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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
NASA NTRS2008

Testing, Modeling and System Impact of Metabolic Heat Regenerated Temperature Swing Adsorption

Metabolic heat regenerated temperature swing adsorption (MTSA) technology is being developed for removal and rejection of carbon dioxide (CO2) and heat from a portable life support system (PLSS) to the Martian environment. Previously, hardware was built and tested to demonstrate using heat from simulated, dry ventilation loop gas to affect the temperature swing required to regenerate an adsorbent used for CO2 removal. New testing has been performed using a moist, simulated ventilation loop gas to demonstrate the effects of water condensing and freezing in the heat exchanger during adsorbent regeneration. In addition, thermal models of the adsorbent during regeneration were modified and calibrated with test data to capture the effect of the CO2 heat of desorption. Finally, MTSA impact on PLSS design was evaluated by performing thermal balances assuming a specific PLSS architecture. Results using NASA s Extravehicular Activity System Sizing Analysis Tool (EVAS_SAT), a PLSS system evaluation tool, are presented.

Lacomini, Christine S.↗
NASA NTRS1997

Comparison of N2O Emissions from Soils at Three Temperate Agricultural Sites

Nitrous oxide (N2O) flux simulations by four models were compared with year-round field measurements from five temperate agricultural sites in three countries. The field sites included an unfertilized, semi-arid rangeland with low N2O fluxes in eastern Colorado, USA; two fertilizer treatments (urea and nitrate) on a fertilized grass ley cut for silage in Scotland; and two fertilized, cultivated crop fields in Germany where N2O loss during the winter was quite high. The models used were daily trace gas versions of the CENTURY model, DNDC, ExpertN, and the NASA-Ames version of the CASA model. These models included similar components (soil physics, decomposition, plant growth, and nitrogen transformations), but in some cases used very different algorithms for these processes. All models generated similar results for the general cycling of nitrogen through the agro-ecosystems, but simulated nitrogen trace gas fluxes were quite different. In most cases the simulated N20 fluxes were within a factor of about 2 of the observed annual fluxes, but even when models produced similar N2O fluxes they often produced very different estimates of gaseous N loss as nitric oxide (NO), dinitrogen (N2), and ammonia (NH3). Accurate simulation of soil moisture appears to be a key requirement for reliable simulation of N2O emissions. All models simulated the general pattern of low background fluxes with high fluxes following fertilization at the Scottish sites, but they could not (or were not designed to) accurately capture the observed effects of different fertilizer types on N2O flux. None of the models were able to reliably generate large pulses of N2O during brief winter thaws that were observed at the two German sites. All models except DNDC simulated very low N2O fluxes for the dry site in Colorado. The US Trace Gas Network (TRAGNET) has provided a mechanism for this model and site intercomparison. Additional intercomparisons are needed with these and other models and additional data sets; these should include both tropical agro-ecosystems and new agricultural management techniques designed for sustainability.

Frolking, S. E.↗
NASA NTRS1971

Xe and Kr analyses of silicate inclusions from iron meteorites.

Measurements have been conducted of the amounts and isotopic composition of Xe and Kr in silicate inclusions of several iron meteorites. It is shown that the Xe and Kr contents are comparable to chondritic values. The isotopic compositions show trapped gas of both chondritic and atmospheric composition. Large spallation effects occur in some of the meteorites; the spallation spectra in some instances differ from those reported for stone meteorites. In several meteorites, very large neutron capture effects on Br and I occur. All samples have pronounced Xe129 excesses which apparently indicate differences in the formation times from chondrites of less than about 100 million years; however, the presence of trapped Xe132 in silicates which were enclosed in molten Fe-Ni and cooled slowly proves that they were not entirely outgassed, so that some of the Xe129 excess may also be trapped.

Bogard, D. D.↗
NASA NTRS1985

Mass transfer across combustion gas thermal boundary layers - Power production and materials processing implications

The effects of Soret diffusion (for vapors) and thermophoresis (for particles) are illustrated using recent optical experiments and boundary layer computations. Mass transfer rate augmentations of up to a factor of 1000 were observed and predicted for submicron-particle capture by cooled solid surfaces, while mass transfer suppressions of more than 10 to the -10th-fold were predicted for 'overheated' surfaces. It is noted that the results obtained are of interest in connection with such technological applications as fly-ash capture in power generation equipment and glass droplet deposition in optical-waveguide manufacture.

Rosner, D. E.↗
NASA NTRS2000

Continuous Processing With Mars Gases

Current Martian missions call for the production of oxygen for breathing, and fuel and oxygen for propulsion to be produced from atmospheric carbon dioxide (CO2). Adsorption and freezing are the two methods considered for capturing CO2 from the atmosphere. However, the nitrogen (N2) and argon (Ar), which make up less than 5 percent of the atmosphere, cause difficulties with both of these processes by blocking the CO2. This results in the capture process rapidly changing from a pressure driven process to a diffusion controlled process. To increase the CO2 capture rates, some type of mechanical pump is usually proposed to remove the N2 and Ar. The N2 and Ar are useful and have been proposed for blanketing and pressurizing fuel tanks and as buffer gas for breathing air for manned missions. Separation of the Martian gases with the required purity can be accomplished with a combination of membranes. These membrane systems do not require a high feed pressure and provide suitable separation. Therefore, by use of the appropriate membrane combination with the Martian atmosphere supplied by a compressor a continuous Supply Of CO2 for fuel and oxygen production can be supplied. This phase of our program has focused on the selection of the membrane system. Since permeation data for membranes did not exist for Martian atmospheric pressures and temperatures, this information had to be compiled. The general trend as the temperature was lowered was for the membranes to become more selective. In addition, the relative permeation rates between the three gases changed with temperature. The end result was to provide design parameters that could be used to separate CO2 from N2 and Ar. This paper will present the membrane data, provide the design requirements for a compressor, and compare the results with adsorption and freezer methods.

Parrish, Clyde↗
NASA NTRS2001

Continuous Processing with Mars Gases

Current Martian missions call for the production of oxygen for breathing, and fuel and oxygen for propulsion to be produced from atmospheric carbon dioxide (CO2). Adsorption and freezing are the two methods considered for capturing CO, from the atmosphere. However, the nitrogen (N2) and argon (Ar), which make up less than 5 percent of the atmosphere, cause difficulties with both of these processes by blocking the CO2, This results in the capture process rapidly changing from a pressure driven process to a diffusion controlled process. To increase the CO, capture rates, some type of mechanical pump is usually proposed to remove the N2 and Ar. The N2 and Ar are useful and have been proposed for blanketing and pressurizing fuel tanks and as buffer gas for breathing air for manned missions. Separation of the Martian gases with the required purity can be accomplished with a combination of membranes. These membrane systems do not require a high feed pressure and provide suitable separation. Therefore, by use of the appropriate membrane combination with the Martian atmosphere supplied by a compressor a continuous supply of CO2 for fuel and oxygen production can be supplied. This phase of our program has focused on the selection of the membrane system. Since permeation data for membranes did not exist for Martian atmospheric pressures and temperatures, this information had to be compiled. The general trend as the temperature was lowered was for the membranes to become more selective. In addition, the relative permeation rates between the three gases changed with temperature. The end result was to provide design parameters that could be used to separate CO2 from N2 and Ar. This paper will present the membrane data, provide the design requirements for a compressor, and compare the results with adsorption and freezer methods.

Parrish, Clyde↗
NASA NTRS2013

X-ray Reflected Spectra from Accretion Disk Models. III. A Complete Grid of Ionized Reflection Calculations

We present a new and complete library of synthetic spectra for modeling the component of emission that is reflected from an illuminated accretion disk. The spectra were computed using an updated version of our code xillver that incorporates new routines and a richer atomic data base. We offer in the form of a table model an extensive grid of reflection models that cover a wide range of parameters. Each individual model is characterized by the photon index Gamma of the illuminating radiation, the ionization parameter zeta at the surface of the disk (i.e., the ratio of the X-ray flux to the gas density), and the iron abundance A(sub Fe) relative to the solar value. The ranges of the parameters covered are: 1.2 <= Gamma <= 3.4, 1 <= zeta <= 104, and 0.5 <= A(sub Fe) <= 10. These ranges capture the physical conditions typically inferred from observations of active galactic nuclei, and also stellar-mass black holes in the hard state. This library is intended for use when the thermal disk flux is faint compared to the incident power-law flux. The models are expected to provide an accurate description of the Fe K emission line, which is the crucial spectral feature used to measure black hole spin. A total of 720 reflection spectra are provided in a single FITS file suitable for the analysis of X-ray observations via the atable model in xspec. Detailed comparisons with previous reflection models illustrate the improvements incorporated in this version of xillver.

X-ray↗
NASA NTRS2016

The Gas-Surface Interaction of a Human-Occupied Spacecraft with a Near-Earth Object

NASA's asteroid redirect mission (ARM) will feature an encounter of the human-occupied Orion spacecraft with a portion of a near- Earth asteroid (NEA) previously placed in orbit about the Moon by a capture spacecraft. Applying a shuttle analog, we suggest that the Orion spacecraft should have a dominant local water exosphere, and that molecules from this exosphere can adsorb onto the NEA. The amount of adsorbed water is a function of the defect content of the NEA surface, with retention of shuttle-like water levels on the asteroid at 10(exp 15) H2O's/m2 for space weathered regolith at T approximately 300 K.

Asteroid↗
NASA NTRS2016

In Situ Measurement of Atmospheric Krypton and Xenon on Mars with Mars Science Laboratory

Mars Science Laboratorys Sample Analysis at Mars (SAM) investigation has measured all of the stable isotopes of the heavy noble gases krypton and xenon in the martian atmosphere, in situ, from the Curiosity Rover at Gale Crater, Mars. Previous knowledge of martian atmospheric krypton and xenon isotope ratios has been based upon a combination of the Viking missions krypton and xenon detections and measurements of noble gas isotope ratios in martian meteorites. However, the meteorite measurements reveal an impure mixture of atmospheric, mantle, and spallation contributions. The xenon and krypton isotopic measurements reported here include the complete set of stable isotopes, unmeasured by Viking. The new results generally agree with Mars meteorite measurements but also provide a unique opportunity to identify various non-atmospheric heavy noble gas components in the meteorites. Kr isotopic measurements define a solar-like atmospheric composition, but deviating from the solar wind pattern at 80Kr and 82Kr in a manner consistent with contributions originating from neutron capture in Br. The Xe measurements suggest an intriguing possibility that isotopes lighter than 132Xe have been enriched to varying degrees by spallation and neutron capture products degassed to the atmosphere from the regolith, and a model is constructed to explore this possibility. Such a spallation component, however, is not apparent in atmospheric Xe trapped in the glassy phases of martian meteorites.

Conrad, P. G.↗
NASA NTRS2026

Mathematical Model of a Regenerative Fuel Cell for System Optimization

This thesis developed a system-level optimization model of a regenerative fuel cell (RFC) system for long-duration, off-world energy storage applications. Prior RFC design studies have typically been limited to reduced parameter sets and simplified constraints due to computational limitations relative to the number of relevant degrees of freedom. As a result, important nonlinear interactions between subsystems have not been fully captured. This work began to address that gap by developing a higher-fidelity, nonlinear optimization framework that incorporates a broader set of design variables and coupled constraints, enabling a multidimensional model that captures the coupled behavior of RFC subsystems and demonstrates the feasibility of applying optimization to such systems. An expanded system-level optimization approach was established that captures interactions between electrochemical performance, structural requirements, and storage design. This enabled a more comprehensive evaluation of trade-offs than conventional formulations. The model integrates four coupled subsystems: a fuel cell, an electrolyzer, reactant gas, and high-pressure storage tanks, and was formulated to accommodate a wide range of mission parameters, including operational time and required output power. It incorporates constraints on available solar array power, reactant mass balance between production and consumption, and pressure-dependent storage requirements. To enable reliable convergence, the optimization problem was reformulated to reduce dimensionality and improve numerical stability, with subsystem models organized for efficient evaluation. Problem dimensionality was reduced by consolidating lower-level design variables into higher-level representative quantities, and subsystem behavior was evaluated within the optimization loop. A multi-start initialization strategy was employed to mitigate sensitivity to local minima and improve solution quality, while nonlinear relationships were solved using robust numerical methods. The results showed that convergence was achieved across a range of required output power values. Specific energy reached a maximum at a critical mission power level, where the electrolyzer power matched the available solar input and operated near its voltage and current density limits. Beyond this point, further increases in required power resulted in less mass-efficient operation, increasing total system mass and reducing overall performance. The developed model represents an advancement in RFC system-level optimization by enabling analysis of a broader and more tightly coupled design space than previous considerations. While convergence behavior and computational cost remain challenges, the methods introduced improve solvability and allow inclusion of additional design variables with minimal loss of physical fidelity. However, the numerical results should not be interpreted as definitive design recommendations, as the model includes simplifying assumptions and omits several higher-order effects. Future work should extend this framework by incorporating additional subsystems and loss mechanisms, such as thermal management, parasitic power consumption, and reactant losses, to improve fidelity and ensure more representative design conclusions.

Electrochemistry↗
NASA NTRSDate not supplied

A GPU-based Approach for Turbomachinery Application

Accurate modeling of coolant airflows, which form protective films over turbine blades, is essential for designing fuel-efficient and environmentally sustainable gas turbine engines. Excessive coolant reduces thermal efficiency, while insufficient coolant leads to blade overheating and causes damage. Therefore, precise prediction of flow field interactions with cooling air is critical for optimizing turbine performance. This study numerically investigates the cooling effectiveness of purge and film cooling flows within a high-pressure turbine (HPT) rotor using Large Eddy Simulation (LES). The study utilizes NASA Glenn Research Center’s Glenn-HT solver. The simulation models ethe conditions of the Penn State University START rotating rig. A high-fidelity structured mesh comprising up to 800 million cells is employed to resolve high-Reynolds number flow (Re ≈ 350,000) and to capture intricate secondary flow structures, including tip leakage and purge-induced vortices. Film cooling effectiveness computations are highly sensitive to boundary conditions at the cooling holes and to grid resolution. Even with well-resolved grids and included plena, strong mixing challenges traditional eddy viscosity models. To address this, a simplified configuration is simulated: a truncated row of shaped holes on the suction side near the leading edge and a row on the pressure side, both fed from internal plena while the purge slot and tip clearance are also modeled. Two isothermal LES cases are conducted at two distinct wall temperatures, which yield the adiabatic wall temperature and the heat transfer coefficient. The definition and means of computation of the effectiveness is discussed in this paper. The simulations reveal detailed three-dimensional unsteady flow features, including coherent vortical structures and secondary flows originating from the purge cavity. Film cooling effectiveness and Nusselt number distributions are presented for both the blade surface and tip, highlighting regions of elevated heat transfer and complex thermal behavior. These findings underscore the importance of high-resolution LES and realistic boundary conditions in capturing the dynamics of purge and film cooling, offering valuable insights for improving turbine blade design and thermal management strategies.

Gas Turbine↗
NASA NTRS1992

Upwind schemes and bifurcating solutions in real gas computations

The area of high speed flow is seeing a renewed interest due to advanced propulsion concepts such as the National Aerospace Plane (NASP), Space Shuttle, and future civil transport concepts. Upwind schemes to solve such flows have become increasingly popular in the last decade due to their excellent shock capturing properties. In the first part of this paper the authors present the extension of the Osher scheme to equilibrium and non-equilibrium gases. For simplicity, the source terms are treated explicitly. Computations based on the above scheme are presented to demonstrate the feasibility, accuracy and efficiency of the proposed scheme. One of the test problems is a Chapman-Jouguet detonation problem for which numerical solutions have been known to bifurcate into spurious weak detonation solutions on coarse grids. Results indicate that the numerical solution obtained depends both on the upwinding scheme used and the limiter employed to obtain second order accuracy. For example, the Osher scheme gives the correct CJ solution when the super-bee limiter is used, but gives the spurious solution when the Van Leer limiter is used. With the Roe scheme the spurious solution is obtained for all limiters.

Suresh, Ambady↗
NASA NTRS2012

NASA Tech Briefs, March 2012

The topics include: 1) Spectral Profiler Probe for In Situ Snow Grain Size and Composition Stratigraphy; 2) Portable Fourier Transform Spectroscopy for Analysis of Surface Contamination and Quality Control; 3) In Situ Geochemical Analysis and Age Dating of Rocks Using Laser Ablation-Miniature Mass Spectrometer; 4) Physics Mining of Multi-Source Data Sets; 5) Photogrammetry Tool for Forensic Analysis; 6) Connect Global Positioning System RF Module; 7) Simple Cell Balance Circuit; 8) Miniature EVA Software Defined Radio; 9) Remotely Accessible Testbed for Software Defined Radio Development; 10) System-of-Systems Technology-Portfolio-Analysis Tool; 11) VESGEN Software for Mapping and Quantification of Vascular Regulators; 12) Constructing a Database From Multiple 2D Images for Camera Pose Estimation and Robot Localization; 13) Adaption of G-TAG Software for Validating Touch and Go Asteroid Sample Return Design Methodology; 14) 3D Visualization for Phoenix Mars Lander Science Operations; 15) RxGen General Optical Model Prescription Generator; 16) Carbon Nanotube Bonding Strength Enhancement Using Metal Wicking Process; 17) Multi-Layer Far-Infrared Component Technology; 18) Germanium Lift-Off Masks for Thin Metal Film Patterning; 19) Sealing Materials for Use in Vacuum at High Temperatures; 20) Radiation Shielding System Using a Composite of Carbon Nanotubes Loaded With Electropolymers; 21) Nano Sponges for Drug Delivery and Medicinal Applications; 22) Molecular Technique to Understand Deep Microbial Diversity; 23) Methods and Compositions Based on Culturing Microorganisms in Low Sedimental Fluid Shear Conditions; 24) Secure Peer-to-Peer Networks for Scientific Information Sharing; 25) Multiplexer/Demultiplexer Loading Tool (MDMLT); 26) High-Rate Data-Capture for an Airborne Lidar System; 27) Wavefront Sensing Analysis of Grazing Incidence Optical Systems; 28) Foam-on-Tile Damage Model; 29) Instrument Package Manipulation Through the Generation and Use of an Attenuated-Fluent Gas Fold; 30) Multicolor Detectors for Ultrasensitive Long-Wave Imaging Cameras; 31) Lunar Reconnaissance Orbiter (LRO) Command and Data Handling Flight Electronics Subsystem; and 32) Electro-Optic Segment-Segment Sensors for Radio and Optical Telescopes.

Source record↗
NASA NTRS2017

Using Neural Networks to Improve the Performance of Radiative Transfer Modeling Used for Geometry Dependent Surface Lambertian-Equivalent Reflectivity Calculations

Surface Lambertian-equivalent reflectivity (LER) is important for trace gas retrievals in the direct calculation of cloud fractions and indirect calculation of the air mass factor. Current trace gas retrievals use climatological surface LER's. Surface properties that impact the bidirectional reflectance distribution function (BRDF) as well as varying satellite viewing geometry can be important for retrieval of trace gases. Geometry Dependent LER (GLER) captures these effects with its calculation of sun normalized radiances (I/F) and can be used in current LER algorithms (Vasilkov et al. 2016). Pixel by pixel radiative transfer calculations are computationally expensive for large datasets. Modern satellite missions such as the Tropospheric Monitoring Instrument (TROPOMI) produce very large datasets as they take measurements at much higher spatial and spectral resolutions. Look up table (LUT) interpolation improves the speed of radiative transfer calculations but complexity increases for non-linear functions. Neural networks perform fast calculations and can accurately predict both non-linear and linear functions with little effort.

Geometry Dependent LER (GLER) capture↗
NASA NTRS2023

Reducing Aerosol Forcing Uncertainty by Combining Models With Satellite and Within-The-Atmosphere Observations: A Three-Way Street

Aerosol forcing uncertainty represents the largest climate forcing uncertainty overall. Its magnitude has remained virtually undiminished over the past 20 years despite considerable advances in understanding most of the key contributing elements. Recent work has produced modest increases only in the confidence of the uncertainty estimate itself. This review summarizes the contributions toward reducing the uncertainty in the aerosol forcing of climate made by satellite observations, measurements taken within the atmosphere, as well as modeling and data assimilation. We adopt a more measurement-oriented perspective than most reviews of the subject in assessing the strengths and limitations of each; gaps and possible ways to fill them are considered. Currently planned programs supporting advanced, global-scale satellite and surface-based aerosol, cloud, and precursor gas observations, climate modeling, and intensive field campaigns aimed at characterizing the underlying physical and chemical processes involved, are all essential. But in addition, new efforts are needed: (a) to obtain systematic aircraft in situ measurements capturing the multi-variate probability distribution functions of particle optical, microphysical, and chemical properties (and associated uncertainty estimates), as well as co-variability with meteorology, for the major aerosol airmass types; (b) to conceive, develop, and implement a suborbital (aircraft plus surface-based) program aimed at systematically quantifying the cloud-scale microphysics, cloud optical properties, and cloud-related vertical velocities associated with aerosol-cloud interactions; and (c) to focus much more research on integrating the unique contributions of satellite observations, suborbital measurements, and modeling, to reduce the persistent uncertainty in aerosol climate forcing.

aerosol climate forcing↗
NASA NTRS1994

The use of silica aerogel to collect interplanetary dust in space

We report on impact experiments to evaluate the suitability of silica aerogel as a capture medium for interplanetary dust particles in space. The structure of silica aerogel is such that even micrometer-sized hypervelocity particles may sense it as a target of very low density; consequently shock stresses and temperatures due to impact should be minimized. We performed impact experiments in a light gas gun that employed projectiles manufactured from forsterite, pyrrhotite, and calcite. From these experiments we have developed techniques that will permit the successful extrication of interplanetary dust particles from aerogel. We note a rough correlation between increasing particle penetration lengths and decreasing aerogel density, and there is a poor correlation of track lengths with impact velocity at laboratory-attainable velocities of 5-7 km/s. We conclude that aerogel track length should not be used even as (crude) velocity indicators. Transmission electron microscope studies show the re covered particulate residues are encased in melted silica aerogel, which possibly protects the residue from some impact damage. Individual minerals within interplanetary dust are expected to exhibit differential survival, and may be vaporized, melted, dehydrated, or structurally reordered. However, some mineral grains should successfully be captured in an unmelted state at encounter velocities less than 8 km/s.

Zolensky, Michael E.↗
NASA NTRSDate not supplied

Loci/STREAM Sharp Interface Model Validation of Cryogenic Propellant Tank Self-Pressurization

This paper documents a model validation effort for the prediction of cryogenic propellant tank selfpressurization physics using the Loci/STREAM sharp interface CFD model developed at NASA MSFC. Cryogenic fluid management (CFM) applications for long duration spaceflight missions require accurate modeling of heat transfer and thermodynamics. Therefore, detailed validation of those physics is important to ensure simulation accuracy. In the past, the MSFC Propulsion Fluid Dynamics Branch has validated and used the Loci/STREAM Volume of Fluid (VOF) module extensively for propellant slosh applications, which are dominated by fluid motion. For cases where the interface gas/liquid interface is essentially static, the Loci/STREAM sharp interface was developed for more rapid and efficient CFM analysis. In the present study, Loci/STREAM sharp interface simulations were compared with the NASA K-site self-pressurization experiment of a flight weight, partially full, LH2 tank in normal gravity. This study investigated several parametric effects and made a number of important observations on the performance of the Loci/STREAM sharp interface method: - First, a homogeneous model was derived to verify the CFD model. The homogeneous model assumes both gas and liquid phases are uniform and are at saturation temperature. The predicted pressure rise rates at 3.5 W/m2 and 2.0 W/m2 with a 49% fill level are all lower than the experimental measurement. This is expected due to the observed temperature stratification near the gas-liquid interface during testing. - The k-w and k-e turbulence models predict comparable pressurization rates, which are much lower than the experiment measurement. On the other hand, the pressure values and pressurization rates from both models are almost the same as those of the homogeneous model. The current turbulence model is too diffusive and is not capable of capturing the thermal stratification in the liquid and ullage. - When using the laminar flow model, the pressurization rate is found to be very close to the experimental value when a quasi-steady flow field is allowed to develop by continuously venting the tank prior to pressurization as was done during testing. On the other hand, without initial venting, the rate is not constant. Additionally, the development time to reach a quasi-steady flow field differed from the experiment due to the lack of turbulent mixing away from the gas-liquid interface that is expected in reality. - Using the laminar flow model and appropriate initial conditioning, the pressurization rate is within 15% of the experimental value for 49% fill level at 3.5 W/m 2 and is within 18% for 2.0 W/m 2 heat loading. - Using the laminar flow model and appropriate initial conditioning, the pressurization rate is within 18% of the experimental value for a 29% fill level and within 15% for an 83% fill level.

H. Q. Yang↗