Modified Quasi-Steady-State Method to Evaluate the Mean Power Profiles of Nuclear Excursions in Fissile Solution

A modified quasi-steady-state method has been developed in order to evaluate the mean power during a nuclear excursion in fissile solution. The conventional method used the critical equation based on the one-group theory in order to calculate the reactivity. However, the one-group approximation reduces the calculation accuracy, and the geometrical buckling used in the critical equation is not applicable to complex geometries. Thus, we have modified the method to use the reactivity feedback coefficients, which are widely used in the calculation of one-point reactor kinetics. Although the modified method requires an external calculation to obtain the feedback coefficients, it is applicable to complex geometries and provides more accurate results than does the one-group approximation when the proper coefficients are given.

Moreover, a new method to calculate the boiling power has been developed. In this method, the power corresponding to the void fraction that compensated for the inserted reactivity along with the temperature feedback was calculated using the relationship, which was derived using the French SILENE experimental data.

Experimental analyses have been conducted to validate the new method for the French CRAC and Japanese TRACY experiments. The analytical results showed close agreement with the experimental results.     

Sensitivity of reactivity insertion limits with respect to safety parameters in a typical MTR

The sensitivity of various safety parameters, affecting the reactivity insertion limits imposed by clad melting temperature for a typical pool type research reactor, have been investigated in this work. The analysis was done for low enriched uranium (LEU) core with scram disabled conditions. The temperature coefficients of fuel and coolant, void/density coefficient and β_eff were individually varied and the reactor behavior for different ramp reactivity transients was studied. In this work ramp reactivity insertions from 1.6 to 2 $/0.5 s were selected and peak power, maximum fuel, clad and coolant temperatures were determined. Results show that peak power decreases with an increase in the Doppler coefficient of reactivity. However, it rises with an increase in the reactivity insertion. Core remains insensitive to the coolant temperature coefficient of reactivity for ramps in the range of 1.6–1.9/0.5 s. Peak power decreases with an increase in the void coefficient of reactivity (0.1 $/%void to 0.8 $/%void). With a decrease in the void coefficient of reactivity, the maximum fuel and clad temperatures show a non-linear rise. Power and temperature peaks in the transient are sensitive to the values of β_eff. Finally, it can be concluded that LEU is a safe core due to its smaller β_eff, larger Doppler coefficient and void coefficient of reactivity. It is inferred through this work that reactivity insertion limits of LEU core are quite insensitive to β_eff, the Doppler coefficient and the coolant temperature coefficient of reactivity. They are highly sensitive to the change of the void coefficient of reactivity in the core.     

A linear equation of characteristic time profile of power in subcritical quasi-steady state

ABSTRACT

An equation of power in subcritical quasi-steady state has been derived based on one-point kinetics equations for the purpose of utilizing it for the development of timely reactivity estimation from complicated time profile of neutron count rate. It linearly relates power, P, to a new variable q, which is a function of time differential of the power.

It has been confirmed that the points (q, P) calculated by using one-point kinetics code, AGNES, are perfectly in a line described by the new equation and that the points (q, P) calculated from transient subcritical experiment data measured by using TRACY made a line with a slope indicated by the new equation.     

Simulation of reactivity transients in a miniature neutron source reactor core

Computer simulation was carried out for reactivity induced transients in a HEU core of a tank-in-pool reactor, a miniature neutron source reactor (MNSR). The reactivity transients without scram at initial power of 3 W were studied. From the low power level, the power steadily increased with time and then rose sharply to higher peak values followed by a gradual decrease in value due to temperature feedback effects. The trends of theoretical results were found to be similar to measured values and the peak powers agreed well with experimental results. For ramp reactivity equivalent of clean core cold excess reactivity of 4 mk (4×10⁻³ Δk/k), the predicted peak power of 100.8 kW agrees favourably with the experimental value of 100.2 kW. The measured outlet temperature of 72.6 °C is also in agreement with the calculated value of 72.9 °C for the release of the core excess reactivity. Theoretical results for the postulated accidents due to fresh fuel replacement of reactivity worth 6.71 mk and addition of incorrect thickness of Be plates resulting in 9 mk reactivity insertion were 187.23 and 254.3 kW, respectively. For these high peak powers associated with these reactivity insertions, it is expected that nucleate boiling will occur within the flow channels of the reactor core.     

Simulation of reactivity transients in current MTRs

This work aims at simulation of reactivity induced transients in High Enriched Uranium (HEU) and Low Enriched Uranium (LEU) cores of a typical Material Test research Reactor (MTR) using PARET code. The transient problem was forced through specification of externally inserted reactivity as a function of time. Reactivity insertions are idealized by ramps and steps. Superdelayed-critical transients, superprompt-critical transients and quasistatic transients are selected for the analysis. Ramp and step reactivity functions were employed to simulate these perturbations. The effect of initial power on transient behavior has also been investigated. The low enriched uranium core is analyzed for transients without scram. The magnitudes of maximum reactivity insertions are chosen to be in the range of $0.05 to 2.0 for different reactivity insertion times. Transient simulation with scram reveals that response of both HEU and LEU-cores is similar for selected ‘ramps’ and ‘steps’. The difference is observed in the peak values of power and coolant, clad and fuel temperatures. Trip level is achieved earlier in case of LEU-core. The peak clad temperatures in both LEU and HEU-cores remain below the melting point of aluminum-clad for the selected reactivity insertions. Simulation show that the LEU-core is more sensitive to perturbations at low power as compared to the transients at full power. For reactivity transients at low power level, power rises sharply to a higher peak value. In transients at full power, the peak power barely exceeds the trip level. The power oscillations after the first peak are observed for transients without scram.     

Measurement and analysis of feedback reactivity in the Monju restart core

The purpose of this study is to develop a feedback reactivity measurement technique in the Japanese prototype fast breeder reactor Monju and to validate calculation methodology to forecast the nuclear feedback phenomena. A feedback reactivity measurement technique has been developed based on a reactivity model featuring components that depend on the reactivity coefficients, denoted as reactor power (K_R) and reactor vessel inlet temperature (K_in). This technique can precisely measure the two reactivity components simultaneously and was applied to the feedback reactivity experiment conducted in the Monju system start-up test in May 2010. A thorough evaluation considering all possible biases and uncertainties demonstrated that the reactivity coefficients can be evaluated with a measurement uncertainty smaller than 3%. The evaluated reactivity coefficients were simulated considering the temperature distribution in the core. The calculated and measured values of K_R agreed within 1%, and the value of K_in was consistent with that reported in a previous isothermal temperature coefficient experiment. The measured and calculated fuel subassembly outlet temperatures also agreed well within 0.2°C, which supports the validity of the temperature calculation.     

Burn-up effect on inherent safety parameters and reactivity insertion transient analysis of Pakistan Research Reactor-1

Burn-up dependent feedback coefficients of reactivity for the reference operating core of Pakistan Research Reactor-1 (PARR-1), have been calculated employing standard computers codes WIMSD/4 and CITATION. Fast reactivity insertion transient (1.5 $/0.5 s) is simulated at each burn step using computer code RELAP5/MOD3.4 and PARET. Calculation reveals that fuel temperature coefficient of reactivity is 1.77 %Δk/k/ΔT less negative while moderator temperature and void coefficients of reactivity are 7.74 %Δk/k/ΔT and 2.04 %Δk/k/ΔT more negative at end of cycle (EOC), respectively. Fast reactivity insertion transient analysis shows that due to larger value of prompt generation time (Λ), reactor response to transient is slow at EOC. Therefore peak power, maximum fuel centreline and clad temperature decrease as the fuel is burned. This is the sign of enhanced inherent safety with the burn-up of reference operating core of PARR-1. Removal of in-pile experiment accident has also been modelled in RELAP5/MOD3.4 and results in this study are compared with PARET.     

铀氢锆反应堆脉冲参数分析

介绍了铀氢锆反应堆计算模型和程序，分析了反应性引入速率，反应性引入量，燃料瞬发负温度系数，燃料热容和瞬发中子寿命对脉冲参数的影响。计算结果表明，脉冲峰功率与反应性引入量的平方成正比；一次脉冲释放能量与反应性引入量成正比；燃料元件热容随燃料温度变化，脉冲峰功率和释放能量随燃料热容增大而增大。     

Neutronics analysis of megawatt-class gas-cooled space nuclear reactor design

ABSTRACT

Neutronics analysis was conducted for a proposed megawatt-class gas cooled space nuclear reactor design. The reactor design has a high operating temperature of up to 1500 K. Annular UO₂ fuel rods were used to reduce the central temperature of the fuel. The thermal power is 2.3 MWt and is converted into electric power by a direct Brayton cycle. The control rods were arranged in different configurations and were analyzed in order to evaluate the influence on the reactor design in different scenarios. The calculation results reveal that the control rods arrangements have influences on the begin-of-life (BOL) excess reactivity and the shutdown reactivity. The distribution of control rods affects the neutron economy and leakage in the fuel region, consequently affecting the reactivity. It is also known that the reactivity in flooding scenarios are not sensitive to different control rod arrangements. Meanwhile, according to calculation results, the proposed reactor design has enough shutdown reactivity margin which will allow for flexible control strategy. Further analysis is still needed for more detailed and accurate parameters of the reactor design.     

Safety Analysis of Abnormal Reactivity Events in HTTR

Abstract

To confirm the safety of the High Temperature Engineering Test Reactor (HTTR) facility which is being constructed as the first high temperature gas cooled reactor in Japan, the representative abnormal reactivity events assumed in the safety analysis of the HTTR were analyzed. The HTTR is a graphite moderated and He-gas-cooled reactor with thermal power of 30 MW, inlet coolant temperature of 395°C and outlet coolant temperature of 950°C.

This report presents the analytical results of two representative events, “Abnormal control rod withdrawal from a subcritical condition” and “Abnormal control rod withdrawal during the full power operation”, showing that the safety of the HTTR is secured in conformity with the unique features of the HTTR with respect to the maximum fuel temperature, which is a key factor for the safety criteria.

The results of the safety analysis could demonstrate the safety of the HTTR facility with respect to abnormal reactivity events postulated in the HTTR, showing that the maximum fuel temperature is lower than the limit of the maximum fuel temperature of 1,600°C.     

Analysis of reactivity induced accidents at Pakistan Research Reactor-1

Analysis of reactivity induced accidents in Pakistan Research Reactor-1 (PARR-1) utilizing low enriched uranium (LEU) fuel, has been carried out using standard computer code PARET. The present core comprises of 29 standard and five control fuel elements. Various modes of reactivity insertions have been considered. The events studied include: start-up accident; accidental drop of a fuel element on the core; flooding of a beam tube with water; removal of an in-pile experiment during reactor operation etc. For each of these transients, time histories of reactor power, energy released and clad surface temperature etc. were calculated. The results reveal that the peak clad temperatures remain well below the clad melting temperature during these accidents. It is concluded that the reactor, which is operated safely at a steady-state power level of 10 MW, with coolant flow rate of 950 m³/h, will also be safe against any possible reactivity induced accident and will not result in a fuel failure.     

Measurements of the isothermal,power and temperature reactivity coefficients of the IPR-R1 TRIGA reactor

The aim of this paper is to present the experimental results of the isothermal, power and temperature coefficients of reactivity of the IPR-R1 TRIGA reactor at the Nuclear Technology Development Center – CDTN in Brazil. The measured isothermal reactivity coefficient, in the temperature range measured, was −0.5 ¢/°C, and the reactivity measurements were performed at 10 W to eliminate nuclear heating. The reactor forced cooling system was turned off during the measurements. When the reactor is at zero power there is no sensible heat being released in the fuel, and the entire reactor core can be characterized by a single temperature. The power coefficient of reactivity obtained was approximately −0.63 ¢/kW, and the temperature reactivity coefficient of the reactor was −0.8 ¢/°C. It was noted that the rise in the coolant temperature has contributed only with a small fraction to the observed negative effect of the reactivity. The power defect, which is the change in reactivity taking place between zero power and full power (250 kW), was 1.6 $. Because of the prompt negative temperature coefficient, a significant amount of reactivity is needed to overcome temperature and allow the reactor to operate at the higher power levels in steady state.     

Experimental Study on the Fuel Behavior during Reactivity Accident at Power Operation Condition

In the Nuclear Safety Research Reactor (NSRR) program of Japan Atomic Energy Research Institute (JAERI), the fuel behavior in reactivity initiated accidents (RIAs) has been studied through irradiation tests with simulated power burst using fresh or preirradiated test fuel rods. In order to investigate possible influence of the difference of initial temperature profile in the fuel pellet on the fuel failure behavior, two tests were conducted with fresh fuel rods for RIAs at power operation using the newly developed NSRR operation mode and the results were compared with the results of previous irradiation tests which were for RIAs at zero power.

In the tests for RIAs at power, the reactivity of 2.0$ or 2.3$ was inserted rapidly after the linear heat rate of the test fuel rod was kept constant at 39kW/m for 5s. It has been shown through this study with fresh fuel rods that the fuel enthalpy of the failure threshold for RIAs at power is the same as that for RIAs at zero power and that the failure mechanism is the same as that of RIA at zero power. It has been clarified that there is no obvious influence of initial temperature distribution on the fuel behavior during RIAs in case of fresh fuels. The evaluation method of fuel enthalpy with which the fuel failure threshold is described was also studied.     

Measurement of Xenon Reactivity in the Reactor of the Nuclear Ship “MUTSU”

Abstract

This report deals with the measurement of reactivity changes caused by the increase and decrease of xenon concentration in the reactor core of the nuclear ship “MUTSU” after a change from long-term operation at 70% to zero power. The change in xenon reactivity was compensated by control-rod movements and the compensated reactivity was measured using a digital reactivity meter. The xenon override peak was recognized five and half hours after the start of power reduction. The equilibrium and peak reactivities of xenon were estimated by reading the initial and peak values of a theoretical curve which was fitted to the measured variation in xenon reactivity. The xenon reactivity results obtained by the present method can be considered to be accurate since no control-rod worth data were used and the measured quantity was the reactivity itself.     

Measurements of Doppler Effect of Coated Particle Fuel Rod in SHE-14 Core Using Sample Heating Device

Reactivity decrease due to temperature rise of a single fuel rod sample was measured in the SHE-14 core using a sample heating device with purpose to verify the calculation accuracy of the Doppler effect for resonance neutron absorption in a Very High Temperature Reactor. The fuel rod sample was a stuck of coated particle fuel compacts containing 4% enriched UO₂ kernels, and it was heated up to about 700°C in a sample heating tube which was placed along the axis of the core.

The difference of reactivity decrease between the two same size samples of fuel rod and graphite rod due to temperature rise can be interpreted as the increased resonance neutron capture of ²³⁸U, i.e. Doppler effect. The SRAC code system was applied to the Doppler effect calculation where the collision probability method was used in the cell calculation and the one-dimensional, multi-group diffusion approximations were adopted in the core calculation. The results gave a ratio of the calculated to the measured Doppler effect of 0.93.     

Feedback reactivity coefficients and their coupling

Coupled reactivity feedback coefficients which accounts for variation in fuel temperature and moderator void simultaneously, have been determined for swimming pool type research reactor namely Pakistan Research Reactor PARR-1. The state of art is core criticality calculations, employing lattice cell code WIMS-D/4 and application of Taylor series expansion for core reactivity up to third order, involving two variables, i.e. fuel temperature and coolant void. The spectral effects in one region due to change of parameter in other region have also been studied. When spectral changes in moderator region due to 20 K change in fuel temperature have been incorporated in the calculation of fuel temperature coefficient, the results seems to be improved by 4.12%. Further, the results of void coefficient of reactivity show the improvement of 0.1% when the spectral effect in fuel region due to 5% change in void in moderator region is taken into account. These differences seem to be an improvement in the results, as physically any change in one region is accompanied by change in the other region.     

Development of a Fine and Ultra-Fine Group Cell Calculation Code SLAROM-UF for Fast Reactor Analyses

A cell calculation code SLAROM-UF has been developed for fast reactor analyses to produce effective cross sections with high accuracy in practical computing time, taking full advantage of fine and ultra-fine group calculation schemes.

The fine group calculation covers the whole energy range in a maximum of 900-group structure. The structure is finer above 52.5 keV with a minimum lethargy width of 0.008. The ultra-fine group calculation solves the slowing down equation below 52.5 keV to treat resonance structures directly and precisely including resonance interference effects. Effective cross sections obtained in the two calculations are combined to produce effective cross sections over the entire energy range.

Calculation accuracy and improvements from conventional 70-group cell calculation results were investigated through comparisons with reference values obtained with continuous energy Monte Carlo calculations. It was confirmed that SLAROM-UF reduces the difference in k-infinity from 0.15 to 0.01% for a JOYO MK-I fuel subassembly lattice cell calculation, and from ?0.21 % to less than a statistical uncertainty of the reference calculation of 0.03% for a ZPPR-10A core criticality calculation.     

核反馈实时模拟程序

为了在堆外实验中实现核反馈实时模拟,用C 语言开发了核反馈模拟程序.该程序由3个主要模块组成:反应性反馈模拟、功率控制系统模拟及反应堆模拟.采用的主要物理模型有:点堆模型、一维均匀流体模型、瞬态导热模型等;堆功率控制系统模拟方案为平均温度控制方案;其他辅助计算包括物性参数、几何参数的计算.用Retran-02计算分析数据对模拟程序进行了测试,结果表明,模拟程序的数学模拟正确,运算速度快,计算准确.     

Experiments and Analyses on Fuel Expansion and Bowing Reactivity Worth in Mock-up Cores of Metallic Fueled Fast Reactors at FCA

Axial fuel expansion and radial fuel bowing were simulated in mock-up cores of metallic fueled fast reactors at the Fast Critical Assembly (FCA). Reactivity worth caused by the simulation was measured and compared with calculations. Based on these experiments and calculations, the applicability of current calculation methods was discussed for both the first order perturbation theory (FOP) and the exact perturbation theory (EP).

For the axial fuel expansion reactivity worth, both FOP and EP showed 10 to 20% smaller values than the experiment. This underestimation was consistent to a C/E trend of axial distributions of plutonium sample worth. No significant difference was observed between FOP and EP, when transport correction was applied.

For the radial fuel bowing reactivity worth, the FOP showed about 10% larger values than the EP. Near the core central plane, the EP with transport correction showed good agreement with the experiment, while FOP showed overestimation by 14%. At the core axial edge, however, both FOP and EP underestimated the reactivity worth by more than 10%.     

Heavy Water Zero Power Reactor (HWZPR) mixed core first criticality,calculation and experiments

HWZPR original fuel is natural U metal fuel but other kinds of fuel can also be utilized. In a research work on UO₂ fuel, reactor fuel was partially replaced by natural UO₂ fuel and physical parameters of the new core were compared with original core. Thirty six natural U metal fuel rods were substituted by natural UO₂ fuel assemblies. Prior to the first criticality operation with the new core, it was simulated by stochastic and deterministic calculation methods i.e. MCNP-4C and WIMS-CITATON codes, respectively. In order to investigate criticality and safety of the mixed core, important reactor physics parameters such as effective multiplication factor (K_eff) at different water levels, critical water level, reactivity worth of D₂O and reactivity worth of safety and control rods were calculated.The calculated results ensured reactor criticality and satisfied reactor safety criteria. Therefore, with the permission of the reactor safety committee, the first criticality operation was performed successfully. Later, during a series of reactor operations important physical parameters were measured experimentally. There is good consistency between the theoretical and experimental results.