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NASA NTRS1995

Three-dimensional unstructured method for flows past bodies in 6-DOF relative motion

A three dimensional, unstructured-mesh methodology was developed to simulate unsteady flows past bodies in relative motion, where the trajectory was determined from the instantaneous aerodynamics. The method coupled the equations of fluid flow and those of rigid-body dynamics, and captured the time-dependent interference between stationary and moving boundaries. The unsteady, compressible Euler equations were solved on dynamic, unstructured meshes by an explicit, finite-volume, upwind method. The grid adaptation was performed within a window placed around the moving body. The Euler equations of dynamics were solved by a Runge-Kutta integration scheme. The flow solver and the adaptation scheme were validated by simulating the transonic, unsteady flow around a wing undergoing a forced, periodic pitching motion, then comparing the results with the experimental data. To validate the trajectory code, the six-degrees-of-freedom (DOF) motion of a store separating from a wing was computed using the experimentally determined force and moment fields, then comparing with an independently generated trajectory. Finally, the overall methodology was demonstrated by simulating the unsteady flowfield and the trajectory of a store dropped from a wing. The methodology, its computational cost notwithstanding, has proven to be accurate, automated, easy for dynamic gridding, and relatively efficient for the required man-hours.

Singh, K. P.↗

NASA NTRS2002

Progress in Unsteady Turbopump Flow Simulations Using Overset Grid Systems

This viewgraph presentation provides information on unsteady flow simulations for the Second Generation RLV (Reusable Launch Vehicle) baseline turbopump. Three impeller rotations were simulated by using a 34.3 million grid points model. MPI/OpenMP hybrid parallelism and MLP shared memory parallelism has been implemented and benchmarked in INS3D, an incompressible Navier-Stokes solver. For RLV turbopump simulations a speed up of more than 30 times has been obtained. Moving boundary capability is obtained by using the DCF module. Scripting capability from CAD geometry to solution is developed. Unsteady flow simulations for advanced consortium impeller/diffuser by using a 39 million grid points model are currently underway. 1.2 impeller rotations are completed. The fluid/structure coupling is initiated.

Kiris, Cetin C.↗

NASA NTRS1990

Two-dimensional Euler and Navier-Stokes Time accurate simulations of fan rotor flows

Two numerical methods are presented which describe the unsteady flow field in the blade-to-blade plane of an axial fan rotor. These methods solve the compressible, time-dependent, Euler and the compressible, turbulent, time-dependent, Navier-Stokes conservation equations for mass, momentum, and energy. The Navier-Stokes equations are written in Favre-averaged form and are closed with an approximate two-equation turbulence model with low Reynolds number and compressibility effects included. The unsteady aerodynamic component is obtained by superposing inflow or outflow unsteadiness to the steady conditions through time-dependent boundary conditions. The integration in space is performed by using a finite volume scheme, and the integration in time is performed by using k-stage Runge-Kutta schemes, k = 2,5. The numerical integration algorithm allows the reduction of the computational cost of an unsteady simulation involving high frequency disturbances in both CPU time and memory requirements. Less than 200 sec of CPU time are required to advance the Euler equations in a computational grid made up of about 2000 grid during 10,000 time steps on a CRAY Y-MP computer, with a required memory of less than 0.3 megawords.

Boretti, A. A.↗

NASA NTRS1996

Modeling the effect of unsteady flows on the time average flow field of a blade row embedded in an axial flow multistage turbomachine

The role of unsteady flow processes in establishing the performance of axial flow turbomachinery was investigated. The development of the flow model, as defined by the time average flow equations associated with the passage of the blade row embedded in a multistage configuration, is presented. The mechanisms for unsteady momentum and energy transport is outlined. The modeling of the unsteady momentum and energy transport are discussed. The procedure for simulating unsteady multistage turbomachinery flows is described.

Adamczyk, John J.↗

NASA NTRS2014

Towards Full Aircraft Airframe Noise Prediction: Detached Eddy Simulations

Results from a computational study on the aeroacoustic characteristics of an 18%-scale, semi-span Gulf-stream aircraft model are presented in this paper. NASA's FUN3D unstructured compressible Navier-Stokes solver was used to perform steady and unsteady simulations of the flow field associated with this high-fidelity aircraft model. Solutions were obtained for free-air at a Mach number of 0.2 with the flap deflected at 39 deg, with the main gear off and on (the two baseline configurations). Initially, the study focused on accurately predicting the prominent noise sources at both flap tips for the baseline configuration with deployed flap only. Building upon the experience gained from this initial effort, subsequent work involved the full landing configuration with both flap and main landing gear deployed. For the unsteady computations, we capitalized on the Detached Eddy Simulation capability of FUN3D to capture the complex time-dependent flow features associated with the flap and main gear. To resolve the noise sources over a broad frequency range, the tailored grid was very dense near the flap inboard and outboard tips and the region surrounding the gear. Extensive comparison of the computed steady and unsteady surface pressures with wind tunnel measurements showed good agreement for the global aerodynamic characteristics and the local flow field at the flap inboard tip. However, the computed pressure coefficients indicated that a zone of separated flow that forms in the vicinity of the outboard tip is larger in extent along the flap span and chord than measurements suggest. Computed farfield acoustic characteristics from a FW-H integral approach that used the simulated pressures on the model solid surface were in excellent agreement with corresponding measurements.

Khorrami, Mehdi R.↗

NASA NTRS1992

Runge-Kutta methods combined with compact difference schemes for the unsteady Euler equations

Recent development using compact difference schemes to solve the Navier-Stokes equations show spectral-like accuracy. A study was made of the numerical characteristics of various combinations of the Runge-Kutta (RK) methods and compact difference schemes to calculate the unsteady Euler equations. The accuracy of finite difference schemes is assessed based on the evaluations of dissipative error. The objectives are reducing the numerical damping and, at the same time, preserving numerical stability. While this approach has tremendous success solving steady flows, numerical characteristics of unsteady calculations remain largely unclear. For unsteady flows, in addition to the dissipative errors, phase velocity and harmonic content of the numerical results are of concern. As a result of the discretization procedure, the simulated unsteady flow motions actually propagate in a dispersive numerical medium. Consequently, the dispersion characteristics of the numerical schemes which relate the phase velocity and wave number may greatly impact the numerical accuracy. The aim is to assess the numerical accuracy of the simulated results. To this end, the Fourier analysis is to provide the dispersive correlations of various numerical schemes. First, a detailed investigation of the existing RK methods is carried out. A generalized form of an N-step RK method is derived. With this generalized form, the criteria are derived for the three and four-step RK methods to be third and fourth-order time accurate for the non-linear equations, e.g., flow equations. These criteria are then applied to commonly used RK methods such as Jameson's 3-step and 4-step schemes and Wray's algorithm to identify the accuracy of the methods. For the spatial discretization, compact difference schemes are presented. The schemes are formulated in the operator-type to render themselves suitable for the Fourier analyses. The performance of the numerical methods is shown by numerical examples. These examples are detailed. described. The third case is a two-dimensional simulation of a Lamb vortex in an uniform flow. This calculation provides a realistic assessment of various finite difference schemes in terms of the conservation of the vortex strength and the harmonic content after travelling a substantial distance. The numerical implementation of Giles' non-refelctive equations coupled with the characteristic equations as the boundary condition is discussed in detail. Finally, the single vortex calculation is extended to simulate vortex pairing. For the distance between two vortices less than a threshold value, numerical results show crisp resolution of the vortex merging.

Yu, Sheng-Tao↗

NASA NTRS2013

Design of a Variational Multiscale Method for Turbulent Compressible Flows

A spectral-element framework is presented for the simulation of subsonic compressible high-Reynolds-number flows. The focus of the work is maximizing the efficiency of the computational schemes to enable unsteady simulations with a large number of spatial and temporal degrees of freedom. A collocation scheme is combined with optimized computational kernels to provide a residual evaluation with computational cost independent of order of accuracy up to 16th order. The optimized residual routines are used to develop a low-memory implicit scheme based on a matrix-free Newton-Krylov method. A preconditioner based on the finite-difference diagonalized ADI scheme is developed which maintains the low memory of the matrix-free implicit solver, while providing improved convergence properties. Emphasis on low memory usage throughout the solver development is leveraged to implement a coupled space-time DG solver which may offer further efficiency gains through adaptivity in both space and time.

Design↗

NASA NTRS1991

Numerical simulations of a nonequilibrium argon plasma in a shock-tube experiment

A code developed for the numerical modeling of nonequilibrium radiative plasmas is applied to the simulation of the propagation of strong ionizing shock waves in argon gas. The simulations attempt to reproduce a series of shock-tube experiments which will be used to validate the numerical models and procedures. The ability to perform unsteady simulations makes it possible to observe some fluctuations in the shock propagation, coupled to the kinetic processes. A coupling mechanism by pressure waves, reminiscent of oscillation mechanisms observed in detonation waves, is described. The effect of upper atomic levels is also briefly discussed.

Cambier, Jean-Luc↗

NASA NTRS1995

Evaluation of F/A-18A HARV inlet flow analysis with flight data

The F/A-18A aircraft has experienced engine stalls at high angles-of-attack and yaw flight conditions which were outside of its flight envelope. Future aircraft may be designed to operate routinely in this flight regime. Therefore, it is essential that an understanding of the inlet flow field at these flight conditions be obtained. Due to the complex interactions of the fuselage and inlet flow fields, a study of the flow within the inlet must also include external effects. Full Navier-Stokes (FNS) calculations on the F/A-18A High Alpha Research Vehicle (HARV) inlet for several angles-of-attack with sideslip and free stream Mach numbers have been obtained. The predicted forebody/fuselage surface static pressures agreed well with flight data. The surface static pressures along the inlet lip are in good agreement with the numerical predictions. The major departure in agreement is along the bottom of the lip at 30 deg and 60 deg angle-of-attack where a possible streamwise flow separation is not being predicted by the code. The circumferential pressure distributions at the engine face are in very good agreement with the numerical results. The variation in surface static pressure in the circumferential direction is very small with the exception of 60 angle-of-attack. Although the simulation does not include the effect of the engine, it appears that this omission has a second order effect on the circumferential pressure distribution. An examination of the unsteady flight test data base has shown that the secondary vortex migrates a significant distance with time. In fact, the extent of this migration increases with angle-of-attack with increasing levels of distortion. The effects of the engine on this vortex movement is unknown. This implies that the level of flow unsteadiness increases with increasing distortion. Since the computational results represent an asymptotic solution driven by steady boundary conditions, these numerical results may represent an arbitrary point in time. A comparison of the predicted total pressure contours with flight data indicates that the numerical results are within the excursion range of the unsteady data which is the best the calculations can attain unless an unsteady simulation is performed.

Smith, C. Frederic↗

NASA NTRS2005

Control of Combustion-Instabilities Through Various Passive Devices

It is well known that under some operating conditions, rocket engines (using solid or liquid fuels) exhibit unstable modes of operation that can lead to engine malfunction and shutdown. The sources of these instabilities are diverse and are dependent on fuel, chamber geometry and various upstream sources such as pumps, valves and injection mechanism. It is believed that combustion-acoustic instabilities occur when the acoustic energy increase due to the unsteady heat release of the flame is greater than the losses of acoustic energy from the system [1, 2]. Giammar and Putnam [3] performed a comprehensive study of noise generated by gasfired industrial burners and made several key observations; flow noise was sometimes more intense than combustion roar, which tended to have a characteristic frequency spectrum. Turbulence was amplified by the flame. The noise power varied directly with combustion intensity and also with the product of pressure drop and heat release rate. Karchmer [4] correlated the noise emitted from a turbofan jet engine with that in the combustion chamber. This is important, since it quantified how much of the noise from an engine originates in the combustor. A physical interpretation of the interchange of energy between sound waves and unsteady heat release rates was given by Rayleigh [5] for inviscid, linear perturbations. Bloxidge et al [6] extended Rayleigh s criterion to describe the interaction of unsteady combustion with one-dimensional acoustic waves in a duct. Solutions to the mass, momentum and energy conservation equations in the pre- and post-flame zones were matched by making several assumptions about the combustion process. They concluded that changes in boundary conditions affect the energy balance of acoustic waves in the combustor. Abouseif et al [7] also solved the one-dimensional flow equations, but they used a onestep reaction to evaluate the unsteady heat release rate by relating it to temperature and velocity perturbations. Their analysis showed that oscillations arise from coupling between entropy waves produced at the flame and pressure waves originating from the nozzle. Yang and Culick [8] assumed a thin flame sheet, which is distorted by velocity and pressure oscillations. Conservation equations were expressed in integral form and solutions for the acoustic wave equations and complex frequencies were obtained. The imaginary part of the frequency indicated stability regions of the flame. Activation energy asymptotics together with a one-step reaction were used by McIntosh [9] to study the effects of acoustic forcing and feedback on unsteady, one-dimensional flames. He found that the flame stability was altered by the upstream acoustic feedback. Shyy et al [10] used a high-accuracy TVD scheme to simulate unsteady, one-dimensional longitudinal, combustion instabilities. However, numerical diffusion was not completely eliminated. Recently, Prasad [11] investigated numerically the interactions of pressure perturbations with premixed flames. He used complex chemistry to study responses of pressure perturbations in one-dimensional combustors. His results indicated that reflected and transmitted waves differed significantly from incident waves.

Frendi, Kader↗

NASA NTRS2001

Experimental Investigation of Transition to Turbulence as Affected By Passing Wakes

This paper presents experimental results from a study of the effects of periodically passing wakes upon laminar-to-turbulent transition and separation in a low-pressure turbine passage. The test section geometry is designed to simulate unsteady wakes in turbine engines for studying their effects on boundary layers and separated flow regions over the suction surface by using a single suction surface and a single pressure surface to simulate a single turbine blade passage. Single-wire, thermal anemometry techniques are used to measure time-resolved and phase averaged, wall-normal profiles of velocity, turbulence intensity and intermittency at multiple streamwise locations over the turbine airfoil suction surface. These data are compared to steady-state wake-free data collected in the same geometry to identify the effects of wakes upon laminar-to-turbulent transition. Results are presented for flows with a Reynolds number based on suction surface length and stage exit velocity of 50,000 and an approach flow turbulence intensity of 2.5%. While both existing design and experimental data are primarily concerned with higher Reynolds number flows (Re greater than 100,000), recent advances in gas turbine engines, and the accompanying increase in laminar and transitional flow effects, have made low-Re research increasingly important. From the presented data, the effects of passing wakes on transition and separation in the boundary layer, due to both increased turbulence levels and varying streamwise pressure gradients are presented. The results show how the wakes affect transition. The wakes affect the flow by virtue of their difference in turbulence levels and scales from those of the free-stream and by virtue of their ensemble- averaged velocity deficits, relative to the free-stream velocity, and the concomitant changes in angle of attack and temporal pressure gradients. The relationships between the velocity oscillations in the freestream and the unsteady velocity profile shapes in the near-wall flow are described. In this discussion is support for the theory that bypass transition is a response of the near-wall viscous layer to pressure fluctuations imposed upon it from the free-stream flow. Recent transition models are based on that premise. The data also show a significant lag between when the wake is present over the surface and when transition begins.cous layer to pressure fluctuations imposed upon it from the free-stream flow. Recent transition models are based on that premise. The data also show a significant lag between when the wake is present over the surface and when transition begins.cous layer to pressure fluctuations imposed upon it from the free-stream flow. Recent transition models are based on that premise. The data also show a significant lag between when the wake is present over the surface and when transition begins.

Kaszeta, Richard W.↗

NASA NTRS2004

Unsteady, Cooled Turbine Simulation Using a PC-Linux Analysis System

The fist stage of the high-pressure turbine (HPT) of the GE90 engine was simulated with a three-dimensional unsteady Navier-Sokes solver, MSU Turbo, which uses source terms to simulate the cooling flows. In addition to the solver, its pre-processor, GUMBO, and a post-processing and visualization tool, Turbomachinery Visual3 (TV3) were run in a Linux environment to carry out the simulation and analysis. The solver was run both with and without cooling. The introduction of cooling flow on the blade surfaces, case, and hub and its effects on both rotor-vane interaction as well the effects on the blades themselves were the principle motivations for this study. The studies of the cooling flow show the large amount of unsteadiness in the turbine and the corresponding hot streak migration phenomenon. This research on the GE90 turbomachinery has also led to a procedure for running unsteady, cooled turbine analysis on commodity PC's running the Linux operating system.

List, Michael G.↗

NASA NTRS2010

A General Algorithm for Reusing Krylov Subspace Information. I. Unsteady Navier-Stokes

A general algorithm is developed that reuses available information to accelerate the iterative convergence of linear systems with multiple right-hand sides A x = b (sup i), which are commonly encountered in steady or unsteady simulations of nonlinear equations. The algorithm is based on the classical GMRES algorithm with eigenvector enrichment but also includes a Galerkin projection preprocessing step and several novel Krylov subspace reuse strategies. The new approach is applied to a set of test problems, including an unsteady turbulent airfoil, and is shown in some cases to provide significant improvement in computational efficiency relative to baseline approaches.

Carpenter, Mark H.↗

NASA NTRS2013

Assessments of a Turbulence Model Based on Menter's Modification to Rotta's Two-Equation Model

The main objective of this paper is to construct a turbulence model with a more reliable second equation simulating length scale. In the present paper, we assess the length scale equation based on Menter s modification to Rotta s two-equation model. Rotta shows that a reliable second equation can be formed in an exact transport equation from the turbulent length scale L and kinetic energy. Rotta s equation is well suited for a term-by-term modeling and shows some interesting features compared to other approaches. The most important difference is that the formulation leads to a natural inclusion of higher order velocity derivatives into the source terms of the scale equation, which has the potential to enhance the capability of Reynolds-averaged Navier-Stokes (RANS) to simulate unsteady flows. The model is implemented in the PAB3D solver with complete formulation, usage methodology, and validation examples to demonstrate its capabilities. The detailed studies include grid convergence. Near-wall and shear flows cases are documented and compared with experimental and Large Eddy Simulation (LES) data. The results from this formulation are as good or better than the well-known SST turbulence model and much better than k-epsilon results. Overall, the study provides useful insights into the model capability in predicting attached and separated flows.

Abdol-Hamid, Khaled S.↗

NASA NTRS2020

Juncture Flow Computations using kL-Based Turbulence Models

The development and implementation of kL-based Reynolds-Average Navier-Stokes (RANS) two-equation turbulence models are reported in this paper. The kL model is based on Abdol-Hamid's closure and Menter's modification to Rotta's two-equation model. Rotta showed that a reliable transport equation can be formed from the turbulence length scale L, and the turbulence kinetic energy k. Rotta's kL equation is well suited for a term-by-term modeling and displays useful features compared to other scale formulations. One of the important differences is the inclusion of higher-order velocity derivatives in the source terms of the scale equation. This can enhance the ability of RANS solvers to simulate unsteady flows in URANS mode. The k-kL scheme has been modified to include the Algebraic Reynolds Stress Model (ARSM) and the Quadratic Constitutive Relation (QCR) as nonlinear models. These models have gone through extensive validations using two-dimensional benchmark problems. The present study documents the application of the k-kL schemes to simulate flow around the Juncture Flow Model (JFM). The k-kL prediction results show generally good comparisons with measurements. The results from this formulation are similar to, or better than results using the SA-RC-QCR2000 two-equation turbulence model. The ARSM and the QCR formulations of k-kL show promise with a similar level of computational resources as basic two-equation turbulence models.

K S Abdol-Hamid↗

NASA NTRS1990

Unsteady transonic Navier-Stokes computations for an oscillating wing using single and multiple zones

Modern jet transports and maneuvering tactical fighters operating in the transonic regime often give rise to time-dependent fluid physics that interact with flexible structural components, e.g., vortical flow, shocks, and separation. Efficient computational fluid dynamic (CFD) methods are required to study such computationally intensive problems. In this work a numerical method is presented to address this problem. Time-dependent, compressible, Navier-Stokes equations are used to simulate unsteady transonic flow about a three-dimensional rigid wing undergoing a forced periodic motion in angle of attack. An efficient, implicit, diagonal algorithm is utilized because of its low operation count per time step compared to other methods that solve systems of block matrix equations. The formal time accuracy is addressed theoretically and demonstrated numerically by comparison of computational results with experimental data. A zonal grid approach, capable of treating complex geometries, is presented and its time accuracy is demonstrated by comparing a zonal computation with a single grid computation and experimental data.

Chaderjian, Neal M.↗

NASA NTRS2007

Runtime and Pressurization Analyses of Propellant Tanks

Multi-element unstructured CFD has been utilized at NASA SSC to carry out analyses of propellant tank systems in different modes of operation. The three regimes of interest at SSC include (a) tank chill down (b) tank pressurization and (c) runtime propellant draw-down and purge. While tank chill down is an important event that is best addressed with long time-scale heat transfer calculations, CFD can play a critical role in the tank pressurization and runtime modes of operation. In these situations, problems with contamination of the propellant by inclusion of the pressurant gas from the ullage causes a deterioration of the quality of the propellant delivered to the test article. CFD can be used to help quantify the mixing and propellant degradation. During tank pressurization under some circumstances, rapid mixing of relatively warm pressurant gas with cryogenic propellant can lead to rapid densification of the gas and loss of pressure in the tank. This phenomenon can cause serious problems during testing because of the resulting decrease in propellant flow rate. With proper physical models implemented, CFD can model the coupling between the propellant and pressurant including heat transfer and phase change effects and accurately capture the complex physics in the evolving flowfields. This holds the promise of allowing the specification of operational conditions and procedures that could minimize the undesirable mixing and heat transfer inherent in propellant tank operation. It should be noted that traditional CFD modeling is inadequate for such simulations because the fluids in the tank are in a range of different sub-critical and supercritical states and elaborate phase change and mixing rules have to be developed to accurately model the interaction between the ullage gas and the propellant. We show a typical run-time simulation of a spherical propellant tank, containing RP-1 in this case, being pressurized with room-temperature nitrogen at 540 R. Nitrogen, shown in blue on the right-hand side of the figures, enters the tank from the diffuser at the top of the figures and impinges on the RP-1, shown in red, while the propellant is being continuously drained at the rate of 1050 lbs/sec through a pipe at the bottom of the tank. The sequence of frames in Figure 1 shows the resultant velocity fields and mixing between nitrogen and RP-1 in a cross-section of the tank at different times. A vortex is seen to form in the incoming nitrogen stream that tends to entrain propellant, mixing it with the pressurant gas. The RP-1 mass fraction contours in Figure 1 are also indicative of the level of mixing and contamination of the propellant. The simulation is used to track the propagation of the pure propellant front as it is drawn toward the exit with the evolution of the mixing processes in the tank. The CFD simulation modeled a total of 10 seconds of run time. As is seen from Figure 1d, after 5.65 seconds the propellant front is nearing the drain pipe, especially near the center of the tank. Behind this pure propellant front is a mixed fluid of compromised quality that would require the test to end when it reaches the exit pipe. Such unsteady simulations provide an estimate of the time that a high-quality propellant supply to the test article can be guaranteed at the modeled mass flow rate. In the final paper, we will discuss simulations of the LOX and propellant tanks at NASA SSC being pressurized by an inert ullage. Detailed comparisons will be made between the CFD simulations and lower order models as well as with test data. Conditions leading to cryo collapse in the tank will also be identified.

Field, Robert E.↗

NASA NTRS2007

Analysis of Complex Valve and Feed Systems

A numerical framework for analysis of complex valve systems supports testing of propulsive systems by simulating key valve and control system components in the test loop. In particular, it is designed to enhance the analysis capability in terms of identifying system transients and quantifying the valve response to these transients. This system has analysis capability for simulating valve motion in complex systems operating in diverse flow regimes ranging from compressible gases to cryogenic liquids. A key feature is the hybrid, unstructured framework with sub-models for grid movement and phase change including cryogenic cavitations. The multi-element unstructured framework offers improved predictions of valve performance characteristics under steady conditions for structurally complex valves such as pressure regulator valve. Unsteady simulations of valve motion using this computational approach have been carried out for various valves in operation at Stennis Space Center such as the split-body valve and the 10-in. (approx.25.4-cm) LOX (liquid oxygen) valve and the 4-in. (approx.10 cm) Y-pattern valve (liquid nitrogen). Such simulations make use of variable grid topologies, thereby permitting solution accuracy and resolving important flow physics in the seat region of the moving valve. An advantage to this software includes possible reduction in testing costs incurred due to disruptions relating to unexpected flow transients or functioning of valve/flow control systems. Prediction of the flow anomalies leading to system vibrations, flow resonance, and valve stall can help in valve scheduling and significantly reduce the need for activation tests. This framework has been evaluated for its ability to predict performance metrics like flow coefficient for cavitating venturis and valve coefficient curves, and could be a valuable tool in predicting and understanding anomalous behavior of system components at rocket propulsion testing and design sites.

Ahuja, Vineet↗