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When plasma is compressed by magnetic forces, a pinch phenomenon is observed. Pinch plasma has received significant attention as an efficient source of radiation and a way for high-density plasma physics analysis. In this study, a non-ideal magnetohydrodynamics (MHD) model is applied to a smoothed particle hydrodynamics (SPH) framework to analyze pinch plasmas whose local resistivity varies with temperature and pressure. The proposed SPH model incorporates several numerical treatments, such as a correction term to satisfy the ∇·B constraint and some artificial dissipation terms to govern the shock wave. Moreover, it includes the evaluation of a novel SPH discretization for non-ideal MHD terms, including current density calculations. Furthermore, the proposed model is validated with three benchmark cases: (1) Brio and Wu shock tube (ideal MHD), (2) resistive MHD shock simulation, and (3) magnetized Noh Z-pinch problem. The simulation results are compared with the results of some reference Eulerian MHD simulations and analytical solutions. The simulations agree well with the reference data, and the introduced numerical treatments are effective. Finally, X-pinch simulations are performed using the proposed model. The simulations well produce the micro Z-pinch and jet shapes, which are important X-pinch features. Overall, the proposed SPH model has extensive potential for studying the complex pinch plasma phenomena.

We performed a numerical study of the jamming that stops the flow of granular material from a three-dimensional hopper discharging due to gravity. When the hopper outlet is not much larger than the particles, granular material clogs the hopper outlet due to the formation of an arch or dome. For a wide range of particle diameters, we obtained the size distribution of the “avalanche,” defined as the number of particles that fall before jamming. We repeated this process through a discrete element method model verified with a simple experiment. From these distributions, we determined the probability of the flow jamming before N particles pass through the hopper. As the ratio between the hopper outlet diameter and the particle diameter increases, the probability that an arch will block the outlet decreases. We show here that the probability of one particle passing through the hopper is not constant when there are not sufficient particles. Then, we propose a new model that can quantify changes in particle passing probability. Using this model, we derive the particle passing probability in a hopper with shallow columns and confirm that the probability of one particle passing through the hopper is closely related to the pressure acting on the bottom of the hopper.

Advanced modeling and analysis techniques are always essential for development of safe and reliable nuclear systems. The numerical methods in nuclear thermal-hydraulics and safety analysis are generally based on mesh-based (or grid-based) methods. These mesh-based methods have a long history and thus are very mature both mathematically and numerically. Based on their robustness and efficiency, they have been successfully applied to many applications for decades. However, the mesh-based methods suffer from difficulties in handling complex phenomena accompanied by highly non-linear deformations, which are frequently encountered in the recent nuclear safety issues related to natural disaster and severe accidents. Recent advances in Lagrangian-based CFD techniques have opened up possibilities for addressing this issue effectively. In this study, a Lagrangian-based CFD code (named as SOPHIA) has been developed based on Smoothed Particle Hydrodynamics (SPH), one of the best-known Lagrangian methods which can extensively handle various physics because of its simplicity in expressing and solving mathematical equations. The SOPHIA code incorporates basic conservation equations (mass, momentum, and energy) and various physical models including heat transfer, turbulence, multi-phase, surface tension, diffusion, etc. In addition, to handle multi-phase, multi-component, and multi-resolution flows, the code newly formulates density and continuity equations in terms of a normalized-density. One of the biggest technical challenges in the Largrangian-based CFD is its high computational cost. Therefore, the code is parallelized using multi-GPUs through multi-parallel computing techniques. Through the optimized algorithm based on these techniques, the computational performance has been improved drastically and the code obtains the capability of high resolution and large scale simulation. In order to demonstrate its applicability to nuclear safety-related issues, this study performs the simulations on three benchmark experiments related to nuclear safety: (1) water jet breakup of FCI, (2) LMR core sloshing, and (3) bubble lift force. The simulation results are compared with the experimental data both qualitatively and quantitatively, and they shows a good agreement with highly reliable visualizations.