Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Accounting”

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 1,117 records · Page 62

Fatigue Behavior and Deformation Mechanisms in Inconel 718 Superalloy Investigated

The nickel-base superalloy Inconel 718 (IN 718) is used as a structural material for a variety of components in the space shuttle main engine (SSME) and accounts for more than half of the total weight of this engine. IN 718 is the bill-of-material for the pressure vessels of nickel-hydrogen batteries for the space station. In the case of the space shuttle main engine, structural components are typically subjected to startup and shutdown load transients and occasional overloads in addition to high-frequency vibratory loads from routine operation. The nickel-hydrogen battery cells are prooftested before service and are subjected to fluctuating pressure loads during operation. In both of these applications, the structural material is subjected to a monotonic load initially, which is subsequently followed by fatigue. To assess the life of these structural components, it is necessary to determine the influence of a prior monotonic load on the subsequent fatigue life of the superalloy. An insight into the underlying deformation and damage mechanisms is also required to properly account for the interaction between the prior monotonic load and the subsequent fatigue loading. An experimental investigation was conducted to establish the effect of prior monotonic straining on the subsequent fatigue behavior of wrought, double-aged, IN 718 at room temperature. First, monotonic strain tests and fully-reversed, strain-controlled fatigue tests were conducted on uniform-gage-section IN 718 specimens. Next, fully reversed fatigue tests were conducted under strain control on specimens that were monotonically strained in tension. Results from this investigation indicated that prior monotonic straining reduced the fatigue resistance of the superalloy particularly at the lowest strain range. Some of the tested specimens were sectioned and examined by transmission electron microscopy to reveal typical microstructures as well as the active deformation and damage mechanisms under each of the loading conditions. In monotonically strained specimens, deformation during the subsequent fatigue loading was mainly confined to the deformation bands initiated during the prior monotonic straining. This can cause dislocations to move more readily along the previously activated deformation bands and to pile up near grain boundaries, eventually making the grain boundaries susceptible to fatigue crack initiation. The mechanisms inferred from the microstructural investigation were extremely valuable in interpreting the influence of prior monotonic straining on the subsequent fatigue life of Inconel 718 superalloy.

Source record↗

Conceptual Design Method Developed for Advanced Propulsion Nozzles

As part of a contract with the NASA Lewis Research Center, a simple, accurate method of predicting the performance characteristics of a nozzle design has been developed for use in conceptual design studies. The Nozzle Performance Analysis Code (NPAC) can predict the on- and off-design performance of axisymmetric or two-dimensional convergent and convergent-divergent nozzle geometries. NPAC accounts for the effects of overexpansion or underexpansion, flow divergence, wall friction, heat transfer, and small mass addition or loss across surfaces when the nozzle gross thrust and gross thrust coefficient are being computed. NPAC can be used to predict the performance of a given nozzle design or to develop a preliminary nozzle system design for subsequent analysis. The input required by NPAC consists of a simple geometry definition of the nozzle surfaces, the location of key nozzle stations (entrance, throat, exit), and the nozzle entrance flow properties. NPAC performs three analysis "passes" on the nozzle geometry. First, an isentropic control volume analysis is performed to determine the gross thrust and gross thrust coefficient of the nozzle. During the second analysis pass, the skin friction and heat transfer losses are computed. The third analysis pass couples the effects of wall shear and heat transfer with the initial internal nozzle flow solutions to produce a system of equations that is solved at steps along the nozzle geometry. Small mass additions or losses, such as those resulting from leakage or bleed flow, can be included in the model at specified geometric sections. A final correction is made to account for divergence losses that are incurred if the nozzle exit flow is not purely axial.

Nadell, Shari-Beth↗

Using Microwave and Infrared Radiances from Off-Nadir Pixels: Application of Radiative Transfer to Slanted Line-of-Sight and Comparisons with NASA EOS Aqua Data

The passive infrared and microwave nadir sounders such as (A)TOVS observe the atmosphere from a polar orbit by directing their scan pointed at the ground up to about 49 degrees from nadir. Except for the pixels located right on the satellite ground track, the radiance measurements collected by these instruments characterize hence atmospheric emission paths which are slanted with respect to the zenithal direction at the ground. At the outer swath edges, the deviations from nadir reach about 60 degrees in terms of Satellite Zenith Angle (SZA). The radiative transfer codes used in operational Numerical Weather Prediction applications make the appropriate corrections to account for the extra path induced by the non-zero SZA. However, no corrections are made to account for the fact that the atmospheric profiles along the slanted line-of-sight (LOS) are different from the vertical because of horizontal gradients in the atmosphere. Using NASA EOS Aqua satellite's orbits, zenith and azimuth angles, as well as three-dimensional fields of temperature, water vapor, and ozone produced by the NASA Global Modeling and Assimilation Office, we extracted slanted atmospheric profiles for actual soundings performed by the AIRS and AMSU-A instruments onboard EOS Aqua. We will present the results of our study comparing the calculated brightness temperatures along slanted LOS and vertical LOS with AIRS and AMSU-A observations.

Poli, Paul↗

Ring Current Dynamic in the Presence of EMIC Waves

The effect of EMIC waves, generated by a positive ion temperature anisotropy on Earth s RC ions is one of the best known examples of wave-particle interaction in the magnetosphere and the most controversial mechanism of RC losses. Under certain conditions, relativistic electrons with energy 21 MeV can be removed from the outer RB by EMIC wave scattering during a magnetic storm much faster than by any other loss mechanisms. That is why the calculation of EMIC waves is a very critical part of the NASA LWS program. The new RC model that we have developed and present for the first time has several new features that we have combine together in a one single model: (a) several lower frequency cold plasma wave modes are taken into account; (b) wave tracing of these wave has been incorporated in the energy EMIC wave equation; (c) no assumptions regarding wave shape spectra have been made; (d) no assumptions regarding the shape of particle distribution have been made to calculate the growth rate; (e) pitch- angle, energy, and mix diffusions are taken into account together for the first time; (f) the exact loss-cone RC analytical solution has been found and coupled with bounce-averaged numerical solution of kinetic equation; (g) LHW are included as an additional factor that contributes to saturation process of EMIC waves; and (h) the hot ions were included in the real part of dielectric permittivity tensor. We compare our theoretical results with the different EMIC waves models as well as RC experimental data.

Khazanov, G. V.↗

A Three-fold Outlook of the Ultra-Efficient Engine Technology Program Office (UEET)

The Ultra-Efficient Engine Technology (UEET) Office at NASA Glenn Research Center is a part of the Aeronautics Directorate. Its vision is to develop and hand off revolutionary turbine engine propulsion technologies that will enable future generation vehicles over a wide range of flight speeds. There are seven different technology area projects of UEET. During my tenure at NASA Glenn Research Center, my assignment was to assist three different areas of UEET, simultaneously. I worked with Kathy Zona in Education Outreach, Lynn Boukalik in Knowledge Management, and Denise Busch with Financial Management. All of my tasks were related to the business side of UEET. As an intern with Education Outreach I created a word search to partner with an exhibit of a Turbine Engine developed out of the UEET office. This exhibit is a portable model that is presented to students of varying ages. The word search complies with National Standards for Education which are part of every science, engineering, and technology teachers curriculum. I also updated a Conference Planning/Workshop Excel Spreadsheet for the UEET Office. I collected and inputted facility overviews from various venues, both on and off site to determine where to hold upcoming conferences. I then documented which facilities were compliant with the Federal Emergency Management Agency's (FEMA) Hotel and Motel Fire Safety Act of 1990. The second area in which I worked was Knowledge Management. a large knowledge management system online which has extensive documentation that continually needs reviewing, updating, and archiving. Knowledge management is the ability to bring individual or team knowledge to an organizational level so that the information can be stored, shared, reviewed, archived. Livelink and a secure server are the Knowledge Management systems that UEET utilizes, Through these systems, I was able to obtain the documents needed for archiving. My assignment was to obtain intellectual property including reports, presentations, or any other documents related to the project. My next task was to document the author, date of creation, and all other properties of each document. To archive these documents I worked extensively with Microsoft Excel. different financial systems of accounting such as the SAP business accounting system. I also learned the best ways to present financial data and shadowed my mentor as she presented financial data to both UEET's project management and the Resources Analysis and Management Office (RAMO). I analyzed the June 2004 financial data of UEET and used Microsoft Excel to input the results of the data. This process made it easier to present the full cost of the project in the month of June. In addition I assisted in the End of the Year 2003 Reconciliation of Purchases of UEET.

Graham, La Quilia E.↗

Fast Rotating Scalar and Multi-component Bose Gases

We show that in the limit of large angular momentum, many equilibrium and dynamical phenomena of scalar and multi-component Bose gases can be accounted for by approximating the system to reside in an effective lowest Landau level. This method explains the origin of the mysterious stripe formation in fast rotating Bose gas recently observed at JILA, and accounts for all the dynamical details observed in this experiment. To further demonstrate the usefulness of this method, we present its predictions of the interference patterns of two vortex lattices, and rich vortex lattice structures in multi-component Bose gases.

Ho, TIn-Lun Jason↗

Design Tool Developed for Probabilistic Modeling of Ceramic Matrix Composite Strength

Ceramic matrix composites are being evaluated as candidate materials for many high temperature applications such as engine combustor liners for the High-Speed Civil Transport (HSCT). They are required to have an assured life of several thousand hours. Estimating the reliability of these components is quite a complex process and requires knowledge of the uncertainties that occur at various scales. The properties of ceramic matrix composites (CMC) are known to display a considerable amount of scatter due to variations in fiber/matrix properties, interphase/coating properties, bonding, amount of matrix voids, and many geometry- and fabrication-related parameters such as ply thickness and ply orientations. The objective of this research effort is to account for these uncertainties in a formal way by probabilistically analyzing both the stiffness- and strength related properties of CMC's. In current deterministic approaches, uncertainties are usually accounted for by safety factors. This approach often yields overly conservative designs, thereby reducing the potential of many advanced composite materials.

Murthy, Pappu L. N.↗

CARES/Life Ceramics Durability Evaluation Software Enhanced for Cyclic Fatigue

The CARES/Life computer program predicts the probability of a monolithic ceramic component's failure as a function of time in service. The program has many features and options for materials evaluation and component design. It couples commercial finite element programs--which resolve a component's temperature and stress distribution--to reliability evaluation and fracture mechanics routines for modeling strength-limiting defects. The capability, flexibility, and uniqueness of CARES/Life have attracted many users representing a broad range of interests and has resulted in numerous awards for technological achievements and technology transfer. Recent work with CARES/Life was directed at enhancing the program s capabilities with regards to cyclic fatigue. Only in the last few years have ceramics been recognized to be susceptible to enhanced degradation from cyclic loading. To account for cyclic loads, researchers at the NASA Lewis Research Center developed a crack growth model that combines the Power Law (time-dependent) and the Walker Law (cycle-dependent) crack growth models. This combined model has the characteristics of Power Law behavior (decreased damage) at high R ratios (minimum load/maximum load) and of Walker law behavior (increased damage) at low R ratios. In addition, a parameter estimation methodology for constant-amplitude, steady-state cyclic fatigue experiments was developed using nonlinear least squares and a modified Levenberg-Marquardt algorithm. This methodology is used to give best estimates of parameter values from cyclic fatigue specimen rupture data (usually tensile or flexure bar specimens) for a relatively small number of specimens. Methodology to account for runout data (unfailed specimens over the duration of the experiment) was also included.

Nemeth, Noel N.↗

Curved Thermopiezoelectric Shell Structures Modeled by Finite Element Analysis

"Smart" structures composed of piezoelectric materials may significantly improve the performance of aeropropulsion systems through a variety of vibration, noise, and shape-control applications. The development of analytical models for piezoelectric smart structures is an ongoing, in-house activity at the NASA Glenn Research Center at Lewis Field focused toward the experimental characterization of these materials. Research efforts have been directed toward developing analytical models that account for the coupled mechanical, electrical, and thermal response of piezoelectric composite materials. Current work revolves around implementing thermal effects into a curvilinear-shell finite element code. This enhances capabilities to analyze curved structures and to account for coupling effects arising from thermal effects and the curved geometry. The current analytical model implements a unique mixed multi-field laminate theory to improve computational efficiency without sacrificing accuracy. The mechanics can model both the sensory and active behavior of piezoelectric composite shell structures. Finite element equations are being implemented for an eight-node curvilinear shell element, and numerical studies are being conducted to demonstrate capabilities to model the response of curved piezoelectric composite structures (see the figure).

Lee, Ho-Jun↗

A new Mars radiation environment model with visualization

A new model for the radiation environment to be found on the planet Mars due to Galactic Cosmic Rays (OCR) has been developed at the NASA Langley Research Center. Solar modulated primary particles rescaled for Mars conditions are transported through the Martian atmosphere, with temporal properties modeled with variable timescales, down to the surface, with altitude and backscattering patterns taken into account. The Martian atmosphere has been modeled by using the Mars Global Reference Atmospheric Model--version 2001 (Mars-GRAM 2001). The altitude to compute the atmospheric thickness profile has been determined by using a model for the topography based on the data provided by the Mars Orbiter Laser Altimeter (MOLA) instrument on board the Mars Global Surveyor (MGS) spacecraft. The Mars surface composition has been modeled based on averages over the measurements obtained from orbiting spacecraft and at various landing sites, taking into account the possible volatile inventory (e.g., CO2 ice, H2O ice) along with its time variation throughout the Martian year. Particle transport has been performed with the HZETRN heavy ion code. The Mars Radiation Environment Model has been made available worldwide through the Space Ionizing Radiation Effects and Shielding Tools (SIREST) website, a project of NASA Langley Research Center. c2004 COSPAR. Published by Elsevier Ltd. All rights reserved.

NASA Center LaRC↗

Ring Current-Electromagnetic Ion Cyclotron Waves Coupling

The effect of Electromagnetic Ion Cyclotron (EMIC) waves, generated by ion temperature anisotropy in Earth s ring current (RC), is the best known example of wave- particle interaction in the magnetosphere. Also, there is much controversy over the importance of EMIC waves on RC depletion. Under certain conditions, relativistic electrons, with energies 21 MeV, can be removed from the outer radiation belt (RB) by EMIC wave scattering during a magnetic storm. That is why the calculation of EMIC waves must be a very critical part of the space weather studies. The new RC model that we have developed and present for the first time has several new features that we have combine together in a one single model: (a) several lower frequency cold plasma wave modes are taken into account; (b) wave tracing of these wave has been incorporated in the energy EMIC wave equation; (c) no assumptions regarding wave shape spectra have been made; (d) no assumptions regarding the shape of particle distribution have been made to calculate the growth rate; (e) pitch-angle, energy, and mix diffusions are taken into account together for the first time; (f) the exact loss-cone RC analytical solution has been found and coupled with bounce-averaged numerical solution of kinetic equation; (g) the EMIC waves saturation due to their modulation instability and LHW generation are included as an additional factor that contributes to this process; and (h) the hot ions were included in the real part of dielectric permittivity tensor. We compare our theoretical results with the different EMIC waves models as well as RC experimental data.

Khazanov, G. V.↗

Data-Mining Toolset Developed for Determining Turbine Engine Part Life Consumption

The current practice in aerospace turbine engine maintenance is to remove components defined as life-limited parts after a fixed time, on the basis of a predetermined number of flight cycles. Under this schedule-based maintenance practice, the worst-case usage scenario is used to determine the usable life of the component. As shown, this practice often requires removing a part before its useful life is fully consumed, thus leading to higher maintenance cost. To address this issue, the NASA Glenn Research Center, in a collaborative effort with Pratt & Whitney, has developed a generic modular toolset that uses data-mining technology to parameterize life usage models for maintenance purposes. The toolset enables a "condition-based" maintenance approach, where parts are removed on the basis of the cumulative history of the severity of operation they have experienced. The toolset uses data-mining technology to tune life-consumption models on the basis of operating and maintenance histories. The flight operating conditions, represented by measured variables within the engine, are correlated with repair records for the engines, generating a relationship between the operating condition of the part and its service life. As shown, with the condition-based maintenance approach, the lifelimited part is in service until its usable life is fully consumed. This approach will lower maintenance costs while maintaining the safety of the propulsion system. The toolset is a modular program that is easily customizable by users. First, appropriate parametric damage accumulation models, which will be functions of engine variables, must be defined. The tool then optimizes the models to match the historical data by computing an effective-cycle metric that reduces the unexplained variability in component life due to each damage mode by accounting for the variability in operational severity. The damage increment due to operating conditions experienced during each flight is used to compute the effective cycles and ultimately the replacement time. Utilities to handle data problems, such as gaps in the flight data records, are included in the toolset. The tool was demonstrated using the first stage, high-pressure turbine blade of the PW4077 engine (Pratt & Whitney, East Hartford, CT). The damage modes considered were thermomechanical fatigue and oxidation/erosion. Each PW4077 engine contains 82 first-stage, high-pressure turbine blades, and data from a fleet of engines were used to tune the life-consumption models. The models took into account not only measured variables within the engine, but also unmeasured variables such as engine health parameters that are affected by degradation of the engine due to aging. The tool proved effective at predicting the average number of blades scrapped over time due to each damage mode, per engine, given the operating history of the engine. The customizable tools are available to interested parties within the aerospace community.

Litt, Jonathan S.↗

Associative Flow Rule Used to Include Hydrostatic Stress Effects in Analysis of Strain-Rate-Dependent Deformation of Polymer Matrix Composites

designing reliable composite engine cases that are lighter than the metal cases in current use. The types of polymer matrix composites that are likely to be used in such an application have a deformation response that is nonlinear and that varies with strain rate. The nonlinearity and the strain-rate dependence of the composite response are due primarily to the matrix constituent. Therefore, in developing material models to be used in the design of impact-resistant composite engine cases, the deformation of the polymer matrix must be correctly analyzed. However, unlike in metals, the nonlinear response of polymers depends on the hydrostatic stresses, which must be accounted for within an analytical model. By applying micromechanics techniques along with given fiber properties, one can also determine the effects of the hydrostatic stresses in the polymer on the overall composite deformation response. First efforts to account for the hydrostatic stress effects in the composite deformation applied purely empirical methods that relied on composite-level data. In later efforts, to allow polymer properties to be characterized solely on the basis of polymer data, researchers at the NASA Glenn Research Center developed equations to model the polymers that were based on a non-associative flow rule, and efforts to use these equations to simulate the deformation of representative polymer materials were reasonably successful. However, these equations were found to have difficulty in correctly analyzing the multiaxial stress states found in the polymer matrix constituent of a composite material. To correct these difficulties, and to allow for the accurate simulation of the nonlinear strain-rate-dependent deformation analysis of polymer matrix composites, in the efforts reported here Glenn researchers reformulated the polymer constitutive equations from basic principles using the concept of an associative flow rule. These revised equations were characterized and validated in an experimental program carried out through a university grant with the Ohio State University, wherein tensile and shear deformation data were obtained for a representative polymer for strain rates ranging from quasi-static to high rates of several hundred per second. Tensile deformation data also were obtained over a variety of strain rates and fiber orientation angles for a representative polymer matrix composite composed using the polymer.

Goldberg, Robert K.↗

Sub-Grid Modeling of Electrokinetic Effects in Micro Flows

Advances in micro-fabrication processes have generated tremendous interests in miniaturizing chemical and biomedical analyses into integrated microsystems (Lab-on-Chip devices). To successfully design and operate the micro fluidics system, it is essential to understand the fundamental fluid flow phenomena when channel sizes are shrink to micron or even nano dimensions. One important phenomenon is the electro kinetic effect in micro/nano channels due to the existence of the electrical double layer (EDL) near a solid-liquid interface. Not only EDL is responsible for electro-osmosis pumping when an electric field parallel to the surface is imposed, EDL also causes extra flow resistance (the electro-viscous effect) and flow anomaly (such as early transition from laminar to turbulent flow) observed in pressure-driven microchannel flows. Modeling and simulation of electro-kinetic effects on micro flows poses significant numerical challenge due to the fact that the sizes of the double layer (10 nm up to microns) are very thin compared to channel width (can be up to 100 s of m). Since the typical thickness of the double layer is extremely small compared to the channel width, it would be computationally very costly to capture the velocity profile inside the double layer by placing sufficient number of grid cells in the layer to resolve the velocity changes, especially in complex, 3-d geometries. Existing approaches using "slip" wall velocity and augmented double layer are difficult to use when the flow geometry is complicated, e.g. flow in a T-junction, X-junction, etc. In order to overcome the difficulties arising from those two approaches, we have developed a sub-grid integration method to properly account for the physics of the double layer. The integration approach can be used on simple or complicated flow geometries. Resolution of the double layer is not needed in this approach, and the effects of the double layer can be accounted for at the same time. With this approach, the numeric grid size can be much larger than the thickness of double layer. Presented in this report are a description of the approach, methodology for implementation and several validation simulations for micro flows.

Chen, C. P.↗

Probabilistic Analysis Techniques Applied to Complex Spacecraft Power System Modeling

Electric power system performance predictions are critical to spacecraft, such as the International Space Station (ISS), to ensure that sufficient power is available to support all the spacecraft s power needs. In the case of the ISS power system, analyses to date have been deterministic, meaning that each analysis produces a single-valued result for power capability because of the complexity and large size of the model. As a result, the deterministic ISS analyses did not account for the sensitivity of the power capability to uncertainties in model input variables. Over the last 10 years, the NASA Glenn Research Center has developed advanced, computationally fast, probabilistic analysis techniques and successfully applied them to large (thousands of nodes) complex structural analysis models. These same techniques were recently applied to large, complex ISS power system models. This new application enables probabilistic power analyses that account for input uncertainties and produce results that include variations caused by these uncertainties. Specifically, N&R Engineering, under contract to NASA, integrated these advanced probabilistic techniques with Glenn s internationally recognized ISS power system model, System Power Analysis for Capability Evaluation (SPACE).

Hojnicki, Jeffrey S.↗

Identifying and Characterizing Discrepancies Between Test and Analysis Results of Compression-Loaded Panels

Results from a study to identify and characterize discrepancies between validation tests and high-fidelity analyses of compression-loaded panels are presented. First, potential sources of the discrepancies in both the experimental method and corresponding high-fidelity analysis models were identified. Then, a series of laboratory tests and numerical simulations were conducted to quantify the discrepancies and develop test and analysis methods to account for the discrepancies. The results indicate that the discrepancies between the validation tests and high-fidelity analyses can be attributed to imperfections in the test fixture and specimen geometry; test-fixture-induced changes in specimen geometry; and test-fixture-induced friction on the loaded edges of the test specimen. The results also show that accurate predictions of the panel response can be obtained when these specimen imperfections and edge conditions are accounted for in the analysis. The errors in the tests and analyses, and the methods used to characterize these errors are presented.

Thornburgh, Robert P.↗

An Optimal Orthogonal Decomposition Method for Kalman Filter-Based Turbofan Engine Thrust Estimation

A new linear point design technique is presented for the determination of tuning parameters that enable the optimal estimation of unmeasured engine outputs such as thrust. The engine s performance is affected by its level of degradation, generally described in terms of unmeasurable health parameters related to each major engine component. Accurate thrust reconstruction depends upon knowledge of these health parameters, but there are usually too few sensors to be able to estimate their values. In this new technique, a set of tuning parameters is determined which accounts for degradation by representing the overall effect of the larger set of health parameters as closely as possible in a least squares sense. The technique takes advantage of the properties of the singular value decomposition of a matrix to generate a tuning parameter vector of low enough dimension that it can be estimated by a Kalman filter. A concise design procedure to generate a tuning vector that specifically takes into account the variables of interest is presented. An example demonstrates the tuning parameters ability to facilitate matching of both measured and unmeasured engine outputs, as well as state variables. Additional properties of the formulation are shown to lend themselves well to diagnostics.

Litt, Jonathan S.↗

Comparison of Grammar-Based and Statistical Language Models Trained on the Same Data

This paper presents a methodologically sound comparison of the performance of grammar-based (GLM) and statistical-based (SLM) recognizer architectures using data from the Clarissa procedure navigator domain. The Regulus open source packages make this possible with a method for constructing a grammar-based language model by training on a corpus. We construct grammar-based and statistical language models from the same corpus for comparison, and find that the grammar-based language models provide better performance in this domain. The best SLM version has a semantic error rate of 9.6%, while the best GLM version has an error rate of 6.0%. Part of this advantage is accounted for by the superior WER and Sentence Error Rate (SER) of the GLM (WER 7.42% versus 6.27%, and SER 12.41% versus 9.79%). The rest is most likely accounted for by the fact that the GLM architecture is able to use logical-form-based features, which permit tighter integration of recognition and semantic interpretation.

Hockey, Beth Ann↗