KR20090100505A - A two dimentional kinetics code for fluid fuel reactors and the method of simulation using it - Google Patents

Abstract

PURPOSE: A two dimensional kinetic code for analyzing a neutron conduct at a fluid fuel reactor, and a simulation method using the same are provided to calculate realistic value in analyzing a kinetic property of a molten salt reactor. CONSTITUTION: A conduct of neutron and a nuclear fuel is analyzed at a fluid fuel reactor by calculating value of a time-dependent group 2 neutron diffusion equation considering a flow rate of a z-axial. A pseudo-nuclide approximate equation is included in order to consider a radioactive nuclide concentration change due to removal of a nuclear fuel material and a generation material dissolved from the nuclear fuel material.

Description

A two dimentional kinetics code for fluid fuel reactors and the method of simulation using it}

The present invention relates to a novel two-group, two-dimensional code, and stability-related process simulation method for evaluating the spatial dependence of nuclear fuel and neutron behavior in a molten salt reactor and analyzing its dynamics. This is the field of research on the theory of neutron density and power-dependent time-dependent behavior of reactor cores for the safety analysis of reactor systems.

In particular, the present invention relates to a two-dimensional dynamic equation that can be applied in a molten salt nuclear power system and a method for analyzing safety of a reactor using the same.

Nuclear power is responsible for one-sixth of the world's electricity generation and CO, the main culprit of global warming.₂It is the most realistic energy source capable of coping with the sudden increase in power demand due to the improvement of living standard and the increase of population. Despite these facts, it is difficult to be optimistic about the future of nuclear energy due to the emotional weaknesses of nuclear technology itself, the economic causes of excessive initial costs, and various social problems such as waste and proliferation. Much effort is being made globally to overcome this uncertain environment and provide a long-term vision. Future fuel cycles and the development of innovative reactor systems are key tasks. Molten salt nuclear fuel reactor has the ideal advantages as a nuclear energy system such as high proliferation resistance and minimization of high level radioactive waste production. Since the concept was proposed in the ORNL (Oak Ridge National Laboratory) in the 1960s, come. The Molten Salt Nuclear System Code developed by ORNL is unique to molten salt reactors considering the fuel flow characteristics such as the change of delayed neutron seed species density and reactivity loss with respect to the one-point one-point neutron dynamic equations applied in the existing commercial reactors using solid fuel. The dynamic characteristics of can be simulated. However, due to the nature of the molten salt reactor in which the nuclear fuel moves, the variation of the power distribution according to the position must be taken into account, and in particular, when a multi-zone core including an epi-thermal neutron spectral region is constructed to satisfy the performance requirements of the innovative reactor, multi-group multi-dimensional Dynamic analysis must be performed.

An important part of the study of molten salt nuclear systems is the need to simulate and analyze the nuclear and thermodynamic dynamic behaviors to analyze the stability of the system in the event of an accident or anomalous conditions. However, in the case of the reactor using the conventional solid fuel, the molten salt reactor using the flow fuel is different in positional properties due to the movement of the fuel, whereas the nuclear-thermal reaction in the same position until the nuclear fuel is loaded and taken out. Therefore, the application of the classical neutron transport or diffusion model to the molten salt reactor, which assumes that the neutrons move and reacts in the nuclear material structure arranged at a specific position, reduces the accuracy of the dynamic behavior simulation and the reliability of the reactor system design. It is difficult to prove the conservatism of the system and safety system design. In addition, there are difficulties in the analysis of changes in nuclear properties due to the on-line injection and removal of fuel from molten salt reactors and changes in fuel components due to changes in core residence time due to fuel flow rate.

Therefore, the present invention is a two-dimensional dynamic equation that takes into account the fuel flow applicable to molten salt reactors in order to simulate and analyze the nuclear and thermodynamic dynamic behavior for analyzing the stability of the system in the event of accidents and abnormalities in the molten salt nuclear system. And to make the process simulation method using the same as the top priority to solve.

In another aspect, the present invention provides a method for deriving a neutron diffusion model and macroscopic cross-section perturbation model considering fuel flow characteristics and verifying the dynamic behavior analysis code for the molten salt reactor based on the second problem.

The final task is to examine the validity as a model applicable to the actual molten salt reactor by verifying and comparing the results of the MSRE stability test with the one-point dynamic system code.

The present invention provides an equation for analyzing the two-dimensional dynamic characteristics of the flow fuel in order to solve the above problems, and in particular provides a flow dependent two-dimensional dynamic characteristic equation. This is represented by the following formula.

(식1.a)

(Equation 1.a)

(식1.b)

(Equation 1.b)

(식1.c)

(Equation 1.c)

는 z-축방향의 핵연료 유속으로 동일한 특성으로 설정된 영역에서는 동일한 속도를 가지며

는 j-군 지발중성자 모핵종 수밀도의 z-축방향 변화율이다.)(here

Has the same velocity in the region set to the same characteristic as the fuel velocity in the z-axis direction

Is the z-axis rate of change of j-group late neutrophil number density.)

Using the two-dimensional dynamic equations of the present invention, unlike conventional commercial furnaces using solid fuels, it is possible to obtain a very realistic solution for analyzing the dynamic characteristics of a molten salt reactor in which the nuclear fuel itself is in a liquid state. In addition, there is an advantage that the neutron spectrum which can not be dealt with in the one-point dynamic characteristic equation of the system analysis code which is generally used for safety analysis can deal with the multi-domain core which is greatly different.

In addition, if the present invention is applied to the actual flow reactor, it is possible to secure the conservatism and reliability of the safety analysis, and in particular, it can simulate the dynamic characteristics of the core model composed of largely different neutron spectra, which satisfies the performance requirements of the fourth generation reactor system. It is very effective in developing new molten salt reactor.

Hereinafter, the present invention will be described in more detail with reference to formulas and drawings.

Equation 1 is a time-dependent two-group neutron diffusion equation considering the flow velocity in the z-axis direction of the present invention. In the case of molten salt reactors, the flow direction of the nuclear fuel moves at a constant velocity in the z-direction, which causes the late neutron parent species generated in the furnace to flow out of the furnace. At this time, the change in water density due to the migration of late neutrophil nuclide is affected by the time delay corresponding to the cycle of fuel material in the system. The same cause also changes the distribution of z-direction late neutrophil parental density.

In the present invention, as the initial condition and the boundary condition, the core outer boundary values are all set to zero, and the core internal boundary values are set to have a value at equilibrium. At this time, more than 80% of the half-life of the late neutron neutrophils that have been released outside the furnace exceeds the residence time, and 10% of the circulating fuel bypasses the high temperature chemical process. The relatively small increase in the number density of late neutrophils contained in the incoming fuel after recirculation within the system is negligible. Therefore, the late neutron distribution model assumes that there is no significant change in the flow rate dependent characteristics.

(식1.a)

(Eq. 1.a)

(식1.b)

(Equation 1.b)

(식1.c)

(Equation 1.c)

는 z-축방향의 핵연료 유속으로 동일한 특성으로 설정된 영역에서는 동일한 속도를 가지며

는 j-군 지발중성자 모핵종 수밀도의 z-축방향 변화율이다.)(here

Has the same velocity in the region set to the same characteristic as the fuel velocity in the z-axis direction

Is the z-axis rate of change of j-group late neutrophil number density.)

Equation 2 takes into account the radionuclide concentration due to the removal of fission products dissolved in the fuel material in the Pyro reactor. For this purpose, an approximation equation is assumed for the pseudo-nuclide, similar to the density equation. This is because the characteristics of the properties (reaction cross section, temperature, etc.) must be taken into account because the fuel material constituting the molten salt changes the retention characteristics and the nuclear reaction with the neutrons according to the movement path and speed in the reactor. However, the change is less than the change in late neutrophil number density.

(식2)

(Eq. 2)

는 의사핵종의 붕괴상수, 상수

는 중성자흡수반응에 의한 의사핵종의 손실률에 대응하는 물리적 의미가 부여되며 각 상수는 다양한 출력밀도 상태에서 연소진행에 따른 각 격자의 거시단면적 Where constant

Is the decay constant and constant of the pseudonuclide

Is given a physical meaning corresponding to the loss rate of pseudonuclides due to neutron absorption, and each constant is the macroscopic cross-sectional area of each lattice as the combustion progresses at various power densities.

는 외부에서 공급하는 핵연료물질 또는 온라인 재처리 후 재주입되는 핵종의 주입률 및 Xe이나 제어봉과 같은 중성자 흡수율이 큰 물질이 생성 혹은 삽입을 고려하기 위해 거시단면적의 시간증분으로 변환한 값으로서 섭동입력 자료로 사용되었다.The change is calculated using HELIOS 1.5 and then calculated from these results. And

Is the value converted from the macromolecular area time increment to consider the generation or insertion of externally supplied fuel material or material with high neutron absorption rate such as Xe or control rod after re-injection of nuclear species. It was used as data.

Equation 3 shows the change in responsiveness of the output transition process according to the change of core state. In general, three requirements of external reactivity, toxic reactivity, and temperature reactivity should be considered as reactivity insertion conditions for core state changes. In the case of toxic reactivity, the change in time such as ¹³⁵ Xe generated by fission is considered, but in the case of the present invention, ¹³⁵ Xe generated by fission is fine because nuclear fuel is an upflow liquid in the z-axis direction. As bubbles are accelerated and raised by buoyancy inside liquid fuel, they do not significantly affect the equilibrium nuclide density. Therefore, the resiliency change considered in the present invention reflects only the reactivity feedback rate according to the external reactivity and the temperature or output change.

(식 3)

(Equation 3)

는

를 나타내고,

는

를 각각 를 나타낸다.here

Is

Indicates,

Is

Denotes each.

와

값을 갖는 것으로 가정하였다.Equation 4 represents the fourth-order quadratic differential equation that reflects the initial and boundary conditions in Equation 1. As an initial condition, it is assumed that the reactor has been operated at normal output from t = -∞ with normal output. As the boundary condition, the neutron flux and late neutron nucleus species density at the core interface are

Wow

It is assumed to have a value.

(Equation 4a)

(Equation 4b)

(Equation 4c)

Where the prefix 0 represents the steady state and initial state, and z represents the axial direction. The other letters follow the usual convention.

을 초기상태값으로 하여 경계조건을 만족하는 초기정상상태 고유치

및 고유함수

를 구하는 것으로서 이에 대응되는 수치방정식은 유한차분법(Finite difference method)을 사용하여 유도한 정규행렬방정식 형태이다. 위 식들의 해를 구하기 위한 반복계산의 수렴가속을 위해 Chebyshev polynomial method를 사용하였다.The two-dimensional boundary value problem above is given a steady-state military constant.

Initial steady state eigenvalue satisfying boundary condition

And eigenfunctions

The corresponding numerical equation is the normal matrix equation derived using the finite difference method. The Chebyshev polynomial method was used to accelerate the convergence of the iteration to solve the above equations.

Equation 5 converts Equation 1 into a numerical equation. In this case, we use the SOR (Successive over-relaxation method) as the implicit method and the convergence acceleration method as the iterative calculation method for the finite difference approximation model, similar to the initial state equation. The numerical solution of the finite-difference method for time-dependent problems is sensitive to the magnitude of the time increment, and the smaller the time increment, the more theoretically accurate the result will be. It is desirable to use it after determining the optimal time increment size since it will be consumed. In addition, the explicit method of the numerical equation model has a problem of easily diverging due to the accumulation of truncation errors, while the implicit method does not cause a divergence of calculation because the cutting error can be kept constant. Although the equations are slightly complicated in consideration of the computational stability, the implicit method is used in the calculation of the dynamic characteristics.

(Eq. 5)

Equation 6 shows the time-varying macroscopic cross section in the liquid fuel system. Unlike solid fuels, the rate of change of macroscopic cross-sectional area in liquid fuels has a significant effect on core dynamics within a time constant range similar to that of late neutron nucleus species. Therefore, the quasi-static approximation is used to account for this.

(Equation 6)

1 is a flowchart showing a flow chart of applying the equation of the present invention to a liquid reactor to find a solution. In the flowchart, the steady state operation is assumed, and the initial condition calculation and the dynamic characteristic calculation are performed over the transition time after perturbation. The steady-state calculation first uses the grid code to provide the calculated grid constants and fuel steady flow rates for the absence of fuel flow in the z-axis direction as input data, and the neutron flux, delayed neutron seedling density and multiplication factor. Assuming the initial value is equal to 1.0, converged values are obtained while performing internal and external iterations.

Since the neutron flux and delayed neutron nucleus species density are sensitive to time change, the calculation time increment unit is set short, and the time increment is calculated to have a relatively long value when calculating the macroscopic area dependent on the rate of change of nuclide density.

2 is a diagram showing the concentration distribution of axial late neutron parent species.

In the case of molten salt reactors, the most distinctive feature from the commercial reactors is the change in late neutron distribution due to fuel flow. As shown in FIG. 2, it can be seen that the distribution of late neutron nuclides is axially oriented in the direction of fuel flow. This is different from the cosine distribution in commercial furnaces, and since the shape can be changed by changing the flow rate or the partial reactivity, it is not possible to calculate precisely by one point kinetics. Can be considered, resulting in more accurate calculations.

EXAMPLE

In order to verify the validity of the equations shown in Equations 1 to 6 of the present invention and the calculation results according to the flowchart shown in FIG. 1, the experimental results were compared using the frequency response method using the MSRE reactor.

The frequency response test method used in the embodiment generates signals of Pseudo Random Binary Sequence (PRBS) and Pseudo Random Ternary Sequence (PRTS), and uses the Flux demand test at high power and the Rod-jog test method at low power. After the measurement, the measurement data were analyzed by CPSD and CABS. In addition, this result is compared with the one point kinetics developed by ORNL for analyzing a conventional molten salt reactor, and the results are shown in FIGS. 3 to 8.

In the frequency response of the present invention, the output change ratio and the phase change ratio in response to the inserted reactivity according to the above-described experimental method were measured as stability parameters while operating at 8 MW, 5 MW and 2 MW of heat output. The measured data were summarized with reference to the graph shown in RC Steffy Jr .: "Frequency response testing of the molten salt reactor experiments", ORNL, (1970), and the values calculated by the equations of the present invention were placed thereon. It is shown together for easy direct comparison.

Overall, the value calculated by the equation of the present invention was considered to be closer to the experimental results than the MSRE system analysis code because it can consider the intrinsic characteristics of molten salt fuel such as the change in the distribution of the late neutron nuclide concentration. In particular, the output change ratio tends to be closer than the phase change ratio, which is believed to be due to the weakness of the thermal hydraulic model and the system recirculation model which have more influence on the phase change, and the refinement of the model will allow more sophisticated results. It is expected. In addition, the MSRE system code using the one-point dynamic characteristic equation shows a resonance between 0.2 rad and 0.4 rad, which can be considered as a feedback effect due to the reflow of nuclear fuel leaving the core after system circulation. On the other hand, since the calculation result by the equation of the present invention does not include a phylogenetic model, such a resonance effect does not appear, and it is found to represent a more realistic result.

1 is a flowchart showing a flow chart of applying the equation of the present invention to a liquid reactor to find a solution.

2 is a diagram showing the concentration distribution of axial late neutron parent species.

3 is a graph showing a frequency response to an 8MW output change.

4 is a graph showing the frequency response to 8MW output change with phase delay.

5 is a graph showing a frequency response to a 5MW output change.

6 is a graph showing the frequency response to a 5MW output change with phase delay.

7 is a graph showing a frequency response to a 2MW output change.

8 is a graph showing a frequency response to a 5MW output change with phase delay.

Claims (4)

a method of analyzing the behavior of nuclear fuel and neutrons in a flow reactor by solving the following time-dependent two-group neutron diffusion equations (Equations 1.a to 1.c) taking into account the flow velocity in the z-axis direction;

(Eq. 1.a)

(Equation 1.b)

(Equation 1.c) (here

Has the same velocity in the region set to the same characteristic as the fuel velocity in the z-axis direction

Is the z-axis rate of change of j-group late neutrophil number density.) The method according to claim 1, In order to consider the change in radionuclide concentration as the fuel material and its dissolved products are removed, the following pseudo-nuclide approximation equation (2) is used. How to interpret the behavior;

(Eq. 2) Where constant

Is the decay constant and constant of the pseudonuclide

Is the loss rate of pseudonuclides due to neutron absorption.) Converting the equations of claims 1 and 2 into the following numerical equations to analyze the behavior of nuclear fuel and neutrons in a flow reactor;

(Eq. 5)

(Equation 6) (here,

Is the fraction of convergence solution of (t + 1) time to the convergence solution of time t, M is the coefficients of Equations 1.a and 1.b and P is the coefficient of Equation 1.c,

And

The rate of change of the neutron response on the right side Rate of change of neutron velocity,

Means amplified by, l is the spatial lattice in the z-axis direction,

Is the time grid and m and i are the grid and energy groups, respectively.) In calculating the equation of claims 1 to 3; A method of interpreting the behavior of nuclear fuel and neutrons in a fluidized reactor, characterized in that the dynamic mode equations that require calculations for short time increments are changed frequently, and the less time-sensitive pseudonuclide change equations are calculated less.

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