Thermal Hydraulic Analysis of the Oregon State TRIGA Reactor Using RELAP5-3D

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ISBN 13 :
Total Pages : 302 pages
Book Rating : 4.:/5 (221 download)

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Book Synopsis Thermal Hydraulic Analysis of the Oregon State TRIGA Reactor Using RELAP5-3D by : Wade R. Marcum

Download or read book Thermal Hydraulic Analysis of the Oregon State TRIGA Reactor Using RELAP5-3D written by Wade R. Marcum and published by . This book was released on 2008 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: Oregon State University has recently conducted a complete core conversion analysis as part of the Reduced Enrichment for Research and Test Reactors Pprogram. The goals of the thermal hydraulic analyses were to calculate natural circulation flow rates, coolant temperatures and fuel temperatures as a function of core power for both the Highly Enriched Uranium (HEU) and Low Enriched Uranium (LEU) cores; for steady state and pulsed operation, calculate peak values of fuel temperature, cladding temperature, surface heat flux as well as critical heat flux ratio (CHFR) and temperature profiles in hot channel for both the HEU and LEU cores; finally, perform accident analyses for the accident scenarios identified in the Oregon State TRIGA® Reactor (OSTR) Safety Analysis Report (SAR). RELAP5-3D Version 2.4.2 was used for all computational modeling during the thermal hydraulics analysis. This is a lumped parameter code forcing engineering assumptions to be made during the analysis. A single hot channel model's results are compared to that produced from more refined two and eight channel models in order to identify variations in thermal hydraulic characteristics as a function of spatial refinement.

A Thermal Hydraulics Analysis of a Molybdenum Production Element for Implementation in TRIGA Reactors

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ISBN 13 :
Total Pages : 99 pages
Book Rating : 4.:/5 (851 download)

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Book Synopsis A Thermal Hydraulics Analysis of a Molybdenum Production Element for Implementation in TRIGA Reactors by : Patrick Byfield

Download or read book A Thermal Hydraulics Analysis of a Molybdenum Production Element for Implementation in TRIGA Reactors written by Patrick Byfield and published by . This book was released on 2013 with total page 99 pages. Available in PDF, EPUB and Kindle. Book excerpt: The metastable isotope of technetium-99 (Tc-99m) is an important diagnostic tool used in the field of nuclear medicine due to the isotope's 6.0 hour half-life, 140.5 keV [gamma]-decay mechanism, and multiple oxidation states [1,2]. Approximately 70% of the world's nuclear medicine procedures involve the use of Tc-99m [3]. The conventional source of Tc-99m comes from the [beta]-decay of molybdenum-99 (Mo-99), an isotope which may be produced via the fission of uranium-235 (U-235) atoms [2]. As Mo-99 has a half-life of 2.7 hours [2]; it is difficult to produce anything but short-term stockpiles of Tc-99m. A handful of geographically dispersed facilities maintain a continuous production of Mo-99 via U-235 fission as a means to satisfy the demand of nuclear medicine worldwide [4]. However, 96% of all Mo-99 production is concentrated among only 4 facilities [4]. This centralized production dynamic has been shown to leave the world susceptible to Tc-99m shortages in the event of multiple reactor shutdowns [5]. Oregon State University (OSU) has undertaken a study to investigate the safety of implementing a fueled experiment, known as the "molybdenum element," within the OSU TRIGA® reactor (OSTR) for the purpose of producing Mo-99. This study investigates both steady-state and select transient conditions within the OSTR core with the use of the lumped parameter code RELAP5-3D version 2.4.2. Key thermal hydraulic parameters which may impact the safety of the OSTR are identified and presented, and discussed herein.

Nuclear Reactors

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Publisher : BoD – Books on Demand
ISBN 13 : 9535100181
Total Pages : 354 pages
Book Rating : 4.5/5 (351 download)

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Book Synopsis Nuclear Reactors by : Amir Mesquita

Download or read book Nuclear Reactors written by Amir Mesquita and published by BoD – Books on Demand. This book was released on 2012-02-10 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a comprehensive review of studies in nuclear reactors technology from authors across the globe. Topics discussed in this compilation include: thermal hydraulic investigation of TRIGA type research reactor, materials testing reactor and high temperature gas-cooled reactor; the use of radiogenic lead recovered from ores as a coolant for fast reactors; decay heat in reactors and spent-fuel pools; present status of two-phase flow studies in reactor components; thermal aspects of conventional and alternative fuels in supercritical water?cooled reactor; two-phase flow coolant behavior in boiling water reactors under earthquake condition; simulation of nuclear reactors core; fuel life control in light-water reactors; methods for monitoring and controlling power in nuclear reactors; structural materials modeling for the next generation of nuclear reactors; application of the results of finite group theory in reactor physics; and the usability of vermiculite as a shield for nuclear reactor.

Thermal Hydraulic Analysis of a Pressurized Water Reactor

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ISBN 13 :
Total Pages : 150 pages
Book Rating : 4.:/5 (929 download)

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Book Synopsis Thermal Hydraulic Analysis of a Pressurized Water Reactor by : Joan Marie Oylear

Download or read book Thermal Hydraulic Analysis of a Pressurized Water Reactor written by Joan Marie Oylear and published by . This book was released on 1979 with total page 150 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Thermal Hydraulic and Safety Analysis of the University of Wisconsin Nuclear Reactor

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ISBN 13 :
Total Pages : 392 pages
Book Rating : 4.:/5 (89 download)

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Book Synopsis Thermal Hydraulic and Safety Analysis of the University of Wisconsin Nuclear Reactor by : Brian J. Vitiello

Download or read book Thermal Hydraulic and Safety Analysis of the University of Wisconsin Nuclear Reactor written by Brian J. Vitiello and published by . This book was released on 2008 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Thermal Hydraulic Analysis of a Reduced Scale High Temperature Gas-Cooled Reactor Test Facility and Its Prototype with MELCOR

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ISBN 13 :
Total Pages : 228 pages
Book Rating : 4.:/5 (865 download)

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Book Synopsis Thermal Hydraulic Analysis of a Reduced Scale High Temperature Gas-Cooled Reactor Test Facility and Its Prototype with MELCOR by : Bradley Aaron Beeny

Download or read book Thermal Hydraulic Analysis of a Reduced Scale High Temperature Gas-Cooled Reactor Test Facility and Its Prototype with MELCOR written by Bradley Aaron Beeny and published by . This book was released on 2013 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: Pursuant to the energy policy act of 2005, the High Temperature Gas-Cooled Reactor (HTGR) has been selected as the Very High Temperature Reactor (VHTR) that will become the Next Generation Nuclear Plant (NGNP). Although plans to build a demonstration plant at Idaho National Laboratories (INL) are currently on hold, a cooperative agreement on HTGR research between the U.S. Nuclear Regulatory Commission (NRC) and several academic investigators remains in place. One component of this agreement relates to validation of systems-level computer code modeling capabilities in anticipation of the eventual need to perform HTGR licensing analyses. Because the NRC has used MELCOR for LWR licensing in the past and because MELCOR was recently updated to include gas-cooled reactor physics models, MELCOR is among the system codes of interest in the cooperative agreement. The impetus for this thesis was a code-to-experiment validation study wherein MELCOR computer code predictions were to be benchmarked against experimental data from a reduced-scale HTGR testing apparatus called the High Temperature Test Facility (HTTF). For various reasons, HTTF data is not yet available from facility designers at Oregon State University, and hence the scope of this thesis was narrowed to include only computational studies of the HTTF and its prototype, General Atomics' Modular High Temperature Gas-Cooled Reactor (MHTGR). Using the most complete literature references available for MHTGR design and using preliminary design information on the HTTF, MELCOR input decks for both systems were developed. Normal and off-normal system operating conditions were modeled via implementation of appropriate boundary and inititial conditions. MELCOR Predictions of system response for steady-state, pressurized conduction cool-down (PCC), and depressurized conduction cool-down (DCC) conditions were checked against nominal design parameters, physical intuition, and some computational results available from previous RELAP5-3D analyses at INL. All MELCOR input decks were successfully built and all scenarios were successfully modeled under certain assumptions. Given that the HTTF input deck is preliminary and was based on dated references, the results were altogether imperfect but encouraging since no indications of as yet unknown deficiencies in MELCOR modeling capability were observed. Researchers at TAMU are in a good position to revise the MELCOR models upon receipt of new information and to move forward with MELCOR-to-HTTF benchmarking when and if test data becomes available. The electronic version of this dissertation is accessible from http://hdl.handle.net/1969.1/148182

Thermal-Hydraulic Analysis of Nuclear Reactors

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Publisher : Springer
ISBN 13 : 3319174347
Total Pages : 667 pages
Book Rating : 4.3/5 (191 download)

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Book Synopsis Thermal-Hydraulic Analysis of Nuclear Reactors by : Bahman Zohuri

Download or read book Thermal-Hydraulic Analysis of Nuclear Reactors written by Bahman Zohuri and published by Springer. This book was released on 2015-09-09 with total page 667 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text covers the fundamentals of thermodynamics required to understand electrical power generation systems and the application of these principles to nuclear reactor power plant systems. It is not a traditional general thermodynamics text, per se, but a practical thermodynamics volume intended to explain the fundamentals and apply them to the challenges facing actual nuclear power plants systems, where thermal hydraulics comes to play. Written in a lucid, straight-forward style while retaining scientific rigor, the content is accessible to upper division undergraduate students and aimed at practicing engineers in nuclear power facilities and engineering scientists and technicians in industry, academic research groups, and national laboratories. The book is also a valuable resource for students and faculty in various engineering programs concerned with nuclear reactors. This book also: Provides extensive coverage of thermal hydraulics with thermodynamics in nuclear reactors, beginning with fundamental definitions of units and dimensions, thermodynamic variables, and the Laws of Thermodynamics progressing to sections on specific applications of the Brayton and Rankine cycles for power generation and projected reactor systems design issues Reinforces fundamentals of fluid dynamics and heat transfer; thermal and hydraulic analysis of nuclear reactors, two-phase flow and boiling, compressible flow, stress analysis, and energy conversion methods Includes detailed appendices that cover metric and English system units and conversions, detailed steam and gas tables, heat transfer properties, and nuclear reactor system descriptions

Thermal-hydraulic Analysis for the Proposed Upgrade of the University of Illinois Advanced TRIGA Reactor to 3 MW

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ISBN 13 :
Total Pages : 222 pages
Book Rating : 4.:/5 (368 download)

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Book Synopsis Thermal-hydraulic Analysis for the Proposed Upgrade of the University of Illinois Advanced TRIGA Reactor to 3 MW by : Lucia Golchert

Download or read book Thermal-hydraulic Analysis for the Proposed Upgrade of the University of Illinois Advanced TRIGA Reactor to 3 MW written by Lucia Golchert and published by . This book was released on 1995 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Large Lead-cooled Reactor with Flexible Conversion Ratio

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ISBN 13 :
Total Pages : 200 pages
Book Rating : 4.:/5 (547 download)

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Book Synopsis Large Lead-cooled Reactor with Flexible Conversion Ratio by : Anna S. Nikiforova (S.M.)

Download or read book Large Lead-cooled Reactor with Flexible Conversion Ratio written by Anna S. Nikiforova (S.M.) and published by . This book was released on 2008 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: (Cont.) The transient simulation of station blackout (SBO) using the RELAP5-3D/ATHENA code shows that inherent shutdown without scram can be accommodated within the cladding temperature limit by the enhanced RVACS and PSACS by removing a fraction of decay power with the PSACS. The PSACS was designed such that the balance between two limiting cases was achieved: (1) peak cladding temperature limit is satisfied during unprotected station blackout with a minimum (two) number of PSACS trains operated, and (2) the minimum coolant temperature is kept above the freezing point with a maximum (four) number of PSACS trains operated. The PSACS design satisfies the conditions of both unity and zero conversion ratio cores. The other SBO accident conditions are bounded by the above cases. In addition, two other transients are considered: loss-of-flow accident (LOFA) and inadvertent reactivity insertion transient (UTOP). Both reactors show good performance during these additional transients.

An Assessment of Thermal Hydraulic Analysis Methods for Pressurized Thermal Shock Evaluations

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ISBN 13 :
Total Pages : 218 pages
Book Rating : 4.:/5 (549 download)

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Book Synopsis An Assessment of Thermal Hydraulic Analysis Methods for Pressurized Thermal Shock Evaluations by : Eric P. Young

Download or read book An Assessment of Thermal Hydraulic Analysis Methods for Pressurized Thermal Shock Evaluations written by Eric P. Young and published by . This book was released on 2002 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: Improved methods of determining temperature transients in reactor systems are desired because of recent interest in Pressurized Thermal Shock (PTS) issues. The research presented herein was performed in support of the Nuclear Regulatory Commission's effort to re-evaluate its existing PTS rules. These rules are particularly important to the re-licensing of aging nuclear power plants. The much advanced computational power available to industry may offer a tool that allows the accurate calculation of temperatures inside the reactor vessel while not being inaccessibly expensive. It is proposed that an off-the-shelf Computational Fluid Dynamic (CFD) code, STAR-CD, can be a competitive tool in solving the thermal hydraulic domain of a reactor system. A comparison of the methodology and accuracy of the code types that have been previously used in PTS and one that has not been used extensively, CFD, is provided. A review of the literature shows that computer codes have been validated for solving PTS scenarios. The highly specialized program, REMIX, has been utilized extensively from 1986 to 1991 to interpret accident scenarios in reactor systems. Other programs are also available that can calculate downcomer temperatures including system and CFD type codes. Three codes representing the three different types of programs available are described in detail in the literature review section. Data appropriate for assessing a program's ability to calculate the response of a system to a PTS scenario is available from the current matrix of PTS tests being completed at the APEX-CE facility of the Oregon State University Nuclear Engineering department. The facility is a reduced scale integral test facility originally built for modeling the then-proposed AP-600 plant designed by Westinghouse. For the current test series, the facility was modified to model the Palisades nuclear power plant, a Combustion Engineering Pressurized Water Reactor (PWR). Two of the tests were chosen for their PTS typical conditions to compare with calculations of STAR-CD, REMIX, and RELAP. The computer models in each of the programs were either created, modified from a previous version, or the calculations for the comparisons were contributed. The downcomer temperatures at several locations and cold leg temperature gradients, where available, were extracted from the data and calculations and compared. Comparisons are presented in chapter 5 with graphs, along with some interpretation of the comparisons. It was found that STAR-CD agreed best with the data set in the downcomer and is the only program that calculated the temperature gradient in the cold legs. The agreement of STAR-CD with the cold leg data is also very good. REMIX and RELAP calculations agreement with data for downcomer temperatures are found to be good for all comparisons made, qualitatively more than quantitatively when contrasted with the STAR-CD calculations.

RELAP5 Thermal-hydraulic Analysis of the SNUPPS Pressurized Water Reactor

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ISBN 13 :
Total Pages : 77 pages
Book Rating : 4.:/5 (222 download)

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Book Synopsis RELAP5 Thermal-hydraulic Analysis of the SNUPPS Pressurized Water Reactor by : Craig M. Kullberg

Download or read book RELAP5 Thermal-hydraulic Analysis of the SNUPPS Pressurized Water Reactor written by Craig M. Kullberg and published by . This book was released on 1990 with total page 77 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Thermal Hydraulic and Fuel Performance Analysis for Innovative Small Light Water Reactor Using VIPRE-01 and FRAPCON-3

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ISBN 13 :
Total Pages : 151 pages
Book Rating : 4.:/5 (773 download)

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Book Synopsis Thermal Hydraulic and Fuel Performance Analysis for Innovative Small Light Water Reactor Using VIPRE-01 and FRAPCON-3 by : Anh T. Mai

Download or read book Thermal Hydraulic and Fuel Performance Analysis for Innovative Small Light Water Reactor Using VIPRE-01 and FRAPCON-3 written by Anh T. Mai and published by . This book was released on 2012 with total page 151 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Multi-Application Small Light Water Reactor (MASLWR) is a small natural circulation pressurized light water reactor design that was developed by Oregon State University (OSU) and Idaho National Engineering and Environmental Laboratory (INEEL) under the Nuclear Energy Research Initiative (NERI) program to address the growing demand for energy and electricity. The MASLWR design is geared toward providing electricity to small communities in remote locations in developing countries where constructions of large nuclear power plants are not economical. The MASLWR reactor is designed to operate for five years without refueling and with fuel enrichment up to 8 %. In 2003, an experimental thermal hydraulic research facility also known as the OSU MASLWR Test Facility was constructed at Oregon State University to examined the performance of new reactor design and natural circulation reactor design concepts. This thesis is focused on the thermal hydraulics analysis and fuel performance analysis of the MASLWR prototypical cores with fuel enrichment of 4.25 % and 8 %. The goals of the thermal hydraulic analyses were to calculate the departure nucleate boiling ratio (DNBR) values, coolant temperature, cladding temperature and fuel temperature profiles in the hot channel of the reactor cores. The thermal hydraulic analysis was performed for steady state operation of the MASLWR prototypical cores. VIPRE Version 01 is the code used for all the computational modeling of the prototypical cores during thermal hydraulic analysis. The hot channel and hot rod results are compared with thermal design limits to determine the feasibility of the prototypical cores. The second level of analysis was performed with a fuel performance code FRAPCON for the limiting MASLWR fuel rods identified by the neutronic and thermal hydraulic analyses. The goals of the fuel performance analyses were to calculate the oxide thickness on the cladding and fission gas release (FGR). The oxide thickness results are compared with the acceptable design limits for standard fuel rods. The results in this research can be helpful for future core designs of small light water reactors with natural circulation.

RELAP5 Thermal-hydraulic Analysis of the WNP1 Pressurized Water Reactor

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ISBN 13 :
Total Pages : 63 pages
Book Rating : 4.:/5 (334 download)

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Book Synopsis RELAP5 Thermal-hydraulic Analysis of the WNP1 Pressurized Water Reactor by : R. P. Martin

Download or read book RELAP5 Thermal-hydraulic Analysis of the WNP1 Pressurized Water Reactor written by R. P. Martin and published by . This book was released on 1991 with total page 63 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Thermal-Hydraulics of Water Cooled Nuclear Reactors

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Publisher : Woodhead Publishing
ISBN 13 : 0081006799
Total Pages : 1200 pages
Book Rating : 4.0/5 (81 download)

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Book Synopsis Thermal-Hydraulics of Water Cooled Nuclear Reactors by : Francesco D'Auria

Download or read book Thermal-Hydraulics of Water Cooled Nuclear Reactors written by Francesco D'Auria and published by Woodhead Publishing. This book was released on 2017-05-18 with total page 1200 pages. Available in PDF, EPUB and Kindle. Book excerpt: Thermal Hydraulics of Water-Cooled Nuclear Reactors reviews flow and heat transfer phenomena in nuclear systems and examines the critical contribution of this analysis to nuclear technology development. With a strong focus on system thermal hydraulics (SYS TH), the book provides a detailed, yet approachable, presentation of current approaches to reactor thermal hydraulic analysis, also considering the importance of this discipline for the design and operation of safe and efficient water-cooled and moderated reactors. Part One presents the background to nuclear thermal hydraulics, starting with a historical perspective, defining key terms, and considering thermal hydraulics requirements in nuclear technology. Part Two addresses the principles of thermodynamics and relevant target phenomena in nuclear systems. Next, the book focuses on nuclear thermal hydraulics modeling, covering the key areas of heat transfer and pressure drops, then moving on to an introduction to SYS TH and computational fluid dynamics codes. The final part of the book reviews the application of thermal hydraulics in nuclear technology, with chapters on V&V and uncertainty in SYS TH codes, the BEPU approach, and applications to new reactor design, plant lifetime extension, and accident analysis. This book is a valuable resource for academics, graduate students, and professionals studying the thermal hydraulic analysis of nuclear power plants and using SYS TH to demonstrate their safety and acceptability. Contains a systematic and comprehensive review of current approaches to the thermal-hydraulic analysis of water-cooled and moderated nuclear reactors Clearly presents the relationship between system level (top-down analysis) and component level phenomenology (bottom-up analysis) Provides a strong focus on nuclear system thermal hydraulic (SYS TH) codes Presents detailed coverage of the applications of thermal-hydraulics to demonstrate the safety and acceptability of nuclear power plants

Issues in Water and Power Engineering: 2013 Edition

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Publisher : ScholarlyEditions
ISBN 13 : 1490110941
Total Pages : 743 pages
Book Rating : 4.4/5 (91 download)

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Book Synopsis Issues in Water and Power Engineering: 2013 Edition by :

Download or read book Issues in Water and Power Engineering: 2013 Edition written by and published by ScholarlyEditions. This book was released on 2013-05-01 with total page 743 pages. Available in PDF, EPUB and Kindle. Book excerpt: Issues in Water and Power Engineering / 2013 Edition is a ScholarlyEditions™ book that delivers timely, authoritative, and comprehensive information about Fusion Engineering. The editors have built Issues in Water and Power Engineering: 2013 Edition on the vast information databases of ScholarlyNews.™ You can expect the information about Fusion Engineering in this book to be deeper than what you can access anywhere else, as well as consistently reliable, authoritative, informed, and relevant. The content of Issues in Water and Power Engineering: 2013 Edition has been produced by the world’s leading scientists, engineers, analysts, research institutions, and companies. All of the content is from peer-reviewed sources, and all of it is written, assembled, and edited by the editors at ScholarlyEditions™ and available exclusively from us. You now have a source you can cite with authority, confidence, and credibility. More information is available at http://www.ScholarlyEditions.com/.

Nuclear Power

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Publisher : BoD – Books on Demand
ISBN 13 : 9533075066
Total Pages : 208 pages
Book Rating : 4.5/5 (33 download)

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Book Synopsis Nuclear Power by : Pavel Tsvetkov

Download or read book Nuclear Power written by Pavel Tsvetkov and published by BoD – Books on Demand. This book was released on 2011-09-06 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: At the onset of the 21st century, we are searching for reliable and sustainable energy sources that have a potential to support growing economies developing at accelerated growth rates, technology advances improving quality of life and becoming available to larger and larger populations. The quest for robust sustainable energy supplies meeting the above constraints leads us to the nuclear power technology. Today's nuclear reactors are safe and highly efficient energy systems that offer electricity and a multitude of co-generation energy products ranging from potable water to heat for industrial applications. Catastrophic earthquake and tsunami events in Japan resulted in the nuclear accident that forced us to rethink our approach to nuclear safety, requirements and facilitated growing interests in designs, which can withstand natural disasters and avoid catastrophic consequences. This book is one in a series of books on nuclear power published by InTech. It consists of ten chapters on system simulations and operational aspects. Our book does not aim at a complete coverage or a broad range. Instead, the included chapters shine light at existing challenges, solutions and approaches. Authors hope to share ideas and findings so that new ideas and directions can potentially be developed focusing on operational characteristics of nuclear power plants. The consistent thread throughout all chapters is the "system-thinking" approach synthesizing provided information and ideas. The book targets everyone with interests in system simulations and nuclear power operational aspects as its potential readership groups - students, researchers and practitioners.

Thermal Hydraulic Calculations to Support Increase in Operating Power in McClellen Nuclear Radiation Center(MNRC) TRIGA Reactor

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Publisher :
ISBN 13 :
Total Pages : 11 pages
Book Rating : 4.:/5 (683 download)

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Book Synopsis Thermal Hydraulic Calculations to Support Increase in Operating Power in McClellen Nuclear Radiation Center(MNRC) TRIGA Reactor by :

Download or read book Thermal Hydraulic Calculations to Support Increase in Operating Power in McClellen Nuclear Radiation Center(MNRC) TRIGA Reactor written by and published by . This book was released on 1998 with total page 11 pages. Available in PDF, EPUB and Kindle. Book excerpt: The RELAP5/Mod3.1 computer program has been used to successfully perform thermal-hydraulic analyses to support the Safety Analysis for increasing the MNRC reactor from 1.0 MW to 2.0 MW. The calculation results show the reactor to have operating margin for both the fuel temperature and critical heat flux limits. The calculated maximum fuel temperature of 705 C is well below the 750 C operating limit. The critical heat flux ratio was calculated to be 2.51.