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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.

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At least 703 records · Page 39
All sourcesNASA NTRSDOE OSTI
NASA NTRS1987

Forced cocurrent smoldering combustion

An analytical model of cocurrent smoldering combustion through a very porous solid fuel is developed. Smoldering is initiated at the top of a long radially insulated uniform fuel cylinder, so that the smolder wave propagates downward, opposing an upward-forced flow of oxidizer, with the solid fuel and the gaseous oxidizer entering the reaction zone from the same direction (hence, cocurrent). Radiative heat transfer was incorporated using a diffusion approximation, and smoldering was modeled using a one-step reaction mechanism. The results indicate that, for a given fuel, the final temperature depends only on the initial oxygen mass flux, increasing logarithmically with the mass flux. The smolder velocity is linearly dependent on the initial oxygen mass flux, and, at a fixed value of the flux, increases with initial oxygen mass fraction. The mathematical relationship determining the conditions for steady smolder propagation is presented.

Dosanjh, Sudip S.↗
NASA NTRS1995

Results of Tests Performed on the Acoustic Quiet Flow Facility Three-Dimensional Model Tunnel

The test results briefly described in this report were obtained on the three-dimensional 1:48 scale tunnel modeled on the design proposed by Messrs. D.S.M.A. Corporation. More particularly, while the test chamber dimensions were indeed scaled down in the ration of 1:48, including the contraction and the collector as well, the duct system itself leading to and from the chamber was adapted to suit laboratory conditions and space limitations. Earlier tests with the two-dimensional model showed that blowing mode was preferred as against the suction mode, hence all tests were performed with blowing only. At the exit of the contraction the maximum airspeed attained with the 1 HP blower unit was about 200 ft/sec. This airspeed may be increased in future if desired. The test results show that pressure recovery in the diffuser was about 34 percent due to the large blockage at its entrance. Velocity traverses taken across the diffuser entrance explain the reason for this blockage. Recirculation, studied with both, hot-wire anemometry and flow-visualization techniques, was largely affected by the design of the test chamber itself and the amount of vent-air admitted to the chamber. Vent-air helped to decrease the level of turbulence.

Barna, P. S.↗
NASA NTRS1999

The Effect of Velocity on the Extinction Behavior of a Diffusion Flame during Transient Depressurization

Current fire suppression plans for the International Space Station include the use of venting (depressurization) as a method for extinguishing a fire. Until recently this process had only been examined as part of a material flammability experiment performed on Skylab in the early 1970's. Due to the low initial pressure (0.35 Atm) and high oxygen concentration (65%), the Skylab experimental results are not applicable for understanding the effects of venting on a fire in a space station environment (21%O2, 1 Atm). Recent research examined the extinction behavior of a diffusion flame over a polymethyl methacrylate (PMMA) cylinder during a transient depressurization in low-gravity. The numerical model was used to examine extinction limits as a function of depressurization rate, forced flow velocity, and initial solid phase temperature. The experimental and numerically predicted extinction data indicated that as the solid phase temperature increased the pressure required to extinguish the flame decreased. The numerical model was also used to examine conditions not obtainable in the low-gravity experiments. From these simulations, a series of extinction boundaries were generated that showed a region of increased flammability existed at a forced flow of 10 cm/s. Analysis of these extinction boundaries indicated that they were quasi-steady in nature, and that the final extinction conditions were independent of the transient process. The velocity range in the previous study was limited and thus the results did not examine the effects of velocities less than 1 cm/s or greater than 20 cm/s. This study utilized low-gravity experiments performed on NASA's Reduced-gravity Research Aircraft Laboratory and numerical simulations to examine conditions applicable to the Space Station environment. This paper extends the analysis of the previous study to a comprehensive examination of the effect of increased velocity on extinction behavior and extinction limits during a transient depressurization in low-gravity. This is achieved by examining extinction data from buoyant (normal-gravity) and low-buoyant (low-gravity) depressurization. experiments, as well as from numerical predictions of flame behavior during depressurization in a non-buoyant (zero-gravity) environment.

Goldmeer, Jeffrey S.↗
NASA NTRS2001

Three-Dimensional Upward Flame Spreading in Partial-Gravity Buoyant Flows

Reduced-gravity environments have been used to establish low-speed, purely forced flows for both opposed- and concurrent-flow flame spread studies. Altenkirch's group obtained spacebased experimental results and developed unsteady, two-dimensional numerical simulations of opposed-flow flame spread including gas-phase radiation, primarily away from the flammability limit for thin fuels, but including observations of thick fuel quenching in quiescent environments. T'ien's group contributed some early flame spreading results for thin fuels both in opposed flow and concurrent flow regimes, with more focus on near-limit conditions. T'ien's group also developed two- and three-dimensional numerical simulations of concurrent-flow flame spread incorporating gas-phase radiative models, including predictions of a radiatively-induced quenching limit reached in very low-speed air flows. Radiative quenching has been subsequently observed in other studies of combustion in very low-speed flows including other flame spread investigations, droplet combustion and homogeneous diffusion flames, and is the subject of several contemporary studies reported in this workshop. Using NASA aircraft flying partial-gravity "parabolic" trajectories, flame spreading in purely buoyant, opposed-flow (downward burning) has been studied. These results indicated increases in flame spread rates and enhanced flammability (lower limiting atmospheric oxygen content) as gravity levels were reduced from normal Earth gravity, and were consistent with earlier data obtained by Altenkirch using a centrifuge. In this work, experimental results and a three-dimensional numerical simulation of upward flame spreading in variable partial-gravity environments were obtained including some effects of reduced pressure and variable sample width. The simulation provides physical insight for interpreting the experimental results and shows the intrinsic 3-D nature of buoyant, upward flame spreading. This study is intended to link the evolving understanding of flame spreading in purely-forced flows to the purely-buoyant flow environment, particularly in the concurrent flow regime; provide additional insight into the existence of steady flame spread in concurrent flows; and stimulate direct comparisons between opposed- and concurrent-flow flame spread. Additionally, this effort is intended to provide direct practical understanding applicable to fire protection planning for the habitable facilities in partial gravity environments of anticipated Lunar and Martian explorations.

Sacksteder, Kurt R.↗
NASA NTRS1995

On the Importance of the Dynamics of Discretizations

It has been realized recently that the discrete maps resulting from numerical discretizations of differential equations can possess asymptotic dynamical behavior quite different from that of the original systems. This is the case not only for systems of Ordinary Differential Equations (ODEs) but in a more complicated manner for Partial Differential Equations (PDEs) used to model complex physics. The impact of the modified dynamics may be mild and even not observed for some numerical methods. For other classes of discretizations the impact may be pronounced, but not always obvious depending on the nonlinear model equations, the time steps, the grid spacings and the initial conditions. Non-convergence or convergence to periodic solutions might be easily recognizable but convergence to incorrect but plausible solutions may not be so obvious - even for discretized parameters within the linearized stability constraint. Based on our past four years of research, we will illustrate some of the pathology of the dynamics of discretizations, its possible impact and the usage of these schemes for model nonlinear ODEs, convection-diffusion equations and grid adaptations.

Sweby, Peter K.↗
NASA NTRS1999

Optical Flow-Field Techniques Used for Measurements in High-Speed Centrifugal Compressors

The overall performance of a centrifugal compressor depends on the performance of the impeller and diffuser as well as on the interactions occurring between these components. Accurate measurements of the flow fields in each component are needed to develop computational models that can be used in compressor design codes. These measurements must be made simultaneously over an area that covers both components so that researchers can understand the interactions occurring between the two components. Optical measurement techniques are being used at the NASA Lewis Research Center to measure the velocity fields present in both the impeller and diffuser of a 4:1 pressure ratio centrifugal compressor operating at several conditions ranging from design flow to surge. Laser Doppler Velocimetry (LDV) was used to measure the intrablade flows present in the impeller, and the results were compared with analyses obtained from two three-dimensional viscous codes. The development of a region of low throughflow velocity fluid within this high-speed impeller was examined and compared with a similar region first observed in a large low-speed centrifugal impeller at Lewis. Particle Image Velocimetry (PIV) is a relatively new technique that has been applied to measuring the diffuser flow fields. PIV can collect data rapidly in the diffuser while avoiding the light-reflection problems that are often encountered when LDV is used. The Particle Image Velocimeter employs a sheet of pulsed laser light that is introduced into the diffuser in a quasi-radial direction through an optical probe inserted near the diffuser discharge. The light sheet is positioned such that its centerline is parallel to the hub and shroud surfaces and such that it is parallel to the diffuser vane, thereby avoiding reflections from the solid surfaces. Seed particles small enough to follow the diffuser flow are introduced into the compressor at an upstream location. A high-speed charge-coupled discharge (CCD) camera is synchronized to the laser pulse rate; this allows it to capture images of seed particle position that are separated by a small increment in time. A crosscorrelation of a particle's position in two consecutive images provides an estimate of flow velocity and direction. Multiple image pairs obtained in rapid succession at a particular flow condition provide enough measurements for statistical significance. PIV provides simultaneous velocity measurements over the entire plane that is illuminated by the light sheet instead of at a single point, as is the case when LDV is used. PIV has a further advantage in that the laser light pulse can be triggered by an external source such as a high-response pressure transducer. This feature will allow PIV to synchronize flow imaging to physical phenomena such as rotating stall or stall precursor waves. We hope that this technique can be used to obtain images of the flow field during and just prior to stall.

Skoch, Gary J.↗
NASA NTRS1999

The Effects of Buoyancy and Dilution on the Structure and Lift-Off of Coflow Laminar Diffusion Flames

The ability to predict the coupled effects of complex transport phenomena with detailed chemical kinetics in diffusion flames is critical in the modeling of turbulent reacting flows and in understanding the processes by which soot formation and radiative transfer take place. In addition, an understanding of those factors that affect flame extinction in diffusion flames is critical in the suppression of fires and in improving engine efficiency. A goal of this work is to bring to microgravity flame studies the detailed experimental and numerical tools that have been used to study ground-based systems. This will lead to a more detailed understanding of the interaction of convection, diffusion and chemistry in a nonbuoyant environment. To better understand these phenomena, experimental and computational studies of a coflow laminar diffusion flame have been carried out. To date, these studies have focused on a single set of flow conditions, in which a nitrogen-diluted methane fuel stream (65% methane by volume) was surrounded by an air coflow, with exit velocities matched at 35 cm/s. Of particular interest is the change in flame shape due to the absence of buoyant forces, as well as the amount of diluent in the fuel stream and the coflow velocity. As a sensitive marker of changes in the flame shape, the number densities of excited-state CH (A(exp 2 delta) denoted CH*), and excited-state OH (A(exp 2 sigma, denoted OH*) are measured. CH* and OH* number densities are deconvoluted from line-of-sight chemiluminescence measurements made on the NASA KC135 reduced-gravity aircraft. Measured signal levels are calibrated, post-flight, with Rayleigh scattering. In extending the study to microgravity conditions, improvements to the computational model have been made and new calculations performed for a range of gravity conditions. In addition, modifications to the experimental approach were required as a consequence of the constraints imposed by existing microgravity facilities. Results from the computations and experiments are presented.

Walsh, Kevin T.↗
DOE OSTI2025

Q2 Report for FY25 Theory and Simulation Performance Target: Development of an integrated modeling framework for fusion reactor design and assessment

This report describes the work and activities carried out towards the completion of each of the following milestones in FY25 Q2: 1. Demonstrate workflow for generating self-consistent CESOL plasma profiles + first wall and divertor loading prediction and generate the CAT plasma and neutron loading needed for further engineering analysis: $\circ$ Run CESOL with BOUT++/Hermes-3 and immersed boundary condition to directly map to wall: • Run BOUT++/Hermes-3 through the IPS workflow to find radial particle and energy diffusivities to match either the Eich or the physics-based scaling of the SOL heat flux width, and • Expand source of first wall heat flux to include charged particles, neutrals, and radiation from the core+edge. 2. Generate medium fidelity parametrized CAD: $\circ$ Develop the TRACER tool to read an existing CAD, regenerate the geometry based on vertex location and connectivity information, define vertex translation and parameters needed for scaling the CAD, and $\circ$ Utilize the FreeGS code to determine CAT PF coil placement, including minimizing the number of coils, coil current, and electromechanical stresses. 3. Utilize plasma loading for engineering analysis: $\circ$ Couple the plasma loading to input for OpenFOAM and demonstrate initial test of thermal analysis of CAT first wall loading with typical DCLL blanket component cooling boundary conditions. 4. Demonstrate nuclear analysis: $\circ$ Apply initial analysis of tritium transport in DCLL blanket by evaluating spatially resolved tritium generation rates, tritium diffusion and convection.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS2007

Multi-Scale Modeling of Magnetospheric Reconnection

One of the major challenges in modeling the magnetospheric magnetic reconnection is to quantify the interaction between large-scale global magnetospheric dynamics and microphysical processes in diffusion regions near reconnection sites. There is still considerable debate as to what degree microphysical processes on kinetic scales affect the global evolution and how important it is to substitute numerical dissipation and/or ad hoc anomalous resistivity by a physically motivated model of dissipation. Comparative studies of magnetic reconnection in small scale geometries demonstrated that MHD simulations that included non-ideal processes in terms of a resistive term $\eta J$ did not produce the fast reconnection rates observed in kinetic simulations. For a broad range of physical parameters in collisionless magnetospheric plasma, the primary mechanism controlling the dissipation in the vicinity of the reconnection site is non-gyrotropic effects with spatial scales comparable with the particle Larmor radius. We utilize the global MHD code BATSRUS and incorporate nongyrotropic effects in diffusion regions in terms of corrections to the induction equation. We developed an algorithm to search for magnetotail reconnection sites, specifically where the magnetic field components perpendicular to the local current direction approaches zero and form an X-type configuration. Spatial scales of the diffusion region and magnitude of the reconnection electric field are calculated selfconsistently using MHD plasma and field parameters in the vicinity of the reconnection site. The location of the reconnection sites is updated during the simulations. To clarify the role of nongyrotropic effects in diffusion region on the global magnetospheric dynamic we perform simulations with steady southward IMF driving of the magnetosphere. Ideal MHD simulations with magnetic reconnection supported by numerical resistivity produce steady configuration with almost stationary near-earth neutral line (NENL). Simulations with non-gyrotropic corrections demonstrate dynamic quasi-periodic response to the steady driving condition. The loading/unloading cycle in non-gyrotropic MHD results has a non-stationary reconnection site in the magnetotail, with the retreating during the stretching phase and then a new NENL forming in the resulting thin plasma sheet. We expect that this model will lead to improved representations of space weather event in the magnetosphere.

Kuznetsova, M. M.↗
DOE OSTI2025

Corrosion of 316 L stainless steel under the natural circulation of molten NaCl-MgCl 2 salt

The corrosion behavior of 316 L stainless steel (SS) was studied via the natural circulation of molten eutectic NaCl-MgCl 2 salt through a microloop. The post-corrosion tested 316 L SS microloop sections were characterized with microscopy techniques to determine the microstructural and microchemical changes that occurred at the alloy/salt interface. It was found that 316 L SS showed heterogeneous dissolution at the hot-leg, whereas deposition of corrosion products occurred at the cold-leg. For the first time, experimentally obtained molten salt flow-induced corrosion of 316 L SS results were combined with computational thermodynamic-kinetic models to validate the dissolution and deposition in terms of elemental compositional changes at the alloy/salt interface. The thermodynamic-kinetic modeling predicted that the heterogeneous dissolution of Cr and Fe from the hot-leg section of 316 L SS persisted throughout the salt circulation. The model also estimated that, despite Cr deposition starting earlier than Fe, the total redeposition of Fe is expected to be significantly greater than that of Cr over the circulation of salt. Furthermore, the modeling accurately predicted the subsurface enrichment of Mo which is attributed to the reduced Cr activity and the relatively higher diffusion rate of Mo within the alloy matrix. Here, the agreement between modeling and experimental results confirms that Fe chlorides dissolve at the hot-leg and subsequently deposit at the cold-leg due to activity changes driven by the thermal gradient. By contrast, Cr was not detected in the cold-leg deposits, which is attributed to its weaker temperature dependence on activity, limiting its redeposition under these conditions.

36 - MATERIALS SCIENCE↗
NASA NTRS1979

Mathematical model investigation of long-term transport of ocean-dumped sewage sludge related to remote sensing

An existing, three-dimensional, Eulerian-Lagrangian finite-difference model was modified and used to examine the transport processes of dumped sewage sludge in the New York Bight. Both in situ and laboratory data were utilized in an attempt to approximate model inputs such as mean current speed, horizontal diffusion coefficients, particle size distributions, and specific gravities. The results presented are a quantitative description of the fate of a negatively buoyant sewage sludge plume resulting from continuous and instantaneous barge releases. Concentrations of the sludge near the surface were compared qualitatively with those remotely sensed. Laboratory study was performed to investigate the behavior of sewage sludge dumping in various ambient density conditions.

Kuo, C. Y.↗
NASA NTRS1993

Comment on 'Ionospheric evidence of hot oxygen in the upper atmosphere of Venus'

The conclusion of Mahajan et al. (1992) that 'the existence of O(+) as dominant at (Venusian) ionopause altitudes in excess of 500-1000 km can only be explained if atomic oxygen is the major neutral constituent' is argued to be incorrect. It is suggested that at a transition region of about 200 km, thermal atomic oxygen is the dominant neutral gas, and hot oxygen is a minor species; thus the O(+) to H(+) ratio at high altitudes is not an indicator of the presence of hot oxygen at these altitudes. A 1D model for H(+) and O(+) appropriate for the dayside ionosphere of Venus shows that within hot atomic oxygen density values from 1000 to 10 exp 6/ cu cm at 150 km, the calculated H(+) and O(+) densities did not change in any meaningful way, because the hot oxygen population remained a minor neutral constituent below 200 km, which is the approximate height of the transition between chemical and diffusive equilibrium conditions for the ions.

Nagy, Andrew F.↗
NASA NTRS1994

Gamma-ray constraints on supernova nucleosynthesis

Gamma-ray spectroscopy holds great promise for probing nucleosynthesis in individual supernova explosions via short-lived radioactivity, and for measuring current global Galactic supernova nucleosynthesis with longer-lived radioactivity. It was somewhat surprising that the former case was realized first for a Type II supernova, when both Co-56 and Co-57 were detected in SN 1987A. These provide unprecedented constraints on models of Type II explosions and nucleosynthesis. Live Al-26 in the Galaxy might come from Type II supernovae, and if it is eventually shown to be so, can constrain massive star evolution, supernova nucleosynthesis, and the Galactic Type II supernova rate. Type Ia supernovae, thought to be thermonuclear explosions, have not yet been detected in gamma-rays. This is somewhat surprising given current models and recent Co-56 detection attempts. Ultimately, gamma-ray measurements can confirm their thermonuclear nature, probe the nuclear burning conditions, and help evaluate their contributions to Galactic nucleosynthesis. Type Ib/c supernovae are poorly understood. Whether they are core collapse or thermonuclear events might be ultimately settled by gamma-ray observations. Depending on details of the nuclear processing, any of these supernova types might contribute to a detectable diffuse glow of Fe-60 gamma-ray lines. Previous attempts at detection have come very close to expected emission levels. Remnants of any type of age less that a few centuries might be detectable as individual spots of Ti-44 gamma-ray line emission. It is in fact quite surprising that previous surveys have not discovered such spots, and the constraints on the combination of nucleosynthesis yields and supernova rates are very interesting. All of these interesting limits and possibilities mean that the next mission, International Gamma-Ray Astrophysics Laboratory (INTEGRAL), if it has sufficient sensitivity, is very likely to lead to the realization of much of the great potential of gamma-ray spectroscopy for understanding supernovae.

Leising, Mark D.↗
NASA NTRS1999

Determination of Creep Behavior of Thermal Barrier Coatings Under Laser Imposed High Thermal and Stress Gradient Conditions

A laser sintering/creep technique has been established to determine the creep behavior of thermal barrier coatings under steady-state high heat flux conditions. For a plasma sprayed zirconia-8 wt. % yttria coating, a significant primary creep strain and a low apparent creep activation energy were observed. Possible creep mechanisms involved include stress induced mechanical sliding and temperature and stress enhanced cation diffusion through the splat and grain boundaries. The elastic modulus evolution, stress response, and total accumulated creep strain variation across the ceramic coating are simulated using a finite difference approach. The modeled creep response is consistent with experimental observations.

Zhu, Dongming↗
NASA NTRS1995

The neutral oxygen spectrum. 2: Pumping by hydrogen Lyman-beta under the optically thin condition: A first application to the classical novae

A calculation, employing a detailed model of neutral oxygen, is carried out to give fluorescent line intensities expected in a long-proposed photoexcitation by accidental resonance (PAR) process in which hydrogen Lyman-beta photoexcites the oxygen spectrum. The results pertain to the optically thin case but provide an upper limit to the fluorescent intensities which can be attained. They are applied to analyze line ratios involving the strong 8446 A line observed in classical novae during the diffusion-enhanced and Orion phases. Operation of the PAR process in the novae is verified. It is found that photoexcitation rates in the ejecta reach values greater than 0.1/sec, corresponding to hydrogen Lyman-beta radiation field intensities greater than 1250 ergs/cm/sec/sr.

Kastner, S. O.↗
NASA NTRS1987

Monitoring biological impacts of space shuttle launches from Vandenberg Air Force Base: Establishment of baseline conditions

Space shuttle launches produce environmental impacts resulting from the formation of an exhaust cloud containing hydrogen chloride aerosols and aluminum oxide particulates. Studies have shown that most impacts occur near-field (within 1.5 km) of the launch site while deposition from launches occurs far-field (as distant as 22 km). In order to establish baseline conditions of vegetation and soils in the areas likely to be impacted by shuttle launches from Vandenberg Air Force Base (VAFB), vegetation and soils in the vicinity of Space Launch Complex-6 (SLC-6) were sampled and a vegetation map prepared. The areas likely to be impacted by launches were determined considering the structure of the launch complex, the prevailing winds, the terrain, and predictions of the Rocket Exhaust Effluent Diffusion Model (REEDM). Fifty vegetation transects were established and sampled in March 1986 and resampled in September 1986. A vegetation map was prepared for six Master Planning maps surrounding SLC-6 using LANDSAT Thematic Mapper imagery as well as color and color infrared aerial photography. Soil samples were collected form the 0 to 7.5 cm layer at all transects in the wet season and at a subsample of the transects in the dry season and analyzed for pH, organic matter, conductivity, cation exchange capacity, exchangeable Ca, Mg, Na, K, and Al, available NH3-N, PO4-P, Cu, Fe, Mn, Zn, and TKN.

Schmaizer, Paul A.↗
NASA NTRS1990

Influence of convection on microstructure

In eutectic growth, as the solid phases grow they reject atoms to the liquid. This results in a variation of melt composition along the solid/liquid interface. In the past, mass transfer in eutectic solidification, in the absence of convection, was considered to be governed only by the diffusion induced by compositional gradients. However, mass transfer can also be generated by a temperature gradient. This is called thermotransport, thermomigration, thermal diffusion or the Soret effect. A theoretical model of the influence of the Soret effect on the growth of eutectic alloys is presented. A differential equation describing the compositional field near the interface during unidirectional solidification of a binary eutectic alloy was formulated by including the contributions of both compositional and thermal gradients in the liquid. A steady-state solution of the differential equation was obtained by applying appropriate boundary conditions and accounting for heat flow in the melt. Following that, the average interfacial composition was converted to a variation of undercooling at the interface, and consequently to microstructural parameters. The results obtained show that thermotransport can, under certain circumstances, be a parameter of paramount importance.

Wilcox, William R.↗
NASA NTRS2008

Extraction of Thermal Performance Values from Samples in the Lunar Dust Adhesion Bell Jar

A simulation chamber has been developed to test the performance of thermal control surfaces under dusty lunar conditions. The lunar dust adhesion bell jar (LDAB) is a diffusion pumped vacuum chamber (10-8 Torr) built to test material samples less than about 7 cm in diameter. The LDAB has the following lunar dust stimulant processing capabilities: heating and cooling while stirring in order to degas and remove absorbed water; RF air-plasma for activating the dust and for organic contaminant removal; RF H/He-plasma to simulate solar wind; dust sieving system for controlling particle sizes; and a controlled means of introducing the activated dust to the samples under study. The LDAB is also fitted with an in situ Xe arc lamp solar simulator, and a cold box that can reach 30 K. Samples of thermal control surfaces (2.5 cm diameter) are introduced into the chamber for calorimetric evaluation using thermocouple instrumentation. The object of this paper is to present a thermal model of the samples under test conditions, and to outline the procedure to extract the absorptance, emittance, and thermal efficiency from the pristine and sub-monolayer dust covered samples

Gaier, James R.↗