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[en] The pebble bed type gas cooled high temperature reactor (HTR) appears to be a good candidate for the next generation nuclear reactor technology. These reactors have unique characteristics in terms of the randomness in geometry, and require special techniques to analyze their systems. This study includes activities concerning the testing of computational tools and the qualification of models. Indeed, it is essential that the validated analytical tools be available to the research community. From this viewpoint codes like MCNP, ORIGEN and RELAP5, which have been used in nuclear industry for many years, are selected to identify and develop new capabilities needed to support HTR analysis. The geometrical model of the full reactor is obtained by using lattice and universe facilities provided by MCNP. The coupled MCNP-ORIGEN code is used to estimate the burnup and the refuelling scheme. Results obtained from Monte Carlo analysis are interfaced with RELAP5 to analyze the thermal hydraulics and safety characteristics of the reactor. New models and methodologies are developed for several past and present experimental and prototypical facilities that were based on HTR pebble bed concepts. The calculated results are compared with available experimental data and theoretical evaluations showing very good agreement. The ultimate goal of the validation of the computer codes for pebble bed HTR applications is to acquire and reinforce the capability of these general purpose computer codes for performing HTR core design and optimization studies
[en] This paper discusses the use of the dimension-wise expansion model for cross-section parameterization. The components of the model were approximated with tensor products of orthogonal polynomials. As we demonstrate, the model for a specific cross-section can be built in a systematic way directly from data without any a priori knowledge of its structure. The methodology is able to construct a finite basis of orthogonal polynomials that is required to approximate a cross-section with pre-specified accuracy. The methodology includes a global sensitivity analysis that indicates irrelevant state parameters which can be excluded from the model without compromising the accuracy of the approximation and without repetition of the fitting process. To fit the dimension-wise expansion model, Randomised Quasi-Monte-Carlo Integration and Sparse Grid Integration methods were used. To test the parameterization methods with different integrations embedded we have used the OECD PBMR 400 MW benchmark problem. It has been shown in this paper that the Sparse Grid Integration achieves pre-specified accuracy with a significantly (up to 1-2 orders of magnitude) smaller number of samples compared to Randomised Quasi-Monte-Carlo Integration.
[en] Highlights: • The stationary and moving pebbles in a PBR are numerically studied by DEM. • The packing structure of stationary pebbles is simulated by a filling process. • The packing structural properties are obtained and analyzed. • The dynamic behavior of pebbles is predicted and discussed. - Abstract: This paper presents a numerical study of the stationary and moving pebbles in a pebble bed reactor (PBR) by means of discrete element method (DEM). The packing structure of stationary pebbles is simulated by a filling process that terminates with the settling of the pebbles into a PBR. The packing structural properties are obtained and analyzed. Subsequently, when the outlet of the PBR is opened during the operation of the PBR, the stationary pebbles start to flow downward and are removed at the bottom of the PBR. The dynamic behavior of pebbles is predicted and discussed. Our results indicate the DEM can offer both macroscopic and microscopic information for PBR design calculations and safety assessment
[en] Highlights: ► A modified kinematic method is proposed for analysis of pebble flow velocity. ► Experiments are performed to derive the coefficients and to verify the results. ► The method and result can be used for the advanced analysis of pebble bed reactor. - Abstract: A pebble bed reactor is filled by a large number of pebbles, which are randomly piled up in the core region. During the process of fuel loading and extraction, the pebbles flow downward through the core. The basic physics of the dense granular flow such as pebble flow is not fully understood; hence, the dynamic core of the pebble bed reactor has been a subject of concern among designers and regulators. The kinematic model is one of the representative models for the reconstruction of the granular flow velocity, however, it is noted that there are some limitations in the reconstruction ability. In this study, a modified kinematic model was proposed to enhance the reconstruction ability of the pebble velocity profile. Pebble flow experiments were performed to derive the coefficients needed for the modified kinematic model and to verify the reconstruction ability and the applicability of the proposed method in the annular core. The modified kinematic model can contribute to accurate velocity evaluation as well as large applicability for the specific core types such as an annular core. Also, the results can be used for reference data in the design of a pebble bed reactor
[en] Highlights: • Effect of density difference on packing structure and flow pattern are studied. • Equivalent density and voidage are analyzed to describe spatial distribution. • Light particles tend to be pushed to side walls by heavy ones during circulation. • Higher density ratio may lead to more obvious squeezing phenomenon. • Different velocity patterns in lower and upper parts of the bed are observed. - Abstract: Based on the discrete element method, this work simulates the mixing flow of particles with different density in packed bed. The aim of this work is to explore the effect of density difference on the spatial distribution and flow characteristics of particles. After a premixed stacking, the particles start to discharge at fixed number rates being extracted from the bottom and then reinserted into the top of the bed to maintain the circulating flow. The results reveal that although different density can affect the local equivalent density, it has little influence on the uniformity and compactness of the whole bed with overall average voidage of about 0.39. The wall effects on particle distribution and voidage are observed near the wall. In addition, during the unloading time (time after the start of discharge), the proportion of light particles near the wall is always higher than 0.5 and keeps increasing. The increasing proportion and much higher number fraction of light particles compared with heavy one indicate that the heavy particles have the tendency to push the light particles to the side during the circulation process. Besides, the higher the ratio is, the more obvious this phenomenon is. Last but not least, both the axial and radial velocity profiles are analyzed, which show different patterns between the bottom and upper part of the packed bed.
[en] Highlights: • PTV study of flow fields of pebble bed reactor with different configurations are carried out. • Some criteria are proposed to quantify vertical velocity field and flow uniformity. • The effect of different pebble bed configurations is also compared by the proposed criteria. • The displacement thickness is used analogically to analyze flow field characteristics. • The effect of mass flow variation in the stagnated region of the funnel flow is measured. - Abstract: The flow field characteristics are of fundamental importance in the design work of the pebble bed high temperature gas cooled reactor (HTGR). The different effects of bed configurations on the flow characteristics of pebble bed are studied through the PTV (Particle Tracking Velocimetry) experiment. Some criteria, e.g. flow uniformity (σ) and mass flow level (α), are proposed to estimate vertical velocity field and compare the bed configurations. The distribution of the Δθ (angle difference between the individual particle velocity and the velocity vector sum of all particles) is also used to estimate the resultant motion consistency level. Moreover, for each bed configuration, the thickness of displacement is analyzed to measure the effect of the funnel flow zone based on the boundary layer theory. Detailed information shows the quantified characteristics of bed configuration effects on flow uniformity and other characteristics; and the sequence of levels of each estimation criterion is obtained for all bed configurations. In addition, a good design of the pebble bed configuration is suggested and these estimation criteria can be also applied and adopted in testing other geometry designs of pebble bed.
[en] Highlights: • A 3D DEM study on particle–wall/particle friction in pebble bed reactor is carried out. • Characteristic values are defined to evaluate features of pebble flow pattern quantitatively. • Particle–wall friction is dominant to determine flow pattern in a specific pebble bed. • Friction effect of hopper part on flow field is more critical than that of cylinder part. • Three cases of 1:1 full scale practical pebble beds are simulated for demonstration. - Abstract: Friction affects pebble flow pattern in pebble-bed high temperature gas-cooled reactor (HTGR) significantly. Through a series of three dimensional DEM (discrete element method) simulations it is shown that reducing friction can be beneficial and create a uniform and consistent flow field required by nuclear engineering. Particle–wall friction poses a decisive impact on flow pattern, and particle–particle friction usually plays a secondary role; relation between particle–wall friction and flow pattern transition is also concluded. Moreover, new criteria are created to describe flow patterns quantitatively according to crucial issues in HTGR like stagnant zone, radial uniformity and flow sequence. Last but not least, it is proved that friction control of hopper part is more important than that of cylinder part in practical pebble beds, so reducing friction between pebbles and hopper surface is the engineering priority.
[en] Highlights: • Development of a 3D Monte Carlo based code for pebble bed reactors. • Dancoff sensitivity to clad, moderator and fuel cross sections is considered. • Sensitivity of Dancoff to number of energy groups is considered. • Sensitivity of Dancoff to number of fuel and their arrangement is considered. • Excellent agreements vs. MCNP code. - Abstract: The evaluation of multigroup constants in reactor calculations depends on several parameters. One of these parameters is the Dancoff factor which is used for calculating the resonance integral and flux depression in the resonance region in heterogeneous systems. In the current paper, a computer program (MCDAN-3D) is developed for calculating three dimensional black and gray Dancoff coefficients, based on Monte Carlo, escape probability and neutron free flight methods. The developed program is capable to calculate the Dancoff factor for an arbitrary arrangement of fuel and moderator pebbles. Moreover this program can simulate fuels with homogeneous and heterogeneous compositions. It might generate the position of Triso particles in fuel pebbles randomly as well. It could calculate the black and gray Dancoff coefficients since fuel region might have different cross sections. Finally, the effects of clad and moderator are considered and the sensitivity of Dancoff factor with fuels arrangement variation, number of TRISO particles and neutron energy has been studied
[en] In order to achieve highly efficient natural uranium utilization with a once-through fuel cycle, an idea of a pebble bed type fast reactor is investigated. The effective multiplication factor of 1.049 is obtained in the case of zero radial buckling for an optimum fuel velocity. The discharged fuel burnup becomes 439 GWd/tHM for mean power density of 50 W/cc, which is equivalent to the utilization of 457% of natural uranium
[en] Highlights: ► A summarized plant description of the Pebble Bed Micro Model (PBMM) is given. ► A Flownex simulation provides input–output data of different sections of the plant. ► Linear system identification techniques are used to obtain mathematical models. ► The Flownex simulation and linear system identification results are compared. - Abstract: Linear system identification techniques will be applied to obtain mathematical models of a simulation of the Pebble Bed Micro Model (PBMM). The PBMM is a conceptual model of the Pebble Bed Modular Reactor (PBMR), a new high temperature gas nuclear reactor. The basis of the PBMR and PBMM is a three-phase Brayton Power Generation Cycle. The Brayton cycle will in this paper be simulated by the use of Flownex, a general thermal-fluid network analysis code solver. A description of the Brayton Power Generation Cycle, as well as a description of the Flownex modelling program, will also be given.