• Nuclear Engineering and Technology
• /
• 제21권1호
• /
• pp.56-61
• /
• 1989

Borresen의 1.5군 소격 확산이론에 의거하여 2군 중성자 속에 대한 adjoint 함수를 근사적으로 계산할 수 있는 한가지 간단한 방법을 제안하였다. 이 방법에서는 열 중성자 속에 대한adjoint 함수의 누설항을 1.5군 이론의 원리에 입각하여 기하학적 buckling에 의해 근사적으로 기술하게 되는데 이때 그 기하학적 buckling은 속중성자속의 adjoint 함수로부터 구하게 된다. 한편 제안된 계산 방법의 정확도를 알기 위해 adjoint함수 계산에 대한 KIDD 전산코드의 계산결과와 제안된 방법의 계산결과를 비교하였으며 이로부터 제안된 방법이 정확도면에서 만족스런 adjoint함수를 예측 할 수 있다는 것을 보였다. 뿐만 아니라 이 방법은 섭동 이론과 관련하여 반응도 평가에 유용하게 이용될 수 있다는 것도 보였다.

• Nuclear Engineering and Technology
• /
• 제48권6호
• /
• pp.1291-1302
• /
• 2016

This paper presents a new and efficient scheme to determine the optimal neutron source position in a model near-equilibrium pressurized water reactor, which is based on the OPR1000 Hanul Unit 3 Cycle 7 configuration. The proposed scheme particularly assigns importance of source positions according to the local adjoint flux distribution. In this research, detailed pin-by-pin reactor adjoint fluxes are determined by using the Monte Carlo KENO-VI code from solutions of the reactor homogeneous critical adjoint transport equations. The adjoint fluxes at each allowable source position are subsequently ranked to yield four candidate positions with the four highest adjoint fluxes. The study next simulates ex-core detector responses using the Monte Carlo MAVRIC code by assuming a neutron source is installed in one of the four candidate positions. The calculation is repeated for all positions. These detector responses are later converted into an inverse count rate ratio curve for each candidate source position. The study confirms that the optimal source position is the one with very high adjoint fluxes and detector responses, which is interestingly the original source position in the OPR1000 core, as it yields an inverse count rate ratio curve closest to the traditional 1/M line. The current work also clearly demonstrates that the proposed adjoint flux-based approach can be used to efficiently determine the optimal geometry for a neutron source and a detector in a modern pressurized water reactor core.

• 에너지공학
• /
• 제17권4호
• /
• pp.233-240
• /
• 2008

최근 새로운 2계 자기 수반형(self-adjoint) 중성자 수송 방정식으로 기존의 우성 및 기성 수송 방정식 외에 SAAF(Self-Adjoint Angular Flux) 수송 방정식이 소개되어, 이에 대한 적절한 경계조건, 수치해법, 정확도 등에 관한 논의가 활발히 진행되고 있다. 본 연구에서는 SAAF 수송 방정식의 수학적, 물리적 의미를 고찰하고 기존의 우성 및 기성 수송 방정식과의 연관성을 명확히 하였으며, Boltzmann 수송 방정식의 1계 차분식에서 2계의 SAAF 수송 방정식의 차분식을 유도하는 방법을 확산 가속법(diffusion synthetic acceleration method)과 함께 소개하였다. 유도된 SAAF 차분법이 계산 효율성과 수송해의 정확도를 증가시킴을 수치결과로 확인하였다.

• Nuclear Engineering and Technology
• /
• 제53권1호
• /
• pp.30-43
• /
• 2021

In the 2D/1D method, a global adjoint CMFD based on the generalized equivalence theory is built to synthesize the 2D radial MOC adjoint and 1D axial NEM adjoint calculation and also to accelerate the iteration convergence of 3D whole-core adjoint transport calculation. Even more important, an advanced yet accurate two-level (TL) CMFD acceleration technique is proposed, in which an equivalent one-group adjoint CMFD is established to accelerate the multi-group adjoint CMFD and then to accelerate the 3D whole-core adjoint transport calculation efficiently. Based on these method, a new code is developed to perform 3D adjoint neutron flux calculation. Then a set of VERA and C5G7 benchmark problems are chosen to verify the capability of the 3D adjoint calculations and the effectiveness of TL CMFD acceleration. The numerical results demonstrate that acceptable accuracy of 2D/1D adjoint calculations and superior acceleration of TL CMFD are achievable.

• Advances in Energy Research
• /
• 제3권2호
• /
• pp.125-131
• /
• 2015

Prompt neutron lifetime calculations have been performed for the NIRR-1 reactor HEU and LEU cores using the 1/v insertion and the Adjoint flux weighing methods. Results of calculations obtained for the HEU and LEU cores are respectively $57.3{\pm}0.8$ and $47.5{\pm}0.7$ for the 1/v insertion and $56.9{\pm}0.3$ and $46.3{\pm}0.5$ for the Adjoint flux. There is a good agreement seen between the two methods for both cores. The prompt neutron lifetime was observed to be shorter in the LEU than for the HEU as expected. However, the Adjoint flux weighing method seemed to be the easiest method in calculating the prompt neutron lifetime for NIRR-1.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• 제3권2호
• /
• pp.161-171
• /
• 1999

Aerodynamic sensitivity analysis codes are developed via the hand-differentiation using a direct differentiation method and an adjoint method respectively from discrete two-dimensional compressible Navier-Stokes equations. Unlike previous other researches, Baldwin-Lomax algebraic turbulence model is also differentiated by hand to obtain design sensitivities with respect to design variables of interest in turbulent flows. Discrete direct sensitivity equations and adjoint equations are efficiently solved by the same time integration scheme adopted in the flow solver routine. The required memory for the adjoint sensitivity code is greatly reduced at the cost of the computational time by allowing the large banded flux jacobian matrix unassembled. Direct sensitivity code results are found to be exactly coincident with sensitivity derivatives obtained by the finite difference. Adjoint code results of a turbulent flow case show slight deviations from the exact results due to the limitation of the algebraic turbulence model in implementing the adjoint formulation. However, current adjoint sensitivity code yields much more accurate sensitivity derivatives than the adjoint code with the turbulence eddy viscosity being kept constant, which is a usual assumption for the prior researches.

• 한국원자력학회:학술대회논문집
• /
• 한국원자력학회 1998년도 춘계학술발표회논문집(1)
• /
• pp.112-117
• /
• 1998

A generalized perturbation program has been developed for the purpose of estimating zonal power variation of a CANDU reactor upon refueling operation. The forward and adjoint calculation modules of RFSP code were used to construct the generalized perturbation program. The numerical algorithm for the generalized adjoint flux calculation was verified by comparing the zone power estimates upon refueling with those of forward calculation. It was, however, noticed that the truncation error from the iteration process of the generalized adjoint flux is not negligible.

• 한국원자력학회:학술대회논문집
• /
• 한국원자력학회 1998년도 춘계학술발표회논문집(1)
• /
• pp.93-98
• /
• 1998

PEN(1)(다항식전개 노달) 해법을 육방형 노심의 과도상태 해석과 Adjoint flux(수반 중성자속)해법에 응용하여 여러가지 Benchmark문제들(3)(4)(5)을 풀고 그 결과를 다른 수치기법 결과와 비교·분석하였다. 2차원 육방형 대형중수로 과도상태 Benchmark문제(5)를 다항식전개 노달해법에 의한 과도상태 해석·검증의 대상으로 삼았으며 그 기준 계산치로서 FX2-TH 코드의 계산결과를 사용하였다 대형중수로 노심의 과도상태 해석 결과, 기준해와 비교해 집합체 낙하시작 3초 후에 집합체가 낙하한 위치에서 Normalized Flux 오차가 0.5% 이내, 집합체가 낙하하지 않은 위치에서 Normalized Flux 오차가 1% 이내의 정확한 결과를 보였다. Adjoint flux 해의 검증을 위해서는 VENTURE 코드(2)의 계산 결과를 기준해로 하였으며, 계산능 검증을 위해 사용된 대부분 의 Benchmark 문제들에서 작은 오차를 보였으나 반사체가 포함된 IAEA 문제에서는 큰 오차를 보였다.

• Nuclear Engineering and Technology
• /
• 제27권3호
• /
• pp.374-384
• /
• 1995

해석함수 전개 노달방법의 수학적 수한해를 AFEN코드에 약간의 수정을통하여 AFEN노달 방정식의 전치행 렬 방정식을 풀어서 계산하였다. 또한 이 수반해를 사용하여 섭동이론(정확한 섭동이론과 일차근사 섭동이론)을 이용한 계산이 반응도 변화를 예측하기 위해 두개의 잘 알려진 표준문제를 통하여 수행되었다. 본 연구에서 수반해의 계산방법은 물리적 수반해 및 정방정식의 고유치를 필요로 하지 않는다. 계산결과들은 본 논문에서 계산된 수반해가 AFEN방법의 정화한 수학적 수반해임을 보여준다.

• 대한원격탐사학회:학술대회논문집
• /
• 대한원격탐사학회 1999년도 Proceedings of International Symposium on Remote Sensing
• /
• pp.221-226
• /
• 1999

A data assimilation system for a 1-dimensional mixed layer model has been constructed using the adjoint method. The classical adjoint method does not work well for the mixed layer variabilities due to the occurrence of spikes in the gradient of the cost function. To solve this problem, the two techniques of scaling the cost function and optimization in the frequency space are used. As a result, the heat flux can be reliably estimated with an accuracy of 8Wm$^{-2}$ rms error in the identical twin experiments. We then applied this system to the tropical Pacific TOGA-TAO buoy data. The air-sea heat flux as well as the mixed layer variability were estimated in close approximation to the buoy data, particularly on time scales longer than the seasonal one.