A fuzzy-logic approach to HTR nuclear power plant model control

The fuzzy-set theory is used to incorporate linguistic ‘rules of the thumb’ of a human operator in the HTR nuclear power plant controller. The results of the extensive computer simulations are encouraging and confirm the usefulness of this approach in nuclear power plant control. In the Appendix a short introduction to fuzzy logic is given.     

Comparison of analytical and variational solutions of steady-state neutron-diffusion problems

Classical variational techniques are used to obtain accurate solutions to the multigroup multiregion 1-D steady-state neutron-diffusion equation. Analytic solutions are constructed for benchmark verification. Functionals with cubic trial functions and conservational Lagrangian constraints are developed and compared with non-conservational functionals. Eigenvalues, neutron balance and relative flux and current values at interfaces are compared to exact analytical results. Excellent agreement is obtained with conservational functionals using cubic trial functions in comparisons with analytic solutions.     

Computation accuracy and efficiency of a polynomial nodal method for diffusion and spatial burnup problems

The aim of this paper is to demonstrate the accuracy and computational efficiency of a polynomial nodal method (PNM) in solving multigroup neutron diffusion problems in three space dimensions, particularly the long-term burnup problems in PWRs, with their inevitable power-dependent effects. With this in mind, PNM is accurately assessed against other well-grounded nodal methods such as the analytic nodal method (ANM) and the nodal expansion method (NEM), in the case of a well-known PWR benchmark problem, and appears to be as accurate and efficient, as regards the determination of both node-average values and detailed flux distributions inside homogenized nodes. Moreover, the practical applicability of the method to the analysis of fuel cycles in actual PWRs is documented positively.     

The implication of sensitivity analysis on the safety and delayed-neutron parameters for fast breeder reactors

The delayed-neutron energy spectra for LMFBRs are not as well known as those for LWRs. These spectra are necessary for kinetics calculations which play an important role in safety and accident analyses. A sensitivity analysis was performed to study the response of the reactor power and power density to uncertainties in the delayed-neutron spectra during a rod-ejection accident. The accidents studied were central control-rod ejections with ejection times of 2, 10 and 30s. A two-energy group and two-precursor group model was formulated for the International Nuclear Fuel Cycle Evaluation (INFCE) reference design MOX-fueled LMFBR.The sensitivity analysis is based on the use of adjoints so that it is not necessary to repeatedly solve the governing (kinetics) equations to obtain the sensitivity derivatives. This is of particular importance when large systems of equations are used.The power and power-density responses were found to be most sensitive to uncertainties in the spectrum of the second delayed-neutron precursor group, resulting from the fission of²³⁸U, producing neutrons in the first energy group. It was found, for example, that for a rod-ejection time of 30 s, an uncertainty of 7.2% in the fast components of the spectra resulted in a 24% uncertainty in the predicted power and power density. These responses were recalculated by repeatedly solving the kinetics equations. The maximum discrepancy between the recalculated and the sensitivity analysis response was only 1.6%. The results of the sensitivity analysis indicate the need for improved delayed-neutron spectral data in order to reduce the uncertainties in accident analyses.     

Monte Carlo simulation of the emergency shutdown system for the high-temperature pebble-bed nuclear reactor

A theoretical model of the emergency shutdown system for the high-temperature pebble-bed nuclear reactor is presented. The stochastic trajectory of an absorbent ball has been described as a fall with ‘absorption’ along the vertical axis and with planar diffusion in the horizontal directions. Small samples of the random packing of hard spheres and the absorbent balls' trajectories in them have been simulated by the direct Monte Carlo method. The values of model parameters have been estimated from the simulated distributions of the absorbent balls' displacement vectors. The estimated values agree qualitatively with experimental data.     

Scalar flux spectra for 6.2 MeV source photons penetrating cyclindrical ducts in concrete shields

Experimentally-determined benchmark scalar flux spectra are presented for 6.2 MeV photons from a 0.86 m diameter disc source penetrating cylindrical ducts of varying diameters up to 500 mm, machined through concrete shields of thicknesses up to 4.74 m.f.p. Measurements taken with a 76 mm cylindrical NaI spectrometer were unfolded using the code radak. Spectral and exposure dose-rate characteristics have been analysed for shields with and without the ducts. The introduction of a duct into the concrete shield causes an increase in the emerging dose rate which is more pronounced with increasing shield thickness and duct diameter.     

A heuristic approach to the reinforcement-learning control of the one-dimensional model of an HTR core

Results of calculations are presented, which are concerned with applications of the heuristic linear reinforcement systems to the control of pebble-bed HTRs with the OTTO-loading scheme. Control results of three types of systems applications are presented and discussed. The systems were found to be satisfactory for control of the complex physical plants.     

Heavy species enrichment by pulsed gas diffusion

Heavy species enrichment based on pulsed gas diffusion was tested with a constant volume concentrator. The separation factors measured were in good agreement with theory. Enrichment/recovery of heavy species in a constant pressure concentrator is also discussed.     

An axial xenon oscillation model

A two-point xenon oscillation model was developed for PWRs. The model employs the nonlinear xenon and iodine balance equations and the one group, one-dimensional neutron diffusion equation having nonlinear power reactivity feedback. A two-term spatial harmonic series solution was assumed for the flux, xenon and iodine distributions. The system was made as close to critical as possible with the assumed distributions using a variational principle. The xenon and iodine concentrations were then obtained from their governing differential equations.The input/output nature of the model makes it ideal for simulation of xenon-induced reactor transients. A comparison of the simulated plant to actual plant data was made. The period of oscillation, stability index and flux amplitude of the simulated plant were all found to match the actual plant data with less than 10% error.     

Author index to volume 79

Scaling criteria for a natural circulation loop under single phase and two-phase flow conditions have been derived. For a single phase case the continuity, integral momentum, and energy equations in one-dimensional area average forms have been used. From this, the geometrical similarity groups, friction number, Richardson number, characteristic time constant ratio, Biot number, and heat source number are obtained. The Biot number involves the heat transfer coefficient which may cause some difficulties in simulating the turbulent flow regime. For a two-phase flow case, the similarity groups obtained from a perturbation analysis based on the one-dimensional drift-flux model have been used. The physical significance of the phase change number, subcooling number, drift-flux number, friction number are discussed and conditions imposed by these groups are evaluated. In the two-phase flow case, the critical heat flux is one of the most important transients which should be simulated in a scale model. The above results are applied to the LOFT facility in case of a natural circulation simulation. Some preliminary conclusions on the feasibility of the facility have been obtained.     

Preparation, sintering and leaching of optimized uranium thorium dioxides

Mixed actinide dioxides are currently studied as potential fuels for several concepts associated to the fourth generation of nuclear reactors. These solids are generally obtained through dry chemistry processes from powder mixtures but could present some heterogeneity in the distribution of the cations in the solid. In this context, wet chemistry methods were set up for the preparation of U_1−xTh_xO₂ solid solutions as model compounds for advanced dioxide fuels. Two chemical routes of preparation, involving the precipitation of crystallized precursor, were investigated: on the one hand, a mixture of acidic solutions containing cations and oxalic acid was introduced in an open vessel, leading to a poorly-crystallized precipitate. On the other hand, the starting mixture was placed in an acid digestion bomb then set in an oven in order to reach hydrothermal conditions. By this way, small single-crystals were obtained then characterized by several techniques including XRD and SEM. The great differences in terms of morphology and crystallization state of the samples were correlated to an important variation of the specific surface area of the oxides prepared after heating, then the microstructure of the sintered pellets prepared at high temperature. Preliminary leaching tests were finally undertaken in dynamic conditions (i.e. with high renewal of the leachate) in order to evaluate the influence of the sample morphology on the chemical durability of the final cohesive materials.     

Radiochemical separation of thorium from 18O induced reaction with natural uranium

A radiochemical procedure used to separate and purify trace concentration thorium produced in heavy ion reaction with uranium targets is presented.The procedure can rapidly yield thorium fraction suitable for gamma-ray spectroscopy studies.The resultant gamma-ray spectra showed that Th was isolated from a large number of elements produced in the reaction,and there were only a few contaminating activities of isotopes of Sc,Cd,In,etc.The decontamination factors for the main reaction products are given.     

Uranium mononitride: Heat capacity and thermal conductivity from 298 to 1000 °K

The heat capacity and the thermal diffusivity of uranium mononitride were measured by a laser flash method at temperatures ranging from 298 to 1000 °K. The samples were arc-melted UN having nearly zero porosity and sintered UN having porosity of 10.1%. The heat capacity of UN was represented by C_p = 12.08 + 2.548 × 10 ^{− 3}T − {−1.252 × 10⁵T⁻² cal/mol · deg K (298–1000 °K)}. From the heat capacity data, entropy, enthalpy and the Gibbs energy function of UN were calculated. The thermal conductivities of arc-melted UN, calculated from the heat capacity and the thermal diffusivity data, at 350 and 1000 °K were 0.031 and 0.045 cal/ cm · sec · deg K, respectively. The results agreed reasonably well with those of Moore et al. obtained at lower temperatures.     

Analysis of radon, uranium 238 and thorium 232 in potable waters: Dose to adult members of the Moroccan urban population

Uranium (²³⁸U) and thorium (²³²Th) concentrations as well as radon (²²²Rn) and thoron (²²⁰Rn) alpha-activities per unit volume have been measured inside various potable water samples collected from nineteen cities in Morocco by using CR-39 and LR-115 type II solid state nuclear track detectors (SSNTDs). Measured radon alpha-activities ranged from (0.37 ± 0.02) Bq l⁻¹ to (13.6 ± 1.10) Bq l⁻¹ for the potable water samples studied. Alpha-activities due to radon from the ingestion of the studied potable water samples were determined in different compartments of the gastrointestinal system by using the ICRP compartmental model for radon. Annual committed equivalent doses due to radon were evaluated in the gastrointestinal compartments from the ingestion of the potable water samples studied. The influence of the target tissue mass, radon intake and alpha-activity integral due to radon on the annual committed equivalent doses in the gastrointestinal compartments was investigated.     

Heat capacity and enthalpy of cesium iodide from 300 to 830 K

The enthalpy and the heat capacity of CsI have been determined from 300 to 830 K by the drop calorimetry. The calorimeter was operated at 323 K and 520 K for normal and inverse drop procedure, respectively. Heat-capacity measurements were also made with use of a differential scanning calorimeter(DSC) from 300 to 520 K in order to confirm the results. The present results of heat capacity agree well and merge smoothly at 300 K with the published low-temperature values. The heat capacity-temperature curve was found to show a slight upward deviation above 400 K from the linear temperature dependence, which was analyzed to be caused by vacancy formation. By taking this into account, a heat-capacity equation for CsI was derived, which was applicable over the whole temperature range investigated. The thermal functions of CsI were calculated by using this equation from 298 to 899 K(melting point).     

Sorption studies of uranium and thorium on activated carbon prepared from olive stones: Kinetic and thermodynamic aspects

Activated carbon prepared by the chemical activation of olive stone was examined for the sorption of uranium and thorium from aqueous solutions. Precursor/activating agent (ZnCl₂) ratio (1:2) and 500 °C carbonization temperature were used for the preparation of the sorbent. The total sorption capacities were found to be 0.171 and 0.087 mmol g^?1 for uranium and thorium, respectively. The sorption of uranium and thorium was studied as a function of shaking time, pH, initial metal ion concentration, temperature and adsorbent concentration in a batch system. The sorption followed pseudo-second-order kinetics. ΔH° and ΔS° values for thorium and uranium sorption were calculated from the slope and intercept of plots of ln K_d versus 1/T. The positive values of ΔH° indicate the endothermic nature of the process for both metals and decrease in the value of ΔG° with rise in temperature show that the sorption is more favorable at high temperature.     

Measurement of natural radioactivity and radon exhalation rate from rock samples of Jaduguda uranium mines and its radiological implications

The Singhbhum shear zone is a 200 km long arcuate belt in Jharkhand state situated in eastern India. The central part between Jaduguda-Bhatin-Nimdih, Narwapahr-Garadih-Turamdih is rich in uranium. Presence of uranium in the host rocks and the prevalence of a confined atmosphere within mines could result in enhanced concentration of radon (²²²Rn) gas and its progeny. Inhalation of radon daughter products is a major contributor to the radiation dose to exposed subjects. By using high resolution γ-ray spectroscopic system various radionuclides in the rock samples, collected from different places of Jaduguda uranium mines have been identified quantitatively based on the characteristic spectral peaks. The activity concentrations of the natural radionuclides, uranium (²³⁸U), thorium (²³²Th) and potassium (⁴⁰K) were measured in the rock samples and radiological parameters were calculated. Uranium concentration was found to vary from 123 ± 7 Bq kg⁻¹ to 40,858 ± 174 Bq kg⁻¹. Activity of thorium was not significant in the samples, whereas, few samples have shown potassium activity from 162 ± 11 Bq kg⁻¹ to 9024 ± 189 Bq kg⁻¹. Radon exhalation rates from these samples were also measured using “Sealed Can technique” and found to vary from 4.2 ± 0.05 to 13.7 ± 0.08 Bq m⁻² h⁻¹. A positive correlation was found between the radon exhalation rate and the uranium activity. The absorbed dose rates vary from 63.6 to 18876.4 nGy h⁻¹, with an average value of 7054.2 nGy h⁻¹. The annual external effective dose rates vary from 0.7 to 23.2 mSv y⁻¹. Radium equivalent activities (Ra_eq) varied from 134.3 to 40858.0 Bq kg⁻¹. Value of external hazard index (H_ex) varied from 0.4 to 110.4 with an average value of 41.2.