CN112069670B - Monte Carlo simulation method for active critical device in critical approaching process - Google Patents
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- 229910052778 Plutonium Inorganic materials 0.000 description 3
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- OYEHPCDNVJXUIW-UHFFFAOYSA-N plutonium atom Chemical compound [Pu] OYEHPCDNVJXUIW-UHFFFAOYSA-N 0.000 description 3
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- ZQPKENGPMDNVKK-UHFFFAOYSA-N nitric acid;plutonium Chemical compound [Pu].O[N+]([O-])=O ZQPKENGPMDNVKK-UHFFFAOYSA-N 0.000 description 1
- 230000009257 reactivity Effects 0.000 description 1
- 230000004044 response Effects 0.000 description 1
- 239000002915 spent fuel radioactive waste Substances 0.000 description 1
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Abstract
The invention relates to a Monte Carlo simulation method of an active critical device in a critical approaching process, which is applicable to the field of neutron physics analysis of a nuclear critical device with an external neutron source. The method decomposes the continuous neutron transport process into generation-by-generation simulation calculation, and performs weighted summation according to the effective neutron multiplication factors of the generation-by-generation system and the generation-by-generation physical quantity statistical count to obtain the final calculation results of physical quantities such as the nuclear critical device power level, neutron flux distribution and the like. The method realizes Monte Carlo simulation of the external neutron source transportation process in the process that the nuclear critical device approaches to the critical process, avoids the condition that infinite transportation calculation of a certain external neutron source is not terminated due to randomness of the Monte Carlo method, and is an advanced Monte Carlo simulation method of the neutron transportation process of the active critical device with engineering feasibility.
Description
Technical Field
The invention relates to a neutron physics analysis technology of a nuclear critical device, in particular to a Monte Carlo simulation method of an active critical device in a critical approaching process.
Background
When a nuclear critical experiment is carried out, in order to better monitor the physical state of the nuclear critical device, an external neutron source with certain intensity is generally required to be configured in the nuclear critical device, meanwhile, neutron detectors are arranged at different positions, and characteristic parameters such as the subcritical degree, the reactivity introduction rate and the like of the nuclear critical device are estimated by monitoring neutron flux distribution and the change rate of the neutron flux distribution at different positions, so that the nuclear critical related experiment is carried out safely and efficiently.
Therefore, when the design of the nuclear critical device is developed, the data such as neutron flux distribution of each detection point in the process of approaching the critical device to the critical device needs to be calculated and analyzed in detail so as to be used for the range design and debugging operation reference of the neutron detector. Computational analysis typically employs a three-dimensional monte carlo procedure, and the following problems are often encountered in computational analysis: system itself k eff When the probability is larger, for example, the probability is larger than 0.99, the Monte Carlo simulation condition that the neutron source infinite transportation calculation is not terminated and the effective neutron transportation process is difficult to develop exists due to the randomness of the Monte Carlo method, so that the data such as neutron flux distribution of each detection point cannot be obtained, and great difficulty is brought to the aspects of measuring range design, flux value reference during debugging operation and the like of the neutron detector of each detection point.
In addition, similar technical difficulties are encountered in reactor physical designs such as passive start-up of the nuclear power plant core, calculation of the detector response of the reactor core dynamic rod etching, and the like. In engineering design, an approximate calculation method such as direct critical calculation is generally adopted, so that small calculation deviation is brought.
From the research situation in the field of neutron physics analysis of nuclear critical devices with external neutron sources at home and abroad, a few researchers have studied the multiplication effect of the external neutron sources, and are aware that the method adopts 1/(1-k) according to the direct critical calculation eff ) Calculating the multiplication effect of the external neutron source is unsuitable because the arrangement position of the external neutron source and the energy thereof are all effective for the multiplication effect of the neutron source, and k eff But is a feature of the system itself, independent of the external neutron source. For example, in the case of an external neutron source arranged in the center of the device, the measured neutron density ratio is 1/(1-k) eff ) The neutron flux density calculated to calculate the external neutron source multiplication effect is high.
Later, the researcher defines the effective multiplication coefficient k of the active subcritical neutrons s To develop the source multiplication method measurement analysis of the active subcritical system. k (k) s Defined as the ratio of fissile neutrons to total neutron sources, which is dependent on the characteristics of the external neutron sources in addition to the characteristics of the breeder system, and relates to the efficiency of utilization of the external neutron sources. Through experimental measurement, when the field measurement technology applies a source multiplication method, when a neutron source is positioned in nuclear fuel, the measured k is s Greater than k eff It is used to measure security conservatively; when the neutron source is located outside the nuclear fuel, the measured k s Less than k eff It is dangerous to use it to measure security. ( See: shi Yongqian, zhu Qingfu, etc., supervision field measurement techniques in nuclear critical safety-certain problems of source multiplication methods, nuclear power engineering, volume 25, phase 2, month 4 2004. )
From the investigation situation, the related research is mostly used for experimental measurement analysis, the simulation of neutron physics analysis in the process of approaching a critical device with an external neutron source is carried out less, and the system is k eff Beyond 0.99, the problem that infinite transport calculation of a neutron source outside a certain generation is not terminated and an effective neutron transport process is difficult to develop, which occurs during Monte Carlo program simulation, has not been provided by researchers. Neutron physics analysis simulation of critical device with external neutron source, k of system itself, developed in a small amount of literature eff Typically not exceeding 0.99. ( See: sun Yanting, a simulation study and verification of improved source-time expansion, intense laser and particle beam, volume 30, 1 st, month 1 of 2018. )
From the engineering application point of view, the construction requirement of the spent fuel post-treatment plant is urgent to the research requirement of the development critical experimental device, and when the nuclear critical device design is developed, the requirement of detailed calculation and analysis of physical quantities such as device power level, neutron flux distribution of each detection point and the like in the process of approaching the nuclear critical device to critical is met, so that the development of an active critical device Monte Carlo simulation method with engineering feasibility in the process of approaching the critical is very necessary.
Disclosure of Invention
The invention aims to provide a Monte Carlo simulation method suitable for a nuclear critical device with an external neutron source, which meets the calculation requirements of physical quantities such as neutron transport process simulation, solving of the power level of the nuclear critical device, neutron flux distribution and the like of the nuclear critical device in the process of approaching a critical.
The technical scheme of the invention is as follows: according to a chain fission reaction process initiated by an external neutron source in a nuclear critical device, the fission reaction is treated as absorption, information of the fission reaction is recorded, the neutron continuous transportation process is decomposed into generation-by-generation analog calculation in a mode of starting source item information of neutrons of a next generation source, and a final calculation result of related physical quantity is obtained by weighting and summing according to effective multiplication factors of neutrons of a generation-by-generation system and statistics counts of physical quantity of generation-by-generation, wherein the statistics counts of physical quantity refer to statistics results of physical quantity counts caused by neutrons of each source in Monte Carlo simulation.
The physical quantities include nuclear critical device power levels, power distribution, neutron flux distribution, energy deposition distribution, various nuclear reaction rates, and the like.
Further, in the monte carlo simulation method of the active critical device, before simulation calculation, source item input of the monte carlo program is set according to actual positions and energy parameters of an external neutron source, physical quantity statistical counts needing to be calculated are output after calculation generation by generation, and meanwhile physical quantity statistical counts of any generation are not discarded.
Further, the number of particles to be charged for each generation of calculation should be sufficiently large so that the relative statistical deviation of the statistical count of the physical quantity calculated for each generation satisfies the calculation requirement of the monte carlo method.
Further, the method for simulating the Monte Carlo of the active critical device as described above, wherein the weighted calculation of the physical quantity statistical count is performed by adopting the following formula:
wherein F is the final calculation result of the physical quantity, N is the total algebra of calculation, F i Counting the physical quantity calculated for the ith generation, c i The weighting factor, k, of the counting result is counted for the physical quantity calculated for the ith generation a 、f a And respectively counting the effective proliferation factors and physical quantity in the stably calculated system.
Further, the i-th generation calculated physical quantity statistical count f i The following formula is adopted for calculation:
wherein A is i The physical quantity statistical count output after the calculation of the ith generation is the physical quantity statistical count average value calculated by the generation and the previous generation.
The weighting factor c of the physical quantity counting result of the ith generation of calculation i The following formula is adopted for calculation:
wherein k is j Effective multiplication factor of system neutron obtained by calculation of jth generation。
The steady calculated system neutron effective multiplication factor and physical quantity statistics counting result k a 、f a The following formulas are used for calculation:
to ensure k a 、f a Reliability of calculation result, corresponding to k N/2 To k N And (3) carrying out statistical analysis on the data, and confirming that the data meets the relative statistical deviation requirement of the Monte Carlo program on neutron effective proliferation factors and physical quantity statistical counting results.
The beneficial effects of the invention are as follows:
according to the Monte Carlo simulation method of the active critical device in the critical approaching process, the continuous transportation process is decomposed into generation-by-generation simulation calculation by adopting a three-dimensional Monte Carlo program, and physical calculation results such as the power level of the nuclear critical device, neutron flux distribution and the like are obtained through weighting according to the effective neutron multiplication factors of the generation-by-generation system and the statistics count of the generation-by-generation physical quantity. The method realizes Monte Carlo simulation of neutron transport process in the process that the nuclear critical device approaches the critical process, avoids the condition that infinite transport calculation of a neutron source is not terminated outside a certain generation caused by randomness of the Monte Carlo method, and is an advanced Monte Carlo simulation method of neutron transport process of the active critical device with engineering feasibility.
The invention effectively solves the problem that the nuclear critical device with an external neutron source is in the process of approaching critical (for example, the system k eff Over 0.99), the infinite transport calculation of a neutron source outside a certain generation caused by the randomness of the Monte Carlo method is not terminated, and the Monte Carlo simulation of an effective neutron transport process is difficult to develop. The nuclear critical device system k is realized by the Monte Carlo simulation method of the external neutron source in the critical approaching process eff Over 0.99 and even over 0.997, monte Carlo simulation of an effective neutron transport process can be carried out, and through verification,the physical quantity calculation results such as the power level of the nuclear critical device, the neutron flux distribution and the like are correct and reliable, can be applied to the field of neutron physical analysis of the nuclear critical device with an external neutron source, and solves the Monte Carlo simulation problem of the neutron transport process in the process that the nuclear critical device approaches the critical process.
Drawings
FIG. 1 is a diagram of a plutonium solution critical apparatus model with an external neutron source and a related neutron flux station layout.
FIG. 2 shows k at different liquid level heights for a plutonium solution critical apparatus eff And source neutron multiplication factor results obtained by different calculation methods.
FIG. 3 shows the result of calculating the neutron flux (normalized to one exogenous neutron) at each measuring point position obtained by the Monte Carlo simulation method of the external neutron source.
Detailed Description
The present invention will be described in further detail with reference to the drawings and examples, in order to make the objects, technical solutions and advantages of the present invention more apparent. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the scope of the invention.
According to the Monte Carlo simulation method of the active critical device in the approaching critical process, according to the chain fission reaction process initiated by an external neutron source in the nuclear critical device, the fission reaction is treated as absorption, namely, when the fission reaction is initiated by neutrons, the neutrons are considered to be absorbed, and the fission neutrons are not directly generated to continue neutron transport calculation; meanwhile, information of fission reaction (including information of position coordinates, fission reaction nuclide, neutron generation number of a fission source, energy, direction and the like) is recorded and used as initial source item information (including position coordinates, energy, direction) of the neutrons of the next generation source, so that a continuous transportation process is decomposed into generation-by-generation simulation calculation, and physical quantity calculation results such as nuclear critical device power level, power distribution, neutron flux distribution, energy deposition distribution, various nuclear reaction rates and the like are obtained by weighting according to effective multiplication factors of the neutrons of the generation-by-generation system and generation-by-generation physical quantity statistical counts (statistical results of physical quantity counts caused by each source neutron in Monte Carlo simulation).
This example illustrates how the invention can be applied to the physical analysis of neutrons in a nuclear critical device with an external neutron source, taking as an example a cylindrical critical device containing a plutonium solution.
As shown in FIG. 1, the solution tank of the embodiment has a height of 80cm, an inner diameter of 26cm and a wall thickness of 0.5cm, and is filled with plutonium nitrate solution, and the device is made to approach a critical state by adjusting the height of the solution. 9 neutron detectors are arranged in the height direction of the solution tank and are used for measuring neutron flux data. And a dot-shaped external neutron source is arranged at the center of the bottom of the solution tank.
Firstly, a three-dimensional Monte Carlo program is adopted to establish a three-dimensional calculation model, a critical calculation mode of the Monte Carlo program is adopted to approximately simulate the calculation mode of the invention, parameters such as the initial neutron source position and the like of critical calculation are set to be the same as parameters such as the actual position and the like of an external neutron source (bottom center and punctiform neutron source), and the physical quantity statistical count required to be calculated is output after each generation of calculation of the program is set, and meanwhile, the physical quantity statistical count of any generation is not abandoned. The number of particles input for each generation of calculation should be sufficiently large (4000000 here), so that the relative statistical deviation of the physical quantity statistical count of each generation of calculation can meet the calculation requirement (below 5%) of the monte carlo method. The total calculated was 100 generations.
By carrying out the above calculation, the following calculation results can be obtained: physical quantity statistical count A output after ith generation of calculation i Effective multiplication factor k in system neutron i . Then, the physical quantity statistical count f calculated in the ith generation is calculated by using the formula (2) i Calculating a weighting factor c for the physical quantity count result of the ith generation by using the above formula (3) i Calculating by adopting the formula (4) to obtain the effective multiplication factor and the physical quantity counting result k of the system neutron which is calculated stably a 、f a 。
To ensure k a 、f a Reliability of calculation result, for k N/2 To k N Data between are statistically analyzed, k N/2 To k N Between 50 k j Data surrounds its mean k a The root mean square relative error of (a) is 0.6% N/2 To k N Between 50 f i Data around its mean f a The root mean square relative error of (2) is 1.5%, the statistical expansion of (2) is within an acceptable range, and the requirements of Meng Kacheng sequences on the neutron effective multiplication factor relative statistical deviation (less than 1 per mill) and the physical quantity statistical count relative statistical deviation (less than 5%) are respectively met.
Finally, the final calculation results of the physical quantities such as the power level, neutron flux distribution and the like are obtained by calculation by adopting the formula (1). The calculation process recovers the statistical count of the physical quantity calculated in each generation from the statistical count average of the physical quantity calculated in each generation according to the mode of the simulation calculation in each generation, calculates the weighting factor (namely the attenuation coefficient of the neutron quantity in each generation) of the physical quantity calculation result according to the effective proliferation factor of the neutron in the system calculated in each generation, obtains the effective proliferation factor and the physical quantity calculation result of the neutron in the system calculated stably according to the calculation result of each generation after the neutron distribution of the fission source is stable, and obtains the final calculation result of the physical quantity such as the power level, the neutron flux distribution and the like of the nuclear critical device by carrying out weighted summation on the physical quantity calculation results of each generation calculated in the development calculation and taking the physical quantity calculation result of each generation after the stabilization into consideration by adopting the mode of equal ratio series summation.
By contrast, a three-dimensional Monte Carlo program is also adopted to establish a three-dimensional calculation model, and in an external neutron source calculation mode, enough particle numbers (20000000 is set here) are calculated, so that the relative statistical deviation of the finally obtained physical quantity statistical count can meet the calculation requirement (below 5%) of the Monte Carlo method.
For the present embodiment, the system itself k eff The calculation mode of the external neutron source is more than three points of 0.995, so that the situation that the infinite transportation calculation of the external neutron source is not terminated in a certain generation can occur, and the Monte Carlo simulation of the effective neutron transportation process can not be carried out. The relative deviation of the multiplication factor of the source neutrons was compared for each previous state point, and as can be seen from fig. 2, the two are basically overlapped, and the relative deviation is within + -3%. In contrast, if the conventional critical calculation mode is directly adopted for developing phasesThe analysis and calculation results are very different.
In addition, the neutron flux calculation results of the detection points are compared in detail, and the relative deviation is within +/-4%. Therefore, the Monte Carlo simulation method of the external neutron source provided by the invention is correct and reliable.
FIG. 3 shows the result of calculating the neutron flux (normalized to an exogenous neutron) at each measuring point position obtained by the Monte Carlo simulation method of the external neutron source. As can be seen from the figure, the different systems themselves k eff The Monte Carlo simulation method of the active critical device can be used for carrying out calculation, so that the calculation results of physical quantities such as power level, neutron flux distribution and the like in the process that the nuclear critical device approaches the critical process can be obtained.
It will be evident to those skilled in the art that the inventive method is not limited to the details of the foregoing illustrative embodiments, and that the present method may be embodied in other specific forms without departing from the spirit or essential characteristics thereof. The present embodiments are, therefore, to be considered in all respects as illustrative and not restrictive, the scope of the inventive method being indicated by the appended claims rather than by the foregoing description, and all changes which come within the meaning and range of equivalency of the claims are therefore intended to be embraced therein. Any reference sign in a claim should not be construed as limiting the claim concerned.
Furthermore, it should be understood that although the present disclosure describes embodiments, not every embodiment is provided with a separate embodiment, and that this description is provided for clarity only, and that the disclosure is not limited to the embodiments described in detail below, and that the embodiments described in the examples may be combined as appropriate to form other embodiments that will be apparent to those skilled in the art.
Claims (4)
1. A Monte Carlo simulation method of an active critical device in a critical approaching process is characterized in that: according to a chain fission reaction process initiated by an external neutron source in a nuclear critical device, processing fission reaction as absorption, recording information of the fission reaction, decomposing a neutron continuous transportation process into generation-by-generation analog calculation in a mode of taking the information as initial source item information of neutrons of a next generation source, and carrying out weighted summation according to effective multiplication factors of the neutrons of the generation-by-generation system and statistics and counting of physical quantities of the generation-by-generation so as to obtain a final calculation result of related physical quantities;
the weighting calculation of the physical quantity statistical count is performed using the following formula:
wherein F is the final calculation result of the physical quantity, N is the total algebra of calculation, F i Counting the physical quantity calculated for the ith generation, c i The weighting factor, k, of the counting result is counted for the physical quantity calculated for the ith generation a 、f a Respectively counting the effective proliferation factors and physical quantity in the stably calculated system;
the physical quantity statistical count f calculated in the ith generation i The following formula is adopted for calculation:
wherein A is i The physical quantity statistical count output after the calculation of the ith generation is the physical quantity statistical count average value calculated by the calculation of the ith generation and the previous generation;
the weighting factor c of the physical quantity counting result of the ith generation of calculation i The following formula is adopted for calculation:
wherein k is j The effective proliferation factor of the system neutron obtained by calculation of the jth generation;
the stable calculation systemStatistics and counting result k of effective multiplication factor and physical quantity in unified sub-system a 、f a The following formulas are used for calculation:
to ensure k a 、f a Reliability of calculation result, corresponding to k N/2 To k N And (3) carrying out statistical analysis on the data, and confirming that the data meets the relative statistical deviation requirement of the Monte Carlo program on neutron effective proliferation factors and physical quantity statistical counting results.
2. The active critical device monte carlo simulation method of claim 1, wherein: the physical quantities include nuclear critical device power level, power distribution, neutron flux distribution, energy deposition distribution, various nuclear reaction rates.
3. The active critical device monte carlo simulation method of claim 1, wherein: before analog calculation, source item input of a Monte Carlo program is set according to the actual position and energy parameters of an external neutron source, and physical quantity statistical counts needing to be calculated are output after generation-by-generation calculation, and meanwhile physical quantity statistical counts of any generation are not abandoned.
4. The active critical device monte carlo simulation method according to claim 3, wherein: the number of particles that are input for each generation of calculation should be sufficiently large so that the relative statistical deviation of the statistical count of the physical quantity calculated for each generation satisfies the calculation requirements of the monte carlo method.
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