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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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At least 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Improvements to the Blade Element Momentum Formulation of OpenFAST for Skewed Inflows

In this work, we modify the blade element momentum algorithm of OpenFAST to improve its predictions under large skewed inflow conditions. We use the well-known Glauert's skew correction and introduce continuous extension of the model for high-thrust conditions. We present the rationale behind Glauert's empirical model and discuss the different conventions possible for the axial induction factor. We verify the model against the higher-fidelity lifting-line vortex method and blade-resolved computational fluid dynamics, and we observe that the new implementation enhances the accuracy and reliability of OpenFAST's aerodynamic modeling capabilities in conditions involving large skew angles. For the parametric studies run using the different codes, we find that the power changes with the skew angle as cos 1.7 (θ skew ) and the thrust as cos 0.65 (θ skew ). An analysis of the azimuthal variation of the induced velocities in the rotor plane reveals that current redistribution models used in blade element momentum codes may need to be refined.

17 WIND ENERGY↗
DOE OSTI2024

Wind Farm Wakes and Farm-to-Farm Interactions: Lidar and Wind Tunnel Tests

Recent experimental and numerical evidence has shown that the cumulative wake generated from the overlapping of multiple wakes within a wind farm could reduce power performance and enhance fatigue loads of wind turbines installed in neighboring downstream wind farms and may also extend up to distances one order of magnitude larger than those typically considered for intra-farm wake interactions. Similar to individual wind turbine wakes, wind farm wakes have a velocity deficit and added turbulence intensity, both affected by the turbine rotor thrust forces and the incoming turbulence intensity. Therefore, the evolution of wind farm wakes will vary for different operational and atmospheric conditions. In this paper, lidar measurements collected during the American WAKE experimeNt (AWAKEN) and wind tunnel tests of wind farms reproduced by porous disks are leveraged to investigate wind farm wakes.

17 WIND ENERGY↗
DOE OSTI2024

Search for 3D topological superconductors using laser-based spectroscopy (Final Technical Report)

The three-dimensional topological superconductor (3D TSC) is a novel quantum phase of matter that is predicted to exhibit exotic thermal and electrical properties, which may serve applications ranging from precision thermal management and sensing technologies to fault-tolerant quantum information processing. Over the past decade, there has been an intensive effort to realize 1D and 2D TSCs by artificially engineering them from combinations of already existing materials. For example, coupling conventional superconductors to spin-orbit coupled 1D nanowires or to 2D topological insulator surfaces by the proximity effect provides a route to realizing 1D and 2D TSCs respectively. However no artificial engineering strategy is available for a 3D TSC. Therefore, current searches are limited to intrinsically superconducting compounds whose topological properties are difficult to predict. The overarching goal of this project was to realize and to identify 3D TSCs in bulk single crystals using novel laser-based spectroscopic techniques. One major thrust was to develop ultralow temperature and ultra-high-resolution angle-resolved photoemission spectroscopy (ARPES) to directly measure the dispersion of Majorana excitations that are predicted to exist on the surfaces of 3D TSCs. Another major thrust was to develop a rational route to realize 3D TSCs by identifying their precursor phases. It is theoretically proposed that the critical fluctuations of certain ordered electronic phases can mediate Cooper pairing in odd-parity channels and lead to topological superconductivity. Therefore, 3D TSCs may potentially emerge upon suppressing these inversion symmetry broken precursor phases to a critical point with external perturbations such as pressure, strain or even light. To test this hypothesis, we studied candidate materials using a suite of symmetry-sensitive optical probes including rotational anisotropy optical second harmonic generation (RA-SHG) and time-resolved coherent phonon spectroscopy, all operable under high-pressure and low temperature environments.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Optimizing Alabama’s CO 2 Storage in Shelby County (Project OASIS) Milestone 6.0: Evaluation of Class VI Readiness

Introduction. Project OASIS is approximately 30 miles southeast of Birmingham, Alabama, and approximately 5 miles north-northwest of Alabama Power Company's Plant Gaston. Geologically, the Project area is in the Alabama fold and thrust belt province. This work builds on the initiatives of the Southeast Regional Carbon Utilization and Storage Acceleration Partnership (SECARB-USA, DE-FE0031830) that identified nearly 500 million metric tonnes of CO 2 emitted on an annual basis that is not collocated with prospective storage geology (the Coastal Plain of the Southeastern US in this context). This observation suggests costly investments in connective infrastructure (e.g., pipelines) or exploratory well drilling campaigns to identify CO 2 storage opportunities in under explored areas. While not traditionally thought of for saline storage, these studies suggest that storage prospects in the Valley and Ridge Province occur in relatively flat lying structural panels between thrust faults. For the Project OASIS region, available geologic studies related to hydrocarbon exploration suggest that Cambro-Ordovician carbonates and Cambrian clastic units offer multiple potential storage intervals, and that regional confining systems are present, such as the tectonically thickened Floyd-Parkwood Shale. The Project OASIS surface property is owned by a timber and land stewardship company, The Westervelt Company, Inc., who worked with the Project Team to select and prepare adequate sites for geologic assessment. The purpose of drilling the Westover Stratigraphic Test Well #2 was to collect geologic data to model the feasibility of commercial scale CO 2 injection and storage in an under explored region. This initiative benefits the regions emitters as the data generated from this study can inform their own internal decision making. The field program included geological and geophysical evaluations, reservoir engineering analyses, and risk assessments. This report evaluates existing data, as well as a variety of modeling scenarios to evaluate project readiness. Importantly, the impact of this study is not limited to Alabama as there are numerous large emitters throughout Appalachia, in similar geologic settings, contemplating their decarbonization options.

20 FOSSIL-FUELED POWER PLANTS↗
DOE OSTI2025

Optimizing Alabama’s CO 2 Storage in Shelby County (Project OASIS): Task 8 Deliverable 8.0 - Commercialization Plan

The “Optimizing Alabama’s CO 2 Storage in Shelby County: Project OASIS” CarbonSAFE Phase II Project seeks to build on regional data sets that demonstrate that the subsurface within Shelby County, Alabama has the potential to store commercial volumes of CO 2 safely, permanently, and economically. This work builds on the initiatives of the Southeast Regional Carbon Utilization and Storage Acceleration Partnership (SECARB-USA, DE-FE0031830) that identified nearly 500 million metric tonnes of CO 2 emitted on an annual basis from industrial facilities that are not collocated with prospective storage geology (i.e., the Coastal Plain of the Southeastern U.S. in this context). This observation suggests costly investments in connective infrastructure (e.g., pipelines) or exploratory well drilling campaigns are required to identify CO 2 storage opportunities in under-developed areas. While not traditionally thought of for saline storage, these studies suggest that storage prospects in the Valley and Ridge Province of the Appalachian Fold and Thrust Belt occur in relatively flat lying structural panels between thrust faults. For the Project OASIS region, available geologic studies related to hydrocarbon exploration suggest that Cambro-Ordovician carbonates and Cambrian clastic units offer multiple potential storage intervals, and that regional confining systems are present, such as the tectonically thickened Floyd-Parkwood Shale.

20 FOSSIL-FUELED POWER PLANTS↗
DOE OSTI2025

Study of the Design and Characteristics of a Modified Pulsed Plasma Thruster with Graphite and Tungsten Trigger Electrodes

The paper presents experimental results for a modified pulsed plasma thruster (PPT) with solid propellant, using a coaxial anode–cathode design. Graphite from pencil leads served as propellant, and a tungsten trigger electrode was tested to reduce carbonization effects. Experiments were performed in a vacuum chamber at 0.001 Pa, employing diagnostics such as discharge current/voltage recording, power measurement, ballistic pendulum, time-of-flight (TOF) method, and a Faraday cup. Current and voltage waveforms matched an oscillatory RLC circuit with variable plasma channel resistance. Key discharge parameters were measured, including current pulse duration/amplitude and plasma channel formation/decay dynamics. Impulse bit values, obtained with a ballistic pendulum, reached up to 8.5 μN·s. Increasing trigger capacitor capacitance reduced thrust due to unstable “pre-plasma” formation and partial pre-discharge energy loss. Using TOF and Faraday cup diagnostics, plasma front velocity, ion current amplitude, current density, and ion concentration were determined. Tungsten electrodes produced lower charged particle concentrations than graphite but offered better adhesion resistance, minimal carbonization, and stable long-term performance. The findings support optimizing trigger electrode materials and PPT operating modes to extend lifetime and stabilize thrust output.

Faraday cup↗
DOE OSTI2024

Integrated Steady-State System Package for Nuclear Thermal Propulsion Analysis Using Multi-Dimensional Thermal Hydraulics and Dimensionless Turbopump Treatment

Nuclear thermal propulsion is an evolving technology that can be utilized for long-distance space travel. This technology yields the advantage of a high thrust and specific impulse, but requires an examination of the potential design adjustments necessary to enhance its feasibility. The development of nuclear thermal propulsion requires a comprehensive understanding of the system-level behavior during transient and steady-state operation. This paper extends our previous research by including the proper handling of turbomachinery with multi-channel thermal hydraulic simulations only for steady-state solutions. The system-level approach presented here enables the treatment of the turbopump components through non-dimensional analysis that eliminates the assumption of constant efficiencies. All the other components within the system (e.g., reflector and core) can be discretized to multiple channels and layers, in which the full thermal hydraulic solution is established. The approach chosen here enables the realistic modeling of the propellant flow within the expander cycle by capturing the pressure losses, mass flow rate splits, and enthalpy gain for various operational conditions. The verification of the package is completed through point comparisons of previous investigations into similar system designs. Furthermore, sensitivity studies are used to benchmark the capabilities of the package and investigate solution variations due to the perturbation of operational conditions and regimes. The sensitivity studies performed here are important to capture variation in flow characteristics (e.g., temperature, pressure, mass flow rates) for different design objectives such as the thrust and specific impulse. This work demonstrates that system-level simulations lacking multi-channel capability and proper turbomachinery treatment may yield higher uncertainties in understanding the engine’s response and characteristics to changing various requirements. This is extremely important when screening the design space of such propulsion systems and when transient simulations are required.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2024

Piston for use in internal combustion engines and method of making the piston

An additive manufactured piston having a crown portion and a skirt portion form of an aluminum-cerium-silicon alloy. The piston includes a least one recess pocket in an unstressed region located at an interface between an inner surface of the crown portion and an outer surface of the skirt portion. The skirt portion includes an outer panel surface defining an external rib adjacent a peripheral end surface, at least one stiffening rib extending from a pin boss to a skirt end, and a wall thickness of between 0.2 mm and 1.0 mm in a region between the external rib and the at least one stiffening rib. The skirt portion further includes an internal first rib having a width W1 on a thrust side portion and an internal second rib having a width W2 located on an anti-thrust side portion, in which W1 is greater than W2.

Petrus, Ronald John↗
DOE OSTI2024

Enterprise: Exploration of Concepts, Perspectives and Implications for Systems Engineering

The purpose of this paper is to explore the concept of ‘enterprise’ in the context of Systems Engineering (SE). The term ‘enterprise’ has been used extensively to generally describe large complex entities that have an extensive scope of operations. However, a deeper examination of ‘enterprise’ significance for SE can provide insights as our challenges continue with increasingly complex, uncertain, ambiguous, and integrated entities struggling to thrive in the future. The paper explores three central topics. First, the concept of enterprise is introduced as a central aspect of the future focus for SE, as recognized in the INCOSE SE Vision 2035. Second, a more detailed examination of the enterprise concept is developed in relationship to SE. The thrust of this examination is to understand the nature and role of ‘enterprise’ across a broad spectrum of literature and knowledge, ultimately providing a more informed perspective of enterprise for SE. As part of this exploration, a bibliometric analysis of the term ‘enterprise’ is performed. This exploration extracts key themes (clusters) in the ‘enterprise’ literature. Third, challenges for further development and inculcation of ‘enterprise’ within the SE discipline and support for realization of the SE 2035 Vision are suggested. These challenges point out the need to ‘think differently’ about ‘enterprise’ within the SE context. ‘Enterprise’ is proposed as a central, albeit different, perspective for the SE discipline. Finally, the paper closes with a first–generation perspective for ‘enterprise’ in pursuit of the SE Vision 2035.

42 ENGINEERING↗
DOE OSTI2024

Implementation and Validation of a Generalized Actuator Disk Parameterization for Wind Turbine Simulations Within the FastEddy Model

ABSTRACT Fast and accurate large‐eddy simulation (LES) of the atmospheric boundary layer plays a crucial role in advancing wind energy research. Long‐duration wind farm studies at turbine‐resolving scales have become increasingly important to understand the intricate interactions between large wind farms and the atmospheric boundary layer. However, the prohibitive computational cost of these turbulence‐ and turbine‐resolving simulations has precluded such modeling to be exercised on a regular basis. To that end, we implement and validate the generalized actuator disk (GAD) model in the computationally efficient, graphics processing unit (GPU)–resident, LES model FastEddy. We perform single‐turbine simulations under three atmospheric stabilities (neutral, unstable, and stable) and compare them against observations from the Scaled Wind Farm Technology (SWiFT) facility and other LES codes from the recent Wakebench turbine wake model benchmark. Our idealized LES results agree well with observed wake velocity deficit and downstream recovery across stability regimes. Turbine response in terms of rotational speed, generated power, torque, and thrust coefficient are well predicted across stability regimes and are consistent with the LES results from the benchmark. The FastEddy simulations are found to be at least two orders of magnitude more efficient than the traditional CPU‐based LES models, opening the door for realistic LES simulations of full wind plants as a viable standard practice.

17 WIND ENERGY↗
DOE OSTI2024

A Green's Function Wind Turbine Induction Model That Incorporates Complex Inflow Conditions

ABSTRACT In this work, we develop a new analytical turbine induction model that can incorporate complex inflow conditions including cases where the wind velocity and temperature profiles can vary as functions of height. This induction model is derived from the linearized Navier–Stokes and leads to a second‐order ODE that can be solved using a Green's function formulation. The corresponding Green's function for several configurations are found including the infinite domain, semi‐infinite domain with ground plane, and a power law velocity inflow profile. The results of this approach are then compared with simulations of the turbine induction field using the AMR‐Wind CFD solver with a uniformly loaded actuator disk model. These comparisons show that the Green's function approach captures the centerline blockage, three‐dimensional blockage flow field, and streamwise velocity slow down, with very good agreement for lower thrust conditions and at larger distances away from rotor disk. The effects of shear on the turbine blockage were also compared using a power law inflow profile, and we show that this approach matches the CFD predictions for the cases considered.

17 WIND ENERGY↗
DOE OSTI2026

Multipoint Aerostructural Optimization of Wind Turbine Rotors Using a Coupled Blade‐Resolved Aerostructural Solver

Physics‐based design optimization workflows thread the needle between computational cost limitations and simulation complexity, often compromising between modeling detail and the range of operating design conditions. Multipoint aerostructural optimization of wind turbine rotors has so far been confined to low‐fidelity analyses or to high‐fidelity studies with simplified structural models, leaving the most complex design trade‐offs unexplored. We close this gap by performing the first tightly coupled gradient‐based multipoint aerostructural rotor optimization using 3D aerodynamic and structural solvers with discrete coupled adjoints. The optimizer simultaneously varies blade planform, airfoil shapes, and structural thickness through more than 270 design variables, minimizing a weighted combination of rotor mass and power across multiple wind speeds. Applied to a modified DTU 10‐MW benchmark under conservative structural and aerodynamic constraints, our multipoint optimization reduces rotor mass by up to 36% and increases power by 12%–15% across the main operating conditions; biasing the objective toward power yields power gains up to 18% and a 17% mass reduction. For a nominal wind distribution, 3‐point rotor designs accounting for low RPM and high thrust conditions capture dominant trade‐offs and outperform single‐point designs. Adding two off‐design points changes individual‐condition power by less than 3% but leaves the weighted average within 0.5%, and the mass‐power bias has a stronger effect on the final design than the operating‐point weighting itself. Our framework extends naturally to richer load cases and site‐specific wind distributions, providing a basis for high‐fidelity multipoint design earlier in industrial workflows.

17 WIND ENERGY↗
DOE OSTI2026

An analytic result for the 0 → ggHHH amplitude

We present a fully analytic calculation of the leading-order one-loop amplitude for triple Higgs production via gluon fusion, gg → HHH, retaining full dependence on the mass of the heavy quark circulating in the loop. This amplitude provides a direct probe of the triple and quartic Higgs self-couplings, the measurement of which is a central goal of current and future colliders. The amplitude can be presented in compact form thanks to the use of analytic reconstruction techniques, based on finite-field and p-adic evaluations, multivariate partial fraction decompositions, and primary decompositions to identify common numerator factors. Although full analytic results are given in the text and in the supplementary material, the main thrust of this paper is to further test and illustrate these analytic reconstruction techniques in a concrete physical example. Our results provide a compact and efficient representation of the matrix element for this process, enabling evaluations that are more than an order of magnitude faster than existing numerical alternatives. Full analytic control of the leading-order, loop-induced amplitude is an important step towards handling more complex 2-loop or real-radiation corrections to this and related processes.

Campbell, John M. [Fermilab] (ORCID:00000002136193↗
DOE OSTI2025

Precision e + e − hemisphere masses in the dijet region with power corrections

We derive high-precision results for the e + e − heavy jet mass (HJM) dσ/dρ and dihemisphere mass (DHM) d 2 σ/(ds 1 ds 2 ) distributions, for s 1 ~ s 2 , in the dijet region. New results include: i) the N 3 LL resummation for HJM of large logarithms ln n (ρ) at small ρ including the exact two-loop non-global hemisphere soft function, the 4-loop cusp anomalous dimension and the 3-loop hard and jet functions, ii) N 3 LL results for DHM with resummation of logarithms ln(s 1,2 /Q 2 ) when there is no large separation between s 1 and s 2 , iii) profile functions for HJM to give results simultaneously valid in the peak and tail regions, iv) a complete two-dimensional basis of non-perturbative functions which can be used for double differential observables, that are needed for both HJM and DHM in the peak region, and v) an implementation of renormalon subtractions for large-angle soft radiation to $\mathcal{O}$ (α$^{3}_{s}$) together with a resummation of the additional large ln(Qρ/Λ QCD ) logarithms. Here Q is the e + e − center-of-mass energy. Our resummation results are combined with known fixed-order $\mathcal{O}$ (α$^{3}_{s}$) results and we discuss the convergence and remaining perturbative uncertainty in the cross section. We also prove that, at order 1/Q, the first moment of the HJM distribution involves an additional non-perturbative parameter compared to the power correction that shifts the tail of the spectrum (where 1 ≫ ρ ≫ Λ QCD /Q). This differs from thrust where a single non-perturbative parameter at order 1/Q describes both the first moment and the tail, and it disfavors models of power corrections employing a single non-perturbative parameter, such as the low-scale effective coupling model. In this paper we focus only on the dijet region, not the far-tail distribution for ρ ≳ 0.2 beyond which the trijet factorization and resummation become important.

Factorization↗
DOE OSTI2025

Dynamic response of a freely rotating butterfly valve in the advanced test reactor − dynamic coefficients modeling

Here, in evaluating the water hammer issue pertaining to the primary-coolant-regulating butterfly valve in the Advanced Test Reactor, the dynamic fluid body interaction (DFBI) approach was implemented in the analysis covered in Part I. Although DFBI modeling accurately and simultaneously solved the dynamic motion of the valve’s disk along with the flow field of the surrounding fluid, it shed little light on the reason behind such motion. For Part II, the reacting torque of the fluid on the disk was decomposed into representations of the dynamic coefficients in terms of stiffness, damping, and added mass. These were evaluated via simulations with steady-state static (stiffness), constant angular speed (damping), and variable angular speed (added mass) disks. Substituting the dynamic coefficients into Newton’s second law enabled the response trajectories to be obtained. Stable (by average) and unstable equilibrium positions and thrust tendencies of the valve were determined based on the stiffness coefficient (or static torque), the response amplitude was dampened or enlarged by the damping coefficient (minorly affected by added mass), and the response frequency was altered by the damping and added mass coefficients. Although the dynamic coefficient approach renders slightly different trajectories, due to the averaging effect of the torque in comparison to the DFBI method, the overall trend of the response aligns with the DFBI simulation, thus confirming the conclusion in Part I that a fix to the current butterfly valve is necessary.

22 - GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2025

Fuel cells for single-aisle regional aircraft: System configuration, performance and cost

A hydrogen fuel cell propelled electric aircraft can compete with incumbent turbofan technologies for single-aisle regional aircraft by coupling design of stack, air handling, thermal management, propulsion, and airframe to optimize performance. The stack operates at 95°C to facilitate heat rejection during take-off and below 75°C during cruise to extend lifetime and is oversized to satisfy power requirements at end of life. A multi-stage turbocompressor with a compression ratio >10 is selected to reach high stack power density at 11,300-m cruise altitude. The propulsion system is configured to accommodate air handling within the core duct, an inclined heat exchanger in the outer duct to limit the nacelle size, and variable area nozzles to independently control mass flows through the core and bypass ducts. The airframe is modified for maximum lift coefficient and longer balanced field length for dramatically reduced thrust during take-off, and the fuselage is stretched by 20% to store liquid hydrogen (LH 2 ). Modularization of power systems promotes safety in one engine inoperative scenarios and allows reaching specific power metrics for stack, balance-of-plant and fuel cell system (FCS), necessary for acceptable take-off weight. In conclusion, cost parity requires increase in FCS lifetime, LH 2 cost reduction, and improved FCS specific power.

Catalyst durability↗
DOE OSTI2026

Overview of advanced plasma-facing materials testing for Fusion Pilot Plants at DIII-D

Characterization and testing of advanced plasma-facing materials (PFMs) for Fusion Pilot Plants (FPP) is being conducted at the DIII-D National Fusion Facility through the ongoing two-year FPP Candidate Materials Thrust. Year one tested 17 novel materials utilizing the Divertor Materials Evaluation System (DiMES), with samples analyzed pre- and post-experiment via SEM, EDS, and confocal microscopy. Repeatable reference discharges were developed to ensure uniformity between experiments, including a new strike-point rastering scenario to provide more uniform heat/particle flux across DiMES during ELMing H-mode discharges. Various sample geometries and temperatures were used to achieve FPP-relevant conditions, including samples angled 10° towards the incident plasma flux and pre-heating up to 500 °C. The first exposure of liquid lithium (Li) capillary porous structures in a tokamak demonstrated uniform emission of Li vapor and suppression of Li droplets in H-mode when preheated to 350 °C. Dispersoid-strengthened W with 1 wt% TaC, TiC, and ZrC exposed to H-mode showed cracking and dispersoid ejection for all varieties except TiC, providing a clear down-selection. Ultra-high temperature ceramic materials TiB 2 and ZrB 2 showed minimal degradation under L-mode exposure. Silicon carbide (SiC) fiber composites showed arcing along edges, while CVD SiC remained pristine. Atmospheric plasma-sprayed W and SiC coatings endured H-mode exposure without macroscopic delamination; SiC exhibited granular ejection, while W showed increased outgassing. Additional W-based alloys were stress tested in H-mode, including Ni-based W heavy alloys, W f SiC f /W composites, W multi-principle element alloys, and functionally-graded W/SiC, to varying degrees of success.

DIII-D↗
DOE OSTI2025

Microscopic analysis of irradiated UN–Mo–W for space nuclear propulsion

Nuclear propulsion is an effective method of providing thrust in deep space, allowing for shorter mission duration for long-term surface missions to Mars. The fuel for nuclear propulsion systems must exhibit superior mechanical and thermal properties, to decrease the possibility of fuel failure and to increase reactor efficiency. Here, the objective of the Sirius project is to fabricate and irradiate cermet fuels at the Idaho National Laboratory Transient Reactor Facility to determine the properties of the fuel after irradiation at prototypical nuclear propulsion start-up conditions. The Sirius project featured 3 test capsules, Sirius-1 featured uranium nitride fuel dispersed in a matrix of tungsten and rhenium, while Sirius-2A and -2B featured uranium nitride-molybdenum-tungsten fuel (UN-Mo-W). The fuel samples from the Sirius-2A and -2B capsules were examined after irradiation using optical microscopy, scanning electron microscopy, and X-ray diffraction analyses. The mechanical properties of the fuel from Sirius-2A and -2B are discussed in a previous work. In this study, the results of the optical microscopy, scanning electron microscopy, and X-ray diffraction analyses are discussed.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗