Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “3D Modeling”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 1,405 records · Page 78
All sourcesNASA NTRSDOE OSTI
DOE OSTI2016

Study of Convection Heat Transfer in a Very High Temperature Reactor Flow Channel: Numerical and Experimental Results

Very High Temperature Reactors (VHTRs) are one of the Generation IV gas-cooled reactor models proposed for implementation in next generation nuclear power plants. A high temperature/pressure test facility for forced and natural circulation experiments has been constructed. This test facility consists of a single flow channel in a 2.7 m (9’) long graphite column equipped with four 2.3kW heaters. Extensive 3D numerical modeling provides a detailed analysis of the thermal-hydraulic behavior under steady-state, transient, and accident scenarios. In addition, forced/mixed convection experiments with air, nitrogen and helium were conducted for inlet Reynolds numbers from 500 to 70,000. Our numerical results were validated with forced convection data displaying maximum percentage errors under 15%, using commercial finite element package, COMSOL Multiphysics. Based on this agreement, important information can be extracted from the model, with regards to the modified radial velocity and property gas profiles. Our work also examines flow laminarization for a full range of Reynolds numbers including laminar, transition and turbulent flow under forced convection and its impact on heat transfer under various scenarios to examine the thermal-hydraulic phenomena that could occur during both normal operation and accident conditions.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
NASA NTRS2002

An Illumination Modeling System for Human Factors Analyses

Seeing is critical to human performance. Lighting is critical for seeing. Therefore, lighting is critical to human performance. This is common sense, and here on earth, it is easily taken for granted. However, on orbit, because the sun will rise or set every 45 minutes on average, humans working in space must cope with extremely dynamic lighting conditions. Contrast conditions of harsh shadowing and glare is also severe. The prediction of lighting conditions for critical operations is essential. Crew training can factor lighting into the lesson plans when necessary. Mission planners can determine whether low-light video cameras are required or whether additional luminaires need to be flown. The optimization of the quantity and quality of light is needed because of the effects on crew safety, on electrical power and on equipment maintainability. To address all of these issues, an illumination modeling system has been developed by the Graphics Research and Analyses Facility (GRAF) and Lighting Environment Test Facility (LETF) in the Space Human Factors Laboratory at NASA Johnson Space Center. The system uses physically based ray tracing software (Radiance) developed at Lawrence Berkeley Laboratories, a human factors oriented geometric modeling system (PLAID) and an extensive database of humans and environments. Material reflectivity properties of major surfaces and critical surfaces are measured using a gonio-reflectometer. Luminaires (lights) are measured for beam spread distribution, color and intensity. Video camera performances are measured for color and light sensitivity. 3D geometric models of humans and the environment are combined with the material and light models to form a system capable of predicting lighting conditions and visibility conditions in space.

Huynh, Thong↗
DOE OSTI2015

Numerical Model of Thermoelectric Topping Cycle of Coal-Fired Power Plant

Traditional fossil fuel power generation process typically has low efficiency. Large amount of the energy loss in Rankine cycle steam turbines (ST) is due to the temperature difference between the combustion flame temperature ~2250 K (adiabatic) and the high pressure steam temperature up to 900 K. However, some of this energy can be harvested using solid-state thermoelectric (TE) power generators which are placed into the gap between the flame temperature and the steam temperature that produce additional electrical power. This study investigates the potential placement of TE on water tube wall inside a boiler at a coal-fired power plant. Three-dimensional (3D) numerical model of a simplified TE module is developed, and hot gas temperature and steam temperature from the boiler are used as boundary conditions at the hot side and cold side of the TE. The numerical results are compared with analytical calculations. The 3D effects of the thermal spreading in the TE module are investigated. Parameters such as TE leg cross section area and TE fill factor are examined in order to maximize the electrical power production of the TE without sacrificing the boiler efficiency (i.e., reducing the steam temperature). The study also looks into the various locations inside the boiler that have good potential for TE installation.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2025

ThinCurr: An open-source 3D thin-wall eddy current modeling code for the analysis of large-scale systems of conducting structures

In this paper we present a new thin-wall eddy current modeling code, ThinCurr, for studying inductively-coupled currents in 3D conducting structures -- with primary application focused on the interaction between currents flowing in coils, plasma, and conducting structures of magnetically-confined plasma devices. The code utilizes a boundary finite element method on an unstructured, triangular grid to accurately capture device structures. The new code, part of the broader Open FUSION Toolkit, is open-source and designed for ease of use without sacrificing capability and speed through a combination of Python, Fortran, and C/C++ components. Scalability to large models is enabled through use of hierarchical off-diagonal low-rank compression of the inductance matrix, which is otherwise dense. Ease of handling large models of complicated geometry is further supported by automatic determination of supplemental elements through a greedy homology approach. Here, a detailed description of the numerical methods of the code and verification of the implementation of those methods using cross-code comparisons against the VALEN code and Ansys commercial analysis software is shown.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1993

Design strategies and functionality of the Visual Interface for Virtual Interaction Development (VIVID) tool

Development of interactive virtual environments (VE) has typically consisted of three primary activities: model (object) development, model relationship tree development, and environment behavior definition and coding. The model and relationship tree development activities are accomplished with a variety of well-established graphic library (GL) based programs - most utilizing graphical user interfaces (GUI) with point-and-click interactions. Because of this GUI format, little programming expertise on the part of the developer is necessary to create the 3D graphical models or to establish interrelationships between the models. However, the third VE development activity, environment behavior definition and coding, has generally required the greatest amount of time and programmer expertise. Behaviors, characteristics, and interactions between objects and the user within a VE must be defined via command line C coding prior to rendering the environment scenes. In an effort to simplify this environment behavior definition phase for non-programmers, and to provide easy access to model and tree tools, a graphical interface and development tool has been created. The principal thrust of this research is to effect rapid development and prototyping of virtual environments. This presentation will discuss the 'Visual Interface for Virtual Interaction Development' (VIVID) tool; an X-Windows based system employing drop-down menus for user selection of program access, models, and trees, behavior editing, and code generation. Examples of these selection will be highlighted in this presentation, as will the currently available program interfaces. The functionality of this tool allows non-programming users access to all facets of VE development while providing experienced programmers with a collection of pre-coded behaviors. In conjunction with its existing, interfaces and predefined suite of behaviors, future development plans for VIVID will be described. These include incorporation of dual user virtual environment enhancements, tool expansion, and additional behaviors.

Nguyen, Lac↗
NASA NTRS1992

Shinnery oak bidirectional reflectance properties and canopy model inversion

Field measurements are presented, together with the results of a 3D canopy-model inversion for sand shinnery oak community in western Texas. The spectral bidirectional radiance measurements were in three spectral channels encompassing both the complete land surface and sky hemispheres. The changes in canopy reflectance that occur with variations in solar zenith angle and view direction for two seasons of the year were evaluated, and the 3D radiation-interaction model was inverted to estimate the oak leaf area index and canopy density from the reflectance data.

Deering, Donald W.↗
DOE OSTI2012

Orebody Modelling for Exploration: The Western Mineralisation, Broken Hill, NSW

The Western Mineralisation in the Broken Hill deposit was studied to identify the zonation sequence of lithogeochemical haloes along and across the strike of the orebody. Samples used are from 77 drill holes and the samples were assayed for Pb, Zn, Fe, S, Cu, Ag, Cd, Sb, Bi and As. Variogram analyses were calculated for all the elements and kriging was used to construct the 3D block model. Analysis of cross sections along and across the strike of the orebody shows that Bi and Sb form broader halos around sulphide masses and this suggests that they are pathfinder elements for the Pb and Zn elements of this orebody. The threshold concentrations (minimum anomaly) of the 10 elements were determined using the concentration-area analysis. On east-west vertical cross sections, the values of linear productivity, variability gradient and zonality index were calculated for each element. Based on the maximum zonality index of each element, the sequence of geochemical zonation pattern was determined from top to bottom of the orebody. The result shows that S, Pb, Zn and Cd tend to concentrate in the upper part of the mineralisation whereas Ag, Cu, Bi and As have a tendency to concentrate in the lower part of the mineralised rocks. Also, an empirical product ratio index was developed based on the position of the elements in the zonation sequence. The methods and results of this research are applicable to exploration of similar Zn and Pb sulphide ore deposits.

58 GEOSCIENCES↗
DOE OSTI2015

Atomistic to continuum modeling of solidification microstructures

We summarize recent advances in modeling of solidification microstructures using computational methods that bridge atomistic to continuum scales. We first discuss progress in atomistic modeling of equilibrium and non-equilibrium solid–liquid interface properties influencing microstructure formation, as well as interface coalescence phenomena influencing the late stages of solidification. The latter is relevant in the context of hot tearing reviewed in the article by M. Rappaz in this issue. We then discuss progress to model microstructures on a continuum scale using phase-field methods. We focus on selected examples in which modeling of 3D cellular and dendritic microstructures has been directly linked to experimental observations. Finally, we discuss a recently introduced coarse-grained dendritic needle network approach to simulate the formation of well-developed dendritic microstructures. The approach reliably bridges the well-separated scales traditionally simulated by phase-field and grain structure models, hence opening new avenues for quantitative modeling of complex intra- and inter-grain dynamical interactions on a grain scale.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Small-Scale Variability of Solar Radiation (S2VSR) Field Campaign Report

Clouds introduce significant variability in solar radiation, in particular for shallow cumulus and other convective cloud types. Variability at small spatio-temporal scales (specifically below 1 min and 1 km) is, however, not properly resolved by current satellite observations nor atmospheric models. Additionally, 3D photon transport is commonly neglected in analyses and causes significant deviations in 1D radiative transfer simulations at such small scales. A specific challenge is to account for the point-like nature of traditional surface radiative flux measurements in comparison to spatially averaged quantities such as satellite pixel radiances or fluxes representing model grid boxes.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2013

Design optimization of MR-compatible rotating anode x-ray tubes for stable operation

Purpose: Hybrid x-ray/MR systems can enhance the diagnosis and treatment of endovascular, cardiac, and neurologic disorders by using the complementary advantages of both modalities for image guidance during interventional procedures. Conventional rotating anode x-ray tubes fail near an MR imaging system, since MR fringe fields create eddy currents in the metal rotor which cause a reduction in the rotation speed of the x-ray tube motor. A new x-ray tube motor prototype has been designed and built to be operated close to a magnet. To ensure the stability and safety of the motor operation, dynamic characteristics must be analyzed to identify possible modes of mechanical failure. In this study a 3D finite element method (FEM) model was developed in order to explore possible modifications, and to optimize the motor design. The FEM provides a valuable tool that permits testing and evaluation using numerical simulation instead of building multiple prototypes.Methods: Two experimental approaches were used to measure resonance characteristics: the first obtained the angular speed curves of the x-ray tube motor employing an angle encoder; the second measured the power spectrum using a spectrum analyzer, in which the large amplitude of peaks indicates large vibrations. An estimate of the bearing stiffness is required to generate an accurate FEM model of motor operation. This stiffness depends on both the bearing geometry and adjacent structures (e.g., the number of balls, clearances, preload, etc.) in an assembly, and is therefore unknown. This parameter was set by matching the FEM results to measurements carried out with the anode attached to the motor, and verified by comparing FEM predictions and measurements with the anode removed. The validated FEM model was then used to sweep through design parameters [bearing stiffness (1×10{sup 5}–5×10{sup 7} N/m), shaft diameter (0.372–0.625 in.), rotor diameter (2.4–2.9 in.), and total length of motor (5.66–7.36 in.)] to increase the fundamental frequency past the operating range at 50 Hz.Results: The first large vibration during the prototype motor operation was obtained at 21.64±0.68 Hz in the power spectrum. An abrupt decrease in acceleration occurred at 21.5 Hz due to struggling against the resonance vibrations. A bearing stiffness of 1.2×10{sup 5} N/m in the FEM simulation was used to obtain a critical speed of 21.4 Hz providing 1.1% error. This bearing stiffness value and the 3D model were then confirmed by the experiments with the anode removed, demonstrating an agreement within 6.4% between simulation results and measurements. A calculated first critical frequency (fundamental frequency) of 68.5 Hz was obtained by increasing the bearing stiffness to 1×10{sup 7} N/m and increasing the shaft diameter by 68.0%. Reducing the number of bearings in the design permits decreasing the total length of the motor by 1.7 in., and results in a fundamental frequency of 68.3 Hz in concert with additional changes (shaft diameter of 0.625 in., rotor diameter of 2.4 in., and bearing stiffness of 1×10{sup 6} N/m).Conclusions: An FEM model of the x-ray tube motor has been implemented and experimentally validated. A fundamental frequency above the operational rotation speed can be achieved through modification of multiple design parameters, which allows the motor to operate stably and safely in the MR environment during the repeated acceleration/deceleration cycles required for an interventional procedure. The validated 3D FEM model can now be used to investigate trade-offs between generated torque, maximum speed, and motor inertia to further optimize motor design.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
NASA NTRS2021

Cold Season Performance of the NU-WRF Regional Climate Model in the Great Lakes Region

As Earth’s largest collection of freshwater, the Laurentian Great Lakes have enormous ecological and socio-economic value. Their basin has become a regional hotspot of climatic and limnological change, potentially threatening its vital natural resources. Consequentially, there is a need to assess the current state of climate models regarding their performance across the Great Lakes region and develop the next generation of high-resolution regional climate models to address complex limnological processes and lake-atmosphere interactions. In response to this need, the current paper focuses on the generation and analysis of a 20-member ensemble of 3-km National Aeronautics and Space Administration (NASA)-Unified Weather Research and Forecasting (NU-WRF) simulations for the 2014-2015 cold season. The study aims to identify the model’s strengths and weaknesses; optimal configuration for the region; and the impacts of different physics parameterizations, coupling to a 1D lake model, time-variant lake-surface temperatures, and spectral nudging. Several key biases are identified in the cold-season simulations for the Great Lakes region, including an atmospheric cold bias that is amplified by coupling to a 1D lake model but diminished by applying the Community Atmosphere Model radiation scheme and Morrison microphysics scheme; an excess precipitation bias; anomalously early initiation of fall lake turnover and subsequent cold lake bias; excessive and overly persistent lake ice cover; and insufficient evaporation over Lakes Superior and Huron. The research team is currently addressing these key limitations by coupling NU-WRF to a 3D lake model in support of the next generation of regional climate models for the critical Great Lakes Basin.

Michael Notaro↗
DOE OSTI2021

Three-dimensional Hydrodynamic Simulations of Convective Nuclear Burning in Massive Stars Near Iron Core Collapse

Nonspherical structure in massive stars at the point of iron core collapse can have a qualitative impact on the properties of the ensuing core-collapse supernova explosions and the multimessenger signals they produce. Strong perturbations can aid successful explosions by strengthening turbulence in the postshock region. Here we report on a set of 4π 3D hydrodynamic simulations of O- and Si-shell burning in massive star models of varied initial masses using MESA and the FLASH simulation framework. We evolve four separate 3D models for roughly the final 10 minutes prior to and including iron core collapse. We consider initial 1D MESA models with masses of 14, 20, and 25 M ⊙ to survey a range of O/Si-shell density and compositional configurations. Further, we characterize the convective shells in our 3D models and compare them to the corresponding 1D models. In general, we find that the angle-average convective speeds in our 3D simulations near collapse are three to four times larger than the convective speeds predicted by MESA at the same epoch for our chosen mixing length parameter of α MLT = 1.5. In three of our simulations, we observe significant power in the spherical harmonic decomposition of the radial velocity field at harmonic indices of ℓ = 1–3 near collapse. Our results suggest that large-scale modes are common in massive stars near collapse and should be considered a key aspect of presupernova progenitor models.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2019

An integrated two-dimensional modeling method for predicting ductility of thin-walled die cast magnesium

In this paper, a two-dimensional (2D) microstructure-based modeling method is developed in order to predict the ductility of a thin-walled high pressure die cast magnesium (Mg) by considering the three-dimensional (3D) thru-thickness pore distributions. For this purpose, a series of 3D synthetic microstructure-based finite element models and the corresponding 2D models are first generated with various pore volume fractions, pore size distributions and pore shapes. The input material properties for the 2D models are determined based on the 3D cubic model with a spherical pore and the generalized Neuber’s rule. Based on the resulting ductility of the 3D and 2D models, a 3D/2D ductility correlation curve is developed as a function of the characteristics/shape of the input fracture strain curve used in the 3D model. The validity of the ductility correlation curve is examined with casting samples with actual microstructures. Here, the results show that the suggested 2D modeling methodology can be used together with the ductility correlation curve in predicting the ductility of thin-walled Mg castings.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Second-generation dust in planetary systems: the case of HD 163296

Observations indicate that large, dust-laden protoplanetary discs are common. Some features, like gaps, rings, and spirals, suggest they may host young planets, which can excite the orbits of nearby leftover planetesimals. Energetic collisions among these bodies can lead to the production of second-generation dust. Grains produced by collisions may have a dynamical behaviour different from that of first-generation, primordial dust out of which planetesimals and planets formed. Here, we aim to study these differences for the HD 163296 system and determine whether dynamical signatures in the mixture of the two dust populations can help separate their contributions. We use three-dimensional (3D) hydrodynamic models to describe the gaseous disc with three, Saturn- to Jupiter-mass, embedded planets. Dust grains, of sizes $1\, \mu \mathrm{m}$–$1\, \mathrm{mm}$, are treated as Lagrangian particles with resolved thermodynamics and mass-loss. Initial disc and planet configurations are derived from observation-based work, which indicates low gas viscosity. The 3D approach also allows us to detect the formation of vortices induced by Rossby waves, where dust becomes concentrated and may contribute to planetesimal formation. We find that the main differences in the dynamical behaviour of first- and second-generation dust occur in the vertical distribution. The two populations have similar distributions around the disc mid-plane, although second-generation dust shows longer residence times close to the radial locations of the planets’ gas gaps. Sedimentation rates of $\mu$m-sized grains are comparable to or lower than the production rates by planetesimals’ collisions, making this population potentially observable. These outcomes can be extended to similar systems harbouring giant planets.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

Gulf of Mexico miocene CO₂ site characterization mega transect

This project characterized the Miocene-age sub-seafloor stratigraphy in the near-offshore portion of the Gulf of Mexico adjacent to the Texas coast. The large number of industrial sources of carbon dioxide (CO₂) in coastal counties and the high density of onshore urbanization and environmentally sensitive areas make this offshore region extremely attractive for long-term storage of carbon dioxide emissions from industrial sources (CCS). The study leverages dense existing geologic data from decades of hydrocarbon exploration in and around the study area to characterize the regional geology for suitability and storage capacity. Primary products of the study include: regional static storage capacity estimates, sequestration “leads” and prospects with associated dynamic capacity estimates, experimental studies of CO₂-brine-rock interaction, best practices for site characterization, a large-format ‘Atlas’ of sequestration for the study area, and characterization of potential fluid migration pathways for reducing storage risks utilizing novel high-resolution 3D (HR3D) seismic surveys. In addition, three subcontracted studies address source-to-sink matching optimization, offshore well bore management and environmental aspects. The various geologic data and interpretations are integrated and summarized in a series of cross-sections and maps, which represent a primary resource for any near-term commercial deployment of CCS in the area. The regional study characterized and mapped important geologic features (e.g., Clemente-Tomas fault zone, the regionally extensive Marginulina A and Amphistegina B confining systems, etc.) that provided an important context for regional static capacity estimates and specific sequestration prospects of the study. A static capacity estimate of the majority of the Study area (14,467 mi 2 ) was estimated at 86 metric Gigatonnes. While local capacity estimates are likely to be lower due to reservoir-scale characteristics, the offshore Miocene interval is a storage resource of National interest for providing CO₂ storage as an atmospheric emissions abatement strategy. The natural petroleum system was used as an analog to infer seal quality and predict possible migration pathways of fluids in an engineered system of anthropogenic CO₂ injection and storage. The regional structural features (e.g., Clemente-Tomas fault zone) that exert primary control on the trapping and distribution of Miocene hydrocarbons are expected to perform similarly for CCS. Industrial-scale CCS will require storage capacity utilizing well-documented Miocene hydrocarbon (dominantly depleted gas) fields and their larger structural closures, as well as barren (unproductive, brine-filled) closures. No assessment was made of potential for CO₂ utilization for enhanced oil and gas recovery. The use of 3D numerical fluid flow simulations have been used in the study to greatly assist in characterizing the potential storage capacity of a specific reservoir. Due to the complexity of geologic systems (stratigraphic heterogeneity) and inherent limitations on producing a 3D geologic model, these simulations are typically simplified scenarios that explore the influence of model property variability (sensitivity study). A specific site offshore San Luis Pass (southern Galveston Island) was undertaken successfully, indicating stacked storage potential. Downscaling regional capacity estimates to the local scale (and the inverse) has proven challenging, and remains an outstanding gap in capacity assessments. In order to characterize regional seal performance and identify potential brine and CO₂ leakage pathways, results from three high-resolution 3D (HR3D) seismic datasets acquired by the study using novel HR3D (P-Cable) acquisition system showed steady and significant improvements in data quality because of improved acquisition and processing technique. Finely detailed faults and stratigraphy in the shallowest 1000 milliseconds (~800 m) of data allowed for the identification and mapping of unconformable surfaces including what is probably a surface associated with the last Pleistocene glacial lowstand. The identification of a previously unrecognized (in commercial seismic data) gas chimney that was clearly defined in the 2013 HR3D survey, indicates that HR3D surveys may be useful as both a characterization tool for the overburden of a potential carbon sequestration site and as an additional monitoring tool for future engineered injection sites. Geochemical modeling indicated that injection of CO₂ would result in minor dissolution of calcite, K-feldspar and albite. In addition, modeling of typical brines in Miocene age rocks indicate that approximately 5% of injection capacity would result from CO₂ dissolution into the brine. After extensive searches, no rock samples of the Marginulina A and Amphistegina B seals (“caprocks”) were obtained, but analyses of available core samples of other Miocene age mudrocks (seals or caprocks) indicate that they have sealing ability sufficient for potential CO 2 storage in underlying sandstone units.

01 COAL, LIGNITE, AND PEAT↗
DOE OSTI2015

Modification of transparent materials with ultrashort laser pulses: What is energetically and mechanically meaningful?

A comprehensive analysis of laser-induced modification of bulk glass by single ultrashort laser pulses is presented which is based on combination of optical Maxwell-based modeling with thermoelastoplastic simulations of post-irradiation behavior of matter. A controversial question on free electron density generated inside bulk glass by ultrashort laser pulses in modification regimes is addressed on energy balance grounds. Spatiotemporal dynamics of laser beam propagation in fused silica have been elucidated for the regimes used for direct laser writing in bulk glass. 3D thermoelastoplastic modeling of material relocation dynamics under laser-induced stresses has been performed up to the microsecond timescale when all motions in the material decay. The final modification structure is found to be imprinted into material matrix already at sub-nanosecond timescale. Modeling results agree well with available experimental data on laser light transmission through the sample and the final modification structure.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1994

Core magnetic field enhancement in single X line, multiple X line and patchy reconnection

Magnetic flux transfer events often show a significant increase of the magnetic field strength at the center of the events. Similar magnetic field observations have been reported for structures in or near the plasma sheet of the magnetotail at about 20 R(sub E). We have carried out two-dimensional (2D) and three-dimensional (3D) and simulations of single X line reconnection (SXR), multiple X line reconnection (MXR), and patchy reconnection to determine and compare the amplification of the magnetic field in the center of the developing flux tubes. The various processes are achieved by appropriate choices of 2D or 3D resistivity models. The simulations show that the increase in magnetic field strength depends on both the property of the initial configuration and the particular reconnection geometry. For the chosen initial conditions the MXR process leads to a larger increase in the core magnetic field than the patchy reconnection and SXR caused by larger magnetic tensions in the MXR process. The 3D processes always lead to a larger amplification than the corresponding 2D processes. In the 3D cases, force imbalance in the y direction will accelerate plasma out of the flux tube. This process reduces the thermal pressure and leads to a further compression of the flux rope, which yields an additional increase in the interior magnetic field strength.

Ma, Z. W.↗