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At least 91 records · Page 5

Molten pool dynamics and humping suppression in high-speed laser welding via tailored beam configurations

High-speed laser welding is essential for increasing the production rate of fuel cell fabrication. However, when the welding speed exceeds a critical limit, humping occurs and reduces the weld quality. In this study, two tailored beam configurations, including an adjustable ring mode and a dual-beam configuration, were employed to suppress humping. Computational fluid dynamics simulations were performed to elucidate the underlying suppression mechanisms. Here, the results show that, in the adjustable ring mode, humping mitigation arises from a reduced backward cross-sectional melt flow rate and a more stable molten pool. In the dual-beam configuration, humping suppression is attributed to the deceleration of melt flow, the conduction-mode behavior of the trailing beam, and the widening of the molten pool induced by the trailing laser. Furthermore, because the dual-beam configuration directly modifies the trailing molten pool dynamics, it achieves more effective humping suppression, extending the welding speed limit to 1.50 m/s, compared with 1.00 m/s for the adjustable ring mode.

08 HYDROGEN↗

Tool-workpiece stick-slip conditions and their effects on torque and heat generation rate in the friction stir welding

Friction stir welding (FSW) has found increased applications in automotive and aerospace industries due to its advantages of solid-state bonding, no fusion and melting, and versatility in various working conditions and material combinations. However, the relationship among processing parameters, material properties, and bonding extent and fidelity remains largely empirical, primarily because of the lack of the mechanistic understanding of the tool-workpiece frictional behavior that affects our subsequent understanding of microstructural evolution and interface bonding formation. While the tool-workpiece stick-slip condition is believed to dictate the resulting torque and heat generation rate during the welding process, it remains rare and elusive to conduct a quantitative experimental measurement of such interfacial field. On the other hand, numerical simulations based on Computational Fluid Dynamics (CFD) rely on ad hoc assumptions of interfacial pressure and shear-stress conditions, but predictions can only be validated via the medium- and far-range temperature field which is known to be insensitive to the interfacial frictional behavior. This work first presents a comparison among two CFD-based simulation methodologies and the Coupled Eulerian Lagrangian (CEL) model in finite element method, the last of which uses the Coulomb friction so that the stick-slip is naturally developed. Based on the Hill-Bower similarity relationship in the contact analysis, an analytical model is developed here to prove why a constant stick-slip fraction will be developed in the steady state, to correlate the stick-slip fraction to processing parameters such as the tool spin rate, and further to derive dimensionless functions for torque and heat-generation-rate predictions. Pros and cons of various numerical approaches in predicting stick-slip are discussed, and our analytical model has been found to agree well with our numerical simulation and literature experimental results. These analyses provide the critical strain-rate and temperature fields that are needed for the bonding analysis in our future work.

36 MATERIALS SCIENCE↗

Reduction of Methane Leaks through Corrosion Mitigation Pre-treatments for Pipelines with Field Applied Coatings

Corrosion of buried, coated steel pipelines transporting natural gas is a significant source of methane emissions, from pipeline venting required for maintenance and repairs and from pipeline leaks and incidents. Corrosion of steel under field applied coatings is an important safety concern for the pipeline industry. This project investigates the application of a field applied alloy over girth welds to mitigate external corrosion of buried coated steel pipelines. Various metallic coating options were considered, which were required to meet several criteria: (1) it must resist corrosion under open-circuit or mild cathodic protection conditions, (2) it must protect the substrate steel, and (3) it must not negatively affect the adhesion of the field coating. Finite element models and lab testing were performed of alloy coating compositions to identify promising alloy types underneath disbonded coatings. Polarization curves of coating alloys were generated to provide the boundary conditions for the COMSOL model to compute potential and current distributions around coated areas. Sacrificial and corrosion-resistant metal alloy coatings were evaluated and optimized using corrosion modeling and laboratory electrochemical testing, where aluminum alloy 5356 (5% Mg) and steel alloy B9 (9% Cr) were selected. Corrosion test coupons were designed and fabricated using thermal spray aluminum 5356 and welded B9 steel overlays on API 5L grade X42 line pipe steel. The corrosion test coupons, with simulated pipe coating damage, were tested in a laboratory soil box and a field pipeline site in Texas for 3-months. Corrosion test coupons were then tested for 6-months at field pipeline sites in Texas and Tennessee to quantify corrosion rates and performance of the aluminum and steel alloys under polyethylene tape and 2-part epoxy coatings, various coating holidays, and with and without cathodic protection.

03 NATURAL GAS↗

A FEASIBILITY STUDY ON CRACK REPAIR IN AUSTENITIC STAINLESS STEEL DRY STORAGE CANISTERS USING ISOTHERMAL FRICTION STIR WELDING

In recent time, solid state crack repair techniques in spent nuclear fuel dry storage canisters (SNF-DSC) have garnered significant interest. Plates of austenitic stainless steels are usually arc welded to fabricate the cylindrical canisters which are prone to chloride-induced stress corrosion cracking. Friction stir welding (FSW) is considered to be a potential candidate for damage repair. In this work, electrical discharge machining was used to simulate cracks in 304L stainless steel plates of 12.7 mm thickness. Subsequently, isothermal FSW was carried out at two different temperatures (725 and 825°C) in order to repair the simulated crack. Microstructure-mechanical property correlations in FSWed plates were studied in detail. Significant grain refinement observed in the stir zone (SZ) was attributed to dynamic recrystallization occurring during FSW. A comparison of Vickers microhardness showed higher hardness and homogeneity in the 725°C SZ than its 825°C counterpart. The fraction of S3 boundary is found to be low in the SZ as compared to base metal (BM). Yield strength of the joints was found to be approximately 100 MPa higher than that of the BM accompanied by a drop in ductility by a factor of 2. Residual stress profile across 825°C weld was measured using x-ray diffraction.

Bhattacharyya, Madhumanti↗

Galvanic corrosion of AZ31B joined to dual-phase steel with and without Zn layer by ultrasonic and friction stir welding

Galvanic corrosion of AZ31B joined with bare or Zn-coated DP590 steel by ultrasonic spot welding or linear friction stir welding was quantitatively studied by pre-defining anode and cathode in the lap joint samples. Corrosion volume and depth from Mg anode surfaces exposed to 0.1 M sodium chloride solution was analyzed as functions of cathode surface type and welding method. Characterization of as-welded joints was performed to identify any microstructural feature of the bonding zone that could impact galvanic corrosion behavior. COMSOL modeling with modified user subroutine was conducted to simulate the progression of Mg corrosion in the same joint and electrode configurations used for the corrosion experiments. The experimental results indicated that Zn-coated cathode surface can reduce Mg galvanic corrosion significantly as galvanic polarization and cathodic current on Zn-coated surface remained relatively low for Mg in the weld joints. COMSOL modeling described the growth of Mg galvanic corrosion in a reasonable manner but showed limitation by underestimating the corrosion volume as it did not capture self-corrosion.

36 MATERIALS SCIENCE↗

A Hybrid AI/ML and Computational Mechanics Based Approach for Time-Series State and Fatigue Life Estimation of Nuclear Reactor Components

Environmental fatigue modeling is a complex problem due to multiple failure modes and their intermixing. The failure modes are function of various underlying causes in addition to the corrosive effect of reactor coolant environment. Some of the major causes are time-dependence of material associated with cyclic loading, load sequence effect associated with random/variable amplitude loading, effect of strain amplitude and rates, effect of varying temperature (along both temporal and spatial directions) and the effect of mean strain and stress. The nonlinear intermixing of failure modes associated with above mentioned causing parameters makes the environmental fatigue modeling is a challenging task. Because of this challenge, fatigue is traditionally being modeled based on experimental data. However, test based empirical approach often requires hundreds of fatigue tests to model the above-mentioned intermixing failure causes even for a single material system. The problem is further exaggerated for reactor component made from multi-material systems such as made from both carbon and stainless-steel base metals and their similar and dissimilar metal welds. With the difficulty of conducting hundreds of fatigue tests to capture the above-mentioned intermixing failure causes, fatigue modeling approaches often depends on empirical models based on limited available test data such as available through ASME code and NUREG 6909. However, these limited test-data-based models may not be enough to accurately predict the life of reactor components. Accurate prediction of life of reactor component would become a necessity, particularly when the license of the reactors to be extended for long-term-operation (LTO) that is for well beyond its original design life of 40 years. The requirement of extending the license of reactor under LTO requires hundreds of fatigue tests to be conducted to understand the mechanism associated with the above-mentioned interdependent failure causes. However, conducting large number of fatigue tests is not a feasibility due to the cost involved. To address this issues Argonne National Laboratory (ANL) with the sponsorship of DOE Light Water Reactor Sustainability (LWRS) program trying to develop a hybrid predictive modeling approach. This is based on limited experiment-data, Artificial-intelligence (AI) – Machine-Learning (ML) - Deep-Learning (DL) based techniques and Multiphysics-computational-mechanics based modeling tools. The hybrid approach not-only can improve the accuracy of the existing stress analysis and fatigue modeling approach but also can reduce the over-dependency on test-based approach. Towards this goal following are some of the major contributions based on ANL’s FY-20 environmental fatigue modeling activities: 1) A cyclic plasticity material model database for 82/182 dissimilar metal weld, which can be readily shared with US nuclear industry and regulatory agency on request. 2) A well validated analytical modeling methodology to perform cycle-by-cycle stress prediction under both constant amplitude fatigue loading and variable amplitude fatigue loading (with load-sequence effect). 3) An AI/ML/DL based methodology to predict unmeasurable cyclic strain based on other available sensor signals. This type of approach can be used for estimating strain in real reactor components from other sensor readings. 4) An AI/ML based approach to improve the US capability on environmental fatigue testing. This is by improving ANL’s existing environmental fatigue testing capacity to conduct ASME required strain-controlled tests (by controlling strain amplitudes and its rate), while not measuring the strain (due to the difficulty of placing an extensometer in a narrow autoclave in a PWR-water-test system). 5) A simulation and experiment based probabilistic modeling methodology for time-series fatigue state and life estimation of reactor metal such as dissimilar metal weld.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

On-target uniformity of the OMEGA 60-beam inertial confinement fusion laser

Successful direct-drive inertial confinement fusion (ICF) experiments require excellent on-target laser 9 irradiance uniformity maintained over the duration of the pulse. Achieving this symmetry relies on maintaining an 10 energy, power, and fluence balance among all beams in a multibeam laser system. As a result of the improvements 11 described in this paper, the OMEGA 60-beam laser performance has been assessed at approximately 2% on-target 12 irradiance nonuniformity using an updated performance assessment metric that accounts for the laser diagnostic noise 13 floor. The performance is measurement-limited, prompting the need for an improved diagnostic suite. This manuscript 14 provides a comprehensive first-order assessment of extant status of on-target energy, power, and fluence uniformity 15 and explores avenues for improvements.

Diagnostics↗

Time-Dependent 600 °C Post-Weld Heat Treatment Response of Laser-Wire-Directed Energy Deposited Austenitic Stainless Steel Claddings on Carbon Steel

Austenitic stainless steel overlay claddings are often used to protect nuclear reactor pressure vessels from corrosion. Arc welding processes are traditionally employed, which require a high heat input to bond the dissimilar metals, creating a large heat-affected zone and high residual stress that demands a lengthy stress-relieving post-weld heat treatment, up to 48 hours. High energy beam (e.g., laser, electron beam) directed energy deposition-based overlay cladding processes show promise for fabricating claddings with superior performance compared to arc welded ones because of their localized heat input; however, their necessity and time of post-weld heat treatment are currently unclear. In this research, we investigate the time dependence of a 600 C stress-relieving post-weld heat treatment of austenitic stainless steel clad on low carbon steel by laser-wire-directed energy deposition, comparing the microstructure and mechanical properties of the as-fabricated condition to 2-, 10-, and 48-hour heat treatment times. Diffusion simulations and microscopy show a gradual carburization of the stainless steel cladding and decarburization of the heat-affected zone/base metal. Nanoindentation testing shows up to a 1.8–2.69 embrittlement in the cladding and a 0.33 to 0.69 softening in the heat-affected zone after the 48-hour post-weld heat treatment. Tensile testing of the cladding composites reveals that increasing post-weld heat treatment time raises clad cracking susceptibility due to intergranular carbide formation and shows that laser-wire-directed energy deposition claddings may not require post-weld heat treatment.

Coating↗

Process-driven roadmap for depositing super duplex stainless steel via wire Arc additive manufacturing

Here, this study systematically investigates the effects of shielding gas, bead spacing, weld mode, and travel speed on the phase balance, porosity, and hardness of wire arc additively manufactured (WAAM) super duplex stainless steel (ER2594). Robotic WAAM was employed to fabricate multilayer walls under systematically varied process conditions, followed by phase transformation simulations, X-ray computed tomography (XCT), electron backscatter diffraction (EBSD), and microhardness evaluation. Thermodynamic simulations predicted rapid cooling of AM process can suppress the potential formation of deleterious precipitates which was later validated via cross-sectional microstructure analyses of printed samples. XCT revealed porosity levels below 0.2% for all deposits, with reduced travel speed significantly lowering defect volume. Microstructural analyses revealed the evolution of various austenite precipitates, including grain boundary austenite (GBA), Widmanstätten austenite (WA), and intergranular austenite (IGA), sequentially upon cooling of the ferrite phase. Among all process parameters, weld transfer mode exhibited the strongest influence on phase balance; pulsed mode promoted higher ferrite retention (~ 36%) compared to RapidX mode. No consistent relationship between stabilized phase fraction and captured microhardness was observed. This work provides critical insights for optimizing WAAM parameters to control phase balance and mechanical performance, which is essential for producing high-integrity super duplex stainless-steel components for nuclear and marine applications.

Grain orientation↗

Deep reinforcement learning for optimal control of induction welding process

Optimizing induction welding (IW) process parameters for the application of joining thermoplastic composites is challenging as it requires achieving complex spatiotemporal thermal characteristics along the weld-line to obtain desired weld quality. We formulate an optimal control problem which captures these requirements and seeks to optimize the IW coil speed using a fast-acting dynamic IW process model. We develop a novel Deep Reinforcement Learning (DRL) framework to solve this computationally challenging control problem and demonstrate via simulation study that the learned DRL feedback control policy results in better spatiotemporal thermal characteristics as compared to the current state-of-the-art.

36 MATERIALS SCIENCE↗

Advanced Coating Compositions and Microstructures to Improve Uptime and Operational Flexibility in Cyclic, Low-Load Thermal Utility Plants

GE, the University of Tennessee, and Oak Ridge National Laboratory collaborated from 2020 to 2023 developing two key technologies for improving the viability of fuel switching and load following in thermal utility plants: a) cost-effective weld overlay compositions for boiler tubing b) cathodic arc coatings that deliver improvements in both erosion resistance and oxidation resistance in high temperature steam for HP turbine blades The team worked through a robust, logical project map to de-risk these two technologies and advance them from TRL 3 to TRL 6. For the cost-effective weld overlay, the team developed a ferritic filler material which was fabricated at a vendor for 18% the average market cost of Inconel 625 wire, had a corrosion rate 3x lower in conditions simulating a biomass-fired superheater and 10x lower in conditions simulating a coal-fired superheater, and was fabricated into prototype overlaid tubing that passed ASME requirements including transverse bending, dye penetrant inspection, and ASTM G-76 evaluation. For the cathodic arc coatings applied to steam turbine blades, the team developed a novel composition that was successfully transferred to a qualified vendor. The vendor was able to produce coated prototypes with 4x the as-deposited erosion resistance and 10.4x the post-steam-exposure erosion resistance of the TiN coating the vendor currently applies on GE steam turbine components, without significantly increasing process cost. These coated prototypes also passed a GE inspection and showed favorable performance in high temperature erosion, nanoindentation, sliding wear, scratch adhesion, and high cycle fatigue testing. If successfully deployed by GE, it is anticipated that the technologies will enable the following: • 25%-50% increase in time between outages for both boilers and HP turbines. • 50% decrease in cost for weld overlay on a per foot basis relative to todays NiCr alloys. • Adequate oxidation resistance and erosion for HP turbine inlet steam at >620°C and >220 bar. • No need for changes in component supply chain or any notable Capital Expenditures. 5 Decreasing component cost, increasing performance, and extending time between outages represent direct value propositions to GE and their customers. For the American consumer, these objectives translate into increased grid reliability (fewer unexpected outages), decreased Levelized Cost of Electricity, and improved environmental health (low-loading/load following to accelerate penetration of renewables). The results also have implications for wear resistant tooling, wire arc additive manufacturing, more durable components for syngas cleanup, and deployment of more efficient thermochemical pathways for carbon negative fuel production

09 BIOMASS FUELS↗

Benchmarking of Probabilistic Fracture Mechanics Models in Grizzly

In 2020, as part of contract/task order 31310019N0006/31310020F0060, the Nuclear Regulatory Commission tasked Idaho National Laboratory (INL) with benchmarking the MOOSE/GRIZZLY code against the NRC’s Fracture Analysis of Vessels - Oak Ridge (FAVOR), version 16.1 code. Both codes can predict large light-water reactor vessel integrity deterministically and probabilistically. In fact, such predictions are the primary purpose of the FAVOR code, and are a main focus of the GRIZZLY code, although GRIZZLY is capable of modeling a wider range of geometries and problems. The vessel integrity modeling capabilities of the GRIZZLY code are still under development and being gradually expanded, and the capability to model vessel fracture by crack growth has not yet been integrated into GRIZZLY (although it does exist in pre-release versions). Thus, the present benchmark study focused on comparing predictions for the conditional probability of crack growth initiation (CPI) between GRIZZLY and FAVOR v16.1. The present benchmarking study expands on a previous study completed in 2020, which focused on single plate regions, various flaw types, and full vessel studies. The previous study was limited in scope and revealed some relatively large discrepancies, particularly in the case of weld regions. In the present study, detailed investigations into the sources of discrepancies between GRIZZLY and FAVOR were performed, with a focus on weld regions.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Pressure Spike in The LBNF Absorber Core s Gun Drilled Cooling Channel from an Accident Beam Pulse

The LBNF Absorber consists of thirteen 6061-T6 aluminum core blocks. The core blocks are water cooled with de-ionized (DI) water which becomes radioactive during beam operations. The cooling water flows through gun-drilled channels in the core blocks. The cooling water is supplied by the LBNF Absorber Radioactive Water (RAW) cooling system which is designed as per ASME B31.3 Normal Fluid Service [1]. An uninhibited beam accident pulse striking the water channels was identified as a credible accident scenario. In this study, it is assumed that the beam pulse hits the Absorber directly without interacting with any of the other upstream beamline components. The beam parameters used for the LBNF beam are 120 GeV, 2.4 MW with a 1.2 s cycle time. The accident pulse lasts for 10 μs. The maximum energy is deposited in the 3rd aluminum core block. For the sake of simplicity, it is assumed that the accident pulse strikes the 1 in. ID water channel directly. The analysis here simulates the pressure rise in the water during and after the beam pulse and its effects on the aluminum piping components that deliver water to the core blocks. The weld strengths as determined by the Load and Resistance Factor Design (LRDF) and the Allowable Strength Design (ASD) are compared to the forces generated in the weld owing to the pressure spike. A transient structural analysis was used to determine the equivalent membrane, peak, and bending stresses and they were com-pared to allowable limits.

43 PARTICLE ACCELERATORS↗

Pressure Spike in The LBNF Absorber Core s Gun Drilled Cooling Channel from an Accident Beam Pulse

he LBNF absorber consists of thirteen 6061-T6 aluminum core blocks. The core blocks are water cooled with de-ionized (DI) water which becomes radioactive during beam operations. The cooling water flows through gun-drilled channels in the core blocks. The cooling water is supplied by the LBNF absorber radioactive water (RAW) cooling system which is designed as per ASME B31.3 normal fluid service. An uninhibited beam accident pulse striking the water channels was identified as a credible accident scenario. In this study, it is assumed that the beam pulse hits the absorber directly without interacting with any of the other upstream beamline components. The beam parameters used for the LBNF beam are 120 GeV, 2.4 MW with a 1.2 s cycle time. The accident pulse lasts for 10 µs. The maximum energy is deposited in the 3rd aluminum core block. For the sake of simplicity, it is assumed that the accident pulse strikes the 1 in. ID water channel directly. The analysis here simulates the pressure rise in the water during and after the beam pulse and its effects on the aluminum piping components that deliver water to the core blocks. The weld strengths as determined by the Load and Resistance Factor Design (LRDF) and the Allowable Strength Design (ASD) are compared to the forces generated in the weld owing to the pressure spike. A transient structural analysis was used to determine the equivalent membrane, peak, and bending stresses and they were compared to allowable limits.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Synchrotron X-ray diffraction analysis of constituent phases in transition joint between nickel alloy 738LC and a MnFeCoNiCu alloy

Synchrotron x-ray diffraction (XRD) analysis was performed on transition joints between a single-phase MnFeCoNiCu alloy and Ni-base Alloy 738LC to efficiently identify the constituent phases across the interface, with different levels of material intermixing generated by laser-welding with variable power. Here, the intermixing extent was quantified by postmortem energy dispersive x-ray spectroscopy mapping. Diffraction-based analyses on complex composition spaces with limited prior data present significant challenges because elemental substitution in both disordered and ordered phases is more extensive than in conventional alloy spaces, which may effectuate relatively large shifts in the observed lattice parameters that convolute the analysis. Therefore, thermodynamic simulations and crystallographic literature data were employed to construct a system-specific diffraction library of twelve prospective phases for the composition space investigated. Subsequently, for predicted disordered cubic phases, statistical hard-sphere models were established to estimate the lattice parameters and predict diffraction peak positions for inclusion in the library. The library was then employed to analyze diffraction profiles measured from the variably intermixed transition joints, with focus on accounting for both high and low-intensity peaks. 99.0 % of diffraction peaks with relative intensity greater than 0.001 were assigned to phases from the system-specific library, exemplifying rigorous peak accounting and indicating that no unexpected phases were present. Up to six of the twelve library phases were experimentally found in the transition joints. The lattice parameters predicted by the statistical hard-sphere model based upon thermodynamic simulations agree reasonably well with the measured values for the disordered FCC matrix phase.

36 MATERIALS SCIENCE↗

Removing Rotational Variations from Shoulder Thermocouples in Friction Stir Welding

Thick plate and lower temperature friction stir welding results in good post-weld properties by welding at very low tool rotational speeds. Low speeds cause large variations in the measured shoulder temperature, making temperature control difficult. This paper describes a computationally light method to correct for oscillating measured temperatures. Data is collected over the previous two revolutions and used to build a compensation table and calculate a derivative. In simulation, measured temperature variations are reduced by a factor of five to ten. Temperature data is preserved and not cornered, nor is any time delay induced by this method, unlike with filtering methods.

Friction Stir Welding, Temperature↗

Infrared triggered dwell and active cooling thermal control effects on microstructural uniformity in DED

Directed Energy Deposition (DED) offers rapid large scale fabrication, but difficulty in delivering consistent microstructures and properties hinders the use of DED fabricated components in safety or performance critical applications. Variability stems from the complex thermal cycles generated by the toolpath used to print the required geometry. Several practical methods have become established in DED to regulate overheating, such as active cooling of the baseplate structure or the use of an infrared camera to inject interlayer pauses to ensure the top layer of the component cools to a set temperature, which have been shown to affect microstructure. However, no critical assessment has been performed as to how effective these controls are in promoting microstructural uniformity in the context of complex layer timing commonly generated by non-prismatic geometries. Here we show how controls influence the thermal field, phase transformations, and dynamic annealing of a low-temperature transformation steel using infrared imaging and operando neutron diffraction. Counterintuitively, common thermal homogenization process controls can reduce microstructural uniformity because these approaches stabilize peak temperature while overlooking temperatures near the solid-state phase transformation fronts. Instead, the cyclic reheating induces spatially-variant dynamically annealed regions which can be modulated via control parameters. We show that these controls have spatially linked effects centimeters away from the active weld, which implies that microstructure control must co-optimize thermal input across many subsequent layers. In conclusion, our results demonstrate the pressing need for higher order controls that integrate predictive elements of simulation data to stabilize printed properties for future qualification of DED components.

Directed energy deposition↗

A Fast and Accurate Reduced-Order Model for High-Intensity Transferred Arc Discharges

Arc discharges are widely used in welding, plasma smelting, and other industrial processes, where variations in operating conditions strongly affect arc stability, temperature distribution, and energy transfer. Accurate modeling of these phenomena typically requires computationally expensive high-fidelity simulations. This study presents a hierarchy of three arc discharge models with progressively reduced physical fidelity. The high-fidelity model provides a fully physics-resolved reference, the reduced-order model reproduces the dominant thermal and flow characteristics of the arc with reasonable accuracy, and the Elenbaas-Heller model captures key trends in a simplified, rapid formulation. This hierarchy demonstrates that reduced-order model can effectively balance predictive fidelity and computational efficiency, providing practical tools for arc simulation and parametric studies.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗