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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.

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All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Quantitative assessment of fitting errors associated with streak camera noise in Thomson scattering data analysis

Thomson scattering measurements in high energy density experiments are often recorded using optical streak cameras. In the low-signal regime, noise introduced by the streak camera can become an important and sometimes the dominant source of measurement uncertainty. In this paper, we present a formal method of accounting for the presence of streak camera noise in our measurements. We present a phenomenological description of the noise generation mechanisms and present a statistical model that may be used to construct the covariance matrix associated with a given measurement. This model is benchmarked against simulations of streak camera images. We demonstrate how this covariance may then be used to weight fitting of the data and provide quantitative assessments of the uncertainty in the fitting parameters determined by the best fit to the data and build confidence in the ability to make statistically significant measurements in the low-signal regime, where spatial correlations in the noise become apparent. These methods will have general applicability to other measurements made using optical streak cameras.

47 OTHER INSTRUMENTATION↗
DOE OSTI2025

State Dependent Optimization with Quantum Circuit Cutting

Quantum circuits can be reduced through optimization to better fit the constraints of quantum hardware. One such method, initial-state dependent optimization (ISDO), reduces gate count by leveraging knowledge of the input quantum states. Surprisingly, we found that ISDO is broadly applicable to the downstream circuits produced by circuit cutting. Circuit cutting also requires measuring upstream qubits and has some flexibility of selection observables to do reconstruction. Therefore, we propose a state-dependent optimization (SDO) framework that incorporates ISDO, our newly proposed measure-state dependent optimization (MSDO), and a biased observable selection strategy. Building on the strengths of the SDO framework and recognizing the scalability challenges of circuit cutting, we propose nonseparate circuit cutting-a more flexible approach that enables optimizing gates without fully separating them. We validate our methods on noisy simulations of QAOA, QFT, and BV circuits. Results show that our approach consistently mitigates noise and improves overall circuit performance, demonstrating its promise for enhancing quantum algorithm execution on near-term hardware.

Li, Xinpeng↗
DOE OSTI2025

Predictions of Cell-to-Cell Propagation and Vent Gas Production in the Thermal Runaway of Lithium-Ion Battery Stacks

This work presents the thermal runaway propagation model LIM1TR (Lithium-ion Modeling with 1-D Thermal Runaway) as an efficient tool to predict different cell-to-cell thermal runaway propagation scenarios. Here, we explored the vent gas volume production and reaction duration highlighting the relationship between these parameters and thermal runaway propagation due to convection by the vented gases. Two metrics based on gas production rate and heating rate are utilized as good indicators of the start and end of thermal runaway. LIM1TR results are compared with and validated by experiments from the literature for single-cell and multicell array experiments of 5 Ah and 10 Ah cells. By accounting for intraparticle diffusion of reacting species in the electrodes, we were able to capture the general dynamics of thermal runaway propagation and estimate acceptable reaction durations compared with the experimental values. Simulation results further demonstrated that varying heating modes lead to distinct reaction durations, consistent with experimental observations. Vent gas volume predictions indicate the need to consider both full and partial oxidation of the electrolyte. The outcomes of this work are building blocks for further investigations of module-to-module propagation by vented gases through convective heat transfer.

25 ENERGY STORAGE↗
DOE OSTI2022

Initial Microstructure Examination of High Burnup Fuel with Varying Operational Burnups

his report presents an initial examination of the microstructure of high burnup UO 2 under pre- and postloss of coolant accident (LOCA) conditions. This work builds upon work previously conducted on high burnup UO 2 fuel at Oak Ridge National Laboratory. Studying microstructure evolutions that occur in UO 2 during irradiation, particularly in high burnup fuel, will provide a deeper understanding of fuel fragmentation under simulated LOCA conditions. High burnup UO 2 microstructural data is also needed to improve constitutive models intended to predict high burnup fuel fragmentation. The objective of this work is to begin the process of examining high burnup fuel microstructural features before and after LOCA testing to better understand mechanisms driving experimental observations. Several high burnup fuel samples were available from historic fuel shipments to ORNL. These samples were leveraged along with state-of-the-art microscopy capabilities. This report summarizes the current ongoing work using these fuel samples to interpret and analyze high burnup fuel microstructures.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2023

Investigating Hydrogen Isotope Exchange Reactions on Lithium Aluminate Pellets in TPBAR (FY22 Report)

We developed a novel operando Raman spectroscopy method for investigation of hydrogen (H) isotope exchange reactions in the lithium aluminate (γ-LiAlO 2 ) that allows modeling of tritium behaviors in high temperature and in an irradiated environment. The lithium aluminate pellet is a main component in the Tritium-Producing Burnable Absorber Rod (TPBAR). We used deuterium ( 2 H or D) as a surrogate to simulate tritium ( 3 H or T). We used a surface analysis tools in situ/operando Raman spectroscopy to observe the transformation OH and OD compositional changes. We also used ToF-SIMS to analyze the lithium aluminate pellet control sample to build the base line for future in situ/operando analysis. To conduct operando Raman spectroscopy, we developed a custom reaction cell with a detachable micro heater using microelectromechanical systems (MEMS) and 3D printing techniques. Multiple versions were developed and tested. Using the new reaction cell, we demonstrated operando Raman spectroscopy of water (H 2 O) and deuterated water (D 2 O) with nitrogen (N 2 ) exposure onto the lithium aluminate (LiAlO2) pellet specimen, respectively, using a wet gas injection setup. We also successfully developed a detachable microheater that can heat up to ~250°C for ~90 mins. The Raman spectra did not show clear H 2 O and D 2 O characteristic peaks, which indicates that introducing H 2 O and D 2 O onto the surface of the pellet is challenging due to its dense structure nature. Our efforts suggest that various improvements are needed, such as increasing reaction cell operating gas pressure and thinning pellet sample thickness, to obtain meaningful measurements.

07 ISOTOPE AND RADIATION SOURCES↗
DOE OSTI2024

NEAMS Burnup Extension Accomplishments and Remaining Modeling Gaps

The economic viability of light-water reactors (LWRs) in the United States is declining in heavily subsidized markets, and as a result, the nuclear industry is looking for opportunities to enhance the economic competitiveness of nuclear power. This is not a foreign concept to the nuclear industry: in the mid-2000s, the nuclear industry set out to achieve zero fuel failures by 2010. The goal in this effort was to drive down the cost of reactor shut down by replacing a pin or bundle in response to fuel rod failure. 2010 brought about the initiative to deliver the nuclear promise to reduce operating cost by 30% to improve nuclear energy’s economic competitiveness before 2020. The emergence of accident-tolerant fuel also offers the nuclear industry an opportunity to build on these past successes and deliver affordable, clean energy. Accident-tolerant fuel has been shown to provide superior performance compared to traditional Zircaloy/UO2 fuel concepts, offering the unique ability to remove operational limitations that inhibit the economic viability of nuclear power. This has led the industry to begin building a technical case to extend the peak rod average burnup beyond 62 GWd/tU to extend pressurized water reactor cycle lengths to 24 months and to develop more efficient boiling water reactor core designs. The Nuclear Energy Advanced Modeling and Simulation (NEAMS) program mission is to develop advanced modeling and simulation tools and capabilities to accelerate the deployment of advanced nuclear energy technologies. The primary safety concern inhibiting the nuclear industry from extending burnup is related to high-burnup fuel fragmentation, relocation, and dispersal. Therefore, the NEAMS program developed a targeted 5-year plan to support the industry’s efforts to extend burnup. This milestone report summarizes the 5-year plan that was enacted in FY20, followed by a discussion of the ongoing activates required to fulfill the 5-year plan, as well as the approach to address the current modeling gaps. Additionally, an LWR stakeholder meeting was held to communicate work performed in the NEAMS program over the past three years, to assess the LWR community’s perspective on the impact of the program, and to identify remaining significant gaps in the NEAMS suite of capabilities. This engagement will be documented by the Electric Power Research Institute and used by NEAMS to redirect current LWR scope as needed and to develop the next phase for LWR research and development.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2021

Big Box Retail Grocery Store and Electric Vehicle Station Load Profiles

This dataset includes yearlong, one-minute resolution time series profiles for the big box retail grocery stores stores simulated in Phoenix, Houston, Denver, and Minneapolis, as well as electric vehicle charging time series profiles for the various ports, charging levels, and station utilizations produced for the study "Impact of electric vehicle charging on the power demand of retail buildings", published in 2021 (https://doi.org/10.1016/j.adapen.2021.100062). Please cite as: Gilleran, M., Bonnema, E., Woods, J. et al. Impact of electric vehicle charging on the power demand of retail buildings. Advances in Applied Energy 4, (2021). https://doi.org/10.1016/j.adapen.2021.100062

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
DOE OSTI2022

Snowmass Computational Frontier: Topical Group Report on Quantum Computing

Quantum computing will play a pivotal role in the High Energy Physics (HEP) science program over the early parts of the 21$^{st}$ Century, both as a major expansion of our capabilities across the Computational Frontier, and in synthesis with quantum sensing and quantum networks. This report outlines how Quantum Information Science (QIS) and HEP are deeply intertwined endeavors that benefit enormously from a strong engagement together. Quantum computers do not represent a detour for HEP, rather they are set to become an integral part of our discovery toolkit. Problems ranging from simulating quantum field theories, to fully leveraging the most sensitive sensor suites for new particle searches, and even data analysis will run into limiting bottlenecks if constrained to our current computing paradigms. Easy access to quantum computers is needed to build a deeper understanding of these opportunities. In turn, HEP brings crucial expertise to the national quantum ecosystem in quantum domain knowledge, superconducting technology, cryogenic and fast microelectronics, and massive-scale project management. The role of quantum technologies across the entire economy is expected to grow rapidly over the next decade, so it is important to establish the role of HEP in the efforts surrounding QIS. Fully delivering on the promise of quantum technologies in the HEP science program requires robust support. It is important to both invest in the co-design opportunities afforded by the broader quantum computing ecosystem and leverage HEP strengths with the goal of designing quantum computers tailored to HEP science.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Examination of Digital-Delay Rossi-$\alpha$ for 252 Cf-Driven Highly Enriched Uranium Using Organic Scintillators

Neutron noise techniques constitute several analysis methods applicable to non-destructive assay. One technique is the Rossi-α method to calculate the prompt neutron decay constant (α) or its inverse, the prompt neutron period (1/α), for assemblies of fissionable material. This work evaluates a high-data-throughput measurement at the National Criticality Experiments Research Center (NCERC) with organic scintillators measuring a subcritical assembly of highly enriched uranium (HEU) metal (93% 235 U). The assembly comprises hemi shells stacked together to form fully closed shells and is driven by a Cf source at the center. The assembly is a total of 59.85 kg HEU and a k eff of 0.99, according to MCNP6.2 KCODE simulations. Measurements were acquired with a three-by-four array of 5.08-cm-diameter by 5.08-cm-length trans-stilbene crystals 166 cm from the assembly center. Two types of coincident binning methods are used to build the Rossi-α distribution of coincident neutron detections: A) type 1 binning, also known as any-and-all forward time differences, and B) type 1 binning with a digital-delay technique that is analogous to Orndoff’s use of delay cabling in early Rossi-alpha measurements. Method B) disregards same-detector coincidences and once all nearest time coincidences are collected between all detectors after a trigger, a time delay of 0.75 µs is implemented. The measured prompt neutron decay constants for both techniques are calculated from single exponential fits and the two methods are compared. Method A) shows an apparent timing discontinuity near 500 ns time differences. This timing discontinuity interferes with the fitting method used to calculate the prompt neutron decay constant. Method B) mitigates the artificial timing discontinuity and removes the disagreement of the fit. Future work will model the time-dependent detector response to discern why this timing discontinuity occurs, discern how Method B) reduces the amplitude of this timing discontinuity, and apply this method to critical assembly measurements to ultimately confirm the recommendation to use Method B) for high-data-throughput measurements.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2025

Improving the Quasi‐Biennial Oscillation via a Surrogate‐Accelerated Multi‐Objective Optimization

Accurate simulation of the quasi-biennial oscillation (QBO) is challenging due to uncertainties in representing convectively generated gravity waves. We develop an end-to-end uncertainty quantification workflow that calibrates these gravity wave processes in E3SM for a realistic QBO. Central to our approach is a domain knowledge-informed, compressed representation of high-dimensional spatio-temporal wind fields. By employing a parsimonious statistical model that learns the fundamental frequency from complex observations, we extract interpretable and physically meaningful quantities capturing key attributes. Building on this, we train a probabilistic surrogate model that approximates the fundamental characteristics of the QBO as functions of critical physics parameters governing gravity wave generation. Leveraging the Karhunen–Loève decomposition, our surrogate efficiently represents these characteristics as a set of orthogonal features, capturing cross-correlations among multiple physics quantities evaluated at different pressure levels and enabling rapid surrogate-based inference at a fraction of the computational cost of full-scale simulations. Finally, we analyze the inverse problem using a multi-objective approach. Our study reveals a tension between amplitude and period that constrains the QBO representation, precluding a single optimal solution. To navigate this, we quantify the bi-criteria trade-off and generate a set of Pareto optimal parameter values that balance the conflicting objectives. This integrated workflow improves the fidelity of QBO simulations and offers a versatile template for uncertainty quantification in complex geophysical models.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Design and performance evaluation of a dual-circuit thermal energy storage module for air conditioners

We present experimental results and a validated numerical model of a dual-circuit phase-change thermal energy storage module for air conditioners. The module incorporates a phase-change material encapsulated in compressed expanded natural graphite foam. We used n-tetradecane as the PCM with a transition temperature (~4.5 °C) suitable for air-conditioning applications. Heat exchange to and from the module is accomplished through two fluid loops operating as a heat source and sink embedded inside multiple slabs of the composite material. This dual-circuit design enables easier integration with air-conditioning equipment and provides enhanced flexibility in system operation as compared to the state-of-the-art thermal storage systems. When integrated with an air-conditioner, this design will enable peak-load shaving and enhances operational efficiency. The thermal storage device was designed for a nominal storage capacity of ~ 3.5 kWh. We evaluated the heat transfer and energy storage performance of this device using standalone heat transfer experiments to estimate key thermal resistances and identify design improvements before integration with an air conditioner. The numerical model of the heat exchanger uses a combination of discretized and lumped parameter approaches to maintain a balance between accuracy and computational expense. Our analyses show that the geometric features and integration of fluid tubes are key contributors to the thermal contact resistance between the fluid and the thermal storage material, and consequently, to the overall performance of the thermal storage module. Our standalone experiments also identified important operating scenarios in which this thermal storage module can be used for air-conditioning in buildings.

25 ENERGY STORAGE↗
DOE OSTI2025

Thermal performance and energy consumption validation of an occupied local government office building outfitted with ceiling tile phase change materials

Buildings present an opportunity for energy conservation and the modulation of peak energy demand through controlled Heating, Ventilation, and Air Conditioning (HVAC) energy use. The administrative and office building stock in the United States holds potential to achieve energy and demand savings through retrofits such as insulation, weatherization, and thermal energy storage. Specifically, there is a need to validate passive phase change material (PCM) applications in full scale in aging administrative buildings in the US to evaluate the energy benefits. Aim of this study was to conduct a whole building level thermal and energy validation of an operational building and explore an alternative method for evaluating energy efficiency. To accomplish this, the study employed PCMs in the drop ceiling and carry out an energy audit and on-site measurement of HVAC systems' energy demand and consumption. A full-scale EnergyPlus energy model, modeled by the authors, served as a baseline for evaluation. The results show that calibrated model's envelope temperature measures fall within the accepted errors. HVAC energy simulation results also fall within the accepted errors for monthly and hourly pre- and post- PCM retrofit electricity and natural gas data. The novelty of this study is that it employees energy scales per Heating Degree Hour and Cooling Degree Hour, in contrast to the commonly used Heating Degree Days and Cooling Degree Days as reported in the literature to analyze energy savings. These findings underscore the pivotal role of a calibrated model in assessing the efficacy of a singular energy measure, like a PCM-retrofitted ceiling, in an occupied office building.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2025

MLSPICE: Machine Learning based SPICE Modeling Platform for Power Magnetics

Electrical power converters are critical to a wide range of applications ranging from renewable integration to transportation electrification, and can be a key factor determining the size, weight, and efficiency of energy conversion systems. Magnetic components are typically the largest and least efficient components in power electronics. While there have been major strides in the modeling and analysis of power semiconductor devices and circuit simulations, the necessary advances in the design of power magnetics have lagged. In this project, we have transformed the modeling and design of power magnetics with machine learning enabled methods and catalyze simultaneous disruptive improvements for ML-based power electronics design tools. A fully automated open-source machine learning based magnetics modeling platform – the MagNet project - with innovations in full stack have been developed to greatly accelerate the design process and provide new insights to magnetic material and geometry design. The ARPA-E funded MagNet platform contains three major building blocks: 1) a ML-Integrated Data Acquisition System (MIDAS): a highly automated data acquisition testbed which is capable of measuring a large number of magnetic cores with a wide range of electrical circuit excitations; 2) a ML-integrated Core Loss Model (MICLM): a machine-learning trained modeling method for modeling the core loss and saturation effects of magnetic materials for arbitrary excitation waveforms; 3) ML-guided Magnetics SPICE Simulation Tool (PMSPICE): a fully integrated CAD tool which can simulate the magnetics in SPICE. It can help the designers to quickly model the linear and non-linear characteristics of magnetic components and evaluate their behavior in SPICE simulations. The developed MagNet system has fully demonstrated the proposed performance target and has been open sourced to the entire power electronics community to advance the modeling and design of power magnetics from many different angles.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Understanding Impacts of Data Integrity Attacks on Transactive Control Systems

With the rapid growth of internet-connected smart devices capable of exchanging energy price information and adaptively controlling energy consumption of connected loads, the role of transactive control is expected to become more prominent in the modern grid. Transactive control systems integrate the wholesale and retail energy markets, and enable active participation of end users, thereby playing a key role in managing the rising number of distributed assets in the smart grid. The use of internet for the communication of data between the controllers at the building, distribution, and transmission levels makes the system susceptible to cyber-attacks. A skilled adversary can potentially manipulate the exchanged data with the intention of inflicting damage to the system. In this paper, four categories of metrics are put forth for evaluating the performance of the system when under data integrity attacks. A model for scaling-based data integrity attack has been described, and co-simulations have been performed on a 240 bus WECC transmission system model with detailed modeling of distribution systems at specific buses. Our results show that scaling-based data integrity attacks can have non-trivial impacts on the operational, financial, and comfort aspects of the transactive control system.

Smart grid, transactive control system, Buildings-↗
DOE OSTI2021

PSTN-051: Survey Strategy and Cadence Choices for the Vera C. Rubin Observatory Legacy Survey of Space and Time (LSST)

A summary of survey strategy and cadence choices, simulated and evaluated by the Vera C. Rubin Observatory Legacy Survey of Space and Time (LSST) Scheduler Team, prepared for the Survey Cadence and Optimization Committee (SCOC). A large telescope survey, covering the entire visible sky repeatedly every few days in multiple bandpasses over the course of ten years, is the core idea of the LSST. An area of about 20,000 square degrees observed under a wide range of conditions to deep coadded limiting magnitudes in bandpasses ugrizy enables cosmological studies and studies of the Milky Way structure with unprecedented precision; the same survey, when cadenced well, can serve to open new windows into our understanding of transient and variable stars, and extend our knowledge of small bodies throughout the Solar System by orders of magnitude. The outlines of, and some basic necessary requirements for these goals are outlined in the LSST Science Requirements Document (SRD). Finding options for the observing strategy to meet more detailed needs of an even wider range of science goals, as well as building the LSST Scheduler and Metrics Analysis Framework, has been the work of the LSST Scheduler Team with support and input from the astronomical community, including the Community Observing Strategy Evaluation Paper (COSEP), the Call for White Papers, numerous performance metrics, and guidance from the LSST Science Advisory Committee in their Recommendations for Operations Simulator Experiments. This report will help enable the SCOC to make its recommendation for the preferred survey strategy.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Developing a Control Strategy for Minimum Airflow Setting Considering CO2 Level and Energy Consumption in a Variable Air Volume System

In an office building equipped with a Variable Air Volume (VAV) system, this paper introduces a novel method for controlling the minimum supply airflow fraction in each zone’s VAV box, having a capability to consider indoor CO2 level and energy consumption. The EnergyPlus simulation using the medium office prototype model was employed, which evaluated the performance of the energy and CO2 concentration for five VAV box airflow control strategies. The paper focuses on CO2 concentration-based airflow control method and compares it with other four methods including conventional single-max, reduced minimum single-max, demand-controlled ventilation(DCV), and dualmax control methods according to guidelines and common practices. The newly proposed control strategy directly correlates the minimum airflow fraction to CO2 concentration. A general trend emerged when comparing CO2 concentrations—lower minimum airflow fractions were associated with higher concentrations. The proposed control method effectively maintained low CO2 concentrations and enabled a lower airflow fraction contributing to energy consumption reduction. It was confirmed that heating energy consumption in climate zone 4A, 5B, and 6A showed a maximum saving of approximately 30% compared to the conventional single-max and dual max control strategies. It was found that cooling energy consumption in climate zone 4A and 6A can achieve a maximum saving of approximately 10% compared to the conventional control strategies. The proposed CO2 concentration-based control logic is promising as it not only improves the indoor air quality lowering the CO2 concentration in the occupied spaces, but also contributes to HVAC energy savings.

Lee, Jong Man↗
DOE OSTI2023

A unified non-equilibrium phase change model for injection flow modeling

The homogenous relaxation model (HRM) is one of the most widely used models to describe the liquid- gas phase transition. However, in its original formulation, it is unable to handle multispecies vapor-liquid equilibrium (VLE), which limits its applicability to single-component fluids. In this work, a unified non-equilibrium phase change model that considers the VLE of multicomponent mixtures is proposed building upon the HRM's structure. A time factor is introduced to mimic the effect of different phase change timescales due to different mechanisms, e.g., cavitation, flash-boiling, and evaporation. Here to assess the model's performance, computational fluid dynamics simulations of the internal and near-nozzle injection flow of the Engine Combustion Network's Spray G injector were performed using the nine-component PACE-20 fuel with both the unified model and the original HRM. The predicted fuel density in the near-nozzle region matched well with X-ray tomography measurements. The simulation results indicated that, whereas the HRM failed to capture the vaporization due to convective mixing between the fuel and ambient gas, the unified model performed well in predicting the mixing-driven vaporization and the corresponding evaporative cooling. Further comparisons using the nine-component fuel formula and a single-component fuel surrogate demonstrated the unified model's ability to predict preferential vaporization, which affects the predictions of local mixture composition and rate of vaporization. Finally, it is shown that the unified model is capable of representing multiple phase change mechanisms, and the relaxation time factor plays an important role in determining the degree of phase change due to the different mechanisms.

33 ADVANCED PROPULSION SYSTEMS↗
DOE OSTI2024

Residual stress accumulation in large-scale Ti-6Al-4V wire-arc additive manufacturing

Large-scale additive manufacturing (AM) is of interest in the manufacturing industry to produce components of dimensions on the order of hundreds of millimeters to meters in scale. Wire-arc AM (WAAM) of Ti-6Al-4V (Ti64) is an attractive technique for large-scale AM in the aerospace industry, give the high strength-to-weight ratio of the material and high deposition rate of the process. However, due to the large scale, significant distortion and residual stresses are developed in the material during deposition and cooling, potentially leading to part failure. WAAM of a prototypical large-scale Ti64 machine tool component is studied in this work via finite element analysis (FEA). Element activation/deactivation technique is employed to simulate deposition and the resulting distortion and residual stress (RS) predictions are analyzed to evaluate the possibility of crack formation. Significant distortion (∼10 mm) and RS (>1300 MPa) is predicted, suggesting the formation of cracks and possible crack propagation into the build region. Incorporation of fillets significantly reduces RS concentration regions, thus reducing the possibility of part failure. Material deposition sequence also affects the RS pattern in the build.

Mathews, Ritin↗