Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Agreements”

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.

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

At least 307 records · Page 17
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Real-Time Xenon Sensor Analysis Report

Radiotracer release experiments were performed at the Nevada National Security Site in October 2022. The overall experiment was called the RElease ACTivity (REACT) experiment. Twenty-two real-time xenon sensors were deployed for each of four releases. Initial, quick-look analysis results were reported in December 2022. This report reviews the more comprehensive offline analysis effort that was conducted during the remainder of fiscal year 2023 by the Dynamic Networks venture. Improved energy stabilization routines were implemented along with an improved background subtraction routine compared to the original quicklook calculations. The relative detection efficiencies of all real-time sensors were examined. Finally, simulated detector response functions were coupled to two different meteorological models using the measured conditions for the final release (REACT-04) to compare simulated detections with measurements. While there is some agreement between the models and measured data on the detection locations and timing, there is less agreement on the magnitude of those detections. Future sensor and meteorological modeling work will be needed to improve the agreement and to examine the additional releases (REACT-01 through REACT-03).

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2025

High-Temperature Gas-Cooled Reactors Multiphysics Simulation Demonstration and Code Validation

This study presents a comprehensive benchmarking and verification effort of several thermal-hydraulic and multiphysics capabilities for high-temperature gas-cooled reactor applications. The first part of this effort focuses on the running-in verification of Griffin’s multiphysics capabilities, specifically for simulating the evolution of pebble-bed reactor cores from startup to equilibrium. Since Fiscal Year 2024, improvements and enhancements have been implemented in Griffin, including simplifying the process to specify streamlines and developing the online cross-section generation capability. In the absence of validation data, code-to-code comparisons are conducted with kugelpy, showing good agreement for integral quantities like k-eff predictions and predictions for maximum power density. However, accuracy issues are noted for more detailed quantities like the spatial distribution of fission rate densities which will require further work to address. The second part of this report presents an improved System Analysis Module (SAM) core channel model where the effects of cross flow are considered during the pressurized loss of forced cooling transient, resulting in an improved agreement of the predicted pebble temperature with respect to the predictions from the SAM 2D porous media model. Additionally, the wall channeling effect due to variable porosity at the near wall region of the core is also investigated. Furthermore, to demonstrate Griffin’s online cross-section generation capability, a Multiphysics simulation is performed by coupling Griffin to the SAM core channel model. In the third part of the report, as a part of the Organisation for Economic Co-operation and Development/Nuclear Energy Agency (OECD/NEA) thermal-hydraulic code validation benchmark activity for a high-temperature gas-cooled reactor, the High Temperature Test Facility (HTTF) is investigated first using the NekRS computational fluid dynamics (CFD) code to study the flow mixing phenomenon in the lower plenum of the facility. Then, code-to-code and code-to-data comparisons are performed for Test PG27, which is a pressurized conduction cooldown (PCC) test, using five different codes by six organizations from five countries. The different simulations show good agreements in terms of the general trend but there are differences in some results such as the peak temperatures of different regions and heat removal rate.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2023

Novel 3D Force Sensors for a Cost-Effective 3D Force Plate for Biomechanical Analysis

Three-dimensional force plates are important tools for biomechanics discovery and sports performance practice. However, currently, available 3D force plates lack portability and are often cost-prohibitive. To address this, a recently discovered 3D force sensor technology was used in the fabrication of a prototype force plate. Thirteen participants performed bodyweight and weighted lunges and squats on the prototype force plate and a standard 3D force plate positioned in series to compare forces measured by both force plates and validate the technology. For the lunges, there was excellent agreement between the experimental force plate and the standard force plate in the X-, Y-, and Z-axes (r = 0.950–0.999, p < 0.001). For the squats, there was excellent agreement between the force plates in the Z-axis (r = 0.996, p < 0.001). Across axes and movements, root mean square error (RMSE) ranged from 1.17% to 5.36% between force plates. Although the current prototype force plate is limited in sampling rate, the low RMSEs and extremely high agreement in peak forces provide confidence the novel force sensors have utility in constructing cost-effective and versatile use-case 3D force plates.

42 ENGINEERING↗
DOE OSTI2023

Survey Operations for the Dark Energy Spectroscopic Instrument

The Dark Energy Spectroscopic Instrument (DESI) survey is a spectroscopic survey of tens of millions of galaxies at 0 < z < 3.5 covering 14,000 sq. deg. of the sky. In its first 1.1 yr of survey operations, it has observed more than 14 million galaxies and 4 million stars. We describe the processes that govern DESI's observations of the 15,000 fields composing the survey. This includes the planning of each night's observations in the afternoon; automatic selection of fields to observe during the night; real-time assessment of field completeness on the basis of observing conditions during each exposure; reduction, redshifting, and quality assurance of each field of targets in the morning following observation; and updates to the list of future targets to observe on the basis of these results. We also compare the performance of the survey with historical expectations and find good agreement. Simulations of the weather and of DESI observations using the real field-selection algorithm show good agreement with the actual observations. After accounting for major unplanned shutdowns, the dark time survey is progressing about 7% faster than forecast, which is good agreement given approximations made in the simulations.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Simulation of radon-222 with the GEOS-Chem global model: Emissions, seasonality, and convective transport

Radon-222 (222Rn) is a short-lived radioactive gas naturally emitted from land surface, and has long been used to assess convective transport in atmospheric models. In this study, we simulate 222Rn using the GEOS-Chem chemical transport model with aims to improve our understanding of 222Rn emissions and surface concentration seasonality, and to characterize convective transport associated with two Goddard Earth Observing System (GEOS) meteorological products, MERRA and GEOS-FP. We evaluate four available 222Rn emission scenarios by comparing model results with surface observations at 51 global surface sites. The default emission scenario in GEOS-Chem yields a moderate agreement with global surface observations (< 70% data within a factor of 2) and a large underestimate of wintertime surface 222Rn concentrations at Northern Hemisphere mid- and high-latitudes due to an oversimplified formulation of 222Rn emission fluxes (1 atom cm-2 s-1 over land with a reduction by a factor of 3 under freezing conditions). We compose a new global 222Rn emission scenario based on Zhang et al. (2011) and show its potential to improve simulated surface 222Rn concentrations and seasonality. The regional components of this emission scenario include spatially and temporally varying emission fluxes derived from previous measurements of soil radium content and soil exhalation models, which are key factors to 222Rn emission flux rates. However, large model underestimates of surface 222Rn concentrations still exist in Asia, suggesting unusually high regional 222Rn emissions. We propose a conservative up-scaling factor of 1.2 for 222Rn emission fluxes in China, as also constrained by the observed deposition fluxes of 210Pb (decay daughter of 222Rn). With this modification, the model shows better agreement with the observations in Europe and North America (>80% data within a factor of 2), and reasonable agreement in Asia (close to 70%). Further constraints on 222Rn emissions would require additional observations of surface 222Rn concentrations and emission fluxes in central U.S., Canada, Africa, and Asia. We also compare and assess convective transport in model simulations driven by MERRA and GEOS-FP using observed 222Rn vertical profiles during northern mid-latitude summertime and from two short-term airborne campaigns. While the simulations with both GEOS products are able to capture the observed vertical gradient of 222Rn concentrations in the lower troposphere (0-4 km), neither correctly represents the level of convective detrainment, resulting in biases in the middle and upper troposphere. Compared to GEOS-FP, MERRA leads to stronger convective transport of 222Rn, which is partially compensated by its weaker large-scale vertical advection, resulting in similar global vertical distributions of 222Rn concentrations between the two simulations.

Zhang, Bo↗
DOE OSTI2025

Field intercomparison of ice nucleation measurements: the Fifth International Workshop on Ice Nucleation Phase 3 (FIN-03)

Abstract. The third phase of the Fifth International Ice Nucleation Workshop (FIN-03) was conducted at the Storm Peak Laboratory in Steamboat Springs, Colorado, in September 2015 to facilitate the intercomparison of instruments measuring ice-nucleating particles (INPs) in the field. Instruments included two online and four offline measurement systems for INPs, which are a subset of those utilized in the laboratory study that comprised the second phase of FIN (FIN-02). The composition of the total aerosols was characterized using the Particle Analysis by Laser Mass Spectrometry (PALMS) and Wideband Integrated Bioaerosol Sensor (WIBS) instruments, and aerosol size distributions were measured by a laser aerosol spectrometer (LAS). The dominant total particle compositions present during FIN-03 were composed of sulfates, organic compounds, and nitrates, as well as particles derived from biomass burning. Mineral-dust-containing particles were ubiquitous throughout and represented 67 % of supermicron particles. Total WIBS fluorescing particle concentrations for particles with diameters of > 0.5 µm were 0.04 ± 0.02 cm−3 (0.1 cm−3 highest; 0.02 cm−3 lowest), typical of the warm season in this region and representing ≈ 9 % of all particles in this size range as a campaign average. The primary focus of FIN-03 was the measurement of INP concentrations via immersion freezing at temperatures > −33 °C. Additionally, some measurements were made in the deposition nucleation regime at these same temperatures, representing one of the first efforts to include both mechanisms within a field campaign. INP concentrations via immersion freezing agreed within factors ranging from nearly 1 to 5 times on average between matched (time and temperature) measurements, and disagreements only rarely exceeded 1 order of magnitude for sampling times coordinated to within 3 h. Comparisons were restricted to temperatures lower than −15 °C due to the limits of detection related to sample volumes and very low INP concentrations. Outliers of up to 2 orders of magnitude occurred between −25 and −18 °C; a better agreement was seen at higher and lower temperatures. Although the 5–10 factor agreement of INP measurements found in FIN-03 aligned with the results of the FIN-02 laboratory comparison phase, giving confidence in progress of this measurement field, this level of agreement still equates to temperature uncertainties of 3.5 to 5 °C that may not be sufficient for numerical cloud modeling applications that utilize INP information. INP activity in the immersion-freezing mode was generally found to be an order of magnitude or more, making it more efficient than in the deposition regime at 95 %–99 % water relative humidity, although this limited data set should be augmented in future efforts. To contextualize the study results, an assessment was made of the composition of INPs during the late-summer to early-fall period of this study inferred through comparison to existing ice nucleation parameterizations and through measurement of the influence of thermal and organic carbon digestion treatments on immersion-freezing ice nucleation activity. Consistent with other studies in continental regions, biological INPs dominated at temperatures of > −20 °C and sometimes colder, while arable dust-like or other organic-influenced INPs were inferred to dominate below −20 °C.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Multiscale assessment of North American terrestrial carbon balance

Abstract. Comparisons of carbon uptake estimates from bottom-up terrestrial biosphere models (TBMs) to top-down atmospheric inversions help assess how well we understand carbon dioxide (CO2) exchange between the atmosphere and terrestrial biosphere. Previous comparisons have shown varying levels of agreement between bottom-up and top-down approaches, but they have almost exclusively focused on large, aggregated scales (e.g., global or continental), providing limited insights into reasons for the mismatches. Here we explore how consistency, defined as the spread in net ecosystem exchange (NEE) estimates within an ensemble of TBMs or inversions, varies with at finer spatial scales ranging from 1∘×1∘ to the continent of North America. We also evaluate how well consistency informs accuracy in overall NEE estimates by filtering models based on their agreement with the variability, magnitude, and seasonality in observed atmospheric CO2 drawdowns or enhancements. We find that TBMs produce more consistent estimates of NEE for most regions and at most scales relative to inversions. Filtering models using atmospheric CO2 metrics causes ensemble spread to decrease substantially for TBMs, but not for inversions. This suggests that ensemble spread is likely not a reliable measure of the uncertainty associated with the North American carbon balance at any spatial scale. Promisingly, applying atmospheric CO2 metrics leads to a set of models with converging flux estimates across TBMs and inversions. Overall, we show that multiscale assessment of the agreement between bottom-up and top-down NEE estimates, aided by regional-scale observational constraints is a promising path towards identifying fine-scale sources of uncertainty and improving both ensemble consistency and accuracy. These findings help refine our understanding of biospheric carbon balance, particularly at scales relevant for informing regional carbon-climate feedbacks.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

Snowfall and snow accumulation during the MOSAiC winter and spring seasons

Data from the Multidisciplinary drifting Observatory for the Study of Arctic Climate (MOSAiC) expedition allowed us to investigate the temporal dynamics of snowfall, snow accumulation and erosion in great detail for almost the whole accumulation season (November 2019 to May 2020). We computed cumulative snow water equivalent (SWE) over the sea ice based on snow depth and density retrievals from a SnowMicroPen and approximately weekly measured snow depths along fixed transect paths. We used the derived SWE from the snow cover to compare with precipitation sensors installed during MOSAiC. The data were also compared with ERA5 reanalysis snowfall rates for the drift track. We found an accumulated snow mass of 38 mm SWE between the end of October 2019 and end of April 2020. The initial SWE over first-year ice relative to second-year ice increased from 50 % to 90 % by end of the investigation period. Further, we found that the Vaisala Present Weather Detector 22, an optical precipitation sensor, and installed on a railing on the top deck of research vessel Polarstern, was least affected by blowing snow and showed good agreements with SWE retrievals along the transect. On the contrary, the OTT Pluvio 2 pluviometer and the OTT Parsivel 2 laser disdrometer were largely affected by wind and blowing snow, leading to too high measured precipitation rates. These are largely reduced when eliminating drifting snow periods in the comparison. ERA5 reveals good timing of the snowfall events and good agreement with ground measurements with an overestimation tendency. Retrieved snowfall from the ship-based K a -band ARM zenith radar shows good agreements with SWE of the snow cover and differences comparable to those of ERA5. Based on the results, we suggest the K a -band radar-derived snowfall as an upper limit and the present weather detector on RV Polarstern as a lower limit of a cumulative snowfall range. Based on these findings, we suggest a cumulative snowfall of 72 to 107 mm and a precipitation mass loss of the snow cover due to erosion and sublimation as between 47 % and 68 %, for the time period between 31 October 2019 and 26 April 2020. Extending this period beyond available snow cover measurements, we suggest a cumulative snowfall of 98–114 mm.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS1958

Approximate Solutions for the Flow About Flat-Top Wing-Body Configurations at High Supersonic Airspeeds

The flow about slender flat-top wing-body configurations traveling at high supersonic speeds and small angles of attack is investigated analytically. In the case of conical configurations, approximate algebraic solutions to the flow field are obtained. In the case of configurations which are conical at the vertex but curved in the stream direction, these solutions are combined with a slender-body approximation to the generalized shock-expansion method to obtain the flow downstream of the vertex. Surface pressures were obtained experimentally at Mach numbers from 3.0 to 6.0 and angles of attack up to 6 deg for several flat-top wing-body configurations. These configurations consisted of half-bodies of revolution mounted beneath thin highly swept wings. Three different bodies were employed. The two conical bodies consisted of one-half of a fineness-ratio-5 cone and one-half of a fineness-ratio-2-1/2 cone. The body of the third configuration consisted of one-half of a fineness-ratio-5 ogive. For the ogive configuration, the leading edges of the wing were curved and designed to just maintain the theoretically determined bow shock along the leading edge at a Mach number of 5.0 and an angle of attack of 3 deg. The predictions of the conical flow theory of this paper for the surface pressures are found to be in good agreement with experiment at Mach numbers of 5.0 and 6.0 up to angles of attack of approximately 3 deg. Estimated lift, drag, and pitching-moment coefficients, as well as maximum lift-drag ratio, are also in good agreement with existing experimental data at a Mach number of 5.0 for a conical configuration having an arrow plan-form wing. It is also found that the generalized shock-expansion method yields reasonable good agreement with experiment for the surface pressures on the half-ogive configuration at a Mach number of 5.0 and an angle of attack of 3 deg.

Savin, Raymond C.↗
NASA NTRS1971

Vibration characteristics of Z-ring-stiffened 60 deg conical shell models of a planetary entry spacecraft

An experimental investigation of the vibration characteristics of a 60 deg conical shell model of a planetary entry vehicle is described and the results presented. Model configurations include the shell with or without one or two Z-ring stiffeners and with or without a simulated payload. Tests were conducted with the model clamped at the small diameter and with the model suspended at the simulated payload. Additionally, calculated results obtained from application of several analytical procedures reported in the literature are presented together with comparisons between experimental and calculated frequencies and meridional mode shapes. Generally, very good frequency agreement between experimental and calculated results was obtained for all model configurations. For small values of circumferential mode number, however, the frequency agreement decreased as the number of ring stiffeners increased. Overall agreement between experimental and calculated mode shapes was generally good. The calculated modes usually showed much larger curvatures in the vicinity of the rings than were observed in the experimentally measured mode shapes. Dual resonances associated with modal preference were noted for the shell without Z-ring stiffeners, whereas the addition of stiffeners produced resonances for which the model responded in two or more modes over different sections of the shell length.

Naumann, E. C.↗
NASA NTRS1972

Magnetostriction and magnetoelastic quantum oscillations in P-type lead telluride

A detailed experimental and theoretical study of quantum oscillations in the magnetostriction and Young's modulus of p-PbTe is presented. The valance band of PbTe is approximated by a spheroidal, nonparabolic model in which the effects of strain on the valance band parameters are described by a deformation potential model. Using appropriate thermodynamic derivatives of the modified Lifshitz-Kosevich expression for the oscillatory parts of the electronic free energy, it is shown that both types of oscillations arise mainly from relative shifts of the valance band maxima due to shear strains, accompanied by intervalley charge transfer. Band parameters derived from the periods, phases, and spin splitting of the oscillations are in generally good agreement with values reported by other workers. A detailed comparison is made of the experimentally observed oscillation amplitudes with those predicted by theory, and satisfactory agreement is found. The ratio of the amplitudes of the two effects yields a value of the valance band deformation potential in good agreement with a value found from piezoresistance experiments by Burke.

Thompson, T. E.↗
NASA NTRS1971

A comparison and evaluation of satellite derived positions of tracking stations

A comparison is presented of sets of satellite tracking station coordinate values published in the past few years by a number of investigators, i.e. Goddard Space Flight Center, Smithsonian Astrophysical Observatory, Ohio State University, The Naval Weapons Laboratory, Air Force Cambridge Research Laboratories, and Wallops Island. The comparisons have been made in terms of latitude, longitude and height. The results of the various solutions have been compared directly and also with external standards such as local survey data and gravimetrically derived geoid heights. After taking into account systematic rotations, latitude and longitude agreement on a global basis is generally 15 meters or better, on the North American Datum agreement is generally better than 10 meters. Allowing for scale differences (of the order of 2 ppm) radial agreement is generally of the order of 10 meters.

Vincent, S. F.↗
NASA NTRS1972

A theoretical study of mixing downstream of transverse injection into a supersonic boundary layer

A theoretical and analytical study was made of mixing downstream of transverse hydrogen injection, from single and multiple orifices, into a Mach 4 air boundary layer over a flat plate. Numerical solutions to the governing three-dimensional, elliptic boundary layer equations were obtained using a general purpose computer program. Founded upon a finite element solution algorithm. A prototype three-dimensional turbulent transport model was developed using mixing length theory in the wall region and the mass defect concept in the outer region. Excellent agreement between the computed flow field and experimental data for a jet/freestream dynamic pressure ratio of unity was obtained in the centerplane region of the single-jet configuration. Poorer agreement off centerplane suggests an inadequacy of the extrapolated two-dimensional turbulence model. Considerable improvement in off-centerplane computational agreement occured for a multi-jet configuration, using the same turbulent transport model.

Baker, A. J.↗
NASA NTRS1973

Theoretical and experimental studies of reentry plasmas

A viscous shock-layer analysis was developed and used to calculate nonequilibrium-flow species distributions in the plasma layer of the RAM vehicle. The theoretical electron-density results obtained are in good agreement with those measured in flight. A circular-aperture flush-mounted antenna was used to obtain a comparison between theoretical and experimental antenna admittance in the presence of ionized boundary layers of low collision frequency. The electron-temperature and electron-density distributions in the boundary layer were independently measured. The antenna admittance was measured using a four-probe microwave reflectometer and these measured values were found to be in good agreement with those predicted. Measurements were also performed with another type of circular-aperture antenna and good agreement was obtained between the calculations and the experimental results. A theoretical analysis has been completed which permits calculation of the nonequilibrium, viscous shock-layer flow field for a sphere-cone body. Results are presented for two different bodies at several different altitudes illustrating the influences of bluntness and chemical nonequilibrium on several gas dynamic parameters of interest. Plane-wave transmission coefficients were calculated for an approximate space-shuttle body using a typical trajectory.

Dunn, M. G.↗
NASA NTRS1973

Access of solar protons to the earth's polar caps.

Energetic solar proton observations in the interplanetary medium by Explorer 33 and Explorer 35 and over the polar caps by Injun 5 during the period from September 1968 through March 1970 have been examined in detail. The solar proton intensities observed over the polar regions were compared with the interplanetary intensities on an absolute basis. The high polar latitude (HPL) proton intensities tracked the magnetic field aligned interplanetary intensities well (solar-antisolar intensities as determined from the sectored Explorer data). The tracking was in agreement with the open magnetosphere model about 90% of the time - i.e., the intensities observed on the HPL magnetic lines of force, which would be connected to magnetic lines of force from the sun in an interconnected geomagnetic and interplanetary magnetic field, were in agreement with the maximum intensity of the interplanetary proton pitch angle distribution. The intensities observed at the HPL region of the opposite polar cap were in agreement with the minimum intensity of the interplanetary pitch angle distribution. The low polar latitude intensities generally tracked the maximum interplanetary intensity very well.

Fennell, J. F.↗
NASA NTRS1974

Dynamic properties of aircraft tires

A research program has investigated the use of the von Schlippe string-type tire model for predicting the dynamic behavior of aircraft tires. The transfer-function method was used for theory evaluation. A more flexible two-constant modification to the string theory tire model is presented. Experiments were conducted on four types of scale model aircraft tires. Two types were of conventional bias construction, one type was an isotropic toroid, and one type was of unbelted radial construction. The conventional string theory and model gave predictions that were in good agreement with experimental data for bias constructed tires. The two-constant modification to string theory provided better agreement between predictions and experiment for the unconventional tires. The results indicate that the string theory tire model using static and slow-rolling tire properties predicts dynamic aircraft tire properties that have the same trends as the measured dynamic properties and, in most cases, provides good quantitative agreement.

Clark, S. K.↗
NASA NTRS1976

Comparisons of measured and theoretical thermospheric daily composition variations

A comparison of the diurnal component of the daily variation in the neutral composition data from the San Marco 3 Nace (Neutral Atmospheric Composition Experiment) mass spectrometer at 220, 250, and 280 km, the OGO-6 model data at 450 km, rocket measurements of nitrogen between 140 and 300 km, and the two-constituent theoretical model of Mayr and Volland (1973) gives good agreement for molecular nitrogen and atomic oxygen. The Nace and rocket measurements overlap in altitude, and there is good agreement in the amplitude and phase of the diurnal and semidiurnal components for molecular nitrogen. The helium diurnal amplitude and phase of the theoretical model are in fair agreement with the Nace results, while the amplitude from the OGO-6 model at 450 km is much larger than the model predicts, a result suggesting that the OGO-6 model diurnal amplitude may be overestimated as the result of an incomplete separation of local-time and seasonal effects.

Kasprzak, W. T.↗
NASA NTRS1976

Mixing and combustion of an underexpanded H2 jet in supersonic flow

Theoretical calculations are compared with experimental data in an investigation of the injection, mixing, and combustion of an underexpanded hydrogen jet in a supersonic test stream. The experimental tests in reacting and nonreacting flows were conducted by use of air and nitrogen as test media. Tests were conducted in a free jet and a ducted mode. Theoretical calculations were performed with a modified viscous characteristics analysis. The computer program employs finite rate chemistry and a turbulent viscosity model which varies radially and axially; it handles exit shock waves, expansion fans, and thermal compressions generated in the reacting flow fields. Comparison of the theory and experimental data indicates good agreement for the near flow field; this agreement is directly related to the explicit handling of the near-field shock and expansion waves. Less satisfactory agreement at downstream locations for both free jet and ducted flows is attributed to the lack of continued computation of the shocks and expansions in the far field.

Jenkins, R. V.↗