JP3679866B2 - Core performance calculator - Google Patents

Description

【０１５０】
ここで、ｘは集合体境界からの距離、κは熱中性子拡散距離の逆数、ａは水ギャップ変化幅である。
【０１５１】
集合体内熱中性子束分布の変化は、ｘ方向およびｙ方向の１次元分布の積δΨ（ｘ）δΨ（ｙ）により近似できる。この手法は、解析モデルに基づくため予め詳細計算によるテーブルの準備をしておく必要がないという利点がある。
【０１５２】
（ｃ）単一集合体中性子束不連続因子拡散モデル
次に、集合体内の非均質熱中性子束分布を計算する非均質熱中性子束計算手段を設け、Ｄ格子バンドルとオフセットバンドルの水ギャップ幅が異なることによる効果を、無限格子計算により得られる集合体中性子束不連続因子を用いて考慮する。したがって、マルチ集合体計算を必要としない。この手法は、各集合体を均質化したノードからなる系に対して、中性子束不連続因子を用いた拡散ノード法により集合体内中性子束分布を求め、この中性子束分布より集合体核特性変化量を評価する。
【０１５３】
すなわち、中性子束不連続因子を用いた拡散理論に基づいて各集合体を均質化したノード内の均質熱中性子束分布を計算し、無限格子計算において評価された「集合体境界での非均質熱中性子束の均質熱中性子束に対する比」と「集合体内での均質熱中性子束の非均質熱中性子束に対する比」を掛け合わせた因子を、均質熱中性子束分布の熱中性子拡散による過渡成分の補正係数とする。これにより集合体内の非均質熱中性子束分布を計算する。そして、この非均質熱中性子束計算手段による非均質中性子束分布を用いて集合体平均核定数を補正して炉心固有値、炉内中性子束分布、出力分布を計算する。
【０１５４】
ここで、集合体中性子束不連続因子は、無限格子体系において、集合体の各面の平均中性子束の集合体平均中性子束に対する比として定義される。不連続因子を用いた多群拡散ノード法そのものについては既に知られており、例えば、文献 "Assembly Homogenization Techniques for Light Water Reactor Analysis,"K.S.Smith,Progress in Nuclear Energy,vol.17,p303,1986に記載されている。
【０１５５】
また、ノード法計算により得られる中性子束分布を用いて、集合体内の局所出力分布を計算する方法の一例は、"SIMULATE-3 Pin Power Reconstruction Methodology and Benchmarking,"K.R.Rempe et.al,Proceedings of lnternational Reactor Physics Conference,111ー19,Jackson Hole,1988 に記載されている。
【０１５６】
Ｄ格子バンドルとオフセットバンドルでは、水ギャップ幅が異なるため集合体内中性子束分布が異なり、集合体中性子不連続因子も異なる。上記 K.Smithの文献に示されるように、中性子束不連続因子は、拡散ノード法において、集合体をそれぞれ均質化したノードの境界における中性子束に対する境界条件を与える。すなわち、例えば着目集合体ｎと隣接集合体ｍのｘ方向境界において、中性子束に対する以下の境界条件を与える。
【０１５７】
【数２】

【０１５８】
ここで、ｆは境界面の中性子束不連続因子、Ψは境界面における中性子束を表す。着目集合体と隣接集合体が無限格子体系において同じ格子タイプであれば、中性子不連続因子も等しく、上記の境界条件は単に中性子束の連続性を表すにすぎない。しかし、隣接する集合体間の隣接面における中性子不連続因子ｆが異なると、上記の境界条件に基づいてノード境界に中性子の仮想ソースが生じるため、集合体不連続因子の違いから水ギャップ幅の違いによる集合体内の中性子束分布の変化が計算できる。多群拡散ノード法では、熱中性子束に対する中性子束不連続因子を用いた全炉心計算により、ノード平均熱中性子束および、ノード境界熱中性子束が与えられる。
【０１５９】
次に、ノード平均中性子束、ノード境界中性子束等を用いて、均質化した集合体内の中性子束分布を展開計算することができる。一例として、前記 K.Rempeの文献では、均質化した集合体ノード内の熱中性子束Ψ₂の２次元分布を次式の形式で展開している。
【０１６０】
【数３】

【０１６１】
ここでΨ₁は高速中性子束であり、ｃ_iは展開係数、ｆ_iはｓｉｎｈ、ｃｏｓｈ関数である。
【０１６２】
非均質中性子束の均質中性子束に対する比が知られていれば、非均質中性子束は、上記（３）式の均質熱中性子束分布にこの比を掛けることで計算できる。拡散ノード法では、前記 K.Rempe の文献に示されるように、この比が無限格子計算で得られる非均質中性子束分布Ψ^hetと均質中性子束分布Ψとの比で近似できるもの仮定している。すなわち、炉心中に置かれた集合体ノード内の非均質熱中性子束分布Ψ₂ ^hetは、次式で計算される。
【０１６３】
【数４】

【０１６４】
ここで、記号∞は無限格子計算値を示す。
【０１６５】
しかしながら、発明者らがこの手法をオフセットバンドル体系に適用したところ、ノード平均中性子束や、ノード境界中性子束およびノード境界中性子流については、拡散ノード法の結果はマルチ集合体詳細計算と良く一致するにもかかわらず、燃料棒局所出力については誤差が大きいことが判明した。この原因は、熱中性子束分布については、上記の「非均質中性子束の均質中性子束に対する比が、無限格子計算で得られる非均質中性子束分布と均質中性子束分布の比で近似できる」という仮定が成り立たないためであることがわかった。
【０１６６】
ノード内均質熱中性子束から非均質熱中性子束分布を精度良く計算するために、発明者らは、無限格子体系において評価された「集合体境界での非均質熱中性子束の均質熱中性子束に対する比」と「集合体での均質熱中性子束の非均質熱中性子束に対する比」を掛け合わせた因子を、均質熱中性子束分布の熱中性子拡散による過渡成分の補正係数とすることにより、集合体ノード内の非均質熱中性子束分布を精度良く計算できることを見出した。
【０１６７】
均質熱中性子束分布の熱中性子拡散による過渡成分は（３）式の第２項で与えられる。従って、本手法では非均質熱中性子束は、（４）式の代わりに、下記の（５）式で与えられる。
【０１６８】
【数５】

【０１６９】
ここで、「集合体境界での非均質熱中性子束の均質熱中性子束に対する比」を表す係数Ｗは、４つの集合体境界面に関する荷重平均により、次式で表すことができる。
【０１７０】
【数６】

【０１７１】
集合体内の非均質熱中性子束分布が計算されると、非均質中性子束分布の関数である集合体平均核定数が計算され、オフセットバンドル隣接を補正した炉内出力分布が計算される。また、集合体内の非均質熱中性子束分布から燃料棒局所出力分布が直ちに計算され、これより集合体の線出力密度が計算できる。
【０１７２】
また、燃料棒Ｒ因子分布は、燃料棒局所出力分布より計算することができ、これから限界出力比が計算できる。
【０１７３】
集合体の各面における集合体中性子束不連続因子は、予め単一集合体詳細計算（反射境界条件を用いた無限格子計算）により集合体毎に準備する。図４に熱中性子束に対する集合体不連続因子のチャンネルボックスのオフセット量に対する関数形の一例を示す。
【０１７４】
この手法の計算精度を示す一例として、オフセットバンドル隣接による効果を示した従来の図１９と同様に、Ｄ格子バンドルのまわりに制御棒を挟んで２体のオフセットバンドルが隣接した場合の、集合体内局所出力分布を本手法により計算し、マルチ集合体詳細計算による参照解と比較した結果を図５に示す。図５において、上段は詳細計算、中段は本発明による手法、下段はその差である。参照計算によれば、オフセットバンドルの隣接により集合体最大局所ピーキング係数は約１０％変化しているが本手法はこれを良く再現している。
【０１７５】
この手法では、集合体中性子束不連続因子のテーブルを準備する際にマルチ集合体詳細計算が不要であり、燃料集合体の各面の中性子束不連続因子を着目集合体の各面の関数として独立に計算すればよい。このように、本手法はマルチ集合体計算を要する前述の手法に比べて、テーブルの準備や参照が簡単であるという利点がある。
【０１７６】
拡散モデルとして、修正１群拡散モデルに基づく方法では、全炉心計算においては高速中性子束分布のみを解く。熱中性子束は炉心計算で得られた高速中性子束と、無限格子体系における「熱中性子束と高速中性子束の比（スペクトルインデクス）」とを用いて計算する。隣接集合体間でスペクトルインデクスが異なると、熱中性子の空間移動が生じるが、これによる熱中性子束の無限格子からの変化は、着目集合体と隣接集合体をそれぞれ均質化したノードからなる系に対して、拡散モデルを適用することにより計算される。
【０１７７】
修正１群ノード法では、この系の拡散方程式を解析的に解くことによりノード内の均質熱中性子束を求める。この方法の詳細は、例えば、文献 "Verification of LOGOS Nodal Method with Heterogeneous Burnup Calculations for a BWR core,"T.I wamoto et al.,Transaction of American Nuclear Society,vol.71,
p251,1994に記載されている。
【０１７８】
修正１群法においても、チャンネルボックス変形による熱中性子束変化は、着目集合体と隣接集合体をそれぞれ均質化したノードからなる系において、熱中性子束に対する境界条件に中性子束不連続因子を用いることで、前述の多群ノード法におけると同じ原理で計算できる。
【０１７９】
（ｄ）単一集合体中性子束不連続因子境界摂動モデル
中性子束不連続因子を用いる他の方法としては、境界摂動法と組み合わせたものである。これは、中性子束不連続因子を用いた拡散理論算に基づいて各集合体を均質化したノード境界面の中性子束および中性子流を計算するノード境界値計算手段を設け、水ギャップ幅の違いによる集合体不連続因子の差を利用して、集合体境界における中性子束および中性子流を求め、この境界値の無限格子からの変化とそれに対する集合体核特性の感度係数を用いて、集合体核特性の変化を計算する。これは、前述のように、中性子束不連続因子を用いた拡散ノード法は、集合体境界における中性子束および中性子流については精度が良いことに着目したものである。
【０１８０】
境界摂動法に基づき、集合体境界における摂動量として「中性子流／中性子束」を用いて集合体内局所ピーキングを計算する例が、文献 "A Boundary Condition Perturbation Method for Prediction of Pin Power Distribution in Light Water Reactor,"F.Rahnema et al.,Proceedings of Topical Meeting on Reactor Physics and Shielding,Chicago,1984 に記載されている。
【０１８１】
この手法では例えば、燃料棒（ｘ，ｙ）に対する集合体内局所出力ＬＰＦ（ｘ，ｙ）は、下記の（８）式により計算する。
【０１８２】
【数７】

【０１８３】
感度係数Ｆは、予め境界条件を変化させた単一集合体詳細計算あるいはマルチ集合体詳細計算により準備しておく。
【０１８４】
しかし、前記Rahnemaの文献においては、拡散理論に基づいて境界面での中性子流／中性子束を求める際に、集合体中性子束不連続因子が用いられていないため、オフセットバンドル隣接の場合のように水ギャップ近傍での局所的な中性子束分布変化による中性子流／中性子束の変化を計算することができない。
【０１８５】
そこで、ノード境界値ｒは前述の拡散ノード法の様に、着目集合体と隣接集合体をそれぞれ均質化したノードからなる系に対して、中性子束不連続因子を用いて多群の拡散ノード法を適用して求める。あるいは、修正１群差分法においてはノード境界熱中性子束は、経験的荷重因子を用いて隣接するノードのスペクトルインデクスと中性子束不連続因子から計算してもよい。この場合、ノードｍとノードｎの境界の熱中性子束Ψ_2nは、下記（９）式で示される。
【０１８６】
【数８】

【０１８７】
式（８）は集合体局所出力に関する境界摂動法による補正計算法を示すものであるが、他の集合体核特性量の補正計算も、それぞれの核特性量の中性子流／中性子束に対する感度係数を用い、同様な方法で計算することができる。
【０１８８】
燃料集合体が位置ずれしたまま燃焼が進むと、水ギャップ幅変化による集合体内の中性子スペクトル変化の履歴効果や燃焼度分布の効果が蓄積され、瞬時的に集合体が位置ずれした場合の効果との差が生じる。これは中性子スペクトル（熱中性子束の高速中性子束に対する比）が無限体系から変化することにより、ウランの燃焼遅れやプルトニウムの蓄積の増加が生じるためで、スペクトル履歴効果とよばれる。
【０１８９】
拡散ノード法では、マルチ集合体詳細計算による燃焼計算のようには、燃焼履歴効果を直接に考慮できない。拡散ノード法による炉心性能計算において、異なる中性子スペクトルを持つ燃料集合体が隣接した際のスペクトル干渉によるスペクトル履歴効果を補正する方法としては、例えば、特願平６−２１０２４３号「原子炉の炉心性能計算方法および装置」に記載されているように、炉心内での中性子スペクトルと無限格子体系でのスペクトルの比の燃焼度平均値であるスペクトル履歴をパラメータとして補正する手法がある。
【０１９０】
本発明では、この手法をオフセットバンドル隣接によるスペクトル履歴効果に応用し、水ギャップ幅の変化による熱中性子束分布の変化効果を補正した燃料集合体内における燃焼度分布およびスペクトル履歴分布を計算し、燃焼履歴効果による集合体平均核定数、燃料棒局所出力分布等の補正量を計算する。例えば、燃料棒局所出力については、集合体内の燃料棒位置（ｘ，ｙ）におけるスペクトル履歴ＳＨ（ｘ，ｙ）を、次の（１０）式で表す。
【０１９１】
【数９】

【０１９２】
ここで、Ｅは燃焼度、Ψ₂、Ψ₁はそれぞれオフセットバンドル隣接を考慮して計算された位置（ｘ，ｙ）での熱中性子束、高速中性子束であり、また∞は無限格子体系での値を示す。スペクトル履歴を考慮した局所出力分布ＬＰＦの補正は、熱群核分裂断面積Σに対するスペクトル履歴補正係数（∂Σ／∂ＳＨ）を用いることにより、次の（１１）式で与えられる。
【０１９３】
【数１０】

【０１９４】
同様に、オフセットバンドル隣接により、ノード内に燃焼度分布が生じることによる履歴効果についても、前記文献に示されるように、燃焼度に関する感度係数を用いて補正することができる。
【０１９５】
次に、チャンネルボックスの変形に対する第２の実施の形態について、説明する。チャンネルボックス変形を考慮した炉心核特性を精度良く計算するには、以下の［１］〜［５］の処理により達成する。
【０１９６】
［１］炉心性能計算によりチャンネルボックスの各面における高速中性子照射量または燃焼度を積算し、チャンネルボックスの対向する面における照射成長量を各面の高速中性子照射量または燃焼度の関数として計算し、チャンネルボックスの変形量を対向する面における照射成長量の差から計算する。
［２］着目集合体と隣接集合体におけるチャンネルボックス変形を考慮して、集合体平均核定数、燃料棒局所出力、中性子検出器位置熱中性子束、制御棒位置熱中性子束等の集合体核特性を計算する。
［３］チャンネルボックス変形量より上記の集合体核特性の変化を計算するには、以下のようなマルチ集合体詳細計算モデルまたは中性子拡散モデルに基づく。
【０１９７】
（ａ）マルチ集合体詳細２次元計算モデル
着目集合体と隣接集合体に対するマルチ集合体詳細２次元計算により、予め集合体平均核定数、燃料棒出力分布、燃料棒Ｒ因子分布などの集合体核特性変化量を直接、着目集合体の各面の水ギャップ幅の変形量のテーブルとして準備する。ここで、マルチ集合体詳細２次元計算とは集合体を小数体（通常４〜１６体）組み合わせて炉心の一部分を模擬した系に対して、各集合体の非均質性をそのまま考慮した詳細計算を行うことにより、着目集合体に対する隣接集合体の影響を詳細に評価する方法である。
【０１９８】
（ｂ）単一集合体中性子束不連続因子拡散モデル
チャンネルボックス変形量から集合体中性子束不連続因子の変化量を計算し、これより各集合体を均質化したノードに対して均質拡散モデルに基づいて集合体内熱中性子束分布を求め、この熱中性子束分布より核特性変化量を評価する。ここで、集合体不連続因子は、無限格子体系において、集合体の各面の平均中性子束の集合体平均中性子束に対する比として定義される。集合体中性子束不連続因子の変化量は予めチャンネルボックス変形量のテーブルとして、単一集合体詳細計算により準備する。また、均質拡散モデルとしては、多群ノード法、修正１群ノード法等を用いることができる。
【０１９９】
（ｃ）単一集合体中性子束不連続因子境界摂動モデル
集合体中性子束不連続因子を用いた均質拡散ノード法に基づいて各集合体を均質化したノード境界の中性子束と中性子流を求める。
【０２００】
無限格子体系において評価された、集合体境界での中性子束と中性子流の変化に対する集合体核特性の変化を感度係数として使用し、上記のノード境界の中性子束および中性子流から集合体核特性変化を計算する。
【０２０１】
均質拡散モデルとしては、多群ノード法、修正１群ノード法、修正１群差分法等を用いることができる。
【０２０２】
（ｄ）解析的拡散モデル
チャンネルボックス変形量から、水ギャップと燃料領域をそれぞれ均質化した２領域拡散モデルの解析解に基づいて集合体内熱中性子束分布の変化を求め、この熱中性子束分布より核特性変化量を評価する。
【０２０３】
［４］チャンネルボックス変形を考慮した限界出力比計算では、集合体内のＲ因子変化を直接求める他に、燃料棒出力変化からも計算することができる。
［５］チャンネルボックス変形に伴う燃焼履歴効果を、チャンネルボックス変形に伴う集合体内の燃焼度分布および熱中性子束の高速中性子束に対する比の燃焼度平均値として定義されるスペクトル履歴分布を用いて補正する。
【０２０４】
このように、この第２の実施の形態では、炉心性能計算によりチャンネルボックスの各面における高速中性子照射量あるいは燃焼度を積算するので、中性子照射によるチャンネルボックス変形量を予測評価して、チャンネルボックス変形を考慮した炉心核特性を計算することが可能となる。
【０２０５】
さらに、チャンネルボックス変形を考慮した炉心核特性の計算は、着目集合体と隣接集合体のチャンネルボックス変形量から、マルチ集合体詳細計算により準備したテーブルや拡散モデルに基づき計算し、またチャンネルボックス変形の履歴効果も考慮するから、核特性の変化を精度良く計算できる。
【０２０６】
また、従来は無視されていた、炉心の臨界固有値や炉内出力分布、炉内中性子検出器の計数値と検出器照射量、制御棒照射量等へのチャンネルボックス変形の影響も考慮できる。
【０２０７】
図６は、本発明の第２の実施の形態を示すブロック構成図である。炉内出力分布計算手段１９は炉心の状態データを入力して、炉内の中性子束分布と炉心固有値を拡散モデルに基づき計算するものである。拡散モデルとしては、例えば前述したJ.Wooly の文献に示されるような修正１群差分モデルや、K.Smithの文献に示されるような多群ノード法モデル等を用いる。炉内出力分布は中性子束分布を基に計算され、集合体断面平均出力が計算される。
【０２０８】
チャンネルボックス照射量計算手段２０では、この中性子束分布を基に、集合体のチャンネルボックスの各面における高速中性子照射量を計算する。ここで、面ｎにおける高速中性子束Ψ_nは、多群拡散ノード法ではあらわに計算され、また修正１群差分モデルでは着目集合体と周辺の集合体のノード平均中性子束を多項式を用いて内外挿することにより計算できる。これにより高速中性子照射量φは、高速中性子束を時間積分することにより（１２）式のように計算できる。ここで、ｄｔは時間幅である。
【０２０９】
【数１１】

【０２１０】
チャンネルボックス変形量計算手段２１では、各面の高速中性子照射量を用いて、中性子照射によるチャンネルボックスの変形量を照射成長モデルを用いて評価する。評価方法としては、チャンネルボックスの対向する面における軸方向の照射成長量から計算できる（請求項２５）。
【０２１１】
チャンネルボックス変形量計算方法では、対向する２面Ａ、Ｂにおける照射成長量の差に伴い、チャンネルボックスの軸方向の曲がりが一様な曲率を持つとしてチャンネルボックス変形量を解析的に計算する（請求項３３）。すなわち、図７に示されるように、チャンネルボックスの面Ａ、Ｂの軸方向平均の高速中性子照射量をそれぞれφ_A、φ_Bとし、チャンネルボックスの軸（Ｚ）方向の曲がりの曲率は、曲がりが小さいとして、下記の（１３）式で示される。そして、軸方向高さＺでの曲がり量は（１３）式を積分して、（１４）式のように示される。従って、上下端を固定した場合の曲がり量は（１５）式で表される。また、照射成長関数は（１６）式および（１７）式のように示される。この関数形の一例を図８に示す。
【０２１２】
【数１２】

【０２１３】
ここで、ａ、ｂ、ｃ、ｄ、ｅはフィッティング係数である。本係数は実験式から求めることができる。また本係数は、チャンネル製造時の残留応力の開放によるランダムな曲がり、ジルカロイの照射成長のばらつき等に依存する誤差を補正するために、過去におけるチャンネルボックス変形量の実測値を用いて決定してもよい。
【０２１４】
チャンネルボックス変形量の計算方法としては、上記（１５）式の解析的手法とは別に有限要素法に基づく手法もある。図９に示すように、チャンネルを軸方向ノードに分割し、各ノードｉ毎にチャンネルの向かい合う両Ａ、Ｂの照射成長後の長さｌＡⁱ、ｌＢⁱを求める。このノードを軸方向に積み重ねた後、チャンネルのＡ面またはＢ面の上下端を結ぶ直線と各ノード間の距離を曲がり量δⁱとして求めることができる。
【０２１５】
なお、照射成長を引き起こす高速中性子はエネルギ１ＭｅＶ以上の中性子であり、炉心性能計算で与えられる全高速中性子とは必ずしも一致しない。そこで、高速中性子照射量計算に用いる高速中性子の全高速中性子に占める割合ｆを、下記の（１８）式のように、燃焼度Ｅとボイド率Ｖのテーブルとして計算することができる。
【０２１６】
【数１３】

【０２１７】
また、この第２の実施の形態では、高速中性子照射量と燃焼度が一対一で対応することを用いた照射成長モデルを用いて炉心性能計算装置を構成する。この場合、図１のチャンネルボックス照射量計算手段２０に代えて、燃焼度分布計算手段を設ける。
【０２１８】
次に、燃焼度分布計算手段における集合体のチャンネルボックスの各面における燃焼度の計算方法について説明する。ここで、面ｎにおける燃焼度Ｅｎは、多群拡散ノード法ではノード内出力分布があらわに計算されることから、チャンネルボックス位置における出力密度を時間積分することにより計算される。また修正１群差分モデルでは着目集合体および周辺の集合体のノード平均燃焼度を多項式を用いて内外挿することにより計算できる。
【０２１９】
燃焼度を用いたモデルでは、中性子照射によるチャンネルボックスの照射成長歪み量を各面の燃焼度Ｅの関数として、例えば次の（１９）式および（２０）式のように計算することができる。
【０２２０】
【数１４】

【０２２１】
ここで、ａ、ｂ、ｃ、ｄ、ｅはフィッティング係数である。本係数は実験式から求めることができる。また本係数は、チャンネル製造時の不確定さ等に依存する誤差を補正するために、過去におけるチャンネルボックス変形量の実測値を用いて決定してもよい。図１０にε（Ｅ）の関数形の一例を示す。
【０２２２】
次に、炉内出力分布再計算手段２２では、上述のようにしてチャンネルボックス変形量計算手段２１により評価したチャンネルボックス変形量を用いて、チャンネルボックス変形効果を補正した集合体核定数および中性子束不連続因子を計算し、これを用いて、炉心の臨界固有値、炉内出力分布、燃料集合体断面平均出力分布を再計算する。
【０２２３】
綿出力密度計算手段２３では、炉心の熱的制限値として、チャンネルボックス変形効果を補正した燃料棒局所出力分布により与えられる集合体の最大局所出力ピーキング係数と炉心内出力分布計算による集合体断面平均出力を用いて、各燃料集合体断面の最大線出力密度を計算する。なお、チャンネルボックス変形効果を補正した燃料棒局所出力分布の中から集合体の最大局所出力ピーキング係数を求めるかわりに、精度は低下するが、集合体の最大局所出力ピーキング係数に対して直接にチャンネルボックス変形効果を補正してもよい。
【０２２４】
また、限界出力比計算手段２４では、チャンネルボックス変形を考慮した燃料棒Ｒ因子分布の中から求めた集合体最大Ｒ因子と、集合体平均出力を用いて、各燃料集合体の燃料棒の焼損の監視指標である限界出力比を計算する。なお、燃料棒Ｒ因子分布は前述の燃料棒局所出力分布から計算することも可能である。また、チャンネルボックス変形効果を補正した燃料棒Ｒ因子分布の中から集合体の最大Ｒ因子を求める代わりに、精度は低下するが、集合体の最大Ｒ因子に対して直接にチャンネルボックス変形効果を補正してもよい。
【０２２５】
これらの線出力密度、限界出力比等の計算においては、計算に用いる燃料集合体平均出力として、チャンネルボックス変形量を補正した核定数を用いて再計算された燃料集合体平均出力を用いることにより精度を向上することができる。
【０２２６】
次に、炉内中性子束計測器計数値計算手段２５では、チャンネルボックス変形を考慮した炉内中性子計測器位置における熱中性子束を用いて、炉内中性子検出器計数値と照射量とを計算する。炉内中性子束検出器として可動型炉内中性子束検出器（ＴＩＰ）の場合の計数の計算法の一例が前述のWoolyの文献に記載されている。また、検出器照射量は炉内中性子計測器位置における熱中性子束の時間積分で与えられる。
【０２２７】
図６には示されていないが、チャンネル変形を補正した炉内中性子検出器計数値の計算値の実測値に対する誤差を、前記Tuikiの文献の手法等に基づいて学習することにより、炉内出力分布計算値を補正することもできる。また、制御棒照射量計算手段２６では、チャンネルボックス変形効果を補正した制御棒位置熱中性子束の時間積分により制御棒照射量を計算する。
【０２２８】
次に、チャンネルボックス変形効果を補正した集合体平均核定数、集合体不連続因子、燃料棒局所出力、燃料棒Ｒ因子、中性子計測器位置における熱中性子束等を計算する３つの異なる手法について詳細に説明する。
【０２２９】
（ａ）マルチ集合体詳細２次元計算モデル
まず、手法１として、着目集合体および隣接集合体のチャンネルボックス変形量に対する集合体平均核定数、燃料棒局所出力、燃料棒Ｒ因子、中性子計測器位置における熱中性子束等の核特性変化をテーブルまたはフィッティング式として準備しておき、チャンネルボックス変形効果を補正した燃料集合体内の核特性変化を直接的に計算する。着目集合体および隣接集合体のチャンネルボックス変形量に対する着目集合体の特性量の変化のテーブルまたはフィッティング式は、マルチ集合体２次元詳細計算により評価する。
【０２３０】
ここで、マルチ集合体詳細２次元計算とは集合体を小数体（通常４〜１６体）組み合わせて炉心の一部分を模擬した系に対して、各集合体の非均質性をそのまま考慮した詳細計算を行うことにより、着目集合体に対する隣接集合体の影響を詳細に評価する方法である。
【０２３１】
このテーブルないしフィッティング式は着目集合体の各面の変形量のみならず、隣接する集合体の隣接面の変形量の関数であり、一般には多変量の組み合わせに対する複雑な関数である。これに対して、特開平４−１１０６９８号公報のものでは、単に燃料集合体の位置ずれ量から計算するとのみ記述されており、評価方法が全く明確ではない。本手法では、この関数を着目集合体のチャンネルボックス各面に対する水ギャップ幅のテーブルとして整理する。このテーブルも、各面の水ギャップ幅に対する多変量関数（４変量関数）となるが、比較的簡単な参照法としては例えば次のような方法が考えられる。
【０２３２】
まず、第１ステップとして、着目集合体に隣接する集合体のチャンネルボックス変形が無いと仮定し、着目集合体のチャンネルボックス２ｂだけが変形した場合を考える。図１１に示すように、着目集合体のチャンネルボックス２ｂのｘ方向左側における水ギャップ変形量δｘｌ（ｉ）とｘ方向右側における水ギャップ変形量δｘｒ（ｉ）の大きさが等しく（絶対値が等しく符号が反対）δｘであるとする。同様に、着目集合体チャンネルボックス２ｂのｙ方向上側における水ギャップ変形量δｙｔ（ｉ）とｙ方向下側における水ギャップ変形量δｙｂの大きさが等しくδｙであるとする。チャンネルボックスの変形による集合体核特性変化をｖ（δｘ，δｙ）の形式の２次元テーブルないしフィッティング式として整理し、また参照する。
【０２３３】
次に第２ステップとして、着目集合体に隣接する集合体チャンネルボックスの隣接面の変形による水ギャップ幅の変化による影響を考慮し補正する。図１１では変形後のチャンネルボックスの位置を点線で示している。この場合、例えば着目集合体チャンネルボックス２ｂのｘ方向左側における水ギャップ変形量δｘｌは、着目集合体チャンネルボックス２ｂの左面と左側隣接集合体チャンネルボックス２ａの右面の変形量δｘｒ（ｉ−１）との和となる。ｘ方向右側における水ギャップ変形量δｘｒについても同様である。
【０２３４】
両隣の集合体チャンネルボックスの変形量は一般に異なるから、両隣の集合体チャンネルボックスの変形を考慮に入れると、δｘｌ（ｉ）≠δｘｒ（ｉ）となる。ここで、ｄｘ＝δｘｌ−δｘｒとする。ｙ方向も同様に、ｄｙ＝δｙｔ−δｙｂとする。そこで、前記テーブルはまず、ｖ（δｘｌ、δｙｔ）として参照し、これに対する補正量をｗ（ｄｘ，ｄｙ）として整理し、また参照する。最終的に核特性変化はｖ＋ｗで与えられる。
【０２３５】
図１２に、δｘ＝δｙおよびδｙ＝０の場合の集合体最大局所ピーキング係数のδｘに対する関数形の一例を示している。また、図１３に、ｄｘ＝ｄｙおよびｄｙ＝０の場合の集合体最大局所ピーキング係数の補正量のｄｘに対する関数形の一例を示す。
【０２３６】
（ｂ）単一集合体中性子束不連続因子拡散モデル
次に、手法２について説明する。この手法２では、着目集合体および隣接集合体のチャンネルボックス変形量から集合体中性子束不連続因子の変化量を計算し、各集合体を均質化した系に対して、中性子束不連続因子を用いた拡散ノード法により集合体内中性子束分布を求め、この中性子束分布より集合体核特性変化量を評価する。ここで、集合体中性子束不連続因子は、無限格子体系において、集合体の各面の平均中性子束の集合体平均中性子束に対する比として定義される。
【０２３７】
不連続因子を用いた多群拡散ノード法計算法については、前述のように、文献"Assembly Homogenization Techniques for Light Water Reactor Analysis,"K.S.Smith,Progress in Nuclear Energy,vol.17,p303,1986に記載されている。また、ノード法計算により得られる中性子束分布を用いて、集合体内の局所出力分布を計算する方法の一例は、"SIMULATE‐3 Pin Power Reconstruction Methodology and Benchmarking,"K.R.Rempe et.al,Proceedings of International Reactor Physics Conference,III-19,Jackson Hole,1988 に記載されている。
【０２３８】
チャンネルボックスが変形すると水ギャップ幅変化により集合体内中性子束分布が変化するため、集合体中性子不連続因子も変化する。上記K.Smithの文献に示されるように、中性子束不連続因子は、拡散ノード法において、集合体をそれぞれ均質化したノードの境界における中性子束に対する境界条件を与える。すなわち、例えば着目集合体ｎと隣接集合体ｍのｘ方向境界において、中性子束に対する（２）式の境界条件を与える。ここで、（２）式において、ｆは境界面の中性子束不連続因子、Ψは境界面における中性子束を表す。
【０２３９】
着目集合体と隣接集合体が無限格子体系において同じ格子タイプであれば、中性子不連続因子も等しく、上記の境界条件は単に中性子束の連続性を表すにすぎない。しかし、チャンネルボックス変形により、隣接する集合体間の隣接面における中性子不連続因子ｆが異なると、上記の境界条件に基づいてノード境界に中性子の仮想ソースが生じるため、集合体不連続因子の違いからチャンネルボックス変形による集合体内の中性子束分布の変化が計算できる。多群拡散ノード法では、中性子束不連続因子を用いた熱中性子束に対する全炉心計算により、ノード平均熱中性子束および、ノード境界熱中性子束が与えられる。
【０２４０】
次に、ノード平均中性子束、ノード境界中性子束等を用いて、均質化した集合体内の中性子束分布を展開計算することができる。一例として、前記K.Rempeの文献では、均質化した集合体ノード内の熱中性子束Ψ₂の２次元分布を（３）式の形式で展開している。ここで、（３）式において、Ψ₁は高速中性子束であり、ｃ_iは展開係数、ｆ_iはｓｉｎｈ、ｃｏｓｈ関数である。
【０２４１】
均質化された集合体内の熱中性子束分布が求まれば、これに無限格子計算で得られた非均質な中性子束分布を合成することにより、集合体内の非均質熱中性子束分布が計算できる。非均質中性子束分布の関数である集合体平均核定数や、燃料棒局所出力分布はこれより直ちに計算できる。燃料棒Ｒ因子分布は燃料棒局所出力分布より計算できる。
【０２４２】
集合体の各面におけるチャンネルボックス変形量に対する集合体中性子束不連続因子の変化量は、予め単一集合体詳細計算（無限格子計算）によりチャンネルボックス変形量のテーブルとして準備する。熱中性子束に対する集合体不連続因子の水ギャップ幅変化δｘに対する関数形の一例を図１４に示す。
【０２４３】
本手法の計算精度を示す例として、チャンネルボックス変形の局所出力分布への影響を示した図２１と同様に、着目集合体のチャンネルボックスがｘ，ｙ方向に２ｍｍづつ変形し、隣接集合体には変形が無いとした場合、すなわちδｘ＝δｙ＝２ｍｍの場合の、集合体内局所出力分布を本手法により計算し、マルチ集合体詳細計算による参照解と比較した結果は、図５に示す場合と同様になる。燃料棒局所出力計算法は前記K.Rempeの文献に記載されているものと基本的に同様の手法を用いたが、熱中性子束分布の変化に対して前述の集合体の非均質性の補正を加えた。参照計算によれば、チャンネルボックス変形により集合体最大局所ピーキング係数は約１０％変化しているが本手法はこれを良く再現している。
【０２４４】
この手法では、チャンネルボックス変形量から集合体中性子束不連続因子の変化量のテーブルを準備する際にマルチ集合体詳細計算が不要であること、また着目集合体および隣接集合体のチャンネルボックス変形量から集合体核特性の変化を計算する際には、燃料集合体の各面の中性子束不連続因子を着目集合体のチャンネルボックス各面の変形量のみの関数として独立に計算すればよい。このように、手法２は手法１に比べて、テーブルが各面の変位量の組み合わせによらず、テーブルの準備や参照が簡単であるという利点がある。
【０２４５】
拡散モデルとして、修正１群拡散モデルに基づく方法では、全炉心計算においては高速中性子束分布のみを解く。熱中性子束は炉心計算で得られた高速中性子束と、無限格子体系における「熱中性子束と高速中性子束の比（スペクトルインデクス）」を用いて計算する。隣接集合体間でスペクトルインデクスが異なると、熱中性子の空間移動が生じるが、これによる熱中性子束の無限格子からの変化は、着目集合体と隣接集合体をそれぞれ均質化したノードからなる系に対して、拡散モデルを適用することにより計算される。修正１群ノード法では、この系の拡散方程式を解析的に解くことによりノード内の均質熱中性子束を求める。この方法の詳細は例えば文献"Verification of LOGOS Nodal Methodwith Heterogeneous Burnup Calculations for a BWR core,"T.lwamoto et al.,Transaction of American Nuclear Society,vol.71,p251,1994に記載されている。
【０２４６】
修正１群法においても、チャンネルボックス変形による熱中性子束変化は、着目集合体と隣接集合体をそれぞれ均質化したノードからなる系において、熱中性子束に対する境界条件に中性子束不連続因子を用いることで、前述の多群ノード法におけると同じ原理で計算できる。なお、熱中性子束および熱中性子流は、拡散方程式を解く代わりに、よく知られているように経験的荷重因子を用いて、隣接するノードのスペクトルインデクスから計算することもできる。
【０２４７】
（ｃ）単一集合体中性子束不連続因子境界摂動モデル
中性子束不連続因子を用いる他の方法としては、境界摂動法と組み合わせたものを用いる。この手法では水ギャップ幅の違いによる集合体不連続因子の差を利用して、集合体境界における中性子束および中性子流を求め、この境界値の無限格子からの変化とそれに対する集合体核特性の感度係数を用いて、集合体核特性の変化を計算する。これは、前述のように、中性子束不連続因子を用いた拡散ノード法は、集合体境界における中性子束および中性子流については精度が良いことに着目したものである。
【０２４８】
境界摂動法に基づき、集合体境界における摂動量として「中性子流／中性子束」を用いて集合体内局所ピーキングを計算する例が、文献"A Boundary Condition Ferturbation Method for Prediction of Pin Power Distribution in Light Water Reactors,"F.Rahnema et a1.,Proceedings of Topical Meeting on Reactor Physics and Shielding・Chicago,1984に記載されている。
【０２４９】
この手法では、例えば、燃料棒（ｘ，ｙ）に対する集合体内局所出力ＬＰＦ（ｘ，ｙ）は、前述の（８）式より計算する。（８）式での感度係数Ｆは、予め境界条件を変化させた単一集合体詳細計算あるいはマルチ集合体詳細計算により準備しておく。
【０２５０】
しかし、前記Rahnemaの文献においては、拡散理論に基づいて境界面での中性子流／中性子束を求める際に、集合体中性子束不連続因子が用いられていないため、オフセットバンドル隣接の場合のように水ギャップ近傍での局所的な中性子束分布変化による中性子流／中性子束の変化を計算することができない。
【０２５１】
本発明では、ノード境界値ｒは前述の拡散ノード法の様に、着目集合体と隣接集合体をそれぞれ均質化したノードからなる系に対して、中性子束不連続因子を用いて多群の拡散ノード法を適用して求めることができる。あるいは、修正１群差分法においてはノード境界熱中性子束は、経験的荷重因子を用いて隣接するノードのスペクトルインデクスと中性子束不連続因子から計算してもよい。この場合、ノードｍとノードｎの境界の熱中性子束Ψ_2nは、前述の（９）式で示される。
【０２５２】
前述の（８）式は集合体局所出力に関する境界摂動法による補正計算法を示すものであるが、他の集合体核特性量の補正計算も、それぞれの核特性量の中性子流／中性子束に対する感度係数を用い、同様な方法で計算することができる。
【０２５３】
（ｄ）解析的拡散モデル
次に、手法３について説明する。この手法３は、手法２で拡散ノード法を用いて集合体内の熱中性子束を求めるかわりに、着目集合体および隣接集合体のチャンネルボックス変形量から拡散方程式に対する解析的モデルに基づいて集合体内の熱中性子束分布の変化を求め、この熱中性子束分布より、核特性変化量を評価するものである。この手法３では、例えば水ギャップおよびチャンネルボックス内部の燃料領域をそれぞれ均質化した２領域の１次元体系について、水ギャップ幅を与えた時の中性子束分布を解析的に計算する。
【０２５４】
このとき、ｘ方向１次元拡散モデルによる水ギャップ変化による燃料領域の熱中性子束変化の解析式は、前述の（１）式で与えられる。（１）式において、ｘは集合体境界からの距離、κは熱中性予拡散距離の逆数、ａは水ギャップ変化幅である。集合体内熱中性子束分布の変化は、ｘ方向およびｙ方向の１次元分布の積δΨ（ｘ）δΨ（ｙ）により近似できる。この手法３は、解析モデルに基づくため予めテーブルの準備をしておく必要がないという利点がある。
【０２５５】
集合体が位置ずれしたまま燃焼が進むと、水ギャップ幅変化による集合体内の中性子スペクトル変化の履歴効果や燃焼度分布の履歴効果が蓄積され、瞬時的に集合体が位置ずれした場合の効果との差が生じる。中性子スペクトル（熱中性子束の高速中性子束に対する比）が無限体系から変化することにより、ウランの燃焼遅れやプルトニウムの蓄積の増加が生じる現象はスペクトル履歴効果とよばれる。また、集合体内の燃焼度分布によりウランの燃焼遅れ等が生じる効果を片燃え効果と呼ぶ。これらの効果は一般的に瞬時効果を相殺する方向に働くため、熱的制限値計算において過度のマージンをとらないためには、これらの効果を適切に考慮する必要がある。
【０２５６】
チャンネルボックス変形量は集合体の燃焼とともに増加し、チャンネル変形によるスペクトル変化も燃焼とともに変化する。このため、チャンネル変形の燃焼履歴効果を、マルチ集合体による詳細燃焼計算では評価する場合には、燃焼ステップ毎に変形量を変化させればよいが、計算の複雑さが増加する。
【０２５７】
これを避けるためには、マルチ集合体計算では瞬時効果のみを評価し、スペクトル履歴効果および片燃え効果については、炉心性能計算で補正する方法がある。不連続因子を用いた拡散ノード法の場合も、チャンネル変形効果は瞬時的効果としてしか計算できないから、スペクトル履歴効果および片燃え効果については、炉心性能計算で補正する。
【０２５８】
炉心性能計算において、異なる中性子スペクトルを持つ燃料集合体が隣接した際のスペクトル干渉によるスペクトル履歴効果を補正する方法としては、例えば、特願平６−２１０２４３号「原子炉の炉心性能計算方法および装置」に記載されているように、炉心内での中性子スペクトルと無限格子体系でのスペクトルの比の燃焼度平均値であるスペクトル履歴をパラメータとして補正する手法がある。
【０２５９】
そこで、本発明では、この手法をチャンネルボックス変形によるスペクトル履歴効果に応用し、チャンネルボックスの変形効果を補正した燃料集合体内における燃焼度分布およびスペクトル履歴分布を計算し、チャンネル変形の燃焼履歴効果による集合体平均核定数、燃料棒局所出力分布等の補正量を計算する。例えば燃料棒局所出力については、集合体内の燃料棒位置（ｘ，ｙ）におけるスペクトル履歴ＳＨ（ｘ，ｙ）を、前述の（１０）式で表す。（１０）式において、Ｅは燃焼度、Ψ₂、Ψ₁はそれぞれチャンネルボックス変形を考慮して計算された位置（ｘ，ｙ）での熱中性子束、高速中性子束であり、また∞は無限格子体系での値を示す。スペクトル履歴を考慮した局所出力分布ＬＰＦの補正は、熱群核分裂断面積Σに対するスペクトル履歴補正係数（∂Σ／∂ＳＨ）を用いることにより、前述の（１１）式で与えられる。
【０２６０】
同様に、チャンネル変形による熱中性子束分布変化によりノード内に燃焼度分布が生じることによる履歴効果についても、前記文献に示されるように、燃焼度に関する感度係数を用いて補正することができる。
【０２６１】
【発明の効果】
以上述べたように、本発明の炉心性能計算装置によれば、Ｄ格子バンドルとオフセットバンドルが隣接することによる効果を考慮した炉心核特性の計算は、Ｄ格子バンドルとオフセットバンドルとの組み合わせに応じたマルチ集合体詳細計算により予め用意された補正テーブル、あるいは集合体不連続因子を用いた拡散ノード法、または解析的拡散モデルに基づき計算するから、炉心の臨界固有値や炉内出力分布、最大線出力密度、限界出力比、炉内中性子検出器計数と検出器照射量、制御棒照射量等を精度良く計算できるというすぐれた効果を奏する。
【０２６２】
また、高速中性子照射によるチャンネルボックス変形に対して、炉心出力分布計算によりチャンネルボックスの各面における高速中性子照射量を積算し、照射成長モデルに基づいて中性子照射によるチャンネルボックス変形量を予測評価できるので、チャンネルボックス変形を考慮した炉心核特性を計算することが可能となる。さらに、チャンネルボックス変形を考慮した炉心核特性の補正計算は、着目集合体と隣接集合体のチャンネルボックス変形量より、マルチ集合体詳細計算により予め用意された補正テーブルあるいは拡散モデルに基づき、チャンネル変形履歴効果も補正して計算するから、炉心の臨界固有値や炉内出力分布、最大線出力密度、限界出力比、炉内中性子検出器計数と検出器照射量、制御棒照射量等を精度良く計算できるというすぐれた効果を奏する。
【図面の簡単な説明】
【図１】本発明の第１の実施の形態を示すブロック構成図。
【図２】Ｄ格子バンドルとオフセットバンドルとの組み合わせパターンを示す説明図。
【図３】オフセットバンドル隣接体系における局所ピーキング係数の燃焼度依存性の一例を示す特性図。
【図４】チャンネルボックスのオフセット量と集合体中性子束不連続因子の関係を示す特性図。
【図５】本発明の第１の実施の形態による局所出力分布計算の効果を示す説明図。
【図６】本発明の第２の実施の形態を示すブロック構成図。
【図７】照射成長によるチャンネルボックスの軸方向の曲がり量の評価モデルを示した説明図。
【図８】高速中性子照射による照射成長関数の一例を示す特性図。
【図９】照射成長によるチャンネルボックスの軸方向の曲がり量を有限要素法で求める場合の説明図。
【図１０】燃焼度による照射成長関数の一例を示す特性図。
【図１１】本発明の第２の実施の形態におけるチャンネル変形量と水ギャップ変形量との関係を示す説明図。
【図１２】着目集合体の水ギャップ幅変形量（δｘ＝δｙおよびδｙ＝０の場合）に対する最大燃料棒局所出力の変化例を示す特性図。
【図１３】隣接集合体の水ギャップ幅変形量（ｄｘ＝ｄｙおよびｄｙ＝０の場合）に対する最大燃料棒局所出力の変化例を示す特性図。
【図１４】着目集合体の水ギャップ幅変形量に対する集合体中性子束不連続因子の変化例を示す特性図。
【図１５】沸騰水型原子炉の燃料集合体の一部切欠き斜視図。
【図１６】沸騰水型原子炉の燃料集合体における水ギャップの位置関係の説明図。
【図１７】Ｄ格子バンドルの説明図。
【図１８】制御棒まわりの２体がオフセットバンドルに置き換えられた状態を示す説明図。
【図１９】オフセットバンドル隣接による集合体内局所出力分布の変化の一例を示した説明図。
【図２０】高速中性子照射によるチャンネルボックスの軸方向の曲がりを示した説明図。
【図２１】チャンネルボックスの変形による水ギャップの位置関係を示した説明図。
【符号の説明】
１ 燃料集合体
２ チャンネルボックス
３ 燃料棒
４ 水ギャップ
５ 制御棒
６ 計装管
１１ 集合体平均核定数計算手段
１２ 炉内出力分布計算手段
１３ 局所出力分布計算手段
１４ 線出力計算手段
１５ 限界出力比計算手段
１６ 炉内中性子束計測器計数値計算手段
１７ 炉内出力分布補正手段
１８ 制御棒照射量計算手段
１９ 炉内出力分布計算手段
２０ チャンネルボックス照射量計算手段
２１ チャンネルボックス変形量計算手段
２２ 炉内出力分布再計算手段
２３ 線出力密度計算手段
２４ 限界出力比計算手段
２５ 炉内中性子束計測器計数値計算手段
２６ 制御棒照射量計算手段[0001]
BACKGROUND OF THE INVENTION
The present invention relates to a core performance calculation apparatus in a boiling water reactor.
[0002]
[Prior art]
The core of a boiling water reactor is configured after a plurality of fuel assemblies (bundles) are inserted. FIG. 15 is a partially cutaway perspective view of the fuel assembly 1. As shown in FIG. 15, the fuel assembly 1 is configured by bundling a plurality of fuel rods 3 in a channel box 2. In the core, cooling water enters from the lower part of the core, so that in the channel box 2, the cooling water flows from the lower direction to the upper direction. The cooling water flows between the fuel rods 3 in the channel box 2, receives heat from the fuel during that time, boils and exits from the upper part of the core.
[0003]
FIG. 16 is an explanatory diagram of the arrangement of the fuel assemblies 1 in the core. As shown in FIG. 16, a water gap 4 for flowing non-boiling cooling water exists between channel boxes 2 a to 2 d of four adjacent fuel assemblies 1. Control rods 5 are provided as necessary at the positions of the water gaps 4 at the corners sandwiched between the channel boxes 2a to 2d of the four fuel assemblies 1, and the water gaps 4 at the corners at the diagonal positions are provided. Is provided with an instrumentation tube 6 for the in-core neutron flux measuring instrument.
[0004]
Here, as shown in FIG. 17, the initial boiling water reactor is a so-called D lattice in which the water gap width LW on the control rod 5 side is wider than the water gap width LN on the in-core neutron flux instrumentation tube side. A fuel core is used. Such a D-lattice fuel assembly has a large neutron moderation effect in a wide water gap LW (hereinafter referred to as a wide gap), so that the thermal neutron flux on the wide gap LW side is narrower than that on the narrow water gap LN (hereinafter referred to as narrow gap) side. As a result, the thermal neutron flux distribution in the fuel assembly 1 becomes asymmetric. For this reason, in order to flatten the fuel rod local power distribution, it is necessary to reduce the enrichment of the fuel rod 3 on the wide gap LW side and increase the enrichment on the narrow gap LN side.
[0005]
Thus, if the enrichment distribution is not symmetrical, for example, when the channel box shakes during an earthquake, the thermal neutron flux distribution may shift to the highly enriched side due to the change in the water gap width. In such a case, reactivity may be applied, leading to scram. In order to avoid this, it is conceivable to make the widths of the wide gap LW and the narrow gap LN closer to each other in the D lattice fuel core. This is realized by decentering the center of the channel box 2 of the D lattice bundle to the control rod 5 side within a range not interfering with the control rod 5. The D lattice bundle in which the center of the channel box 2 is eccentric to the control rod 5 side is called an offset bundle.
[0006]
This offsetting is realized by replacing the D lattice bundle with the offset bundle step by step for each cycle. FIG. 18 shows a stage where the two D lattice bundles surrounding the control rod 5 are offset bundled. In FIG. 18, the channel boxes 2b and 2c of the fuel assembly 1 are offset.
[0007]
In the core performance calculation in the nuclear reactor, the neutron flux distribution and power distribution in the core are calculated based on the three-dimensional nuclear thermal-hydraulic coupled physical model of the core. The fuel rod power normalized by the cross section of the assembly is called local power, and the thermal limit value of the core is calculated from the average power of the cross section of the assembly and the local power of the fuel rod. The maximum line power density of the assembly is defined by the product of the maximum fuel rod local power peaking coefficient of the assembly cross section and the assembly cross-section average output. Further, the limit power ratio, which is a monitoring index of burnout of the fuel rods, is calculated as a function of the fuel rod R-factor representing the pattern of local power distribution around each fuel rod, the assembly average power, and the channel flow rate. .
[0008]
The calculation method of these thermal limit values is described in, for example, the document “Three-dimensional BWR core simulator,” J.A. Wooly, Licensing topic a1 report, NEDO-20953, 1976, General E1ectric Company.
[0009]
In order to improve the accuracy of the three-dimensional nuclear thermal-hydraulic coupled physical model of the core, for example, the document "TARMS: An on-Line Boiling Water Reactor Management System Based on Core Physics Simulator," M. Tsuiki et al., Proceedings As described in of a topical meeting on Advances in Reactor Computations, Salt Lake City, 1983, the measured and calculated values of the neutron flux detector in the core are used to correct the neutron flux distribution in the core. The accuracy is improved.
[0010]
Furthermore, in the core performance calculation, the irradiation amount of the neutron detector is integrated in order to monitor the life of the neutron detector. Similarly, in order to monitor the life of the control rod, the amount of control rod irradiation is integrated.
[0011]
In the core three-dimensional calculation, the core average eigenvalue for the homogenized node of each assembly is used, and the core core core eigenvalues, the in-core neutral flux distribution, and the in-core power distribution are determined by the coarse mesh node method based on the neutron diffusion theory. Calculate The aggregate average nuclear constant is generally calculated by detailed calculation in an infinite lattice system to which a reflection boundary condition is applied at the boundary of each aggregate. In a normal core, the water gap width of the adjacent surface of the aggregate of interest and the adjacent aggregate is the same, so the infinite lattice calculation using the reflection boundary condition is a good approximation.
[0012]
[Problems to be solved by the invention]
However, when the D lattice bundle and the offset bundle are adjacent to each other, the water gap widths of the adjacent surfaces are different, so that the approximation of the reflection boundary condition in the infinite lattice system when the respective node average nuclear constants are calculated becomes worse. This is because the distribution of the thermal neutron flux locally changes in the vicinity of the water gap due to the change in the water gap width, resulting in a change in the aggregate nuclear characteristics. It should be noted that the fast neutron flux hardly changes, and it can be said that the change in the aggregate nucleus characteristics is almost caused by the change in the vicinity of the water gap of the thermal neutron flux. This change occurs in both adjacent D-lattice bundles and offset bundles.
[0013]
If the offset amount is large, the effect on the core characteristics will be large.In the core performance calculation, the core critical eigenvalue, the reactor power distribution, the fuel rod power distribution in the reactor, the thermal limit value, the neutron detector count value, In order to monitor the performance of the core, it is necessary to consider the thermal neutron flux change at the control rod position.
[0014]
As shown in FIG. 18, in the example of the nuclear property change by the offset bundle, consider a case where two offset bundles, each having a channel box center offset by 2 mm toward the control rod, are loaded around the control rod. FIG. 19 shows the characteristics of the local power distribution in the assembly in the D lattice bundle in this case compared with the fuel rod local power distribution of the infinite lattice system. In FIG. 19, the upper part shows a mixed system, the middle part shows an infinite lattice system, and the lower part shows the difference.
[0015]
In this case, the local output distribution of the reference solution was evaluated by multi-aggregate inhomogeneous calculation. Adjacent offset bundles will substantially reduce the wide gap of the D lattice bundle and increase the narrow gap. According to the reference solution, the maximum local peaking coefficient of the D-lattice bundle changes by about 10% due to the adjacency of the offset bundle, and the importance of core monitoring in consideration of the adjacency effect with the offset bundle is shown. Has been.
[0016]
On the other hand, a similar problem occurs when the channel box 2 is deformed by fast neutron irradiation. That is, the channel box 2 is made of, for example, a zirconium alloy. The upper and lower ends of the fuel rod are supported by the upper tie plate and the lower tie plate. The fuel assembly 1 is under conditions of high temperature, high pressure and high radiation, and the channel box 2 is deformed by fast neutron irradiation.
[0017]
If there is a difference in the amount of fast neutron irradiation between the surfaces of the opposing channel box 2, as shown in FIG. 20, a difference occurs in the amount of irradiation growth in the axial direction of the channel box 2, so that bending occurs in the axial direction. FIG. 20 shows a state in which bending occurs in the axial direction due to irradiation growth of the channel box 2 by fast neutron irradiation.
[0018]
Thus, when the channel box 2 is bent, as shown in FIG. 21, the width of the water gap 4 of the fuel assembly 1 changes from the normal width. Therefore, mechanically, there is an effect that the control rod 5 is prevented from being inserted into the water gap 4.
[0019]
When the channel box of the target assembly and the adjacent assembly is bent due to irradiation growth, the width of the water gap between adjacent fuel assemblies changes from the normal width, which changes the nuclear characteristics of the fuel assembly. Arise. Therefore, in the core performance calculation, it is important to consider the core performance change due to the channel box deformation in monitoring the core performance.
[0020]
That is, when the channel box of the target assembly and the adjacent assembly is bent due to irradiation growth, the width of the water gap between the adjacent fuel assemblies changes from the normal width. When the gap width changes, the neutron moderation effect and absorption effect are changed, and the thermal neutron flux distribution in the vicinity of the water gap changes, resulting in a change in the nuclear characteristics of the fuel assembly.
[0021]
It should be noted that the fast neutron flux hardly changes, and it can be said that the change in the aggregate nucleus characteristics is almost caused by the change in the vicinity of the water gap of the thermal neutron flux. When the channel box deformation is large, the effect on the core characteristics is large, and in the core performance calculation, the core critical eigenvalue, reactor power distribution, fuel rod power distribution in the assembly, thermal limit value, neutron detection In order to monitor the performance of the core, it is necessary to take into account the count value of the reactor and the change in thermal neutron flux at the control rod position.
[0022]
Conventionally, the operation of a reactor core that predicts deformation of the channel box 2 due to neutron irradiation and avoids the interference between the control rod 5 and the channel box 2 is disclosed in Japanese Patent Application Laid-Open No. 2-176497, “Channel Box Deformation Evaluation Method” And an evaluation apparatus thereof, Japanese Patent Laid-Open No. 2-201291 “Reactor Operating Method”, and Japanese Patent Laid-Open No. 4-204084 “Channel Box Reuse Method”.
[0023]
However, these documents do not consider the influence on the core performance calculation due to the deformation of the channel box. An example of changes in nuclear characteristics due to channel box deformation will be described. For example, as shown in FIG. 21, due to the deformation of the channel box 2, the water gap 4 on the control rod 5 side of the fuel assembly 1 of interest now decreases by 2 mm, and the water gap 4 on the instrumentation tube 6 side for the neutron detector Is increased by 2 mm, and other adjacent assemblies 1 are not deformed. In this case, the result of comparison between the local power distribution in the assembly and the fuel rod local power distribution of the infinite lattice system has the same characteristics as FIG. 19 when the offset bundle is employed.
[0024]
In this case, the local output distribution of the reference solution was evaluated by multi-aggregate inhomogeneous calculation. According to this, the aggregate maximum local peaking coefficient is changed by about 10% due to the channel box deformation, which shows the importance of monitoring the core in consideration of the channel box deformation.
[0025]
Here, in the core performance calculation, the thermal limit value is evaluated in consideration of the influence on the fuel rod output due to the deviation of the fuel assembly from the design normal position. It is indicated by the “core monitoring device”.
[0026]
In Japanese Patent Application Laid-Open No. 4-110698, four fuel assemblies surrounding a control rod or a neutron detector in a reactor core are defined as one unit cell, and fuel rod output changes due to the misalignment of the assembly within each unit cell. It is supposed to calculate.
[0027]
Generally, the fuel rod output change in the target assembly in the unit cell depends on the combination of the positional deviation amount and the positional deviation direction of the four fuel assemblies in the unit cell. However, it is only described that the calculation is based on the amount of displacement of the fuel assembly, and the evaluation method is not clear.
[0028]
Further, in Japanese Patent Application Laid-Open No. 4-110698, the influence of the displacement of the assembly adjacent to the target assembly from the outside of the target unit cell is ignored, and the change in fuel rod output cannot be evaluated with high accuracy. was there. Furthermore, there is no specific method for evaluating the limit output ratio from the change in fuel rod output due to the misalignment of the assembly.
[0029]
Moreover, in the thing of Unexamined-Japanese-Patent No. 4-110698, to the critical eigenvalue of a core by position shift of a fuel assembly, the reactor power distribution, the count value of a reactor neutron detector, the detector irradiation amount, the control rod irradiation amount, etc. The effect of is not considered at all. In particular, the count of the neutron flux detector in the reactor is sensitive to changes in the water gap width, and in order to learn the error from the measured value of the neutron flux detector and correct the reactor power distribution, the calculated value of the detector must be accurate. It is necessary to ask well.
[0030]
In addition, if combustion proceeds with the fuel assembly misaligned, the combustion history effect and burnup distribution effect of neutron spectrum changes in the fuel assembly due to changes in the water gap width will accumulate, and the assembly will be misaligned instantaneously The difference with the effect of is produced. This history effect generally occurs in a direction that cancels out the instantaneous effect, but the history effect is not taken into account in Japanese Patent Laid-Open No. 4-110698.
[0031]
Regarding the deformation of the channel box, JP-A-4-110698 does not describe a method for evaluating the positional deviation from the normal position of the aggregate channel box due to the deformation of the channel box by neutron irradiation. There was a problem that the thermal limit value could not be calculated by predicting channel box deformation due to irradiation growth.
[0032]
In addition, if combustion proceeds while the assembly is misaligned due to channel box deformation, the combustion history effect and burnup distribution effect of changes in the neutron spectrum in the assembly due to changes in the water gap width accumulate, and the assembly is instantaneously misaligned. A difference from the effect of doing so occurs. This history effect generally occurs in a direction that cancels out the instantaneous effect, but the history effect is not taken into account in Japanese Patent Laid-Open No. 4-110698.
[0033]
An object of the present invention is to provide a core performance calculation apparatus capable of accurately calculating core nuclear characteristics in consideration of instantaneous and hysteresis effects when offset bundles are adjacent in a D lattice core or when a channel box is deformed. .
[0034]
[Means for Solving the Problems]
  The invention of claim 1Based on the diffusion model using the nodal mean nuclear constant,In-core power distribution calculation means for calculating the core core eigenvalue, neutron flux distribution, and power distribution, and homogeneous thermal neutron flux in the nodes where each assembly is homogenized based on diffusion theory using neutron flux discontinuity factor "The ratio of the inhomogeneous thermal neutron flux to the homogeneous thermal neutron flux at the aggregate boundary" and the "ratio of the homogeneous thermal neutron flux to the inhomogeneous thermal neutron flux in the aggregate" evaluated in the infinite lattice calculation. And a non-homogeneous thermal neutron flux calculation means for calculating the non-homogeneous thermal neutron flux distribution in the aggregate by using the factor multiplied by the correction coefficient of the transient component due to thermal neutron diffusion of the homogeneous thermal neutron flux distribution, The core eigenvalue, the in-core neutron flux distribution, and the power distribution are calculated by correcting the assembly average nuclear constant using the inhomogeneous neutron flux distribution by the inhomogeneous thermal neutron flux calculating means.
[0035]
  Claim1In the invention, the power distribution calculation means in the furnace isBased on the diffusion model using the nodal mean nuclear constant,Calculate the core critical eigenvalue, neutron flux distribution, and power distribution. And the inhomogeneous thermal neutron flux calculation means calculated the homogeneous thermal neutron flux distribution in the node which homogenized each aggregate based on the diffusion theory using neutron flux discontinuity factor, and was evaluated in infinite lattice calculation Homogeneous thermal neutron flux distribution is a factor that multiplies the ratio of the inhomogeneous thermal neutron flux to the homogeneous thermal neutron flux at the aggregate boundary and the ratio of the homogeneous thermal neutron flux to the inhomogeneous thermal neutron flux in the aggregate. Is used to calculate the inhomogeneous thermal neutron flux distribution in the aggregate by using the correction factor for the transient component due to thermal neutron diffusion, and the average nuclear constant of the aggregate is corrected using the inhomogeneous neutron flux distribution by the non-homogeneous thermal neutron flux calculator The core eigenvalue, in-core neutron flux distribution, and power distribution are calculated.
[0036]
  Claim2The invention ofBased on the diffusion model using the nodal mean nuclear constant,In-core power distribution calculation means for calculating critical eigenvalue, neutron flux distribution, and power distribution of the core, and homogeneous thermal neutron flux distribution in nodes where each assembly is homogenized based on diffusion theory using neutron flux discontinuity factor The ratio of the inhomogeneous thermal neutron flux to the homogeneous thermal neutron flux at the aggregate boundary and the ratio of the homogeneous thermal neutron flux to the inhomogeneous thermal neutron flux in the aggregate were evaluated in the infinite lattice calculation. A non-homogeneous neutron flux calculating means for calculating the non-homogeneous thermal neutron flux distribution in the assembly by using the multiplied factor as a correction factor for a transient component due to thermal neutron diffusion of the homogeneous thermal neutron flux distribution, and the power distribution in the reactor Line output of the fuel assembly by using the average cross-section output of the assembly calculated by the calculation means and the local output of the fuel rod calculated from the non-uniform neutron flux distribution by the non-uniform thermal neutron flux calculation means Those having a linear power density calculation means for calculating degrees.
[0037]
  Claim2In the invention, the power distribution calculation means in the furnace isBased on the diffusion model using the nodal mean nuclear constant,Calculate the core critical eigenvalue, neutron flux distribution, and power distribution. The inhomogeneous neutron flux calculation means calculates the homogeneous thermal neutron flux distribution in the node that homogenizes each aggregate based on the diffusion theory using the neutron flux discontinuity factor, and was evaluated in the infinite lattice calculation. The factor of the ratio of the inhomogeneous thermal neutron flux to the homogeneous thermal neutron flux at the aggregate boundary and the ratio of the homogeneous thermal neutron flux to the inhomogeneous thermal neutron flux in the aggregate is The non-homogeneous thermal neutron flux distribution in the assembly is calculated by using the correction factor for the transient component due to thermal neutron diffusion, and the line power density calculation means The linear power density of the fuel assembly is calculated by using the fuel rod local power calculated from the inhomogeneous neutron flux distribution by the homogeneous thermal neutron flux calculator.
[0038]
  Claim3The invention ofBased on the diffusion model using the nodal mean nuclear constant,In-core power distribution calculation means for calculating critical eigenvalue, neutron flux distribution, and power distribution of the core, and homogeneous thermal neutron flux distribution in nodes where each assembly is homogenized based on diffusion theory using neutron flux discontinuity factor The ratio of the inhomogeneous thermal neutron flux to the homogeneous thermal neutron flux at the aggregate boundary and the ratio of the homogeneous thermal neutron flux to the inhomogeneous thermal neutron flux in the aggregate were evaluated in the infinite lattice calculation. A non-homogeneous neutron flux calculating means for calculating the non-homogeneous thermal neutron flux distribution in the assembly by using the multiplied factor as a correction factor for a transient component due to thermal neutron diffusion of the homogeneous thermal neutron flux distribution, and the power distribution in the reactor Line output of the fuel assembly by using the average cross-section output of the assembly calculated by the calculation means and the local output of the fuel rod calculated from the non-uniform neutron flux distribution by the non-uniform thermal neutron flux calculation means A linear power density calculating means for calculating the degree, and a fuel rod R factor calculated by using the assembly cross-sectional average power calculated by the in-furnace power distribution calculating means and the fuel rod local power by the linear power density calculating means And a limiting power ratio calculating means for calculating a limiting power ratio of the fuel assembly.
[0039]
  Claim3In the invention, the power distribution calculation means in the furnace isBased on the diffusion model using the nodal mean nuclear constant,Calculate the core critical eigenvalue, neutron flux distribution, and power distribution. The inhomogeneous neutron flux calculation means calculates the homogeneous thermal neutron flux distribution in the node that homogenizes each aggregate based on the diffusion theory using the neutron flux discontinuity factor, and was evaluated in the infinite lattice calculation. The factor of the ratio of the inhomogeneous thermal neutron flux to the homogeneous thermal neutron flux at the aggregate boundary and the ratio of the homogeneous thermal neutron flux to the inhomogeneous thermal neutron flux in the aggregate is The inhomogeneous thermal neutron flux distribution in the aggregate is calculated by using the correction factor of the transient component due to thermal neutron diffusion. Further, the linear power density calculation means uses the fuel rod local power calculated from the aggregate cross-sectional average power calculated by the in-core power distribution calculation means and the non-homogeneous neutron flux distribution by the non-homogeneous thermal neutron flux calculation means. The line power density of the fuel assembly is calculated, and the limit power ratio calculation means is calculated by using the assembly cross-sectional average power calculated by the reactor power distribution calculation means and the fuel rod local power by the line power density calculation means. The limit output ratio of the fuel assembly is calculated from the fuel rod R factor.
[0056]
  Claim4In the invention of, we calculated the homogeneous thermal neutron flux distribution in the node where each assembly was homogenized based on the diffusion theory using the neutron flux discontinuity factor, and was evaluated in the infinite lattice calculation. Transient component of homogeneous thermal neutron flux distribution due to thermal neutron diffusion by multiplying factor of "ratio of homogeneous thermal neutron flux to homogeneous thermal neutron flux" and "ratio of homogeneous thermal neutron flux to inhomogeneous thermal neutron flux" Non-uniform thermal neutron flux calculation means for calculating the non-homogeneous thermal neutron flux distribution in the aggregate by using the correction coefficient of the aggregate, and the average nuclear constant of the aggregate using the non-homogeneous neutron flux distribution by the non-uniform thermal neutron flux calculation means And a means for calculating the core eigenvalue, the in-core neutron flux distribution, and the power distribution.
[0057]
  Claim5In the invention of, we calculated the homogeneous thermal neutron flux distribution in the node where each assembly was homogenized based on the diffusion theory using the neutron flux discontinuity factor, and was evaluated in the infinite lattice calculation. Transient component of homogeneous thermal neutron flux distribution due to thermal neutron diffusion by multiplying factor of "ratio of homogeneous thermal neutron flux to homogeneous thermal neutron flux" and "ratio of homogeneous thermal neutron flux to inhomogeneous thermal neutron flux" By using the non-homogeneous neutron flux calculation means for calculating the inhomogeneous thermal neutron flux distribution in the aggregate by using the correction coefficient of Means for correcting and calculating the core eigenvalue, in-core neutron flux distribution and power distribution, means for calculating the fuel rod local power distribution from the non-homogeneous thermal neutron flux distribution by the non-homogeneous thermal neutron flux calculator, and the output Those having a linear power density calculating means for calculating a linear power density of the fuel assembly using fabrics and the fuel rod local power distribution.
[0058]
  Claim6According to the invention, a homogeneous thermal neutron flux distribution in a node where each assembly is homogenized is calculated based on the diffusion theory using a neutron flux discontinuity factor, and evaluated in the infinite lattice calculation. Transient component of homogeneous thermal neutron flux distribution due to thermal neutron diffusion by multiplying factor of "ratio of homogeneous thermal neutron flux to homogeneous thermal neutron flux" and "ratio of homogeneous thermal neutron flux to inhomogeneous thermal neutron flux" The non-uniform thermal neutron flux calculation means for calculating the non-homogeneous thermal neutron flux distribution in the assembly by calculating the correction coefficient of the non-homogeneous thermal neutron flux from the non-homogeneous thermal neutron flux distribution means. Means for calculating the fuel rod R-factor distribution using the fuel rod local power distribution, and means for calculating the limit output ratio of the fuel assembly from the fuel rod R-factor distribution.
[0122]
DETAILED DESCRIPTION OF THE INVENTION
Embodiments of the present invention will be described below. First, in the D-lattice core, core nuclear characteristics such as assembly average nuclear constant, fuel rod local power, fuel rod R factor, in-core neutron detector count, and control rod irradiation amount are calculated with high accuracy considering offset bundle adjacent effects. The case where it does is demonstrated. That is, this is achieved by the following processes [1], [2], and [3].
[0123]
[1] Changes in aggregate nucleus characteristics due to the adjoining of the D lattice bundle and the offset bundle are calculated based on the multi-assembly detailed calculation model or the neutron diffusion model as shown in the following (a) to (d). .
[0124]
(A) Multi-assembly detailed two-dimensional calculation model
Aggregate average nuclear constant, fuel rod output distribution, fuel rod R-factor distribution, etc. due to adjacent D lattice bundle and offset bundle in advance by multi-assembly detailed two-dimensional calculation for the target assembly and adjacent assembly The core characteristic change amount is directly prepared as a table of combinations of aggregates having different water gap widths adjacent to the target aggregate.
[0125]
(B) Analytical diffusion model
Based on the analytical solution of the two-region diffusion model in which the water gap and the fuel region are homogenized, the change in the thermal neutron flux distribution in the assembly is obtained. Evaluate the amount of change.
[0126]
(C) Single assembly neutron flux discontinuity factor diffusion model
Based on the homogeneous diffusion nodal method using the aggregate neutron flux discontinuity factor, the homogeneous neutron flux distribution in the node that homogenizes each aggregate is obtained. Here, the aggregate discontinuity factor is defined as the ratio of the average neutron flux of each face of the aggregate to the aggregate average neutron flux in the infinite lattice calculation.
[0127]
In order to calculate the inhomogeneous neutron flux from the inhomogeneous neutron flux in the node, the "ratio of the inhomogeneous thermal neutron flux to the homogeneous thermal neutron flux at the aggregate boundary" evaluated in the infinite lattice calculation and the homogeneous heat in the node Calculate the inhomogeneous thermal neutron flux distribution in the node by multiplying the factor of the ratio of the neutron flux to the inhomogeneous thermal neutron flux as the correction factor for the transient component due to thermal neutron diffusion of the homogeneous thermal neutron flux distribution. The aggregate nuclear properties are calculated from this inhomogeneous thermal neutron flux distribution. As the homogeneous diffusion model, a multigroup node method, a modified first group node method, or the like is used.
[0128]
(D) Single aggregate neutron flux discontinuity factor boundary perturbation model
Based on the homogeneous diffusion nodal method using the aggregate neutron flux discontinuity factor, the neutron flux and neutron current at the node boundary obtained by homogenizing each aggregate are obtained.
[0129]
Using the change in aggregate nuclear characteristics for changes in neutron flux and neutron flow at the aggregate boundary evaluated in the infinite lattice calculation as the sensitivity coefficient, the aggregate nuclear characteristics from the neutron flux and neutron current at the above node boundary are used. Calculate the change.
[0130]
As the homogeneous diffusion model, a multi-group node method, a modified first group node method, a modified first group difference method, or the like can be used.
[0131]
[2] In the limit power ratio calculation, in addition to directly calculating the R factor change in the assembly, it can also be calculated from the fuel rod output change.
[3] In the diffusion model, the combustion history effect associated with the adjacent offset bundle is corrected using the burnup distribution and the spectrum history distribution within the assembly.
[0132]
As described above, in the present invention, in the D lattice core, the core core characteristics considering the offset bundle adjacency are calculated based on the table and diffusion model prepared by the detailed multi-assembly calculation, and the combustion history effect is also considered. Changes in nuclear properties can be calculated accurately. In addition, the critical eigenvalue of the core, the power distribution in the reactor, the count value of the reactor neutron detector, the detector irradiation amount, the control rod irradiation amount, etc., which have been ignored in the past, can be taken into consideration.
[0133]
FIG. 1 is a block diagram showing a first embodiment of the present invention. The aggregate average nuclear constant calculation means 11 uses the correction amount for the aggregate average nuclear constant or the infinite lattice average nuclear constant evaluated in advance by multi-aggregate detailed calculation according to the combination of the adjacent D lattice bundle and offset bundle. The average nuclear constant is calculated. That is, the node average nuclear constant is calculated as a function of the burnup ratio, void ratio, etc. of the node, and at that time, the aggregate average nuclear constant evaluated in advance by the multi-assembly detailed calculation according to the combination of the adjacent D lattice bundle and offset bundle. Use the number to take into account the effects of neighboring aggregates.
[0134]
The in-core power distribution calculating means 12 calculates the critical eigenvalue, neutron flux distribution, and power distribution of the core based on the core diffusion calculation using the nuclear constant calculated by the aggregate average nuclear constant calculating means 11. The average nuclear constant is used to calculate the neutron flux distribution and core eigenvalue in the reactor based on the diffusion model. As the diffusion model, for example, a modified one-group difference model as shown in the above-mentioned J. Wooly document, a multi-group node method model as shown in the K. Smith document described later, and the like can be used. The power distribution in the reactor is calculated based on the neutron flux distribution, and the aggregate cross-section average power is calculated.
[0135]
The local output distribution calculating means 13 calculates a correction amount for the fuel rod local output in the fuel assembly or the infinite lattice fuel rod local output evaluated in advance by the multi-assembly detailed calculation according to the combination of the adjacent D lattice bundle and the offset bundle. Used to calculate the fuel rod local power.
[0136]
Next, the line power density calculating unit 14 uses the assembly cross-sectional average output calculated by the in-core power distribution calculating unit 12 and the fuel rod local output calculated by the local power distribution calculating unit 13 to output the line output of the assembly. Calculate the density. In this linear power density calculation means 14, as a thermal limit value of the core, a set given by the fuel rod local power distribution evaluated in advance by the multi-assembly detailed calculation according to the combination of the adjacent D lattice bundle and the offset bundle. The maximum linear power density of each fuel assembly cross section is calculated using the maximum local power peaking coefficient of the body and the average power of the cross section of the assembly based on the power distribution calculation in the core. In this case, the accuracy can be further improved by using the output obtained by correcting the offset bundle adjacency effect as the aggregate section average output by the in-core power distribution calculation means 12.
[0137]
In the limit power ratio calculation means 15, the aggregate maximum R factor obtained from the fuel rod R factor distribution evaluated in advance by the multi-assembly detailed calculation according to the combination of the adjacent D lattice bundle and the offset bundle, The limit output ratio, which is a monitoring index of burnout of the fuel rods of each fuel assembly, is calculated using the body average output. The fuel rod R factor can also be calculated from the fuel rod local output obtained by the local output distribution calculating means 13.
[0138]
Next, the in-reactor neutron flux measuring device count value calculation means 16 determines the thermal neutron flux at the in-reactor neutron measuring device position previously evaluated by the multi-assembly detailed calculation according to the combination of the adjacent D lattice bundle and the offset bundle. Is used to calculate the in-reactor neutron detector count and the detector dose. Then, the in-core power distribution correction means 17 adapts the calculated value of the in-core neutron flux measuring device count value corrected for the adjacent effect of the D lattice bundle and the offset bundle to the actually measured value of the in-core neutron flux measuring device. To correct the power distribution calculation value in the furnace. The in-core power distribution calculated value can be corrected by learning the error of the calculated value of the in-core neutron detector count value corrected in this way with respect to the actually measured value.
[0139]
Further, the control rod irradiation amount calculation means 18 calculates the control rod irradiation amount using the control rod position thermal neutron flux evaluated in advance by the multi-assembly detailed calculation according to the combination of the adjacent D lattice bundle and the offset bundle. .
[0140]
Next, multi-aggregate calculation is performed to calculate the average nuclear constant, the discontinuity factor, the fuel rod local power, the fuel rod R factor, the thermal neutron flux at the neutron measuring instrument, etc. The method will be described in detail.
[0141]
(A) Multi-assembly detailed two-dimensional calculation model
The adjacent effect between the D lattice bundle and the offset bundle is determined by a combination of the adjacent D lattice bundle and the offset bundle. FIG. 2 shows eight possible patterns for combinations of adjacent bundles centered on the offset bundle. In addition, since the influence of the bundle adjacent from the diagonal diagonal direction with respect to the central bundle of interest is small, it is omitted from the eight patterns here. In FIG. 2, D indicates a D lattice bundle, and S indicates an offset bundle. For each such pattern, multi-aggregate calculation may be performed to evaluate the aggregate nucleus characteristics.
[0142]
When combustion proceeds while the assembly is misaligned, the combustion history effect and the flammability distribution effect due to changes in the neutron spectrum in the assembly due to changes in the water gap width are accumulated. A difference from the effect occurs. In order to incorporate this history effect, it is necessary to perform combustion calculation in multi-aggregate calculation.
[0143]
FIG. 3 is a characteristic diagram showing the combustion change in the aggregate maximum local peaking coefficient of the D lattice bundle and the offset bundle for the multi-aggregate pattern P1 in FIG. 2 in comparison with the infinite lattice system. However, it is assumed that the void ratio of each aggregate is equal. As shown in FIG. 3, it can be seen that the amount of change from the infinite lattice calculation tends to decrease with combustion.
[0144]
Although the number of combination patterns of the D lattice and the offset bundle is not so large, in actuality, the number of combinations increases and the calculation cost increases when considering the difference in burnup and void ratio of each bundle. However, the combination of burnups can be approximated by a combination of burnups of typical batch types if the offset bundle is introduced step by step for each cycle.
[0145]
In order to reduce the error due to the approximation of the combination of multi-aggregates, it is possible to give only the correction component from the infinite lattice calculation, instead of giving the aggregate core characteristic itself by multi-aggregate calculation. In the calculation of aggregate nucleus characteristics in each aggregate, first, aggregate nucleus characteristics are evaluated by infinite lattice combustion calculation as a first approximate value. Since the correction component of the influence of the adjacent bundle is the second order effect, the error is not so large even if it is evaluated by a combination of a typical bundle type, burnup, and void ratio. In this method, since only the correction amount from the infinite lattice calculation needs to be calculated with a typical multi-aggregate combination pattern, the calculation cost can be reduced.
[0146]
Furthermore, as a method for simplifying the correction calculation, a fuel that has been evaluated in advance by a multi-assembly detailed calculation for a combination of a D lattice bundle and an offset bundle that has the strictest thermal limit values such as the maximum linear power density and the limit power ratio. Using the correction amount for the infinite lattice calculation value of the fuel rod local power and fuel rod R factor in the assembly for all D lattice bundles and offset bundles, the core power density and the critical power ratio of the core are corrected by core diffusion calculation. You can also
[0147]
(B) Analytical diffusion model
Next, there is provided a thermal neutron flux change calculating means for calculating the change of the thermal neutron flux distribution in the aggregate with respect to the amount of change of the water gap width of the aggregate of interest from the infinite lattice system, based on the analytical model for the diffusion equation. Changes in the thermal neutron flux distribution in the aggregate due to substantial changes in the water gap width of the aggregate due to the adjacent lattice bundle and offset bundle are obtained based on an analytical model for the diffusion equation. Then, the nuclear property change amount is evaluated from the thermal neutron flux distribution.
[0148]
In this method, for example, for a two-dimensional one-dimensional system in which the water gap and the fuel region inside the channel box are homogenized, the neutron flux distribution when the water gap width is given is analytically calculated. At this time, an analytical expression of the change in the thermal neutron flux in the fuel region due to the change in the water gap by the one-dimensional diffusion model in the x direction is given by the following expression (1).
[0149]
[Expression 1]

[0150]
Here, x is the distance from the aggregate boundary, κ is the reciprocal of the thermal neutron diffusion distance, and a is the water gap change width.
[0151]
The change in the thermal neutron flux distribution in the aggregate can be approximated by the product δΨ (x) δΨ (y) of the one-dimensional distribution in the x and y directions. Since this method is based on an analysis model, there is an advantage that it is not necessary to prepare a table by detailed calculation in advance.
[0152]
(C) Single assembly neutron flux discontinuity factor diffusion model
Next, an inhomogeneous thermal neutron flux calculating means for calculating the inhomogeneous thermal neutron flux distribution in the aggregate is provided, and the effect obtained by the difference in water gap width between the D lattice bundle and the offset bundle is obtained by the infinite lattice calculation. Consider using neutron flux discontinuity factor. Therefore, multi-aggregate calculation is not required. In this method, the neutron flux distribution in the aggregate is obtained by the diffusion node method using the neutron flux discontinuity factor for the system consisting of nodes that homogenize each aggregate, and the amount of change in the nuclear characteristics of the aggregate is calculated from this neutron flux distribution. To evaluate.
[0153]
That is, based on the diffusion theory using neutron flux discontinuity factor, we calculated the homogeneous thermal neutron flux distribution in the node where each aggregate was homogenized, and evaluated the inhomogeneous heat at the boundary of the aggregate evaluated in the infinite lattice calculation. Correction of transient components by thermal neutron diffusion of homogeneous thermal neutron flux distribution by multiplying the factor of "ratio of neutron flux to homogeneous thermal neutron flux" and "ratio of homogeneous thermal neutron flux to non-homogeneous thermal neutron flux in the aggregate" It is a coefficient. This calculates the inhomogeneous thermal neutron flux distribution in the assembly. Then, the core eigenvalue, the in-core neutron flux distribution, and the power distribution are calculated by correcting the assembly average nuclear constant using the inhomogeneous neutron flux distribution by the inhomogeneous thermal neutron flux calculation means.
[0154]
Here, the aggregate neutron flux discontinuity factor is defined as the ratio of the average neutron flux of each face of the aggregate to the aggregate average neutron flux in the infinite lattice system. The multi-group diffusion node method itself using discontinuous factors is already known. For example, in the document "Assembly Homogenization Techniques for Light Water Reactor Analysis," KSSmith, Progress in Nuclear Energy, vol. 17, p303, 1986. Has been described.
[0155]
An example of a method for calculating the local power distribution in the assembly using the neutron flux distribution obtained by the node method calculation is "SIMULATE-3 Pin Power Reconstruction Methodology and Benchmarking," KRRempe et.al, Proceedings of lnternational. Reactor Physics Conference, 111-19, Jackson Hole, 1988.
[0156]
The D lattice bundle and the offset bundle have different water gap widths, so the neutron flux distribution in the aggregate is different, and the aggregate neutron discontinuity factor is also different. As shown in the above-mentioned K. Smith document, the neutron flux discontinuity factor gives a boundary condition for the neutron flux at the boundary of the nodes where the aggregates are homogenized in the diffusion node method. That is, for example, the following boundary conditions for the neutron flux are given at the x-direction boundary between the target assembly n and the adjacent assembly m.
[0157]
[Expression 2]

[0158]
Here, f represents a neutron flux discontinuity factor at the boundary surface, and Ψ represents a neutron flux at the boundary surface. If the aggregate of interest and the adjacent aggregate are the same lattice type in an infinite lattice system, the neutron discontinuity factors are also equal, and the above boundary condition merely represents the continuity of the neutron flux. However, if the neutron discontinuity factor f on the adjacent surface between adjacent aggregates is different, a virtual source of neutrons is generated at the node boundary based on the above boundary condition. The change in neutron flux distribution in the aggregate due to the difference can be calculated. In the multi-group diffusion node method, the nodal average thermal neutron flux and the nodal boundary thermal neutron flux are given by the whole core calculation using the neutron flux discontinuity factor for the thermal neutron flux.
[0159]
Next, using the node average neutron flux, the node boundary neutron flux, and the like, the neutron flux distribution in the homogenized assembly can be expanded and calculated. As an example, in the K. Rempe document, the thermal neutron flux Ψ in a homogenized assembly node Ψ₂Is expanded in the form of the following equation.
[0160]
[Equation 3]

[0161]
Where Ψ₁Is the fast neutron flux, c_iIs the expansion coefficient, f_iAre sinh and cosh functions.
[0162]
If the ratio of the inhomogeneous neutron flux to the homogeneous neutron flux is known, the inhomogeneous neutron flux can be calculated by multiplying the homogeneous thermal neutron flux distribution of the above equation (3) by this ratio. In the diffusion node method, as shown in the above-mentioned K. Rempe document, this ratio is obtained from the inhomogeneous neutron flux distribution Ψ obtained by infinite lattice calculation.^hetAnd a uniform neutron flux distribution Ψ can be approximated. That is, the inhomogeneous thermal neutron flux distribution Ψ in the assembly node placed in the core₂ ^hetIs calculated by the following equation.
[0163]
[Expression 4]

[0164]
Here, the symbol ∞ represents an infinite lattice calculation value.
[0165]
However, when the inventors applied this method to the offset bundle system, the nodal average neutron flux, the nodal boundary neutron flux, and the nodal boundary neutron flow, the results of the diffusion node method agree well with the multi-aggregate detailed calculation. Nevertheless, it was found that there was a large error in the local fuel rod output. The reason for this is that the thermal neutron flux distribution assumes that the ratio of the inhomogeneous neutron flux to the homogeneous neutron flux can be approximated by the ratio of the inhomogeneous neutron flux distribution obtained by infinite lattice calculation to the homogeneous neutron flux distribution. It was found that this was not true.
[0166]
In order to accurately calculate the inhomogeneous thermal neutron flux distribution from the in-node homogeneous thermal neutron flux, the inventors have evaluated "the inhomogeneous thermal neutron flux at the aggregate boundary to the homogeneous thermal neutron flux in the infinite lattice system. Ratio "and" ratio of homogeneous thermal neutron flux to inhomogeneous thermal neutron flux in the aggregate "are used as correction factors for transient components due to thermal neutron diffusion in the homogeneous thermal neutron flux distribution. We found that the inhomogeneous thermal neutron flux distribution in the node can be calculated with high accuracy.
[0167]
The transient component due to thermal neutron diffusion of the homogeneous thermal neutron flux distribution is given by the second term of equation (3). Therefore, in this method, the inhomogeneous thermal neutron flux is given by the following equation (5) instead of the equation (4).
[0168]
[Equation 5]

[0169]
Here, the coefficient W representing the “ratio of the inhomogeneous thermal neutron flux to the homogeneous thermal neutron flux at the aggregate boundary” can be expressed by the following equation using the load average for the four aggregate boundary surfaces.
[0170]
[Formula 6]

[0171]
When the inhomogeneous thermal neutron flux distribution in the assembly is calculated, the assembly average nuclear constant, which is a function of the inhomogeneous neutron flux distribution, is calculated, and the in-core power distribution corrected for the offset bundle adjacency is calculated. In addition, the fuel rod local power distribution is immediately calculated from the inhomogeneous thermal neutron flux distribution in the assembly, and the linear power density of the assembly can be calculated from this.
[0172]
The fuel rod R-factor distribution can be calculated from the fuel rod local power distribution, and the limit power ratio can be calculated from this.
[0173]
The aggregate neutron flux discontinuity factor on each surface of the aggregate is prepared for each aggregate in advance by single aggregate detailed calculation (infinite lattice calculation using reflection boundary conditions). FIG. 4 shows an example of a function form with respect to the offset amount of the channel box of the assembly discontinuity factor with respect to the thermal neutron flux.
[0174]
As an example showing the calculation accuracy of this method, as in the conventional FIG. 19 showing the effect of adjacent offset bundles, the assembly in the case where two offset bundles are adjacent to each other with a control rod sandwiched around the D lattice bundle. The local output distribution is calculated by this method, and the result compared with the reference solution by the multi-aggregate detailed calculation is shown in FIG. In FIG. 5, the upper part shows the detailed calculation, the middle part shows the method according to the present invention, and the lower part shows the difference. According to the reference calculation, the maximum local peaking coefficient of the aggregate is changed by about 10% due to the adjacency of the offset bundle, but this method reproduces this well.
[0175]
This method does not require detailed multi-assembly calculations when preparing a table of assembly neutron flux discontinuity factors, and the neutron flux discontinuity factors for each surface of the fuel assembly are used as a function of each surface of the target assembly. It may be calculated independently. As described above, this method has an advantage that the preparation and reference of the table are simpler than the above-described method that requires multi-aggregate calculation.
[0176]
In the method based on the modified first group diffusion model as the diffusion model, only the fast neutron flux distribution is solved in the whole core calculation. The thermal neutron flux is calculated using the fast neutron flux obtained by the core calculation and the “ratio of thermal neutron flux to fast neutron flux (spectral index)” in the infinite lattice system. If the spectral index is different between adjacent assemblies, thermal neutron spatial movement occurs, but the change from the infinite lattice of the thermal neutron flux due to this changes to a system consisting of nodes in which the target assembly and adjacent assemblies are homogenized. On the other hand, it is calculated by applying a diffusion model.
[0177]
In the modified first group node method, the homogeneous thermal neutron flux in the node is obtained by analytically solving the diffusion equation of this system. Details of this method are described in, for example, the document “Verification of LOGOS Nodal Method with Heterogeneous Burnup Calculations for a BWR core,” T. I wamoto et al., Transaction of American Nuclear Society, vol. 71,
p251,1994.
[0178]
Even in the modified first group method, the thermal neutron flux change due to channel box deformation uses a neutron flux discontinuity factor as a boundary condition for the thermal neutron flux in a system consisting of nodes of homogenized aggregates of interest and adjacent aggregates. Thus, the calculation can be performed based on the same principle as in the above-described multigroup node method.
[0179]
(D) Single aggregate neutron flux discontinuity factor boundary perturbation model
Another method using the neutron flux discontinuity factor is a combination with the boundary perturbation method. This is due to the difference in water gap width by providing node boundary value calculation means to calculate the neutron flux and neutron flow at the node boundary surface where each assembly is homogenized based on diffusion theory calculation using neutron flux discontinuity factor. Using the difference of the aggregate discontinuity factor, the neutron flux and neutron flow at the boundary of the aggregate are obtained, and the change of the boundary value from the infinite lattice and the sensitivity coefficient of the characteristic of the aggregate nucleus to the aggregate nucleus are used. Calculate the change in properties. As described above, this is because the diffusion node method using the neutron flux discontinuity factor pays attention to high accuracy for the neutron flux and neutron flow at the aggregate boundary.
[0180]
Based on the boundary perturbation method, an example of calculating local peaking in an aggregate using “neutron current / neutron flux” as the perturbation at the aggregate boundary is shown in the literature “A Boundary Condition Perturbation Method for Prediction of Pin Power Distribution in Light Water Reactor” , "F. Rahnema et al., Proceedings of Topical Meeting on Reactor Physics and Shielding, Chicago, 1984".
[0181]
In this method, for example, the local output LPF (x, y) within the assembly for the fuel rod (x, y) is calculated by the following equation (8).
[0182]
[Expression 7]

[0183]
The sensitivity coefficient F is prepared in advance by a single aggregate detailed calculation or a multi-aggregate detailed calculation in which boundary conditions are changed.
[0184]
However, in the Rahnema literature, when the neutron current / neutron flux at the interface is calculated based on the diffusion theory, the aggregate neutron flux discontinuity factor is not used. The change in neutron flow / neutron flux due to local neutron flux distribution change near the water gap cannot be calculated.
[0185]
Therefore, the node boundary value r is a multi-group diffusion node method using a neutron flux discontinuity factor for a system composed of nodes in which the aggregate of interest and the adjacent aggregate are homogenized, as in the above-described diffusion node method. Apply to find. Alternatively, in the modified first group difference method, the nodal boundary thermal neutron flux may be calculated from the spectral index of adjacent nodes and the neutron flux discontinuity factor using an empirical weighting factor. In this case, thermal neutron flux Ψ at the boundary between node m and node n_2nIs represented by the following equation (9).
[0186]
[Equation 8]

[0187]
Equation (8) shows the correction calculation method by the boundary perturbation method for the local output of the assembly. However, the correction calculation of other assembly nuclear characteristic quantities is also a sensitivity coefficient for the neutron flow / neutron flux of each nuclear characteristic quantity. Can be calculated in a similar manner.
[0188]
If combustion proceeds while the fuel assembly is misaligned, the history effect of changes in the neutron spectrum in the assembly due to the change in the water gap width and the effect of the burnup distribution are accumulated, and the effect of instantaneous misalignment of the assembly The difference occurs. This is called the spectral history effect because the neutron spectrum (ratio of thermal neutron flux to fast neutron flux) changes from the infinite system, resulting in an increase in uranium combustion delay and plutonium accumulation.
[0189]
In the diffusion node method, the combustion history effect cannot be directly taken into account as in the case of combustion calculation by multi-aggregate detailed calculation. In the core performance calculation by the diffusion node method, as a method for correcting the spectrum history effect due to spectrum interference when fuel assemblies having different neutron spectra are adjacent to each other, for example, Japanese Patent Application No. 6-210243 “Reactor Core Performance” As described in “Calculation method and apparatus”, there is a method of correcting, as a parameter, a spectrum history which is a burnup average value of a ratio of a neutron spectrum in a core and a spectrum in an infinite lattice system.
[0190]
In the present invention, this technique is applied to the spectral history effect due to the adjacent offset bundle, and the burnup distribution and the spectral history distribution in the fuel assembly corrected for the effect of changing the thermal neutron flux distribution due to the change in the water gap width are calculated and the combustion is performed. Calculate the correction amount for the average nuclear constant of the assembly, local distribution of fuel rods, etc. due to the hysteresis effect. For example, for the fuel rod local output, the spectrum history SH (x, y) at the fuel rod position (x, y) in the assembly is expressed by the following equation (10).
[0191]
[Equation 9]

[0192]
Where E is the burnup and Ψ₂, Ψ₁Are the thermal neutron flux and the fast neutron flux at the position (x, y) calculated in consideration of the offset bundle adjacency, and ∞ represents the value in the infinite lattice system. The correction of the local output distribution LPF considering the spectrum history is given by the following equation (11) by using the spectrum history correction coefficient (係数 Σ / ∂SH) for the thermal group fission cross section Σ.
[0193]
[Expression 10]

[0194]
Similarly, the hysteresis effect caused by the burnup distribution occurring in the node due to the offset bundle adjacency can be corrected using the sensitivity coefficient related to the burnup as shown in the above-mentioned document.
[0195]
Next, a second embodiment for the deformation of the channel box will be described. In order to accurately calculate the core characteristics in consideration of the channel box deformation, it is achieved by the following processes [1] to [5].
[0196]
[1] The fast neutron dose or burnup on each face of the channel box is integrated by core performance calculation, and the irradiation growth on the opposite face of the channel box is calculated as a function of the fast neutron dose or burnup on each face. The amount of deformation of the channel box is calculated from the difference in the amount of irradiation growth on the opposing surfaces.
[2] Aggregate nuclear characteristics such as aggregate average nuclear constant, local fuel rod output, neutron detector position thermal neutron flux, control rod position thermal neutron flux, taking into account channel box deformation in the target aggregate and adjacent aggregates Calculate
[3] In order to calculate the change in the above-described aggregate nucleus characteristics from the deformation amount of the channel box, it is based on the following multi-assembly detailed calculation model or neutron diffusion model.
[0197]
(A) Multi-assembly detailed two-dimensional calculation model
By performing multi-assembly detailed two-dimensional calculation for the target aggregate and adjacent aggregates, it is possible to directly determine the amount of change in core characteristics such as the average average nuclear constant, fuel rod output distribution, fuel rod R factor distribution, etc. Prepare as a table of deformation amount of water gap width on the surface. Here, multi-aggregate detailed two-dimensional calculation is a detailed calculation that considers the inhomogeneity of each aggregate as it is for a system that simulates a part of the core by combining a small number of aggregates (usually 4 to 16). This is a method for evaluating in detail the influence of adjacent aggregates on the aggregate of interest.
[0198]
(B) Single assembly neutron flux discontinuity factor diffusion model
The amount of change in the aggregate neutron flux discontinuity factor is calculated from the channel box deformation, and the thermal neutron flux distribution in the aggregate is calculated based on the homogeneous diffusion model for the nodes where each aggregate is homogenized. The nuclear property change is evaluated from the bundle distribution. Here, the aggregate discontinuity factor is defined as the ratio of the average neutron flux of each face of the aggregate to the aggregate average neutron flux in the infinite lattice system. The amount of change of the assembly neutron flux discontinuity factor is prepared in advance by a single assembly detailed calculation as a channel box deformation amount table. As the homogeneous diffusion model, a multigroup node method, a modified first group node method, or the like can be used.
[0199]
(C) Single assembly neutron flux discontinuity factor boundary perturbation model
Based on the homogeneous diffusion nodal method using the aggregate neutron flux discontinuity factor, the neutron flux and neutron current at the node boundary obtained by homogenizing each aggregate are obtained.
[0200]
The change in aggregate nuclear properties from the neutron flux and neutron current at the above node boundary was used as the sensitivity coefficient, which was evaluated in the infinite lattice system, using the change in aggregate nuclear properties with respect to the change in neutron flux and neutron current at the aggregate boundary. Calculate
[0201]
As the homogeneous diffusion model, a multi-group node method, a modified first group node method, a modified first group difference method, or the like can be used.
[0202]
(D) Analytical diffusion model
Based on the analytical solution of the two-region diffusion model in which the water gap and fuel region are homogenized from the channel box deformation, the change in the thermal neutron flux distribution in the assembly is obtained, and the nuclear property change is evaluated from this thermal neutron flux distribution. .
[0203]
[4] In the limit power ratio calculation considering channel box deformation, in addition to directly determining the R factor change in the assembly, it can also be calculated from the fuel rod output change.
[5] Combustion history effect associated with channel box deformation is corrected using a spectral history distribution defined as the burnup distribution within the assembly accompanying the channel box deformation and the burnup average value of the ratio of thermal neutron flux to fast neutron flux To do.
[0204]
As described above, in the second embodiment, the fast neutron irradiation amount or the burnup degree on each surface of the channel box is integrated by the core performance calculation. Therefore, the channel box deformation amount due to the neutron irradiation is predicted and evaluated. It becomes possible to calculate the core characteristics considering the deformation.
[0205]
In addition, the calculation of core characteristics taking into account channel box deformation is calculated based on the table and diffusion model prepared by the detailed multi-assembly calculation from the channel box deformation of the target assembly and the adjacent assembly. Therefore, the change in nuclear characteristics can be calculated with high accuracy.
[0206]
In addition, the influence of channel box deformation on the critical eigenvalue of the core, the power distribution in the reactor, the count value of the neutron detector in the reactor, the detector irradiation amount, the control rod irradiation amount, etc., which have been ignored in the past can be taken into consideration.
[0207]
FIG. 6 is a block diagram showing the second embodiment of the present invention. The in-core power distribution calculation means 19 inputs core state data and calculates the neutron flux distribution and core eigenvalue in the core based on the diffusion model. As the diffusion model, for example, a modified one-group difference model as shown in the above-mentioned J. Wooly document, a multi-group node method model as shown in the K. Smith document, or the like is used. The power distribution in the reactor is calculated based on the neutron flux distribution, and the aggregate cross-section average power is calculated.
[0208]
The channel box dose calculation means 20 calculates the fast neutron dose on each surface of the channel box of the aggregate based on this neutron flux distribution. Where fast neutron flux Ψ in plane n_nCan be calculated by the multi-group diffusion node method, and can be calculated by extrapolating the node average neutron flux of the aggregate of interest and the surrounding aggregate using a polynomial in the modified 1-group difference model. Accordingly, the fast neutron irradiation amount φ can be calculated as shown in the equation (12) by time integration of the fast neutron flux. Here, dt is a time width.
[0209]
## EQU11 ##

[0210]
The channel box deformation amount calculation means 21 evaluates the deformation amount of the channel box by neutron irradiation using the irradiation growth model using the fast neutron irradiation amount of each surface. As an evaluation method, it can be calculated from the irradiation growth amount in the axial direction on the opposing surfaces of the channel box (claim 25).
[0211]
In the channel box deformation amount calculation method, the channel box deformation amount is analytically calculated on the assumption that the axial curvature of the channel box has a uniform curvature in accordance with the difference in irradiation growth amount between the two facing surfaces A and B ( Claim 33). That is, as shown in FIG. 7, the average fast neutron irradiation amount in the axial direction of the surfaces A and B of the channel box is φ_A, Φ_BThe curvature of the bend in the axis (Z) direction of the channel box is expressed by the following equation (13), assuming that the bend is small. Then, the amount of bending at the height Z in the axial direction is expressed as in equation (14) by integrating equation (13). Therefore, the amount of bending when the upper and lower ends are fixed is expressed by equation (15). Further, the irradiation growth function is expressed by the equations (16) and (17). An example of this function form is shown in FIG.
[0212]
[Expression 12]

[0213]
  Here, a, b, c, d, and e are fitting coefficients. This coefficient can be obtained from an empirical formula. This coefficient is determined by using the measured values of channel box deformation in the past in order to correct errors due to random bending due to the release of residual stress during channel manufacturing and variations in irradiation growth of Zircaloy. MoyoYes.
[0214]
As a calculation method of the channel box deformation amount, there is a method based on the finite element method in addition to the analytical method of the above equation (15).TheAs shown in FIG. 9, the channel is divided into axial nodes, and the length lA after irradiation growth of both A and B facing each other for each node i.ⁱ, 1BⁱAsk for. After this node is stacked in the axial direction, the distance between each line and the straight line connecting the upper and lower ends of the A-side or B-side of the channel is the amount of bending δⁱCan be obtained as
[0215]
  Note that fast neutrons that cause irradiation growth are neutrons having an energy of 1 MeV or more and do not necessarily match all fast neutrons given in the core performance calculation. Therefore, the ratio f of the fast neutrons used in the fast neutron dose calculation to the total fast neutrons can be calculated as a table of burnup E and void ratio V as shown in the following equation (18).The
[0216]
[Formula 13]

[0217]
  Further, in the second embodiment, the core performance calculation apparatus is configured using an irradiation growth model using a one-to-one correspondence between the fast neutron irradiation amount and the burnup degree.TheIn this case, instead of the channel box dose calculation means 20 of FIG. 1, burnup distribution calculation means is provided.
[0218]
Next, a method for calculating the burnup on each face of the aggregate channel box in the burnup distribution calculation means will be described. Here, the burn-up En in the plane n is calculated by time-integrating the power density at the channel box position because the intra-node power distribution is calculated with the multi-group diffusion node method. Further, in the modified first group difference model, the node average burnup of the aggregate of interest and the surrounding aggregate can be calculated by interpolation using a polynomial.
[0219]
  Model using burnupLeCan calculate the amount of irradiation growth strain of the channel box by neutron irradiation as a function of the burnup E of each surface, for example, as in the following equations (19) and (20).
[0220]
[Expression 14]

[0221]
  Here, a, b, c, d, and e are fitting coefficients. This coefficient can be obtained from an empirical formula. In addition, this coefficient may be determined using the actual measured value of the channel box deformation in the past in order to correct errors that depend on uncertainty during channel manufacturing.Yes.FIG. 10 shows an example of the function form of ε (E).
[0222]
  Next, the in-reactor power distribution recalculation means 22 uses the channel box deformation amount evaluated by the channel box deformation amount calculation means 21 as described above, and the assembly nuclear constant and the neutron flux with the channel box deformation effect corrected. Calculate the discontinuity factor and use it to recalculate the critical eigenvalue, in-core power distribution, and fuel assembly cross-sectional average power distribution in the coreThe
[0223]
  In the cotton power density calculation means 23, as the thermal limit value of the core, the maximum local power peaking coefficient of the aggregate given by the fuel rod local power distribution corrected for the channel box deformation effect and the average cross-section of the aggregate by calculating the power distribution in the core Use the power to calculate the maximum linear power density for each fuel assembly cross section.TheIn addition, instead of obtaining the maximum local output peaking coefficient of the assembly from the fuel rod local output distribution corrected for the channel box deformation effect, the accuracy is reduced, but the channel directly corresponds to the maximum local output peaking coefficient of the assembly. The box deformation effect may be corrected.
[0224]
  Further, the limit power ratio calculation means 24 uses the aggregate maximum R factor obtained from the fuel rod R factor distribution considering the channel box deformation and the aggregate average output to burn out the fuel rods of each fuel assembly. The critical power ratio, which is the monitoring index ofTheThe fuel rod R-factor distribution can also be calculated from the fuel rod local power distribution described above. Also, instead of obtaining the maximum R factor of the assembly from the fuel rod R factor distribution corrected for the channel box deformation effect, the accuracy is reduced, but the channel box deformation effect is directly applied to the maximum R factor of the assembly. It may be corrected.
[0225]
  In calculating these linear power density, critical power ratio, etc., the fuel assembly average output recalculated using the nuclear constant corrected for the channel box deformation is used as the fuel assembly average output. Accuracy can be improvedThe
[0226]
  Next, the in-core neutron flux counter count value calculating means 25 calculates the in-core neutron detector count value and the irradiation amount by using the thermal neutron flux at the in-core neutron counter position considering the channel box deformation.TheAn example of a counting calculation method in the case of a movable in-core neutron flux detector (TIP) as an in-core neutron flux detector is described in the aforementioned Wooly document. The detector dose is given by the time integration of the thermal neutron flux at the position of the in-core neutron measuring instrument.
[0227]
  Although not shown in FIG. 6, the in-core output is obtained by learning the error of the calculated value of the in-core neutron detector count value corrected for channel deformation based on the method of the Tuiki literature. You can also correct the calculated distributionTheFurther, the control rod irradiation amount calculation means 26 calculates the control rod irradiation amount by time integration of the control rod position thermal neutron flux corrected for the channel box deformation effect.The
[0228]
Next, details on three different methods to calculate the average nuclear constant, the discontinuity factor, the fuel rod local power, the fuel rod R factor, the thermal neutron flux at the neutron measuring instrument, etc. Explained.
[0229]
  (A) Multi-assembly detailed two-dimensional calculation model
  First, as method 1, a table of nuclear characteristic changes such as the average nuclear constant of the aggregate, the local output of the fuel rod, the fuel rod R factor, the thermal neutron flux at the position of the neutron measuring instrument with respect to the channel box deformation of the aggregate of interest and the adjacent aggregate Or it prepares as a fitting type | formula and calculates the nuclear characteristic change in the fuel assembly which correct | amended the channel box deformation effect directly. A table or fitting equation for the change in the characteristic amount of the target aggregate with respect to the channel box deformation of the target aggregate and the adjacent aggregate is evaluated by multi-aggregate two-dimensional detailed calculation.The
[0230]
Here, multi-aggregate detailed two-dimensional calculation is a detailed calculation that considers the inhomogeneity of each aggregate as it is for a system that simulates a part of the core by combining a small number of aggregates (usually 4 to 16). This is a method for evaluating in detail the influence of adjacent aggregates on the aggregate of interest.
[0231]
This table or fitting equation is a function of not only the deformation amount of each surface of the aggregate of interest but also the deformation amount of the adjacent surface of the adjacent aggregate, and is generally a complex function for multivariate combinations. On the other hand, Japanese Patent Application Laid-Open No. 4-110698 discloses only that the calculation is based on the amount of displacement of the fuel assembly, and the evaluation method is not clear at all. In this method, this function is organized as a table of water gap widths for each face of the channel box of the aggregate of interest. This table is also a multivariate function (tetravariate function) for the water gap width of each surface. As a relatively simple reference method, for example, the following method can be considered.
[0232]
First, as a first step, it is assumed that there is no deformation of the channel box of the aggregate adjacent to the aggregate of interest and only the channel box 2b of the aggregate of interest is deformed. As shown in FIG. 11, the water gap deformation amount δxl (i) on the left side in the x direction of the channel box 2b of the aggregate of interest and the water gap deformation amount δxr (i) on the right side in the x direction are equal (absolute values are equal). It is assumed that the sign is δx. Similarly, it is assumed that the water gap deformation amount δyt (i) on the upper side in the y direction of the target aggregate channel box 2b and the water gap deformation amount δyb on the lower side in the y direction are equal to δy. The changes in the aggregate core characteristics due to the deformation of the channel box are organized and referred to as a two-dimensional table or fitting formula in the form of v (δx, δy).
[0233]
Next, as a second step, correction is performed in consideration of the influence of the change in the water gap width due to the deformation of the adjacent surface of the aggregate channel box adjacent to the aggregate of interest. In FIG. 11, the position of the channel box after deformation is indicated by a dotted line. In this case, for example, the water gap deformation amount δxl on the left side in the x direction of the target aggregate channel box 2b is the deformation amount δxr (i−1) of the left side of the target aggregate channel box 2b and the right side of the left adjacent aggregate channel box 2a. The sum of The same applies to the water gap deformation amount δxr on the right side in the x direction.
[0234]
Since the deformation amounts of both adjacent aggregate channel boxes are generally different, if the deformation of both adjacent aggregate channel boxes is taken into consideration, δxl (i) ≠ δxr (i). Here, dx = δxl−δxr. Similarly, in the y direction, dy = δyt−δyb. Therefore, the table is first referred to as v (δxl, δyt), and the correction amount for this is arranged as w (dx, dy) and referred to. Finally, the nuclear property change is given by v + w.
[0235]
FIG. 12 shows an example of a function form with respect to δx of the aggregate maximum local peaking coefficient when δx = δy and δy = 0. FIG. 13 shows an example of a functional form for dx of the correction amount of the aggregate maximum local peaking coefficient when dx = dy and dy = 0.
[0236]
  (B) Single assembly neutron flux discontinuity factor diffusion model
  Next, method 2 will be described. In Method 2, the amount of change in the aggregate neutron flux discontinuity factor is calculated from the channel box deformation of the aggregate of interest and the adjacent aggregate, and the neutron flux discontinuity factor is calculated for the system in which each aggregate is homogenized. The neutron flux distribution in the aggregate is obtained by the diffusion node method used, and the change in the nuclear characteristics of the aggregate is evaluated from this neutron flux distribution.TheHere, the aggregate neutron flux discontinuity factor is defined as the ratio of the average neutron flux of each face of the aggregate to the aggregate average neutron flux in the infinite lattice system.
[0237]
As described above, the multi-group diffusion node method calculation method using discontinuous factors is described in the literature "Assembly Homogenization Techniques for Light Water Reactor Analysis," KSSmith, Progress in Nuclear Energy, vol. 17, p303, 1986. Has been. An example of a method for calculating the local power distribution in an assembly using the neutron flux distribution obtained by the node method calculation is "SIMULATE-3 Pin Power Reconstruction Methodology and Benchmarking," KRRempe et.al, Proceedings of International. Reactor Physics Conference, III-19, Jackson Hole, 1988.
[0238]
When the channel box is deformed, the aggregate neutron discontinuity factor changes because the neutron flux distribution in the aggregate changes due to the change in the water gap width. As shown in the above-mentioned K. Smith document, the neutron flux discontinuity factor gives a boundary condition for the neutron flux at the boundary of the nodes where the aggregates are homogenized in the diffusion node method. That is, for example, the boundary condition of the equation (2) is given to the neutron flux at the boundary in the x direction between the target assembly n and the adjacent assembly m. Here, in equation (2), f is the neutron flux discontinuity factor at the boundary surface, and Ψ is the neutron flux at the boundary surface.
[0239]
If the aggregate of interest and the adjacent aggregate are the same lattice type in an infinite lattice system, the neutron discontinuity factors are also equal, and the above boundary condition merely represents the continuity of the neutron flux. However, if the neutron discontinuity factor f on the adjacent surface between adjacent assemblies differs due to channel box deformation, a virtual source of neutrons is generated at the node boundary based on the above boundary conditions. Therefore, the change of neutron flux distribution in the aggregate due to channel box deformation can be calculated. In the multi-group diffusion node method, the nodal average thermal neutron flux and the nodal boundary thermal neutron flux are given by the whole core calculation for the thermal neutron flux using the neutron flux discontinuity factor.
[0240]
Next, using the node average neutron flux, the node boundary neutron flux, and the like, the neutron flux distribution in the homogenized assembly can be expanded and calculated. As an example, in the K. Rempe document, the thermal neutron flux Ψ in a homogenized assembly node Ψ₂Is expanded in the form of equation (3). Here, in equation (3), Ψ₁Is the fast neutron flux, c_iIs the expansion coefficient, f_iAre sinh and cosh functions.
[0241]
If the thermal neutron flux distribution in the homogenized assembly is obtained, the inhomogeneous thermal neutron flux distribution in the assembly can be calculated by synthesizing the non-homogeneous neutron flux distribution obtained by infinite lattice calculation. The assembly average nuclear constant, which is a function of the inhomogeneous neutron flux distribution, and the fuel rod local power distribution can be calculated immediately. The fuel rod R-factor distribution can be calculated from the fuel rod local power distribution.
[0242]
The change amount of the assembly neutron flux discontinuity factor with respect to the channel box deformation amount on each face of the assembly is prepared in advance as a table of channel box deformation amounts by single assembly detailed calculation (infinite lattice calculation). FIG. 14 shows an example of a functional form for the water gap width change δx of the assembly discontinuity factor with respect to the thermal neutron flux.
[0243]
As an example showing the calculation accuracy of this method, the channel box of the aggregate of interest is deformed by 2 mm in the x and y directions in the same way as in FIG. When there is no deformation, that is, when δx = δy = 2 mm, the local output distribution in the aggregate is calculated by this method, and the result compared with the reference solution by the multi-aggregate detailed calculation is as shown in FIG. It will be the same. The fuel rod local power calculation method was basically the same as that described in the above-mentioned K. Rempe document. However, the above-mentioned inhomogeneity correction of the aggregate was corrected for changes in the thermal neutron flux distribution. Was added. According to the reference calculation, the aggregate maximum local peaking coefficient changes by about 10% due to the channel box deformation, but this method reproduces this well.
[0244]
This method eliminates the need for multi-aggregate detailed calculations when preparing a table of changes in the aggregate neutron flux discontinuity factor from the channel box deformation, and the channel box deformation of the aggregate of interest and adjacent aggregates. When calculating the change of the assembly nucleus characteristics from the above, the neutron flux discontinuity factor of each surface of the fuel assembly may be calculated independently as a function of only the deformation amount of each surface of the channel box of the assembly of interest. As described above, the method 2 has an advantage that the preparation and reference of the table is simpler than the method 1 regardless of the combination of the displacement amounts of the respective surfaces.
[0245]
  One based on the modified group 1 diffusion model as a diffusion modelIn lawSolves only the fast neutron flux distribution in the whole core calculation. The thermal neutron flux is calculated using the fast neutron flux obtained by the core calculation and the “ratio of thermal neutron flux to fast neutron flux (spectral index)” in the infinite lattice system. If the spectral index is different between adjacent assemblies, thermal neutron spatial movement occurs, but the change from the infinite lattice of the thermal neutron flux due to this changes to a system consisting of nodes in which the target assembly and adjacent assemblies are homogenized. On the other hand, it is calculated by applying a diffusion model. In the modified first group node method, the homogeneous thermal neutron flux in the node is obtained by analytically solving the diffusion equation of this system. Details of this method are described, for example, in the document "Verification of LOGOS Nodal Method with Heterogeneous Burnup Calculations for a BWR core," T. lwamoto et al., Transaction of American Nuclear Society, vol. 71, p251, 1994.
[0246]
Even in the modified first group method, the thermal neutron flux change due to channel box deformation uses a neutron flux discontinuity factor as a boundary condition for the thermal neutron flux in a system consisting of nodes of homogenized aggregates of interest and adjacent aggregates. Thus, the calculation can be performed based on the same principle as in the above-described multigroup node method. Note that the thermal neutron flux and thermal neutron flow can be calculated from the spectral indices of adjacent nodes using empirical weighting factors as is well known instead of solving the diffusion equation.
[0247]
  (C) Single assembly neutron flux discontinuity factor boundary perturbation model
  As another method using the neutron flux discontinuity factor, the one combined with the boundary perturbation method is used.TheIn this method, using the difference in the discontinuity factor due to the difference in water gap width, the neutron flux and neutron flow at the boundary of the aggregate are obtained. Use the sensitivity factor to calculate the change in aggregate nuclear properties. As described above, this is because the diffusion node method using the neutron flux discontinuity factor pays attention to high accuracy for the neutron flux and neutron flow at the aggregate boundary.
[0248]
Based on the boundary perturbation method, an example of calculating local peaking in an aggregate using “neutron current / neutron flux” as the amount of perturbation at the aggregate boundary is shown in the document “A Boundary Condition Ferturbation Method for Prediction of Pin Power Distribution in Light Water Reactors” , "F. Rahnema et al., Proceedings of Topical Meeting on Reactor Physics and Shielding, Chicago, 1984".
[0249]
In this method, for example, the local output LPF (x, y) within the assembly for the fuel rod (x, y) is calculated from the above-described equation (8). The sensitivity coefficient F in the equation (8) is prepared in advance by single aggregate detailed calculation or multi-aggregate detailed calculation in which boundary conditions are changed.
[0250]
However, in the Rahnema literature, when the neutron current / neutron flux at the interface is calculated based on the diffusion theory, the aggregate neutron flux discontinuity factor is not used. The change in neutron flow / neutron flux due to local neutron flux distribution change near the water gap cannot be calculated.
[0251]
  In the present invention, the node boundary value r is a multi-group diffusion using a neutron flux discontinuity factor for a system consisting of nodes in which the aggregate of interest and the adjacent aggregate are homogenized, as in the diffusion node method described above. Can be obtained by applying the node methodTheAlternatively, in the modified group 1 difference method, the nodal boundary thermal neutron flux may be calculated from the spectral index of adjacent nodes and the neutron flux discontinuity factor using empirical loading factors.Yes.In this case, thermal neutron flux Ψ at the boundary between node m and node n_2nIs expressed by the above-described equation (9).
[0252]
  Equation (8) aboveIs a collectionThe correction calculation method by the boundary perturbation method for the combined local output is shown.,otherThe correction calculation of the aggregate nuclear characteristic amount of can be calculated by the same method using the sensitivity coefficient of each nuclear characteristic amount with respect to the neutron flow / neutron flux.
[0253]
  (D) Analytical diffusion model
  Next, method 3 will be described. In Method 3, instead of using the diffusion node method in Method 2 to obtain the thermal neutron flux in the aggregate, the channel box deformations of the aggregate of interest and the adjacent aggregates are used to calculate the intra-aggregate based on the analytical model for the diffusion equation. The change in the thermal neutron flux distribution is obtained, and the change in nuclear properties is evaluated from this thermal neutron flux distribution.TheIn Method 3, for example, for a two-dimensional one-dimensional system in which the water gap and the fuel region inside the channel box are homogenized, the neutron flux distribution when the water gap width is given is analytically calculated.
[0254]
At this time, the analytical expression of the change in the thermal neutron flux in the fuel region due to the change in the water gap by the one-dimensional diffusion model in the x direction is given by the above-described equation (1). In equation (1), x is the distance from the aggregate boundary, κ is the reciprocal of the thermal neutral prediffusion distance, and a is the water gap change width. The change in the thermal neutron flux distribution in the aggregate can be approximated by the product δΨ (x) δΨ (y) of the one-dimensional distribution in the x and y directions. Since Method 3 is based on the analysis model, there is an advantage that it is not necessary to prepare a table in advance.
[0255]
If combustion proceeds while the assembly is misaligned, the history effect of neutron spectrum change in the assembly due to the water gap width change and the history effect of the burnup distribution are accumulated, and the effect of instantaneous misalignment of the assembly The difference occurs. The phenomenon in which the neutron spectrum (ratio of thermal neutron flux to fast neutron flux) changes from the infinite system and causes an increase in uranium combustion delay and plutonium accumulation is called the spectral history effect. Also, the effect of causing a uranium combustion delay or the like due to the burnup distribution in the aggregate is called a single burn effect. Since these effects generally work in the direction of canceling out the instantaneous effects, it is necessary to appropriately consider these effects in order to avoid an excessive margin in the calculation of the thermal limit value.
[0256]
The amount of channel box deformation increases with combustion of the aggregate, and the spectral change due to channel deformation also changes with combustion. For this reason, when the combustion history effect of channel deformation is evaluated in the detailed combustion calculation by the multi-aggregate, the deformation amount may be changed for each combustion step, but the calculation complexity increases.
[0257]
In order to avoid this, there is a method in which only the instantaneous effect is evaluated in the multi-aggregate calculation, and the spectral history effect and the single burn-up effect are corrected by the core performance calculation. Even in the diffusion node method using the discontinuous factor, the channel deformation effect can be calculated only as an instantaneous effect. Therefore, the spectral history effect and the single burn-up effect are corrected by the core performance calculation.
[0258]
In the core performance calculation, as a method for correcting the spectrum history effect due to the spectrum interference when fuel assemblies having different neutron spectra are adjacent to each other, for example, Japanese Patent Application No. Hei 6-210243 “Reactor Core Performance Calculation Method and Device” As described in the above, there is a method of correcting, as a parameter, a spectrum history that is a burnup average value of a ratio of a neutron spectrum in a core and a spectrum in an infinite lattice system.
[0259]
  Therefore, in the present invention, this technique is applied to the spectrum history effect due to the channel box deformation, the burnup distribution and the spectrum history distribution in the fuel assembly corrected for the channel box deformation effect are calculated, and the channel history due to the combustion history effect due to the channel deformation. Calculate the correction amount for the assembly average nuclear constant, fuel rod local power distribution, etc.TheFor example, for the fuel rod local output, the spectrum history SH (x, y) at the fuel rod position (x, y) in the assembly is expressed by the above-described equation (10). In equation (10), E is the burnup, Ψ₂, Ψ₁Are the thermal neutron flux and the fast neutron flux at the position (x, y) calculated in consideration of the channel box deformation, respectively, and ∞ represents the value in the infinite lattice system. The correction of the local output distribution LPF considering the spectrum history is given by the above-described equation (11) by using the spectrum history correction coefficient (∂Σ / ∂SH) for the thermal group fission cross section Σ.
[0260]
Similarly, the hysteresis effect caused by the burnup distribution occurring in the node due to the thermal neutron flux distribution change due to the channel deformation can be corrected using the sensitivity coefficient related to the burnup as shown in the above-mentioned document.
[0261]
【The invention's effect】
As described above, according to the core performance calculation apparatus of the present invention, the calculation of the core characteristics considering the effect of the adjacent D-lattice bundle and offset bundle depends on the combination of the D-lattice bundle and the offset bundle. The calculation is based on the correction table prepared in advance by multi-assembly detailed calculation, the diffusion node method using the assembly discontinuity factor, or the analytical diffusion model. The power density, the limit power ratio, the in-core neutron detector count, the detector irradiation amount, the control rod irradiation amount, etc. can be accurately calculated.
[0262]
In addition, the channel box deformation caused by fast neutron irradiation can be estimated by integrating the fast neutron dose on each surface of the channel box by core power distribution calculation and predicting the channel box deformation caused by neutron irradiation based on the irradiation growth model. Therefore, it is possible to calculate the core characteristics considering the channel box deformation. In addition, the calculation of the core characteristics of the core considering channel box deformation is based on the channel table deformation amount of the aggregate of interest and the adjacent aggregate based on the correction table or diffusion model prepared in advance by multi-assembly detailed calculation. Since the hysteresis effect is also corrected, the core critical eigenvalue, reactor power distribution, maximum linear power density, critical power ratio, reactor neutron detector count and detector dose, control rod dose, etc. are accurately calculated. There is an excellent effect that can be done.
[Brief description of the drawings]
FIG. 1 is a block configuration diagram showing a first embodiment of the present invention.
FIG. 2 is an explanatory diagram showing a combination pattern of a D lattice bundle and an offset bundle.
FIG. 3 is a characteristic diagram showing an example of the burnup dependence of a local peaking coefficient in an offset bundle adjacency system.
FIG. 4 is a characteristic diagram showing the relationship between the offset amount of the channel box and the aggregate neutron flux discontinuity factor.
FIG. 5 is an explanatory diagram showing the effect of local output distribution calculation according to the first embodiment of the present invention.
FIG. 6 is a block diagram showing a second embodiment of the present invention.
FIG. 7 is an explanatory diagram showing an evaluation model of the amount of bending in the axial direction of the channel box due to irradiation growth.
FIG. 8 is a characteristic diagram showing an example of an irradiation growth function by fast neutron irradiation.
FIG. 9 is an explanatory diagram in a case where the amount of bending in the axial direction of the channel box due to irradiation growth is obtained by a finite element method.
FIG. 10 is a characteristic diagram showing an example of an irradiation growth function according to burnup.
FIG. 11 is an explanatory diagram showing the relationship between the channel deformation amount and the water gap deformation amount in the second embodiment of the present invention.
FIG. 12 is a characteristic diagram showing a change example of the maximum fuel rod local output with respect to the deformation amount of the water gap of the aggregate of interest (when δx = δy and δy = 0).
FIG. 13 is a characteristic diagram showing a change example of the maximum local fuel rod output with respect to the water gap width deformation amount (when dx = dy and dy = 0) of adjacent assemblies.
FIG. 14 is a characteristic diagram showing an example of change of the assembly neutron flux discontinuity factor with respect to the water gap width deformation of the assembly of interest.
FIG. 15 is a partially cutaway perspective view of a fuel assembly of a boiling water reactor.
FIG. 16 is an explanatory diagram of a positional relationship of water gaps in a fuel assembly of a boiling water reactor.
FIG. 17 is an explanatory diagram of a D lattice bundle.
FIG. 18 is an explanatory view showing a state in which two bodies around the control rod are replaced with offset bundles.
FIG. 19 is an explanatory diagram showing an example of a change in the local output distribution in the aggregate due to adjacent offset bundles.
FIG. 20 is an explanatory view showing the bending in the axial direction of the channel box by fast neutron irradiation.
FIG. 21 is an explanatory diagram showing a positional relationship of water gaps due to deformation of the channel box.
[Explanation of symbols]
1 Fuel assembly
2 Channel box
3 Fuel rod
4 Water gap
5 Control rod
6 Instrumentation pipe
11 Aggregate average nuclear constant calculation means
12 Reactor power distribution calculation means
13 Local output distribution calculation means
14-wire output calculation means
15 Limit output ratio calculation means
16 In-core neutron flux measuring device count value calculation means
17 Reactor power distribution correction means
18 Control rod irradiation amount calculation means
19 Reactor power distribution calculation means
20 Channel box dose calculation means
21 Channel box deformation amount calculation means
22 Recalculation means for power distribution in the furnace
23 Line power density calculation means
24 Limit output ratio calculation means
25 In-core neutron flux measuring instrument count calculation means
26 Control rod irradiation amount calculation means

Claims (6)

  In the core performance calculation of boiling water reactors, in-core power distribution calculation means for calculating the core critical eigenvalue, neutron flux distribution, and power distribution based on the diffusion model using the nodal average nuclear constant, and neutron flux discontinuity The homogeneous thermal neutron flux distribution in the node that homogenizes each aggregate was calculated based on the diffusion theory using factors, and was evaluated in the infinite lattice calculation. Set by multiplying the factor of "ratio to bundle" by "ratio of homogeneous thermal neutron flux to inhomogeneous thermal neutron flux in the aggregate" as a correction factor for transient components due to thermal neutron diffusion of homogeneous thermal neutron flux distribution A non-homogeneous thermal neutron flux calculating means for calculating the inhomogeneous thermal neutron flux distribution in the body, and correcting the average nuclear constant of the assembly using the non-homogeneous thermal neutron flux distribution by the non-homogeneous thermal neutron flux calculating means. Eigenvalues, furnace neutron flux distribution, core performance computing apparatus being characterized in that so as to calculate the output distribution.   In the core performance calculation of boiling water reactors, power distribution calculation means for calculating the critical eigenvalue, neutron flux distribution and power distribution of the core based on the diffusion model using the nodal average nuclear constant, and neutron flux discontinuity factor The homogeneous thermal neutron flux distribution in the node where each assembly was homogenized was calculated based on the diffusion theory using, and was evaluated in the infinite lattice calculation. By multiplying the factor of "ratio to the ratio of homogeneous thermal neutron flux to inhomogeneous thermal neutron flux in the aggregate" by the factor of correction of transient components due to thermal neutron diffusion in the homogeneous thermal neutron flux distribution By means of non-homogeneous neutron flux calculation means for calculating the inhomogeneous thermal neutron flux distribution of the reactor, and by means of the non-homogeneous thermal neutron flux calculation means calculated by the in-reactor power distribution calculation means Core performance calculation apparatus characterized by having a linear power density calculating means for calculating a linear power density of the fuel assembly by using a fuel rod local power calculated from a homogeneous neutron flux distribution.   In the core performance calculation of boiling water reactors, power distribution calculation means for calculating the critical eigenvalue, neutron flux distribution and power distribution of the core based on the diffusion model using the nodal average nuclear constant, and neutron flux discontinuity factor The homogeneous thermal neutron flux distribution in the node where each assembly was homogenized was calculated based on the diffusion theory using, and was evaluated in the infinite lattice calculation. By multiplying the factor of "ratio to the ratio of homogeneous thermal neutron flux to inhomogeneous thermal neutron flux in the aggregate" by the factor of correction of transient components due to thermal neutron diffusion in the homogeneous thermal neutron flux distribution By means of non-homogeneous neutron flux calculation means for calculating the inhomogeneous thermal neutron flux distribution of the reactor, and by means of the non-homogeneous thermal neutron flux calculation means calculated by the in-reactor power distribution calculation means A linear power density calculating means for calculating a linear power density of the fuel assembly by using the fuel rod local power calculated from the homogeneous neutron flux distribution; and an assembly cross-sectional average power calculated by the reactor power distribution calculating means; A core performance calculation apparatus comprising: a limit power ratio calculation means for calculating a limit power ratio of a fuel assembly from a fuel rod R factor calculated using a fuel rod local output by the linear power density calculation means.   In the calculation of the core performance of a boiling water reactor, the distribution of homogeneous thermal neutron flux in the node where each assembly was homogenized was calculated based on the diffusion theory using the neutron flux discontinuity factor, and was evaluated in the infinite lattice calculation. Homogeneous thermal neutron flux distribution is calculated by multiplying the ratio of the ratio of the inhomogeneous thermal neutron flux to the homogeneous thermal neutron flux at the aggregate boundary and the ratio of the homogeneous thermal neutron flux to the inhomogeneous thermal neutron flux in the aggregate. A non-homogeneous thermal neutron flux calculation means for calculating the non-homogeneous thermal neutron flux distribution in the aggregate by using a correction coefficient for the transient component due to thermal neutron diffusion of And a means for calculating the core eigenvalue, the in-core neutron flux distribution, and the power distribution by correcting the assembly average nuclear constant.   In the calculation of the core performance of a boiling water reactor, the distribution of homogeneous thermal neutron flux in the node where each assembly was homogenized was calculated based on the diffusion theory using the neutron flux discontinuity factor, and was evaluated in the infinite lattice calculation. Homogeneous thermal neutron flux distribution is a factor that multiplies the ratio of the inhomogeneous thermal neutron flux to the homogeneous thermal neutron flux at the aggregate boundary and the ratio of the homogeneous thermal neutron flux to the inhomogeneous thermal neutron flux in the aggregate. Using a non-homogeneous neutron flux calculation means for calculating the non-homogeneous thermal neutron flux distribution in the aggregate by using a correction factor for transient components due to thermal neutron diffusion of the neutron, and using the non-homogeneous neutron flux distribution by the non-uniform thermal neutron flux calculation means Means for calculating the core eigenvalue, in-core neutron flux distribution, and power distribution by correcting the assembly average nuclear constant, and the fuel rod local power component from the non-homogeneous thermal neutron flux distribution by the non-homogeneous thermal neutron flux calculator. Means for calculating a, core performance calculation apparatus characterized by having a linear power density calculating means for calculating a linear power density of the fuel assembly using the output distribution and the fuel rod local power distribution.   In the calculation of the core performance of a boiling water reactor, the distribution of homogeneous thermal neutron flux in the node where each assembly was homogenized was calculated based on the diffusion theory using the neutron flux discontinuity factor, and was evaluated in the infinite lattice calculation. Homogeneous thermal neutron flux distribution is calculated by multiplying the ratio of the ratio of the inhomogeneous thermal neutron flux to the homogeneous thermal neutron flux at the aggregate boundary and the ratio of the homogeneous thermal neutron flux to the inhomogeneous thermal neutron flux in the aggregate. From the non-homogeneous thermal neutron flux calculation means by the non-homogeneous thermal neutron flux calculation means for calculating the non-homogeneous thermal neutron flux distribution in the aggregate by using the correction coefficient of the transient component due to the thermal neutron diffusion of Means for calculating the fuel rod local power distribution, means for calculating the fuel rod R-factor distribution using the fuel rod local power distribution, and hand for calculating the critical power ratio of the fuel assembly from the fuel rod R-factor distribution Core performance calculation apparatus characterized by having and.

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