Determination of neutron generation time in miniature neutron source reactor by measurement of neutronics transfer function

The prompt neutron generation time Λ and the total effective fraction of delayed neutrons (including the effect of photoneutrons) β have been experimentally determined for the miniature neutron source reactor (MNSR) of Syria. The neutron generation time was found by taking measurements of the reactor open-loop transfer function using newly devised reactivity-step- ejection method by the reactor pneumatic rabbit system. Small reactivity perturbations i.e. step changes of reactivity starting from steady state, were introduced into the reactor during operation at low power level i.e. zero-power. Relative neutron flux and reactivity versus time were obtained. Using transfer function analysis as well as least square fitting techniques and measuring the delayed neutrons fraction, the neutron generation time was determined to be 74.6±1.57 μs. Using the prompt jump approximation of neutron flux, the total effective fraction of delayed neutrons was measured and found to be 0.00783±0.00017. Measured values of Λ and β were found to be very consistent with calculated ones reported in the Safety Analysis Report.     

Analysis of prompt supercritical process with heat transfer and temperature feedback

The prompt supercritical process of a nuclear reactor with temperature feedback and initial power as well as heat transfer with a big step reactivity (ρ0>β) is analyzed in this paper.Considering the effect of heat transfer on temperature of the reactor,a new model is set up.For any initial power,the variations of output power and reactivity with time are obtained by numerical method.The effects of the big inserted step reactivity and initial power on the prompt supercritical process are analyzed and discussed.It was found that the effect of heat transfer on the output power and reactivity can be neglected under any initial power,and the output power obtained by the adiabatic model is basically in accordance with that by the model of this paper,and the analytical solution can be adopted.The results provide a theoretical base for safety analysis and operation management of a power reactor.     

大阶跃反应性下考虑燃料温度反馈时的中子倍增公式

用有燃料温度反馈的中子倍增公式对输入大阶跃反应性的反应堆超瞬发临界变化过程进行研究。通过与经典中子动力学数值解法进行对比,计算结果基本一致;求得不同初始功率下反应性和功率的变化规律,并进行分析讨论,得出中子数与反应性在反应性大于缓发中子总份额时呈二次函数关系,其结论可作为弹棒事故等大阶跃反应性引入的反应堆安全分析的理论依据。     

Approximate solutions of point kinetics equations with one delayed neutron group and temperature feedback during delayed supercritical process

In the present investigation, the delayed supercritical process of a nuclear reactor with temperature feedback while inserting small step reactivity is analyzed. It is found that there exist some problems in the results obtained in the published literatures. The expression of relation between reactivity and time is derived, and the effects of the small inserted step reactivity and initial power on the delayed supercritical process are analyzed and discussed. To test the developed solution and to prove the validity of the method for application purposes, a comparison with other methods indicates the superiority of temperature prompt jump approximation. Some useful new conclusions are drawn, which can provide an important theory for the safety analysis and operating administration of the nuclear reactor.     

Reactivity feedback coefficients of a material test research reactor fueled with high-density U3Si2 dispersion fuels

The reactivity feedback coefficients of a material test research reactor fueled with high-density U₃Si₂ dispersion fuels were calculated. For this purpose, the low-density LEU fuel of an MTR was replaced with high-density U₃Si₂ LEU fuels currently being developed under the RERTR program. Calculations were carried out to find the fuel temperature reactivity coefficient, moderator temperature reactivity coefficient and moderator density reactivity coefficient. Nuclear reactor analysis codes including WIMS-D4 and CITATION were employed to carry out these calculations. It is observed that the average values of fuel temperature reactivity feedback coefficient, moderator temperature reactivity coefficient and moderator density reactivity coefficient from 20 °C to 100 °C, at the beginning of life, followed the relationships (in units of Δk/k × 10⁻⁵ K⁻¹) −2.116 − 0.118 ρ_U, 0.713 − 37.309/ρ_U and −12.765 − 34.309/ρ_U, respectively for 4.0 ≤ ρ_U (g/cm³) ≤ 6.0.     

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.     

Reactor thermal behaviors under kinetics parameters variations in fast reactivity insertion

The influences of variations in some of the kinetics parameters affecting the reactivity insertion are considered in this study, it has been accomplished in order to acquire knowledge about the role that kinetic parameters play in prompt critical transients from the safety point of view. The kinetics parameters variations are limited to the effective delayed neutron fraction (β_eff) and the prompt neutron generation time (Λ). The reactor thermal behaviors under the variations in effective delayed neutron fraction and prompt neutron generation time included, the reactor power, maximum fuel temperature, maximum clad temperature, maximum coolant temperature and the mass flux variations at the hot channel. The analysis is done for a typical swimming pool, plate type research reactor with low enriched uranium. The scram system is disabled during the accidents simulations. Calculations were done using PARET code. As a result of simulations, it is concluded that, the reactor (ETRR2) thermal behavior is considerably more sensitive to the variation in the effective delayed neutron fraction than to the variation in prompt neutron generation time and the fast reactivity insertion in both cases causes a flow expansion and contraction at the hot channel exit. The amplitude of the oscillated flow is a qualitatively increases with the decrease in both β_eff and Λ.     

Iterative schemes for obtaining dominant alpha-modes of the neutron diffusion equation

Two new methods of obtaining dominant prompt alpha-modes (sometimes referred to as time-eigenfunctions) of the multigroup neutron diffusion equation are discussed. In the first of these, we initially compute the dominant K-eigenfunctions and K-eigenvalues (denoted by λ₁, λ₂, λ₃ … etc.; λ₁ being equal to the K_eff) for the given nuclear reactor model, by existing method based on sub-space iteration (SSI) which is an improved version of power iteration method. Subsequently, a uniformly distributed (positive or negative) 1/v absorber of sufficient concentration is added so as to make a particular eigenvalue λ_i equal to unity. This gives ith alpha-mode. This procedure is repeated to find all the required alpha-modes. In the second method, we solve the alpha-eigenvalue problem directly by SSI method. This is clearly possible for a sub-critical reactor for which the inverse of the dominant alpha-eigenvalues are also the largest in magnitude as required by the SSI method. Here, the procedure is made applicable even to a super-critical reactor by making the reactor model sub-critical by the addition of a 1/v absorber. Results of these calculations for a 3-D two group PHWR test-case are given. These results are validated against the results as obtained by a completely different approach based on Orthomin(1) algorithm published earlier. The direct method based on the sub-space iteration strategy is found to be a simple and reliable method for obtaining any number of alpha-modes. Also comments have been made on the relationship between fundamental α and k values.     

A feasibility study of LEU enrichment uranium fuels for MNSR conversion using MCNP

A neutronics feasibility study has been performed to determine the enrichment that would be required to convert a commercial Miniature Neutron Source Reactor (MNSR) from HEU (90.2%) to LEU (<20%) fuel. Two LEU cores with uranium oxide fuel pins of different dimensions were studied. The one has the same dimensions as the current HEU fuel while the other has the dimensions as the special MNSR, the In-Hospital Neutron Irradiator (INHI), which is a variant of the MNSR. The LEU cores that were studied are of identical core configuration as the current HEU core, except for potential changes in the design of the fuel pins. The following reactor core physics parameters were computed for the two LEU fuel options; clean cold core excess reactivity (ρ_ex), control rod (CR) worth, shut down margin (SDM), neutron flux distributions in the irradiation channels and kinetics data (i.e. effective delayed neutron fraction, β_eff and prompt neutron lifetime, l_f). Results obtained are compared with current HEU core and indicate that it would be feasible to use any of the LEU options for the conversion of NIRR-1 in particular from HEU to LEU.     

Measurement of large negative reactivity in WWER-440. Sources of uncertainty

The sources of uncertainty in measurement of large negative reactivity in WWER-440 by the inverse point kinetics method, are evaluated quantitatively on the example of measurement of the reactivity worth of the shutdown control rod system of WWER-440 at zero power. Considering the specific features of the control rod system of WWER-440, it is demonstrated that using an appropriate formulation of the inverse solution of the equations of point kinetics, the uncertainty of measured reactivity ρ/β introduced by the assumption of constancy of the parameters of kinetics can be reduced to <3–5% for the case of the discussed rod-drop test at zero power. Based on an analysis of both numerically simulated and actual rod-drop transients, it is shown that the uncertainty of measured reactivity ρ/β can be quite considerable due to the underlying delayed neutron data set—the values of ρ/β obtained using different data sets can differ by 15%. Inexact accounting of the share of ²³⁹Pu in the fission neutron source is estimated to contribute to the total uncertainty of measured ρ/β of 1%, whereas possible spatial effects are expected to result in a relative error in ρ/β of 5%.     

Investigation of the reflector temperatures of a space craft thermionic reactor

In a fast incore thermionic spacecraft reactor for nuclear propulsion, the temperature rise due to the neutron heating in the reflector control drums is investigated. The reactor is fuelled with (U-Ta)C, consisting of 80UC-20TaC with a sinter density of 80% and controlled with the help of rotating drums imbedded into the beryllium reflector. The control drums contain natural B₄C strips (with 20% ¹⁰B and 80% ¹¹B) and produce nuclear heat via neutron absorption in ¹⁰B. The neutronic analysis has been conducted in S₁₆-P₃ and S₈-P₃ approximation with the help of one- and two-dimensional neutron transport codes ANISN and DORT, respectively. Calculations are conducted for a reactor with a core radius of 22 cm and core height of 35 cm leading to 50 kW_el in power phase. Reflector drums with 100% natural B₄C in form of strips (drum diameter=13.5 cm, strip width=5 mm) at the outer periphery of the radial reflector of 16 cm thickness would make possible reactivity changes of Δk_eff,max=10.7% without a significant distortion of the fission power profile during all phases of the space mission. A reduction of the B₄C in the strips to 20 and 10% would still allow a reactivity change of Δk_eff,max=8.4 and 7.7%, respectively, amply sufficient for an effective control of a fast reactor during all phases of the space mission. By a nuclear thermal thrust around F=5000 N and a specific impulse of 670 s⁻¹ at an hydrogen exit temperature around 1900 K, the maximum temperature in the drums rises to 1023 K, with 100% natural B₄C content in the strips, far below the melting point of beryllium. The maximum drum temperature is depressed to 663 and 519 K, with 20 and 10% natural B₄C content in the strips, respectively.     

Physics design requirements for the National Spherical Torus Experiment liquid lithium divertor

Recent National Spherical Tokamak Experiment (NSTX) high-power divertor experiments have shown significant and recurring benefits of solid lithium coatings on plasma facing components (PFCs) to the performance of divertor plasmas in both L- and H-mode confinement regimes heated by high-power neutral beams. The next step in this work is installation of a liquid lithium divertor (LLD) to achieve density control for inductionless current drive capability (e.g., about a 15–25% n_e decrease from present highest non-inductionless fraction discharges which often evolve toward the density limit, n_e/n_GW  1), to enable n_e scan capability (×2) in the H-mode, to test the ability to operate at significantly lower density (e.g., n_e/n_GW = 0.25), for future reactor designs based on the Spherical Tokamak, and eventually to investigate high heat-flux power handling (10 MW/m²) with long pulse discharges (>1.5 s). The first step (LLD-1) physics design encompasses the desired plasma requirements, the experimental capabilities and conditions, power handling, radial location, pumping capability, operating temperature, lithium filling, MHD forces, and diagnostics for control and characterization.     

A pressure-tube Advanced Burner Test Reactor concept

A new steady-state fast neutron test reactor has been conceptually designed. This paper presents a new concept for a CANDU-based fast test reactor that is horizontal in orientation, with individual pressure/Calandria tubes (PT/CT) running the entire length of the scattering-medium tank (Calandria) filled with Lead-Bismuth-Eutectic (LBE). This approach for a test reactor will provide more flexibility in refueling, sample removal, and ability to completely reconfigure the core to meet different users’ requirements. Full core neutronic analysis showed a small hexagonal reactor, LBE-cooled, trans-uranics (TRU)-67Zr fuel with HT-9 cladding and structures, with a core power of 100 MW_th produced a fast flux (>0.1 MeV) of 1.4 × 10¹⁵ n/cm² s averaged over the whole length of six irradiation channels with a total testing volume of more than 77 l. Loading of TRU from legacy UO₂ spent fuel allowed core continuous operation for 180 effective full power days with a net fissile-Pu burning rate of 6.4%. Since high neutron fluence impact on PT/CT might be an issue of concern for this design, oxide dispersion strengthened (ODS) ferritic steel was used as PT/CT material without any impact on core neutronic behavior. An innovative shutdown/control system which consisted of the six outermost fuel channels was proven to be effective in shutting the core down when flooded with boric acid as a neutron absorber. The new shutdown/control system has the advantage of causing the minimum perturbation of the axial flux shape when the control channels are partially flooded with boric acid. A preliminary thermal-hydraulic analysis of LBE produced acceptable pumping power and clad temperature. Voiding the core from its LBE coolant resulted in a positive reactivity insertion which is typical of most fast reactors. Hypothetical accidents of draining the Calandria and/or the external LBE reflector tank of the LBE core resulted in negative reactivity insertion which shut the reactor down.     

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.     

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.     

Inhomogeneous point kinetics equations and the source contribution

Inhomogeneous point reactor kinetics equations with one-group of delayed neutrons are solved analytically for linear reactivity insertion as well as for step reactivity insertion in the presence of external neutron source using the prompt jump approximation. The solution is obtained as an infinite series. The methodology is found to be a promising tool for analyzing nuclear reactor kinetics with positive or negative ramp reactivity insertion on a sub-critical or a zero power delayed critical reactor, where the temperature reactivity feedback is negligibly small. To check the consistency and the accuracy of the analytical solution, the results are compared with the numerical solution for different sub-critical and delayed critical states. The comparison is found to be good for all kinds of positive and negative step and ramp reactivity insertions. The analytical solution is arranged into two terms, one as a function of source contribution the other without that. Using the newly rearranged solution, the importance of the source term and the contribution to the error while neglecting source term to the reactor kinetics analysis, can be realized. Contribution to the error is small (less than 0.1%) when the equilibrium power is more than about one megawatt for a medium sized LMFBR. Similarly, the importance of source contribution to the total reactor period as a function of initial equilibrium power is also realized with the newly rearranged analytical solution. The total reactor period is over predicted (larger period in place of smaller period) which is not conservative, if the source contribution is not considered, for considerably small initial equilibrium power. The percentage of error in not considering the source term in period calculation varies as a function of net reactivity and ramp rate. The percentage of error in period determination without considering the source is comparatively high for small ramp rates.     

Systematics of the (p, n) excitation functions belonged to several isotopes at energies <60 MeV

Excitation functions of proton induced charge exchange reaction on nuclei between A = 11 and 238 are studied. All the studied excitation functions of (p, n) reaction show systematic variation with atomic mass in connection with nucleon binding energy. Islands of higher reaction yield appeared to be for nuclei with mass number A = 49, 72, 89, 109, and 139, and proton energy range from 9 to 12 MeV. The more probable occurrence of proton induced charge exchange reaction in these regions are attributed to its extra binding energy per nucleon than other nuclei. The larger contribution of pre-equilibrium processes on the neutron emission appeared on the linearity of the log(σ)–log(E_p) in some energy ranges. The slopes of these linear segments may be related to the excitons configuration in which the neutron is emitted by.     

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.     

Accurate Estimation of Subcriticality Using Indirect Bias Estimation Method, (II)

Subcriticalities were estimated by applying the Indirect Bias Estimation Method to subcritical experiments on a light-water moderated/reflected low-enriched UO₂ lattice cores. Two measurable values, prompt neutron time-decay constant and spatial-decay constant were calculated using MCNP 4A and JENDL-3.2. With these calculation errors, the biases in calculated reactivity were derived from the Indirect Bias Estimation Method. The differences between the calculated and measured spatial-decay constants were more or less at the same extent of experimental errors. These results show that the accuracy of subcriticality estimation of MCNP 4A and JENDL-3.2 ranges within the uncertainty which can be achieved by the exponential experiment. The differences between calculated and measured prompt neutron decay constants derive significant biases in calculated reactivity. The subcriticalities were estimated by using the effective multiplication factors adjusted based on these biases in calculated reactivity.     

Criticality investigations for the fixed bed nuclear reactor using thorium fuel mixed with plutonium or minor actinides

Prospective fuels for a new reactor type, the so called fixed bed nuclear reactor (FBNR) are investigated with respect to reactor criticality. These are ① low enriched uranium (LEU); ② weapon grade plutonium + ThO₂; ③ reactor grade plutonium + ThO₂; and ④ minor actinides in the spent fuel of light water reactors (LWRs) + ThO₂. Reactor grade plutonium and minor actinides are considered as highly radio-active and radio-toxic nuclear waste products so that one can expect that they will have negative fuel costs.The criticality calculations are conducted with SCALE5.1 using S₈–P₃ approximation in 238 neutron energy groups with 90 groups in thermal energy region. The study has shown that the reactor criticality has lower values with uranium fuel and increases passing to minor actinides, reactor grade plutonium and weapon grade plutonium.Using LEU, an enrichment grade of 9% has resulted with k_eff = 1.2744. Mixed fuel with weapon grade plutonium made of 20% PuO₂ + 80% ThO₂ yields k_eff = 1.2864. Whereas a mixed fuel with reactor grade plutonium made of 35% PuO₂ + 65% ThO₂ brings it to k_eff = 1.267. Even the very hazardous nuclear waste of LWRs, namely minor actinides turn out to be high quality nuclear fuel due to the excellent neutron economy of FBNR. A relatively high reactor criticality of k_eff = 1.2673 is achieved by 50% MAO₂ + 50% ThO₂.The hazardous actinide nuclear waste products can be transmuted and utilized as fuel in situ. A further output of the study is the possibility of using thorium as breeding material in combination with these new alternative fuels.