Search NASA⌕ Search

SEARCH · Search NASA

Results for “Thermal modeling software”

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 217 records · Page 12

SAM Code Development for Transient Safety Analyses of Fluoride-salt-cooled High-temperature Reactors

The System Analysis Module (SAM) is under development at Argonne National Laboratory as a modern system-level modeling and simulation tool for advanced non-light water reactor safety analyses. It utilizes the object-oriented application framework MOOSE to leverage the modern software environment and advanced numerical methods. The capabilities of SAM are being extended to enable the transient modeling, analysis, and design of various advanced nuclear reactor systems. The molten-salt-cooled pebble-bed reactor, or pebble-bed FHR (PB-FHR) is a promising candidate among advanced nuclear reactor concepts with its improved passive safety characteristics and high thermal efficiency. To support the development and utilization of the SAM code for PB-FHR safety analysis, activities on SAM code enhancements, reference plant model developments, and code validations have been performed in the past a few years to support near-term industry and NRC needs. This report summarizes recent progress under DOE-NE’s Nuclear Energy Advanced Modeling and Simulation program in SAM code development and demonstration for transient safety analysis of Fluoride-salt-cooled High-temperature Reactors. SAM capabilities has been significantly enhanced over the years to add FHR specific modeling features, including salt freezing and thawing, spherical core channel and pebble bed core modeling, solid-fluid thermal radiation, tritium transport and general species transport in fluids and solids, and the general code enhancements on solver schemes of point kinetics module and reactivity feedback models. A reference PB-FHR model is developed, based on publicly available information from Kairos Power’s generic FHR design and the University of California, Berkeley (UCB) Mk1 design. A reference reactor model is foundational to the methodologies employed by NRC to verify the adequacy of computer codes and evaluation models. The reference FHR model was utilized for a number of selected FHR design basis accidents, including station blackout, loss of heat sink, loss of flow, transient overpower, and overcooling events.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Thermal properties and Thermodynamic Equilibrium Modeling of Cementitious Waste Forms

INTRODUCTION Cementitious matrices are used in the US DOE complex and worldwide to solidify aqueous radioactive, hazardous, mixed salt solutions, and sludges to meet low-level radioactive waste (LLW) disposal requirements. Blended formulations are used for most waste form mix designs. Substitution of pozzolans for Class F fly ash has the potential to alter the processing properties and stabilization properties of the resulting waste forms because they add chemical and mineralogical complexity to the final material. The Savannah River Site saltstone waste form was selected as the test case material. CemGEMS software was chosen as the model for predicting hydrated cementitious phases assemblages and phase evolution. Isothermal calorimetry was used as the method for evaluating processing and properties of fresh, uncured waste forms. The test cases consisted of reference case saltstone, and five natural pozzolan substituted saltstone mixes.

Bustamante, Michael E. [Savannah River National La↗

Novel Temperature Sensors and Wireless Telemetry for Active Condition Monitoring of Advanced Gas Turbines

The objective of the program is to develop and engine test hardware and software technologies that will enable active condition monitoring to be implemented on hot gas path turbine blades in large industrial gas turbines. The specific objectives are (1) to fabricate and install Smart Turbine Blades with thermally sprayed sensors and high temperature wireless telemetry systems in a gas turbine engine, (2) to integrate the component engine test data with remaining useful life (RUL) models and develop an approach for networking the component RUL data with Siemens' Power Diagnostics® engine monitoring system. These significant advances carried out in Phase 1 in temperature wide bandgap telemetry, along with new induced power driver and receiver geometry combined with an innovative approach to transmit digital data wirelessly will enable the opportunity to proceed with more technical innovation. The Phase 2 program focused on validation testing of sensor-wireless telemetry package in spin rig and advanced operation-based assessment (OBA) model utilizing artificial intelligence. Significant efforts were dedicated on the download of the technology onto components to be tested an actual gas turbine engine for full realization of active condition monitoring for Smart Turbine Blades.

03 NATURAL GAS↗

Design and Operability of a Pressurized Oxy Combustion System

Fossil fuel powers more than two-thirds of the world’s electricity, a significant share of which is derived from coal power plants. Despite coal being an abundant and energy-rich fuel, the major halt to its progress is greenhouse gas emissions. Pressurized oxy-combustion cycles can achieve theoretically high thermal efficiencies along with a 90% carbon capture rate. Additionally, the high energy density allows smaller turbomachinery and save capital cost. Thus, the primary objective of this dissertation is to present the design and operability of a pressurized oxy-combustor system. The initial part of the dissertation investigates different thermodynamic cycles and presents a model that can be adapted for existing power plants. The thermodynamic model will be used in the later part to design the proposed combustor. The two cycles analyzed are ENEL and TIPS. This study focuses on qualitative analyses of the cycles using a commercially available software called Aspen Plus®. A detailed benchmark study has been performed to validate the modeling process. ENEL and TIPS cycles are designed in the software, adopting the same principles. Recirculation ratio and pressures are varied to find the efficiency range of the cycles. Power calculations are done to find overall and net efficiency for a fixed recirculation ratio. The efficiencies of the cycles are compared to select an optimum cycle. A recirculation ratio of 50% is selected for implementation. The comparison shows that ENEL is marginally efficient over TIPS, at the cost of a pressure difference of about 70bars. Technology Readiness Level analysis is performed to present the availability of the specialized equipment for the cycles. From the TRL analysis, it is seen that the cost and availability of high viii pressure equipment surmount the edge of TIPS over ENEL. Thus, ENEL is chosen as the better cycle for investigating a scaled experiment considering efficiency and viability. The later part of the dissertation focuses on developing the combustor's design for a pressurized oxy-combustion cycle. The proposed combustor is a powerhead-mounted design aimed to produce 1MW of thermal outputThe different aspects of the design of a down-fired pressurized swirl combustor are presented in this dissertation.

Chowdhury, Mehrin↗

Multispectral and thermal surface imagery and surface elevation mosaics - SGP July 2022

This data set contains high-resolution image products (orthomosaics) acquired from midsized uncrewed aerial systems that have been processed for value-added quality. The instrument itself, a multispectral imager, the Altum by Micasense, captures six spectral bands (red, green blue, NIR, red edge, and LWIR/thermal1) as radiance, which is converted to reflectance via custom code. The code used to develop these images first uses tools from the Micasense Python library2 to apply dark level corrections, row gradient corrections, and radiometric corrections. Next, it uses the processing API from Agisoft Metashape software to align and mosaic the processed imagery, following the processes developed by the USGS' structure from motion workflow documentation.3 Captures at different altitudes (recorded in MSL) produce an orthomosaic, a tif image containing information related to the six spectral bands, and a digital elevation model (DEM), a tif image containing information related to the elevation of the surveyed terraine. Metadata included in every image can be used to extract lat, lon, and reflectance values. 1 https://www.arm.gov/publications/tech_reports/handbooks/doe-sc-arm-tr-281.pdf 2 https://micasense.github.io/imageprocessing/MicaSense%20Image%20Processing%20Setup.html 3 https://pubs.usgs.gov/of/2021/1039/ofr20211039.pdf

54 ENVIRONMENTAL SCIENCES↗

Solar Field Layout and Aimpoint Strategy Optimization

The existing methods that determine heliostat aiming strategies for concentrating solar power (CSP) central receiver plants typically use heuristics and/or are computationally expensive, and they lack flexibility for different desired flux profiles and receiver geometries. Because of the interaction between layout and aimpoint strategy, considering the former without accounting for the latter may yield solutions with superfluous heliostats that cannot be used efficiently without compromising receiver flux constraints. To that end, we develop a software decision tool that uses innovative optimization methods to both optimize aimpoint strategies and improve candidate layouts for the solar collection field of a CSP central receiver plant. A CSP plant’s effectiveness relies on the optical efficiency of the solar field, which may be limited by losses due to (i) the cosine effect, (ii) atmospheric attenuation, (iii) interference (i.e., shading and blocking) between heliostats, (iv) spillage as a result of heliostat positioning and geometry, and (iv) some heliostats’ inability to direct irradiance to the receiver without damage due to excessive thermal flux. The goal of this work is to obtain optimized aiming strategies and improved solar field layouts that reduce capital cost and increase field optical efficiency and utilization, while meeting the power requirements of a given CSP receiver design. We formulate the aimpoint optimization problem as a mixed-integer linear programming model, which we then decompose into submodels that we solve in parallel. The decomposition subdivides the solar field into sections, and aimpoint strategies for each section are obtained independently of the others. To improve existing layouts, we develop a utilization-weighted efficiency metric that we use to relocate heliostats to sections of the solar field with similar efficiency and higher utilization. Finally, to connect our software to high-fidelity flux models, we develop a Python application programming interface for SolarPILOT, a mature software package that characterizes solar field performance and generates the heliostat layouts and flux maps that serve as input to our models.

14 SOLAR ENERGY↗

Degradation of Insulating Glass Units: Thermal Performance, Measurements and Energy Impacts

Insulating glass unit (IGU) degradation has been studied extensively. However, there is limited understanding of how present durability evaluation standards relate to product lifetime. Furthermore, there is debate on how to quantify performance of installed windows over time to better understand degradation processes. More knowledge on these topics is required to link durability evaluation to product lifetime projections based on energy performance. Energy models provide helpful estimations of total annual building energy consumption. However, most models are based on “as installed” performance of envelope components and fail to account for performance degradation. This can lead to an underestimation of building lifetime energy consumption. A better understanding of the relationship between durability and energy performance can inform integration of degradation dynamics into energy modeling software. This will improve lifetime building energy consumption estimations as well as inform appropriate retrofit strategies and timing. This paper reviews current durability literature, various standards for window performance ratings and weathering methods, existing in situ IGU energy performance measurement techniques, and whole-building energy effects. The challenges and disparities among various studies are analyzed and discussed. The authors hope that further work in this area will lead to the development of improved in situ test methods to assess IGU degradation in the field and link this knowledge to improved energy performance modeling approaches.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

COWALKER:EFFECTIVE TRANSPORT PROPERTIES OF COMPOSITE MATERIALS

SF-23-026 This software computes effective transport properties of composite materials involving fibers and nanoparticles using a random-walk algorithm that efficiently scales to an arbitrary number of processes and cores. Effective transport properties (thermal, electrical) are key to bridge the microstructure of complex materials with its macroscopic behavior. Traditional approaches either use effective medium approximations (closed mathematical expressions that are approximation for certain conditions) or continuum simulation models such as finite element or finite volume, which require the generation of a mesh for each configuration explored. cowalker leverages the equivalence between laplacian or heat equation-based models and random walks to compute the asymptotic transport properties from an ensemble of first sojourn times of a random walker moving through the composite material. This allows us to directly define a composite material as a collection of particles and use algorithms developed for molecular dynamics to quickly compute the intersection of the walker with the different interfaces in the material. cowalker is developed in C++, and it relies on the GNU Scientific Library for random generation. cowalker is currently delivered as source code, so the GSL library is not included in cowalker's distribution. A more userfriendly version, cowalker.jl is currently in development and will be released as part of cowalker.

YANGUAS-GIL, ANGEL↗

Phase-curve Pollution of Exoplanet Transmission Spectra

The occurrence of a planet transiting in front of its host star offers the opportunity to observe the planet’s atmosphere filtering starlight. The fraction of occulted stellar flux is roughly proportional to the optically thick area of the planet, the extent of which depends on the opacity of the planet’s gaseous envelope at the observed wavelengths. Chemical species, haze, and clouds are now routinely detected in exoplanet atmospheres through rather small features in transmission spectra, i.e., collections of planet-to-star area ratios across multiple spectral bins and/or photometric bands. Technological advances have led to a shrinking of the error bars down to a few tens of parts per million (ppm) per spectral point for the brightest targets. The upcoming James Webb Space Telescope (JWST) is anticipated to deliver transmission spectra with precision down to 10 ppm. The increasing precision of measurements requires a reassessment of the approximations hitherto adopted in astrophysical models, including transit light-curve models. Recently, it has been shown that neglecting the planet’s thermal emission can introduce significant biases in the transit depth measured with the JWST/Mid-InfraRed Instrument, integrated between 5 and 12 μm. In this paper, we take a step forward by analyzing the effects of the approximation on transmission spectra over the 0.6–12 μm wavelength range covered by various JWST instruments. We present open-source software to predict the spectral bias, showing that, if not corrected, it may affect the inferred molecular abundances and thermal structure of some exoplanet atmospheres.

47 OTHER INSTRUMENTATION↗

Computational Modeling of Graphite Degradation due to Molten Salt Infiltration and Wear

Molten-salt reactors (MSRs) represent a promising next-generation reactor design, with graphite serving as a moderator and/or reflector in several designs. However, due to limited experimental data and operational experience, a technical understanding of the structural integrity of graphite in molten salt environments remains incomplete. This report presents a modeling-based evaluation of graphite degradation in MSR environments, focusing on the effects of salt infiltration in fuel salt-based designs and surface wear in pebble bed reactor designs. The objective of this study is to enhance understanding of the structural integrity challenges posed by these degradation mechanisms and to provide a framework for assessing graphite behavior in MSRs. The first part of the report investigates the phenomenon of molten salt infiltration into graphite. This infiltration occurs when molten salt permeates the interconnected pore structure of the graphite moderator, driven by factors such as pressure differentials and the physical properties of both the salt and graphite. The infiltration process is influenced by characteristics of the pore structure, viscosity of the molten salt, and the interfacial energies between the graphite, salt, and the atmosphere within the graphite pore. Utilizing a coupled multiphysics modeling approach with Grizzly software, the study evaluates the stress induced by internal heat sources due to infiltration, which can lead to structural concerns. This evaluation is crucial for understanding how infiltration affects the mechanical integrity of graphite components in MSRs. The study considers the Molten-Salt Reactor Experiment (MSRE) graphite stringer geometry due to the availability of relevant data. Through detailed finite element analysis, the study examines stress distributions at varying infiltration percentages, revealing that stress levels increase with higher amounts of infiltration. Rare-event simulations, using the parallel subset simulation (PSS) framework, further quantify the failure probabilities under input uncertainties, with a user-specified failure metric. The PSS framework also identifies critical input parameters that significantly affect the stress values, including infiltration amount, thermal conductivity, and power density. Additionally, considering realistic reactor scenarios, the analysis was performed to account for the combined effects of radiation and infiltration, and modeling strategies on how to analyze new reactor designs or new graphite grades are discussed. The second part of the report focuses on wear mechanisms in pebble bed-based MSRs. As graphite fuel pebbles interact with the graphite reflector block, wear can result in material loss and the formation of surface defects, which may act as stress concentrators. A similar multiphysics modeling framework is employed to assess the impact of wear on the structural integrity of graphite components. This study considers a generic fluoride-cooled high-temperature reactor (gFHR) design due to the availability of comprehensive data. Worst-case scenario dimensions of the reflector blocks were analyzed under thermal and radiation conditions. Subsequently, wear in the form of idealized pits and grooves is modeled on the inner surface of the graphite block, with the maximum stress from previous simulations. The simulations show that groove-type defects are more detrimental than pits, leading to higher stress concentrations. Considering worst-case simulation scenarios and experimental wear rates, it was determined that the formation of a surface defect critical enough to affect the stress may not be possible in a gFHR design. Overall, the findings of this research contribute to the development of robust modeling tools for predicting graphite behavior under various operational conditions in MSRs.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Sample problems for Section III, Division 5 design by inelastic analysis of Grade 91 components

This report works through two sample design analyses of representative Grade 91 components using the ASME Boiler & Pressure Vessel Code Section III, Division 5, Appendix HBB-T rules for the strain and deformation and creep-fatigue design criteria using a design by inelastic analysis approach. The component geometries and loadings were selected to span a wide variety of potential applications. The sample components are an endplate geometry, which is fairly representative of typical pressure vessel construction, and a core block, representing a critical component in a heat pipe microreactor, which has a complicated geometry and complex thermal stress history. These sample problems serve several functions. First, they are complete worked examples of how to apply the current design by inelastic analysis rules. Second, they serve as test cases to evaluate the current rules and provide feedback on how they could be optimized to deal with complicated component geometries or to be better automated in modern finite element analysis software. Finally, the analysis here uses an inelastic constitutive model for Grade 91 developed by Argonne National Laboratory and proposed for inclusion in the ASME Boiler & Pressure Vessel Code Section III, Division 5 rules as a reference constitutive model. Using this constitutive model in the sample problem analyses tests the model in the context of the ASME Code rules. The final conclusions of this report are that the material model and the current Code rules are satisfactory, but that the Code rules could be optimized to simplify automation and reduce over conservatism. Future work should address the specific optimization topics discussed in this report.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Multispectral and Thermal Imager Onboard Aerial Platforms Instrument Handbook

The MicaSense Altum imager is an off-the-shelf, synchronized multispectral and thermal camera, combined with a Global Positioning System (GPS) unit and downwelling light sensor (DLS). The Altum takes images of the land surface within its field of view (FOV) across five visible bands and one longwave infrared thermal band. The sensor records the radiance and converts it to digital numbers. Imagery is radiometrically corrected, taking into account the sensor calibration, lens distortions, vignette effects, sun angle, and atmospheric effects (scattering and absorption). The photogrammetry software Agisoft PhotoScan v 1.4 is used to align and stitch the images into a larger composite image using the technique of structure from motion image capture to construct a dense cloud and 3D model of the surface, which is used to produce a digital elevation model of the terrain surveyed and orthomosaic imagery. Land surface leaf area index, albedo, and surface skin temperature are provided for the user. The user can perform raster calculations on the imagery to produce various other vegetative indices, which are used to indicate plant health and land surface characteristics, including Normalized Difference Vegetation Index (NDVI), Green Normalized Difference Vegetation Index (GNDVI), Normalized Difference Water Index (NDWI), surface temperature, and Enhanced_vegetation_index (EVI). This code is provided with the readme file for each data set. The images have a resolution of 20-60 cm/pixel, which are subsampled to 100 cm/pixel.

47 OTHER INSTRUMENTATION↗

First-principles study on structural mechanical and thermodynamic properties of HfMoTaTiZr

This study calculates the phase diagram of HfMoTaTiZr using the TCHEA1 database in Thermo-Calc software. Furthermore, it also investigates the structural and mechanical properties of HfMoTaTiZr by applying first-principles calculations. The elastic and other mechanical properties such as Young’s modulus, pugh ratio, hardness, bulk modulus was derived and discussed. These parameters were found to be in good harmony with previously available experimental reports. Vickers hardness of HfMoTaTiZr predicted from the Tians model agrees with the available experimental result. This study also investigates the thermal coefficient of linear expansion and vibrational heat capacity of the HfMoTaTiZr using the Debye–Grüneisen theory.

36 MATERIALS SCIENCE↗

Full-Loop Simulation of the Combustion of Biomass in a Circulating Fluidized Bed Combustor

Interest in circulating fluidized bed (CFB) boilers as a power generation technology has skyrocketed in recent years because of several advantages this technology offers over conventional boilers, such as increased gas-solid mixing, which results in higher combustion efficiency, and the ability to use lower rank fuels. CFB combustors are operated at lower temperatures than conventional thermal power generation combustors, thus reducing NO x emissions, while SO 2 emissions can be conveniently controlled through the addition of Ca-based sulfur sorbents within the combustor. This report summarizes the development of a comprehensive computational fluid dynamics (CFD) model for biomass combustion in a 50 kW th CFB combustor employing the multiphase particle-in-cell (PIC) approach in the open-source Multiphase Flow with Interphase eXchanges (MFiX) Software Suite at the U.S. Department of Energy (DOE) National Energy Technology Laboratory (NETL). The experimental combustor was designed, built, and operated at CanmetENERGY, Natural Resources Canada in Ottawa, Canada. This work is the culmination of a multi-year collaboration between NETL and CanmetENERGY. The hydrodynamics in the full loop are validated against cold-flow experiments conducted at CanmetENERGY. To mimic the dense packing in the standpipe in the absence of a collisional model in the MFiX-PIC approach, the ram valve in the return leg is partially closed to obstruct the flow. A combustion reaction scheme was developed that considers the volatiles released by the fuel as a lumped species that fully converts to CO 2 and H 2 O. The so-called enhanced simplified combustion scheme produces an excellent match with experimental data in terms of the species concentrations of CO 2 and O 2 at the outlet and the freeboard, demonstrating the utility of the comprehensive model for a range of flow conditions and operating temperatures. Furthermore, the model can be readily adapted to simulate combustion of a variety of biomass fuels as well as co-fired systems under air and oxy-fuel conditions.

09 BIOMASS FUELS↗

Preliminary Radioisotope Screening for Off-site Consequence Assessment of Advanced Non-LWR Systems

Currently a set of 71 radionuclides are accounted for in off-site consequence analysis for LWRs. Radionuclides of dose consequence are expected to change for non-LWRs, with radionuclides of interest being type-specific. This document identifies an expanded set of radionuclides that may need to be accounted for in multiple non-LWR systems: high temperature gas reactors (HTGRs); fluoride-salt-cooled high-temperature reactors (FHRs); thermal-spectrum fluoride-based molten salt reactors (MSRs); fast-spectrum chloride-based MSRs; and, liquid metal fast reactors with metallic fuel (LMRs) Specific considerations are provided for each reactor type in Chapter 2 through Chapter 5, and a summary of all recommendations is provided in Chapter 6. All identified radionuclides are already incorporated within the MACCS software, yet the development of tritium-specific and carbon-specific chemistry models are recommended.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

New Developments and Verification of the Fusion Blanket Simulation Capabilities in the MOOSE Framework

This poster contains new developments and updates in the Multiphysics Object-Oriented Simulation Environment (MOOSE) framework related to fusion modeling and simulation, and forms the basis for an on-going effort in modeling whole fusion devices at Idaho National Laboratory using MOOSE. In this work, a slice of the midplane of a proposed ceramic breeder blanket design for the Fusion Nuclear Science Facility is simulated using a combination of neutronics, 1D system level thermal hydraulics for helium, 3D heat conduction, and tritium transport. Previous work focused on the engineering scale full assembly of a blanket sector, but the simulations here form the basis for software quality and verification efforts to increase confidence as the large scale simulations continue. This poster was presented at the Idaho National Laboratory Intern Poster Session 2023.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Optimal Sizing and Dispatch of Solar Power with Storage

Designers of utility-scale solar plants with storage, seeking to maximize some aspect of plant performance, face multiple challenges. In many geographic locations, there is significant penetration of photovoltaic generation, which depresses energy prices during the hours of solar availability. An energy storage system affords the opportunity to dispatch during higher-priced time periods, but complicates plant design and dispatch decisions. Solar resource variability compounds these challenges, because determining optimal system sizes requires simultaneously considering how the plant will be operated under the imposed market and weather conditions. We develop an approach to analyze the economic performance of hybrid and single-technology solar power plants, which incorporates optimal dispatch, and considers the expected electricity market and weather conditions. We utilize the System Advisor Model software package to simulate the operation of multiple renewable generation and energy storage technologies, in conjunction with hourly-fidelity generation decisions determined by a revenue-maximizing, mixed-integer linear program. We show that, under our assumed market and weather conditions, the lifetime benefit-to-cost ratio can be improved by 6 to 19 percent, relative to a baseline design without optimizing, and that a concentrating solar power with thermal energy storage design produces significantly more energy per year, but is less profitable under our cost assumptions.

black-box optimization↗

Modeling the Nonlinear Rheology of Polymer Additive Manufacturing

This report summarizes molecular and continuum simulation studies focused on developing physics - based predictive models for the evolution of polymer molecular order during the nonlinear processing flows of additive manufacturing. Our molecular simulations of polymer elongation flows identified novel mechanisms of fluid dissipation for various polymer architectures that might be harnessed to enhance material processability. In order to predict the complex thermal and flow history of polymer realistic additive manufacturing processes, we have developed and deployed a high - performance mesh - free hydrodynamics module in Sandia's LAMMPS software. This module called RHEO – short for Reproducing Hydrodynamics and Elastic Objects – hybridizes an updated - Lagrange reproducing - kernel method for complex fluids with a bonded particle method (BPM) to capture solidification and solid objects in multiphase flows. In combination, our two methods allow rapid, multiscale characterization of the hydrodynamics and molecular evolution of polymers in realistic processing geometries.

36 MATERIALS SCIENCE↗