Three-dimensional Simulation Code Research Articles

Differential Rotation in Convecting Spherical Shells with Non-Uniform Viscosity and Entropy Diffusivity

Contemporary three-dimensional physics-based simulations of the solar convection zone disagree with observations. They feature differential rotation substantially different from the true rotation inferred by solar helioseismology and exhibit a conveyor belt of convective “Busse” columns not found in observations. To help unravel this so-called “convection conundrum”, we use a three-dimensional pseudospectral simulation code to investigate how radially non-uniform viscosity and entropy diffusivity affect differential rotation and convective flow patterns in density-stratified rotating spherical fluid shells. We find that radial non-uniformity in fluid properties enhances polar convection, which, in turn, induces non-negligible lateral entropy gradients that lead to large deviations from differential rotation geostrophy due to thermal wind balance. We report simulations wherein this mechanism maintains differential rotation patterns very similar to the true solar profile outside the tangent cylinder, although discrepancies remain at high latitudes. This is significant because differential rotation plays a key role in sustaining solar-like cyclic dipolar dynamos.

Polarization Signature of Companion-fed Supernovae Arising from BH–NS/BH Progenitor Systems

The formation of black hole–neutron star (BH–NS) or BH–BH systems may be accompanied by special supernova (SN) signals, due to the accretion feedback from the companion BH. The additional heating, which is mainly attributed to the Blandford–Payne mechanism, would disrupt the isotropic nature of the luminosity distribution on the surface of the SN ejecta, leading to the appearance of polarization. Here we develop a three-dimensional Monte Carlo polarization simulation code to conduct simulations for these special SNe. We find that the maximum polarization level of ∼2% occurs at the peak time of SN emission in the “close-binary” scenario, while in the “faraway-binary” case maximum polarization (i.e., ∼0.7%) is observed at a considerably later time than the peak of the SN. The magnitude of polarization is dependent on the degree of unevenness in the luminosity distribution and the angle between the line of sight and the equatorial direction. When considering the geometric distortion of SN ejecta at the same time, the magnitude of polarization may either increase (for a oblate ellipsoidal shape) or decrease (for a prolate ellipsoidal shape). The polarization signatures represent a promising auxiliary instrument to facilitate the identification of the companion-fed SNe. Moreover, comparing the event rate of these special SNe with the event rate density of LIGO-Virgo-detected BH–NS/BH systems could further help to distinguish the BH–NS/BH formation channel.

Global variance reduction method for Monte Carlo simulation of thermal radiation transport

The implicit Monte Carlo (IMC) method is an important numerical approximation method of simulating the thermal radiative transfer problems under high temperature condition. However, one problem plaguing the IMC method is that the calculation error distributions of the radiation specific intensities are highly asymmetric in space and time. By theoretical analysis and numerical simulations, we find that the error is affected by the records of track in the tallying mesh. Accordingly, a global variance reduction method for implicit Monte Carlo simulation is developed and the corresponding formulas are derived. This method includes three key techniques: 1) the automated dynamic distribution method for the Monte Carlo simulation source particles; 2) the dynamic weight-window technique and the none-bias weight revise algorithm that is suited to the particle distribution method; 3) the analytical estimation variance reduction method of the radiation specific intensity. In view of the above, a three-dimensional simulation code, named IMC3D, is developed to simulate the thermal radiative transfer phenomena. The typical thermal radiative transport problem, known as Marshak wave, is simulated. The simulation results indicate that the global variance reduction method for implicit Monte Carlo makes the statistical errors much more symmetric in space and time and the maximum of error is controllable, thereby increasing the calculation speed approximately 10 times. The new IMC method and code are used for simulating the radiative transportation in hohlraum of ICF successfully.

Validation of the plasma-wall interaction simulation code ERO2.0 by the analysis of tungsten migration in the open divertor region in the Large Helical Device

• Migration of tungsten sputtered from a tungsten-coated divertor plate was investigated. • The simulation reasonably explained the observed localization of tungsten migration. • The simulation reproduced observed tungsten deposition in the private side. • The simulated tungsten density on the plasma wetted areas disagreed with observation. Tungsten migration in the open divertor region in the Large Helical Device is analyzed for validating the three-dimensional plasma-wall interaction simulation code ERO2.0. The ERO2.0 simulation reproduced the measurement of localized tungsten migration from a tungsten-coated divertor plate installed in the inboard side of the torus. The simulation also explained the measurement of the high tungsten areal density in the private side on a carbon divertor plate, next to the tungsten-coated divertor plate, by the tungsten prompt redeposition in plasma discharges for a low magnetic field strength in a counterclockwise toroidal direction. However, the simulation disagreed with the measurement of low tungsten areal density on the plasma-wetted areas on the carbon divertor plates, which indicated that the actual erosion rate of the redeposited tungsten should be much higher than that used in the ERO2.0 code.

Rotation-induced granular motion on the secondary component of binary asteroids: Application to the DART impact on Dimorphos

Context. NASA’s Double Asteroid Redirection Test (DART) mission will kinetically impact Dimorphos, the secondary component of the Didymos binary asteroid system, which will excite Dimorphos’s dynamical state and lead to significant libration about the synchronous state and possibly chaotic non-principal axis rotation. Although this particular outcome is human caused, many other secondary components of binary systems are also prone to such exotic spin states. Aims. For a satellite in an excited spin state, the time-varying tidal and rotational environment can lead to significant surface accelerations. Depending on the circumstances, this mechanism may drive granular motion on the surface of the secondary. Methods. We modeled the dynamical evolution of a Didymos-like binary asteroid system using a fully coupled, three-dimensional simulation code. Then, we computed the time-varying gravitational and rotational accelerations felt over the entire surface resulting from the secondary’s perturbed dynamical state. Results. We find that an excited spin and orbit can induce large changes in the effective surface slope, potentially triggering granular motion and surface refreshment. However, for the case of the DART impact, this effect is highly dependent on many unknowns, such as Dimorphos’s detailed shape, bulk density, surface geology, and the momentum transferred. Aside from the Didymos system and the DART mission, this effect also has important implications for binary systems in general.

A numerical investigation into Metallic-Melt continuous drainage in the core support plate region of a BWR for the initial phase of core melt progression

Under a typical uncovered core scenario in a Boiling Water Reactor (BWR), it is not clear that a large core molten pool will result as occurred in the Three Mile Island, Unit 2 (TMI-2) accident. Sandia National Laboratories (SNL) has propounded the alternative “Continuous Drainage” melt progression for the scenario, where molten material drains from the core region without the formation of any stable crusts or blockages. Hence the present simulation study was conducted to investigate the behavior of the metallic-melt continuous drainage and the drainage pathways during the initial phase of core melt progression in a BWR under an uncovered core condition like that encountered in the Fukushima Daiichi Nuclear Power Plants (NPPs) accident experienced by Tokyo Electric Power Company Holdings (TEPCO). Researchers around the world have conducted numerous sophisticated and comprehensive studies using simulation codes and experiments to investigate the Fukushima accident. Melt drainage with deforming components is subject to many uncertainties in a core support plate region possessing rather complicated geometries. Additionally, there is very limited experimental and numerical simulation knowledge on melt drainage in such a region. Thus, in recent years, Japan Atomic Energy Agency (JAEA) has experimented on melt drainage using a simplified apparatus to reproduce the behavior. The present paper provides simulation results on melt drainage in the core support region using SAGITTARIUS, an in-house three-dimensional simulation code capable of consistently simulating melt drainage with crust formation, local blockage, and structural damage. The in-vessel simulation target with a prototypic BWR-composition and -geometry is composed of four fuel assemblies (4 × 4 fuel rods per assembly), an absorber blade, a support piece, a core support plate, an Instrument Guide Tube (IGT), and a Control Rod Guide Tube (CRGT) with a Control Rod Drive Housing (CRDH). We estimated the drainage speed for the JAEA experiment to validate the SAGITTARIUS function. The drainage speed was evaluated to be 3.1 m/s, a speed corresponding to that observed in the core support plate region. We also used SAGITTARIUS to simulate the behavior of the metallic-melt drainage and temperature rise of the structure. The results from SAGITTARIUS on the trend and values of the temperature rise agreed with the measured values. On the basis of this finding, we conducted numerical investigations on the metallic-melt drainage of B4C-Stainless Steel (SS) eutectic from the absorber blade and Zry-melt from the fuel rods. The simulation demonstrated the capacity to describe the following features: (i) visual demonstration of metallic-melt drainage from the absorber blade and fuel rods, (ii) aggressive Zry-melt attack to the inlet orifice, (iii) crust formation with local blockage in the narrow drainage paths, and (iv) sedimentation of solidified melt on the bottom faces. These findings were consistent with the concept of the “Continuous Drainage” proposed at SNL and we supported the SNL scenario by the numerical investigation. These investigations probably provide useful knowledge during the discharge of damaged fuels or crust in the Fukushima-Reactor Pressure Vessels (RPVs).

Vortex flow properties in simulations of solar plage region: Evidence for their role in chromospheric heating

Context. Vortex flows exist across a broad range of spatial and temporal scales in the solar atmosphere. Small-scale vortices are thought to play an important role in energy transport in the solar atmosphere. However, their physical properties remain poorly understood due to the limited spatial resolution of the observations. Aims. We explore and analyze the physical properties of small-scale vortices inside magnetic flux tubes using numerical simulations, and investigate whether they contribute to heating the chromosphere in a plage region. Methods. Using the three-dimensional radiative magnetohydrodynamic simulation code MURaM, we perform numerical simulations of a unipolar solar plage region. To detect and isolate vortices we use the swirling strength criterion and select the locations where the fluid is rotating with an angular velocity greater than a certain threshold. We concentrate on small-scale vortices as they are the strongest and carry most of the energy. We explore the spatial profiles of physical quantities such as density and horizontal velocity inside these vortices. Moreover, to learn their general characteristics, a statistical investigation is performed. Results. Magnetic flux tubes have a complex filamentary substructure harboring an abundance of small-scale vortices. At the interfaces between vortices strong current sheets are formed that may dissipate and heat the solar chromosphere. Statistically, vortices have higher densities and higher temperatures than the average values at the same geometrical height in the chromosphere. Conclusions. We conclude that small-scale vortices are ubiquitous in solar plage regions; they are denser and hotter structures that contribute to chromospheric heating, possibly by dissipation of the current sheets formed at their interfaces.

Application of three-dimensional detailed geometry to simulation of melt progression in an intricate BWR lower head

This study analyzes melt progression with core degradation in the core and lower head of a boiling water reactor using a detailed simulation geometry of an in-house three-dimensional simulation code. Since the Fukushima Daiichi nuclear power plant accident of Tokyo Electric Power Company Holdings (TEPCO) in 2011, the condition of the lower head following melt progression has been a topic of interest worldwide. By taking advantage of the unique characteristics of the three-dimensional simulation code, we focus on achieving a more detailed simulation of the reactor pressure vessel in view of future Fukushima decommissioning processes. Molten corium forms in the core and progresses towards the lower head. When the corium reaches water remaining there, it is fragmented and forms fuel debris on the bottom of lower head. Hence evaluating molten corium breakup with water in the lower head is essential for the coolability of fuel debris and the integrity of the lower head to prevent the release of a large amount of radioactive isotopes. To simulate melt progression together with core degradation effectively, we focused on the development of the detailed simulation geometry comprising the core, the core support plate, and the lower head zones as well as the simplified pedestal of the primary containment vessel. The analysis capabilities due to the detailed simulation geometry were preliminarily evaluated under hypothetical conditions (i) melt progression from the core to the pedestal of primary containment vessel, (ii) failure of the core support plate zone due to molten corium, (iii) water pool behavior in the lower head, (iv) the relocation paths of molten materials via the control rod guide tube/control rod drive housing and instrument guide tube, and (v) mixing behavior of molten corium resulting from different fuel assemblies.

Nonlinear simulations of energetic particle-driven instabilities interacting with Alfvén continuum during frequency chirping

Toroidal Alfvén eigenmodes excited by energetic particles (EPs) and their transition to energetic particle modes are investigated using a three-dimensional nonlinear kinetic-magnetohydrodynamic hybrid simulation code. Both the symmetric chirping inside the Alfvén continuum gap for upward and downward directions and the asymmetric chirping affected by the Alfvén continuum are found in the simulations depending on the EP drive and the mode damping. For weak drive and damping, symmetric frequency chirping is observed with a chirping rate consistent with the Berk–Breizman theory (Berk et al 1997 Phys. Lett. A 234 213). For moderate drive and damping, upward chirping is dominant because downward chirping is interrupted by interaction with the Alfvén continuum. For strong drive and damping, two branches of frequency chirping are found for different poloidal harmonics. The dominant chirping is downward into the Alfvén continuum and the other is an upward chirping inside the Alfvén continuum gap. The creation and the propagation of holes and clumps are found in EP phase space, which is qualitatively consistent with the Berk–Breizman theory.

Effect of 14.7-MeV Protons and 3.6-MeV Alpha Particles on Fusion Structural Materials

Fusion reactors will require specially engineered structural materials that will simultaneously satisfy the harsh conditions, such as high thermomechanical stresses, high heat loads, and severe radiation damage, without compromising on safety considerations. The simulation of 14.7-MeV protons and 3.6-MeV α-particles irradiation processing using different fusion structural materials, such as graphite, titanium, zirconium, molybdenum, tantalum, and tungsten, was studied. The open-source three-dimensional computer simulation code SRIM (2013 version) was used to determine the protons and α-particles penetrability into the target material as well as the range dependence of the protons and α-particles energies. The protons and α-particles distribution range and their trajectories in the target materials were determined. The effect of the target materials’ atomic mass on the 14.7-MeV protons and 3.6-MeV α-particles penetration range was determined. Also, the phonons and ionization of the target materials induced by these irradiated particles were studied.

Development of an icing simulation code for rotating wind turbines

This study aims to develop a three-dimensional icing simulation code named WISE (Wind turbine Icing Simulation code with performance Evaluation) integrated into OpenFOAM®. The freely available source code can contribute to icing simulations that require parallel computations. The rotational motion is explained by a Moving Reference Frame (MRF) in both aerodynamic and droplet fields. The thin water film theory is applied in the thermodynamic module. To verify WISE, ice accretion shapes on NREL Phase VI under rime and glaze icing conditions were considered. The ice accretion shapes obtained by WISE were compared against FENSAP-ICE and another numerical simulation without the MRF method for the droplet field. For the rime condition, the icing limits, maximum thickness, and its location are well predicted by WISE compared with FENSAP-ICE while the simulation without the MRF method overestimates the icing limits and maximum thickness. For the glaze condition, only WISE and FENSAP-ICE results are compared where the icing limits are slightly different. On the suction side, WISE accurately predicts the maximum thickness, ice growth direction, and icing limits. However, the thickness of ice on the pressure side is underestimated. It might be necessary to have a turbulence model that can predict the flow transition.

Development of Three-Dimensional Simulation Code for Two-Phase Flow in a Steam Generator

Development of Three-Dimensional Simulation Code for Two-Phase Flow in a Steam Generator

A three-dimensional approach for simulating BWR core melt progression – A validation against CORA-BWR experimental series

A three-dimensional simulation code has been developed for a Boiling Water Reactor (BWR) to perform two missions: realistic simulation of the phenomena induced in in-vessel core melt progression and evaluation of the composition and condition of molten materials/debris. The current stage of the code development focuses on simulation of the core melt progression from increase in cladding temperature to molten materials relocation, in order to decrease the computational uncertainties. To simulate the core melt progression more realistically, the code has several features: (i) a multi-phase, multi-component and multi-velocity-field, (ii) a three-dimensional geometrical configuration of complicated internal components in the core and lower plenum zones in a reactor pressure vessel of BWR, and detailed modelling of (iii) multiple core materials melt and chemical interactions, (iv) a candling phenomenon and (v) melt blockage in narrow zones. Subsequently to the previous qualitative validation of these physical models, more detailed validation was conducted in the present study for the CORA-BWR experimental series. In the validation, the code has semi-quantitatively simulated the temperature escalation and maximum temperature, the melt progression, the post-test configuration of relocated materials and the hydrogen generation of CORA-16 as the reference case first. Furthermore, the CORA-18, CORA-28 and CORA-33 have been evaluated in terms of the effects of scale (18 versus 48 fuel-rod mockup), pre-oxidation and wet/dry core condition. Additionally, through the CORA-16 and -18 validation, the code showed the capability for predicting the post-test configuration of relocated materials visually by comparing the photos.

CPS construction for laser coating with a general-purpose three-dimensional thermohydraulics numerical simulation code SPLICE

CPS construction for laser coating with a general-purpose three-dimensional thermohydraulics numerical simulation code SPLICE

Impurity transport simulation in the peripheral plasma in the large helical device with tungsten closed helical divertor

Long pulse plasma discharges in the Large Helical Device have been often interrupted by iron dust emission induced by electric arcing on the surface of the vacuum vessel. The iron ions in the peripheral plasma induced by the dust emission enhance physical sputtering and self-sputtering on the divertor plates, which can interrupt the long pulse plasma discharges by radiation collapse. The impurity transport simulation for a tungsten divertor configuration is performed using a three-dimensional edge plasma simulation code (EMC3-EIRENE) under the condition where the iron ions produced by the dust emission cause the sputtering on the tungsten divertor plates. The simulation shows that the sputtered tungsten significantly increases the radiation power by a factor of about 20 compared to that for the carbon divertor configuration in a high plasma temperature condition. The simulation reveals that plasma discharge operation with a high plasma density is desirable for the tungsten divertor. In this operational regime, the radiation power by tungsten ions is significantly reduced by the combined effect of the suppression of the sputtered tungsten and the control of the tungsten ion accumulation by the reduced thermal force in the peripheral plasma.

A generalized quasi-neutral fluid-particle hybrid plasma model and its application to energetic-particle-magnetohydrodynamics hybrid simulation

A generalized fluid-particle hybrid model for collisionless plasmas under the assumption of quasi-neutrality is presented. The system consists of fluid ions and electrons as well as arbitrary numbers of species whose dynamics is governed by the Vlasov equation. The proposed model is thus a generalized version of the well-known standard hybrid plasma simulation model, in which the ions are fully kinetic whereas the electrons are assumed to be a fluid. Since the proposed model employs the exact form of the generalized Ohm's law, the mass and energy densities, as well as the charge-to-mass ratio of the kinetic species, are taken to be arbitrary. In the absence of the kinetic species, it reduces to the quasi-neutral two-fluid model [1]. In the opposite situation where the mass and energy densities of the kinetic species are much larger than the fluid ions, it is nothing more than the standard hybrid model with finite electron inertia effect. If the kinetic species is an energetic particle (EP) population having negligible mass density but substantial energy density and the scale size is much larger than the ion and electron inertial lengths, it describes the self-consistent coupling between the magnetohydrodynamics (MHD) and the EP dynamics. The energetic-particle-magnetohydrodynamics (EP-MHD) hybrid model is thus a special case of the more general model described in this paper. Advantages of this approach over the existing models are discussed. A three-dimensional simulation code solving the proposed set of equations is described. The code combines the Particle-in-Cell scheme for solving the kinetic species and a Riemann-solver-based code for the two-fluid equations. Several benchmark simulation results are shown to confirm that the code successfully captures the dynamics of the EP population interacting self-consistently with the MHD fluid.

Validation progress and exploratory analyses of three-dimensional simulation code for BWR in-vessel core degradation

Based on the information obtained from the severe accident at the Fukushima Daiichi Nuclear Power Plant Units 1–3 in 2011, Regulatory Standard and Research Department, Secretariat of Nuclear Regulation Authority (S/NRA/R) started development of a detailed three-dimensional simulation code for in-vessel core degradation. The simulation code aims at applying to BWR core degradation assessment with three-dimensional geometry. The present paper describes the progress of validation and the assessment of BWR in-vessel core degradation for future application by parametric surveys. In-vessel core degradation phenomena were validated mainly using the CORA-18 experiment at Karlsruhe Institute of Technology to estimate axial- and lateral-directional motion of molten corium. Additionally, metallic melt relocation around a BWR core support plate and molten corium breakup in a lower head were validated by the XR-2 experiment at Sandia National Laboratory, and the FARO L-19 and the KROTOS K-37 experiments at Joint Research Centre facilities of the European Commission, respectively. The code results match severe accident relevant phenomena qualitatively well. Furthermore, as a validation process, the exploratory analyses using 1/4 Sector-Core Geometry in a hypothetical severe accident condition have been carried out for a typical middle-power-level BWR with the following variable parameters as initial core conditions: a water level, a decay heat level, a radial power shape and an oxidation of fuel cladding. These efforts showed that the code could be used for application to the actual core degradation evaluation with three-dimensional geometry in the near future.

High Speed Solar Wind Forecast Model from the Solar Surface to 1AU Using Global 3D MHD Simulation

AbstractEmanating from coronals holes (CHs), high speed streams (HSSs) cause recurrent geomagnetic disturbances in the Earth’s magnetosphere. For this reason being able to predict the occurrence and timing of the high speed solar wind is one of the more important issues in space weather forecasting. Currently, it is still difficult to estimate the effect of a CH in case that it extends from high latitudes to lower ones. To monitor the global solar wind condition we have therefore developed a three-dimensional MHD simulation code, the REProduce Plasma Universe (REPPU) code, that is driven by the solar magnetic field from the solar surface to 1AU. The connectivity of magnetic field lines from CHs to Earth’s orbit via HSSs has been investigated. Simulation results are presented and the usefulness of our model is discussed.

The effect of mountain wind on the falling snow deposition

The air-flow over morphologic prominence is of vital importance for the temporal and spatial variations of snow distribution, which may further affect the hydrological cycle, climate system, ecological evolution as well as other natural processes. Most previous studies have neglected the effect of non-uniform mountain wind on the trajectory of falling snow particle and thus the uneven snow distribution over complex terrain is little known. Here in this paper, we carry out a numerical study on the deposition process of mixed grain size snow particles over mountain terrains. A three-dimensional large eddy simulation (LES) code is used to predict the wind field and the fluid-solid coupling effect is considered, the Lagrangian particle tracking method is employed to track the movement of each falling snow particle. Our results suggest the boundary layer flow over steep slopes or complex terrains exhibits obvious uneven characteristics. The mountain wind has obvious effect on the motion of snow particles and finally results in a non-uniform distribution of snow. This research is of significance to understand the evolution of high resolution snow distribution in cold highland areas.

Vertical profiles and two-dimensional distributions of carbon line emissions from C2+−C5+ ions in attached and RMP-assisted detached plasmas of large helical device

In Large Helical Device (LHD), the detached plasma is obtained without external impurity gas feed by supplying an m/n = 1/1 resonant magnetic perturbation (RMP) field to a plasma with an outwardly shifted plasma axis position of Rax = 3.90 m where the magnetic resonance exists in the stochastic magnetic field layer outside the last closed flux surface. The plasma detachment is triggered by the appearance of an m/n = 1/1 island when the density, increased using hydrogen gas feed, exceeds a threshold density. The behavior of intrinsically existing impurities, in particular, carbon originating in the graphite divertor plates, is one of the important key issues to clarify the characteristic features of the RMP-assisted plasma detachment although the particle flux still remains on some divertor plates even in the detachment phase of the discharge. For this purpose, vertical profiles and two-dimensional (2-D) distributions of edge carbon emissions of CIII to CVI have been measured at extreme ultraviolet wavelength range, and the results are compared between attached and RMP-assisted detached plasmas. It is found that the CIII and CIV emissions located in the stochastic magnetic field layer are drastically increased near the m/n = 1/1 island O-point and in the vicinity of both inboard and outboard edge separatrix X-points during the RMP-assisted detachment, while those emissions are only enhanced in the vicinity of the outboard edge X-point in attached plasmas without RMP. The result clearly indicates a change in the magnetic field lines connecting to the divertor plates, which is caused by the growth of the m/n = 1/1 edge magnetic island. In contrast, the intensity of CVI emitted radially inside the magnetic island significantly decreases during the detachment, suggesting an enhancement of the edge impurity screening. The measured carbon distribution is analyzed with a three-dimensional edge plasma transport simulation code, EMC3-EIRENE, for the attached plasmas without RMP. It is found that the narrow strip-shaped impurity trace emitted along the edge X-point and its width are sensitive to the cross-field impurity diffusion coefficient, DZ⊥. As a result, the value of DZ⊥ of C3+ ions is evaluated to be 20 times larger than that of the bulk ions in the Rax = 3.90 m configuration, while the reason is unclear at present. The measured 2-D carbon distribution is also discussed and compared to the structure of the m/n = 1/1 magnetic island, which quickly expanded during the appearance of the plasma detachment.