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NASA NTRS1989

NNEPEQ - Chemical equilibrium version of the Navy/NASA Engine Program

The Navy NASA Engine Program, NNEP, currently is in use at a large number of government agencies, commercial companies and universities. This computer code has been used extensively to calculate the design and off-design (matched) performance of a broad range of turbine engines, ranging from subsonic turboprops to variable cycle engines for supersonic transports. Recently, there has been increased interest in applications for which NNEP was not capable of simulating, namely, high Mach applications, alternate fuels including cryogenics, and cycles such as the gas generator air-turbo-rocker (ATR). In addition, there is interest in cycles employing ejectors such as for military fighters. New engine component models had to be created for incorporation into NNEP, and it was found necessary to include chemical dissociation effects of high temperature gases. The incorporation of these extended capabilities into NNEP is discussed and some of the effects of these changes are illustrated.

Fishbach, L. H.↗

NASA NTRS1972

Exploratory study of the effects of injection configurations and inlet flow conditions on the characteristics of flow in spherical chambers

Flow visualization studies were conducted to evaluate techniques for injecting simulated-fuel and simulated-propellant gases into a spherical cavity for application to open-cycle gaseous-core nuclear rockets. Preliminary studies were conducted with six simulated-fuel injectors and eight simulated-propellant injection configurations. Additional tests were conducted with the best configuration to determine the effect of weight-flow ratio, gas density ratio, injector location, and flow distribution on the simulated-fuel containment characteristics.

Johnson, B. V.↗

DOE OSTI2015

Reaction-space analysis of homogeneous charge compression ignition combustion with varying levels of fuel stratification under positive and negative valve overlap conditions

Full-cycle computational fluid dynamics simulations with gasoline chemical kinetics were performed to determine the impact of breathing and fuel injection strategies on thermal and compositional stratification, combustion and emissions during homogeneous charge compression ignition combustion. The simulations examined positive valve overlap and negative valve overlap strategies, along with fueling by port fuel injection and direct injection. The resulting charge mass distributions were analyzed prior to ignition using ignition delay as a reactivity metric. The reactivity stratification arising from differences in the distributions of fuel–oxygen equivalence ratio (Φ FO ), oxygen molar fraction (χ O2 ) and temperature (T) was determined for three parametric studies. In the first study, the reactivity stratification and burn duration for positive valve overlap valve events with port fuel injection and early direct injection were nearly identical and were dominated by wall-driven thermal stratification. nitrogen oxide (NO) and carbon monoxide (CO) emissions were negligible for both injection strategies. In the second study, which examined negative valve overlap valve events with direct injection and port fuel injection, reactivity stratification increased for direct injection as the Φ FO and T distributions associated with direct fuel injection into the hot residual gas were positively correlated; however, the latent heat absorbed from the hot residual gas by the evaporating direct injection fuel jet reduced the overall thermal and reactivity stratification. These stratification effects were offsetting, resulting in similar reactivity stratification and burn durations for the two injection strategies. The higher local burned gas temperatures with direct injection resulted in an order of magnitude increase in NO, while incomplete combustion of locally over-lean regions led to a sevenfold increase in CO emissions compared to port fuel injection. The final study evaluated positive valve overlap and negative valve overlap valve events with direct injection. Furthermore, relative to positive valve overlap, the negative valve overlap condition had a wider reactivity stratification, a longer burn duration and higher NO and CO emissions associated with reduced fuel–air mixing.

33 ADVANCED PROPULSION SYSTEMS↗

DOE OSTI2015

Suitability of Synthetic Driving Profiles from Traffic Micro-Simulation for Real-World Energy Analysis: Preprint

A shift towards increased levels of driving automation is generally expected to result in improved safety and traffic congestion outcomes. However, little empirical data exists to estimate the impact that automated driving could have on energy consumption and greenhouse gas emissions. In the absence of empirical data on differences between drive cycles from present day vehicles (primarily operated by humans) and future vehicles (partially or fully operated by computers) one approach is to model both situations over identical traffic conditions. Such an exercise requires traffic micro-simulation to not only accurately model vehicle operation under high levels of automation, but also (and potentially more challenging) vehicle operation under present day human drivers. This work seeks to quantify the ability of a commercial traffic micro-simulation program to accurately model real-world drive cycles in vehicles operated primarily by humans in terms of driving speed, acceleration, and simulated fuel economy. Synthetic profiles from models of freeway and arterial facilities near Atlanta, Georgia, are compared to empirical data collected from real-world drivers on the same facilities. Empirical and synthetic drive cycles are then simulated in a powertrain efficiency model to enable comparison on the basis of fuel economy. Synthetic profiles from traffic micro-simulation were found to exhibit low levels of transient behavior relative to the empirical data. Even with these differences, the synthetic and empirical data in this study agree well in terms of driving speed and simulated fuel economy. The differences in transient behavior between simulated and empirical data suggest that larger stochastic contributions in traffic micro-simulation (relative to those present in the traffic micro-simulation tool used in this study) are required to fully capture the arbitrary elements of human driving. Interestingly, the lack of stochastic contributions from models of human drivers in this study did not result in a significant discrepancy between fuel economy simulations based on synthetic and empirical data; a finding with implications on the potential energy efficiency gains of automated vehicle technology.

33 ADVANCED PROPULSION SYSTEMS↗

DOE OSTI2014

Computational Design of Advanced Nuclear Fuels

The objective of the project was to develop a method for theoretical understanding of nuclear fuel materials whose physical and thermophysical properties can be predicted from first principles using a novel dynamical mean field method for electronic structure calculations. We concentrated our study on uranium, plutonium, their oxides, nitrides, carbides, as well as some rare earth materials whose 4f eletrons provide a simplified framework for understanding complex behavior of the f electrons. We addressed the issues connected to the electronic structure, lattice instabilities, phonon and magnon dynamics as well as thermal conductivity. This allowed us to evaluate characteristics of advanced nuclear fuel systems using computer based simulations and avoid costly experiments.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2014

Advanced Fuels Campaign FY 2014 Accomplishments Report

The mission of the Advanced Fuels Campaign (AFC) is to perform Research, Development, and Demonstration (RD&D) activities for advanced fuel forms (including cladding) to enhance the performance and safety of the nation’s current and future reactors; enhance proliferation resistance of nuclear fuel; effectively utilize nuclear energy resources; and address the longer-term waste management challenges. This includes development of a state-of-the art Research and Development (R&D) infrastructure to support the use of a “goal-oriented science-based approach.” In support of the Fuel Cycle Research and Development (FCRD) program, AFC is responsible for developing advanced fuels technologies to support the various fuel cycle options defined in the Department of Energy (DOE) Nuclear Energy Research and Development Roadmap, Report to Congress, April 2010. AFC uses a “goal-oriented, science-based approach” aimed at a fundamental understanding of fuel and cladding fabrication methods and performance under irradiation, enabling the pursuit of multiple fuel forms for future fuel cycle options. This approach includes fundamental experiments, theory, and advanced modeling and simulation. The modeling and simulation activities for fuel performance are carried out under the Nuclear Energy Advanced Modeling and Simulation (NEAMS) program, which is closely coordinated with AFC. In this report, the word “fuel” is used generically to include fuels, targets, and their associated cladding materials. R&D of light water reactor (LWR) fuels with enhanced accident tolerance is also conducted by AFC. These fuel systems are designed to achieve significantly higher fuel and plant performance to allow operation to significantly higher burnup, and to provide enhanced safety during design basis and beyond design basis accident conditions. The overarching goal is to develop advanced nuclear fuels and materials that are robust, have high performance capability, and are more tolerant to accident conditions than traditional fuel systems. AFC management and integration activities included continued support for international collaborations, primarily with France, Japan, the European Union, Republic of Korea, and China, as well as various working group and expert group activities in the Organization for Economic Cooperation and Development Nuclear Energy Agency (OECD-NEA) and the International Atomic Energy Agency (IAEA). Three industry-led Funding Opportunity Announcements (FOAs) and two university-led Integrated Research Projects (IRPs), funded in 2013, made significant progress in fuels and materials development. All are closely integrated with AFC and Accident Tolerant Fuels (ATF) research. Accomplishments made during fiscal year (FY) 2014 are highlighted in this report, which focuses on completed work and results. The process details leading up to the results are not included; however, the lead technical contact is provided for each section.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2023

Comparison Between Pin-by-Pin Subchannel and System Level Thermal Hydraulic Results for High Burnup Loss-of-Coolant Applications

This milestone report summarizes recent work to investigate higher fidelity modeling and simulation practices for large-break loss-of-coolant accident (LBLOCA) analysis in high-burnup pressurized water reactor (PWR) cores. Because of current industry interest in extending fuel cycle lengths ranging from 18 to 24-months, the Nuclear Energy Advanced Modeling and Simulation (NEAMS) program has been investigating the susceptibility of high-burnup core designs to fuel fragmentation, release, and dispersal (FFRD) during accident conditions such as LBLOCA. This work has prioritized developing and demonstrating a methodology for calculating core-wide susceptibility to FFRD and addressing uncertainties identified in the analysis and the US Nuclear Regulatory Commission (NRC) Research Information Letter on FFRD. Part of this investigation seeks to quantify differences between system-level thermal hydraulic behavior and higher fidelity subchannel modeling methods to identify potential safety concerns or opportunities to minimize FFRD susceptibility. To this end, the NEAMS subchannel code, CTF, is being used, along with the NRC system analysis code TRACE, for analysis of LBLOCA in a core containing high-burnup fuel. This project includes two thrusts: (1) improving on the existing TRACE model for a 4-loop PWR for LBLOCA so that the model is higher fidelity and consistent with current USNRC best practices, and (2) using CTF to perform pin-resolved modeling of the core region of the reflood phase of a LBLOCA in a high-burnup PWR.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2013

PAREX, A numerical Code for process design and integration

The modeling approach for process design is illustrated in this paper by the work done to qualify the PAREX code to design the flow sheet of a uranium/plutonium splitting operation in a pulsed column. The different flow sheet experimentations are presented along with the simulation results. The qualified code has been successfully used to design the flow sheet of this operation in the first purification cycle of UP2-800 plant at La Hague. (authors)

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2015

THE MISSION AND ACCOMPLISHMENTS FROM DOE’S FUEL CYCLE RESEARCH AND DEVELOPMENT (FCRD) ADVANCED FUELS CAMPAIGN

AFC Mission↗

DOE OSTI2012

Lattice Boltzmann Methods to Address Fundamental Boiling and Two-Phase Problems

This report presents the progress made during the fourth (no cost extension) year of this three-year grant aimed at the development of a consistent Lattice Boltzmann formulation for boiling and two-phase flows. During the first year, a consistent LBM formulation for the simulation of a two-phase water-steam system was developed. Results of initial model validation in a range of thermo-dynamic conditions typical for Boiling Water Reactors (BWRs) were shown. Progress was made on several fronts during the second year. Most important of these included the simulation of the coalescence of two bubbles including the surface tension effects. Work during the third year focused on the development of a new lattice Boltzmann model, called the artificial interface lattice Boltzmann model (AILB model) for the 3 simulation of two-phase dynamics.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2020

$\mathrm{UPDATED}$ $\mathrm{U3SI2}$ thermal creep model and sensitivity analysis of the $\mathrm{U3SI2-SIC}$ accident tolerant $\mathrm{FUEL}$

U 3 Si 2 is a candidate accident tolerant fuel (ATF) replacement for UO 2 . U 3 Si 2 ’s high uranium density and high thermal conductivity are favorable properties in steady-state and accident conditions. Low power performance of this U3Si2-SiC concept fuel is compared to that of UO 2 -Zr4 fuels by implementing models that describe the properties of U 3 Si 2 and SiC-SiC into Idaho National Laboratory's (INL) fuel performance code, BISON. Included in these material models is a thermal creep model for U 3 Si 2 based on compressive creep data. The simulated results are in keeping with community knowledge that the U 3 Si 2 -SiC concept fuel may serve as a replacement for UO 2 -Zr4 fuels during steady-state operation, provided the mSiC layer remains under compression. Through a moderate power history and three 24-month fuel cycles, the mSiC layer remains under compressive stress through a burnup of 80 MWd/kgU. During low power operation, failure of the mSiC layer generally occurs prior to significant thermal creep in U 3 Si 2 . Generally, U 3 Si 2 creep is temperature sensitive and of little importance at the temperatures and stresses simulated during steady operation and during fuel-to-cladding contact. A parameter variation study including 11,520 individual simulations with variations in nominal fuel thermal creep rate, cladding thermal conductivity, cladding irradiation creep and swelling, cladding gap size, and cladding thickness demonstrated that research priorities for this ATF should revolve around reducing cladding thickness as a means to minimize cladding failure. Generally, despite advances in SiC-SiC compliance, the brittle nature of mSiC excludes U 3 Si 2 -SiC for use where fuel cladding contact may occur.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2019

Experimental Study and Model Predictive Control of a Lean-Burn Gasoline Engine Coupled With a Passive Selective Catalytic Reduction System

Lean-burn gasoline engines have reflected 10–20% engine efficiency gain over stoichiometric engines and are widely considered as a promising technology for meeting the 54.5 miles-per-gallon (mpg) corporate average fuel economy standard by 2025. Nonetheless, nitrogen oxides (NO x ) emissions control for lean-burn gasoline for meeting the stringent Environmental Protection Agency tier 3 emission standards has been one of the main challenges toward the commercialization of highly efficient lean-burn gasoline engines in the United States. Passive selective catalytic reduction (SCR) systems, which consist of a three-way catalyst (TWC) and SCR, have demonstrated great potentials of effectively reducing NO x emissions for lean gasoline engines at low cost. Yet, passive SCR operation may cause significant fuel penalty since rich engine combustion is required for ammonia generation. The purpose of this study is to develop a model-predictive control (MPC) scheme for a lean-burn gasoline engine coupled with a passive SCR system to minimize the total equivalent fuel penalty associated with passive SCR operation while satisfying stringent NO x and ammonia (NH 3 ) emissions requirements. Simulation results demonstrate that the MPC approach can reduce the fuel penalty by 43.9% in a simulated US06 cycle and 28.0% in a simulated urban dynamometer driving schedule (UDDS) cycle, respectively, compared to the baseline control, while achieving over 97% DeNO x efficiency and less than 15 ppm tailpipe ammonia slip. The proposed MPC controller can potentially enable highly efficient lean-burn gasoline engines while meeting the stringent Environmental Protection Agency tier 3 emission standards.

33 ADVANCED PROPULSION SYSTEMS↗

DOE OSTI2020

Requirements Description of the REBUS Software for the Versatile Test Reactor

This report presents the modeling and simulation capabilities of Argonne National Laboratory’s fuel cycle analysis code, the REactor BUrnup System (REBUS), that will be relied on for the VTR project. These capabilities will then be used to establish the set of REBUS verification tasks necessary to verify REBUS for usage on the VTR project. A similar path was followed for the DIF3D software where its’ requirements and verification tasks were established. REBUS has been maintained by Argonne since the early 1960s to support its reactor design mission. That software transitioned from the original REBUS to REBUS-2 in the mid 1970s and to REBUS-3 in the mid 1980s. Since then REBUS has gone through many revisions to the current REBUS-11. Note that this version numbering is consistent with the progression of DIF3D, the base flux solver that REBUS is built upon. The name REBUS refers to a pictorial based puzzle as the original developers were inspired by having to track thousands of unique fuel assemblies as they are inserted into the reactor, depleted, shuffled, discharged, and reprocessed.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

NASA NTRS2003

Probabilistic Analysis of Solid Oxide Fuel Cell Based Hybrid Gas Turbine System

The emergence of fuel cell systems and hybrid fuel cell systems requires the evolution of analysis strategies for evaluating thermodynamic performance. A gas turbine thermodynamic cycle integrated with a fuel cell was computationally simulated and probabilistically evaluated in view of the several uncertainties in the thermodynamic performance parameters. Cumulative distribution functions and sensitivity factors were computed for the overall thermal efficiency and net specific power output due to the uncertainties in the thermodynamic random variables. These results can be used to quickly identify the most critical design variables in order to optimize the design and make it cost effective. The analysis leads to the selection of criteria for gas turbine performance.

Gorla, Rama S. R.↗

DOE OSTI2017

Model predictive control of a lean-burn gasoline engine coupled with a passive selective catalytic reduction system

Lean-burn gasoline engines have demonstrated 10–20% engine efficiency gain over stoichiometric engines and are widely considered as a promising technology for meeting the 54.5 miles-per-gallon (mpg) Corporate Average Fuel Economy standard by 2025. Nevertheless, NOx emissions control for lean-burn gasoline for meeting the stringent EPA Tier 3 emission standards has been one of the main challenges towards the commercialization of highly-efficient lean-burn gasoline engines in the United States. Passive selective catalytic reduction (SCR) systems, which consist of a three-way catalyst and SCR, have demonstrated great potentials of effectively reducing NOx emissions for lean gasoline engines but may cause significant fuel penalty due to ammonia generation via rich engine combustion. The purpose of this study is to develop a model-predictive control (MPC) scheme for a lean-burn gasoline engine coupled with a passive SCR system to minimize the fuel penalty associated with passive SCR operation while satisfying stringent NOx and NH3 emissions requirements. Simulation results demonstrate that the MPC-based control can reduce the fuel penalty by 47.7% in a simulated US06 cycle and 32.0% in a simulated UDDS cycle, compared to the baseline control, while achieving over 96% deNOx efficiency and less than 15 ppm tailpipe ammonia slip. The proposed MPC control can potentially enable high engine efficiency gain for highly-efficient lean-burn gasoline engine while meeting the stringent EPA Tier 3 emission standards.

Chen, Pingen↗

DOE OSTI2016

Modeling and Depletion Simulations for a High Flux Isotope Reactor Cycle with a Representative Experiment Loading

The purpose of this report is to document a high-fidelity VESTA/MCNP High Flux Isotope Reactor (HFIR) core model that features a new, representative experiment loading. This model, which represents the current, high-enriched uranium fuel core, will serve as a reference for low-enriched uranium conversion studies, safety-basis calculations, and other research activities. A new experiment loading model was developed to better represent current, typical experiment loadings, in comparison to the experiment loading included in the model for Cycle 400 (operated in 2004). The new experiment loading model for the flux trap target region includes full length 252 Cf production targets, 75 Se production capsules, 63 Ni production capsules, a 188 W production capsule, and various materials irradiation targets. Fully loaded 238 Pu production targets are modeled in eleven vertical experiment facilities located in the beryllium reflector. Other changes compared to the Cycle 400 model are the high-fidelity modeling of the fuel element side plates and the material composition of the control elements. Results obtained from the depletion simulations with the new model are presented, with a focus on time-dependent isotopic composition of irradiated fuel and single cycle isotope production metrics.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2012

Transuranic Waste Burning Potential of Thorium Fuel in a Fast Reactor - 12423

Westinghouse Electric Company (referred to as 'Westinghouse' in the rest of this paper) is proposing a 'back-to-front' approach to overcome the stalemate on nuclear waste management in the US. In this approach, requirements to further the societal acceptance of nuclear waste are such that the ultimate health hazard resulting from the waste package is 'as low as reasonably achievable'. Societal acceptability of nuclear waste can be enhanced by reducing the long-term radiotoxicity of the waste, which is currently driven primarily by the protracted radiotoxicity of the transuranic (TRU) isotopes. Therefore, a transition to a more benign radioactive waste can be accomplished by a fuel cycle capable of consuming the stockpile of TRU 'legacy' waste contained in the LWR Used Nuclear Fuel (UNF) while generating waste which is significantly less radio-toxic than that produced by the current open U-based fuel cycle (once through and variations thereof). Investigation of a fast reactor (FR) operating on a thorium-based fuel cycle, as opposed to the traditional uranium-based is performed. Due to a combination between its neutronic properties and its low position in the actinide chain, thorium not only burns the legacy TRU waste, but it does so with a minimal production of 'new' TRUs. The effectiveness of a thorium-based fast reactor to burn legacy TRU and its flexibility to incorporate various fuels and recycle schemes according to the evolving needs of the transmutation scenario have been investigated. Specifically, the potential for a high TRU burning rate, high U-233 generation rate if so desired and low concurrent production of TRU have been used as metrics for the examined cycles. Core physics simulations of a fast reactor core running on thorium-based fuels and burning an external TRU feed supply have been carried out over multiple cycles of irradiation, separation and reprocessing. The TRU burning capability as well as the core isotopic content have been characterized. Results will be presented showing the potential for thorium to reach a high TRU transmutation rate over a wide variety of fuel types (oxide, metal, nitride and carbide) and transmutation schemes (recycle or partition of in-bred U-233). In addition, a sustainable scheme has been devised to burn the TRU accumulated in the core inventory once the legacy TRU supply has been exhausted, thereby achieving long-term virtually TRU-free. A comprehensive 'back-to-front' approach to the fuel cycle has recently been proposed by Westinghouse which emphasizes achieving 'acceptable', low-radiotoxicity, high-level waste, with the intent not only to satisfy all technical constraints but also to improve public acceptance of nuclear energy. Following this approach, the thorium fuel cycle, due to its low radiotoxicity and high potential for TRU transmutation has been selected as a promising solution. Additional studies not shown here have shown significant reduction of decay heat. The TRU burning potential of the Th-based fuel cycle has been illustrated with a variety of fuel types, using the Toshiba ARR to perform the analysis, including scenarios with continued LWR operation of either uranium fueled or thorium fueled LWRs. These scenarios will afford overall reduction in actinide radiotoxicity, however when the TRU supply is exhausted, a continued U- 235 LWR operation must be assumed to provide TRU makeup feed. This scenario will never reach the characteristically low TRU content of a closed thorium fuel cycle with its associated potential benefits on waste radiotoxicity, as exemplified by the transition scenario studied. At present, the cases studied indicate ThC as a potential fuel for maximizing TRU burning, while ThN with nitrogen enriched to 95% N-15 shows the highest breeding potential. As a result, a transition scenario with ThN was developed to show that a sustainable, closed Th-cycle can be achieved starting from burning the legacy TRU stock and completing the transmutation of the residual TRU remaining in the core inventory after the legacy TRU external supply has been exhausted. The radiotoxicity of the actinide waste during the various phases has been characterized, showing the beneficial effect of the decreasing content of TRU in the recycled fuel as the transition to a closed Th-based fuel cycle is undertaken. Due to the back-to-front nature of the proposed methodology, detailed designs are not the first step taken when assessing a fuel cycle scenario potential. As a result, design refinement is still required and should be expected in future studies. Moreover, significant safety assessment, including determination of associated reactivity coefficients, fuel and reprocessing feasibility studies and economic assessments will still be needed for a more comprehensive and meaningful comparison against other potential solutions. With the above considerations in mind, the potential advantages of thorium fuelled reactors on HLW management optimization lead us to believe that thorium fuelled reactor systems can play a significant role in the future and deserve further consideration. (authors)

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2015

Application of computational fluid dynamics for the simulation of cryogenic molecular sieve bed absorber of hydrogen isotopes recovery system for Indian LLCB-TBM

One of the most challenging tasks in the design of the fuel cycle system lies in the effective design of Tritium Extraction System (TES) which involves proper extraction and purification of tritium in the fuel cycle of the fusion reactor. Indian Lead Lithium cooled Ceramic Breeder Test Blanket Module (LLCB-TBM) would extract hydrogen isotopes through Cryogenic Molecular Sieve Bed (CMSB) adsorber system. A prototype Hydrogen Isotopes Recovery System (HIRS) is being developed to validate the concepts for tritium extraction by adsorption mass transfer mechanism. In this study, a design model has been developed and analyzed to simulate the adsorption mass transfer kinetics in a fixed bed adsorption column. The simulation leads primarily to effective design of HIRS, which is a state-of-the-art technology. The paper describes the process simulation approach and the results of Computational Fluid Dynamics (CFD) analysis. The effects of different operating conditions are studied to investigate their influence on the hydrogen isotopes adsorption capacity. The results of the present simulation study would be used to understand the best optimized transport phenomenon before realizing the TES as a system for LLCB-TBM. (authors)

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗