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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 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
NASA NTRS1999

Control of Meridional Flow by a Non-Uniform Rotational Magnetic Field

The diffusive mass transfer of species during crystal growth in vertical ampoules is significantly affected by fluid flow in the liquid mother phase (melt). For electrically conductive melts, an elegant way of remotely inducing and controlling this flow is by utilizing a uniform rotational magnetic field (RMF) in the transverse direction. It induces an azimuthal flow which tends to homogenize the thermal and solutal fields. The rotating field also reduces the diffusion boundary layer, stabilizes temperature fluctuations, and promotes better overall crystal growth. For moderate strengths of the applied magnetic field (2-20 m Tesla) with frequencies of up to 400 Hz, the induced secondary meridional flow becomes significant. It typically consists of one roll at the bottom of the liquid column and a second roll (vortex) at the top. The flow along the centerline (ampoule axis) is directed from the growing solid (interface) towards the liquid (melt). In case of convex interfaces (e.g. in floating zone crystal growth) such flow behavior is beneficial since it suppresses diffusion at the center. However, for concave interfaces (e.g. vertical Bridgman crystal growth) such a flow tends to exacerbate the situation in making the interface shape more concave. It would be beneficial to have some control of this meridional flow- for example, a single recirculating cell with controllable direction and flow magnitude will make this technique even more attractive for crystal growth. Such flow control is a possibility if a non-uniform PNE field is utilized for this purpose. Although this idea has been proposed earlier, it has not been conclusively demonstrated so far. In this work, we derive the governing equations for the fluid dynamics for such a system and obtain solutions for a few important cases. Results from parallel experimental measurements of fluid flow in a mercury column subjected to non-uniform RMF will also be presented.

Mazuruk, Konstantin↗
DOE OSTI2025

Scalable Solution-Processed Electrolyte Membranes with Optimized Microstructure for High-Performance Protonic Ceramic Electrochemical Cells

Proton-conducting electrochemical cells (PCECs) are promising for efficient hydrogen production, but achieving dense, uniform, thin electrolyte layers remains a key challenge, particularly for scalable fabrication. Here, we present a solution-processed deposition approach with a mechanistically optimized slurry for uniform electrolyte formation. By tailoring particle size distribution, solid loading, and solvent/additive balance, we regulated wetting behavior and evaporation kinetics of the electrolyte slurry to promote homogeneous electrolyte particle packing. These features facilitate tight grain boundary contact and early stage neck growth during sintering, eliminating residual porosity, and improving mechanical integrity. The resulting ∼15 μm thick electrolyte shows high density, strong electrode adhesion, and stable interfaces outperforming the previously reported spray-based fabricated electrolyte by about 31% at 600 °C in FC mode. Single cells deliver 0.962 W cm –2 at 600 °C in fuel cell mode and 1.31 A cm –2 at 1.3 V in electrolysis mode, maintaining robust performance over 100 h with negligible degradation (≤0.02% h –1 ) in each mode. Scale-up to 2.5 cm diameter substrates confirmed reproducible densification and geometric stability. This work demonstrates a cost-effective, scalable route where control over particle-fluid interactions and drying dynamics enables a superior electrolyte microstructure and high PCEC performance.

dense microstructure↗
DOE OSTI2021

Engineering Challenges of Solution and Slurry-Phase Chemical Hydrogen Storage Materials for Automotive Fuel Cell Applications

In this work, we present the research findings of the DOE-funded Hydrogen Storage Engineering Center of Excellence (HSECoE) related to liquid-phase and slurry-phase chemical hydrogen storage media and their potential as future hydrogen storage media for automotive applications. Chemical hydrogen storage media other than neat liquid compositions will prove difficult to meet the DOE system level targets. Solid- and slurry-phase chemical hydrogen storage media requiring off-board regeneration are impractical and highly unlikely to be implemented for automotive applications because of the formidable task of developing solid- or slurry-phase transport systems that are commercially reliable and economical throughout the entire life cycle of the fuel. Additionally, the regeneration cost and efficiency of chemical hydrogen storage media is currently the single most prohibitive barrier to implementing chemical hydrogen storage media. Ideally, neat liquid-phase chemical hydrogen storage media with net-usable gravimetric hydrogen capacities of greater than 7.8 wt% are projected to meet the 2017 DOE system level gravimetric and volumetric targets. The research presented herein is a collection of research findings that do not in and of themselves warrant a dedicated manuscript. However, the collection of results do, in fact, highlight the engineering challenges and short-comings in scaling up and demonstrating fluid-phase ammonia borane and alane compositions that all future materials researchers working in hydrogen storage should be aware of.

25 ENERGY STORAGE↗
NASA NTRS2012

Porous Foam Based Wick Structures for Loop Heat Pipes

As part of an effort to identify cost efficient fabrication techniques for Loop Heat Pipe (LHP) construction, NASA Goddard Space Flight Center's Cryogenics and Fluids Branch collaborated with the U.S. Naval Academy s Aerospace Engineering Department in Spring 2012 to investigate the viability of carbon foam as a wick material within LHPs. The carbon foam was manufactured by ERG Aerospace and machined to geometric specifications at the U.S. Naval Academy s Materials, Mechanics and Structures Machine Shop. NASA GSFC s Fractal Loop Heat Pipe (developed under SBIR contract #NAS5-02112) was used as the validation LHP platform. In a horizontal orientation, the FLHP system demonstrated a heat flux of 75 Watts per square centimeter with deionized water as the working fluid. Also, no failed start-ups occurred during the 6 week performance testing period. The success of this study validated that foam can be used as a wick structure. Furthermore, given the COTS status of foam materials this study is one more step towards development of a low cost LHP.

Silk, Eric A.↗
DOE OSTI2021

Manipulation and statistical analysis of the fluid flow of polymer semiconductor solutions during meniscus-guided coating

Recent work in structure–processing relationships of polymer semiconductors have demonstrated the versatility and control of thin-film microstructure offered by meniscusguided coating (MGC) techniques. Here, we analyze the qualitative and quantitative aspects of solution shearing, a model MGC method, using coating blades augmented with arrays of pillars. The pillars induce local regions of high strain rates—both shear and extensional—not otherwise possible with unmodified blades, and we use fluid mechanical simulations to model and study a variety of pillar spacings and densities. We then perform a statistical analysis of 130 simulation variables to find correlations with three dependent variables of interest: thin-film degree of crystallinity and transistor field-effect mobilities for charge-transport parallel (Μ para ) and perpendicular (Μ perp ) to the coating direction. Our study suggests that simple fluid mechanical models can reproduce substantive correlations between the induced fluid flow and important performance metrics, providing a methodology for optimizing blade design.

36 MATERIALS SCIENCE↗
DOE OSTI2024

The liquid-conduction, vapor-flow heat pipe model in Sockeye

A single-phase heat pipe flow model implemented in the heat pipe application Sockeye is described. This model solves one-dimensional, compressible flow equations for the vapor phase in the center of a heat pipe, which are coupled to the two-dimensional heat conduction equation for the wick, liquid, and cladding, as well as to an ordinary differential equation tracking the working fluid inventory in the evaporator section of the heat pipe. This model is demonstrated with several test problems, including comparisons to analytic solutions for the vapor flow fields, analytic curves for sonic and capillary limitations of heat pipe operation, and some experimental data. The numerical solution gives excellent agreement for verification problems and good agreement with experimental results. Also, demonstrations show that the model is very robust, allowing for full simulations of heat pipe transients, including frozen startup, sonic-limited (supersonic) flow, and heat pipe shutdown.

42 ENGINEERING↗
DOE OSTI2025

Electrically controlled interlayer trion fluid in electron-hole bilayers

Here, the combination of repulsive and attractive Coulomb interactions in a quantum electron-hole (e-h) fluid can produce correlated phases of multiparticle charge complexes, such as excitons, trions, and biexcitons. We report an experimental realization of an electrically controlled interlayer trion fluid in van der Waals heterostructures. In strongly coupled e-h bilayers, electrons and holes spontaneously form three-particle trion bound states. The interlayer trions can assume 1e-2h and 2e-1h configurations. We show that the two holes in 1e-2h trions form a spin-singlet with a spin gap of approximately one milli–electron volt. By electrostatic gating, the equilibrium state can be continuously tuned into an exciton fluid, a trion fluid, an exciton-trion mixture, or a trion-charge mixture. Our work demonstrates a platform to study correlated phases of tunable Bose-Fermi mixtures.

Qi, Ruishi [University of California, Berkeley, CA↗
NASA NTRS2010

Propellant Sloshing Parameter Extraction from CFD Analysis

Propellant slosh is a potential source of disturbance critical to the stability of space vehicle. The sloshing dynamics is typically represented by a mechanical model of spring mass damper. This mechanical model is then included in the equation of motion of the entire vehicle for Guidance, Navigation and Control analysis. The typical parameters required by the mechanical model include natural frequency of the sloshing, sloshing mass, sloshing mass center coordinates, and critical damping coefficient. During the 1960 s US space program, these parameters were either computed from analytical solution for simple geometry or by experimental testing for the sub-scaled configurations. The purpose of this work is to demonstrate the soundness of a CFD approach in modeling the detailed fluid dynamics of tank sloshing and the excellent accuracy in extracting mechanical properties for different tank configurations and at different fill levels. The validation studies included straight cylinder against analytical solution, and sub-scaled Centaur LOX and LH2 tanks with and without baffles against experimental results. This effort shows that CFD technology can provide accurate mechanical parameters for any tank configuration, and is especially valuable to the future design of propellant tanks, as there is no previous experimental data available for the same size and configuration.

Yang, H. Q.↗
NASA NTRS2012

Investigation of Freeze and Thaw Cycles of a Gas-Charged Heat Pipe

The traditional constant conductance heat pipes (CCHPs) currently used on most spacecraft run the risk of bursting the pipe when the working fluid is frozen and later thawed. One method to avoid pipe bursting is to use a gas-charged heat pipe (GCHP) that can sustain repeated freeze/thaw cycles. The construction of the GCHP is similar to that of the traditional CCHP except that a small amount of non-condensable gas (NCG) is introduced and a small length is added to the CCHP condenser to serve as the NCG reservoir. During the normal operation, the NCG is mostly confined to the reservoir, and the GCHP functions as a passive variable conductance heat pipe (VCHP). When the liquid begins to freeze in the condenser section, the NCG will expand to fill the central core of the heat pipe, and ice will be formed only in the grooves located on the inner surface of the heat pipe in a controlled fashion. The ice will not bridge the diameter of the heat pipe, thus avoiding the risk of pipe bursting during freeze/thaw cycles. A GCHP using ammonia as the working fluid was fabricated and then tested inside a thermal vacuum chamber. The GCHP demonstrated a heat transport capability of more than 200W at 298K as designed. Twenty-seven freeze/thaw cycles were conducted under various conditions where the evaporator temperature ranged from 163K to 253K and the condenser/reservoir temperatures ranged from 123K to 173K. In all tests, the GCHP restarted without any problem with heat loads between 10W and 100W. No performance degradation was noticed after 27 freeze/thaw cycles. The ability of the GCHP to sustain repeated freeze/thaw cycles was thus successfully demonstrated.

Ku, Jentung↗
NASA NTRSDate not supplied

The Influence of Smoke Particle Properties and Cabin Characteristics on Smoke Detection in Lunar Gravity

Spacecraft fires pose a threat to the success of future Lunar, Martian, and deep space exploration missions. As NASA plans to return humans to the Moon in the next decade, novel mission requirements will present new fire safety challenges. For example, materials that are fire resistant on Earth are expected to burn under planned habitat conditions (elevated oxygen concentrations and reduced cabin pressure) and partial gravity (0.16g). Optimal smoke detector placement will depend on a combination of buoyant plume velocities, induced by partial gravity, and Environmental Control and Life Support Systems (ECLSS) parameters, including particle filtration rates, supply and return placement within the cabin, and forced air velocities. These ECLSS parameters must also address the need for rapid Lunar dust removal, as Lunar dust exposure poses a risk to crew health and hardware functionality. Here, we present progress toward a computational fluid dynamics model to evaluate smoke transport in a Lunar habitat. Recent work has demonstrated that if air supplies are placed on ceilings and returns on the floor, a buoyant smoke layer at the ceiling may disperse over the order of minutes even under low forced flow conditions. We expand upon these results to examine the influence of different supply and return configurations on smoke plume development. Additionally, we also address differences in the transport of smoke particles and Lunar dust by varying particle parameters like size, density, and shape factor. Finally, we discuss ongoing and future experimental efforts to measure smoke particle properties and transport under partial gravity, elevated oxygen, and reduced pressure conditions.

Claire Fortenberry↗
NASA NTRS1992

Study and development of an air conditioning system operating on a magnetic heat pump cycle (design and testing of flow directors)

This report describes the fabrication, design of flow director, fluid flow direction analysis and testing of flow director of a magnetic heat pump. The objectives of the project are: (1) to fabricate a demonstration magnetic heat pump prototype with flow directors installed; and (2) analysis and testing of flow director and to make sure working fluid loops flow through correct directions with minor mixing. The prototype was fabricated and tested at the Development Testing Laboratory of Kennedy Space Center. The magnetic heat pump uses rear earth metal plates rotate in and out of a magnetic field in a clear plastic housing with water flowing through the rotor plates to provide temperature lift. Obtaining the proper water flow direction has been a problem. Flow directors were installed as flow barriers between separating point of two parallel loops. Function of flow directors were proven to be excellent both analytically and experimentally.

Wang, Pao-Lien↗
DOE OSTI2020

Imaging viscous flow of the Dirac fluid in graphene

The electron–hole plasma in charge-neutral graphene is predicted to realize a quantum critical system in which electrical transport features a universal hydrodynamic description, even at room temperature. This quantum critical ‘Dirac fluid’ is expected to have a shear viscosity close to a minimum bound, with an interparticle scattering rate saturating1 at the Planckian time, the shortest possible timescale for particles to relax. Although electrical transport measurements at finite carrier density are consistent with hydrodynamic electron flow in graphene a clear demonstration of viscous flow at the charge-neutrality point remains elusive. In this work, we directly image viscous Dirac fluid flow in graphene at room temperature by measuring the associated stray magnetic field. Nanoscale magnetic imaging is performed using quantum spin magnetometers realized with nitrogen vacancy centres in diamond. Scanning single-spin and wide-field magnetometry reveal a parabolic Poiseuille profile for electron flow in a high-mobility graphene channel near the charge-neutrality point, establishing the viscous transport of the Dirac fluid. This measurement is in contrast to the conventional uniform flow profile imaged in a metallic conductor and also in a low-mobility graphene channel. Furthermore, via combined imaging and transport measurements, we obtain viscosity and scattering rates, and observe that these quantities are comparable to the universal values expected at quantum criticality. This finding establishes a nearly ideal electron fluid in charge-neutral, high-mobility graphene at room temperature4. Our results will enable the study of hydrodynamic transport in quantum critical fluids relevant to strongly correlated electrons in high-temperature superconductors9. This work also highlights the capability of quantum spin magnetometers to probe correlated electronic phenomena at the nanoscale.

77 NANOSCIENCE AND NANOTECHNOLOGY↗
NASA NTRS2004

Consideration of Alternate Working Fluid Properties in Gas Lubricated Foil Journal Bearings

The Oil-Free Turbomachinery Program at the NASA Glenn Research center is committed to, revolutionary improvements in performance, efficiency and reliability of turbomachinery propulsion systems. One of the key breakthroughs by which this goal is being achieved is the maturation of air lubricated foil bearing technology. Through experimental testing, foil bearings have demonstrated a variety of exceptional qualities that show them to have an important role in the future of rotordynamic lubrication. Most of the work done with foil bearings thus far has considered ambient air at atmospheric pressure as the working fluid or lubricating fluid in the bearing. However, special applications of oil-free technology require the use of air at non- standard ambient conditions or completely different working fluids altogether. The NASA Jupiter Icy Moon Orbiter program presents power generation needs far beyond that of any previous space exploration effort. The proposed spacecraft will require significant power generation to provide the propulsion necessary to reach the moons of Jupiter and navigate between them. Once there, extensive scientific research will be conducted that will also present significant power requirements. Such extreme needs require exploring a new method for power generation in space. A proposed solution involves a Brayton cycle nuclear fission reactor. The nature of this application requires reliable performance of all reactor components for many years of operation under demanding conditions. This includes the bearings which will be operating with an alternative working fluid that is a combination of Helium and Xenon gases commonly known as HeXe. This fluid has transport and thermal properties that vary significantly from that of air and the effect of these property differences on bearing performance must be considered. One of the most promising applications of oil-free technology is in aircraft turbine engines. Eliminating the oil supply systems from aircraft engines will lead to significant weight and maintenance reduction. In such applications, the lubricating fluid will be high altitude air. This air will be at much lower pressure than that at sea level. Again this property change will result in a change in bearing performance, and analysis is required to quantify this effect. The study of these alternate working fluid properties will be conducted in two ways: analytically and experimentally. Analytical research will include the use of a mathematical code that can predict film thickness profiles for various ambient conditions. Estimations of load capacity can be made based upon the film thickness trends. These values will then be compared to those obtained from classical rigid bearing analysis. Experimental Research will include testing a foil bearing at a variety of ambient air pressures. The analytical and experimental data will be compared to draw conclusions on bearing performance under alternate working fluid properties.

Smith, Matthew J.↗
DOE OSTI2022

Neural network–based pore flow field prediction in porous media using super resolution

Direct pore-scale simulations of fluid flow through porous media are computationally expensive to perform for realistic systems. Previous works have demonstrated using the geometry of the microstructure of porous media to predict the velocity fields therein based on neural networks. However, such trained neural networks do not perform well for unseen porous media with a large degree of heterogeneity. In this study we propose that incorporating a coarse velocity field in the input of neural networks is an effective way to improve the prediction performance. The coarse velocity field can be simulated with a low computational cost and provides global information to regularize the ill-posedness of the learning problem, which is usually caused by the use of local geometries due to the computational resource constraints. We show that incorporating the coarse-mesh velocity field significantly improves the prediction accuracy of the fine-mesh velocity field by comparison to the prediction that relies on geometric information alone, especially for the porous medium with a large interior vuggy pore space. We also show the flexibility of training the network in using coarse velocity fields with various resolutions. The results suggest that even using coarse velocity field with a very low resolution, the predictions are still enhanced and close to the ground truths. The feasibility of the method is further demonstrated by testing the trained network on real rocks. This study highlights the merits of incorporating a coarse-mesh velocity field into the input for neural networks, which provides global, physics-based information for the model, thereby improving the model's generalization capability.

42 ENGINEERING↗
DOE OSTI2023

Fully Implicit Conjugate Heat Transfer Analysis of the ARC-Class Vacuum Vessel

The coupled simulation of fusion reactor blankets including neutronics, thermal-hydraulics and thermo-mechanics is expected to speed up the design cycle of fusion reactor design concepts. In this work we demonstrate tight implicit coupling of conjugate heat transfer using the open-source Computational Fluid Dynamics software OpenFOAM for thermo-fluid mechanics and Diablo for thermo-solid mechanics. The heat transfer analysis is augmented by volumetric energy deposition from neutronic calculations using the Monte Carlo N-particle code on both solid and fluid parts of the vacuum vessel. An additional heat flux is imposed on the first wall estimated from the design power of the reactor. The tight coupling is realized through the open-source coupling library, preCICE, and tested on the vacuum vessel of the affordable, robust, compact reactor design by Commonwealth Fusion Systems. The features of the coupling and the influence of different coupling parameters such as coupling schemes, acceleration techniques and convergence criterion are discussed. The coupled simulation results are compared to a thermal-hydraulics simulation which includes only the fluid domains (the liquid immersion molten salt blanket and cooling channel) to demonstrate usefulness of a coupled simulation. Further analysis is performed to identify regions of hot spots for subsequent design improvement. This introduces the outline for integrating conjugate electromagnetics and fluid/solid mechanics (e.g., allow for deformation of the cooling channel walls) with our present approach for future analysis.

Sircar, Arpan↗
NASA NTRS1972

Evaluation testing of a closed Brayton-cycle electrical-power-conversion system.

Description of the design and testing of a recuperated, closed Brayton-cycle, electrical power conversion system designated the Brayton Cycle Demonstrator (BCD). The system uses electrical heaters as a heat source, argon as the cycle working fluid, and gas-lubricated foil-type bearings. Objectives of the test program include (1) evaluation of the overall system performance characteristics and influences on spacecraft integration, (2) familiarization of personnel with operational methods, and (3) determination of system flexibility by operating at a number of off-design conditions. Results obtained to date are discussed.

Redding, T. E.↗
DOE OSTI2020

A simple and effective five-equation two-phase numerical model for liquid-vapor phase transition in cavitating flows

Numerical difficulties, notably the non-monotonic behavior of the Wood speed of sound and the volume fraction positivity, associated with the reduced five-equation two-phase flow model of Kapila et al. (2001) [A.K. Kapila, R. Menikoff, J.B. Bdzil, S.F. Son, D.S. Stewart, 2001. Two-phase modeling of deflagration-to-detonation transition in granular materials: reduced equations, Physics of Fluids 13(10), 3002–3024] have been resolved in the past through the introduction of a frozen speed of sound and an algebraic approach for mechanical relaxation afforded by a pressure non-equilibrium six-equation model proposed by [R. Saurel, F. Petitpas, R.A. Berry, 2009. Simple and efficient relaxation methods for interfaces separating compressible fluids, cavitating flows and shocks in multiphase mixture, J. Comput. Phys. 228, 1678–1712]. By contrast, it is explored and demonstrated in this work that these difficulties can in fact still be resolved within the numerical scheme for solving the reduced five-equation model by numerically replacing the Wood speed of sound for the estimates of wave speeds in the approximate Riemann solver HLLC with the monotonic mixture speed of sound for a transport five-equation model. For shock interface (artificial mixture separating pure or nearly pure fluids) interaction problems, with the apparent advantage of monotonic behavior of the speed of sound in the interface, the effect of the numerical replacement is also confined to the interface. Differences other than the behavior of the speed of sound within the interface in the solutions due to the replacement diminish with increasing resolution when reasonable solution can be obtained with Wood speed of sound. For cavitating/expansion problems in physical fluid mixture, it is pointed out and explained why acoustics in the numerical solutions still propagate at the Wood speed of sound (therefore consistent with the reduced five-equation model) even though in some cases a much higher speed of sound like the numerical replacement above for solving the reduced five-equation model or the frozen speed of sound for solving a six-equation model is used for the estimates of wave speeds in the HLLC scheme. A variant of the five-equation two-phase flow model by Saurel et al. (2008) [R. Saurel, F. Petitpas, R. Abgrall, 2008. Modelling phase transition in metastable liquids: application to cavitating and flashing flows, J. Fluid Mech. 607, 313–350] is then constructed for liquid-vapor phase transition in cavitating flows. The relaxation toward thermo-chemical equilibrium during phase transition is achieved by solving a simple system of algebraic equations for the equilibrium state variables for better efficiency, following Pelanti and Shyue (2014) [M. Pelanti, K.-M. Shyue, 2014. A mixture-energy-consistent six-equation two-phase numerical model for fluid with interfaces, cavitation and evaporation waves. J. Comput. Phys. 259, 331–357]. Therefore, the current model retains both the simplicity afforded by the five-equation model and the efficiency of the algebraic relaxation solver. An alternative algebraic approach for handling the non-conservative term (the so-called K∇ · u term) in the reduced five-equation model for mechanical equilibrium of a liquid-vapor mixture is also explored by enforcing the thermal equilibrium at the same time. Finally, numerical results of sample tests in both one and two dimensions in the literature as well as that in three dimensions demonstrate the effectiveness and ability of the proposed model to simulate cavitating flows. An interesting mechanism of shock generation by acoustics in water due to phase transition is then found by the numerical simulations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1994

NASA Lewis Research Center Workshop on Forced Response in Turbomachinery

A summary of the NASA Lewis Research Center (LeRC) Workshop on Forced Response in Turbomachinery in August, 1993 is presented. It was sponsored by the following NASA organizations: Structures, Space Propulsion Technology, and Propulsion Systems Divisions of NASA LeRC and the Aeronautics and Advanced Concepts & Technology Offices of NASA Headquarters. In addition, the workshop was held in conjunction with the GUIde (Government/Industry/Universities) Consortium on Forced Response. The workshop was specifically designed to receive suggestions and comments from industry on current research at NASA LeRC in the area of forced vibratory response of turbomachinery blades which includes both computational and experimental approaches. There were eight presentations and a code demonstration. Major areas of research included aeroelastic response, steady and unsteady fluid dynamics, mistuning, and corresponding experimental work.

Stefko, George L.↗