In nuclear reactor theory, nodal diffusion methods have been mainly used for reactor core analysis. The nodal expansion method (NEM) had been developed and other nodal methods such as analytic nodal method had been followed. All these methods invariably adopt transverse integration.
The analytic function expansion nodal (AFEN) method has been developed for last several years at KAIST and it has been successfully applied to static and transient reactor analysis. In contrast to conventional nodal methods, the AFEN method does not use transverse integration. Due to the tight constraints and the use of analytic basis functions, the AFEN method can use assembly size as a mesh size while conventional nodal methods should divide one assembly more than into 2 by 2 sub-domains to give the same accuracy with the AFEN method.
However, as new type of fuel such as MOX has been introduced, the conventional nodal diffusion methods could not properly treat MOX loaded cores which have large flux gradients at the interface of MOX and UOX fuel assemblies. In other words, the equivalence theory under all reflective boundary conditions cannot provide proper assembly discontinuity factor (ADF) to correct neutron leakage at the interface.
Therefore, new approaches are required to remedy the inaccuracy. As an alternative to formal transport solution, the simplified P3 ($SP_3$) method draws interests because the $SP_3$ method is a relatively inexpensive approximation to the transport equation that contains most of the transport physics characteristics lacking in diffusion method. In addition to higher accuracy, the $SP_3$ equations has the form of two-group diffusion equations which leads to fast computing and easy implementation in conventional diffusion codes.
In this thesis, the AFEN method is successfully extended to solve the $SP_3$ equations. To facilitate incorporation of interface and boundary conditions in $SP_3$ nodal solutions, partial current moment transformation is introduced. The partial current transformation transforms the partial current moments into the form of diffusion partial currents so that the $SP_3$ equations can be solved by the same method to solve the diffusion equation such as the AFEN method. The $SP_3$ method are implemented in the COREDAX code which is based on the AFEN method.
The numerical results show significantly improved results compared to diffusion method with the same amount of computing time in steady-state problems and accurate prediction of power change in transient problems.
이 논문에서는 MOX 핵연료와 같이 새로운 핵연료가 장전된 원자로 노심에서의 정확한 중성자 분포와 유효증배계수( eff k )를 예측하기 위해서 중성자수성방정식의 가정된 형태인 $SP_3$ 식을 기존의 해석함수전개노달 (AFEN) 방법론을 이용하여 풀 수 있도록 하였다. $SP_3$ 식에서는 정의된 partial current moment가 확산방정식의 partial current 형태와 다르기 때문에 기존의 노달 방법론들을 이용하여 $SP_3$ 식을 풀기가 상당히 까다롭다. 본 논문에서는 이 문제점을 해결하기 위해서 partial current transformation이라는 개념을 도입하였다. 이는 $SP_3$ 식에서 정의된 partial current moment를 확산방정식의 partial current 형태와 같은 형태로 만들어 주는 변환방법이다. 이 변환방법을 이용한다면 기존 노달 방법론들을 이용하여 $SP_3$ 식을 쉽게 풀 수가 있다. 이 논문에서는 partial current moment transformation이 AFEN 방법론에 적용되었다.
균질화된 핵연료집합체가 장전된 문제를 풀었을 때에 계산결과를 통해서 $SP_3$ 방정식에 의한 결과가 확산방정식의 결과보다 중성자 분포 및 유효증배계수를 훨씬 더 정확하게 예측 하는 것을 보았다. 또한 계산 시간 또한 확산방정식과 비슷한 수준에서 풀 수 있음을 확인하였다.
또한 시간의존적 문제의 경우에도 $SP_3$ 방정식에 의한 결과는 중성자 수송방정식에 의한 결과와 거의 일치한다는 것도 확인하였다.
그러나 아직까지는 $SP_3$ 방정식에 해당되는 균질화 계수들에 대한 연구가 제대로 되어있지 않다. 그러므로 비균질화 핵연료집합체의 문제를 풀기 위해선 좀더 정확한 중성자누출을 예측해야 하고 $SP_3$ 방정식에 해당되는 균질화 계수에 대한 연구가 더 필요하다.
