SEARCH · Search NASA

Results for “Fast Reactor”

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.

SourceResearch connectionFrom yearThrough year

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

At least 127 records · Page 7

All sources NASA NTRS DOE OSTI

DOE OSTI2025

First-Principles Cost Analysis of Advanced High-Temperature Nuclear Plants

Due to the vast number of recent nuclear reactor innovations, particularly those pertaining to generation IV reactor types like high-temperature gas cooled reactors (HTGRs) and sodium-cooled fast reactors (SFRs), and the newer deployment strategies envisioned, such as use of small modular reactors (SMRs) or even microreactors, reliable, detailed, and complete costs of these nuclear innovations are needed in wide availability. The types of models that generally achieve these objectives are those incorporating the fundamental nature of the real-world systems they aspire to predict, such as first-principles models. Furthermore, first principles models typically offer predictiveness that is not attained by most other types of individual-models. However, detailed, first-principles cost modeling of nuclear reactors and entire nuclear plants is relatively limited. To address this limitation in the availability of detailed, predictive models based on fundamentals, we recently developed a range of cost models, mostly based on first-principles methodologies, to project full lifecycle costs (LCCs) of nuclear power plants (NPPs) based on multiple parallel SM-HTG-pebble bed reactors (PBRs) and SM-SFRs.

Prosser, Jacob H. [Strategic Analysis, Inc., Arlin↗

DOE OSTI2024

Pre-Transient Characterization of Historic EBR-II Pins for Transient Testing

Current interest in sodium-cooled fast reactor (SFR) designs, such as TerraPower’s Natrium Reactor, has highlighted the need for advanced reactor fuel technology development. Modern U-Zr and U- Pu-Zr pin designs are primary candidates to fuel SFRs and boast high fuel utilization capacity, increased fuel-cladding compatibility, and improved safety through inherent feedback mechanisms. Despite over 60 years of metallic fuel irradiation, uncertainties exist in the performance of the fuel system, particularly under transient overpower (TOP) and loss of flow (LOF) scenarios. Throughout historical testing within the Experimental Breeder Reactor II (EBR-II) and the Fast Flux Test Facility (FFTF), fuel behavior has demonstrated benign response to transient reactor conditions; however, accurate predictions of failure thresholds to inform operational limitations rely heavily on fuel composition, burnup, and irradiation history. In expanding TOP and LOF testing, the Transient Heat sink Overpower Response (THOR) Capsule will be used to test modern fuel technologies in a static sodium environment in the Transient Reactor Test (TREAT) Facility. The THOR capsule is highly instrumented and will provide time-dependent thermal behavior of SFR fuel pins subjected to accident conditions within TREAT. The THOR-Metallic (THOR- M) campaign aims to validate and expand historical TOP and LOF testing on high burnup U-Zr and U-Pu- Zr fuel alloys previously irradiated in EBR-II by running the rods to failure. This contribution focuses primarily on the pre-transient engineering-scale destructive and non- destructive characterization that has been conducted on both the test and sibling pins used for the TOP and LOF tests. All pins underwent visual examination, neutron radiography, element contact profilometry, and precise gamma scan. The sibling pins used for each test were further analyzed using gas assay, sampling, and recharge analysis (GASR), and optical microscopy. The results from each technique confirmed that the fuel pins were intact and devoid of any atypical developments when compared to historical data. Additionally, the analyzed measurements establish a baseline for comparison to post-transient analysis. Key fuel behaviors quanitifed include axial elongation of the fuel column, diametral strain of the pin, patterns in fluff structure geometry, changes in axial isotope distribution, evolution of constituent redistribution, porosity, and fission gas release. The pre-transient measurements and changes attributed to transient behavior from post-transient measurement will be compared to historical data to capture the behavioral dependence on composition, burnup, and irradiation history. Results from this work advance the initiatives of the THOR-M campaign, which aid in informing fuel performance models and establishing safety criteria for SFR operational limits. The novel combination of test environment, in-situ instrumentation, and comprehensive suite of characterization methods provides greater understanding of transient fuel behavior. Overall, information on the time and condition of pin failure for high burnup U-Pu-Zr will greatly expand the limited existing TOP and LOF test data.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2024

Pre-Transient Characterization of Historic EBR-II Pins for Transient Testing

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2024

Advances in Metallic Fuel Database Development and Data Qualification

The Fuels Irradiation and Physics Database (FIPD [1]) is a comprehensive repository of data and documents related to Uranium-Zirconium based metallic fuel test pins. This database stores operational conditions of these pins, calculated using a suite of Argonne National Laboratory analysis codes developed during the Integral Fast Reactor (IFR) program. Key calculated data include axial distributions of power, temperature, fluence, burnup, and isotopic densities. Additionally, the FIPD holds post-irradiation examination (PIE) data such as fission gas release, gas chemistry measurements, and axial distributions derived from profilometry, gamma scanning, and neutron radiography. Complementing these data is an extensive archive of documents related to various pins and experiments. These include raw PIE records, design details, safety analyses, and operational reports. More detail about FIPD can be found in ref. [2]. The database development is an ongoing effort covering metallic fuel experiments from the Experimental Breeder Reactor II (EBR-II) and the Fast Flux Test Facility (FFTF). The recent improvements to the database and the data QA status are summarized in this paper.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2024

Research Highlight - Dispatch Optimization, System Design and Cost Benefit Analysis of a Nuclear Reactor with Molten Salt Thermal Storage

We highlight our work from our previous publication titled "Dispatch Optimization, System Design, and Cost Benefit Analysis of a Nuclear Reactor with Molten Salt Thermal Storage" published in MDPI Energies 2022 (doi.org/10.3390/en15103599). Variable renewable energy availability has increased the volatility in energy prices in most markets. Nuclear power plants, with a large ratio of capital to variable costs, have historically operated as base load energy suppliers but the need for more flexible operation is increasing. We simulate the techno-economic performance of a 950 MWt nuclear power plant, based on the Westinghouse lead-cooled fast reactor, coupled with molten salt thermal storage as a method for flexible energy dispatch. We use the System Advisor Model to model the nuclear reactor thermal power input and power cycle operating modes. We combine this robust engineering model with a mixed-integer linear program model for optimized dispatch scheduling. We then simulate the coupled nuclear and thermal storage system under different market scenarios with varying price volatility. We find that the coupled plant outperforms the base plant under markets where energy price peaks fluctuate by a factor of two or more about the mean price. We show that a calculated power purchase agreement price for the plant improves by up to 10% when operating under California energy market conditions. Sensitivity analysis on the thermal storage cost shows that the optimal design remains unchanged even when doubling costs.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Preliminary Study of Iodine Gas Removal in Sodium Pools

Potential iodine gas release from failed fuel pins is a critical factor in the source term analysis of oxide fuel-loaded sodium fast reactors (SFRs). The accumulated iodine-containing gas mixtures inside pin plenums are expected to be ejected during pin failures and rise through sodium pool, with potential release of gaseous iodine to the cover gas region. Due to its potential radiological impacts, a proper assessment of iodine behavior is necessary for an accurate source term assessment. Throughout the bubble rise trajectory in the sodium pool, iodine gas is continuously removed or transformed at the bubble interface by diffusion, as the combining reaction between the iodine and sodium to form sodium iodide (NaI) is a chemically preferred process. As the final amount of iodine released from the facility is strongly influenced by the removal phenomenon inside the sodium pool, experiments were previously performed by PNC (Power Reactor and Nuclear Fuel Development Corporation) to provide insight into this phenomenon. To assess the accuracy of present methods for predicting iodine gas removal within sodium pools, several candidate approaches, available in source term analysis codes, have been summarized and evaluated in this study. Spherical cap bubbles and spherical bubbles are considered in accordance with the methods adopted in each approach, and different forms of correlations for major parameters have been implemented in accordance with the original adoptions. Based on the summarized results, important aspects to be considered have been derived.

Decontamination↗

DOE OSTI2025

Comparative post-irradiation examination of high burnup U-19Pu-10Zr: Assessing steady-state irradiation behavior against historical and modeled fuel performance

Here, the development of next-generation sodium-cooled fast reactors necessitates comprehensive research on metallic fuels to maximize economic performance while ensuring safe operation. In this study, we investigated the steady-state irradiation behavior of two high burnup U-19Pu-10Zr fuel pins, DP-36 and DP-40, in preparation for planned safety testing. Post-irradiation examination (PIE) was performed to quantify fuel column elongation, regions of low-density at the top of the fuel column, pin deformation, fission product distribution, fractional fission gas release, microstructural evolution, and fuel constituent redistribution. Benchmarking against existing PIE data from U-19Pu-10Zr fuel pins irradiated in EBR-II revealed consistent patterns in fuel column elongation and cladding diametral strain. However, both pins exhibited longer low-density structures, and destructive examination of DP-36 revealed more complex constituent redistribution patterns compared to previously reported data for ternary fuel pins. The steady-state irradiation of both pins was also modeled using BISON. Comparisons of PIE results with modeled predictions showed overall agreement in fractional fission gas release but consistent overestimation of axial and radial swelling due to gaseous and solid swelling models. These findings underscore the critical importance of pre-test characterization on test and sibling pins to accurately capture steady-state fuel behavior ahead of transient testing, thus establishing a baseline for post-test comparison. Additionally, these analyses identified key data gaps that warrant further investigation to improve the understanding and prediction of fuel swelling, thereby enhancing the synergy between modeling and experimental efforts in supporting accident testing.

BISON↗

DOE OSTI2025

Preliminary Plan to Inform Testing of a Heat Exchanger Test Article

This report presents a preliminary plan to guide the qualification testing of advanced heat exchanger (HX) components for nuclear-to-industrial heat transfer applications. The objective is to establish a defensible, physics-based methodology that integrates computational modeling, targeted experimentation, and in-service inspection considerations to demonstrate component performance and reliability under representative reactor conditions. The analysis identifies Sodium-cooled Fast Reactor (SFR) and High-Temperature Gas-cooled Reactor (HTGR) systems as reference configurations in terms of temperature, pressure, and chemical environment. Within these operating envelopes, dominant degradation mechanisms— including creep–fatigue interaction, flow-induced vibration, corrosion, and diffusion-bond deterioration—were evaluated to define test requirements. A comprehensive computationalexperimental framework is proposed to support life prediction and qualification activities. The framework couples high-fidelity structural-mechanics, thermal-hydraulic, and fluid-structure interaction models with accelerated degradation testing to produce a traceable linkage between microstructural evolution, mechanical performance, and remaining useful life (RUL). The approach adheres to established Verification, Validation, and Uncertainty Quantification (VVUQ) standards (ASME V&V 10/20; NUREG-2152) and incorporates a digital-twin architecture for continuous model refinement through data assimilation. The plan further outlines testing methodologies, including pre-test analyses, test-loop design parameters, and sensor placement strategies that maximize information yield while maintaining mechanistic fidelity. Complementary sections describe in-service inspection (ISI), on-line monitoring (OLM), and structural-health-monitoring (SHM) techniques applicable to compact HX geometries typical of advanced reactors. Collectively, these activities establish the technical foundation for demonstrating 40-60-year equivalent service life of advanced heat exchangers in support of the U.S. Department of Energy’s Advanced Reactor and Integrated Energy Systems programs. The forthcoming phase will execute the defined pre-test analyses, initiate hardware fabrication, and implement the integrated testing campaign to validate the proposed qualification methodology.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2025

Code Coverage Status of the ARC code GAMSRC

The Argonne Reactor Code (ARC) software system supports users in their fast reactor design goals by providing neutronic, thermal-hydraulic, and structural analysis capabilities. GAMSOR serves as procedure to obtain the neutron and gamma power distribution information in the ARC code system. GAMSOR is a specially modified version of DIF3D (dif3d.x becomes dif3d_gamsor.x). After some work, it was determined that carrying out software on GAMSOR was impractical and would not fit well with commercial grade dedication. GAMSRC was written in the last decade to replace GAMSOR such that the user can rely soley upon the verified DIF3D (dif3d.x) code and GAMSRC to obtain the neutron and gamma power distribution information. GAMSRC is also fully verified and ready for commercial grade dedication. In the coming years, GAMSOR will be deprecated and GAMSRC will fully take over in the ARC code system. This document identifies the set of test problems used to assess the code coverage for GAMSRC. The goal is to document what parts of the existing GAMSRC code are touched by the set of test problems and which are not. The code coverage analysis of GAMSRC was performed with the Code Coverage Tool of the Intel Fortran compiler which requires modifications to the compilation of GAMSRC. The code coverage tables are given for each submodule of GAMSRC. Because GAMSRC links to modules in DIF3D, some details on coverage changes to the DIF3D lined files is provided. As will be seen, most of the uncovered parts/files can be ignored because they are either for error message and debugging output or obviously not needed by GAMSRC today.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2025

Code Coverage Status of the ARC Code DASSH-F

The Argonne Reactor Code (ARC) software system supports users in their fast reactor design goals by providing neutronic, thermal-hydraulic, and structural analysis capabilities. DASSH-F serves as a steady state thermal hydraulic capability within the ARC system and replaces the SE2-ANL software that preceded it. This document identifies the set of test problems used to assess the code coverage for DASSH-F. The goal is to document what parts of the existing DASSH-F code are touched by the set of test problems and which are not. Because the verification work remains to be done on DASSH-F, one can assume that most of these issues will be resolved as part of that work. The code coverage analysis of DASSH-F was performed with the Code Coverage Tool of the Intel Fortran compiler which requires modifications to the compilation of DASSH-F. The code coverage tables are given for each submodule of DASSH-F. Because DASSH-F links to modules in DIF3D, some details on coverage changes to the DIF3D linked files is provided. As will be seen, most of the uncovered parts/files can be ignored because they are either for error message and debugging output or obviously not needed by DASSH-F today. Seven features of the DASSH-F code were identified to not be covered by the existing testing suite and thus additional verification test problems are suggested to fully cover these sections.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2025

Preliminary System Interface Failure Mode Analysis for Two Advanced Reactors

This study explores two distinct Balance of Plant (BOP) configurations: the Rankine cycle for a sodium-cooled fast reactor (SFR) and the Brayton cycle for a gas-cooled reactor (GCR). As representative designs, the Power Reactor Innovative Small Module (PRISM) by GE Hitachi Nuclear Energy was selected for the SFR, while the Gas Turbine Modular Helium Reactor (GT MHR) by General Atomics was chosen for the gas-cooled reactor. Both configurations were adapted to deliver high-quality heat for industrial applications. A Failure Modes and Effects Analysis (FMEA) was conducted for each system to identify critical failure modes affecting key components. This study marks the first phase of a two-step design optimization approach, integrating FMEA into the design process. Based on the analysis, design modifications and mitigation strategies were proposed to enhance system resilience. The second phase, to be detailed in a subsequent report, will focus on the role of the control system in mitigating these failures. The FMEA serves as a foundation for defining the control topology, ensuring system resilience against component failures that could compromise essential functions, such as electricity and heat production.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2024

Effect of Heat Treatment on Microstructure and Mechanical Property of 316L Stainless Steel Produced by Laser Powder Bed Fusion

The advanced non-light water reactor designs (Gen IV reactors), including molten salt/ very high temperature/ sodium-cooled and lead-cooled fast reactors, typically operate at higher temperatures and more extreme radiation conditions than light water reactors. An intrinsic part of the deployment and progress of Gen IV reactor designs is selecting the most suitable structural material for a specific application. Additive manufacturing (AM), a fairly new process of making physical, three-dimensional objects from a computer design file, is going to completely change the way of design, build and certify nuclear systems. It offers a range of opportunities to produce complex geometries from existing materials, offers new routes for processing of previously difficult to process materials, allows for design of new high-performance materials, and finally facilitates hybridization of dissimilar materials. This emerging technology has successfully produced cars, wind turbine blade molds and even live cells. It could also open up big opportunities for the nuclear industry to quickly deploy technologies at a fraction of the cost. So far, AM techniques have been preliminarily applied in the field of nuclear reactors, including the classical parts such as the pressure vessel of a small reactor with 508-III steel, the bottom nozzle of a fuel assembly with 304L steel, the fuel cladding with zirconium alloy and the integrated impeller of a pump and the multi-channel valve body with 316L steel [6,7]. The AM applications for operating nuclear reactors started in auxiliary plant components and have slowly migrated to metallic reactors and core components, but many of these are not safety critical components. Although many parts used for nuclear reactors have been fabricated by AM techniques, practical applications in engineering are still a long way off due to the uncertainty factors focused on the processing, material properties, analysis methods and application standards, which feeds the safety and life-cycle of the nuclear reactor. Due to rapid, repeated heating and cooling during production, a high dislocation density was present in the AM material. This microstructure feature is unstable at elevated temperature while high temperature is one of the typical operation environments for nuclear reactors. Thus, it is important to understand the thermal effect on the microstructure of AM material. The objectives of this study are to investigate the effect of heat treatment on the microstructure and mechanical properties of 316L stainless steel produced by laser powder bed fusion additive manufacturing, and to determine an appropriate heat treatment practice that will be applied to the lightweight AM lattice-structured material with the same chemistry. The heat treatment study consisted of annealing the samples at a temperature range of 800 to 1200 oC with a 50 oC increment for different times (1-24 hours), followed by vacuum or air cooling. Microstructural characterization was carried out by Scanning Electron Microscope (SEM). Grain size and crystallographic orientation were investigated by Electron Backscatter Diffraction (EBSD). Vickers hardness tests with a 0.5 kg load were employed to determine the hardness of samples after different heat treatments. After heat treatment, the random crystallographic orientation was preserved, and the volume fraction of high-angle grain boundaries (grain boundary misorientation =15 oC) remained the same. The dislocation density decreased with annealing temperature due to recovery. The fine subgrain structures in the as-printed specimen were quite stable up to 1200 oC. Minimal recrystallization was observed up to 1200 oC. Recrystallization initiated only after 8.5 hours at 1200 oC. The SEM images did not show obvious dependence of microstructure on cooling rate. The hardness of the specimens decreased with increasing annealing temperature as a result of the decrease in dislocation density. It is interesting to note that the AM material showed very similar hardness to the wrought material when annealing at similar temperature, although the microstructures are very different. Annealing at 1050 oC for 1 hour followed by air cooling was selected as the heat treatment procedure for the lattice designed lightweight AM 316L material.

36 MATERIALS SCIENCE↗

DOE OSTI2025

SAS4A/SASSYS-1 Validation with FFTF Tests

The FFTF liquid sodium cooled test reactor was built to assist the development and testing of advanced fuels and material for fast reactors. The goals of the FFTF Passive Safety Testing program included confirming the safety margins of FFTF as a liquid metal reactor, providing data for computer code validation, and demonstrating the inherent and passive safety benefits of its specific design features. The program included thirteen unprotected loss of flow without scram tests. In preparation for the Passive Safety Testing program, a series of individual reactivity feedback tests were performed which were designed to simulate and validate specific features and reactivity feedbacks of the FFTF core.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2025

Progress on the US-Japan Source Term Benchmark Analysis Collaboration

There has been a resurgence in global interest in advanced reactor technology, with a variety of innovative concepts being proposed and developed. Sodium-cooled Fast Reactors (SFRs) have garnered considerable attention given their beneficial characteristics and extensive historical development programs and operating experience. Central to the licensing of non-light water reactor (non-LWR) technology is the characterization of the safety case. At its basics, reactor safety focuses on the prevention and mitigation of the release of radioactive material to the environment.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2025

Conjugate Heat Transfer Modeling of Salt-Filled Fuel Pins for Stable Salt Reactor Safety Analysis

The Stable Salt Reactor (SSR) combines the proven structural design of light water reactor fuel assemblies with the inherent safety and fuel-cycle advantages of molten salt technology. In its fast reactor configuration, the SSR utilizes recycled nuclear waste as fuel, sealed within narrow salt-filled fuel pins and cooled by a surrounding liquid salt coolant. Reliable transfer of heat from the molten fuel salt through the cladding to the external coolant is essential for both reactor safety and performance. This work investigates conjugate heat transfer (CHT) in the SSR’s salt-filled fuel pins using NekRS, a high-fidelity spectral element computational fluid dynamics (CFD) solver. The analyses capture internal natural convection within the molten fuel salt and external forced convection in the coolant, under steady-state and transient operating conditions. Parametric studies evaluate how variations in reactor power and coolant flow rate influence heat transfer distributions and system response. The high-fidelity CFD results are time-averaged and post-processed for direct comparison with moderate-fidelity Reynolds-averaged Navier–Stokes (RANS) models, and for the development of reduced-order models within the SAM system code. These validated models support fast-running safety analyses of normal and off-normal transients, improving predictive capability for key safety margins. By integrating advanced CFD with system-level safety tools, this study strengthens the modeling framework for SSR design, reduces uncertainty in molten salt CHT simulations, and accelerates the engineering and licensing of next-generation nuclear reactors.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2025

Finish development, test and then demonstrate new baseline fuel performance capability for UN fuel swelling models under steady-state and transient conditions

Uranium mononitride (UN) has emerged as a promising candidate for advanced nuclear reactor fuels, particularly for high-temperature and high-power applications such as sodium-cooled fast reactors, space power systems, and TRISO particle fuel designs.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2024

Segmentation and Classification of Fission as Pores in Reactor Irradiated Annular U–10Zr Metallic Fuel Using Machine Learning Models

Metallic fuels, particularly U—10Zr, are promising candidates for next-generation sodium-cooled fast reactors. Irradiation of nuclear fuels in reactors can lead to the formation of solid and gas fission product which subsequently forms microstructural pores, deteriorating fuel performance. Due to the massive amount of pores and complex phases formed, a quantitative description of fission gas pores is not yet available, preventing the development of microstructure-informed fuel performance modeling for fuel qualification. This paper applied a pre-trained deep learning model to ~10,260 high magnification scanning electron microscopy images. This method increased the accuracy of fission gas pore segmentation and allows statistical features to be extracted which cannot be achieved manually. A pre-trained decision tree model worked on the segemenation results and further classified the pores into different categories to produce a correlation between the pores, movement of lanthanides, and temperature gradient during irradiation. Finally, this paper emphasizes the potentials of machine learning models to accelerate fuel research, development, and qualification for advanced reactors.

36 MATERIALS SCIENCE↗

DOE OSTI2024

NSUF BOILER Pre-Irradiation Characterization and High Flux Isotope Reactor Experiment Design

Alumina-forming austenitic (AFA) stainless steels have emerged as a candidate alloy because of their high-temperature strength, formability, cost, and compatibility with primary coolants for lead-cooled fast reactors (LFRs). This class of steels has exceptional high-temperature oxidation performance; however, a high concentration of Ni is required to stabilize the austenite phase and to provide sufficient creep strength. AFA stainless steels are also susceptible to liquid metal embrittlement (LME). Additionally, under neutron irradiation, Ni will enrich at grain boundaries due to radiation-induced segregation (RIS). Nickel RIS can increase the LME under these coupled effects. Oak Ridge National Laboratory (ORNL) and the NSUF program have leveraged its High Flux Isotope Reactor (HFIR) and experience with complex irradiation experiments to design experiment capsules that test the aforementioned coupled effects. These capsules are designed for insertion in the central flux trap, the highest flux region, of HFIR. The experiment capsules will be filled with Pb, designed to passively melt from the gamma heating in HFIR. The specimens were fabricated into miniature tensile specimens from two different alloys, GA05-25Ni and GA05-20Ni, varying Ni concentrations. The experiment capsules are designed to achieve target temperatures of 400 °C and 650 °C with accumulated dosage of 3 dpa. This report documents the specimen alloy characterization, experimental design, and expected performance of the capsules.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗