[en] Method for prognosis of severe accident response progress initiated by large break loss of coolant (LBLOCA) was established, based on transient analysis for M310 reactor. The primary loop is rationally simplified based on characters of LBLOCA. The mass and energy conservation equations were solved approximately and the classical formula were used to prognose emergency condition progression. The active core area was divided into 4 radial rings and 10 axial levels, i.e. 40 cells. Experimental correlations were used to calculate heat transfer in the core and the cladding temperature was obtained. Then the core condition can be judged according to the cladding temperature. A code for prognosis of LBLOCA initiated emergency condition could be developed based on the method established in the paper. (authors)

[en] Highlights: • For a single node it has own expansion order instead of unique order. • Confirm the expansion orders before all of the other calculations. • The computational memory storage and the time cost can be reduced obviously. - Abstract: The Variational Nodal Method (VNM) has been employed as the diffusion module in our PWR core analysis code Bamboo-Core within our PWR fuel management code system NECP-Bamboo. It expands the nodal volumetric flux and surface partial currents into the sums of orthogonal basis functions without using the transverse integration technique. To reduce the extra computing cost by the uniform expansion order setting, an adaptive expansion order technique has been developed in this paper. After estimating the net currents between each pair of neighboring nodes by using the Coarse-Mesh Finite-Difference (CMFD) technique, it estimates the required expansion orders in each node analytically. This technique increases the complexity of the code, but reduces the computational efforts both in computing time and memory storage by a factor of about 5 and 4, respectively. In addition, the CMFD acceleration is also employed to further improve the performance of the code. It is demonstrated by the numerical results that the CMFD acceleration technique can provide a speedup ratio of about 17.

[en] To handle the control rod cusping effect in pressurized water reactor (PWR) fuel management calculation, the variational nodal method (VNM) in the fuel management calculation code system NECP-Bamboo has been extended to tread the heterogeneous cross section distribution by expanding the volumetric cross sections into piece-wise polynomials in the early work. However, the partially inserted control rods also introduces heterogeneous discontinuity factor (DF) on nodal interface. Thus, in this paper, an ultimate solution is proposed to fully handle this problem. Firstly, the surface integral in the VNM is modified to contain the discontinuity of neutron flux, incorporating a continuous discontinuity factor in that term. Secondly, the surface DF is expanded into the sum of pieces-wise orthogonal polynomials to construct the nodal response matrixes. Comparing with current representative re-homogenization methods, the application numerical results of the BEAVRS benchmark problem demonstrate the effectiveness of the heterogeneous VNM with heterogeneous DF. It can eliminate the cusping effect by providing more accurate differential control rode worth curves and pin power distributions. (authors)

[en] Highlights: • The VNM has been improved to treat the heterogeneous discontinuous factors. • Its functional has been modified to account the heterogeneous discontinuous factors. • The heterogeneous discontinuous factors are also expanded by using the basis functions. • It can fully eliminate the control rod cusping effect during realistic calculations. - Abstract: To handle the control rod cusping effect in Pressurized Water Reactor (PWR) core calculation, the heterogeneous Variational Nodal Method (VNM) employed by the fuel management calculation code system NECP-Bamboo has been enhanced to treat heterogeneous discontinuity factor (DF) appearing on nodal interface. To solve the neutron-diffusion equations with heterogeneous DF, firstly, the functional in VNM is modified to contain the discontinuity of neutron flux in the surface integral term. Secondly, other than volumetric flux and surface partial currents, cross sections and surface DF are also expanded into the sum of orthogonal piece-wise polynomials to construct the nodal response matrixes. Four test problems in this paper including the CISE, Henry-Worley, HAFAS benchmark problems and the BEAVRS problems were employed to verify the method in treating heterogeneous DF. It has been demonstrated that the control rod cusping effect can be fully eliminated by the heterogeneous VNM with heterogeneous DF in terms of control rod differential worth and three-dimensional pin-power profile.

[en] Highlights: •The Variational Nodal Method widely employed in fast reactor is applied to PWR. •The Partitioned-Matrix technique is extended to the Fission-Source iteration. •The algorithm is tested in problems with and without discontinuity factors. •Computing effort comparisons indicate the effectiveness of the proposed algorithm. -- Abstract: The Variational Nodal Method (VNM) expands the nodal volumetric flux and surface partial current into the sums of orthogonal basis functions without using the transverse integration technique. The exclusion of the transverse integration provides a number of advantages for employing the VNM in Pressurized Water Reactor (PWR) core simulation. The orthogonality of those basis functions guarantees the conservation of neutron balance regardless of the expansion orders, providing an opportunity to accelerate the computationally expensive full-order iteration by using cheap low-order sweeping with high-order moments fixed. This was named as the Partitioned-Matrix (PM) technique in the legacy VNM code VARIANT, and was applied to the within-group (WG) iteration. It is very effective for neutron-transport calculation, but less effective for neutron-diffusion mainly due to the reduced number of high-order partial current moments. In this paper, we extend the PM technique to the Fission-Source (FS) iteration to accelerate the flux convergence by using low-order flux moments also. From the macroscopic acceleration point of view, it converges the fission- and scattering-source distributions by using computationally cheap low-order iteration faster than the original full-order sweeping. Based on our new VNM code VIOLET, considering the fact that the discontinuity factor used for preserving neutron leakage rates during spatial homogenization slows down the nodal iteration convergence, numerical tests were carried out for two typical PWR problems respectively without and with discontinuity factors. By analyzing both the computational effort in terms of FLOP (FLoating-point OPeration) and computing time, the following conclusions have been demonstrated. The legacy PM technique for WG iteration can provide an acceleration ratio of about 2 for the PWR core neutron-diffusion calculation with or without using discontinuity factors, while the one for FS iteration itself can accelerate by a factor of about 3 which is higher. By accelerating both the WG and FS iteration simultaneously, the acceleration ratio is about 4 for both the two PWR problems. In addition, by extending the PM technique from the WG iteration to the FS iteration, the neutron-diffusion calculation of the VNM can be accelerated very effectively with almost no extra storage or implementation cost to the existing computer code.