Gas-cooled Reactor Research Articles

An Innovational Jacobian-Split Newton-Krylov Method Combining the Advantages of the Jacobian-Free Newton-Krylov Method and the Finite Difference Jacobian-Based Newton-Krylov Method

The Jacobian-free Newton-Krylov (JFNK) method is a widely used and flexible numerical method for solving the neutronic/thermal-hydraulic coupling system. The main property of JFNK is that the Jacobian-vector product is evaluated approximately by finite difference, avoiding the forming and storage of Jacobian explicitly. However, the lack of an efficient preconditioner is a major bottleneck for the JFNK method, leading to poor convergence. The finite difference Jacobian-based Newton-Krylov (DJNK) method is another advanced numerical method, in which the Jacobian matrix is formed and stored explicitly. The DJNK method can provide a better preconditioner for Krylov iteration than JFNK. However, how to compute the Jacobian matrix efficiently and automatically is a key issue for the DJNK method. By fully utilizing the sparsity of the Jacobian matrix and graph coloring algorithm, the Jacobian can be computed efficiently. Unfortunately, when there are dense rows/blocks, a huge computational burden will emerge due to the lack of sparsity, resulting in the extremely poor efficiency of Jacobian computation. In this work, a Jacobian-split Newton-Krylov (JSNK) method is proposed to resolve the dense row/block problem by combining the advantages of JFNK and DJNK. The main feature of the JSNK method is to split the Jacobian matrix into sparse and dense parts. The sparse part of the Jacobian matrix is explicitly constructed using the graph coloring algorithm while for the dense part, the Jacobian-vector product is approximated by finite difference. The computational complexity of the JSNK method is analyzed and compared to the JFNK method and the DJNK method from theoretical and experimental aspects and under different meshes. A simplified two-dimensional (2-D) high-temperature gas-cooled reactor (HTR) model and a simplified 2-D pressurized water reactor model are utilized to demonstrate the superiority of the JSNK method. The numerical results show that the JSNK method successfully resolved the dense rows/blocks. More importantly, its efficiency significantly outperforms the JFNK method and the DJNK method.

GPU-DEM-based heat transfer model for an HTGR pebble bed

Based on the discrete element method (DEM) and GPU parallel computing, a particle heat transfer model is developed to simulate the heat transfer in a pebble bed of the high-temperature gas-cooled reactor (HTGR). The model is implemented based on a previously developed GPU-DEM program by our team and uses the mesh-based neighbor searching algorithm for the heat transfer calculation. This model couples the conduction and radiative heat transfer between the pebbles and incorporates neural networks and empirical fittings to calculate the radiation view factors, which can improve computational efficiency. The effective thermal conductivity of different models and experimental data are used to verify the accuracy of the model, and the influence of different radiation heat transfer models on the results is also compared. The results show that the effective thermal conductivity derived from the current model is comparable to the classical models at different temperatures, and the numerical simulation results based on the current model are in good agreement with the corresponding experimental data. Additionally, the model achieves a single-core speedup ratio of 126–395 times with GPU acceleration, significantly enhancing computational efficiency. In conclusion, the current model has been effectively verified for accuracy and computational efficiency, and it demonstrates great potential in dealing with large-scale pebble flow and heat transfer challenges in HTGRs.

Effect of geometry on the evolution of DLOFC transients in high temperature helium loop

Generation IV high-temperature gas-cooled reactors (HTGR) are designed to exhibit passive safety under all off-normal circumstances. One such scenario, known as depressurized loss of forced circulation (DLOFC), occurs after a break in the inlet/outlet header, allowing helium to leak from the reactor. Upon depressurization, the onset of natural circulation (ONC) can occur causing bulk air ingress leading to the oxidation and degradation of core components. The Transformational Challenge Reactor (TCR) has similar features to those of an HTGR, but the primary difference is the use of a more complex, additively manufactured (AM) fuel geometry. The more compact, additively manufactured, ceramic fuel elements can be conveniently produced with optimally configured channels that suppress the air ingress progress and improve thermofluidic performance. DLOFC and air ingress are experimentally studied in a scaled HTGR flow test setup. The experiments use an AM test element embedded with a distributed temperature sensor as well as a test geometry comprised of spherical pebble bed elements. With the test geometries aligned within a lowercase h-shaped tube flow setup, further data was obtained to improve the understanding of DLOFC. The thermal transient and air ingress data gathered for both test geometries are compared. The results show that the AM part delayed ONC as compared to the pebble bed test piece at higher temperatures. The distributed temperature sensor shows intra-leg circulation at higher temperature tests.

Modifikovani Rankinov ciklus parne turbine bez odbacivanja toplote kondenzacije ciklusa, pokretan termokompresorom koji radi u oblasti vlažne pare

The disclosed concept relates to a novel modified and simplified steam-turbine Rankine cycle without rejection of the cycle waste heat of condensation, which is driven by a thermocompressor (ejector) operating in the wet-vapor region. The thus modified steam-turbine Rankine cycle can theoretically achieve the maximum possible thermal efficiency (~100%). The wet-vapor mixture circulating within the thermocompressor is being separated in a dedicated cylindrical separation tank, so that the saturated water is pumped to a water heater where it receives the cycle heat input, while the saturated vapor is expanded in a backpressure steam turbine producing useful mechanical work and is then recirculated back to the thermocompressor, where it is being re-pressurized by means of the primary fluid (pumped and heated saturated water). The concept can be applied to steam-turbine-cycle power-plants fueled by: coal or solid/liquid/gaseous fuel, waste heat, nuclear fuel (used by boiling water reactors, pressurized water reactors, pressurized heavy-water reactors, gas-cooled reactors, molten salt reactors or liquid-metal-cooled fast reactors) or renewable energy sources (Solar energy, biomass, geothermal). The concept can also be applied as the “bottoming” steam-turbine-cycle part of a combined gas-turbine/steam-turbine cycle power plant.

Design of the gas turbine flow path of a gas-cooled fast reactor secondary circuit

Design of the gas turbine flow path of a gas-cooled fast reactor secondary circuit

A flexible methodology for generating 3D graphite dosimetry data in Advanced Gas-Cooled Reactors

The safety cases for the UKs Advanced Gas-Cooled Reactors require a robust understanding of the structural integrity of their constituent graphite bricks. Both neutron damage and graphite weight loss have significant effects upon material properties. Graphite weight loss occurs via radiolytic oxidation, initiated by neutron and gamma-ray dose. This includes contributions from fast neutrons, gamma-rays from the fuel, and secondary gamma-rays. An accurate knowledge of the dosimetry history of trepanned graphite samples is important, as well as the ability to make forward predictions for any brick within the core. It is therefore necessary to calculate both these dosimetry quantities with a high degree of spatial accuracy, taking into account the time-varying nature of local fuel channel powers as well as the way in which weight loss itself affects the dosimetry data. The Monte Carlo method is the most accurate available for the calculation of radiation dosimetry data. However, it is impractical to undertake full scale Monte Carlo calculations for a whole reactor core and to represent every required period of time and graphite weight loss, which will also vary in time and space. An alternative approach has been developed by Jacobs which exploits the high accuracy afforded by the Monte Carlo method, but is also flexible and practical enough to provide 3D dosimetry data for any graphite brick within the active cores, at any point in time and at any required graphite weight loss. The Power Partitioning Method uses MCBEND-generated dosimetry “Contribution Matrices”, coupled with PANTHER “core follow” fuel powers, to calculate dosimetry data anywhere within selected fuel channels or interstitial bricks.

Reanalysis of graphite nuclear data limits for AGR dosimetry with updated carbon scattering data and Magnox plant measurements

The Advanced Gas-cooled Reactors (AGR) operating in the UK are, like the Magnox reactors that preceded them, graphite moderated and cooled by pressurised CO2 gas. As such, the nuclear data for carbon are of primary importance in neutron dosimetry and nuclear heating calculations. There is evidence from benchmark data and plant measurements of underprediction of neutron fluxes at the lower end of the fast neutron range for thicknesses of graphite greater than ~50 cm. Furthermore, the range of validation is limited to ~70 cm of graphite, with components beyond this being allocated bounding damage rates. Following the previous ISRD, opportunities were taken to: Look again at the carbon scattering cross-sections by incorporating the ENDF/B-VIII.0 Beta 4 carbon data to assess the impact on the analysis of benchmark data. Reassess validation data from the earlier Magnox reactors to put them on a more appropriate equivalent graphite thickness scale to the AGRs. The investigation into graphite nuclear data libraries concluded that the incorporation of ENDF/B-VIII Beta 4 carbon data into the JEF2.2 and ENDF/B-VII.1 data libraries with BINGO collision processing had only a limited effect on the calculated responses. The UKNDL data, with DICE collision processing, currently used in dosimetry calculations for EDF Energy’s AGRs produces the closest agreement with measurement for all calculated responses for graphite thicknesses greater than 10 cm. For reactor plant validation, applying the sensitivity of the 93mNb(n,n’) response to graphite density resulted in a 15 cm increase to the validation database when compared to a simple “straight-line” distance. However, caution is advised in applying the benchmark equivalent distance derived from locations within a graphite column, to ex-core plant measurements.

Dynamic fracture toughness measurement of graphite material considering inertial effect

Graphite materials are widely used as moderators, reflectors, and core structural materials in high-temperature gas-cooled reactors. During operation, graphite materials in nuclear reactors may be subjected to dynamic loads caused by earthquakes or other factors. Therefore, the dynamic fracture properties of graphite materials need to be investigated. In this study, dynamic three-point bending drop hammer impact experiments were conducted on IG-11 graphite specimens with precracks to measure their dynamic fracture toughness under medium- and low-speed impacts using a digital image correlation method. Traditional methods for measuring fracture toughness based on ASTM standards do not consider the influence of the inertial effect, leading to unreasonably large measurement results. To address this disadvantage, the dynamic fracture toughness of IG-11 graphite was evaluated using a spring–mass model that considers the inertial effects of materials. Results indicated that the measured fracture toughness was significantly lower than that obtained based on the ASTM standard and increased almost linearly with increasing impact velocity. The toughening mechanism was analysed by observing the fracture morphology of the samples using a scanning electron microscope. The results showed that as the impact velocity increased, the fracture mode of the graphite samples gradually changed from intergranular to transgranular fracture, and the samples absorbed sufficient energy, resulting in a noticeable toughening phenomenon.

Research on two novel hydrogen-electricity-heat polygeneration systems using very-high-temperature gas-cooled reactor and hybrid-sulfur cycle

The combination of the hybrid-sulfur (HyS) cycle with a very-high-temperature gas-cooled reactor (VHTR) presents a promising nuclear hydrogen production technology. This study proposes two novel hydrogen-electricity-heat polygeneration systems using VHTR and HyS cycle. A thermodynamic model is developed via energy and exergy analyses. Thermodynamic performance analysis and comparison are conducted on the two systems. For the two systems under design basis condition, the recommended variation range of the split ratio is 0–0.6395 and the hydrogen production rate is 0–55.7 mol/s. For systems 1 and 2, the energy utilization efficiencies are 65.91 % and 64.53 %, and the exergy efficiencies are 68.55 % and 67.36 %, at a hydrogen production rate of 55.7 mol/s. The process heat supply unit, steam generator (SG) and HyS cycle exhibit the top three largest exergy loss coefficients of 6.32 %, 6.26 % and 4.21 % at the split ratio of 0.5; therefore, they are key units for improving system performance. The intermediate heat exchanger's primary-side helium outlet temperature and SG's secondary-side main steam temperature both affect the variation range of split ratio. A slightly lower main steam temperature can increase the maximum hydrogen production rate and maximum energy utilization efficiency.

Neutronic Assessment of High-Temperature Gas-Cooled Thorium Burner using Monte Carlo Calculation Method with Full Core Model

In this study, the effective reactivity and burnup analyses have been performed for heterogeneous three-dimensional high-temperature gas-cooled thorium reactor (HTGR) which has 60 MWth full core geometry by using continuous-energy multi-purpose three-dimensional Monte Carlo particle transport Serpent code with ENDF/ B-VII data libraries. Nuclear fuel have been selected as 50 % ThO2+50% RG-PuO2. Firstly, effective reactivity for three different qualities of graphite for operation period have been determined. The effective reactivity showed better performance with increasing densities of graphite. Secondly, it has been also examined to ZrC and SiC cladding materials effect on the effective reactivity. It is observed that SiC has a positive effect on reactivity compared to ZrC. As a results, the full core life low-power thorium-burner HTGR have been calculated as up to ~4500 days depending on the graphite material whereas, the corresponding burn−ups came out to be ~ 189 GWd/ton, for end of life.

Numerical investigation of flow stratification and heat transfer characteristics in a strongly heated horizontal rod bundles with helium-Xenon gas mixture

The helium-xenon(He-Xe) mixture has good heat transfer characteristics with a low Prandtl number(Pr ≈ 0.2 ∼ 0.3) and is suitable for the advanced compact gas-cooled reactor. The characteristics of horizontal flow stratification in the fuel rod bundles with He-Xe mixture under gravity and buoyancy were numerically simulated. Different wall heat flux q+ suitable for the reactor operating conditions were selected for calculation and analysis. Flow stratification is observed as strongly inhomogeneous in the radial direction. With the semi-local wall coordinates and Van-Driest transformation, laminarization is manifested by velocity and temperature profile and turbulent kinetic energy changes. In the horizontal flow, where the buoyancy is orthogonal to the direction of flow development, unique characteristics appear in the flow and heat transfer, and the growing longitudinal momentum and energy transport are considered the main reasons. The influence of flow acceleration and buoyancy under different bundle structures were compared. The buoyancy effect is evident in the loosely spaced rod bundles. In contrast, the thermally-induced flow acceleration effect in the tight-lattice scheme is noticeable.

Mass and efficiency optimization of a He-Xe Brayton cycle for mobile, land-based nuclear microreactors

Nuclear microreactors represent an option for distributed power generation, which can be deployed in military installations, remote off-grid villages, and locations recovering from natural disasters. Small system mass is necessary to achieve their mobility. In this study, a He-Xe gas-cooled reactor coupled with a Closed Brayton cycle (CBC) is optimized in terms of system mass and thermal efficiency. A single-channel model is developed for the reactor to predict the minimum mass according to the thermal–hydraulic limitations. Masses of the heat exchanger and turbo-machines are calculated based on empirical curves. The simple regenerative and intercooling cycles are considered. A parametric study is conducted to investigate the influence of key parameters on system mass and to explore the tradeoffs between different components that satisfy the power requirements of 8 MWe. Furthermore, the Non-dominated Sorting Genetic Algorithm (NSGA-II) is used to optimize the system mass and thermal efficiency. Optimal values of critical parameters on the Pareto Frontier are presented and discussed. Results show that the masses of the reactor core and coolers dominate the total mass in most cases, and increasing the height of the reactor core can help reduce the system mass by allowing a smaller core radius. The Pareto Frontier shows that at thermal efficiencies around 40% or below, the system mass is depressed by using large CPR, molecular weight of the mixture, height of the reactor core, and small recuperator effectiveness. Increasing the recuperator's effectiveness from about 90% is required for higher thermal efficiency design, but its mass increases dramatically and can surpass the mass share of other components. The current analysis can provide a guide for detailed system and component design.

Estimation of transuranic isotopes in irradiated fuel elements for pebble bed HTR on activity vector

Due to the unknown power history of fuel elements in a pebble-bed High-Temperature Reactor, the traditional method of calculating transuranic isotopes through forward burnup calculations using initial loading data is not applicable.This paper presents a novel method for estimating transuranic isotopes within fuel elements in pebble bed HTR. It involves the power history inversion model using activity vector detectable by the online Burnup Measurement System of High Temperature Gas-cooled Reactor Pebble bed Module to predict the power history of the fuel elements. Subsequently, transuranic isotopes are calculated through a forward burnup process.To check the performance of the burnup equation inverse model. Nuclear Inventory Tool were used to generate database that provides known activity vector as target and corresponding power history of a fuel element. Results show that the inverse model leads to a more stable convergence, effectively reconstructing the complex power history. The integrated power estimation error remains below 0.2%, with prediction errors for ten transuranic isotopes of interest below 1.5%.

Experimental measurement of stiffness coefficient of high-temperature graphite pebble fuel elements in helium at high temperatures

Graphite material plays an important role in nuclear reactors especially the high-temperature gas-cooled reactors (HTGRs) by its outstanding comprehensive nuclear properties. The structural integrity of graphite pebble fuel elements is the first barrier to core safety under any circumstances. The correct knowledge of the stiffness coefficient of the graphite pebble fuel element inside the reactor's core is significant to ensure the valid design and inherent safety. In this research, a vertical extrusion device was set up to measure the stiffness coefficient of the graphite pebble fuel element by the Institute of Nuclear and New Energy Technology (INET) of Tsinghua University in China. The stiffness coefficient equations of graphite pebble fuel elements at different temperatures are given (in a helium atmosphere). The result first provides the data on the high-temperature stiffness coefficient of pebbles in helium gas. The result will be helpful for the engineering safety analysis of pebble-bed nuclear reactors.

Energy, Exergy and Thermoeconomic Analyses on Hydrogen Production Systems Using High-Temperature Gas-Cooled and Water-Cooled Nuclear Reactors

The use of nuclear energy is inevitable to reduce the dependence on fossil fuels in the energy sector. High-temperature gas-cooled reactors (HTGRs) are considered as a system suitable for the purpose of reducing the use of fossil fuels. Furthermore, eco-friendly mass production of hydrogen is crucial because hydrogen is emerging as a next-generation energy carrier. The unit cost of hydrogen production by the levelized cost of energy (LCOE) method varies widely depending on the energy source and system configuration. In this study, energy, exergy, and thermoeconomic analyses were performed on the hydrogen production system using the HTGR and high-temperature water-cooled nuclear reactor (HTWR) to calculate reasonable unit cost of the hydrogen produced using a thermoeconomic method called modified production structure analysis (MOPSA). A flowsheet analysis was performed to confirm the energy conservation in each component. The electricity generated from the 600 MW HTGR system was used to produce 1.28 kmol/s of hydrogen by electrolysis to split hot water vapor. Meanwhile, 515 MW of heat from the 600 MW HTWR was used to produce 8.10 kmol/s of hydrogen through steam reforming, and 83.6 MW of electricity produced by the steam turbine was used for grid power. The estimated unit cost of hydrogen from HTGR is approximately USD 35.6/GJ with an initial investment cost of USD 2.6 billion. If the unit cost of natural gas is USD 10/GJ, and the carbon tax is USD 0.08/kg of carbon dioxide, the unit cost of hydrogen produced from HTWR is approximately USD 13.92/GJ with initial investment of USD 2.32 billion. The unit cost of the hydrogen produced in the scaled-down plant was also considered.

Feasibility of using BeO rods as secondary neutron sources in the long-life fuel cycle high-temperature gas-cooled reactor

External sources of neutron provide stable and sufficient neutron for initial startup of a nuclear reactor. They also provide signals for neutron detectors to monitor the safety of reactor during shutdown. In the high temperature engineering test reactor (HTTR), 252Cf is used as the external neutron source. However, the 252Cf sources must be renewed every approximately 7 years because of its relatively short half-life of 2.6 years. The renewal of 252Cf sources requires a high cost and a very complicated procedure. This study investigated the feasibility of using BeO rods as the secondary neutron sources to avoid renewing the 252Cf neutron sources periodically. The BeO rods could exist in the reactor for a long time so that if the reactor operates long enough, the neutron flux at the wide-range monitoring detectors remains more than 10n.s−1.cm−2 even if the reactor is shutdown for as long as 5 years. The results of this study indicated that using BeO rods as the secondary neutron sources would be an attractive option for the future HTGR design with a long-life fuel cycle.

Effect of Reynolds number on the aerodynamic performance of highly loaded helium compressor cascade in high temperature gas-cooled reactor

Closed Brayton cycle power plant with High Temperature Gas-cooled Reactor is one of the most promising solutions for reduction in carbon emission. Helium is being used as a coolant in power conversion unit of these power plants. The output power of these systems is regulated by varying the density of helium in the power conversion unit in such a way that the compressor is required to operate over a wide range of Reynolds numbers. In this paper, the vortices structure in conventional and highly loaded helium compressor cascade are analyzed at low Reynolds numbers. Accordingly, the evolution mechanism of vortex structure in the highly loaded helium compressor cascade was studied and validated by experiments. It is concluded that with the decrease in Reynolds number, the vortex size and total pressure loss coefficient increase gradually. The loss weight factor of the passage vortex (PV) and concentrated shedding vortex (CSV) in the highly loaded helium compressor cascade increases by 262 % and 53.8 %, respectively, in comparison with the conventional compressor cascade.

Advancing production of hydrogen using nuclear cycles – integration of high temperature gas-cooled reactors (HTGR) with solid oxide electrolyzers (SOE)

The work presented in the paper focuses on the investigation of coupling high-temperature gas-cooled nuclear reactor (HTGR) with solid oxide electrolyzers (SOE) for large-scale production of hydrogen. In the analysis, four cases related to loads of the nuclear reactor were under consideration. These included operation at the nominal load (100%), as well part-load operation (25, 50 and 80%).Paper presents the assessment of several alternative modes of operation of the HTGR-SOE hybrid. It can be concluded that under the given assumptions, electrical loading of the electrolyzer can be varied between 5 and 31 A (for 25% and 100% load of HTGR, respectively), and the corresponding voltage is in the range from 1.03 to 1.29 V. In terms of the size of the hydrogen production island, the electric power of the electrolysis was in the range from 12.42 to 96 MW, while the heat necessary to operate the SOE was provided by the steam cycle of the HTGR. The work provides qualitative and quantitative assessment of the possibility of generating hydrogen in a hybrid system which addresses the off-design operation of the nuclear reactor.

Comprehensive analysis of ASTRA benchmark with MCU-HTR and Serpent codes

Key problems in the simulation of pebble-bed high-temperature gas-cooled reactors include approximations of TRISO fuel particles and pebble-bed models, choice of nuclear data libraries, and uncertainty in graphite impurity content. This study is focused on the investigation of these problems for the ASTRA critical facility simulation with MCU-HTR and Serpent Monte Carlo codes. This paper presents a comparative analysis of the ASTRA benchmark (IEU-COMP-THERM-008) through consistent code-to-code comparisons. Some studies were performed on the simplified models of the ASTRA facility. A special care was taken to develop similar models of the ASTRA facility for the calculations using MCU-HTR and Serpent. A good agreement in the multiplication factor (less than 160pcm) between the simulations of ASTRA critical configurations using MCU-HTR and Serpent with ENDF/B-VII.0 cross-section libraries was obtained. In addition, the reactivity impact of different graphite thermal scattering libraries included in ENDF/B-VIII.0 release on the calculated results for the ASTRA benchmark was examined. Graphite evaluations assuming 0, 10, and 30 % porosity were considered in Serpent simulations with ENDF/B-VIII.0 cross-section libraries. The spread of the calculated keff for the measured critical configurations having different core height was found to be approximately 200pcm for most selected models. Consequently, model’s ability to correctly capture the procedure of a reactor loading during startup was proven. However, a significant overestimation of the keff (1000–1500pcm) was observed when we used the equivalent boron content (EBC) in the reflectors graphite adjusted to reproduce the measured graphite absorption cross-section, the EBC in matrix graphite of 1 ppmwt., ENDFB/VIII.0 cross-sections, and 30 % or 10 % porous graphite thermal scattering libraries in the Serpent simulations.

State space modelling development of Micro-High-Temperature Gas-Cooled reactor with helium Brayton cycle

The micro-high-temperature gas-cooled reactor with helium Brayton cycle (Mi-HTR) can be used as a portable micro mobile nuclear power supply. The nonlinear model based on differential equation makes it difficult to reveal the relationship between the internal state of Mi-HTR and the external input and output variables. Based on the operating principles, laws, and theorems, the nonlinear dynamic model between various parameters and external effects in the system is established. According to the nonlinear dynamic model, the state space model of Mi-HTR is obtained by theoretical derivation. The established state space model can describe the relationship between internal intermediate variables. The disturbances with the same boundary conditions are introduced into nonlinear dynamic model and state space model respectively. The accuracy of the established Mi-HTR state space model is proved. The Mi-HTR state space model provides an analytical tool for the design of Mi-HTR control system.