate of the STCR. Simulations predicted the stress levels in the back plate to be higher

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77 than the critical st ress level. However, the material property used in simulation was for a dense alumina while in real experiments a fully dense alumina was not used. Thermal tests were also carried out at the solar simulator at UF. During one of the tests it was observed th at the back plate cracked at the place where simulations predicted thermal stress higher than the critical stresses. There was also a major crack on the periphery of the back plate which the simulations did not predict. In another test temperature profile on the inside surface of the tube was recorded. It was seen that the temperature does not vary linearly as was assumed in the simulation. Current simulations results and experiments seem to suggest that SiC should be the preferred choice of tube materials because of increasing flexural strength. However, it remains to be seen how the simulations results will change when effects of creep, viscoelasticity and pre existing flaws are taken under consideration. Future Work Looking forward, maximum cooling and he ating rates of cavity and absorber tubes will be predicted considering the same assumptions that have been made in this analysis. These results can then be validated by experimentation in the solar simulator. Also, the present analysis covers only the str esses developed during the cycling phase of reactor operation. Similar analysis can be done for the startup heating phase and the shut down cooling phase, as and when temperature distribution profile (for absorber tubes)during these phase are available fro m the in house code. Most of the literature available on the TSA of ceramics suggests that standard material properties of ceramics, like those used in handbooks, should be avoided while predicting thermal stresses in a specimen of different geometric sha pe. This is so because specimens differ in their response to thermal stresses based on differences in

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78 their microstructure, impurities and pre existing flaws. Thus to get more accurate results, flexural strength tests must be carried out to achieve precise strength. Lastly, the effect of creep on stress relaxation and pre existing flaws on stress concentration has to be considered to achieve simulation results which are close to real life scenario.

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79 LIST OF REFERENCES [1] 2009 ; The other kind of solar po wer from http://www.economist.com/node/13725855 [2] Rodriguez L Ana I Marrero P, Gomez C Comparison of solar thermal technologies for applications in seaw ater desalination Desalination 2002; 142 : 135 142. [3] Laing D Steinmann WD, Viebahn P Grater F Bahl C. Economic a nalysis and l ife c ycle a ssessment of c oncrete t hermal e nergy s torage for p arabolic t rough p ower p lants J ournal of Sol ar Energy Eng ineering 2010; 132: 10131 10136 [4] Meier A Steinfeld A. Solar The rmochemical Production of Fuels Adv ances in Science and Technology 2010; 74 : 303 312 [5] 2008, Industry Report from www.solar thermal.com [6] Kutscher C Mehos M Turchi C, Glatzmaier G Line Focus Solar Power Plant Cost Reduction Plan Milestone Report, Colorado National Renewable Energy Laboratory 2010 [7] Steinfeld A Palumbo R. Solar Th ermochemical Process Technology Encyclopedia of Physical Science & Technology, R. A. Meyers Ed., Academic Press 2001; 15 : 237 256 [8] Noring J Fletcher E A. High Temperature Solar Thermochemical Processing Hydrogen and Sulfur from Hydrogen Sulfide Energy 1982; 7: 651 666. [9] JANAF Thermochemical Tables National Bureau of Standards, 3rd ed., Washi ngton D.C. 1985 [10] Charvin P, Abanades S Beche E. Hydrogen production from mixed cerium oxides via three step water splitting cycles. Solid State Ionics 2009; 180 : 1003 1010 [11] Chueh W Haile SM Ceria as a thermochemical reaction medium for selectiv ely generating syngas or methane from H 2 O and CO 2 ChemSusChem 2009; 2: 735 741 [12] Mehdizade M Klausner JF Barde A Nima R Mei R. Investigation of hydrogen production reaction kinetics for an ir on silica magnetically stabilized porous structure Journal of Hydrogen Energy 2012; 37 : 13263 13271 [13] Serpone N Lawless D Terzian R. Solar Fuels:Status and Perspectives Solar Energy 1992 ; 49 : 221 234.

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80 [14] Ld J. Solar thermochemical conversion o f biomass Sola r Energy 1999 ; 65 : 3 13 [15] Perkins ,CM Synthesis gas production by rapid solar thermal gasi fication of corn stover SPCE 2008; from NREL CD 550 42709 [1 6 ] M elchior T Perkins C Li chty P Weimer A W, Steinfeld A. Solar driven biochar gasification in a particle flow reactor Chemical Engineering and Processing 2009 48 1279 1287. [1 7 ] Stamatiou A Loutzenhiser PG Steinfeld A. Solar Syngas Production viaH 2 O/CO 2 Splitting Thermochemical Cycles with Zn/ZnO and FeO/Fe3O4 Redox Reactions. Chem. Mater. 2010; 22 : 851 859 [1 8 ] Steinberg M Fossil fuel decarbonization technology for mitigating global warming Int ernational J ournal of Hydrogen Energy 1999; 24 : 771 777. [1 9 ] Maag G, Zanganeh G Steinfeld A. Solar thermal cracking of methane in a particle flow reactor for the co production of hydrogen and carbon International Journal of Hydrogen Energy 2009; 34 : 7676 7685 [20] Meier A Kirillov V A., Yu I Reller A Steinfeld A. Solar Thermal Decomposition of Hydrocarbons and Carbon Monoxide fo r the Production of Catalytic Filamentous Carbon, Chemical Engineering Science 1999; 54 : 3341 3348. [21] Palumbo R K eunecke M Steinfeld A Reflections on the design of solar thermochemcial reactors: thoughts in transformation Energy 2004; 29 : 727 744 [ 22] H irsch D, Steinfeld A Solar hydrogen production by thermal decomposition of natural gas using a vortex flow reactor International Journal of Hydrogen Energy 2004 ; 29 : 47 55 [23] Ermanoski I McDaniel A. 2012 Solar Hydrogen Production with a Meta l Oxide Based Thermochemical Cycle, DOE Annual Merit Review, Project ID PD081 [24] Rodat S Abanades S Flamant G. Experimental Evaluation of Indirect Heating Tubular Reactors for Solar Methane Pyrolysis International Journal of Chemical reactor Engineer ing 2010; 8 : A25. [25] Piatkowski N Steinfeld A. Solar Gasification of Carbonaceous Waste Feedstocks in a Packed Bed Reactor Dynamic Model ing and Experimental Validation AIChE 2011; 57 : 3522 3533. [26] Melchior T Perkins C, Weimer A.W Steinfeld A. A cavity receiver containing absorber for high temperature thermochemical processing using concentrated solar energy I nternational J ournal of T hermal S cience 2007; 47 : 1496 1503

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81 [27] Melchior T Steinfeld A. Radiative Transfer within a Cylindrical Cavity wi th Diffusely/Specularly Reflecting Inner Walls Containing an Array o f Tubular Absorbers I nternational J ournal of S olar E nergy 2008; 130 : 021013 1 021013 8 [28] Modest, 2005 Thermal Radiation Heat Transfer, 3 rd Ed., CRC press. [29] Petrach, 2011 The Veg as Manual [30] Richard K. Thermal Stresses Advanced Theory and Applications, 1 st Ed, Springer press 2008 [31] Carter J Booker J R. Finite Element Analysis of Fully Coupled Thermoe lasticity, Computer Structures 1989; 31 : 73 80 [32] Kandil A Kady A. Tran sient Thermal Stress Analysis of Thick Walled Cylinder, Int ernational J ournal of M aterial Sci ence 1995; 37 : 721 732 [33] Akiyami S Amada S Estimation of Fracture Conditions of Ceramics by Thermal Shock with Laser Beams based on the Maximum Compressive S tress Criterion, Int ernational Journal of JSME 1992; 34 : 91 94 [34] Lichty P Steinfeld A. Solar Thermal Reactor Materia l Characterization Solar Power and Chemical Energy Systems Symposium 1992 ; www.solarpaces.org [35] Hasselman L Thermal Stress Resistance of Engineering Ceramics, Material Science and Engineering 1984; 71 : 251 264 [3 6 ] Erikson B., Characterization of the University of Florida solar simulator and an inverse solution for identifying intensity dis tributions from multiple flux maps in c oncentrating solar applications M.S Thesis, Department of Mechanical and Aerospace Engineering, University of Florida ; 2012

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82 BIOGRAPHICAL SKETCH Nikhil Sehgal was born in New Delhi, India in 1986. He received his B achelor of Science in m echanical e ngineering from University of Mumbai in 2009. He spent the next two years working as an engineer at Panasia Engineers Pvt. Ltd. and Sterling and Wilson Ltd respectively During his time at Panasia Engineers Pvt. Ltd. he wo rked on design and development of novel refrigeration systems. He published an article in the ISHRAE Journal (Oct 2010) based on his work at Panasia Engineers Pvt. Ltd. Nikhil joined University of Florida in the fall of 2011. He started working on this pro ject in January 2012. His present work involves testing the solar reactor at the solar simulator facility at UF. He received his MS from the University of Florida in the spring of 2013.