Ordered packed beds can enhance particle-to-fluid heat transfer while reducing hydraulic resistance, but their thermo-hydraulic behavior depends on both porosity and packing architecture. This study investigates flow reorganization, pressure gradient, and convective heat transfer in cubic, orthorhombic, and rhombohedral ordered packed beds using pore-scale CFD. A particle-layer stacking model is introduced to quantify transverse packing and axial overlap, and 27 configurations with different normalized inter-particle spacings are analyzed. Results show that packing structure governs pore connectivity and flow pathways, producing distinct thermo-hydraulic responses among bed families. In cubic beds, decreasing transverse packing weakens particle-induced flow disturbance, reducing heat-transfer coefficients by up to 51.37 % while the pressure gradient decreases substantially (maximum 362.14 %). Orthorhombic beds exhibit weak thermal sensitivity, with heat-transfer variations of 0.42–6.75 % due to compensating flow accessibility. Rhombohedral beds show the strongest structure-induced transitions: connected axial passages cause abrupt flow redistribution, heat-transfer variations of 0.84–64.81 %, and pressure-gradient variations up to 48-fold. Although local heat transfer may decrease, the larger reduction in hydraulic resistance improves overall performance, with rhombohedral beds achieving the most favorable heat-transfer-to-pressure-drop trade-off. Structure-dependent Nusselt-number correlations are developed, incorporating packing-architecture effects, with maximum deviations of 14.49 %, 3.26 %, and 9.92 % for cubic, orthorhombic, and rhombohedral beds. These results highlight the limitations of porosity-based characterization and provide a structure-aware framework for predicting and optimizing ordered packed-bed performance in chemical and thermal processes.

3D pin-resolved power reconstruction using ex-core detectors is essential for ensuring operational safety and enhancing the economic performance of nuclear reactors. However, due to the considerable distance between detectors and the active core, the limited quantity of available signals, and the inherent limitations of the traditional two-step calculation method, current ex-core-based methodologies remain restricted to axial and assembly-resolved distributions. Such constraints fail to satisfy the requirements for high-resolution, pin-resolved power reconstruction. To enable pin-resolved power reconstruction, this paper proposes a methodology based on harmonics synthesis method, which utilizes a pin-resolved offline library obtained from high-fidelity transport calculation as prior and ex-core detector signals as constrains. The 2D MOC/1D NEM method, accelerated by the generalized coarse-mesh finite difference scheme, is employed to generate an offline library of pin-resolved detector response functions and high-order harmonics. By coupling ex-core detector signals with the offline library, the online reconstruction determines harmonic expansion coefficients via a least squares algorithm, facilitating the reconstruction of 3D pin-resolved power distributions. Numerical results using a low-temperature heating reactor model confirm that the methodology accurately reconstructs 3D pin-resolved power distributions. Even under operational conditions involving sharp power gradients induced by control rod insertion, discrepancies between the reconstructed power and the reference solutions remain minimal.

The dynamic response of transient strongly nonlinear system model tests is difficult to establish accurate similarity transformation relationships for prototype test prediction in the time domain using classical similarity theory. To achieve the similarity transformation of both amplitude and data trajectory from model test results to the prototype for transient strongly nonlinear systems, this paper deduces and establishes an Iterative Similarity Theory in phase space based on classical similarity theory. This reveals the dynamic variation characteristics of similarity relationships with scaling ratios and proposes that the dependent Pi-term of model tests exhibits a parabolic mapping relationship in phase space. Leveraging the characteristics of parabolic mapping, Renormalization Group Theory is further introduced to establish a phase space iterative similarity transformation method for the mapping functions between prototype and model in phase space. This approach reveals the stability trait of geometric scaling ratios in model tests, forming a similarity transformation technique for converting model test results to prototype amplitude and data trajectory. Taking the underwater explosion stiffened cylindrical shell system as the research subject, this paper designs and conducts several scaling ratios and dozens of model series tests under the guidance of the Iterative Similarity Theory, demonstrating the effectiveness and universality of applying the renormalization equation within the Iterative Similarity Theory for model tests. The research results indicate that the geometric scaling ratio for transient strongly nonlinear system model tests exhibits stability within the neighborhood range of 1:2.5 and 1:6.25 as verified by the Lyapunov exponent. The phase space iterative similarity transformation method established within the framework of the renormalization equation can effectively address the problem of transforming model test results to prototype amplitude and data trajectory. The similarity transformation result exhibits an error of approximately 20% in amplitude conversion for mesoscale model tests, representing an improvement of about 30% compared to the similarity transformation results guided by classical similarity theory. Furthermore, this method enables the similarity transformation of periodic characteristics during the dynamic evolution process, thereby providing a new theoretical basis and methodological support for similarity analysis of nonlinear dynamic systems.

Neutron KERMA factors calculated by the nuclear data processing codes always exhibit erroneous values and do not conform to physical significance because the energy balance of data in evaluated nuclear data libraries cannot be guaranteed or the processing methods in the nuclear data processing codes are incorrect. To provide key information for the improvement and correction of evaluated nuclear data libraries, the neutron KERMA factors of main reaction types are calculated and analyzed based on the FENDL-3.2 and JENDL-5 libraries, including scattering reaction, fission reaction, absorption reaction and radiative capture reaction. All unphysical negative values among these reaction types are identified, classified and collated. The causes of erroneous results are analyzed, and improvement suggestions are proposed to revise the data in the evaluated nuclear data libraries.

High flux reactors (HFRs) exhibit complex geometry due to their high-power levels and unique applications, a feature that imposes strict requirements on reactor physics calculations. The method of characteristics (MOC) is widely used to solve the neutron transport equation due to its geometric flexibility. This work presents a two-dimensional MOC calculation module for HFRs, developed within the high-fidelity, three-dimensional whole-core neutron transport code HNET. To accelerate the computationally expensive MOC calculations, the generalized equivalence theory coarse mesh finite difference (gCMFD) method, combined with a two-level acceleration strategy is implemented. Furthermore, the constructive solid geometry (CSG) technique is employed to model the complex geometry and to ensure proper correspondence between coarse and fine meshes. Finally, verification is performed based on the Wide-spectrum Ultra-high Flux Experimental Reactor (THFR). Results demonstrate that HNET-HFR can perform accurate and efficient transport calculations for the THFR, with gCMFD acceleration reducing the total number of MOC iterations by at least 90% and the total computational time by over 80%. These findings confirm the validity and effectiveness of the developed module for high-fidelity simulations of the THFR.

HNET is a high-fidelity neutron transport program developed for 3D reactor core simulation. To enhance its high-fidelity neutron transport simulation capability for pebble-bed HTR, a three-dimensional Method of Characteristics (3D-MOC) solver with Linear Source Approximation (LSA) is developed in HNET recently. The present work gives a comprehensive description on this newly developed solver with emphasizes on its calculation scheme, geometric modelling capability, parallel strategy and acceleration techniques. Computational efficiency of this 3D-MOC solver is enhanced by using virtual mesh CMFD method (vcCMFD) and modular track arrange strategy. This pebble-bed HTR 3D-MOC solver in HNET is verified with a pebble-bed HTR whole core model developed on HTR-10 benchmark. Results show that it takes about 189 core-hours to perform whole-core criticality simulation, which demonstrates its feasibility and efficiency for pebble-bed HTR high-fidelity neutron transport simulation.

Accurate solutions of partial differential equations (PDEs) in complex curved domains require both faithful geometric representation and effective solution approximation. These two tasks are often coupled in conventional discretizations, making geometric refinement an inherent part of improving solution accuracy. We propose a curved-surface nodal (CSN) framework that separates them by using the surface equations of the physical domain to define curved nodal grids, and independently approximating the solution through high-order local polynomial expansions. The formulation is developed from the general transport equation, providing a unified treatment of representative hyperbolic, elliptic, and parabolic PDEs. Numerical tests include neutron transport, steady and transient heat conduction, and a coupled neutronics-thermal problem. The helical-cruciform neutron transport case demonstrates direct treatment of a continuously twisting boundary without faceting, whereas the cylindrical heat-conduction case achieves results consistent with a 387,111-element finite-element reference using only 1,600 nodal grids. These results indicate that combining analytic geometric representation with high-order polynomial solution expansions can deliver high-fidelity solutions while substantially reducing the number of spatial subdomains required. The CSN framework thus offers a generalizable and high-fidelity approach to PDEs in geometrically complex engineering scenarios.

Transient fluid-structure interaction (FSI) processes often involve strong impact loads and pronounced nonlinear responses. A typical example arises in near-field underwater explosions, which involve highly transient and nonlinear phenomena, including shock waves with strong discontinuities, pulsating bubbles undergoing drastic volume changes, and severe tearing and damage to ship structures. These processes entail complex FSI, placing stringent demands on both the accuracy and computational efficiency of numerical methods. To address the bottleneck in high-resolution, large-scale simulations, this study develops a fully meshless Riemannsmoothed particle hydrodynamics (SPH) and reproducing kernel particle method (RKPM) coupling method with GPU-acceleration for FSI analysis in underwater explosions. Within a unified GPU computing framework, the solutions of fluid dynamics, structural dynamics, and FSI are all organized using "particles" or "stress points" as fundamental parallel units. A unified data structure and a parallel optimization strategy based on a shared linked list are introduced, effectively reducing the overhead associated with neighbor searching and data access. The accuracy and computational efficiency of the proposed method are demonstrated through underwater explosion simulations involving a free-field shock wave, a double-layer cylindrical shell, and a full-scale submarine. Under the same spatial resolution, present single-precision implementation and computational configuration adopted in this study, the GPU-based parallel framework achieves an overall runtime reduction ratio of at least 31 times compared with the CPU-based parallel implementation in typical fluid-structure interaction scenarios. Moreover, it enables efficient large-scale, high-resolution simulations while substantially reducing total computational time.

Coherent scattering, as the primary photoatomic scattering interaction in the low-energy region, is crucial for material structure analysis and nondestructive testing. Nuclear data processing codes typically employ the independent atomic form factor (IAFF) approximation to calculate the angular distribution of secondary photons from coherent scattering. Although this approximation meets accuracy requirements for most energy ranges, it becomes invalid when the incident photon energy approaches atomic absorption edges or falls below the kilo-electron-volt-energy range. This inaccuracy is due to the influence of anomalous scattering and molecular interference effects. In this paper, an improved model incorporating anomalous scattering and molecular interference effects is developed by introducing anomalous scattering factors (ASFs) and molecular interference functions (MIFs), respectively. These two effects are also implemented in the generation of the photoatomic ACE library for practical applications. For verification, the angular distribution is calculated with the IAFF approximation and the model incorporating ASFs and MIFs, respectively. The numerical results indicate that anomalous scattering results in a significant increase in forward scattering, while the inclusion of molecular interference effects yields angular distributions in better agreement with experimental measurements.

Fusion energy is a crucial pathway to achieving deep decarbonization and long-term global energy security. In the neutronics design of fusion blankets, the efficient and accurate calculation of Doppler-broadened cross sections under ultra-high temperatures is of great importance. However, existing Doppler broadening methods cannot achieve high accuracy and high efficiency simultaneously under ultra-high temperatures. Even in offline processing, generating a large-scale library containing hundreds of nuclides and dozens of temperature points (including ultra-high temperatures) often takes two to three days. To address this issue, this paper proposes a hybrid integration algorithm that combines Kernel Broadening with Gaussian-type integration methods. For resonance nuclides, the Kernel Broadening method is employed together with two-point Gauss-Legendre quadrature. For nuclides with smooth cross-section variations, Kernel Broadening is combined with Gauss-Hermite quadrature. Based on this method, a Doppler broadening module is developed in the nuclear data processing code GNAP. Based on the evaluated nuclear data library CENDL-3.2, the proposed method is compared against NJOY2016 at both room temperature and ultra-high temperatures, and further verified using ICSBEP benchmarks. Numerical results demonstrate that the broadened cross sections are in good agreement with those from NJOY2016, while the computational efficiency is improved by up to 72% without sacrificing accuracy.

Curved Surface Nodal Method (CSN) is a deterministic neutron transport method based on the actual irregular, large-scale curved surface geometry of nuclear reactors, which can achieve accurate and efficient solutions to the neutron transport equation. In CSN, there is a set of geometry paraments, which is only related to the geometry information of nodes and not related to solved neutron flux. Geometry parameters are constructed from the surface integral over node boundaries or node integrals. Irregular curved shapes of nodes are common in CSN, which makes the calculation of node integrals with node as the integration region difficult. This paper highlights the impact of geometry parameter accuracy on CSN calculations and provides an accuracy limit for numerically calculated geometry parameters. And a geometry parameter solver based on the quasi-Monte Carlo method has been developed. The results show that when the accuracy of geometry parameters reaches 10^-6 , it has a negligible effect on CSN calculation.

Accurate calculation of the detector response function is critical in power reconstruction using ex-core detectors. The Monte Carlo and 3D discrete ordinates methods have been applied to calculate the ex-core detectors response function. However, since ex-core detectors are located far from the reactor core, the large neutron flux gradients between the core and the ex-core detector, as well as the weak contribution of in-core neutrons to the detector response, lead to significant limitations of the computational efficiency and accuracy for the Monte Carlo method. And for 3D discrete ordinates method, the resolution of the detector response function is limited due to the homogenization approximations. Therefore, achieving efficient and accurate whole-core, pin-resolved detector response function calculations remain a significant challenge. To address the challenges of computational efficiency and resolution inherent in conventional methods, the 2D Method of Characteristics / 1D Nodal Expansion Method coupling method with multi-group coarse mesh finite difference method acceleration is used to carry out high-fidelity adjoint transport calculations, enabling direct pin-resolved detector response function calculation. Numerical verification is performed using the 2D EPRI-9 model, the 3D C5G7 model and the low temperature heating reactor. The results demonstrate that the 2D/1D method can accurately and efficiently compute pin-resolved detector response function, achieving well agreement with Monte Carlo results.

The core structure of high flux experimental reactors is very complicated, and the method of characteristics is one of the effective methods to realize its high-fidelity neutron transport calculation. Refined modeling and division of coarse meshes and fine meshes for the core structure are the key to the realization of the MOC method. Under the conventional regular coarse mesh division, especially in the control drum region, it is difficult to find a correspondence between coarse meshes and fine meshes. In this paper, we use the modeling method of constructive solid geometry and adopt a new mesh division method based on the irregular coarse mesh division, and develop the geometric module and the MOC calculation module of the HNET-HFR program. By comparing with conventional meshing method, this irregular coarse mesh division has a smaller memory consumption and faster modelling time, while the MOC tracing takes less time. The computational results show that the new mesh division method is correct and has higher accuracy.

Curved surface nodal (CSN) method is a novel approach to solve the neutron transport equation with curved surface nodes. The method employs multidimensional polynomials in space to expand angular neutron flux, with expansion coefficients being solved by constructing a linear system using weighted residual equations and integral leakage conditions. However, present research indicates that CSN method may exhibit divergence. The divergence is attributed to the current implementation which only ensures the consistency of integral averaged angular neutron flux in nodes’ boundary, failing to accurately reflect the neutron angular flux continuity at boundaries. This paper proposes two schemes to enhance the boundary conditions, namely endpoint constrained optimization and strict constrained optimization. The effects of these two optimization schemes indicate that strengthening the constraints on boundary conditions can effectively improve CSN convergence. However, the addition of equations leads to an over-determined linear system, which cannot guarantee computational accuracy. Therefore, increasing the number of unknowns and appropriately supplementing the boundary condition constraints to avoid over-determination or under-determination would be a viable approach.

Predicting the collapse direction of large-scale pulsating bubbles is crucial for evaluating the safety performance of marine vessels in ocean applications involving underwater explosions and high-pressure bubble detection. This study develops a rapid forecasting method for large-scale pulsating bubbles under the influence of hybrid boundaries (free surface, bottom, and sidewall) based on the Kelvin impulse theory. The boundary element method was used to simulate bubble jets and clarify the applicability of the analytical solution in predicting the direction of large-scale bubbles. The analytical solution of the Kelvin impulse underestimates the buoyancy effects of bubbles near the bottom. However, near the free surface, the strong interaction between the bubble and free surface strengthens the downward movement of the bubble, resulting in an analytical solution with improved accuracy. A buoyancy correction factor was introduced to rectify inaccuracies in the analytical solution near the bottom. The correction factor was obtained under the condition of a vertically neutral collapse for the bubbles. Comparison of the simulation results with theoretical values across various buoyancy parameters indicate that the modified analytical solution can effectively predict the direction of bubble collapse across most parameter domains. The modification method for analytical solution proposed in this study may serve as a reference for practical operations aimed at protecting marine vessels near underwater explosions or marine seismic sources.

Pebble-bed High Temperature Reactor (HTR) adopts multi-pass refuelling fuel management or MEDUL cycle, where fuel pebbles would run through the core multiple times before reaching their burnup value limits and being discharged. This cycle ultimately leads reactor to an equilibrium state whose characteristics are closely related to the allowed refuelling times in the cycle. Typically, increasing refuelling times permits a more homogeneous equilibrium state with lower maximum power density. Also, atomic density uncertainty, e.g. contributed from nuclear data, inside this equilibrium core would be reduced with increased refuelling times. Although it is beneficial for reactor operation safety, increasing refuelling times also burdens fuel handling system and shortens their service life. Analysing equilibrium state under hypothetical infinite refuelling times will reveal the limiting effect of refuelling times on the characteristics of equilibrium state in pebble-bed HTR, and it could be used to justify fuel management design. This work proposes a Lagrangian burnup framework based infinite refuelling burnup model. A burnup model constructed from HTR-PM (High-Temperature gascooled Reactor Pebble-bed Module) is used to verify the proposed infinite refuelling model, and results are compared with finite refuelling calculations. It is found that infinite refuelling highlights the limiting effects of refuelling times on equilibrium state in terms of neutron flux, regional power density, actinides and fission products' batch averaged atomic density. Increasing refuelling times makes equilibrium state approaching infinite refuelling equilibrium state nonlinearly, and equilibrium state obtained from fifteen times refuelling is quite close to that obtained from infinite times refuelling. As a hypothetical model, the infinite refuelling equilibrium burnup model developed in this work could balance out the randomness as well as uncertainty associated with fuel pebbles' movement inside pebble-bed HTR. It is expected to be a reference for multiple design and analysis of pebble-bed HTR.

The core physical behavior of reactors is essentially the result of multi-physical fields coupling feedback. High-fidelity neutronics/thermal-hydraulics (N/TH) analysis can simulate and predict nuclear reactor core phenomena realistically, providing advanced and reliable technical means during the design and safety analysis of nuclear reactor. In this work, an efficient and robustness coupling method using power density as the coupling parameter, Matrix-Free Newton Krylov (MFNK) method, is successfully developed and innovatively implemented in HNET for high-fidelity N/TH coupling simulation. To enhance the efficiency and stability, the multi-level generalized equivalence theory-based CMFD (ML-gCMFD) iterative acceleration method and ML-gCMFD coupling acceleration method are proposed. In addition, the nonlinear preconditioning and hybrid perturbation size formula are implemented to further improve the convergence. Finally, to evaluate the numerical accuracy, convergence, efficiency and stability of MFNK method, a series of representative problems, including a three-dimensional (3D) single fuel pin problem, VERA Benchmark Problem 6, and VERA Benchmark Problem 7, are analyzed by comparing with the current N/TH coupling methods. Numerical results indicate that MFNK method can obtain strong stability, high convergence performance, and relatively high computational efficiency while ensuring high accuracy. It demonstrates that MFNK method has significant performance advantages and potential for high-fidelity N/TH coupling simulation.

Three-dimensional method of characteristic (3D-MOC) codes have been developed to conduct neutronic simulation for pebble-bed high temperature gas-cooled rector (HTGR). Although parallel strategy such as domain decomposition and acceleration method such as coarse mesh finite difference (CMFD) are applied in these codes, whole core simulation still faces huge computational burden which needs more efficient acceleration method to enhance simulation efficiency. Moreover, considering the cylindrical geometry of pebble-bed HTGR, differential length of coarse meshes will gradually increase along radial direction which will lead convergence problem in conventional CMFD method. In this paper, a virtual mesh based CMFD method is proposed to overcome this issue. Virtual coarse meshes are generated by further dividing CMFD coarse meshes along circumferential direction to reduce the optical thickness of peripheral coarse meshes. The performance of proposed virtual coarse mesh based CMFD acceleration method is verified in a simplified cylindrical pebble-bed model and HTR-10 whole core problem. Numerical results show that virtual coarse mesh based CMFD method can reduce around 30% source iterations of MOC compared with original CMFD method.

Cu-Ag alloys are known for their exceptional combination of high strength and superior electrical and thermal conductivities. However, conventional manufacturing processes typically produce discontinuous Ag-rich precipitates that degrade performance. Through processing a Cu-5wt%Ag alloy with electron beam powder bed fusion (PBF-EB), this study reveals the fundamental potential of solute trapping induced by rapid solidification, offering a new pathway to eliminate detrimental discontinuous precipitates. We demonstrate that high solidification rates, exceeding 1 m/s, can be achieved through process control and inherent high thermal conductivity of Cu. This induces significant solute trapping, resulting in a supersaturated Cu matrix during solidification and the precipitation of uniformly dispersed Ag-rich nanoparticles during in-process aging. Consequently, continuous precipitates form, eliminating the detrimental discontinuous precipitates typically persistent in traditional processes. Specifically, the PBF-EB samples exhibit relative densities of up to 98.78 % and columnar grain structures with a strong <001> texture along building direction. Grain size varies with process parameters and building height, attributed to the variations in solidification conditions affected by heat accumulation and dissipation dynamics. Through altering solidification segregation, solidification rate can be used to govern the size and morphology of Ag-rich precipitates, thus affecting mechanical and electrical properties. Despite the presence of hot cracks at high-angle grain boundaries, the as-built samples exhibit excellent electrical conductivity (85.9 -89.3 % IACS) and mechanical properties (maximum hardness of similar to 87.1 HV, YS of 149 MPa, UTS of 217 MPa), surpassing peak-aged cast counterparts in hardness while maintaining electrical conductivity. These findings establish a generic understanding of solute-trapping-enabled microstructural control in additive manufacturing, providing a foundation for designing high-performance Cu-based alloys for advanced electrical applications.

Early-stage dynamic responses of naval structures under underwater explosion shock loads exhibit high-frequency, intense amplitude fluctuations and short durations, serving as critical factors for the development of plastic deformation and other damage characteristics. These structural dynamics demonstrate prominent nonlinear and non-stationary features. This study focuses on the nonlinear evolutionary patterns of early-stage plastic shock responses in underwater explosion-impacted ship structures. Utilizing phase space reconstruction, unimodal mapping, and symbolic dynamics theory, we analyze the nonlinear and non-stationary characteristics along with their evolutionary patterns in experimental data. First, scaled model experiments under varying shock factors were conducted based on a stiffened cylindrical shell prototype, investigating the spatiotemporal evolution of nonlinear and non-stationary dynamic responses under different shock loads while characterizing their uncertainty features. Second, model tests were performed on deck-type cabin structures and plate frameworks derived from a naval vessel’s deck prototype, further analyzing the evolutionary patterns of early-stage plastic dynamic responses and verifying the method’s effectiveness and universality. Research findings indicate that (1) early-stage plastic shock responses of ships under underwater explosions exhibit multiple dynamical behaviors including chaotic motion, periodic motion, and quasi-periodic motion, and (2) during the initial plastic phase, orbital parameters approximate 0.8, providing guidance for test condition setup and initial parameter selection in underwater explosion experiments on naval structures.