In-depth Investigation And Further Development Of Homogenization Method And Discontinuity Factor Theory

The current nuclear reactor physicis analysis theory was established in 1970 s. Due to the hardware computing capabilities of that time, a lot of approximation was made in the theory to reduce the computing time with the cost of accuracy. The current method with deficiency in the theory is hard to handle the increasingly aggressive core design. There are mainly four basic categories contribute to errors from employing this theory which bases on the homogenization method. They are spatial discretization effect, spatial homogenization effect, group-collapsing effect, and transport effect. Thus, this thesis focuses on the study of pin power reconstruction method, Simplified P3 method(SP3) 、 transport-SP3 homogenization and transport-transport homogenization, as well as the development of SP3 code.The first part of this thesis is based on the current nuclear reactor physics analytical method. Deficiencies of the application of nodal method are discussed. One way to improve its accuracy is to solve the core problem in multi groups. Thus, a high-accuracy mutil-group pin power reconstruction is needed. In this thesis, a group-decoupled direct fitting method is developed for multi-group pin power reconstruction. A unique feature of the method is that in addition to nodal volume and surface average fluxes and corner fluxes, transversely-integrated 1D nodal solution flux profiles are also used as the condition to determine the 2D intra-nodal flux distribution. For each energy group, a two-dimensional expansion with a nine-term polynomial and eight hyperbolic functions is used to perform a constrained least square fit to the 1D intra-nodal flux solution profiles. To speed the method, it is analytically solved in this thesis. Moreover, an optional slowing down source improvement method is also developed to further enhance the accuracy of the reconstructed flux distribution if needed. Test examples are shown with very good results.However, the research by Dr. Dong Lv of Shanghai Jiao Tong University on NGM(Next Generation Method) suggests that to further improve the accuracy of the current nuclear reactor physical method, the theoretical frame needs to change. To use smaller homogenized meshes, multi-energy groups and higher order than P1 approximation should be in the direction of improvements.The second part of this thesis studies on the SP3 method. The basic theory of SP3 method, nodal solution for SP3 equations and transport-SP3 homogenization method are introduced in this part. Firstly, the traditional SP3 theory and Chao-Yamamoto proposal theory are introduced. To solve the SP3 equations, a semi-analytic nodal method(SANM) is applied and SP3 code has been developed. In order to speed up the precedue, the iteration strategy and transversely integrated flux expansions for moments are studied. Besides, two levels of finite difference method are implanted in the SP3 code. The SP3 method is validated with a set of challenging numerical benchmark problems. It is concluded that although SP3 is significantly more accurate than diffusion, diffusion with DF actually gives more accurate results than SP3 without DF(Discontinuity Factor). Via acceleration of finite difference method, the computing time of SP3 precedue is remarkably reduced. Finally, to further improve the accuracy of SP3 method, this thesis follows SP3 theory and works out two specific methodologies of calculating DF for SP3. One performs with the assumption that the 2nd moment surface fluxe is continuous and DF for the 0th moment flux can be determined with this assumption. The other takes DF for diffusion calculation as DF of the 0th moment flux in SP3 calculation, based on the idea that SP3 method is considered as correction to diffusion method through the 2nd moment flux. When SP3 also uses DF its superiority over diffusion is restored. But in case of energy group collapsing or large nodal meshes, the advantage of using SP3 over diffusion diminishes.In the third part,a theory is presented that unifies the calculation of discontinuity factors in diffusion, SP3 and transport calculations. The idea of Even Parity Discontinuity Factor(EPDF) was recently introduced for transport calculation using homogenized pin cells. In this method, even parity of angular flux is discontinueous while odd parity is continueous. DF can be produced via the conservation of surface net current. When DF is applied, it works on the angular flux. Both methods for angular dependent and independent DFs are worked out. This EPDF theory can be easily applied to SP3 and diffusion calculation as special cases. Besides, the definition of boundary DF in single assembly model with reflective boundary condition is discussed. Two different definition from traditional definition are introduced, which are named as “Prime EPDF” and “Renormalized EPDF”. “Prime EPDF” defines no DF at the boundary of assemblies. The normalization target of “Renormalized EPDF” is the sum of the incoming and outgoing partial currents on each surface, while in the traditional definition it is the surface flux. The theory has been tested to work well using mini-core benchmark problems with severe heterogeneity. Moreover, “Prime EPDF” provides more accurate result than “Renormalized EPDF” and traditional DF, comparable to that using SPH factor. For problems containing directionally anisotropic homogenization units, “Prime EPDF” even shows better accuracy than that using SPH factor.