球床堆内冷却剂流动与传热特性的CFD研究

以计算流体力学(CFD)为基础,利用大型商业软件ProE和CFX,对球床式水冷堆堆芯燃料元件进行三维建模、网格划分和数值计算,对堆芯内冷却剂热工水力特性进行了初步的研究.计算比较了燃料元件球间隙和接触情况下冷却剂的速度场、温度场和压力分布,分析了其对堆芯安全的影响.     

Experimental investigation of the overall residence time of pebbles in a pebble bed reactor (PBR) using radioactive pebble

The granular flow of pebbles in a pebble bed reactor (PBR) under the influence of gravity is a dense granular flow with long-lasting frictional contacts. The basic governing physics is not fully understood and hence the dynamic core of a PBR and non-idealities associated with pebbles flow inside the reactor core are of non-trivial significance from the point of view of safety analyses, licensing, and thermal hydraulics. In the current study, overall and zonal pebbles residence time investigation is carried out by implementing noninvasive radioisotope-based flow visualization measurement techniques such as residence time distribution (RTD) and radioactive particle tracking (RPT). The characteristics of overall pebble residence time/transient number, zonal residence time, and the z-component of average zonal velocities at different initial seeding positions of a tracer particle have been summarized. It is found that the overall pebbles residence time/transient number increases (the z-component of average zonal velocities decreases) from the center towards the reactor wall. Also, pebbles’ zonal residence time results (the whole core is divided into three zones) which provide more insight and understanding about PBR core dynamics have been reported. The benchmark data provided could be used for assessment of commercial/in-house computational methodologies related to granular flow investigations.     

Individual pebble temperature peaking factor due to local pebble arrangement in a pebble bed reactor core

Scientists at the German AVR pebble bed nuclear reactor discovered that the surface temperature of some of the pebbles in the AVR core were at least 200 K higher than previously predicted by reactor core analysis calculations. The goal of this research paper is to determine whether a similar unexpected fuel temperature increase of 200 K can be attributed solely or mostly to elevated power production resulting from exceptional configurations of pebbles. If it were caused by excessive pebble-to-pebble local power peaking, there could be implications for the need for core physics monitoring which is not now being considered for pebble bed reactors. The PBMR-400 core design was used as the basis for evaluating pebble bed reactor safety. Through exhaustive Monte Carlo modeling of a PBMR-400 pebble environment, no simple pebble-to-pebble burn-up conditions were found to cause a sufficiently high local power peaking to lead to a 200 K temperature increase. Simple thermal hydraulics analysis was performed which showed that a significant core coolant flow anomalies such as higher than expected core bypass flows, local pebble flow variation or even local flow blockage would be needed to account for such an increase in fuel temperature. The identified worst case scenarios are presented and discussed in detail. The conclusion of this work is that the stochastic nature of the pebble bed cannot lead to highly elevated fuel temperatures but rather local or core-wide coolant flow reductions are the likely cause.     

Numerical solutions for the kinematic model of pebble flow velocity profiles and its applications in pebble-bed nuclear reactor

The modular pebble-bed nuclear reactor (PBR) is a candidate Generation IV reactor being developed. The pebble flow in the very slow draining of fuel pebbles draws attention for its implications on core physical design and reactor physics analysis. One of the effective and simplified methods to address this problem is the kinematic model which is based on continuous theory to derive a diffusion equation for vertical velocity. This paper investigates the appropriate numerical solutions for the kinematic model of pebble flow velocity profiles in PBR geometry. Our method is based on a previously proposed transformed Cartesian coordinates and uses the implicit Crank–Nicholson integration scheme with two different treatments of the boundary conditions. Validations show that this numerical solution gives preferable agreements with the experimental results in the reference. Finally, the simulated velocity profiles are applied in the investigation of two pebble burnup-related issues, which are the pebble residence time prediction and the channel scheme in realistic high-temperature reactor pebble-bed modules reactor core geometry.     

Comparative studies for two different orientations of pebble bed in an HCCB blanket

The Indian Test Blanket Module(TBM) program in ITER is one of the major steps in its fusion reactor program towards DEMO and the future fusion power reactor vision. Research and development(RD) is focused on two types of breeding blanket concepts: lead–lithium ceramic breeder(LLCB) and helium-cooled ceramic breeder(HCCB) blanket systems for the DEMO reactor. As part of the ITER-TBM program, the LLCB concept will be tested in one-half of ITER port no. 2, whose materials and technologies will be tested during ITER operation. The HCCB concept is a variant of the solid breeder blanket, which is presently part of our domestic RD program for DEMO relevant technology development. In the HCCB concept Li_2TiO_3 and beryllium are used as the tritium breeder and neutron multiplier, respectively, in the form of a packed bed having edge-on configuration with reduced activation ferritic martensitic steel as the structural material. In this paper two design schemes, mainly two different orientations of pebble beds, are discussed. In the current concept(case-1), the ceramic breeder beds are kept horizontal in the toroidal–radial direction. Due to gravity, the pebbles may settle down at the bottom and create a finite gap between the pebbles and the top cooling plate, which will affect the heat transfer between them. In the alternate design concept(case-2), the pebble bed is vertically(poloidal–radial) orientated where the side plates act as cooling plates instead of top and bottom plates. These two design variants are analyzed analytically and 2 D thermal-hydraulic simulation studies are carried out with ANSYS, using the heat loads obtained from neutronic calculations.Based on the analysis the performance is compared and details of the thermal and radiative heat transfer studies are also discussed in this paper.     

Optimization of a pebble bed configuration for quasi-direct numerical simulation

A high temperature reactor (HTR) is envisaged to be one of the renewed reactor designs to play a role in nuclear power generation including process heat applications. The HTR design concept exhibits excellent safety features due to the low power density and the large amount of graphite present in the core which gives a large thermal inertia in the event of an accident such as loss of coolant. However, the possible appearance of hot spots in the pebble bed cores of HTR may affect the integrity of the pebbles. This has drawn the attention of several scientists to understand this highly three-dimensional complex phenomenon. A good prediction of the flow and heat transport in such a pebble bed core is a challenge for CFD based on the available turbulence models and computational power. Such models need to be validated in order to gain trust in the simulation of these types of flow configurations. Direct numerical simulation (DNS), while imposing some restrictions in terms of flow parameters and numerical tools corresponding to the available computational resources, can serve as a reference for model development and validation. In the present article, a wide range of numerical simulations has been performed in order to optimize a pebble bed configuration for quasi-DNS which may serve as reference for validation.     

Development of an innovative detection system for pebble bed kinematic studies

Pebble bed reactors enable the circulation of pebble fuel elements when the reactors are in operation.This unique design helps to optimize the burnup and power distribution, reduces the excessive reactivity of the reactor,and provides a mean to identify and segregate damaged fuel elements during operation. The movement of the pebbles in the core, or the kinematics of the pebble bed,significantly affect the above features and is not fully understood. We designed and built a detection system that can measure 3-axis acceleration, 3-axis angular velocity,3-axis rotation angles, and vibration and temperature of multiple pebbles anywhere in the pebble bed. This system uses pebble-shaped detectors that can flow with other pebbles and does not disturb the pebble movement. We used new technologies to enable instant response, precise measurement, and simultaneous collection of data from a large number of detectors. Our tests show that the detection system has a negligible zero drift and the accuracy is better than the designed value. The residence time of the pebbles in a moving pebble bed was also measured using the system.     

Flow visualization in a pebble bed reactor experiment using PIV and refractive index matching techniques

In the advanced gas-cooled pebble bed reactors for nuclear power generation, the fuel is spherical coated particles. The energy transfer phenomenon requires detailed understanding of the flow and temperature fields around the spherical fuel pebbles. Detailed information of the complex flow structure within the bed is needed. Generally, for computing the flow through a packed bed reactor or column, the porous media approach is usually used with lumped parameters for hydrodynamic calculations and heat transfer. While this approach can be reasonable for calculating integral flow quantities, it may not provide all the detailed information of the heat transfer and complex flow structure within the bed. The present experimental study presents the full velocity field using particle image velocimetry technique (PIV) in a conjunction with matched refractive index fluid with the pebbles to achieve optical access. Velocity field measurements are presented delineating the complex flow structure.     

Effects of random pebble distribution on the multiplication factor in HTR pebble bed reactors

In pebble bed reactors the pebbles have a random distribution within the core. The usual approach in modeling the bed is homogenizing the entire bed. To quantify the errors arising in such a model, this article investigates the effect on k_eff of three phenomena in random pebble distributions: non-uniform packing density, neutron streaming in between the pebbles, and variations in Dancoff factor. For a 100 cm high cylinder with reflective top and bottom boundary conditions 25 pebble beds were generated. Of each bed three core models were made: a homogeneous model, a zones model including density fluctuations, and an exact model with all pebbles modeled individually. The same was done for a model of the PROTEUS facility. k_eff calculations were performed with three codes: Monte Carlo, diffusion, and finite element transport. By comparing k_eff of the homogenized and zones model the effect of including density fluctuations in the pebble bed was found to increase k_eff by 71 pcm for the infinite cylinder and 649 pcm for PROTEUS. The large value for PROTEUS is due to the low packing fraction near the top of the pebble bed, causing a significant lower packing fraction for the bulk of the pebble bed in the homogenized model. The effect of neutron streaming was calculated by comparing the zones model with the exact model, and was found to decrease k_eff by 606 pcm for the infinite cylinder, and by 1240 pcm for PROTEUS. This was compared with the effect of using a streaming correction factor on the diffusion coefficient in the zones model, which resulted in Δ_streaming values of 340 and 1085 pcm. From this we conclude neutron streaming is an important effect in pebble bed reactors, and is not accurately described by the correction factor on the diffusion coefficient. Changing the Dancoff factor in the outer part of the pebble bed to compensate for the lower probability of neutrons to enter other fuel pebbles caused no significant changes in k_eff, showing that variations in Dancoff factor in pebble bed reactors can be ignored.     

A discrete element method study on the evolution of thermomechanics of a pebble bed experiencing pebble failure

The discrete element method (DEM) is used to study the thermal effects of pebble failure in an ensemble of lithium ceramic spheres. Some pebbles crushing in a large system is unavoidable and this study provides correlations between the extent of pebble failure and the reduction in effective thermal conductivity of the bed. In the model, we homogeneously induced failure and applied nuclear heating until dynamic and thermal steady-state. Conduction between pebbles and from pebbles to the boundary is the only mode of heat transfer presently modeled. The effective thermal conductivity was found to decrease rapidly as a function of the percent of failed pebbles in the bed. It was found that the dominant contributor to the reduction was the drop in inter-particle forces as pebbles fail; implying the extent of failure induced may not occur in real pebble beds. The results are meant to assist designers in the fusion energy community who are planning to use packed beds of ceramic pebbles. The evolution away from experimentally measured thermomechanical properties as pebbles fail is necessary for proper operation of fusion reactors.     

Survey of dust production in pebble bed reactor cores

Graphite dust produced via mechanical wear from the pebbles in a pebble bed reactor is an area of concern for licensing. Both the German pebble bed reactors produced graphite dust that contained activated elements. These activation products constitute an additional source term of radiation and must be taken under consideration during the conduct of accident analysis of the design. This paper discusses the available literature on graphite dust production and measurements in pebble bed reactors. Limited data is available on the graphite dust produced from the AVR and THTR-300 pebble bed reactors. Experiments that have been performed on wear of graphite in pebble-bed-like conditions are reviewed. The calculation of contact forces, which are a key driving mechanism for dust in the reactor, are also included. In addition, prior graphite dust predictions are examined, and future areas of research are identified.     

Experimental measurement of effective thermal conductivity of packed lithium-titanate pebble bed

Lithium titanate is a promising solid breeder material for the fusion reactor blanket. Packed lithium titanate pebble bed is considered for the blanket. The thermal energy; that will be produced in the bed during breeding and the radiated heat from the reactor core absorbed must be removed. So, the experimental thermal property data are important for the blanket design. In past, a significant amount of works were conducted to determine the effective thermal conductivity of packed solid breeder pebble bed, in helium atmosphere, but no flow of gas was considered. With increase in gas flow rate, effective thermal conductivity of pebble bed increases. Particle size and void fraction also affect the thermal properties of the bed significantly. An experimental facility with external heat source was designed and installed. Experiments were carried out with lithium-titanate pebbles of different sizes at variable gas flow rates and at different bed wall temperature. It was observed that effective thermal conductivity of pebble bed is a function of particle Reynolds number and temperature. From the experimental data two correlations have been developed to estimate the effective thermal conductivity of packed lithium-titanate pebble bed for different particle Reynolds number and at different temperatures. The experimental details and results are discussed in this paper.     

Direct deterministic method for neutronics analysis and computation of asymptotic burnup distribution in a recirculating pebble-bed reactor

A new deterministic method has been developed for the neutronics analysis of a pebble-bed reactor (PBR). The method accounts for the flow of pebbles explicitly and couples the flow to the neutronics. The method allows modeling of once-through cycles as well as cycles in which pebbles are recirculated through the core an arbitrary number of times. This new work is distinguished from older methods by the systematically semi-analytical approach it takes. In particular, whereas older methods use the finite-difference approach (or an equivalent one) for the discretization and the solution of the burnup equation, the present work integrates the relevant differential equation analytically in discrete and complementary sub-domains of the reactor. Like some of the finite-difference codes, the new method obtains the asymptotic fuel-loading pattern directly, without modeling any intermediate loading pattern. This is a significant advantage for the design and optimization of the asymptotic fuel-loading pattern. The new method is capable of modeling directly both the once-through-then-out fuel cycle and the pebble recirculating fuel cycle. Although it currently includes a finite-difference neutronics solver, the new method has been implemented into a modular code that incorporates the framework for the future coupling to an efficient solver such as a nodal method and to modern cross section preparation capabilities. In its current state, the deterministic method presented here is capable of quick and efficient design and optimization calculations for the in-core PBR fuel cycle. The method can also be used as a practical “scoping” tool. It could, for example, be applied to determine the potential of the PBR for resisting nuclear-weapons proliferation and to optimize proliferation-resistant features. However, the purpose of this paper is to show that the method itself is viable. Refinements to the code are under way, with the objective of producing a powerful reactor physics analysis tool for PBRs.     

CFD analysis for thermal mixing in a subcooled water tank under a high steam mass flux discharge condition

A Computational Fluid Dynamics (CFD) analysis for a thermal mixing test was performed for 30 s to develop the methodology for a numerical analysis of the thermal mixing between steam and subcooled water and to apply it to Advanced Power Reactor 1400 MWe (APR1400). In the CFD analysis, the steam condensation phenomenon by a direct contact was simulated by the so-called condensation region model. Thermal mixing phenomenon in the subcooled water tank was treated as an incompressible flow, a free surface flow between the air and the water, and a turbulent flow, which are implemented in the CFX4.4. The comparison of the CFD results with the test data showed a good agreement as a whole, but a small local temperature difference was found at some locations. A sensitivity analysis was performed to find the reason of the temperature difference. The commercial CFD code of CFX4.4 together with the condensation region model can simulate the thermal mixing behavior reasonably well when a sufficient number of mesh distributions and a proper numerical method are selected.     

Optimization of a radially cooled pebble bed reactor

By altering the coolant flow direction in a pebble bed reactor from axial to radial, the pressure drop can be reduced tremendously. In this case the coolant flows from the outer reflector through the pebble bed and finally to flow paths in the inner reflector. As a consequence, the fuel temperatures are elevated due to the reduced heat transfer of the coolant. However, the power profile and pebble size in a radially cooled pebble bed reactor can be optimized to achieve lower fuel temperatures than current axially cooled designs, while the low pressure drop can be maintained.The radial power profile in the core can be altered by adopting multi-pass fuel management using several radial fuel zones in the core. The optimal power profile yielding a flat temperature profile is derived analytically and is approximated by radial fuel zoning. In this case, the pebbles pass through the outer region of the core first and each consecutive pass is located in a fuel zone closer to the inner reflector. Thereby, the resulting radial distribution of the fissile material in the core is influenced and the temperature profile is close to optimal.The fuel temperature in the pebbles can be further reduced by reducing the standard pebble diameter from 6 cm to a value as low as 1 cm. An analytical investigation is used to demonstrate the effects on the fuel temperature and pressure drop for both radial and axial cooling.Finally, two-dimensional numerical calculations were performed, using codes for neutronics, thermal-hydraulics and fuel depletion analysis, in order to validate the results for the optimized design that were obtained from the analytical investigations. It was found that for a radially cooled design with an optimized power profile and reduced pebble diameter (below 3.5 cm) both a reduction in the pressure drop ( bar), which increases the reactor efficiency with several percent, and a reduction in the maximum fuel temperature (C) can be achieved compared to present axially cooled designs.     

Experimental study and analysis of the purge gas pressure drop across the pebble beds for the fusion HCPB blanket

The lithium ceramic and beryllium pebble beds of the breeder units (BU), in the fusion breeding blanket, are purged by helium to extract the bred tritium. Therefore, the objective of this study is to support the design of the BU purge gas system by studying the effect of pebbles diameter, packing factor, pebble bed length, and flow inlet pressure on the purge gas pressure drop. The pebble bed was formed by packing glass pebbles in a rectangular container (56 mm × 206 mm × 396 mm) and was integrated into a gas loop to be purged by helium at BU-relevant pressures (1.1–3.8 bar). To determine the pressure drop across the pebble bed, the static pressure was measured at four locations along the pebble bed as well as at the inlet and outlet locations. The results show: (i) the pressure drop significantly increases with decreasing the pebbles diameter and slightly increases with increasing the packing factor, (ii) for a constant inlet flow velocity, the pressure drop is directly proportional to the pebble bed length and inlet pressure, and (iii) predictions of Ergun's equation agree well with the experimental values of the pressure drop.     

Mechanics of binary and polydisperse spherical pebble assembly

The micromechanical behavior of an assembly of binary and polydisperse spherical pebbles is studied using discrete element method (DEM) accounting for microscopic interactions between individual pebbles. A in-house DEM code has been used to simulate the assemblies consisting of different pebble diameters and the results of the simulations are compared with that of mono-size pebble assemblies. The effect of relative radii and volume fraction of the pebbles on the macroscopic stress–strain response is discussed. Furthermore, the effect of packing factor and coefficient of friction on the overall stress–strain behavior of the system is studied in detail. The shear (tangential) stiffness between the particles is also another influencing parameter. For a very small shear stiffness the system shows a strong dependence on the packing factor while a pebble material dependent shear stiffness shows a rather moderate dependence on the packing factor. For a similar packing factor, the mono-size assembly shows a stiff behavior during loading compared to binary assembly. However, the simulations do not show a significant difference between the two behaviors in contrast to the observations made in the experiments. The discrepancy can be attributed to (i) probable difference in packing factors for mono-size and binary assemblies in the experiments, (ii) arbitrary friction coefficient in the current model and (iii) the tangential interaction (constant shear stiffness) implemented in the present model which needs further modification as a function of the load history on the pebbles. Evolution of other micromechanical characteristics such as coordination number, contact force distribution and stored elastic energy of individual pebbles as a function of external load and system parameters is presented which can be used to estimate important macroscopic properties such as overall thermal conductivity and crushing resistance of the pebble beds.     

CFD analysis of PWR core top and reactor vessel upper plenum internal subdomain models

One aspect of the Westinghouse AP1000™¹ reactor design is the reduction in the number of major components and simplification in manufacturing. One design change relative to current Westinghouse reactors of similar size is that AP1000 reactor vessel has two nozzles/hot legs instead of three. With regard to fuel performance, this design difference creates a different flow field in the reactor vessel upper plenum. The flow exiting from the core and entering the upper plenum must turn toward one of the two outlet nozzles and flow laterally around numerous control rod guide tubes and support columns. Also, below the upper plenum are the upper core plate and the top core region of the 157 fuel assemblies and 69 guidetube assemblies.To determine how the lateral flow in the top of the core and upper plenum compares to the current reactors a CFD model of the flow in the upper portion of the AP1000 reactor vessel was created.Before detailed CFD simulations of the flow in the entire upper plenum and top core regions were performed, conducting local simulations for smaller sections of the domain provided crucial and detailed physical aspects of the flow. These sub-domain models were used to perform mesh sensitivities and to assess what geometrical details may be eliminated from the larger model in order to reduce mesh size and computational requirements. In this paper, CFD analysis is presented for two subdomain models: the top core region and control rod guide tube region. These models are chosen for simulation because guide tube and top core region (including top grid, top nozzle, and hold-down device) are the major components of upper plenum effecting the flow patterns and pressure distribution.The top core region, corresponding to ¼ of fuel assembly, includes components as upper part of the fuel assemblies (top grid, fuel rods, top nozzle), core component hold-down devices, and upper core plates. These components distribute the core flow to different sections of guidetube regions. Mesh sensitivity studies have been conducted for each individual part in order to determine the proper geometrical simplifications. Pressure drop measurement data are compared with the predicted CFD results and act as a guideline for the mesh selection.The guidetube region includes control rod guidetubes themselves, adjacent support columns and open regions. In this study, two models of subdomains are analyzed: (1) a ¼ section of one control rod guide tube by itself and (2) a representative unit cell containing two ¼ sections of adjacent control rod guide tubes and one ¼ section of a neighboring support column.Predicted flow rates at each of the outflow locations in conjunction with results from the mesh sensitivity studies provide guidance on (1) what geometry to preserve or remove, (2) what geometry can be simplified to reduce the required mesh, and (3) an estimate of the total mesh required to model the entire upper plenum and top fuel domain.The commercial CFD code STAR-CCM+ is employed to generate the computational mesh, to solve the Reynolds-averaged Navier–Stokes equations for incompressible flow with a Realizable k–? turbulence model, and to post-process the results.     

Fluctuation and arching formation of very dense and slow pebble flow in a silo bed

Improved particle tracking velocimetry (improved PTV) is proposed for experimental study of very slow dense pebble flow in a silo bed by combining the relaxation method and Voronoï diagram. The improved PTV method is validated by comparison with DEM (discrete element method) simulation and experimental result. Velocity and fluctuation characteristics on different streamlines are investigated to show the macroscopic kinematics of pebble flow. Bulk arches on different locations of the pebble bed are identified. Two local arching characteristics including size distribution and horizontal span are analyzed, and their effects on whole flow regime are discussed. It is found that the arch size distribution follows second-order polynomial distribution in semi-logarithmic scale. The horizontal span of arches provides evidence for transition between the ordered and disordered regimes. The probability distribution of successive angles between the neighbors of arching particles is a good indicator of arch stability. The relation between arch breakdown and contact network change is demonstrated by correlation analysis. High correlation between arching structure and mean velocity in targeted regions is indicated. The characteristic lifetime of arches and autocorrelation time of fluctuation velocity present positive correlation. The bulk arching dynamics is the main reason for fluctuations of particle velocities.     

Fabrication of beryllide pebble as advanced neutron multiplier

Fusion reactors require advanced neutron multipliers with great stability at high temperatures. Beryllium intermetallic compounds, called beryllides such as Be₁₂Ti, are the most promising materials for use as advanced neutron multipliers. However, few studies have been conducted on the development of mass production methods for beryllide pebbles. A granulation process for beryllide needs to have both low cost and high efficiency. To fabricate beryllide pebbles, a new granulation process is established in this research by combining a plasma sintering method for beryllide synthesis and a rotating electrode method using a plasma-sintered electrode for granulation. The fabrication process of the beryllide electrode is investigated and optimized for mass production. The optimized beryllide electrode exhibits higher ductility and can be sintered at a lower temperature for a shorter time, indicating that it is more suitable not only for withstanding the thermal shock from arc-discharge during granulation but also for producing the beryllide pebbles on a large scale. Accordingly, because these optimization results can reduce the time required for electrode fabrication by 40%, they suggest the possibility of great reductions in time and cost for mass production of beryllide pebbles.