核动力工程

Calculation of Effective Multiplication Factor with Dynamic Monte Carlo Method

XIE Qi-lin, LIU Han-gang, YANG Cheng-de, HE Ren-fu, FAN Xiao-qiang

2010, 31(4): 1-4.

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The dynamic method of effective multiplication factor k_eff calculation is discussed and the dynamic Monte Carlo code based on Geant4 toolkit is developed.The effective multiplication factor k_eff of GodivaI reactor（in benchmark） and systems which are far from critical has been calculated using this method. Results show that the K static method is only accurate for the system that is close to critical,and dynamic method can be used not only for the system that is close to critical but also for the system that is far from critical.

Preliminary Concept Design on Blanket Neutronics of a Fusion-Fission Hybrid Reactor for Energy Production

SHI Xue-ming, PENG Xian-jue

2010, 31(4): 5-7,20.

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A concept of energy production reactor is given in this paper.It uses the natural uranium or U-Zr alloy of the spent fuel in PWR as its fuel and cooled by water.This concept is proliferation resistant for it needs no separation of plutonium from spent fuel.Preliminary concept design on blanket neutronics is finished by a burnup code coupled by MCNP and ORIGENS.Designs with natural uranium or spent fuel from PWR as fuels are computed and preliminary reload scheme is given.It requires lower fusion power than ITER and makes full use of ²³⁸U,which is of great significance for the sustainable development of nuclear energy.

Energy Calculation on Fuel Assembly Containing Gadolinium

WANG Jia-chong, AN Ping

2010, 31(4): 8-11.

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Based on the analysis of the physical properties and the calculation result of an assembly, this paper points out that it may cause errors in calculating the assembly parameters containing gadolinium, which is of the simplified formula without considering the energy from capture reaction and the short of the capture cross section and the energy parameter in some nuclear data library.At the same time the correct formula is showed with the improved algorithm and the mature program.

Experimental Research on Prompt Neutron Decay Parameter α for Research Reactors Based on Labview Technology

ZENG He-rong, HAN Wei-shi, DUAN Shi-lin

2010, 31(4): 12-15.

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The prompt neutron decay parameterαfor 300^# research reactor is experimentally studied by the reactor cross power spectral density（CPSD） measurement system.The reactor core is loaded with the used low enriched uranium with a certain burnup.The measurement system uses PCI-6143 high-speed synchronization DAQ and Labview8.5 program as the measurement hardware and development software, respectively.The continuous current signals of neutron in the reactor are acquired by the gamma compensation ionization chambers which are symmetrically positioned in the reactor core.The cross power spectral density,for the two channel signals,is computed using the application program of data acquirement and data process analysis.Finally,using the non-linear least squares method,the prompt neutron decay parameterαis fitted,i.e.α=（83.5±0.6）s^-1.The result accords to the real operation process,which shows that the measurement of the prompt neutron decay parameter α is successful.

Problem and Solution of Tally Segment Card in MCNP Code

JIE Jia-chun, ZHAO Shou-zhi, SUN Zheng, JIA Bao-shan

2010, 31(4): 16-20.

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Wrong results may be given when FS card（tally segment card） was used for tally with other tally cards in Monte Carlo code MCNP.According to the comparison of segment tally results which were obtained by FS card of three different models of the same geometry,the tally results of fuel regions were found to be wrong in fill pattern.The reason is that the fuel cells were described by Universe card and FILL card,and the filled cells were always considered at Universe card definition place.A proposed solution was that the segment tally for filled cells was done at Universe card definition place.Radial flux distribution of one example was calculated in this way.The results show that the fault of segment tally with FS card in fill pattern could be solved by this method.

Perturbation Calculation for Reactivity of Components in IHNI-1

WANG Chun-yi, JIANG Xin-biao, JI Song-tao

2010, 31(4): 21-24.

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The perturbation calculation for the reactivity worth of the components in the first In-Hospital Neutron Irradiator（IHNI-1） was conducted by using MCNP Monte Carlo code（MCNP）,and the reactivity worth of the central control rods,auxiliary control rod,upside Be reflection layer and fuel elements were reasonably calculated.The difference between the calculated value and experimental value was analyzed.The results showed that the calculated value agreed with the experimental value for the components of IHNI-1 reactor,and the calculation precision of the perturbation method meets the requirement on the calculation of reactivity worth of the reactor components.

Transient Analysis of Secondary-Side Passive Residual Heat Removal System

YAN Chun, WANG Jian-jun, YAN Chang-qi

2010, 31(4): 25-30.

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One design scheme for secondary-side passive residual heat removal system is presented based on the prototype of AP1000 primary system.The RELAP5/MOD3.2 is used to simulate and analyze the transient process of the PRHR system during blackout accident.In addition,the factors having effects on the capacity of natural circulation and the stability of interface between cold and hot fluid in density lock are analyzed based on the calculation results.The results show that the core residual heat is able to be removed effectively using natural circulation,and the capacity of system can be assured by the PRHR system which is rationally designed,and the height difference between steam generator and PRHR heat exchanger and the local resistance in density lock are the principal factors having effects on the operating capacity of system.

Numerical Simulation on Near Wall Fluid Temperature of Non-Isothermal Jet with Cross-Flow for Safety Injection Inclined Tube in Reactors

LUO Yu-shan, HE Hui-ning, WANG Hai-jun, ZHANG Yi-xiong, MAO Qing

2010, 31(4): 31-35.

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In order to obtain the characteristics of the near wall fluid temperature variation and distribution of non-isothermal jet with cross-flow for the safety injection（SI） inclined tube with 45°angle in reactor,the numerical simulations were carried out at the velocity ratio range from 0.87 to 40 and when the temperature differences between jet flow and main flow were 30 and 70℃.The numerical simulations were performed at 1/9-scale model using the commercial computational fluid dynamics software CFX.Based on the calculation results,the mixing function of near wall fluid in different regions of SI inclined tube was obtained.Through the comparison of the mixing function of near wall fluid in different region at 30 and 70℃temperature differences,it was discovered that the mixing function values of each measurement point at 30 and 70℃temperature differences were basically changeless,namely,the effect of the temperature difference on the mixing function of each measurement point was small.The calculation results of the mixing function agreed well with the test ones.

An Evaluation of Prediction Methods for Frictional Pressure Drop of Two-Phase Flow in Mini-Channels

SUN Li-cheng, YAN Chang-qi, SUN Zhong-ning

2010, 31(4): 36-40.

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2092 pieces of data for frictional pressure drop of two-phase flow were collected from 18 published papers of which the working fluids include R123,R134a,R22,R236ea,R245fa,R404a,R407C, R410a,R507,CO₂,water and air.The hydraulic diameter ranges from 0.506 to 12mm;Re_gl from 10 to 37000, and Re_gg from 3 to 4×10~5.11 correlations and models for calculating the frictional pressure drop of two-phase flow were evaluated based on these data.The results show that the accuracy of the Lockhart-Martinelli method,Mishima and Hibiki correlation,Zhang and Mishima correlation and Lee and Mudawar correlation in the laminar region is very close to each other,while the Muller-Steinhagen and Heck correlation is the best among the evaluated correlations in the turbulent region.New correlation based on Chishom method was proposed,which is better than other methods in both laminar region and turbulent region.

Comparison Studies on Flow and Heat Transfer Characteristics in Near Wall Region for Jet Flow with Different Injection Angle

LUO Yu-shan, CHEN Feng-yun, WANG Hai-jun, YANG Sheng, MAO Qing, ZHANG Yi-xiong

2010, 31(4): 41-47.

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To the flow and heat transfer characteristics in near wall region for jet flow with different injection angle in the reactor coolant system,based on the test results,the flow characteristics and mixing function and non-dimensional heat transfer coefficient in different regions of T junction components with 45⁰ and 90⁰ injection angle were compared and analyzed at the velocity ratio range from 0 to 2.The research results indicated that the effect of the injection angle on the change trend of the mixing function and non-dimensional heat transfer coefficient is small,and the key parameter determining the change trend is still the velocity ratio:The effect of the injection angle is only on the values of the mixing function and non-dimensional heat transfer coefficient.

Experimental Study on Performance of Pulsed Liquid Jet Pump

XU Wei-hui, GAO Chuan-chang, QIN Hai-xia

2010, 31(4): 48-51.

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The device performance characteristics of transformer type pulsed liquid pump device were experimentally studied.The effects of the area ratio,work pressure and pulse parameters on the performance of the pulsed liquid jet pump device were performed in the tests.The potency of pulsed jet on improving the performance of the liquid jet pump device was also studied through the comparison with invariable jet pump at the same conditions.The results show that the pulsed jet can significantly improve the performance of transformer type jet pump devices.Area ratio and pulse parameters are the critical factors to the performance of the pulsed liquid jet pump device.The jet pump device performances are significantly improved by reducing the area ratio or by increasing the pulsed frequency.The flux characteristics of the pulsed liquid jet pump device presents the typical negative linear,the potency of pulsed jet in improving the performance of jet pump device with small area ratio can be more significant.The efficiency curve of pulsed liquid jet pump is similar to the parabola.At higher pulsed frequency,the top efficiency point of the pulsed jet pump moves to the higher flow ratio.The high efficiency area of the pulsed jet pump also is widened with the increase of the pulsed frequencv.

Theoretical Analysis of Effect of Ocean Condition on Natural Circulation Flow

GONG Hou-jun, YANG Xing-tuan, JIANG Sheng-yao, LIU Zhi-yong

2010, 31(4): 52-56.

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According to the simulation loop of Integrated natural circulation reactor,the mathematical model of natural circulation in non-inertial reference system is established,and the influence mechanism of ocean condition upon natural circulation is analyzed.Software is programmed to investigate the behaviors in the cases of rolling without heating power,static state with different power and rolling with heating power, and calculation results show that:the inertia force added by rolling causes the periodical fluctuating of the flow rate of channels,but it is not the direct reason of core flow fluctuation.The heave changes the driving head,and causes the same flow rate fluctuation of all channels.Inclining makes the core flow rate decrease, but the change of flow rate of different channels is different.

Application of MC Method to Simulate Initiating Event Frequency of Loss of Equipment Cooling Water System in Nuclear Power Plants

YU Yu, TONG Jie-juan, ZHAO Jun, LIU Tao, ZHANG A-ling

2010, 31(4): 57-60.

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Monte Carlo simulation is used in this paper to analyze the initiating event of loss of equipment cooling water system,the frequency of 2.7×10^-3/（reactor·year）^-1 is obtained,and the main contributor is the common cause demand failure of equipment cooling water system pumps and service water system pumps.The traditional fault tree result is 3.8×10^-1/（reactor·year）^-1（the main contributor is independent operation failure of equipment cooling water system pumps/service water system pumps）.This result is more closer to the statistic value 9.7×10^-4//（reactor·year）^-1 in the Nuclear Regulatory Commission（NRC） report NUREG/CR-5750.The reason is that the mission time of the system in initiating event analysis is 1 reactor.year,so the redundant devices and the repair of the fault devices are important factors for the result. And for this type of problem related to the time order,the assumption is too conservative because of lack of time factor in the fault tree,while MC simulation is a dynamic method,and the system behavior can be described adequately,so the result is more closer to the statistic value of the nuclear power plant.

Risk of Loss Power for ATWT in Daya Bay and Ling’ao Nuclear Power Stations

GUO Cheng

2010, 31(4): 61-65.

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In order to analyze the differences between the Anticipated Transient Without Reactor Trip （ATWT） and other reactor protection methods,this paper analyzes in detail the realizing means of ATWT and the effect of lost of power supply on the units based on Daya Bay and Ling’ao Nuclear Power Stations by system wiring diagram.Based on the comprehensive analysis,this paper proposes the sequence for powering when recovering the power source after ATWT power supply（LCC / LNE） loss for Daya Bay and Ling’ao Nuclear Power Stations.

Simulation Study on Improvement of Steam Generator Level Control System of Ling’ao Nuclear Power Station

CHEN Zhi, ZHANG Ying, ZHANG Fan, YU Hong-xing

2010, 31(4): 66-70.

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In order to solve the vibration problem of the main feedwater pipeline and control valve of Ling’ao Nuclear Power Station,the steam generator level control system requires improvement.The improvement plan is analyzed and verified by using CATIA2 design program which used for analyzing the transient and optimizing control system of NPP,according to the NPP typical transient numerical simulation and the corresponding acceptance criteria.The simulation study results show that the improvement plan is feasible and the effect on the reactor control system is acceptable.

Analysis of Amelioration for R Rod Disturbance Problem of Average Temperature Control System

LI Yun-chen, ZHANG Shao-hong, JIANG Xing-hua

2010, 31(4): 71-73,77.

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After the implementation of the advanced fuel management amelioration,the adoption of 4-batch fuel refueling scheme,in Ling’ao Nuclear Power Plant,the preliminary analysis on the frequent disturbance problem on R bank of the average temperature control system are conducted,the implementation of amelioration is summarized,and the incompatible part with the initial reactor design after the amelioration is analyzed.The results show that the optimization on the lead and lag parameters meet the relevant safety requirements.

Optimal Time Control for Load Following Operation of Nuclear Reactors Based on Minimal Value Theory

CHEN Deng-ke, ZHANG Da-fa, CAI Meng

2010, 31(4): 74-77.

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The reactor model was built based on the point-reactor kinetic equation and temperature reactivity feedback equation.An optimal time control method for load following operation of nuclear reactors based on minimal value theory is studied with this model.The simulation results show that the method presented in the paper makes the nuclear reactor meet the optimal time performances.

Analysis of Primary Loop Small-Break Loss-of-Coolant Accident

HUANG Hongwen, LIU Hangang, QIAN Dazhi, XU Xianqi

2010, 31(4): 78-81.

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On the basis of a typical model of the primary loop small-break loss-of-coolant accident,the transient variation of the thermo hydraulics parameters at a loss-of-coolant accident are calculated by RETRAN-02 code.The physical process and the relevant measures for protection under the incident condition are analyzed.The calculation result shows that the reactor has a favorable capacity to resist the accident.

A Methodology to Incorporate Organizational Factors into Human Reliability Analysis

LI Peng-cheng, CHEN Guo-hua, ZHANG Li, XIAO Dong-sheng

2010, 31(4): 82-86.

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A new holistic methodology for Human Reliability Analysis（HRA） is proposed to model the effects of the organizational factors on the human reliability.Firstly,a conceptual framework is built,which is used to analyze the causal relationships between the organizational factors and human reliability.Then,the inference model for Human Reliability Analysis is built by combining the conceptual framework with Bayesian networks,which is used to execute the causal inference and diagnostic inference of human reliability.Finally,a case example is presented to demonstrate the specific application of the proposed methodology.The results show that the proposed methodology of combining the conceptual model with Bayesian Networks can not only easily model the causal relationship between organizational factors and human reliability,but in a given context,people can quantitatively measure the human operational reliability, and identify the most likely root causes or the prioritization of root causes caused human error.

A Method for Survey of Underwater Non-Contact Deformation of Fuel Assemblies

GAO Yong-ming, LI Sheng, LI Li-dan

2010, 31(4): 87-90.

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The survey of underwater non-contact deformation is based on the combined method of the video image-sensor and calibration.After the photography of the targets by five image-sensors at the same time,the images are processed by the image processing system,to get the edge image of the fuel assembly, and then transferred to the video digital signal.The results are analog displayed on the computer,and thus the bending and its future trend of the fuel assembly can be directly displayed.The unknown dimension can be obtained by calibration.

Study on Ground Numerical Models for Floor Response Spectra Analysis of Nuclear Power Plant and Their Influences

LI Jian-bo, LIN Gao, ZHU Xiu-yun, ZHONG Hong, YAN Dong-ming

2010, 31(4): 91-95.

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In the framework of numerical model of lumped parameters,a time-frequency domain coupled model of ground is presented and recommended in this paper to analyze the dynamic interaction,which solves the soil dynamic impedance based on the harmonic response analysis and maintains the necessary accuracy in the numerical transformation between time and frequency domains by using continued fraction expansion. The proposed dynamic analysis method can be easily utilized in practical engineering with inhomogeneous soil layers,and can play a positive role in enhancing the associated seismic analysis of nuclear power plants in China.Finally,by taking the analysis of dynamic stiffness of soil and the floor response spectra for a certain 1000 MW Nuclear Power Plant as an example,specific numerical comparison analyses are carried out to study the impact influences for various soil models,in which the numerical precision for the new proposed method is well validated.

Study on Synthesizing Method of Artificial Ground Motion that Envelopes Target Power Spectrum

ZHANG Yu-shan, ZHAO Feng-xin

2010, 31(4): 96-100.

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In this paper,a synthesizing method,which can generate the artificial ground motion that not only matches the target response spectrum but envelopes the corresponding target power spectrum,is proposed.With respect to every controlling frequency of the response spectrum:firstly,by superimposing the incremental narrow-band time history,the response spectrum of artificial ground motion is made to equal to the target value;and then,with its response spectrum unchanged,the time history is further modulated in the time domain to make its average power spectrum envelope the target one.A numerical example illustrates that not only the ground motion time history generated by this method possesses high matching precision to the target response spectrum,but also its average power spectrum envelopes the target power spectrum.

Study on Distribution and Optimization of Residual Stress inside Plate-Fin Structure after Braze Welding

ZHOU Guo-yan, TU Shan-dong, XUAN Fu-zhen, WANG Zheng-dong

2010, 31(4): 101-105.

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The residual stress inside the plate-fin structure has been analyzed by the finite element method under different operation conditions.The calculated results show that a large scale of residual stress will occur in the plate-fin structure and the maximum value is found at the braze corner.The rapid cooling process and the pressured assembly technology have a significant effect on the distribution of the residual stress.The brazed material owns a better performance with a quicker cooling rate.However,the quicker cooling rate also leads to a tensile residual stress near the brazed seam,which is deleterious to the whole structure.The pressure assembly technology can change the residual stress from a tensile state to the compressed state which can improve the safety and extend the service life of the plate-fin structure effectively.

Analytical Method of Nonlinear Gasket Contact Stress along Width Direction on Bolted Flanged Connections

LIU Lin, GU Bo-qin

2010, 31(4): 106-109.

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In order to evaluate the tightness of bolted flanged connections accurately,the deformation and the contact stress along the radial direction of nonlinear gaskets have been researched using analytical method. The analytical results obtained by analytical method were compared with those by finite element analysis （FEA）,which shows that the results calculated by two methods are fundamentally coincident,but the former is smaller than the latter.The results indicate that both the deformation and the contact stress of gaskets distribute non-uniformly along the gasket radial direction,and they all increase from gasket inner margin to its outer margin.

Fuel Cost Analysis of an Equilibrium Th-U Cycle in Advanced CANDU Reactor

LI Zhe, LIU Yu-xuan, WANG Kan, LIU Jing-quan

2010, 31(4): 110-113,129.

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Based on the nine-factor PWR economic model,we develop a twelve-factor model to calculate the levelised costs of once-through Th-U cycle in Advanced CANDU Reactor and make the sensitivity analysis.The result shows that the three factors,namely the price of natural uranium,tail enrichment and lead time,are significant in the levelised costs of Th-U cycle.

Fatigue Behavior of Titanium Ti-4Al-2V Rods under High Cycle Loading

XIONG Ru, WANG Li, LIU Gui-liang, ZHU Chang-gui, LI Chuan-qian

2010, 31(4): 114-117.

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The high cycle fatigue behavior of titanium alloy Ti-4Al-2V rods at room temperature was evaluated.The common high cycle fatigue（HCF） tests with group specimen and the up-and-down tests were performed under bending and rotating loadings at room temperature in air environment.The experimental data were analyzed and the S-N curve and P-S-N curve were plotted,and the fracture morphology is analyzed by SEM.The results show that Ti-4Al-2V rods have good resistance to high cycle fatigue and the value ofσ_{-1（10）⁷} is about the same with that of the corresponding equation.The fracture morphology of Ti-4Al-2V specimen after fatigue failure presents typical characteristics with three areas of fatigue crack initiation,growth and rupture.

Determination of Air Section Length in Preparation of UO₂ Ceramic Microspheres by Gelation Process

DENG Kuan, GUO Wen-li, JIN Xin, LIANG Tong-xiang

2010, 31(4): 118-120.

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Gelation Process is the main approach to prepare the UO₂ ceramic microspheres,whichserves as the core of the high temperature gas cooled reactor（HTR） fuel elements.In the process of preparing the microspheres,the casting solution is first emitted from the nozzle into an air section in order to obtain droplets with specific degree of sphericity.The droplets are subsequently injected into the gelation section and solidified.The distance from the nozzle to the ammonia section is the length of the air section.To prepare the UO₂ ceramic microspheres with higher sphericity,a mathematical model was established to calculate the optimized length of the air section theoretically and the calculated outcome has been validated by experiment.

Numerical Calculation for Flow Field of Servo-Tube Guided Hydraulic Control Rod Driving System

HE Keyu, HAN Weishi

2010, 31(4): 121-124.

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A new-style hydraulic control rod driving mechanism was put forward by using servo-tube control elements for the design of control rod driving mechanism.The results of numerical simulation by CFD program Fluent for flow field of hydraulic driving cylinder indicate that the bigger the outer diameter of servo-tube,the smaller the resistance coefficient of variable throttle orifice.The zero position gap of variable throttle orifice could be determined on 0.2 mm in the design.The pressure difference between the upper and nether surfaces of piston was mainly created by the throttle function of fixed throttle orifice.It can be effectively controlled by changing the gap of variable throttle orifice.And the lift force of driving cylinder is able to meet the requirement on the design load.

Mathematics Model of Filtration Efficiency of Moisture Separator for Nuclear Reactors

ZHANG Zhen-zhong, JIANG Feng, HUANG Yun-feng

2010, 31(4): 125-129.

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In order to study the filtration mechanism of the moisture separator for water droplet of 5～10μm,this paper set up a physical model.For the mixed meshes,they can be classified into three types: standard meshes,bur meshes and middle meshes.For all fibers of the wire meshes and vertical fibers of standard mixed meshes,a Kuwabara flow field is used to track the particle to get the inertial impaction efficiency and then calculate the total filtration efficiency of the meshes.For other fibers,besides the Kuwabara flow field,an around-flat flow field is added to calculate the efficiency.Lastly,the total efficiency of the moisture separator according to the equation of the filtration efficiency for the filters in series is compared with the experimental data.The result shows that,under the standard condition,the calculation value is consistent with the experimental efficiency data.

Design of Anti-Interference of Control and Protect System of Reactor Based on FPGA

LU Yi

2010, 31(4): 130-132,142.

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The methods of anti-interference in the design of control and protect system which based on field programmable gate array（FPGA）are introduced in this paper,based on the measures,such as the signal isolation,noise and oscillation elimination,and threshold adjustment,in the design of the hardware and the improvement of anti-interference performanceby software,to ensure the safe,reliable and stable operation of the reactors.

Experimental Study on Fundamental Performance of Pulsed Liquid Gas Jet Pump

GAO Chuan-chang, WANG Yu-chuan, CHEN Hao, LEI Ting, CHEN Xiao-jun, WANG Xiao-hui

2010, 31(4): 133-137.

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The fundamental performances of liquid gas jet pump have been investigated using the steady and pulsed liquid jet in the same liquid gas jet pump experimental apparatus.The results show that there is a optimal working pressure for steady liquid gas jet pump,and the performance curves of pulsed liquid gas jet pump are very similar in a certain pulsed frequency and different working pressure;the pulsed jet can produce water hammer effect,which could increase the liquid gas jet pump efficiency 4%～15%under limit working pressure 0.1Mpa～0.15Mpa of experimental apparatus.

Nuclear Forensic Analysis on Nuclear Reactor Characteristics

ZHANG Song-bo, XUE Xiao-dong, WU Jun

2010, 31(4): 138-142.

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Based on the pin-cell model and 3-D burnup calculation code MCCOOR,the nuclides compositions of fuel and moderator are simulated for the 5 MW graphite moderated and gas-cooling reactor. The characteristics of this reactor are analyzed with correlated nuclides analysis.Results are as the followings: the composition of ¹⁴C and ¹⁰Be in moderator could be the signature of total flux,the mainly fission products of radioactive nuclides,¹⁴⁴Ce,¹³⁴Cs,¹⁴⁷pm,¹⁵⁴Eu,⁹⁰Sr and ¹³⁷Cs,could be the signature ofreprocessing time and times of reprocessing,and the correlated nuclide number ratio of ²³⁸u vs.totalPu could be the signature of reactor type.Thus,for nuclear forensic analysis on the dismantlement of production reactor,the sampling data of the nuclides ¹⁴C and ¹⁰Be in moderator could be used to identify the operation history of the reactor, and the sampling data of the main fission product of radioactive nuclides in the reprocessing pool could be used to identify the times of reprocessing.For nuclear forensic analysis on nonproliferation cases,the reactor type of intercepted material could be identified by analyzing the correlated nuclides ratios,²³⁸pu v.s.total Pu and ²⁴²Pu v.s.²⁴⁰Pu,which is essential to narrow down the possible origination range of the intercepted material.

2010 Vol. 31, No. 4