HTGR 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.

Study on the Particle Sorting Performance for Reactor Monte Carlo Neutron Transport on Apple Unified Memory GPUs

In simulation of nuclear reactor physics using the Monte Carlo neutron transport method on GPUs, the sorting of particles plays a significant role in performance of calculation. Traditionally, CPUs and GPUs are separated devices connected at low data transfer rate and high data transfer latency. Emerging computing chips tend to integrate CPUs and GPUs. One example is the Apple silicon chips with unified memory. Such unified memory chips have opened doors for new strategies of collaboration between CPUs and GPUs for Monte Carlo neutron transport. Sorting particles on CPU and transport on GPU is an example of such new strategy, which has been suffering the high CPU-GPU data transfer latency on the traditional devices with separated CPU and GPU. The finding is that for the Apple M2 max and M3 max chip, sorting on CPU leads to better performance per power than sorting on GPU for the ExaSMR whole core benchmark problems and the HTR-10 high temperature gas reactor fuel pebble problem. The partially sorted particle order has been identified to contribute to the higher performance with CPU sort than GPU. The in-house code using both CPU and GPU achieves 7.6 times (M3 max) power efficiency that of OpenMC on CPU for ExaSMR whole core benchmark with depleted fuel, and 130 times (M3 max) for HTR-10 fuel pebble benchmark with depleted fuel.

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.

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.

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.

Spanish research related to SMRs projects

Small modular reactors (SMRs) are advanced nuclear reactors with a power capacity of up to 300 MW(e) per unit. SMRs encompass a variety of reactor technologies including light water reactors, high temperature gas reactors, molten salt reactors, liquid metal cooled fast reactors, and heat pipe technology-based reactors. The research and design of these diverse SMR types require a broad set of technological capabilities related to nuclear engineering and safety. Within this context, this article attempts to assess the current state of research and technological progress achieved by the Spanish research groups and companies. The results reveal a significant level of maturity among these groups and companies in various domains such as neutronic analysis, thermal hydraulic analysis, the improvement of models related to severe accident scenarios and an active involvement in the design of novel SMR.

Micromechanical properties of TRISO coatings by in-situ high temperature nanoindentation and microcantilever fracture

Coated nuclear fuel particles, most commonly tri-structural isotropic (TRISO), are intended for use in advanced high temperature reactors. It is vital to understand the mechanical properties of each coating layer to accurately predict the performance of these fuel particles and how these might change at each stage of their lifecycle. This paper reports results of in-situ nanoindentation, with an emphasis on the structural SiC layer, along with microcantilever testing of the critical SiC-IPyC interface. At 1000 °C the hardness of the SiC layer is ~75% lower than at room temperature implying significantly more plasticity at the reactor operating temperature. The elastic modulus was slightly lower at 1000 °C than at room temperature. Microcantilever fracture at the SiC-IPyC interface shows that failure occurs within the pyrolytic carbon layer rather than an interfacial “debonding” with a strength similar to that of bulk pyrolytic carbon.

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.

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.

High-resolution experiments for mixing in large enclosures

To support further model development and validation for mixing in large enclosures, the MiGaDome facility that is 1/12th scaled from the Modular High-Temperature Gas Reactor (MHTGR) upper plenum has recently been built at the University of Michigan. In this paper, 2D PIV measurements have been conducted on two jets discharging into the MiGaDome facility. Two twin-jet cases of Re=4097 and Re=6021, and an asymmetrical case (Re=6021 v.s. 4097) have been investigated. Intense turbulent mixing with spanwise vortices of various sizes is observed in the instantaneous vector field for all cases. A power spectrum density analysis with a 7.5 Hz cutoff frequency has shown low-frequency fluctuations of St=0.0144 and St=0.0120 in the middle of the two jets for the two uniform injection cases. Besides, the time-averaged flow field shows that a down-wash fountain flow has formed due to wall jet impingement for the two cases, while a clockwise recirculation is created for the asymmetrical case. High-resolution 2D velocity and turbulent statistics fields have been obtained from the time-averaged measurements. In addition, the integral length scales are also calculated based on the two-point spatial cross-correlation.

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.

The deterministic neutron transport calculation for the HTR-PM by the three-dimensional method of characteristics code ARCHER

Due to the strong geometric adaptability, the Three-Dimensional (3-D) Method Of Characteristics (MOC) is a promising candidate for 3-D whole-core high-fidelity neutron transport calculations. However, the 3-D MOC can hardly be applied to large-scale full core problems on account of the huge computational costs in memory and time. In the past, the 3-D MOC was mainly used in traditional Light Water Reactor (LWR) calculations, but rarely used for more complex core calculations. For pebble-bed High Temperature gas-cooled Reactors (HTRs), most 3-D MOC codes are out of ability to construct complex pebble beds, let alone efficient acceleration methods. The 3-D MOC code ARCHER can efficiently simulate the large-scale pebble-bed HTRs through using the Linear Source Approximation (LSA), the Coarse Mesh Finite Difference (CMFD) and the hybrid MPI-OpenMP parallel. In this work, the two-level CMFD acceleration and efficient preconditioners on Krylov subspace linear solvers are implemented in the ARCHER code in order to achieve better performance. In addition, the practical HTR-PM criticality problem is calculated by ARCHER, which is the world’s first high-fidelity neutron transport solution of large-scale pebble-bed HTRs by deterministic numerical method. It also shows that the 3-D MOC has great application potential in other complex reactors.

Numerical study of the flow and heat transfer characteristics in a scale model of the vessel cooling system for the HTTR

The reactor cavity cooling system (RCCS) is a passive reactor safety system commonly present in the designs of High-Temperature Gas-cooled Reactors (HTGR) that removes heat from the reactor pressure vessel by means of natural convection and radiation. It is one of the factors responsible for ensuring that the reactor does not melt down under any plausible accident scenario. For the simulation of accident scenarios, which are transient phenomena unfolding over a span of up to several days, intermediate fidelity methods and system codes must be employed to limit the models’ execution time. These models can quantify radiation heat transfer well, but heat transfer caused by natural convection must be quantified with the use of correlations for the heat transfer coefficient. It is difficult to obtain reliable correlations for HTGR RCCS heat transfer coefficients experimentally due to such a system’s size. They could, however, be obtained from high-fidelity steady-state simulations of RCCSs. The Rayleigh number in RCCSs is too high for using a Direct Numerical Simulation (DNS) technique; thus, a Reynolds-Averaged Navier–Stokes (RANS) approach must be employed. There are many RANS models, each performing best under different geometry and fluid flow conditions. To find the most suitable one for simulating an RCCS, the RANS models need to be validated. This work benchmarks various RANS models against three experiments performed on the HTTR RCCS Mockup by the Japanese Atomic Energy Agency (JAEA) in 1993. This facility is a 1/6 scale model of a vessel cooling system (VCS) for the High Temperature Engineering Test Reactor (HTTR), which is operated by JAEA. Multiple RANS models were evaluated on a simplified 2d-axisymmetric geometry. They were found to reproduce the experimental temperature profiles with errors of up to 22% for the lowest temperature benchmark and 15% for the higher temperature benchmarks. The results highlight that the pragmatic turbulence models need to be validated for high Rayleigh natural convection-driven flows and improved accordingly, more publicly available experimental data of RCCS resembling experiments is needed and indicate that a 2d-axisymmetric geometry approximation is likely insufficient to capture all the relevant phenomena in RCCS simulations.

Optimization of preparation process and study on the properties and microstructures of nuclear natural graphite powder for HTR pebble fuel elements

Nuclear natural graphite powder (NNGP) is the key and main component in the matrix graphite (MG) of pebble fuel elements for high temperature gas-cooled reactors (HTRs). In this study, a modified lab-scale powder preparation process of NNGP proposed for the first time would contribute to a more efficient and lower energy-consumption preparation system. The optimized NNGP was successfully prepared by the modified process, whose properties and microstructures were comprehensively investigated. The results indicated that the optimized NNGP possessed a lower specific surface area, a higher graphitization degree and fewer structural defects. MG pebbles manufactured by the optimized NNGP exhibited higher crush strength and thermal conductivity, a lower corrosion rate, as well as better thermal stability during heat treatment. This indicated that the modified NNGP was conducive to improving the integrity and safety of MG pebbles.

Spatial evolution mechanism of vortex structure in the highly-loaded helium compressor cascade

ABSTRACT The highly loaded design method of helium compressors can effectively solve the difficulty in compressing helium in High Temperature Gas-cooled Reactors (HTGR). But it also causes obviously different attack angle characteristics of blade surface loads in a highly loaded helium compressor compared to air compressors. This difference inevitably affects separation characteristics and flow loss within the compressor. In the current study, the effects of highly loaded design methods and changes in attack angle on the separation characteristics of the compressor cascade are analyzed by applying a numerical simulation method first. Then, the influence of Mach number on the loss characteristics of the cascade for a highly loaded helium compressor is systematically analyzed. Finally, the effect of differences in the material properties of working fluid on the separation characteristics is discussed. The results indicate that the proportion of secondary flow loss to the total loss in highly loaded compressor cascades is 2.46 times larger than that in conventionally loaded ones. While the properties of working fluid have an effect on the performance of the compressor cascade, their effects on the weight factor of vortex loss are highly limited.