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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 163 records · Page 9
All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

Iron Oxide Reduction Rate Affects Iron Product Morphology

Magnetite concentrates from different parts of the Mesabi Range, exhibiting varying tendencies to encapsulate, were reduced using thermogravimetric analysis (TGA) and a high-temperature confocal scanning laser microscope (CSLM). Gas-phase mass-transfer conditions were intentionally varied by employing two reactors with different geometries: the TGA produced significantly slower reduction, whereas the CSLM setup yielded reduction rates up to 20 times faster under mass-transfer-controlled conditions. A preliminary mechanism is proposed to explain the transition from a porous iron product to a dense encapsulating layer. Encapsulation is interpreted as the outcome of competition between pore creation, driven by the reduction rate, and pore elimination, driven by surface diffusion. When pore formation is insufficient to counteract pore coarsening, a dense iron layer develops and restricts further reduction.

encapsulation↗
DOE OSTI2025

Thermo-hydraulic steam pipe models for district heating simulations: Simplifications to balance accuracy and simulation speed

Steam piping networks are essential for optimizing performance in industrial processes and district heating systems. However, dynamic models that balance thermo-hydraulic accuracy with computational efficiency remain limited. In response, this paper presents a new discretized steam pipe model based on the plug flow approach, capturing key thermo-hydraulic behaviors while simplifying steam phase change processes. Implemented in Modelica, the model accurately calculates temperature and pressure distributions along steam pipelines. To improve computational efficiency for district-scale simulations, five model simplifications are introduced: lumped thermo-hydraulic functions, empirical correlations, fluid state approximations, steady-state dynamics and inclusion of flow derivatives. These simplified models achieve 85%-98% accuracy in predicting pressure drop and condensation losses, including dynamic condensate behavior during pipe warm-up—a factor often overlooked in existing models. The models support diverse network configurations, scaling effectively to systems with multiple distribution pipes and connected building loads. Discrete models provide detailed insights but exhibit a cubic increase in simulation time as the network scales by N connected building O(N 2.42 ). In contrast, lumped models simulate 10–28 times faster than discrete, offering quadratic scaling of simulation time O(N 1.73 ). However, they still require 6 times more computation time than a lossless network, highlighting the inherent computational challenges of modeling compressible fluid flow. In conclusion, the steady-state lumped variant, with its near-linear scalability in computational time O(N 1.01 ), emerges as an efficient solution for preliminary design evaluations and extensive parametric studies.

15 GEOTHERMAL ENERGY↗
DOE OSTI2026

Demonstration and analysis of volumetric additive manufacturing via sub-orbital spaceflight testing

Computed Axial Lithography (CAL) represents a significant advancement in the emerging field of Volumetric Additive Manufacturing (VAM). CAL addresses key limitations of traditional photopolymer additive manufacturing technologies, by eliminating the need for layering and support structures. Unlike conventional methods, CAL prints components by illuminating all points within a desired geometry simultaneously, using tomographic reconstruction to form the object in a single step. This unique approach eliminates the relative motion between the object and the precursor material, enabling faster printing speeds and reducing the waste associated with support structures. However, CAL parts require post-processing steps before they can be utilized. CAL's core attributes make it particularly suited for In-Space Manufacturing (ISM), due to its fast fabrication times, wide breadth of materials it can use, and minimized footprint. CAL has been successfully demonstrated in microgravity during parabolic flight experiments. However to fully validate and understand CAL's behaviour in microgravity, all manufacturing and post-processing steps must be integrated. In June 2024, we conducted SpaceCAL Mission 3, testing this entire workflow on a suborbital flight aboard Virgin Galactic's SpaceShipTwo. During ~140 s of microgravity, the system autonomously manufactured and post-processed four parts using PEGDA700 resin. Post-flight analysis showed that 2/4 parts were recognisable, while others were distorted due to bubble formation from residual water droplets, off-axis optical aberrations, and non-uniform solvent rinsing. Despite these limitations, this study represents the first integrated CAL workflow in space, providing an initial experimental demonstration and analysis for closed-loop in-space manufacturing.

Waddell, Taylor [Department of Mechanical Engineer↗
DOE OSTI2025

Modeling the evolution of slip localization: Realization of link to material strength

Slip localization formation is the chief mechanism underlying the deformation of almost all metals, from pure elements to high-performance superalloys. The intensity of individual slip localizations is often related to the ultimate strain level for failure but not to the strength of the metal. Here we show that across 15 distinct metals, the intensity of slip in individual slip localizations and slip localization spacings are strongly related to material yield strength. Using a three-dimensional crystal plasticity-based micromechanical model that explicitly simulates the growth of discrete slip localizations, we reveal that the stronger the metal, the faster and earlier slip localizations intensify. The relationship is attributed to the formation of a zone that surrounds the slip localization where the driving force for slip is absent. We find that the zone size is controlled by the strength of the neighboring crystal. Consequently, as strength increases, slip becomes increasingly preferred within the slip localization itself and formation of other slip localizations becomes more likely further away.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Switching kinetics in ferroelectric zinc magnesium oxide thin films

The switching kinetics of RF-magnetron reactively sputtered ~200 nm thick Zn 1-x Mg x O (ZMO) ferroelectric thin films with x = 0.41 and x = 0.27 prepared on Pt/Ti/SiO 2 /Si substrates were studied at applied fields near the coercive fields, ranging from 3.4 to 5.1 MV cm -1 , and at temperatures ranging from room temperature to 100 °C. Polarization reversal in ZMO followss the Kolmogorov-Avrami-Ishibashi kinetics model for nucleation and growth at applied fields near the coercive field, and obeys an individual column switching (ICS) model at higher applied fields required to switch most of the spontaneous polarization. Switching in the high-applied field regime can be described using either the Gaussian or inverse gamma distribution functions depending on the mole fraction of magnesium in the film. The switching current transients of the high-Mg content ZMO film (x = 0.41) are always bi-modal, whereas the low Mg composition film (x = 0.27) is described by the Gaussian distribution initially following wake-up, and becomes bimodal with continued cycling. Rayleigh-like behavior of the dielectric constant revealed a simultaneous increase of the irreversible and decrease of the reversible contributions to the dielectric constant, which was ascribed to an increase in the density of mobile domain walls with cycling and resulted in faster switching.

30 DIRECT ENERGY CONVERSION↗
DOE OSTI2024

A non-melting additive approach to structural repair of aluminum aircraft fastener holes

The damage to fastener holes in aerospace aluminum structures presents significant challenges for aircraft durability, and conventional bushing methods for repairing oversized holes often fall short due to the lack of metallurgical bonding and limited edge distance availability. This study investigates additive friction stir deposition, a non-melting additive process, as a viable alternative for the structural repair of aerospace fastener holes. The repair process, demonstrated on AA7050 (Al-Zn-Mg-Cu-Zr) hole structures, involves filling oversized holes with new material and machining to restore the original hole size. The repaired hole coupons are defect-free and exhibit good fatigue performance under fully reversed tension-compression loading (R = -1). At a nominal stress amplitude of 123.5 MPa, the average number of cycles to failure is 12,666 for unrepaired baseline coupons and 17,372 for effectively repaired coupons. Restoring complex geometries without compromising fatigue performance has been difficult in aerospace applications; this study marks the first demonstration of additive repair that consistently outperforms the unrepaired baseline coupons. Notably, the result is achieved through a low-energy, cost-effective solution without the need for post-repair heat treatment. Except for a few outliers, the post-repair fatigue performance generally remains inferior to that of undamaged, pristine coupons, likely due to precipitate evolution in AA7050 caused by the thermomechanical processing nature of additive friction stir deposition. This evolution weakens the repair region and the adjacent base material, leading to faster crack initiation and growth compared to the properly aged base material, AA7050-T7451.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Measuring thermomechanical response of large-format printed polymer composite structures via digital image correlation

Large-format additive manufacturing (LFAM) is a branch of additive manufacturing (AM) research with the ability to create large structures typically measuring several meters in scale. LFAM is advantageous for tooling applications, not only because it offers the ability to create complex geometries not easily made using subtractive manufacturing processes, but the cost savings of pelletized feedstock used by these systems result in larger parts printed at faster speeds than traditional AM systems. Fiber reinforced polymer (FRP) is a commonly used feedstock material in LFAM structures because it reduces the distortion experienced during printing. However, FRP introduces highly anisotropic thermomechanical properties and contributes to a nonhomogeneous microstructure that can result in critical distortion of dimensions during tooling. Measuring the global thermomechanical response of LFAM structures requires a more representative method that accounts for not only anisotropic properties but also the nonhomogeneous nature of the final part. This is where traditional techniques to measure thermomechanical response, such as thermomechanical analysis (TMA), fall short as they assume homogeneity. This study evaluated the coefficient of thermal expansion (CTE) of LFAM structures as measured by TMA as compared to a novel digital image correlation oven (DIC Oven) system. The LFAM structures were made from 20 % by weight carbon fiber reinforced acrylonitrile butadiene styrene (CF-ABS). TMA measurements showed significant variations in CTE across a single LFAM bead, confirming the need for a global technique that captures overall thermomechanical response. The CTE values measured using the DIC Oven compared well to average TMA values obtained from localized measurements across the sample. The DIC Oven was also used to quantify the effects of different layer orientations on thermomechanical properties, which cannot be easily captured using TMA. A predictive model was also developed by using localized TMA values across an LFAM bead to predict the overall thermomechanical response of an LFAM structure.

36 MATERIALS SCIENCE↗
DOE OSTI2025

The rigorous upscaling of advection-dominated transport in heterogeneous porous media via the Method of Finite Averages

Systems involving advection-dominated transport through heterogeneous porous and fractured media are ubiquitous in subsurface engineering applications. However, upscaling such systems continues to challenge rigorous modeling efforts, particularly when advection is stronger than diffusion at fine spatial scales (i.e., when the Péclet number is greater than one at length scales that characterize a system’s unit-cells, representative elementary volumes, or averaging regions). Here, in this work, we propose and validate a strategy for extending the Method of Finite Averages (MoFA), a rigorous upscaling methodology for heterogeneous porous media, to upscale transport systems experiencing stronger advection than diffusion at fine scales (i.e., fine-scale Péclet numbers greater than one). We detail the strategy, the physical conditions under which it can be applied while retaining a priori modeling error guarantees, and implement the strategy to obtain a MoFA model for advective-diffusive transport that accommodates advective physics at fine spatial scales. We then perform two numerical experiments considering systems with system-scale Péclet numbers of 300 and 1000 — which correspond to fine-scale Péclet numbers of 30 and 100, respectively — to verify that the error guarantees are met under the strategy. After, we conduct a numerical study to demonstrate the strategy’s advantages over the original MoFA methodology. The results suggest that rigorously-upscaled transport models for heterogeneous porous media experiencing advective physics at finer spatial scales can be derived through MoFA and resolved orders of magnitude faster than their pore-scale counterparts. The results also suggest that the presented strategy is limited to modeling shallow concentration gradients when there are large differences between the time scales related to advection and a system’s temporally-varying boundary conditions. This limitation hinders the strategy’s practicality in modeling more advective systems, and as such, opportunity exists for developing additional strategies that accommodate rapidly-varying boundary conditions — and consequentially, steeper concentration gradients — while modeling advective systems with MoFA.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Impact of salinity on morphology, growth, and pigment profiles of Scenedesmus obliquus HTB1 under ambient air and elevated CO 2 (10 %) conditions

Certain microalgal species, such as Scenedesmus obliquus strain HTB1, thrive under high CO 2 concentrations, making them promising for carbon sequestration to mitigate climate change. Isolated from the Baltimore Inner Harbor, HTB1 grows faster with 10 % CO 2 than with ambient air. To investigate its responses to salinity and elevated CO 2 , two experiments were conducted. In the first, HTB1 was cultured at seven different salinities (0, 17.5, 20, 22.5, 25, 27.5, and 30 ppt) (parts per thousand) under ambient air. Higher salinity caused cell shrinkage, color changes from green to pale white, reduced pigments like zeaxanthin, lutein, and chlorophyll b, but increased canthaxanthin. Growth declined significantly above 22.5 ppt. The second experiment compared HTB1's response to salinity (0, 10, 20 ppt) under air and 10 % CO 2 . Cultures under 10 % CO 2 showed minimal color changes, while those under air shifted from green to brown, with salinity having less inhibitory effects on growth under elevated CO 2 . Interestingly, lutein and canthaxanthin levels rose with salinity in 10 % CO 2 . These findings indicate that elevated CO 2 mitigates salt stress in HTB1, reducing its impact on growth and promoting adaptive pigment changes. This study sheds light on how salinity and CO 2 interact to influence HTB1's morphology, growth, and pigment composition, enhancing our understanding of its resilience and potential applications.

20 FOSSIL-FUELED POWER PLANTS↗
DOE OSTI2026

Design and scale-up of 3D printed bat houses with biomass-derived polymer composites

Biomass (e.g., pine sawdust, especially high–ash content pine sawdust) is commonly disposed of as waste. Combining biomass with polymers to make composite feedstocks for 3D printing has been explored as a method to reduce or repurpose the biomass waste. Although not all biocomposite properties are known, the wood-based polylactic acid (PLA) composite has promising qualities for applications in ecological settings. In this work, pine wood–PLA composite feedstock was used to 3D print supplemental roost structures for endangered tree-roosting bats, which often face a paucity of suitable naturally occurring roosts. This material combination was selected because it is estimated to degrade faster than the synthetic material systems that are used widely in supplemental bat roosting structures to aid in the conservation of tree roosting bats. The layered, rough surface created by the 3D printing process serves as a surface that bats can grip while roosting. Computer-aided design (CAD) models were generated based on natural roost structures, and a full-size bat house was successfully additively manufactured using a pellet-fed large-scale 3D printing system. The 3D printed hexagon exhibited a tensile strength of 22–23 MPa and a Young’s modulus of 3202–3218 MPa in the x-direction. It has been demonstrated that the 3D printed bat house can be installed on a tree in a stable fashion. This successful demonstration of a bat roost manufactured using a bioderived composite should promote its use in other fish and wildlife structures and broader industrial applications such as construction and automobiles.

3D printing↗
DOE OSTI2024

On the convergence of the fixed point method for solving neutron transport alpha eigenvalue problems

It was shown that the Fixed Point Method (also known as the Rayleigh Quotient Method) is several times faster than the Critical Search Method for solving neutron transport alpha eigenvalue problems. It was also shown that the Fixed Point Method is able to determine the alpha eigenvalues of sub-critical systems that are beyond the reach of the Critical Search Method. Despite these significant advances, the Fixed Point Method remains an unproven algorithm. Here, this report provides a proof.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Differentiable hybrid neural network approach for enhancing reactor dynamics simulations

Reactor dynamics simulations provide essential insights into the time-dependent behavior of nuclear reactors under various operating conditions. However, high-fidelity simulations can be computationally intensive, requiring significant computational resources. Here, to address this challenge, this study employs a differentiable hybrid model that utilizes neural networks as a corrector to enhance the performance of a low-fidelity simulation, aligning its predictions with those of a high-fidelity simulation. Low-fidelity and high-fidelity simulations were obtained by adjusting the mesh size in the System Dynamics Analysis Tool. The differentiable hybrid model was trained in two approaches: time-step-wise and sequence-wise. It was then applied to simulate various transients in a molten salt reactor. Its performance was evaluated by comparing its responses to transients against those of the high-fidelity simulation. An additional approach was performed using a data-driven model to correct the low-fidelity simulation. In comparison, the differentiable hybrid model showed significant improvements in transient prediction, effectively addressing the limitations of the low-fidelity simulations. The results highlighted the robustness of the differentiable hybrid model in both training approaches. It delivered simulations that were at least 3.8 times faster than high-fidelity models. In the time-step-wise approach, it achieved at least a 39% improvement in accuracy. In the sequence-wise approach, it showed at least an 81% accuracy improvement over the full transient. This approach offers a promising path for improving computational efficiency without compromising accuracy in nuclear reactor simulations, making it suitable for real-time digital twin applications.

42 - ENGINEERING↗
DOE OSTI2025

A real-time distributed solid oxide electrolysis cell (SOEC) model for cyber-physical simulation

System integration and dynamic operability between SOEC and balance-of-plant (BoP) components are major technical challenges before realizing rapid load following of SOEC systems. Cyber-physical simulation (CPS) is a leading-edge digital engineering approach and is regarded as the next step beyond Digital Twins. CPS approach can be used to research SOEC system integration and develop dynamic controls prior to actual pilot testing without using a real SOEC. To seamlessly couple with BoP hardware and access non-observable operational parameters (e.g., local temperature gradient) during transients, a distributed one-dimensional (1D) real-time SOEC model was developed. Its real-time execution was demonstrated for 20 to 640 nodes at the fixed time step of 5 ms. A higher excess air ratio enabled smaller local temperature gradients on SOEC solid materials and faster transients upon current density step change from 0.15 to 0.55 A cm -2 . During the transients, the magnitude of the peak temperature gradient nearly doubled in 10 s from -3.5 to -5.9 °C cm -1 . This represents a significant operating risk that can impact the dynamic operability of SOEC systems. In addition, the local temperature gradient was found to change directions on all nodes in SOEC solid materials, with the greatest impact on the upstream nodes. The SOEC model was also tested at the thermal neutral voltage using actual process air flow parameters as variable model inputs. Variable process air temperatures were found to induce alternating local temperature gradients on SOEC solid materials. These are new operational mechanisms for SOEC degradation relevant for load following operational modes yet distinct from previous reports. To mitigate these unfavorable features, the SOEC can be operated at voltages that are slightly (±20 mV) deviated from the thermal neutral voltage. Here, the corresponding net thermal energy change was less than 1.6% of the electric power consumption. This 1D real-time SOEC model established the basis of cyber-physical simulation of SOEC hybrid systems.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2026

A transfer learning approach to energy-efficient control of small and medium-sized commercial buildings

Model-free reinforcement learning (RL) provides a data-driven and adaptive approach to optimize building energy use while satisfying occupant comfort. This powerful tool does not need any prior knowledge about the environment and system it is optimizing and can adapt its policy based on the changes in captures. Like any other data-driven tool, it faces high training costs due to the extensive agent-environment interactions required to capture long-term building dynamics and user comfort. Transfer learning, particularly policy distillation, offers a promising way to accelerate training by leveraging pretrained RL agents in different building and system types. Here, this study investigates online student distillation, in which the student model updates its neural network weights using outputs from teacher models. The work introduces a student distillation strategy designed for efficient knowledge transfer, along with a teacher selection method that ensures high-quality guidance. The approach is validated using a highly calibrated whole building energy model for a small/medium commercial building test facility. Results show substantial reductions in training time and data requirements while surpassing the performance of ASHRAE Guideline 36, an advanced rule-based control strategy. The distilled RL model required 45% less data and achieved 20% higher cumulative rewards than a state-of-the-art RL model, with faster convergence and lower energy consumption. These outcomes demonstrate that effective transfer learning enables a scalable and data-efficient energy management solution for commercial buildings.

ASHRAE guideline 36↗
DOE OSTI2025

Designing reinforcement learning algorithms for building HVAC control: From experimental observation to simulation comparisons

Advanced supervisory-level control with reinforcement learning (RL) is regarded as a promising solution for HVAC systems to minimize energy consumption while maintaining thermal comfort and indoor air quality. However, most RL applications were conducted in the simulation environment rather than real-world HVAC systems. This paper developed a value-based RL controller termed Deep Q-Network (DQN) for a typical central HVAC system and evaluated its performance in a building test facility. By comparing DQN with a rule-based controller, the study not only demonstrated the cases where DQN could properly maintain indoor comfort but also discussed possible reasons why DQN failed in some other situations. Recognizing the limitations of value-based RL algorithms from the experimental tests, a simulation study was conducted to compare DQN with an alternative RL approach, an actor–critic algorithm termed Deep Deterministic Policy Gradient (DDPG). In scenarios with a relatively large action space, DDPG outperformed DQN by requiring fewer computational resources and achieving better thermal comfort, lower energy consumption, and more stable control actions. The findings suggest that the ability of DDPG to handle continuous control variables more effectively allows for faster convergence in training and more precise control in practice, which enhances the overall efficiency and reliability of the HVAC system.

Guo, Fangzhou↗
DOE OSTI2025

Local practically safe extremum seeking with assignable rate of attractivity to the safe set

We present Assignably Safe Extremum Seeking (ASfES), an algorithm designed to minimize a measured, static objective function while maintaining a measured, static metric of safety (a control barrier function or CBF) to be positive in a practical sense. We ensure that for trajectories with safe initial conditions, the violation of safety can be made arbitrarily small through appropriately chosen design constants. We also guarantee an assignable “attractivity” rate: from unsafe initial conditions, the trajectories approach the safe set, in the sense of the measured CBF, at a rate no slower than a user-assigned rate. Similarly, from safe initial conditions, the trajectories approach the unsafe set, in the sense of the CBF, no faster than the assigned attractivity rate. The feature of assignable attractivity is not present in the semiglobal version of safe extremum seeking, where the semiglobality of convergence is achieved by slowing the adaptation. We also demonstrate local convergence of the parameter to a neighborhood of the minimum of a quadratic objective function constrained to the safe set with a linear CBF. The ASfES algorithm and analysis are multivariable, but we also extend the algorithm to a Newton-Based ASfES scheme which we show is only useful in the scalar case. The proven properties of the designs are illustrated through simulation examples.

42 ENGINEERING↗
DOE OSTI2025

Near-infrared spectroscopy as a green analytical tool for sustainable biomass characterization for biofuels and bioproducts: An overview

Biomass, a widely used renewable energy source, requires characterization to optimize biofuel and bioproduct processes, customize feedstocks, and ensure economic and environmental sustainability. Conventional wet-chemistry methods for biomass analysis are slow, expensive, and require significant reagents and skilled personnel. In contrast, near-infrared (NIR) spectroscopy, a faster, cost-effective, and reagent-free green technology, enables non-destructive biomass analysis with minimal sample preparation. This study provides an overview of the fundamentals of NIR spectroscopy and explores its recent applications for analyzing various biomass properties important to the biofuel and bioproduct industry. The study also critically evaluates the challenges and opportunities of using NIR spectroscopy for biomass analysis. This review aims to guide future research for rapid and high throughput characterization of biomass in the biomass industry, supporting the United Nations’ sustainable development goal (SDG) 7: producing affordable and sustainable energy.

Biofuels↗
DOE OSTI2024

Effective direct steam regeneration of bis-iminoguanidine solid sorbent used for carbon dioxide capture

A cost-effective, energy-efficient sorbent regeneration process for phase-changing guanidines used for CO 2 capture was developed based on direct-steam stripping. This approach enhances the regeneration rate, simplifies the overall CO 2 capture process, and reduces the energy cost compared to conventional conductive thermal regeneration. A direct-steam sorbent regeneration reactor was developed, demonstrating that aqueous bis(iminoguanidines) (BIG) sorbents, e.g., methylglyoxal-bis(iminoguanidine) (MGBIG) and glyoxal-bis(iminoguanidine) (GBIG), could be efficiently regenerated with up to ~ 99 % CO 2 recovery through direct-steam stripping. Using low-temperature steam at 100 °C, a 4.5 times faster regeneration rate for GBIG carbonate sorbent (e.g., 30 min for 10 g) was demonstrated compared to conductive-heating (e.g., 135 min for 10 g) at 130 °C. Additionally, fully regenerated MGBIG converts into an aqueous MGBIG solution when the steam condenses onto the sorbent surface. Condensed steam with the guanidine can be easily recycled as an aqueous solution into the gas–liquid contactor to achieve a continuous-flow CO 2 -capture process. Molecular dynamics simulation was employed to provide a better understanding of the process. Higher heat transfer rates from steam to guanidine carbonate, compared to air heating, were attributed to the vibration resonance of water molecules within MGBIG with that of vapor molecules and the effective transfer of kinetic energy from vapor to solid. Technoeconomic analysis demonstrated that direct-steam stripping significantly decreases the CO 2 capture cost by 50 % compared to traditional conductive heating methods. Further, enhanced mass transfer facilitated by low-temperature steam and subsequent condensation effectively heats up the H 2 O-containing BIG-carbonate crystals, facilitating the desorption of CO 2 from the solid crystals, thereby leading to fast, effective, and energy-efficient sorbent regeneration.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗