SEARCH · Search NASA

Results for “Code Verification”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

SourceResearch connectionFrom yearThrough year

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

77 records · Page 4

All sources NASA NTRS DOE OSTI

NASA NTRS2004

Energetics of Single Substitutional Impurities in NiTi

Shape-memory alloys are of considerable current interest, with applications ranging from stents to Mars rover components. In this work, we present results on the energetics of single substitutional impurities in B2 NiTi. Specifically, energies of Pd, Pt, Zr and Hf impurities at both Ni and Ti sites are computed. All energies are computed using the CASTEP ab initio code, and, for comparison, using the quantum approximate energy method of Bozzolo, Ferrante and Smith. Atomistic relaxation in the vicinity of the impurities is investigated via quantum approximate Monte Carlo simulation, and in cases where the relaxation is found to be important, the resulting relaxations are applied to the ab initio calculations. We compare our results with available experimental work.

Binary Alloys↗

NASA NTRS2026

The Trash Compaction Processing Systems (TCPS) Ground Unit Control Sample Testing

The Trash Compaction Processing System (TCPS) is being developed by NASA and Sierra Space to process crew trash for long-duration missions. The system compacts and thermally processes mixed spacecraft waste to reduce volume and stabilize the material while managing gas and liquid effluents. A Ground Unit (GU) located at Sierra Space in Madison, Wisconsin was used to run a series of tests using standardized control samples representing different trash conditions, including nominal, high liquid, high cloth, benign, and foam. Gas grab samples were collected during processing and analyzed to identify the compounds present in the effluent stream and compare the concentrations to the NASA spacecraft maximum allowable concentrations (SMACs). Additional testing included odor testing at White Sands Test Facility, aerosol measurements, microbiology, and tile characterization. Overall, the compounds detected in the gas samples were well below the SMAC limits for all trash models tested. The results from this testing are being used to help guide the verification approach and test planning for the TCPS Flight Unit that is planned for on-orbit testing on the International Space Station.

Control Samples↗

NASA NTRS2026

Development and Experimental Validation of a Path-Dependent Spin Forming Finite Element Model

Spin forming is an advanced manufacturing process widely used in the aerospace and defense sectors to produce lightweight, high-strength cylindrical components with tight dimensional tolerances. This study explores the applicability of the path-dependent Mechanical Threshold Stress (MTS) constitutive model by simulating the evolution of geometry, machining forces, and plastic deformation during the spin forming of a 10-mm thick 6061-O aluminum cylinder. While numerical modeling of spin forming has advanced substantially over the past decade, systematic verification and experimental validation of material models remain limited, particularly in predicting through-thickness process evolution. The MTS model, incorporating a Voce hardening rule, is employed for its ability to represent cyclic loading, rapidly varying temperature fields, and strain rates characteristic of spin forming. Numerical convergence analysis indicates discretization uncertainties between 0.3% and 9.2% for key quantities of interest. Experimental validation demonstrates that the MTS model, when implemented with a verified mesh, accurately reproduces both elastic and plastic behavior of 6061-O aluminum, predicting peak roller loads within 11–18% of measurements, geometric tolerances within 3%, and plastic strain distributions within 10% of experimental values. Collectively, these results establish a validated computational framework for predictive spin-forming simulations with quantified confidence, providing a foundation for extension to other alloys, geometries, and forming conditions.

Spin forming↗

NASA NTRSDate not supplied

Helmholtz Motor: A Novel Electric Machine That Enables High Temperature Superconducting Armatures

Electrified aircraft are being developed to increase the efficiency and reduce the cost of operating subsonic transport aircraft. Achieving a substantial impact necessitates focusing on single- and twin-aisle aircraft which use propulsion systems with >20 MW ratings. For these aircraft, multi-MW superconducting electric machines are being developed due to their high specific power and high efficiency. Cryogenic electric machines are a promising technology for multi megawatt electric aircraft drivetrains. Second generation high temperature superconductors (HTS) are the ideal conductor for the field winding (typically the rotor) of superconducting machines, and they have attractive features for the armature winding (typically the stator) of these machines. However, their use in armature windings has been severely limited due to excessive AC losses in conventional electric machines. This presentation will present the working principle, design, and a performance trade study of a novel electric machine – termed a Helmholtz machine – that enables HTS armatures by significantly reducing AC losses. The working principle of the patent pending Helmholtz motor is to optimize the rotor-produced magnetic field (i.e., the field winding) so that it produces a magnetic field almost purely in the plane of the HTS. This is accomplished using 2 rotors that contain a set of matched Helmholtz coil pairs (or matched permanent magnet Halbach arrays). The armature (stator) HTS coils are positioned between the rotors and oriented to minimize the out of plane magnetic field. The armature HTS coils are also designed to minimize the out of plane component of their self field. The presentation will include the lessons learned in the sizing and design of this motor, including equations for how to match the magnet arrays. A performance trade study will be presented for a partially superconducting, radial flux version of the motor. The trade study involved an optimization of a motor design code based on analytical calculations (electromagnetic, AC loss, thermofluid, mechanical, and motor sizing) that determine the motor’s total efficiency and total specific power. The design code will be described in the presentation, with an emphasis on the calculation of magnetic fields, AC loss, and temperature distribution.

Superconducting electric machines↗

NASA NTRSDate not supplied

Risk Reduction Project in Pad Abort-1 Launch Vehicle Loads & Dynamics

The Pad Abort (PA-1) system includes the Launch Abort System (LAS) and the Command Module (CM). The PA-1 abort flight test will launch from the White Sands Missile Range. Prior to the ignition, the vehicle will be resting, without restraints, on a short support structure. The Launch Abort Motor will ignite and burn for less than 5 seconds before a 20 second coast. Then the LAS will separate from the CM and the CM will descend via parachute to a soil landing. The static firing of the Abort Motor (ST-1) for PA-1 Launch Vehicle resulted in unexpected higher levels that superseded the environment predictions and all the design and test loads of all subassemblies and components. A rapid project was put in place to develop the flight environments, loads and associated uncertainties for the Verification Load Cycle (VLC) of PA-1. An acoustic test and shaker test of the CM were planned and executed in support of the developments of damping and transfer functions. Instead of using the traditional structure-borne envelops, the actual ST-1 pressures and forces were used to develop the internal accelerations. The PA-1 motor was cooled to 60 Deg F using thermal conditioning to reduce the thrust profile. The plumes of the abort motor were studied to determine if the airborne environments would be reduced. The combination of all items, noted above, allowed a reduction in loads for VLC.

Sasan C Armand↗

NASA NTRSDate not supplied

Discrete Rotational Energy for Polyatomic Molecules in Direct Simulation Monte Carlo

The environments experienced by vehicles upon entry into planetary atmospheres generally result in severe aerothermodynamic loading. These flows are characterized by the formation of strong shock waves, behind which high temperatures and non-equilibrium environments are generated, and the accurate prediction of internal energy relaxation and chemical kinetics becomes important. This manuscript focuses on the internal relaxation of the rotational energy of polyatomic molecules. Previous work has described the implementation of a discrete rotational energy model for diatomic molecules (linear rotators). Later, Gimelshein et. al extended this model to include polyatomic molecular internal energies. However, they did not include details on how to generate the particles at equilibrium conditions and centrifugal distortion was not included in their model. The purpose of the present study is to extend the afore-mentioned models to the treatment of discrete rotational energy in polyatomic molecules with the addition of centrifugal distortion. An overview of the background theory needed for the implementation of the model will be given followed by the model itself and verification of the model. For example, sampled versus Boltzmann distributions are compared in Figure 1 for CH3 (oblate rotator – two quantum numbers) and examples of thermal relaxation behavior for linear and non-linear rotators are presented in Figure 2. In addition, comparisons of thermophysical properties will be presented, as well as examples of adiabatic relaxation and application to hypersonic flow.

Rarefied Gas Dynamics↗

NASA NTRS2002

Hubble Space Telescope On-orbit NiH2 Battery Performance

This paper summarizes the Hubble Space Telescope (HST) nickel-hydrogen (NiH2) battery performance from launch to the present time. Over the life of HST vehicle configuration, charge system degradation and failures together with thermal design limitations have had a significant effect on the capacity of the HST batteries. Changes made to the charge system configuration in order to protect against power system failures and to maintain battery thermal stability resulted in undercharging of the batteries. This undercharging resulted in decreased usable battery capacity as well as battery cell voltage/capacity divergence. This cell divergence was made evident during on-orbit battery capacity measurements by a relatively shallow slope of the discharge curve following the discharge knee. Early efforts to improve the battery performance have been successful. On-orbit capacity measurement data indicates increases in the usable battery capacity of all six batteries as well as improvements in the battery cell voltage/capacity divergence. Additional measures have been implemented to improve battery performance, however, failures within the HST Power Control Unit (PCU) have prevented verification of battery status. As this PCU fault prevents the execution of on-orbit capacity testing, the HST Project has based the battery capacity on trends, which utilizes previous on-orbit battery capacity test data, for science mission and servicing mission planning. The Servicing Mission 38 (SM-3B) in March 2002 replaced the faulty PCU. Following the servicing mission, on-orbit capacity test resumed. A summary of battery performance is reviewed since launch in this paper.

Rao, Gopalakrishna M.↗

NASA NTRS2026

Improvement in the Thermal-to-Structural Model Mapping Process for Integrated Modeling for the Roman Space Telescope

Integrated Modeling has been a key component of verifying optical requirements for the Nancy Grace Roman Space Telescope (RST) that are either impossible or impractical to verify exclusively through ground testing. Two major areas for integrated Modeling are Jitter and Thermal Distortion that require the exchanges of model performance predictions across disciplines. In both cases, distortions are impressed on optical models to evaluate the impact on boresight alignment and wave front error. In the case of Jitter, the disturbances are driven by reactions to motions most often from actuators; however, in the case of thermal distortion, the motions are driven by thermal expansion or contraction as a result of changing temperatures. This then requires a link further upstream to the thermal model, which is used to predict the thermal performance and temperature gradients and stability. The process for mapping temperatures from a thermal model to a corresponding structural model has been performed numerous times through the RST project lifecycle, with improvements in the accuracy, verification, and effort sought throughout. This paper describes some of the recent improvements to the process, including: capture of the visualization parameters, automatic generation of the mapped images for both the thermal and structural model groupings, and reduction in the effort to assemble the full set of mapped temperatures. These upgrades have greatly reduced the manual effort associated with thermal mapping and allowed for faster turn-around of Integrated Modeling predictions.

Thermal Mapping↗

NASA NTRS1992

Development and application of a 3-D geometry/mass model for LDEF satellite ionizing radiation assessments

A computer model of the three dimensional geometry and material distributions for the LDEF spacecraft, experiment trays, and, for selected trays, the components of experiments within a tray was developed for use in ionizing radiation assessments. The model is being applied to provide 3-D shielding distributions around radiation dosimeters to aid in data interpretation, particularly in assessing the directional properties of the radiation exposure. Also, the model has been interfaced with radiation transport codes for 3-D dosimetry response predictions and for calculations related to determining the accuracy of trapped proton and cosmic ray environment models. The methodology is described used in developing the 3-D LDEF model and the level of detail incorporated. Currently, the trays modeled in detail are F2, F8, and H12 and H3. Applications of the model which are discussed include the 3-D shielding distributions around various dosimeters, the influence of shielding on dosimetry responses, and comparisons of dose predictions based on the present 3-D model vs those from 1-D geometry model approximations used in initial estimates.

B. L. Colborn↗

NASA NTRS1997

The Effect of Gravity on the Combustion of Bulk Metals

In recent years, metal combustion studies at the University of Colorado have focused on the effects of gravity (g) on the ignition and burning behavior of bulk metals. The impetus behind this effort is the understanding of the ignition conditions and flammability properties of structural metals found in oxygen (O,sub>2 ) systems for space applications. Since spacecraft are subjected to higher-than-1g loads during launch and reentry and to a zero-gravity environment while in orbit, the study of ignition and combustion of bulk metals at different gravitational accelerations is of great practical concern. From the scientific standpoint, studies conducted under low gravity conditions provide simplified boundary conditions, since buoyancy is removed, and make possible the identification of fundamental ignition and combustion mechanisms. This investigation is intended to provide experimental verification of the influence of natural convection on the burning behavior of metals. In addition, the study offers the first findings of the influence of gravity on ignition of bulk metals and on the combustion mechanism and structure of metal-oxygen, vapor-phase diffusion flames in a buoyancy-free environment. Titanium (Ti) and magnesium (Mg) metals were chosen because of their importance as elements of structural materials and their simple chemical composition-pure metals instead of multicomponent alloys to simplify chemical and spectroscopic analyses. In addition, these elements present the two different combustion modes observed in metals: heterogeneous or surface burning (for Ti) and homogeneous or gas-phase reaction (for Mg). Finally, Mg, Ti, and their oxides exhibit a wide range of thermophysical and chemical properties. Metal surface temperature profiles, critical and ignition temperatures, propagation rates, burning times, and spectroscopic measurements are obtained under normal and reduced gravity. Visual evidence of all phenomena is provided by high-speed photography.

Melvyn C Branch↗

NASA NTRS1985

Summary of recent NASA propeller research

Advanced high speed propellers offer large performance improvements for aircraft that cruise in the Mach 0.7 to 0.8 speed regime. At these speeds, studies indicate that there is a 15 to near 40 percent block fuel savings and associated operating cost benefits for advanced turboprops compared to equivalent technology turbofan powered aircraft. Recent wind tunnel results for five eight to ten blade advanced models are compared with analytical predictions. Test results show that blade sweep was important in achieving net efficiencies near 80 percent at Mach 0.8 and reducing nearfield cruise noise about 6 dB. Lifting line and lifting surface aerodynamic analysis codes are under development and some results are compared with propeller force and probe data. Also, analytical predictions are compared with some initial laser velocimeter measurements of the flow field velocities of an eight bladed 45 swept propeller. Experimental aeroelastic results indicate that cascade effects and blade sweep strongly affect propeller aeroelastic characteristics. Comparisons of propeller nearfield noise data with linear acoustic theory indicate that the theory adequately predicts nearfield noise for subsonic tip speeds, but overpredicts the noise for supersonic tip speeds.

Daniel C Mikkelson↗

NASA NTRSDate not supplied

Spike-Nosed Bodies and Forward Injected Jets in Supersonic Flow

The paper contains new numerical simulation and experimental test results of blunt body drag reduction using thin spikes mounted in front of a body and one- or two-phase jets injected against a supersonic flow. Numerical simulations utilizing the NASA CFL3D code were conducted at the Hampton University Fluid Mechanics and Acoustics Laboratory (FM&AL) and experimental tests were conducted using the facilities of the IM/MSU Aeromechanics and Gas Dynamics Laboratory. Previous results were presented at the 37 t h AIAA/ASME/SAE/ASEE Joint Propulsion Conference. Those results were based on some experimental and numerical simulation tests for supersonic flow around spike-nosed or shell-nosed bodies, and numerical simulations were conducted only for a single spike-nosed or shell-nosed body at zero attack angle, alpha=0 o . In this paper, experimental test results of gas, liquid and solid particle jet injection against a supersonic flow are presented. In addition, numerical simulation results for supersonic flow around a multiple spike-nosed body with non-zero attack angles and with a gas and solid particle forward jet injection are included. Aerodynamic coefficients: drag, C D , lift, C L , and longitudinal momentum, M z , obtained by numerical simulation and experimental tests are compared and show good agreement.

M Gilinsky↗

NASA NTRSDate not supplied

Spike-Nosed Bodies and Forward Injected Jets in Supersonic Flow

The paper contains new numerical simulation and experimental test results of blunt body drag reduction using thin spikes mounted in front of a body and one- or two-phase jets injected against a supersonic flow. Numerical simulations utilizing the NASA CFL3D code were conducted at the Hampton University Fluid Mechanics and Acoustics Laboratory (FM&AL) and experimental tests were conducted using the facilities of the IM/MSU Aeromechanics and Gas Dynamics Laboratory. Previous results were presented at the 37th AIAA/ASME/SAE/ASEE Joint Propulsion Conference. Those results were based on some experimental and numerical simulation tests for supersonic flow around spike-nosed or shell-nosed bodies, and numerical simulations were conducted only for a single spike-nosed or shell-nosed body at zero attack angle, alpha = 0 degrees. In this paper, experimental test results of gas, liquid and solid particle jet injection against a supersonic flow are presented. In addition, numerical simulation results for supersonic flow around a multiple spike-nosed body with non-zero attack angles and with a gas and solid particle forward jet injection are included. Aerodynamic coefficients: drag, C (sub D), lift, C(sub L), and longitudinal momentum, M(sub z), obtained by numerical simulation and experimental tests are compared and show good agreement.

M Gilinsky↗

NASA NTRSDate not supplied

Lunar Nuclear Reactor Neutron Fluence and Gamma Dose Estimates

NASA aims to deploy a fission reactor on the lunar surface by 2030 to generate 100 kWe of power for at least 10 years without maintenance or refueling. To assess system and subsystem survivability according to those requirements, a model of the reactor pallet was created in the radiation transport code MCNP to determine the neutron fluences and gamma doses that the materials and systems would be exposed to. The model was based on the 2025 government design. The model indicated that the control drum motors, Brayton cycle engines, and pipes and valves would be exposed to neutron fluences of 1×10 15 – 1×10 16 n/cm 2 per year and gamma doses ranging from 10 to 500 Mrad per year. The electronics box housing the instrumentation and control elements is expected to receive 1×10 14 – 1×10 15 n/cm 2 per year and gamma doses in the range of 1–5 Mrad per year. These doses necessitate that the control drum motors, Brayton cycle engines, valve components, control electronics, and other components be radiation-hardened (>10 16 n/cm 2 and >10 Mrad gamma dose) or additionally shielded to survive the 10-year lunar mission.

Radiation-Hardened Materials↗

NASA NTRS2006

The 2004 NASA Aerospace Battery Workshop

Topics covered include: Super NiCd(TradeMark) Energy Storage for Gravity Probe-B Relativity Mission; Hubble Space Telescope 2004 Battery Update; The Development of Hermetically Sealed Aerospace Nickel-Metal Hydride Cell; Serial Charging Test on High Capacity Li-Ion Cells for the Orbiter Advanced Hydraulic Power System; Cell Equalization of Lithium-Ion Cells; The Long-Term Performance of Small-Cell Batteries Without Cell-Balancing Electronics; Identification and Treatment of Lithium Battery Cell Imbalance under Flight Conditions; Battery Control Boards for Li-Ion Batteries on Mars Exploration Rovers; Cell Over Voltage Protection and Balancing Circuit of the Lithium-Ion Battery; Lithium-Ion Battery Electronics for Aerospace Applications; Lithium-Ion Cell Charge Control Unit; Lithium Ion Battery Cell Bypass Circuit Test Results at the U.S. Naval Research Laboratory; High Capacity Battery Cell By-Pass Switches: High Current Pulse Testing of Lithium-Ion; Battery By-Pass Switches to Verify Their Ability to Withstand Short-Circuits; Incorporation of Physics-Based, Spatially-Resolved Battery Models into System Simulations; A Monte Carlo Model for Li-Ion Battery Life Projections; Thermal Behavior of Large Lithium-Ion Cells; Thermal Imaging of Aerospace Battery Cells; High Rate Designed 50 Ah Li-Ion Cell for LEO Applications; Evaluation of Corrosion Behavior in Aerospace Lithium-Ion Cells; Performance of AEA 80 Ah Battery Under GEO Profile; LEO Li-Ion Battery Testing; A Review of the Feasibility Investigation of Commercial Laminated Lithium-Ion Polymer Cells for Space Applications; Lithium-Ion Verification Test Program; Panasonic Small Cell Testing for AHPS; Lithium-Ion Small Cell Battery Shorting Study; Low-Earth-Orbit and Geosynchronous-Earth-Orbit Testing of 80 Ah Batteries under Real-Time Profiles; Update on Development of Lithium-Ion Cells for Space Applications at JAXA; Foreign Comparative Technology: Launch Vehicle Battery Cell Testing; 20V, 40 Ah Lithium Ion Polymer Battery for the Spacesuit; Low Temperature Life-Cycle Testing of a Lithium-Ion Battery for Low-Earth-Orbiting Spacecraft; and Evaluation of the Effects of DoD and Charge Rate on a LEO Optimized 50 Ah Li-Ion Aerospace Cell.

Source record↗

NASA NTRS2025

On the Stability Analysis of Astrophysical Cooling Functions

To model the temperature evolution of optically thin astrophysical environments at MHD scales, radiative and collisional cooling rates are typically either pretabulated or fit into a functional form and then input into MHD codes as a radiative loss function. Thermal balance requires estimates of the analogous heating rates, which are harder to calculate, and due to uncertainties in the underlying dissipative heating processes these rates are often simply parameterized. The resulting net cooling function defines an equilibrium curve that varies with density and temperature. Such cooling functions can make the gas prone to thermal instability (TI), which will cause departures from equilibrium. There has been no systematic study of thermally unstable parameter space for nonequilibrium states. Motivated by our recent finding that there is a related linear instability, catastrophic cooling instability, that can dominate over TI, here we carry out such a study. We show that Balbus instability criteria for TI can be used to define a critical cooling rate, Λc, that permits a nonequilibrium analysis of cooling functions through the mapping of TI zones. We furthermore illustrate how thermal conduction modifies the shape of TI zones. Upon applying a Λc-based stability analysis to coronal loop simulations, we find that loops undergoing periodic episodes of coronal rain formation are linearly unstable to catastrophic cooling instability, while TI is stabilized by thermal conduction.

Amanda Stricklan↗

NASA NTRSDate not supplied

Revisiting the Soyuz-1 Parachute Failure in the Context of Safety in the Modern Era

The Soyuz‑1 accident remains one of the most consequential parachute related failures in human spaceflight history and provides enduring lessons for modern Entry, Descent, and Landing (EDL) system design. Occurring during the height of the Cold War and the Space Race, the mission unfolded under extraordinary political and schedule pressure as the Soviet Union sought to maintain its early leadership in space achievements following the death of chief designer Sergei Korolev. Despite unresolved propulsion, electrical, and parachute system deficiencies, Soyuz‑1 proceeded to launch and immediately encountered critical inflight anomalies, including a failed solar panel deployment, attitude control issues, and communication dropouts. Upon reentry, a malfunction in the parachute system, driven by a primary main canopy that failed to deploy, and subsequent entanglement of the reserve main canopy with the primary drogue parachute, resulted in insufficient deceleration and the fatal crash of cosmonaut Vladimir Komarov. Subsequent investigations revealed deep rooted cultural and organizational issues within the Soviet space program, including inadequate testing, suppression of dissent, undocumented last minute design changes, and the absence of integrated parachute system verification. More than 200 design flaws were identified after the accident, and firsthand accounts, including those from Yuri Gagarin, highlighted widespread concern prior to launch. Over time, the Soviet program implemented substantial reforms: systematic design corrections, rigorous process documentation, and an extensive series of drop tests that ultimately transformed the Soyuz system into one of the world’s most reliable human-rated return vehicles. This paper examines the technical architecture of the Soyuz‑1 parachute system, reconstructs the likely deployment sequence and failure mechanism, and analyzes the cultural contributors that shaped the accident. The study draws parallels to modern spacecraft parachute development, emphasizing the critical importance of integrated system testing, transparent engineering culture, and continuous hardware surveillance. These lessons remain directly relevant to today’s NASA and Commercial Crew Programs (CCP), where the Government continues to refine its understanding of aggregate risk and strengthen overall astronaut safety in the face of increasingly complex parachute systems.

Aaron L Morris↗

NASA NTRS1993

Development of global/chemistry model for jet-fuel thermal stability based on observations from static and flowing experiments

Two global-chemistry models for oxidative deposition of jet fuels are evaluated by integrating them into a Computational Fluid Dynamics with Chemistry (CFDC) code. A previously developed two-step global-chemistry model was found to be insufficient to describe the thermal-oxidation and -deposition rates associated with a Jet-A fuel. A new global-chemistry model has been developed systematically based on observations from flowing and static experiments. The global-autoxidation reaction is modified such that the reaction rate becomes zeroth-order with respect to the dissolved oxygen concentration. The generation of deposit-forming precursor is coupled with the autoxidation reaction by introducing a radical species ROO. A formulation for the sticking probability has also been developed. Deposition profiles are well represented by this new model under a variety of temperature and flow conditions. The model correctly predicts the changes in magnitude and spatial location of the deposition peak due to changes in flow. The CFDC model, which is designed for flowing systems, has been extended to static experiments. The model incorporates a non-depleting species F(sub s) representing all non-oxygen compounds responsible for deposition. Static experiments were found to provide a useful and inexpensive method for estimating the concentration of F(sub s) in the fuel.

V. R. Katta↗