1274354 (1) 玖、發明說明 【發明所屬之技術領域】 本發明係有關一種核反應器，尤指決定在核反應器內 的中子通量的系統及方法。 【先前技術】 沸水型核反應器（BWR)的反應爐壓力容器（RPV) 通常爲圓柱體狀且封閉在兩端、例如一底端及一可移除的 頂端。 一頂導件一般是設於RP V內的一核心板上方，與核 心板間隔開，一核心罩通常圍繞該核心且由一罩支撐結構 加以支撐。該罩子一般爲圓柱體狀且環繞核心板及頂導件 。在圓柱體狀反應爐壓力容器及圓柱體狀罩子之間設有一 空間或圓環。 反應器核心具有一列四方形截面的燃料束，該等燃料 束在下部藉由一燃料支座來支承。各燃料支座支承一組由 四只燃料束構成的燃料束組。在核心內產生的熱可藉由插 入控制桿來降低’而產生的熱可藉由自核心縮回控制桿來 增加。在一些BWR中，控制桿是十字形截面，具有葉片 可插入由四只燃料束組之間。 核反應器的安全及有效作業需對在核心內的中子通量 加以監控。核心內任一點的中子通量密度決定了在該點的 燃料燃耗速率，在該點的核心熱功率，及決定在該點接收 的輻射劑量機械性及結構性分量。在核心內任一點的中子 -4 - 1274354 ·. (2) 通纛無法簡易的直接量測。習知估計反應器核心內某一點 的中子通量的方法包括，在相關點附近的數個位置直接量 測，及推斷在該相關點的量測値，及藉在電腦上模擬反應 器虜力容器的內部而計算估算的通量。 當核能電廠老化時，有需要對反應器壓力容器及其內 部構件的老化相關劣化有較佳的認識。 【發明內容】 φ 在一型態中，本發明提供一種模擬輻射通量在一容積 內的三維空間分佈的方法。該方法包括爲該容積及容裝在 該容積內的構件製備物理幾何資料庫、爲該容積及容裝在 該容積內的構件製備材料輻射反應資料庫、計算在該容積 內一高度的水平面內的輻射通量、以該容積內的一軸向高 度當函數，計算輻射通量的相對差異、及將計算出的輻射 通量結果之相對軸向差異與在一水平面內的輻射通量結果 相組合。 _ 在另一型態中，本發明提供一種模擬中子質點通量在 一核反應器壓力容器（RPV )內的三維空間分佈的方法， 該核反應器壓力容器（RPV )內具有複數構件。該方法包 括爲該RPV及容裝在該RPV內的構件製備具有物理幾何 資料的輸入資料庫、爲該RPV及容裝在該RPV內的構件 製備包含材料輻射反應資料的另一輸入資料庫、計算在該 RPV內一高度的水平面內的中子質點通量、以該RPV內 的一軸向高度當函數，計算中子質點通量的相對差異、及 -5- 1274354 (3) 將計算出的中子質點通量結果之相對軸向差異與在〜水平 面內的中子質點通量結果相組合。 在另一型態中，本發明提供一種用以模擬中子質點通 量在一核反應器壓力容器（RPV )內的三維空間分佈的系 統。該系統包含一電腦，設計成可爲該RPV及容裝在該 RPV內的構件製備物理幾何資料庫、爲該RPV及容裝在 該 RPV內的構件製備材料輻射反應資料庫、計算在該 RPV內一高度的水平面內的中子質點通量、以該RPv內 的一軸向高度當函數，計算中子質點通量的相對差異、及 將計算出的中子質點通量結果之相對軸向差異與在〜水平 面內的中子質點通量結果相組合。 在另一型態中，本發明提供一種模擬中子質點通量在 一核反應器壓力容器（RPV )內的三維空間分佈的電腦程 式產品。該程式包含一電腦可用的媒介’該電腦可用的媒 介具有一電腦可讀取的程式碼段，可爲該RPV及容裝在 該RPV內的構件製備物理幾何資料庫、爲該RPV及容裝 在該RPV內的構件製備材料輻射反應資料庫、計算在該 RPV內一高度的水平面內的中子質點通量、以該RPV內 的一軸向高度當函數，計算中子質點通量的相對差異、及 將計算出的中子質點通量結果之相對軸向差異與在一水平 面內的中子質點通量結果相組合。1274354 (1) Description of the Invention [Technical Field] The present invention relates to a nuclear reactor, and more particularly to a system and method for determining neutron flux in a nuclear reactor. [Prior Art] The reactor pressure vessel (RPV) of a boiling water type nuclear reactor (BWR) is generally cylindrical and closed at both ends, for example, a bottom end and a removable top end. A top guide is generally disposed above a core plate in the RP V, spaced apart from the core plate, a core cover generally surrounding the core and supported by a cover support structure. The cover is generally cylindrical and surrounds the core plate and the top guide. A space or a ring is provided between the cylindrical reactor pressure vessel and the cylindrical casing. The reactor core has a series of four-section fuel beams that are supported at the bottom by a fuel support. Each fuel support supports a set of fuel bundles of four fuel bundles. The heat generated in the core can be reduced by inserting the lever to reduce heat generated by retracting the lever from the core. In some BWRs, the lever is a cross-section with blades that can be inserted between four fuel beam sets. The safe and efficient operation of the nuclear reactor requires monitoring of the neutron flux within the core. The neutron flux density at any point within the core determines the fuel burn rate at that point, the core thermal power at that point, and the mechanical and structural components that determine the radiation dose received at that point. Neutrons at any point in the core -4 - 1274354 ·. (2) It is not easy to measure directly. Conventional methods for estimating neutron flux at a point within the reactor core include direct measurement at several locations near the relevant point, and inferring measurements at the relevant point, and simulating the reactor on a computer. The estimated flux is calculated inside the force vessel. When nuclear power plants are aged, there is a need to have a better understanding of the ageing-related degradation of the reactor pressure vessel and its internal components. SUMMARY OF THE INVENTION In one form, the present invention provides a method of simulating a three-dimensional spatial distribution of radiant flux over a volume. The method includes preparing a physical geometric database for the volume and components housed in the volume, preparing a material radiation reaction database for the volume and components housed in the volume, and calculating a level in a height within the volume The radiant flux, as a function of the axial height in the volume, calculates the relative difference in radiant flux, and the relative axial difference in the calculated radiant flux results with the radiant flux results in a horizontal plane. combination. In another form, the present invention provides a method of simulating a three-dimensional spatial distribution of neutron particle fluxes in a nuclear reactor pressure vessel (RPV) having a plurality of components within a pressure vessel (RPV). The method includes preparing an input data library having physical geometric data for the RPV and components housed in the RPV, preparing another input data library containing material radiation reaction data for the RPV and components housed in the RPV, Calculating the neutron particle flux in a horizontal plane at a height within the RPV, calculating the relative difference in neutron particle flux as a function of the axial height in the RPV, and -5 - 1274354 (3) will calculate The relative axial difference in the neutron particle flux results is combined with the neutron particle flux results in the ~ horizontal plane. In another version, the present invention provides a system for simulating the three-dimensional spatial distribution of neutron particle fluxes in a nuclear reactor pressure vessel (RPV). The system includes a computer designed to prepare a physical geometric database for the RPV and components housed in the RPV, to prepare a material radiation reaction database for the RPV and components housed in the RPV, and calculate the RPV at the RPV. The neutron particle flux in the horizontal plane of the inner height is calculated as a function of the axial height in the RPv as a function, and the relative difference of the neutron particle flux is calculated, and the relative axial direction of the calculated neutron particle flux result is calculated. The difference is combined with the neutron particle flux results in the ~ horizontal plane. In another form, the present invention provides a computer program product that simulates the three-dimensional spatial distribution of neutron particle fluxes in a nuclear reactor pressure vessel (RPV). The program includes a computer usable medium. The computer usable medium has a computer readable code segment for preparing a physical geometric database for the RPV and components housed in the RPV, and for the RPV and the container. Calculating the neutron particle flux in the RPV component, calculating the neutron particle flux in a horizontal plane at a height within the RPV, and calculating the neutron particle flux as a function of the axial height in the RPV The difference, and the calculated relative axial difference in the neutron particle flux results, are combined with the neutron particle flux results in a horizontal plane.
【實施方式J 下文揭示一種模擬輻射通量在一核能發生系統的容積 -6- 1274354 (4) 內的二維空間分佈的系統及方法。該等系統及方法不侷限 於所揭示的特定實施例。相反的，各系統的構件及各方法 可與其他構件及方法相互獨立及分離的實施。各構件及方 法可與其他構件及方法相互組合使用。本發明將針對可發 電的沸水型核反應器（B WR )加以說明。 藉電腦以模擬核反應器壓力容器的內部結構及構件， 及計算中子在反應器壓力容器內的性能，可產生有利的設 計及運作。 分析核反應數據的程序包括將試驗量測値及理論模型 相組合，以精確判斷核反應數據基本的實際値。一些分析 試圖提供所有截面、成品產量、及能量及角度的成品分佈 。這些較完整的分析對核系統效能的徹底計算是必須的， 因此，這些分析需以電腦可讀取的標準格式呈現。目前， 幾乎所有的徹底分析是使用源自於美國的 E N D F ( Evaluated Nuclear Data File ;核數據分析檔案）格式。 個別分析通常加入用以提供完整的核計算結果的資料 庫內，這些資料庫被給予一具有版本識別的特徵名稱以供 簡易辨識。現有的其中一著名的核資料庫是EN D F / B - V I ; 這是美國的標準核數據分析檔案，其是由美國能源部的剖 面分析工作組（Cross Section Evaluation Working Group )所控制，且由設於布魯克海文國立試驗室（Brookhaven[Embodiment J] A system and method for simulating a two-dimensional spatial distribution of radiant flux in a nuclear energy generation system -6 - 1274354 (4) is disclosed below. The systems and methods are not limited to the specific embodiments disclosed. Conversely, the components and methods of the various systems can be implemented independently and separately from other components and methods. The various components and methods can be used in combination with other components and methods. The present invention will be described with respect to a boiling water type nuclear reactor (B WR ) which can be activated. The use of a computer to simulate the internal structure and components of a nuclear reactor pressure vessel and to calculate the performance of neutrons in a reactor pressure vessel can result in advantageous design and operation. The procedure for analyzing nuclear reaction data involves combining the test metrics with the theoretical models to accurately determine the basic practical enthalpy of the nuclear reaction data. Some analyses attempt to provide a finished product distribution of all cross-sections, finished product yields, and energy and angles. These more complete analyses are necessary for the thorough calculation of the performance of the nuclear system, so these analyses need to be presented in a computer-readable standard format. Currently, almost all thorough analysis uses the E N D F (Evaluated Nuclear Data File) format derived from the United States. Individual analyses are typically added to a database that provides complete nuclear calculation results, and these databases are given a feature name with version identification for easy identification. One of the well-known nuclear databases available is EN DF / B - VI; this is the US standard nuclear data analysis archive, which is controlled by the US Department of Energy's Cross Section Evaluation Working Group. Located at the Brookhaven National Laboratory (Brookhaven
National Laboratory )的國立核數據中心（NNDC )所維 護。 一般上，ENDF-格式資料庫是電腦可讀取核數據檔 1274354 (5) 揭示核反應截面、反應成品的能量及角度分佈、核反應時 產生的各種原子核、蛻變模式及因放射性原子核蛻變所造 成的成品光譜、及在該等量內的估計誤差。 END F-格式資料庫旨在用於廣泛的用途，這些用途需 要計算通過材料的中子、光子及帶電粒子的丨專輸、此輻射 與材料及其等的環境的相互作用細目、及與核化處理相關 的放射性的時間演化。 DORT是一般目的的分立縱座標（discrete or di nates )傳輸碼’用以解決不同領域的中子傳輸問題，尤其是因 輻射的深入穿透例、如施行厚屏蔽所造成的問題。其利用 分立縱座標（discrete ordinates )的方法來解決線性波爾 么么受傳輸方程式（Β ο 11 z m a η n t r a n s ρ 〇 r t e q u a t i ο η )的積分 —微分形式。 在一較佳實施例中，該等資料庫及傳輸碼軟體存在於 電腦可讀取媒體、例如軟碟、硬碟、CD驅動器或DVD驅 動器的電腦程式內。在範例性實施例中，該電腦是網路的 P C工作站。在另一實施例中，乃採用一主框架電腦。 圖1顯示一沸水核反應器壓力容器（RPV )的剖面圖 ’其中有一部份被切割。Rp V I 0——般爲圓柱體狀且以底 端1 2封閉一端，及以一可移除的頂端M封閉另一端。一 側壁1 6由底端1 2延伸至頂端1 4，側壁]6具有一頂凸緣 1 8，頂端1 4連接至頂凸緣1 8。一圓柱體狀核心罩2 0圍 繞一反應器核心2 2及一通稱爲反射器2 1的水旁通區。核 心罩2 0 —端由一罩支撐件2 4加以支撐，且具有一相對的 -8- 1274354 (6) 可移除罩頭26。一下水管區28是形成於核心罩20及側 壁1 6之間的環形物。圓環形的泵底板3 0在罩支撑件24 及RPV側壁1 6之間延伸；泵底板3 0具有複數圓形開口 32，各開口容納一噴射泵34。噴射泵34環繞核心罩20 成圓周向分佈。一入口升管3 6藉一過渡總成3 8連接至兩 噴射泵34。各噴射泵34具有一入口攪拌器40、及一擴散 器4 2。入口升管3 6及兩相連接的噴射泵3 4構成一噴射 泵總成4 4。 φ 熱在核心22內產生’核心22具有複數由可分裂的材 料構成的燃料束4 6。通過核心2 2向上循環的水至少部分 轉變成蒸汽。複數蒸汽分離器4 8將蒸汽與水分離，而水 可再循環。複數蒸汽烘乾器5 0自蒸汽中移除，殘餘的水份 。蒸汽經靠近容器頂端]4的蒸汽出口 5 2離開RPV 1 0。 產生於核心2 2內的熱量係藉插入及抽回複數由中子 吸收材料、例如飴（hafnium )、製成的控制桿54來調整 。當控制桿5 4插入抵毗鄰燃料束4 6的程度時，控制桿會 鲁 吸收中子。如杲中子存在的話，它將促進連鎖反應而在核 心D內產生熱。 各控制桿5 4經一控制桿驅動管5 6與一控制桿驅動機 構（CRDM ) 58相連接而形成一控制桿裝置60。CRDM 58 使控制桿54相對一核心支撐板64及毗鄰的燃料束46移 動。CRDM 58穿過底端12延伸且封裝在一控制桿驅動機 構殼體6 6內。一控制桿導管5 6由控制桿驅動機構殻體 66延伸至核心支撐板64。控制桿導管56在控制桿54插 -9- 1274354 (7) 。控制桿導 、長方形、 入及抽回時，可限制控制桿5 4的非垂直移動 管56可以是任何形狀，例如十字形、圓柱形 Y—形及任何適當的多邊形。 圖2是一種模擬中子通量存Rpv ]迎里仕V 1 〇內的三維空間分 佈的方法8 0的流程圖。在一範例性實例中，方法8 〇包括 製備82包含有核反應器物理幾何資料的輸入資料、製備 84包含有核反應器材料剖面資料的材料剖面輸入資料、 及依據該物理輸入資料及剖面輸入資料來計算86在核反 應器內的一水平面上的中子通量。方法80也包括依據該 物理輸入資料及剖面輸入資料來計算8 8通量相對於軸向 闻度的差異、及將該通量之相對差異結果與該在水平面上 的中子通量結果相組合，以產生中子通量在RP V 1 〇內的 三維空間分佈。 製備82核心模型的物理輸入資料庫包括模擬反應器 在核心中間水平高度或其他選定高度的幾何型態。 該計算的模式包括數個放射狀材料區、例如三個核心 內區、反射器2 1、核心罩2 0、下水管區2 8、噴射泵3 4 及RP V側壁1 6 (圖1 )。爲了節省在RP V流出物不顯著 的區域的計算努力，故不對最內部的五或六排的燃料束造 型。作爲替代者，採用位在核心最內部區的等效半徑的反 射性邊界3 ] 4 (圖3 )。在各核心區的冷卻劑密度係由核 心模擬器資料的週期開始（B 0 C )及週期結束（E 0 C )編 排所導出的週期平均、暴露相關 （c)7cle-averaged exposure-dependent)的水密度。在（r’ z) 5十算中’在 -10- 1274354 (8) 核心區內的水密度軸向差異是經分析的燃料節 期平均値（bundle_specific cycle_averagecl v 均數。中子源密度的空間分佈係假定是與在各 料束位置的相對週期平均能量產能成正比。在 的成分是視爲一均勻混合物。在核心區內的固 卻劑的容積分率係依據燃料束設計數據計算出 件的原子密度及其中子產量與分裂能量，係以 函數，以一柵格設計碼，例如T G B L A計算出 料成分係由廠設計數據獲得。B W R下水管構 精確造模在二維計算中並不實際。爲了評價中 內的互動影響，在（r，z )計算中乃採用三種 管模式。第一種模式是將下水管區視爲僅單獨 的水組成，不含任何金屬成分。此爲保守的態 模式是假設下水管是冷卻劑及金屬的均勻混合 造成的有效中子散射在某種程度上有加以考慮 式是將下水管視爲由不同成分的材料區所組成 射泵及升管爲個別構件。各構件在極座標內的 該構件實際圓形面積。此第三種模式是該範例 用的下水管模式。爲了（ r，z )計算，第二模 模擬在下水管區內的材料組成。 製備84用於分立縱座標傳輸計算中的材 資料庫包括以一核化剖面處理包來處理該數據 性實施例中，係採用D 0 RT來計算。在另一實 採用DORTG01。採用的基礎glj面資料庫是由 的特定束週 a 1 u e s )的平 燃料節及燃 各材料區內 體材料及冷 。各燃料元 燃料暴露當 。核心外材 件及材料的 子在下水管 不同的下水 由再次冷卻 度。第二種 物，因鋼所 。第三種模 ’其中各噴 剖面積等於 性實施例採 式被採用以 料剖面輸入 。在一範例 施例中，係 洛阿拉摩斯 -11 - 1274354 (9) (Los Alamos )國立實驗室爲反應器物理應用所產生的 MATXS庫。MATXS庫包含80組不同溫度及自行屏蔽參 數（σ。）的無限稀釋中子剖面。此資料庫係用以執行共 振自行屏蔽、空間自行屏蔽、彈性移除修正、反應器及細 胞通量解答、及剖面冷凝成較少組。用在D 0 RT計算的一 範例性工作庫是一包含26組與空間及成分相關的微觀剖 面組。National Laboratory) is maintained by the National Nuclear Data Center (NNDC). In general, the ENDF-format database is a computer-readable nuclear data file 1274354 (5) revealing the cross-section of the nuclear reaction, the energy and angular distribution of the reaction product, the various nucleus generated during the nuclear reaction, the enthalpy mode, and the finished product due to the metamorphosis of the radioactive nucleus. The spectrum, and the estimated error within the equivalent. The END F-format database is intended for a wide range of applications, including the calculation of the interaction of neutrons, photons and charged particles through materials, the interaction of this radiation with materials and their environment, and the nucleus Time-dependent evolution of radioactivity associated with processing. DORT is a general purpose discrete or di nates transmission code' to solve neutron transmission problems in different fields, especially due to deep penetration of radiation, such as the implementation of thick shielding. It uses the method of discrete ordinates to solve the integral-differential form of the linear equation of transmission (Β ο 11 z m a η n t r a n s ρ 〇 r t e q u a t i ο η ). In a preferred embodiment, the databases and transport code software reside in a computer readable medium such as a floppy disk, hard drive, CD drive or DVD drive. In an exemplary embodiment, the computer is a networked P C workstation. In another embodiment, a main frame computer is employed. Figure 1 shows a cross-sectional view of a boiling water nuclear reactor pressure vessel (RPV) with a portion cut. Rp V I 0 is generally cylindrical and closed at one end with a bottom end 12 and closed at the other end with a removable top end M. A side wall 16 extends from the bottom end 1 2 to the top end 14 and the side wall 6 has a top flange 18. The top end 14 is connected to the top flange 18. A cylindrical core casing 20 surrounds a reactor core 2 2 and a water bypass zone known as reflector 2 1 . The core cover 20 is supported by a cover support member 24 and has an opposite -8- 1274354 (6) removable cover head 26. The lower water tube region 28 is an annulus formed between the core cover 20 and the side wall 16 . The toroidal pump base plate 30 extends between the cover support member 24 and the RPV side wall 16; the pump base plate 30 has a plurality of circular openings 32, each of which accommodates a jet pump 34. The jet pump 34 is circumferentially distributed around the core cover 20. An inlet riser 36 is coupled to the two jet pumps 34 by a transition assembly 38. Each jet pump 34 has an inlet agitator 40 and a diffuser 42. The inlet riser 36 and the two-phase connected jet pump 34 form an injection pump assembly 44. φ heat is generated in the core 22 The core 22 has a plurality of fuel bundles 46 composed of a cleavable material. The water circulating upward through the core 22 is at least partially converted into steam. A plurality of vapor separators 48 separate the steam from the water, and the water can be recycled. The multiple steam dryers 50 are removed from the steam and the remaining moisture. The steam exits RPV 1 0 via a steam outlet 5 2 near the top of the vessel. The heat generated in the core 2 2 is adjusted by the neutron absorbing material, for example, hafnium, and the control rod 54 made by the insertion and withdrawal number. When the lever 54 is inserted to the extent adjacent to the fuel bundle 46, the lever will absorb the neutrons. If neutrons exist, it will promote a chain reaction and generate heat in core D. Each control lever 54 is coupled to a lever drive mechanism (CRDM) 58 via a lever drive tube 56 to form a lever assembly 60. The CRDM 58 moves the lever 54 relative to a core support plate 64 and an adjacent fuel bundle 46. The CRDM 58 extends through the bottom end 12 and is enclosed within a lever drive mechanism housing 66. A lever catheter 56 is extended by the lever drive mechanism housing 66 to the core support plate 64. The lever catheter 56 is inserted into the control lever 54 -9 - 1274354 (7). The non-vertical movement tube 56 that limits the control rod 54 can be of any shape, such as a cross, a cylindrical Y-shape, and any suitable polygon, when the lever is guided, rectangular, in and withdrawn. Fig. 2 is a flow chart showing a method 80 of simulating the three-dimensional spatial distribution of neutron flux storage Rpv] Yingli Shi V 1 〇. In an illustrative example, method 8 includes preparing 82 input data comprising physical geometry of the nuclear reactor, preparing 84 material profile input data including profile information of the nuclear reactor material, and based on the physical input data and profile input data. The neutron flux at 86 on a level in the nuclear reactor is calculated. The method 80 also includes calculating a difference of the 8 8 flux relative to the axial sensation based on the physical input data and the profile input data, and combining the relative difference result of the flux with the neutron flux result at the horizontal plane To produce a three-dimensional spatial distribution of neutron fluxes within RP V 1 〇. The physical input library for the preparation of the 82 core model includes the geometry of the simulated reactor at the core intermediate level or other selected height. The calculated pattern includes a plurality of radial material zones, such as three core inner zones, a reflector 21, a core shroud 20, a downpipe zone 28, a jet pump 34, and an RP V sidewall 16 (Fig. 1). In order to save computational effort in areas where RP V effluent is not significant, the innermost five or six rows of fuel bundles are not modeled. As an alternative, the reflective boundary 3] 4 (Fig. 3) of the equivalent radius located in the innermost region of the core is used. The coolant density in each core region is derived from the cycle start (B 0 C ) and end of cycle (E 0 C ) layout of the core simulator data. (c) 7cle-averaged exposure-dependent Water density. In the (r' z) 5 ten calculations, the axial difference in water density in the core region of -10- 1274354 (8) is the average fuel enthalpy of analysis (bundle_specific cycle_averagecl v mean. space of neutron source density) The distribution is assumed to be proportional to the relative cycle average energy capacity at each bundle location. The composition is considered to be a homogeneous mixture. The volume fraction of the solids in the core region is calculated based on the fuel beam design data. The atomic density and its neutron yield and splitting energy are obtained by a grid design code, such as TGBLA. The material composition is obtained from the plant design data. The accurate design of the BWR downpipe structure is not practical in 2D calculation. In order to evaluate the interaction effects in the middle, three tube modes are used in the (r, z) calculation. The first mode is to treat the sewer area as a separate water component, without any metal components. This is conservative. The state mode assumes that the effective neutron scattering caused by the uniform mixing of the water pipe and the coolant is considered to some extent by considering the downpipe as a material zone composed of different components. The jet pump and riser are individual components. The actual circular area of the component in each pole member. This third mode is the downpipe mode used in this example. For the (r, z) calculation, the second die is simulated in the downpipe Material composition in the zone. Preparation 84 is used in the calculation of the material data in the discrete ordinate transmission calculation. The data is processed by a nucleation profile processing package, which is calculated using D 0 RT. DORTG01. The basic glj surface database used is the flat fuel section of the specific bundle period a 1 ues ) and the body material in the various material zones and the cold material. Each fuel element is exposed to fuel. The core outer material and the material of the material are in the lower water pipe. The second thing, because of steel. The third mode' has a spray area equal to that of the embodiment. In an exemplary embodiment, the Los Alamos -11 - 1274354 (9) (Los Alamos) National Laboratory is the MATXS library produced for reactor physics applications. The MATXS library contains 80 sets of infinitely diluted neutron profiles with different temperatures and self-shielding parameters (σ.). This database is used to perform self-shielding self-shielding, space self-shielding, elastic removal correction, reactor and cell flux solutions, and profile condensation into fewer groups. An exemplary working library for D 0 RT calculations consists of 26 sets of micro-sections related to space and composition.
上述冷卻劑密度及材料成分的核素原子密度係倂入一 微觀剖面組以形成巨觀混合物剖面組，該巨觀混合物剖面 組近似具有弟3級魯善道爾（Legendre)多項展開式（Ρ3 )。迨些數據組被進一步轉變成一與DORT輸入値相容的 組織成群組的格式。 V 在該範例性實施例中，係採用包含在MATXS 11庫內 的氧、氫及個別鐵同位素的ENDF/B-VI剖面。 中子通量的三維空間分佈係藉組合兩個別的二維傳輸 分析値的結果來模擬。第一項計算8 6係在（r，0 )幾何 上執行，且提供在靠近核心中間平面之高度處，在核心內 的通量相對於容器的徑向及方位角的變化。該（1·，0 ) 分析採用極座標來界定該計算出的模式爲介於反應器方位 角0 °及9 0 °之間的平面區段。反射性邊界條件係假定是 在0 °及9 0 °之邊界處。如果核心設計是對稱的八分圓， 則（r，Θ )計算可模擬是介於〇 °及4 5 °之間的區段。核 心模型的物理數據係模擬在核心中間平面高度、或其他選 定高度的物理數據。該計算的模型包括數個放射狀的材料 -12- 1274354 (10) 區，例如，三個核心內區22、反射器2 1、核心罩20、下 水管區28、噴射泵34及RPV側壁16。爲了節省在RPV 流出物不顯著的區域的計算努力，故不對最內部的五或六 排的燃料束造型。作爲替代者，是採用位在核心最內部區 的等效半徑的反射性邊界。 在一角度座標Θ中，篩孔尺寸是每一篩孔分級是半度 或低於半度。在徑向方向的篩孔尺寸在各區均有所差異。 一般上，細微的篩孔設於材料介面附近，因爲在此預期會 有顯著的通量梯度。細微的篩孔也應用在設於小容室22 8 、RPV襯墊222附近、及RPV側壁最內部。充分細微的 篩孔分級被提供以模擬核心22的外輪廓。該篩孔分級是 足夠的細微，使得該（r，Θ )表述將重現實際的物理性 燃料束區至約0.5百分比內。 第二項計算8 8係在（r，z )幾何上執行，且提供通 量相對於高度的變化。該（r，z )分析是用以決定將應用 在核心中間平面（r，Θ )分析結果上的軸向調整因素的 基礎。一般上係採用 S8或較高的角正交集（angular quadrature set )以模製分立的縱座標。（r，z )計算結果 @核心模型模擬核心在一選定方位角的剖面積。以往的經 @顯示通量在軸向的變化對選定的方位角不是非常敏感。 #〜範例性實施例中，極大核心半徑的方位角被選定爲供 計算8 8使用。核心2 2對2 5個軸向節的每一個節提供一 外方核心區3 02、一內方核心區3 04、及——內部核心區 3 0 6，共爲7 5個核心區。與（r，0 )模式一樣的，各燃 -13- 1274354 (11) 料節具有數個在二個核心區（反射器2 i、核心 水管區2 8、及RP v側壁1 6 )之外的區。用在 模式上的徑向細微篩孔也用在（r，z )模式上。 向，核心中間平面附近比終端區採用較細微的菌 式係假定下水管是冷卻劑及金屬的均勻混合物， 造成的有效中子散射在某種程度上有加以考慮。 利用下列界定在點（r，0 ，z )的通量必的 將中子質點通量的相對差異結果與在一水平面J： 點通量結果相組合9 0 : 0(1·， 0 ，z)=0(r， 0)z，*[0(r，z)e，/0(r 其中 0 (r，0 )广是DORT(r，0 )計算的結果，是 處以核心數據模擬得的，而z ’通常是選定在核心 ，或是與所預期的RPV通量尖峰相對應的高度。 必（r，ζ)θ，是在（r，z)平面處以 DORT(r， 的通量’該（r ’ z )平面是模擬在方位角β ’的 Θ，通常與極大核心半徑，或是檢查小容室的方 應。 0(r，ζ’）θ’是在半徑r及高度ζ’的DORT(r， 答，高度z’與DORT(r，0 )計算的高度相對應。 圖 3顯示一樣品（r，0 )模式的槪示圖， 2 2分割成四個區：一外方核心區3 0 2、一內方杉 、一中央核心區3 0 6及一最內部核心區3 0 8。 )分析採用極座標來界定該計算出的模式爲介The above-mentioned coolant density and the nuclide atom density of the material composition are intruded into a microscopic section group to form a macroscopic mixture profile group, and the macroscopic mixture profile group has a similar three-stage Legendre multi-expansion (Ρ3). . These data sets are further transformed into a format that is organized into groups that are compatible with the DORT input. V In this exemplary embodiment, the ENDF/B-VI profile of oxygen, hydrogen, and individual iron isotopes contained in the MATXS 11 library is employed. The three-dimensional spatial distribution of neutron flux is modeled by combining the results of two other two-dimensional transmission analyses. The first calculation 8 6 is performed on the (r, 0) geometry and provides a change in the flux in the core relative to the radial and azimuthal angles of the vessel at a height near the center plane of the core. The (1·,0) analysis uses polar coordinates to define the calculated pattern as a planar segment between the reactor azimuth angles of 0° and 90°. Reflective boundary conditions are assumed to be at the boundaries of 0 ° and 90 °. If the core design is a symmetric octant, the (r, Θ) calculation can simulate a segment between 〇 ° and 4 5 °. The physical data of the core model simulates physical data at the height of the core midplane, or at other selected heights. The calculated model includes a plurality of radial materials -12-1274354 (10) zones, for example, three core inner zones 22, reflectors 21, core hood 20, downpipe zone 28, jet pump 34, and RPV sidewalls 16 . In order to save computational effort in areas where RPV effluent is not significant, the innermost five or six rows of fuel bundles are not modeled. Instead, a reflective boundary with an equivalent radius located in the innermost region of the core is employed. In an angular coordinate ,, the mesh size is half or less than half of each mesh. The size of the mesh in the radial direction varies in each zone. In general, fine mesh openings are placed near the material interface because a significant flux gradient is expected here. The fine mesh holes are also applied to the small chamber 22 8 , the RPV gasket 222, and the RPV sidewall. A sufficiently fine mesh grading is provided to simulate the outer contour of the core 22. The mesh grading is sufficiently subtle that the (r, Θ) expression will reproduce the actual physical fuel beam zone to within about 0.5 percent. The second calculation 8 8 is performed on the (r, z) geometry and provides a change in flux versus height. This (r,z) analysis is the basis for determining the axial adjustment factors that will be applied to the core midplane (r, Θ) analysis results. Typically, S8 or a higher angular quadrature set is used to mold the discrete ordinates. (r, z) Calculation Results @Core model simulates the core area at a selected azimuth. In the past, @display flux changes in the axial direction are not very sensitive to the selected azimuth. In the exemplary embodiment, the azimuth of the maximal core radius is selected for use in calculations 8 8 . Each of the cores 2 2 to 2 5 axial sections provides a peripheral core zone 322, an inner core zone 309, and an internal core zone 306, for a total of 75 core zones. As with the (r,0) mode, each fuel-13-13274354 (11) section has several of the two core zones (reflector 2 i, core water pipe zone 28, and RP v side wall 16) District. The radial fine mesh used in the mode is also used in the (r, z) mode. Towards, the use of finer bacteria in the vicinity of the core mesoscopic plane than in the terminal zone assumes that the downpipe is a homogeneous mixture of coolant and metal, and the effective neutron scattering caused is considered to some extent. Using the following definition of the flux at the point (r, 0, z), the relative difference between the neutron particle flux must be combined with the J: point flux result in the horizontal plane. 9 0 : 0 (1·, 0 , z )=0(r, 0)z,*[0(r,z)e,/0(r where 0 (r,0) is the result of DORT(r,0) calculation, which is simulated by core data And z ' is usually chosen at the core, or the height corresponding to the expected RPV flux spike. Must (r, ζ) θ, is the flux of DORT(r, in the (r, z) plane' The (r ' z ) plane is simulated in the azimuth angle β ', usually with the maximum core radius, or the square of the small chamber is checked. 0(r,ζ')θ' is at the radius r and heightζ' The DORT (r, A, height z' corresponds to the height calculated by DORT(r, 0). Figure 3 shows a plot of a sample (r, 0) pattern, 2 2 divided into four zones: one foreign The core area 3 0 2, one inner Fangshan, one central core area 3 0 6 and one innermost core area 3 0 8)) The analysis uses polar coordinates to define the calculated mode as
罩 20、下 (r，Θ ) 在 z —方 5孔。該模 且因鋼所 ]方程式， :的中子質 ，ζ，）θ，] 在高度Ζ’ ,、中間平面 Ζ )計算得 核心，而 位角相對 Ζ)通量解 其中核心 $心區3 0 4 該（r，0 於在 RPV -14 - (12) 1274354 方位角0°的邊界3l〇及在RPV方位角9〇。的邊界312之 間的平面區段。反射性邊界條件係假定是在邊界3 1 0及 3 1 2處。如果核心設計是對稱的八分圓，則（r，0 )計 算可模擬是介於〇 °及4 5。之間的區段。在一實施例中， 核心模型的物理數據係模擬在核心中間平面高度的物理數 據。在其他實施例中，該物理數據係模擬任何其他選定的 高度的物理數據。該計算的模型一般上包括數個放射狀的 材料區：三個核心內區3 0 2、3 0 4及3 0 6、反射器2 1、核 心罩2 0、下水管區2 8、噴射泵3 4、升管3 6及RPV側壁 16。對不具有噴射泵的BWR，圓環28當作是只包含再冷 卻水。爲了節省在RPV流出物不顯著區域的計算努力， 故不對最內部的五或六排的燃料束造型。作爲替代者，是 採用位在核心最內部區3 0 8的等效半徑的反射性邊界3 1 4 〇 圖4是一典型的（1·，z )計算模式。（r，z )平面計 算結果的核心模型模擬核心2 2在一選定方位角0的剖面 積。通量在軸向的變化對選定的方位角Θ不是非常敏感。 在該範例性實施例中，極大核心半徑的方位角被選定爲供 該計算使用。而在其他實施例則採用其他方位角。核心 2 2對2 5個軸向節的每一個節提供一外方核心區3 0 2、一 內方核心區3 0 4、及一內部核心區3 0 6 ’共爲7 5個核心區 。與（r , Θ )模式一樣的，各燃料節具有數個在三個核 心區（反射器2 1 0、核心罩20、下水管區2 1 4、及RPV側 壁]6 )之外的區。用在（r ’ 0 )模式的徑向細微篩孔也 -15- 1274354 (13) 用在（1·，Z )模式上。在Z—方向，核心2 2中間平面附近 比終端區採用較細微的篩孔。（r，z )計算模式除了（r， 0 )計算模式內的構件之外，還有位在核心2 2下方的核心 入口 4 0 2及核心支撐板6 4，及位在核心上方的上方反射 器404、頂部導件4 0 6、及蒸汽分離器50。 本發明不侷限於上述各實例，本文的說明旨在敘述範 例，而非用以侷限本發明的範疇。本藝之人士可在本發明 範疇內對上述實施例進行修飾或變異。 φ 【圖式簡單說明】 圖1顯示一沸水核反應器壓力容器的剖面圖。 圖2是依據本發明一實施例的一種模擬中子通量在反 應器內的三維空間分佈的方法的流程圖。 圖3係一樣品（r，0 )計算模式的槪意示圖。 圖4係一樣品（1·，z)計算模式的槪意示圖。 主要元件對照表 10 沸水核反應器壓力容器（RPV ) 12 底端 14 頂端 16 側壁 18 頂凸緣 20 核心罩 2 1 反射器 -16 - 反應器核心 罩支撐件 可移除罩頭 下水管區 泵底板 圓形開口 噴射泵 入口升管 過渡總成 入口攪拌器 擴散器 噴射泵總成 燃料束 蒸汽分離器 蒸汽烘乾器 蒸汽出口 控制桿 控制桿驅動管 控制桿驅動機構（CRDM ) 控制桿裝置 核心支撐板 控制桿驅動機構殼體 方法 製備第一輸入資料庫 -17- 製備第二輸入資料庫 計算在核反應器內的一水平面上的中子通量 計算通量相對於容積內的高度的相對差異 將該通量之相對差異結果與該在一高度處的 水平面上的中子通量結果相組合 反射器 下水管區 襯墊 小容室 外方核心區 內方核心區 內部核心區、 最內部核心區 邊界 邊界 反射性邊界 核心入口 上方反射器 頂部導件 -18-Cover 20, lower (r, Θ) in z — square 5 holes. The model and the steel equation], the neutron mass, ζ, θ,] in the height Ζ ', the middle plane Ζ) calculate the core, and the position angle is relative to Ζ) flux solution core core area 3 0 4 The (r, 0 is in the plane segment between the boundary 3l of the azimuth angle of 0° and the boundary 312 of the azimuth of the RPV of 9〇. The reflective boundary condition is assumed to be At boundaries 3 1 0 and 3 1 2 . If the core design is a symmetric octant, the (r, 0 ) calculation can simulate a segment between 〇° and 45. In an embodiment The physical data of the core model simulates physical data at the height of the core midplane. In other embodiments, the physical data simulates physical data of any other selected height. The calculated model generally includes a plurality of radial materials. Zone: three core inner zones 3 0 2, 3 0 4 and 3 0 6 , reflector 2 1 , core cover 20, downpipe zone 28, jet pump 34, riser pipe 36 and RPV side wall 16. Without the BWR of the jet pump, the ring 28 is considered to contain only re-cooling water. To save the calculation of areas where the RPV effluent is not significant Efforts, therefore, do not shape the innermost five or six rows of fuel bundles. As an alternative, a reflective boundary with an equivalent radius of 3 0 8 in the innermost region of the core is used. 3 4 4 Figure 4 is a typical ( 1·, z) calculation mode. The core model of the (r, z) plane calculation results simulates the cross-sectional area of the core 2 at a selected azimuth angle 0. The change in flux in the axial direction is not very sensitive to the selected azimuth angle 。. In the exemplary embodiment, the azimuth of the maximal core radius is selected for use in the calculation, while in other embodiments other azimuths are employed. The core 2 2 provides an outer portion for each of the 5 5 axial segments. The core core area 3 0 2, an inner core area 3 0 4, and an internal core area 3 0 6 ' are a total of 75 core areas. Like the (r, Θ) mode, each fuel section has several Zones outside the three core zones (reflector 210, core cover 20, downpipe zone 2 1 4, and RPV sidewalls) 6). Radial fine mesh holes used in the (r '0) mode are also -15 - 1274354 (13) Used in the (1·, Z) mode. In the Z-direction, the vicinity of the core 2 2 intermediate plane is more than the terminal area. Micro-mesh hole. (r, z) calculation mode In addition to the components in the (r, 0) calculation mode, there are core inlets 4 0 2 and core support plates 64 under the core 2 2, and The upper reflector 404, the top guide 406, and the vapor separator 50 above the core. The present invention is not limited to the above examples, and the description herein is intended to describe the examples and not to limit the scope of the present invention. Modifications or variations of the above-described embodiments are possible within the scope of the invention. φ [Simple description of the drawing] Figure 1 shows a cross-sectional view of a boiling water nuclear reactor pressure vessel. 2 is a flow chart of a method of simulating a three-dimensional spatial distribution of neutron flux within a reactor, in accordance with an embodiment of the present invention. Figure 3 is a schematic representation of a sample (r, 0) calculation mode. Figure 4 is a schematic representation of a sample (1, z) calculation mode. Main Components Comparison Table 10 Boiling Water Nuclear Reactor Pressure Vessel (RPV) 12 Bottom 14 Top 16 Side Wall 18 Top Flange 20 Core Cover 2 1 Reflector-16 - Reactor Core Cover Support Removes Cover Head Down Zone Pump Floor Circular opening jet pump inlet riser transition assembly inlet agitator diffuser jet pump assembly fuel beam steam separator steam dryer steam outlet control lever control rod drive tube control rod drive mechanism (CRDM) control rod device core support plate Control lever drive mechanism housing method for preparing first input data library -17 - preparing a second input data bank to calculate a relative difference in the neutron flux calculation flux on a horizontal surface in the nuclear reactor relative to the height within the volume The relative difference in flux results in combination with the neutron flux result at the horizontal plane at one height. The reflector is in the lower water pipe area. The outer core core area inner core area inner core area and the innermost core area boundary boundary Reflector Boundary Core Entrance Above Reflector Top Guide -18-