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論文

High temperature nanoindentation of (U,Ce)O$$_{2}$$ compounds

Frazer, D.*; Saleh, T. A.*; 松本 卓; 廣岡 瞬; 加藤 正人; McClellan, K.*; White, J. T.*

Nuclear Engineering and Design, 423, p.113136_1 - 113136_7, 2024/07

ナノインデンテーション法では、微小な試験片を用いてヤング率,硬度及びクリープ強度といった機械物性を評価することが可能である。本研究ではMOX燃料の代替物質として(U,Ce)O$$_{2}$$を用いて、高温ナノインデンテーション試験を実施した。試料のCe含有率は0.1、0.2及び0.3mol%とし、温度は800$$^{circ}$$Cまでの測定を行い、ヤング率、硬度及びクリープ強度の評価を行った。温度の上昇に伴い、ヤング率は線形的に低下し、硬度は指数関数的に低下する結果が得られた。また、800$$^{circ}$$Cにおいては、応力指数n=4.7$$sim$$6.9のクリープ変形が得られた。

論文

MAAP code analysis for the in-vessel phase of Fukushima-Daiichi Nuclear Power Station Unit 1 and comparison of the results among Units 1 to 3

佐藤 一憲; 吉川 信治; 山下 拓哉; 下村 健太; Cibula, M.*; 溝上 伸也*

Nuclear Engineering and Design, 422, p.113088_1 - 113088_24, 2024/06

The accident progression of the in-vessel phase of Fukushima Daiichi Nuclear Power Station Unit 1 was analyzed using the MAAP code. Although there is a large uncertainty in the initial stage of accident progression behavior in Unit 1 with little measurement data, it is presumed to have similarities to that of Unit 3. As a result, in Unit 1, since there was almost no alternative water injection during the in-vessel phase, cooling of the debris transferred to the lower plenum was small. It was likely that a large molten pool of metals had formed, and that the steam supply to the high-temperature core materials was suppressed and metal oxidation was relatively small. The analysis results for Unit 1 were compared with those for Units 2 and 3, and differences between units such as the thermal conditions of the debris that relocated to the pedestal and the degree of metal oxidation were shown.

論文

A Systematic approach for the adequacy analysis of a set of experimental databases: Application in the framework of the ATRIUM activity

Baccou, J.*; Glantz, T.*; Ghione, A.*; Sargentini, L.*; Fillion, P.*; Damblin, G.*; Sueur, R.*; Iooss, B.*; Fang, J.*; Liu, J.*; et al.

Nuclear Engineering and Design, 421, p.113035_1 - 113035_16, 2024/05

In the Best-Estimate Plus Uncertainty (BEPU) framework, the use of best-estimate code requires to go through a Verification, Validation and Uncertainty Quantification process (VVUQ). The relevance of the experimental data in relation to the physical phenomena of interest in the VVUQ process is crucial. Adequacy analysis of selected experimental databases addresses this problem. The outcomes of the analysis can be used to select a subset of relevant experimental data, to encourage designing new experiments or to drop some experiments from a database because of their substantial lack of adequacy. The development of a specific transparent and reproducible approach to analyze the relevance of experimental data for VVUQ still remains open and is the topic of this contribution. In this paper, the concept of adequacy initially introduced in the OECD/NEA SAPIUM (Systematic APproach for model Input Uncertainty quantification Methodology) activity is formalized. It is defined through two key properties, called representativeness and completeness, that allows considering the multifactorial dimension of the adequacy problem. A new systematic approach is then proposed to analyze the adequacy of a set of experimental databases. It relies on the introduction of two sets of criteria to characterize representativeness and completeness and on the use of multi-criteria decision analysis method to perform the analysis. Finally, the approach is applied in the framework of the new OECD/NEA ATRIUM activity which includes a set of practical IUQ exercises in thermal-hydraulics to test the SAPIUM guideline in determining input uncertainties and forward propagating them on an application case. It allows evaluating the adequacy of eight experimental databases coming from the Super Moby-dick, Sozzi-Sutherland and Marviken experiments and identifying the most adequate ones.

論文

Application of analytical wall functions to CFD analysis of condensation flow

相馬 秀; 石垣 将宏*; 安部 諭; 柴本 泰照

Nuclear Engineering and Design, 416, p.112754_1 - 112754_18, 2024/01

 被引用回数:0 パーセンタイル:0.01(Nuclear Science & Technology)

The wall function (WF) enables analyzing condensation flow in a nuclear reactor containment vessel with reasonable computational costs. However, conventional wall treatments rely on the logarithmic laws for velocity, temperature, and concentration, limiting applicability. In this paper, we applied the analytical wall function approach to the condensation flow analysis of steam/air mixtures. This approach features the analytical integration of transport equations considering the buoyancy, the material property change, and the convective terms. We conducted CFD analysis with the analytical wall function models for the forced, mixed, and natural convection and confirmed good prediction, especially when the log law does not hold.

論文

MAAP code analysis focusing on the fuel debris conditions in the lower head of the pressure vessel in Fukushima-Daiichi Nuclear Power Station Unit 3

佐藤 一憲; 吉川 信治; 山下 拓哉; 下村 健太; Cibula, M.*; 溝上 伸也*

Nuclear Engineering and Design, 414, p.112574_1 - 112574_20, 2023/12

Based on the updated knowledge from plant-internal investigations, experiments and computer-model simulations until now, the in-vessel phase of Fukushima-Daiichi Nuclear Power Station Unit 3 was analyzed using the MAAP code. In Unit 3, it is considered that ca. 40 percent of UO$$_{2}$$ fuel was molten when core materials relocated to the lower plenum of the reactor pressure vessel. Initially relocated molten materials would have been fragmented by mixing with liquid water, while solid materials would have relocated later on. With this two-step relocation, debris in the lower plenum seems to have been permeable for coolant, thus debris seems to have been once cooled down effectively. Although the present MAAP analysis seems to slightly underestimate core-material oxidation during the relocation period, this probable underestimation was compensated for by an existing study that was considered more reliable, so that more realistic debris conditions in the lower plenum could be obtained. Probable debris reheat-up behavior was evaluated based on interpretation of the pressure data. This evaluation predicted that the fuel debris in the lower plenum was basically in solid-phase at the time when it relocated to the pedestal. With this study, basic validity of the former prediction of the Unit 3 accident progression behavior was confirmed, and detailed boundary conditions for future studies addressing the later phases were provided.

論文

Numerical simulation technologies for safety evaluation in plant lifecycle optimization method, ARKADIA for advanced reactors

内堀 昭寛; 堂田 哲広; 青柳 光裕; 曽根原 正晃; 曽我部 丞司; 岡野 靖; 高田 孝*; 田中 正暁; 江沼 康弘; 若井 隆純; et al.

Nuclear Engineering and Design, 413, p.112492_1 - 112492_10, 2023/11

 被引用回数:1 パーセンタイル:72.91(Nuclear Science & Technology)

ナトリウム冷却高速炉に代表される革新炉に対し、安全性評価やそれに基づく設計最適化を自動で行うARKADIAを開発している。通常運転もしくは設計基準事象の範囲で設計最適化を行うARKADIA-Designについては、核特性-熱流動-炉心変形のマルチレベル連成解析手法等を中心技術として開発し、その基本的機能を確認した。シビアアクシデントまで含む範囲で安全性評価を行うARKADIA-Safetyの基盤技術として、炉内/炉外事象一貫解析手法の整備を進め、仮想的なシビアアクシデント事象を解析することで基本的機能を確認した。また、炉外事象に対する解析モデルの高度化、設計最適解の探索工程を合理化するAI技術の開発に着手した。

論文

Hierarchical Bayesian modeling to quantify fracture limit uncertainty of high-burnup advanced fuel cladding tubes under loss-of-coolant accident conditions

成川 隆文; 濱口 修輔*; 高田 孝*; 宇田川 豊

Nuclear Engineering and Design, 411, p.112443_1 - 112443_12, 2023/09

 被引用回数:0 パーセンタイル:0.01(Nuclear Science & Technology)

For realizing a highly reliable fracture limit evaluation of fuel cladding tubes during loss-of-coolant accidents (LOCAs) in light-water reactors, we developed a method to quantify the fracture limit uncertainty of high-burnup advanced fuel cladding tubes. This method employs a hierarchical Bayesian model that can quantify uncertainty even with limited experimental data. The fracture limit uncertainty was quantified as a probability using the amount of oxidation (Equivalent cladding reacted: ECR) and the initial hydrogen concentration (the hydrogen concentration in the fuel cladding tubes before the LOCA-simulated tests) as explanatory variables. We divided the regression coefficients of this model into a hierarchical structure with an overall average term common to all types of fuel cladding tubes and a term representing differences among various types of fuel cladding tubes. This hierarchical structure enabled us to quantify the fracture limit uncertainty through the effective use of prior knowledge and data, even for high-burnup advanced fuel cladding tubes with a small number of data points. The fracture limits representing a 5% fracture probability with 95% confidence of the high-burnup advanced fuel cladding tubes evaluated by the hierarchical Bayesian model were higher than 15% ECR for the initial hydrogen concentrations of up to 700-900 wtppm and restraint loads below 535 N. These fracture limits were comparable to the limit of the unirradiated Zircaloy-4 cladding tube, indicating that the burnup extension and use of the advanced fuel cladding tubes do not significantly lower the fracture limit of fuel cladding tubes. Further, we proposed a method to reduce the fracture limit uncertainty by using non-binary data, instead of the binary data, depending on the condition of the fuel cladding tube specimens after performing the LOCA-simulated test, thereby increasing the amount of information in the data.

論文

Comparative study of a glovebox dismantling facility for manual and remote glovebox dismantlement activities

北村 哲浩; 平野 宏志*; 吉田 将冬

Nuclear Engineering and Design, 411, p.112435_1 - 112435_14, 2023/09

 被引用回数:0 パーセンタイル:0.01(Nuclear Science & Technology)

本研究では解体設備の開発経緯、設備の特徴、実積について解説した後、グリーンハウス方式と比較した場合の利点について評価した。また、解体設備における直接解体と遠隔解体の比較を行いそれぞれの特徴を議論した。さらに作業被ばくについて定量的な評価を行った。最後に現在行っている廃止措置技術開発へのフィードバックについて述べた。

論文

A Simple correlation to estimate agglomerated debris formation based on experiments of melt jet-breakup using a metallic melt

岩澤 譲; 杉山 智之; 金子 暁子*

Nuclear Engineering and Design, 409, p.112348_1 - 112348_15, 2023/08

 被引用回数:0 パーセンタイル:0.01(Nuclear Science & Technology)

The agglomeration can form the massive debris (so-called agglomerated debris) by merging of melt particles with others when the particles accumulate on the floor of a containment vessel after relocation of the molten core (so-called corium or melt) in severe accidents in a light water reactor. This paper presents a modification of the simple correlation to estimate the mass fraction of the agglomerated debris proposed by the previous study [Iwasawa et al., Nucl. Eng. Des., 386 (2022), 111575] based on the experiments of melt jet-breakup using a metallic melt. The methodology is required to estimate the mass fraction of the agglomerated debris in the reactor conditions because the agglomerated debris can have a serious impact on the debris bed coolability. The present study focused the effects of the melt jet injection conditions (nozzle diameter and inlet velocity) on the mass fraction of agglomerated debris to add the experimental data base for the previous study that focused only the effects of the melt temperature, coolant temperature, and coolant depth on the mass fraction of the agglomerated debris. The visualized observation using a high-speed camera and morphological investigation of the recovered debris revealed the effects of the nozzle diameter and inlet velocity on the mass fraction of agglomerated debris. The extrapolation of the modified simple correlation showed the mass fraction of the agglomerated debris in the anticipated reactor conditions.

論文

Development of a statistical evaluation method for core hot spot temperature in sodium-cooled fast reactor under natural circulation conditions

堂田 哲広; 井川 健一*; 岩崎 隆*; 村上 諭*; 田中 正暁

Nuclear Engineering and Design, 410, p.112377_1 - 112377_15, 2023/08

 被引用回数:0 パーセンタイル:0.01(Nuclear Science & Technology)

ナトリウム冷却高速炉の安全性を高めるためには、強制循環設備への交流電源供給が喪失した場合でも、自然循環によって炉心の崩壊熱を除去する必要がある。自然循環条件下では、ナトリウムの流れが浮力によって駆動され、流速と温度分布が互いに影響を与えるため、流れと熱に影響を与える不確かさを決定論的に考慮することで炉心高温点温度を評価することは困難である。そこで、モンテカルロサンプリング法を使用した炉心高温点温度の統計的評価手法を開発し、ループ型ナトリウム冷却高速炉の代表的な3つの自然循環崩壊熱除去事象に適用して、その有効性を実証した。

論文

Large-eddy simulation on two-liquid mixing in the horizontal leg and downcomer (the TAMU-CFD Benchmark), with respect to fluctuation behavior of liquid concentration

安部 諭; 岡垣 百合亜

Nuclear Engineering and Design, 404, p.112165_1 - 112165_14, 2023/04

 被引用回数:0 パーセンタイル:0.01(Nuclear Science & Technology)

Pressurized Thermal Shock (PTS) is induced potentially by the rapid cooling of the cold-leg and downcomer wall in the primary system of a Pressurized Water Reactor (PWR) due to the initiation of Emergency Core Cooling System (ECCS). Thus, fluids mixing in a horizontal cold-leg and downcomer should be predicted accurately; however, turbulence production and damping often hinders this prediction due to the presence of the density gradients. Hence, the Fifth International Benchmark Exercise, the cold-leg mixing Computational Fluid Dynamics (CFD) Benchmark, was conducted under the support of OECD/NEA. The experiment was designed for visualization of the mixing phenomena of two liquids with different densities. The heavy liquid was a simulant of cold water from ECCS, in a horizontal leg and downcomer. We used the Large-eddy Simulation (LES) to investigate the time fluctuation behaviors of velocity and liquid concentration. The CFD simulation was performed with two turbulence models and three different numerical meshes. We investigated the characteristics of the appearance frequency of the heavy liquid concentration with the statistical method. Based on our findings, we propose further experiments and numerical investigations to understand the fluid mixing phenomena related to PTS.

論文

Attention-based time series analysis for data-driven anomaly detection in nuclear power plants

Dong, F.*; Chen, S.*; 出町 和之*; 吉川 雅紀; 関 暁之; 高屋 茂

Nuclear Engineering and Design, 404, p.112161_1 - 112161_15, 2023/04

 被引用回数:3 パーセンタイル:90.12(Nuclear Science & Technology)

To ensure nuclear safety, timely and accurate anomaly detection is of utmost importance in the daily condition monitoring of Nuclear Power Plants (NPPs), as any slight anomaly in a plant may result in an irreversible and serious accident, as well as high costs of maintenance and management. Nevertheless, due to the unique inherent attributes of anomalies, the difficulty of automatic detection in NPPs is increased. Previous model-driven anomaly detection approaches required skilled priori knowledge, leading to their limited usability. Commonly adopted deep learning-based data-driven anomaly detection approaches may not easily acquire the most relevant features when dealing with sensor data containing redundant information with uneven distribution of anomalies. To alleviate these issues, this paper propose an attention-based time series model for anomaly detection to ensure safety in NPPs. First, we employ one-dimension convolutional neural network (1D-CNN) backbone for feature extraction to preserve original inherent features of time series inputs. Subsequently, we originally adopt soft-attention mechanism to automatically extract the most relevant temporal features considering the specificity of anomaly detection in NPPs. The performance of the proposed model was experimentally validated on the High Temperature Gas-cooled Reactor (HTGR) anomaly case dataset simulated using the analytical code. The experimental results indicate that the proposed model was capable of detecting anomalies in NPPs with superior performance to the baseline model, while ensuring fast detection at short time steps.

論文

MAAP code analysis focusing on the fuel debris condition in the lower head of the pressure vessel in Fukushima-Daiichi Nuclear Power Station Unit 2

佐藤 一憲; 吉川 信治; 山下 拓哉; Cibula, M.*; 溝上 伸也*

Nuclear Engineering and Design, 404, p.112205_1 - 112205_21, 2023/04

 被引用回数:2 パーセンタイル:90.12(Nuclear Science & Technology)

これまでのプラント内部調査、実験、コンピュータモデルシミュレーションから得られた最新の知見に基づき、福島第一原子力発電所2号機の原子炉圧力炉容器内フェーズに対するMAAP解析を実施した。2号機では、炉心物質が圧力容器の下部プレナムに移動し、そこで冷却材によって冷却されて固化したときのエンタルピーが比較的低かったと考えられる。MAAPコードは、炉心物質リロケーション期間中の炉心物質の酸化の程度を過小評価する傾向があるが、酸化に係るより信頼性の高い既存研究を活用することによって補正を行うことで、下部プレナム内の燃料デブリ状態の、より現実的な評価を行った。この評価により、2号機事故進展挙動に係る既往予測の基本的妥当性が確認され、今後の後続過程研究を進めるための詳細な境界条件を提供した。下部ヘッドの破損とペデスタルへのデブリ移行に至るデブリ再昇温プロセスに対処する将来研究に、本研究で得た境界条件を反映する必要がある。

論文

Development and validation of analysis code for spallation products behavior in LBE coolant system of ADS comparing with the distribution data in MEGAPIE spallation target

宮原 信哉*; 有田 裕二*; 中野 敬太; 前川 藤夫; 佐々 敏信; 大林 寛生; 武井 早憲

Nuclear Engineering and Design, 403, p.112147_1 - 112147_17, 2023/03

 被引用回数:0 パーセンタイル:0.01(Nuclear Science & Technology)

通常運転時と事故時の両方の場合における放射線障害の安全性研究のために、加速器駆動システム(ADS)の鉛ビスマス共晶(LBE)冷却システムにおけるポロニウム210を含む核破砕生成物(SP)のインベントリと放出および輸送挙動を評価することが重要である。福井大学と日本原子力研究開発機構(JAEA)は、多様な運転状況におけるADSのLBE冷却システム内のSPの時間依存挙動を予測するコンピューター解析コードTRAIL(Transport of Radionuclides In Liquid metal systems)を開発している。LBE冷却材中の放射性SPと安定SPの両方のソースタームが入力として与えられ、放射性SPの放射性崩壊連鎖モデルがコードに実装され、SPの移動性が評価される。本論文では、最近のコード開発の進捗状況と検証結果を、MEGAPIE破砕ターゲットにおける揮発性SPの分布データと比較して示す。

論文

New approach for the detection of defects in the core support structure of SFRs using EMAT based on a Halbach magnet

山口 智彦; Mihalache, O.

Nuclear Engineering and Design, 401, p.112084_1 - 112084_14, 2023/01

 被引用回数:1 パーセンタイル:31.61(Nuclear Science & Technology)

This paper investigated a new method based on a combination of electromagnetic and ultrasonic sensors for inspecting the core support structure of the reactor vessel in sodium-cooled fast reactors from a position located outside of the vessel. Using an electromagnetic acoustic transducer (EMAT) sensor with a Halbach magnet, the feasibility of the detection of the defects in the reactor core support structure was investigated via experimental measurements using a reduced half-scale mock-up model in a sodium-free environment. The amplitude of the signal from various small slits was enhanced using a combination of EMAT sensor geometry, Halbach magnet configuration, and signal processing methodology in view of increasing the signal-to-noise ratio when the EMAT continuously scanned the area of interest for defects deep inside the metallic structure.

論文

Study on evaluation method of kernel migration of TRISO fuel for High Temperature Gas-cooled Reactor

深谷 裕司; 沖田 将一朗; 佐々木 孔英; 植田 祥平; 後藤 実; 大橋 弘史; Yan, X.

Nuclear Engineering and Design, 399, p.112033_1 - 112033_9, 2022/12

 被引用回数:0 パーセンタイル:0.01(Nuclear Science & Technology)

高温ガス炉のTRISO燃料の核移動を解析し潜在的な支配的な影響を調査した。核移動は主要な燃料破損モードであり、高温工学試験研究炉HTTRでは燃料の寿命を決定するために支配的な要因である。しかし、本研究では、結果と信頼性が評価方法に依存することを示す。この研究で使用される評価方法は、被覆燃料粒子の実際の分布と、結果として生じる非均質な燃料温度計算を考慮している。結果として、最も保守的な評価と比較して、核移動速度が約10%低い評価が得られることが分かった。

論文

Advanced thermal-hydraulic experiments and instrumentation for heavy liquid metal reactors

Pacio, J.*; Van Tichelen, K.*; Eckert, S.*; Wondrak, T.*; Di Piazza, I.*; Lorusso, P.*; Tarantino, M.*; Daubner, M.*; Litfin, K.*; 有吉 玄; et al.

Nuclear Engineering and Design, 399, p.112010_1 - 112010_15, 2022/12

 被引用回数:5 パーセンタイル:84.97(Nuclear Science & Technology)

加速器駆動システムや次世代高速炉の一次冷却材として、鉛や鉛ビスマス共晶合金(LBE)などの重液体金属(HLM)が提案されており、欧州では、MYRRHA(LBE)とALFRED(鉛)がHLMを用いたリファレンスシステムとして使用されている。本論文では、プール型とループ型のHLM実験に関するこれまでの経験と現在進行中の活動の概要について述べる。プール実験では、いくつかのシナリオにおける強制循環と自然循環のフローパターンの測定を実施しており、ループ試験では燃料集合体,制御棒,熱交換器のモックアップのような特定の構成要素の評価に重点を置いた試験を実施している。これらの試験では、流量や圧力差などの変数と、温度や速度、振動などのローカルな数量の測定を行っている。測定技術に関してはコンパクトな形状で正確な測定を行うために高温と腐食に耐えることができる高度な計測器が必要であり、従来の技術に加え、光ファイバーに基づく計測器、超音波や電磁力を利用した測定方法について説明する。

論文

Present status of JAEA's R&D toward HTGR deployment

柴田 大受; 西原 哲夫; 久保 真治; 佐藤 博之; 坂場 成昭; 國富 一彦

Nuclear Engineering and Design, 398, p.111964_1 - 111964_4, 2022/11

 被引用回数:2 パーセンタイル:53.91(Nuclear Science & Technology)

日本原子力研究開発機構は、高温ガス炉の研究開発を進めている。原子炉技術の研究開発は、高温工学試験研究炉(HTTR)を用いて行われている。HTTRは2021年に大規模な補強無しで運転再開された。2022年1月には、OECD/NEAのLOFCプロジェクトにおける安全性実証試験を実施した。原子力機構は、熱化学法ISプロセスによるカーボンフリー水素製造の研究開発を進めている。また、高温ガス炉の実用化に向けた設計研究を行っている。HTTRによる水素製造の実証に関する新たな試験プログラムが開始された。2030年までの最初の実証のため、メタンの水蒸気改質による水素製造システムが選定された。

論文

Friction factor and Reynolds number correlation for finned tube bundle of the air cooler of Monju reactor

素都 益武

Nuclear Engineering and Design, 396( ), p.111893_1 - 111893_27, 2022/09

 被引用回数:0 パーセンタイル:0.01(Nuclear Science & Technology)

新規制基準を適用するための設計基準を超えた安全解析では、解析モデルの正確性、より高い温度とより低い流量条件での冷却能力の解析モデルの適用性が長期の全電源喪失などの重大な事故を解析するために不可欠である。本研究では、流路への複雑な管束形状を有する圧力損失挙動の実験についての調査と実機の設備形状およびプラント試験データに基づく解析評価を記述する。具体的にはフィン付き管群の実験データおよび実機の形状に基づくCFDによる解析結果との比較評価、不確実性を考慮し摩擦係数の適用可能な相関式を提案している。これにより、管群部の圧力損失の寄与は、設計段階よりも明確になり、本研究の成果、すなわち実験データの調査とCFDを使用した評価は、低レイノルズ数での冷却能力が要求された場合の空気冷却器の設計に適用可能である。

論文

Calculation of shutdown gamma distribution in the high temperature engineering test reactor

Ho, H. Q.; 石井 俊晃; 長住 達; 小野 正人; 島崎 洋祐; 石塚 悦男; 後藤 実; Simanullang, I. L.*; 藤本 望*; 飯垣 和彦

Nuclear Engineering and Design, 396, p.111913_1 - 111913_9, 2022/09

 被引用回数:1 パーセンタイル:31.61(Nuclear Science & Technology)

Estimation of decay gamma distribution in a reactor core is essential for safely conducting various works after reactor shutdown such as periodic maintenance, shuffling fuel, removing spent fuel at the end of cycle, etc. Because of the dependency on the complex operating history of the reactor, attempting to calculate the decay gamma rays distribution in the core remains a challenge. This study showed a method to calculate the shutdown gamma distribution in the HTTR core by coupling a Monte-Carlo transport calculation code MCNP6 and an activation code ORIGEN2 to take advantage of spatial dependence and transportation abilities of MCNP6 and the detailed fission products tracking during burnup and cooling of ORIGEN2. As result, the three-dimensional shutdown gamma distribution in the HTTR core for different cooling times and spatial locations could be obtained accurately.

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