Pebble Bed Reactor Research Articles

Fast Neutron Irradiation Influence Analysis in Thermal-Hydraulics Aspect of HTR-10 Reactor Using Modified PEBBLE Program

Pebble Bed Reactor is a Gen-IV reactor that uses spherical fuel loaded into an active core. This reactor uses graphite that can be found on fuel and reflectors as a neutron moderator. The fast neutron can damage the atomic structure of fuel because the neutron with high energy can displace the graphite lattice. As its effect, the value of fuel thermal conductivity is influenced. PEBBLE is the program used for thermal-hydraulic calculation for pebble bed reactor type (PBR), and mPEBBLE was developed based on PEBBLE. The main difference between the two is that the mPEBBLE can take into account the fast neutron factor in the calculation. In this study, the thermal-hydraulics calculation for HTR-10 was performed using the mPEBBLE code. The result obtained is compared to the results from two different programs; THERMIX and WIMSTER. The comparison between the mPEBBLE and THERMIX has a temperature difference, which is relatively high at 63.3°C at the near-wall position. For the comparison between mPEBBLE and WISMTER, the noticeable difference happens in pebble center temperature, which is 65.3°C for the temperature difference.

Investigation on Criticality and Burnup Performance of Pebble Bed Reactor with Thorium-based Nuclear Fuel

Thorium-based nuclear fuel has become an interesting subject for a variety of research with a wide range of applications. Research focusing on thorium-based fuel is aimed to overcome the scarcity and limitation of natural uranium resources as an alternative nuclear fuel in a thermal reactor. As thorium has no naturally occurring fissile isotope, it requires other fissile isotopes in order to be converted into fissile 233U to produce energy. The isotopes 235U and 2359Pu are two of the few alternatives available as the fissile nuclei for a thorium-fueled reactor. The purpose of this paper is to investigate the criticality and burnup performance of pebble bed reactor using two options of thorium-based fuel–namely, UO2-ThO2 and PuO2-ThO2. The HTR-10 was chosen as the reactor model. A series of criticality calculations with various uranium contents in UO2-ThO2 fuel and various plutonium contents in PuO2-ThO2 fuel was conducted using the Monte Carlo transport code MCNP6 and continuous energy nuclear data library ENDF/B-VII. The calculation result shows that 35% plutonium content in PuO2-ThO2 fuel has comparable criticality with 80% uranium content in UO2-ThO2 fuel. The former is shown to be better to ensure longer reactor operational time. However, that is due to the higher fissile fraction compared to that of the latter fuel. Meanwhile, thorium played little part in prolonging reactor criticality, as 233U production is not particularly significant.

Study of Clogging Phenomenon for a Conical Hopper: The Influence of Particle Bed Height and Hopper Angle

The granular flow is one of the principal issues for the design of pebble bed reactors. Particularly, the clogging phenomenon raises an important issue for pebble bed reactors. In this paper, we conduct experiments and discrete particle simulation of two-dimensional discharge granular flow from a conical hopper, to study the effect of the particle bed height h and hopper angle α on the clogging phenomenon. In general, the clogging probability J increases with height h and starts to saturate when h is larger than a critical value. The experimental result trends are supported by discrete simulations. To understand the underlying physical mechanism, we conduct discrete particle simulations for various h values, focusing on the following parameters: the statistical averaging of the volume fraction, velocity, and contact pressure of particles near the aperture during the discharge. We found that, among all relevant variables, the contact pressure of particles is the main cause of the increasement of J when h increases. An exponential law between the pebble bed h and clogging probability J has been established based on these observations and Janssen model. As for hopper angle α , J shows an almost constant behavior for any rise in α followed by a sudden regression at α = 75 ° . Surprisingly, the effect of α is most obvious for intermediate values of h , where we observe a sharp increasement of clogging probability. The same trend is observed in the two-dimensional discrete simulation results.

Rattlesnake: A MOOSE-Based Multiphysics Multischeme Radiation Transport Application

Advanced reactor concepts span the spectrum from heat pipe–cooled microreactors, through thermal and fast molten-salt reactors, to gas- and salt-cooled pebble bed reactors. The modeling and simulation of each of these reactor types comes with their own geometrical complexities and multiphysics challenges. However, the common theme for all nuclear reactors is the necessity to be able to accurately predict neutron distribution in the presence of multiphysics feedback. We argue that the current standards of modeling and simulation, which couple single-physics, single-reactor-focused codes via ad hoc methods, are not sufficiently flexible to address the challenges of modeling and simulation for advanced reactors. In this work, we present the Multiphysics Object Oriented Simulation Environment (MOOSE)–based radiation transport application Rattlesnake. The use of Rattlesnake for the modeling and simulation of nuclear reactors represents a paradigm shift away from makeshift data exchange methods, as it is developed based on the MOOSE platform with its very natural form of shared data distribution. Rattlesnake is well equipped for addressing the geometric and multiphysics challenges of advanced reactor concepts because it is a flexible finite element tool that leverages the multiphysics capabilities inherent in MOOSE. This paper focuses on the concept and design of Rattlesnake. We also demonstrate the capabilities and performance of Rattlesnake with a set of problems including a microreactor, a molten-salt reactor, a pebble bed reactor, the Advanced Test Reactor at the Idaho National Laboratory, and two benchmarks: a multiphysics version of the C5G7 benchmark and the LRA benchmark.

Spent fuel management strategies for fluoride-cooled pebble bed reactors

Spent nuclear fuel from fluoride-salt-cooled high-temperature reactors presents different set of storage and handling challenges than fuel from light water reactors and requires the implementation of new strategies. This study explores potential strategies involving pool storage (in helium or FLiNaK) and cask storage/transportation in sequential phases and assesses the feasibility of such strategies in terms of thermal-hydraulics, criticality safety and radiation shielding. The most demanding constraints to the design of the pool storage system are set by criticality safety and require distributing the spent fuel in separate containers. Subcriticality of the fuel in the casks can be maintained by mixing boron-doped graphite spheres with the spent pebbles. High dose rates at the cask surface impede immediate loading of the pebbles in storage/ transportation casks, but the use of steel and lead based overpacks offers effective radiation shielding and good thermal properties, and allows loading spent fuel in the casks after as few as two years of pool storage.

Experimental investigation of turbulent characteristics in pore-scale regions of porous media

The study of flow dynamics in porous media or randomly packed beds is essential because these systems are commonly applied in a wide array of engineering applications, such as thermal energy storage, catalytic reactors for processing and distillation, oil recovery, fuel cells, and pebble bed nuclear reactor cores. The flow mixing and turbulence characteristics in pore-scale regions of an experimental facility composed of randomly packed spheres with an aspect ratio of 4.4 were experimentally investigated in this study. Velocity measurements at several pores in the test facility were conducted by combining the matched-index-of-refraction and time-resolved particle image velocimetry techniques, and these measurements were performed at Reynolds numbers of 490, 1023, and 1555. The results obtained from the velocity measurements in the pore regions revealed different and complex flow patterns depending on the pore geometries. In pore region 1, it was found that a strong axial flow entered the pore and impinged into the sphere’s surface when it encountered another flow entering laterally. These dynamic interactions created a high level of turbulent mixing, a recirculation flow region, and a shear layer, as observed in the computed statistical results for $$u^{\prime }_\mathrm{{rms}}$$ , $$v^{\prime }_\mathrm{{rms}}$$ , and $$u^{\prime }v^{\prime }$$ . In other pore regions, the flow field results exhibited complex interactions among jet flows discharging into the pores from various flow gaps created by neighboring spheres. These mutual interactions between the entering jet flows were found to create highly turbulent mixing regions at the pore’ centers and low-velocity or stagnation-flow regions in the vicinity of the sphere surfaces. Flapping shear layers were also observed when two jet flows with unequal strengths entered the pores. The characteristics of turbulent flow mixing in different pore regions were investigated via the spatiotemporal two-point correlation of fluctuating velocities along the velocity streamlines. This approach mitigated the constraints of the random geometries of pore regions on the extent of spatial separation lengths in the two-point velocity correlations. Using this approach, spatial distributions of integral length scales and convection velocities were estimated along the streamlines within the random geometries of pore regions. It was found that the estimated values of the integral length scales and convection velocities were spatially dependent on the localized flow characteristics within the pores. The integral length scales were found to be less than $$0.4D_\mathrm{{sp}}$$ , experimentally confirming the pore-scale prevalence hypothesis that turbulent structures in porous media are restricted by the pore sizes. In addition, the ratio of the convection velocity to the interstitial velocity (or local velocity magnitude) decreased as the Reynolds number increased.

Heat transfer and fluid flow of helium coolant in a model of the core zone of a pebble-bed nuclear reactor

Using the RNG k-ε model of turbulence in the approximation for porous media, a numerical study of fluid flow and heat transfer in a model of the core zone of a pebble-bed nuclear reactor was performed. Validations of the results of simulations against experimental data (for the friction factor) and analytical solutions (for the velocity profiles) confirmed applicability of the RNG k-ε model of turbulence for the stated problem. An unsteady mode of operation with a decrease in the coolant mass flowrate at the inlet to the reactor core zone model, as well as a steady-state mode were studied. The effect of the pebble bed permeability on the dynamics of flow temperature variation was also investigated.

An explicit expression of empirical parameter in ZBS model for predicting pebble bed effective thermal conductivity

The pebble bed effective thermal conductivity is a key parameter in the design and safety analysis of the high temperature pebble bed reactor. The ZBS model is widely used to predict the pebble bed effective thermal conductivity. However, the predictive ability of the ZBS model is greatly affected by the selected values of the empirical parameter contact area fraction φ. In this paper, a semi-empirical formula is proposed to estimate the empirical parameter contact area fraction φ, which is related with the contact radius ratio γ and coordination number Nc. The stagnant effective thermal conductivities in the three types of ordered pebble beds are numerically studied to provide the values of φ with corresponding contact radius ratios γ and coordination numbers Nc. Then the multiple linear regression is performed and the proposed semi-empirical formula is determined asφ=0.15Nc1.1γ. The predicted values by the improved ZBS model with the estimation of contact area fraction φ agree rather well with the numerical results of the random pebble bed. Compared with SANA experimental data, the improved ZBS model is proved to be better than other models. Compared with HTTU experimental data, the improved ZBS model is able to predict the effective thermal conductivity in the bulk region of pebble beds. However, the improved ZBS model needs to be further improved in the near-wall region.

Effects of %FIMA on Storage-Safety Parameters of Spent Fuel from Experimental Pebble-Bed Reactor

The back end of the utilization of nuclear technology is safety and management of spent fuel, which is a key element contributing to the success of the nuclear power plant program. Indonesia’s National Nuclear Energy Agency resolved to establish an experimental power reactor, called RDE, as a nuclear power plant demo. The fuel of this reactor is similar to that of German’s experimental pebble-bed reactor (PBR), Arbeitsgemeinschaft Versuchsreaktor(AVR). In this study, the spent fuel of AVR was studied to obtain the safety parameter data for storage of RDE spent fuel by varying the fission in the initial metallic atoms (%FIMA). These parameters that must be studied include the radioactivity, decay heat, proliferation threats of both 239Pu and 235U, and the presence of 137Cs, a dangerous fission product that can escape from damaged spent fuels. The calculation was conducted by ORIGEN 2.1. The result of the study demonstrates a higher %FIMA indicates a higher safety level that is required since the activity and decay heat of the spent fuel will increase and, as will be the total amounts of 239Pu and 137Cs. However, the 235U amount will decrease. For a 100 years storage of spent fuel, the optimum %FIMA is 8.2 with a canister capacity of 1,900 pebbles. Further, the activity and decay heat of the spent nuclear fuel are 2.013 × 1013 Bq and 6.065 W, respectively. The activities of 239Pu, 137Cs, and 235U are 5.187 ×1011, 7.100 × 1012, and 7.339 × 107 Bq, respectively.

Coupled Computational Fluid Dynamics–Discrete Element Method Study of Bypass Flows in a Pebble Bed Reactor

In the high-temperature reactor design, it is common practice to leave gaps between the graphite blocks of the reflectors to accommodate thermal dilatation and material swelling, as well as to provide an additional cooling source during operation. These gaps give rise to bypass flows entering the reactor core. The bypass flows can change friction factors and heat exchange coefficients obtained in the bulk of the pebble bed. In this paper, a coupled computational fluid dynamics–discrete element method (CFD-DEM) model is proposed. In this model, the pebbles are resolved by the CFD grid and the turbulent field is partially captured using a detached eddy simulation method. The DEM model is first validated against empirical correlations for the packing of the pebbles, and the coupled model is then tested against thermal measurements in the SANA experiment. Then the model is used to perform three-dimensional studies of the effects of the bypass flows in a representative pebble bed configuration. It is determined that the effect of cross flows can be approximately bounded to the first two layers of pebbles next to the reflector wall. Additionally, an increase of ~12% in the Nusselt number in the pebbles next to the reflector is predicted, with a maximum local increase in the pebble of ~100%.

Pronghorn: A Multidimensional Coarse-Mesh Application for Advanced Reactor Thermal Hydraulics

This paper presents an overview of Pronghorn, a multiscale thermal-hydraulic (T/H) application developed by Idaho National Laboratory and the University of California, Berkeley. Pronghorn, built on the open-source finite element Multiphysics Object-Oriented Simulation Environment (MOOSE), leverages state-of-the-art physical models, numerical methods, and nonlinear solvers to deliver fast-running advanced reactor T/H simulation capabilities within a modern software engineering environment. This work summarizes the physical models, multiphysics and multiscale coupling, and numerical discretization in Pronghorn with emphasis on our initial target application to pebble bed reactors (PBRs). A diverse set of applications are shown to depressurized natural circulation in the SANA experiments, forced convection in the Pebble Bed Modular Reactor, three-dimensional (3-D)/one-dimensional coupling of Pronghorn and RELAP-7 systems T/H for loop analysis in the High Temperature Reactor Power Module, and forced convection in the Mark-1 Pebble Bed Fluoride-Salt-Cooled High-Temperature Reactor. A multiphysics coupling of Pronghorn, RELAP-7, and Griffin deterministic neutronics for a gas-cooled PBR demonstrates the capability of the MOOSE framework for reactor design calculations. These applications highlight the verification and validation underlying Pronghorn’s software development while emphasizing features that improve upon capabilities offered by legacy tools in areas such as 3-D unstructured meshing, physics modeling, and multiphysics coupling.

CFD validation with optimized mesh using benchmarking data of pebble-bed high-temperature reactor

In this study, a computational fluid dynamics (CFD) analysis conducted to predict the thermo-hydraulic performance of the HTR-10, which is an experimental pebble bed reactor (PBR). The PBR with a modular model with a realistic approach and finite volume method (FVM) instead of porous media is used to predict the distribution of the critical thermal-hydraulics parameters like temperature, pressure, velocity, and heat transfer coefficient (HTC) over the pebbles as well as the reactor core. In the simulation study, an optimized mesh used as a replacement of the large size mesh. The simulation results, for the boundary conditions such as coolant inlet and outlet temperatures, mass flow, and other thermal-hydraulics parameters, were validated with the data published by the IAEA benchmark document. This study demonstrates that the CFD analysis using an optimized mesh is capable of predicting the nature thermo-hydraulic behavior of PBR core, maintaining design safety limits like maximum fuel temperature, and coolant flows distribution.

Pebble Bed High Temperature Reactor for Electric and Cogeneration Application

Specific energy demand of Indonesia with its distributed energy demand required a special energy supply solution. The energy supply solution should be able to fulfil the electric demand of huge and growing population which spread in many different islands also to fulfil the energy demand to process abundances yet distributed natural sources. This paper proposes a pebble bed high temperature reactor as an energy supply in the form electric and/or cogeneration application. A parametric survey of the core geometry of a 150MWt Pebble Bed Reactor called PeLUIt is performed, follow by an equilibrium analysis of the optimized design. An accident analysis of depressurized loss of forced cooling (DLOFC) is performed to show the strong passive safety features of the design. Finally the heat-mass balance of the plant is also presented.

Study on Control Rod Reactivity of Small Pebble Bed Reactor with Wallpaper Fuel Design

The control rod reactivity is a crucial reactor parameter designed to shut down the reactor and to control the safety of reactor core under any operation conditions. This paper discusses the control rod reactivity of small pebble bed reactor with wallpaper fuel design. The geometric configuration of RDE was selected for the reactor core model. A number of simulations with Monte Carlo n-particle transport code MCNP6 based on evaluated nuclear data library ENDF/B-VII were employed to investigate the total and individual control rod worth and reactivity in stuck rod condition. In the simulation model, the total amount of uranium per pebble was kept constant at 5 g by varying the hexagonal lattice pitch calculated for different radius of the central graphite zone. The simulation results show that the total control rod achieves the best effectiveness on the central graphite radius of 1.0 cm. The highest worth of individual rods in the wallpaper fueled core are almost greater than that of standard fueled core. The stuck rod criterion in all simulation results confirm that, the failure of one rod with highest worth will not prevent the control system from shutting down the reactor. These results conclude that selecting a central graphite radius of wallpaper fuel is one of the strategies to be carefully considered and a radius of 1.0 cm is the best one in controlling reactor safety and ensuring the control system could shut down the reactor safely.

Burnup computations of multi-pass fuel loading scenarios in HTR-10 using a pre-generated fuel composition library

This study aims to precisely investigate the core characteristics of HTR-10 using an online-refueling fuel loading scenario through an innovative approach that incorporates a pre-generated fuel composition library. HTR-10 is an experimental high-temperaturegas- cooled pebble-bed reactor constructed in China. Applying multi-pass fuel loading scenario, the pebbles in HTR-10 pass through the core several times via onlinerefueling. In this study, we proposed a model that simulates the dynamic operation of HTR-10 by using continuously static calculations. The model was constructed by dividing the core into 3 flow channels with different amounts of horizontal zones according to the residence time of fuel pebbles. However, random distribution of the pebbles with various burnup values complicates the refueling process. In order to simulate online-refueling more conveniently, a comprehensive method based on multipass fuel loading scenarios was thus developed. Firstly, a pre-generated fuel composition library containing the content of both actinides and fission products of fuel pebbles as a function of burnup, was built by implementing full core depletion calculations. During the refueling processes, a specific ratio of discharged fuel pebbles to fresh fuel pebbles was reloaded into the top zones. Thus, the average burnup values in the top zones can be resulted by considering the supplement of fresh fuel pebbles. Eventually, the fuel composition in the top zones were obtained by interpolating the average burnup value from the pre-generated library. In this study, all the calculations were performed using the MCNP6 computer code together with the ENDF/B-VII continuous energy neutron data library. The results revealed that the core reached a state of equilibrium after seven refueling processes with an increased rate of volume fraction. Our findings correspond to those of other studies. Another model constructed by locating the actual distribution of fresh pebbles also confirms the verification of the refueling method. Eventually, the burnup characteristics as well as the power and flux distributions in the HTR-10 core were analyzed using the simulation method.

Cardinal: A Lower-Length-Scale Multiphysics Simulator for Pebble-Bed Reactors

This paper demonstrates a multiphysics solver for pebble-bed reactors, in particular, for Berkeley’s pebble-bed -fluoride-salt-cooled high-temperature reactor (PB-FHR) (Mark I design). The FHR is a class of advanced nuclear reactors that combines the robust coated particle fuel form from high-temperature gas-cooled reactors, the direct reactor auxiliary cooling system passive decay removal of liquid-metal fast reactors, and the transparent, high-volumetric heat capacitance liquid-fluoride salt working fluids (e.g., FLiBe) from molten salt reactors. This fuel and coolant combination enables FHRs to operate in a high-temperature, low-pressure design space that has beneficial safety and economic implications. The PB-FHR relies on a pebble-bed approach, and pebble-bed reactors are, in a sense, the poster child for multiscale analysis. Relying heavily on the MultiApp capability of the Multiphysics Object-Oriented Simulation Environment (MOOSE), we have developed Cardinal, a new platform for lower-length-scale simulation of pebble-bed cores. The lower-length-scale simulator comprises three physics: neutronics (OpenMC), thermal fluids (Nek5000/NekRS), and fuel performance (BISON). Cardinal tightly couples all three physics and leverages advances in MOOSE, such as the MultiApp system and the concept of MOOSE-wrapped applications. Moreover, Cardinal can utilize graphics processing units for accelerating solutions. In this paper, we discuss the development of Cardinal and the verification and validation and demonstration simulations.

The Effects of the Number of Coated Fuel Particles on the Neutronic Aspects of 25 MWt Pebble Bed Reactor with Thorium Fuel

High-Temperature Gas Reactor (HTGR) is a type of reactor that continues to be developed because of its advantages in terms of economic aspects, proliferation resistance, and safety aspects. One of the safety aspect improvements is due to the use of the Coated Fuel Particle (CFP). A coated fuel particle is a fuel with a diameter smaller than 1 mm and is protected by several carbon layers. In the Pebble Bed Reactor (PBR) type of HTGR design, the CFP is placed in a 6 cm fuel ball. How much CFP is put into the fuel ball will determine the neutronic characteristics of the reactor. In this study, the effect of the amount of CFP in the fuel ball on the 25 MWt PBR design using Thorium fuel and its impact on several important neutronic aspects, such as the effective multiplication factor, the amount of fuel enrichment, the utilization of fissile material, and the density of the fissile material formed. The calculation was performed by the Monte Carlo MVP / MVP-BURN code. This study found that the coated fuel particle fraction of 15% was the optimum value for the studied neutronic parameters.

Multiscale thermal-hydraulic modeling of the pebble bed fluoride-salt-cooled high-temperature reactor

The complex core geometry of Pebble Bed Reactors (PBRs) necessitates multiscale techniques for fast-turnaround design and analysis. This paper describes the multiscale model implemented in the Pronghorn PBR simulation tool and demonstrates application to steady-state analysis of the Mark-1 Pebble Bed Fluoride-Salt-Cooled High-Temperature Reactor (PB-FHR). Verification of the pebble model with fully-resolved heat conduction shows that material-wise pebble temperatures are predicted to within 10°C over a wide range in thermal conditions. Anisotropic drag models are correlated for the outer reflector blocks using COMSOL, providing closures for modeling of bypass flows. With a porous media model of the outer reflectors, the core bypass fraction and fuel, reflector, and structural material temperatures are predicted for a number of different inflow conditions. This work demonstrates the full-core analysis capabilities of the Pronghorn application and enables comprehensive reactor analysis with the Multiphysics Object-Oriented Simulation Environment (MOOSE) framework.

PBMR-400 BENCHMARK SOLUTION OF EXERCISE 1 AND 2 USING THE MOOSE BASED APPLICATIONS: MAMMOTH, PRONGHORN

High temperature gas cooled reactors (HTGR) are a candidate for timely Gen-IV reactor technology deployment because of high technology readiness and walk-away safety. Among HTGRs, pebble bed reactors (PBRs) have attractive features such as low excess reactivity and online refueling. Pebble bed reactors pose unique challenges to analysts and reactor designers such as continuous burnup distribution depending on pebble motion and recirculation, radiative heat transfer across a variety of gas-filled gaps, and long design basis transients such as pressurized and depressurized loss of forced circulation. Modeling and simulation is essential for both the PBR’s safety case and design process. In order to verify and validate the new generation codes the Nuclear Energy Agency (NEA) Data bank provide a set of benchmarks data together with solutions calculated by the participants using the state of the art codes of that time. An important milestone to test the new PBR simulation codes is the OECD NEA PBMR-400 benchmark which includes thermal hydraulic and neutron kinetic standalone exercises as well as coupled exercises and transients scenarios. In this work, the reactor multiphysics code MAMMOTH and the thermal hydraulics code Pronghorn, both developed by the Idaho National Laboratory (INL) within the multiphysics object-oriented simulation environment (MOOSE), have been used to solve Phase 1 exercises 1 and 2 of the PBMR-400 benchmark. The steady state results are in agreement with the other participants’ solutions demonstrating the adequacy of MAMMOTH and Pronghorn for simulating PBRs.

Investigation on the mechanism of enhancing heat transfer in a pebble bed by adding in the non-fixed number of smaller-sized spheres

Enhancing heat transfer in the pebble bed reactor could reduce the surface temperatures and lower the possibility of forming hot-spots. The effectiveness of inserting a smaller sphere into a structured pebble bed on optimizing the heat transfer has been confirmed, and yet, the mechanism of heat transfer enhancement is still not fully understood. The impact of the quantity and size of the small spheres on the heat transfer characteristics has been investigated in this study and the mechanism of enhancement was analyzed. It was found that: (1) When the volume or the surface area of the inserted sphere was kept the same, the overall heat transfer coefficients (HTC) of the pebble bed in case 2 or case 3 respectively demonstrated 1.4% or 2.8% higher than that of the bed in case 1; (2) the overall HTC showed an increasing trend with the decreasing ratio of the surface area to the volume; (3) the varying trends of local HTCs along the designated direction were similar among 3 cases and the strongest heat transfer positions were found near pebble-sphere contact points. Such findings will help to design a better pebble bed core.