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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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NASA NTRSDate not supplied

Application of an Affine Nonlinear Galerkin Reduced-order Model to Compressible Fluid Flows

Galerkin reduced-order models (ROMs) often struggle to accurately capture multiscale fluid physics in challenging flow regimes such as flows experiencing compressibility effects. This in part stems from the global nature of both the basis construction problem and the spectral formulation itself. In this work, a multi-basis ROM is developed in an affine space based on proper orthogonal decomposition (POD) by projecting the full Navier-Stokes equations expressed in terms of the specific volume, velocity, and pressure primitive variables. The model is applied to high-fidelity numerical simulation datasets obtained for a canonical compressible flow configuration: the flow over a backward facing step at different subsonic Mach numbers. It is observed that application of an eigenvalue reassignment (ER) stabilization method is required to avoid early divergence of the ROM predictions for this configuration in the three Mach numbers tested. The sensitivity of the POD-ROM results to the choice of parameters in the stabilization algorithm is discussed.

reduced-order model↗
NASA NTRS2002

Astrobiology: A Roadmap for Charting Life in the Universe

Astrobiology is the study of the origin, evolution and distribution of life in the universe. It provides a biological perspective to many areas of NASA research. It links such endeavors as the search for habitable planets, exploration missions to Mars and the outer Solar System, efforts to understand the origins and early evolution of life, and charting the potential of life to adapt to future challenges, both on Earth and in space. Astrobiology addresses the following three basic questions, which have been asked in some form for generations. How does life begin and evolve? Does life exist elsewhere in the universe? What is future of life on Earth and beyond? The NASA Astrobiology Roadmap provides guidance for research and technology development across several NASA Enterprises: Space Science, Earth Science, and the Human Exploration and Development of Space. The Roadmap is formulated in terms of eight Science Goals that outline key domains of investigation that might require perhaps decades of effort to consolidate. For each of these goals, Science Objectives outline more specific high priority near-term efforts for the next three to five years. These twenty objectives will be integrated with NASA strategic planning.

DesMarais, David J.↗
NASA NTRS2010

Comparison of Comet Enflow and VA One Acoustic-to-Structure Power Flow Predictions

Comet Enflow is a commercially available, high frequency vibroacoustic analysis software based on the Energy Finite Element Analysis (EFEA). In this method the same finite element mesh used for structural and acoustic analysis can be employed for the high frequency solutions. Comet Enflow is being validated for a floor-equipped composite cylinder by comparing the EFEA vibroacoustic response predictions with Statistical Energy Analysis (SEA) results from the commercial software program VA One from ESI Group. Early in this program a number of discrepancies became apparent in the Enflow predicted response for the power flow from an acoustic space to a structural subsystem. The power flow anomalies were studied for a simple cubic, a rectangular and a cylindrical structural model connected to an acoustic cavity. The current investigation focuses on three specific discrepancies between the Comet Enflow and the VA One predictions: the Enflow power transmission coefficient relative to the VA One coupling loss factor; the importance of the accuracy of the acoustic modal density formulation used within Enflow; and the recommended use of fast solvers in Comet Enflow. The frequency region of interest for this study covers the one-third octave bands with center frequencies from 16 Hz to 4000 Hz.

Grosveld, Ferdinand W.↗
NASA NTRS2022

Nutrient Limitation Predisposes A Cultivate of Burkholderia Contaminans From the ISS Water Processor Assembly to Biofilm Formation Under Simulated Microgravity.

The International Space Station (ISS) Water Processor Assembly (WPA) experiences intermittent dormancy between water recycling events thus promoting biofilm formation within the system. In this work we aimed to gain a deeper understanding of the impact of nutrient limitation on bacterial growth and biofilm formation under microgravity in support of biofilm mitigation efforts in exploration water recovery systems. A representative species of bacteria that is commonly cultured from the ISS WPA was cultured in an WPA influent water ersatz formulation tailored for microbiology studies. Burkholderia contaminans was cultured under a simulated microgravity (SµG) treatment in a vertically rotating high-aspect rotating vessel (HARV), with a rotating control (R) in the horizontal plane at the determined optimal rpm of 15 along with a stationary (S) control. At different time points, the bacterial culture and ersatz were harvested for bacterial counts, transcriptomic and nutrient content analyses. Under the test conditions, the culture under SµG treatment consumed the essential nutrients faster than the R and S control cultures in the early stage of growth, thus approaching a nutrient limited growth condition earlier than the controls. The rapid uptake and subsequent depletion of essential nutrients was further illustrated in the transcriptomic response of the SµG culture when compared to the transcriptomic response of the R and S control conditions. The observed starvation response may serve as one element to explain a moderate enhancement of biofilm formation in the SµG treatment. One implication of this investigation is that biofilm mitigation in the ISS environment could be supported by ensuring a steady flow of water as a vehicle for essential nutrients within the WPA to avoid complete consumption which occurs in times of no flow lending to undesired biofilm formation.

Angie Diaz↗
NASA NTRS1996

Waveform Perturbations os Spherical Transiet Waves Propagating in a Random Medium

Of those aspects of sonic-boom propagation that are not yet fully understood, one of the more important is that which relates to the perturbations of the waveform. This phenomenon, which arises also in connection with the propagation of other types of transient waves in real media, generally take the form, in the case of sonic-boom N-waves, of a random high-frequency structure (sometimes called fine structure) that is most prominent in the regions immediately behind each of the shocks. The perturbations in those regions can be large, occasionally attaining magnitudes comparable to that of th incident wave itself. Such magnitudes, in combination with the high-frequency character of the perturbations, can lead to a considerable increase in the perceived noisiness of the sonic boom. Waveform perturbations are consequently an important factor as regards the question of sonic-boom acceptability. On the basis of observations, and some early theoretical studies, it is now generally accepted that perturbations of sonic-boom waveforms are a manifestation of the effect on the propagating wave of relatively small-scale variations in the acoustic properties of the atmosphere- variations that are usually associated with turbulence. Although the mechanism underlying perturbations of sonic-boom waveforms seems thus to be well understood, no fully-satisfactory theory of such perturbations has emerged. Indeed, even for the relatively simple case of an incident step-function pulse, no theory of waveform perturbations, formulated in a realistic three-dimensional context, has been advanced that is valid in the region of strongest perturbations; viz., the region immediately behind, and including, the wave front. The work reported herein represents an attempt to develop such a theory.

Wenzel, Alan R.↗
NASA NTRS2018

Physical, Chemical, and Petrological Characteristics of Chondritic Materials and Their Relationships to Small Solar System Bodies: Chapter - 2

Chondrite materials with varying abundances of volatile-bearing phases are expected at the destinations for the asteroid sample-return missions Hayabusa2 and OSIRIS-REx. The targets of the missions are 162173 (1999 JU3) Ryugu and 101955 (1999 RQ36) Bennu. Spectroscopic analyses of these asteroids suggest that their surface materials are related to types 1 and 2 carbonaceous chondrites. Some studies suggest that the parent bodies of these chondrites may have also experienced some thermal and/or shock metamorphism. The physical properties of boulders at asteroid surfaces and fine particles in asteroid regoliths are consequences of the diverse processes that fragmented them, mobilized them, and redeposited them in unique accumulations. Sample-return missions are likely to encounter a broad range of carbonaceous chondrite (CC)-like materials, to which aqueous alteration, thermal, and shock metamorphism imparted changes affecting their sub-micron- to meter-scale physical properties. Consequently, implementation of scale-dependent analytical techniques to the study of the chemical, physical, and geotechnical characteristics of these CC-like materials is fundamental to safe mission operations, sample selection, and return. However, most of the available knowledge for informing and formulating expectations about regolith processes, products, and properties on carbonaceous small bodies comes from missions that studied anhydrous (e.g., Itokawa studied by Hayabusa) and/or much larger asteroids (e.g., Vesta studied by Dawn). No previous mission is likely directly relevant to small ice-free carbonaceous NEOs 162173 Ryugu or 101955 Bennu, although the Rosetta Spaceraft performed a flyby of the large asteroid Lutetia which has variously been classified as M and C type (Pätzold et al., 2011). Carbonaceous chondrites carry the best record of the history, distribution, and activity of water in the early solar system. Ordinary and Enstatite chondrites carry only partial records, but these are still critical to understanding the full story. We will describe the records of water-rock interactions on asteroids, as recorded in these meteorites, with particular emphasis on the timing, nature, settings, and fluid compositions. An integral part of this story is the rare, but fortunate, preservation of actual early solar system water as aqueous fluid inclusions.

Zolensky, Michael E.↗
NASA NTRSDate not supplied

HyTEC Hybrid Thermally Efficient Core

As part of the NASA Advanced Air Vehicles Program (AAVP), a new project is being formulated called Hybrid Thermally Efficient Core (HyTEC) in which NASA intends to accelerate the development of small turbofan engine core technologies, culminating in an advanced core demonstration in the 2026 timeframe. NASA Glenn Research Center plans to issue a NASA Research Announcement (NRA) for HyTEC Small Core Technology Demonstration, in preparation the HyTEC Project is holding an industry day February 24, 2021. The HyTEC goal is to demonstrate increased thermal efficiency with integrated high power-density core engine technologies achieving a 5- to 10-percent fuel burn benefit, versus 2020 best in class, for early 2030s entry into service (EIS) single-aisle aircraft. In order to accomplish this, NASA intends to collaborate with industry in a cost sharing arrangement on key technologies that NASA can accelerate to strengthen the US industry position on highly efficient, power dense small cores for a future single aisle aircraft.

Anthony Nerone↗
NASA NTRS2019

Innovative Approaches to Using the International Space Station as a Mars Transit Analog

Human research on the International Space Station (ISS) crew has made significant advances in understanding of the effects of physiology on human health in space missions. However, ISS has not been as suitable for research on other hazards of human spaceflight such as isolation and communications delay. NASA recently completed a special assessment of whether modifications could be made to operations or facilities so that ISS could be used more effectively as an analog to simulate long-duration crew missions beyond low earth orbit. A cross-disciplinary team met to identify concept of operations, trade spaces, challenges, and opportunities to making ISS more operationally relevant as a Mars transit mission analog, and the results and implementation plans are summarized in this manuscript. In addition to the use case of 12-month missions (already in planning by the NASA ISS Program to bound expected Mars transit durations), three new use cases where ISS could provide valuable high-fidelity experience were identified. (1) Testing of operations procedures and medical care could be enhanced by demonstrating crew handling a simulated medical event in microgravity, autonomously, and with significant communications delay. (2) Isolation and confinement effects of deep space transit could be studied on ISS to validate current habitable volume requirements for Mars transit as well as provide context for evaluating the results of the extensive ground-based simulations in HERA and NEK. A trade study of possible operational and hardware changes that would make ISS applicable to these use cases was completed. (3) Surface operations after the physiological deconditioning of a long transit could be conducted to validate crew ability to perform critical ground tasks after 6-month Mars transit and aid in conceptual design of Mars surface element architectures. Each of the case studies includes a trade space between operational impacts on nominal ISS activities and degree of fidelity. A phased approach to implementation means that several "quick start" activities can be done in 2019-2020 at the same time as planning continues for more complex exploration analog options beginning as early as 2022. The team determined that many of these quick-start tasks could be done with available assets, entirely independent of other exploration system development timelines (such as Orion, Space Launch System). The consideration of the full suite of human spaceflight capabilities in the lunar vicinity can also be included as each step in human exploration serves as a simulation opportunity for some aspect of subsequent missions. Further discussions of options with the international community are critical for considering the benefits as well as impacts of simulation activities on ISS, as well as to better formulate future mission architectures.

Robinson, Julie A.↗
NASA NTRS1989

Combined control-structure optimization

An approach for combined control-structure optimization keyed to enhancing early design trade-offs is outlined and illustrated by numerical examples. The approach employs a homotopic strategy and appears to be effective for generating families of designs that can be used in these early trade studies. Analytical results were obtained for classes of structure/control objectives with linear quadratic Gaussian (LQG) and linear quadratic regulator (LQR) costs. For these, researchers demonstrated that global optima can be computed for small values of the homotopy parameter. Conditions for local optima along the homotopy path were also given. Details of two numerical examples employing the LQR control cost were given showing variations of the optimal design variables along the homotopy path. The results of the second example suggest that introducing a second homotopy parameter relating the two parts of the control index in the LQG/LQR formulation might serve to enlarge the family of Pareto optima, but its effect on modifying the optimal structural shapes may be analogous to the original parameter lambda.

Salama, M.↗
NASA NTRS1988

Toward an understanding of global change: Initial priorities for US contributions to the International Geosphere-Biosphere Program

A limited number of high-priority research initiatives are recommended for early implementation as part of the U.S. contribution to the preparatory phase of the International Geosphere-Biosphere Program. The recommendations are based on the committee's analysis of the most critical gaps in the scientific knowledge needed to understand the changes that are occurring in the earth system not being addressed by existing programs. The report articulates a number of important key issues and interactions that characterize global change in the geosphere-biosphere system on time scales of decades to centuries; identifies the knowledge that is the most urgently needed to improve understanding of those issues and interactions; and formulates initial priorities for initial U.S. contributions to the IGBP, recognizing the contributions of other ongoing and proposed programs.

Source record↗
NASA NTRS1994

Equations for Estimating the Strength of TV Signals Scattered by Wind Turbines

During the late 1970's and early 1980's, concerns about the potential interference of wind turbine generators with electromagnetic communication signals led to a series of research studies, both in the laboratory and in the field, conducted by the staff of the University of Michigan Radiation Laboratory. These studies were sponsored by organizations such as the U.S. Department of Energy, the Solar Energy Research Institute, and private developers of wind power stations. Research objectives were to identify the mechanisms by which wind turbines might adversely affect communication signals, estimate the severity of these effects for different types of signals (e.g. television, radio, microwave, and navigation), and formulate mathematical models with which to predict the sizes of potential interference zones around wind turbines and wind power plants. This work formed the basis for preliminary standards on assessing electromagnetic interference (EMI) by wind turbines. With the current renewal of interest in wind energy projects, it is appropriate that the many experimental and analytical aspects of this pioneering work be reviewed and correlated. The purpose of this study is to combine test data and theory from previously published and unpublished research reports into a unified and consistent set of equations which are useful for estimating potential levels of television interference from wind turbines. To be comprehensive, these equations will include both horizontal-axis and vertical-axis wind turbines (HAWT's and VAWT's), blade configuration parameters (e.g. number, size, material, twist, and coning), signal frequency and power, and directional characteristics of the receiving antenna. The approach that is followed in this report is as follows. First, some basic equations that describe electromagnetic signals with interference are presented without detailed derivations, since the latter are available in the references. Minor changes in terminology are made for purposes of consistency. Next, the concept of a signal scatter ratio is introduced, which defines the fraction of the signal impinging on a wind turbine that is scattered by its blades onto a nearby receiver. Equations from references are modified for the calculation of experimental scatter ratios (from measured signals containing interference) and idealized scatter ratios (from rotor characteristics and relative locations of the transmitter, the turbine, and the receiver). Experimental and idealized scatter ratios are then calculated and compared for 75 cases from the literature, in which TVI measurements were made around a variety of wind turbines. An empirical equation is then defined for estimating the probability that an actual scatter ratio will differ from an idealized ratio by a given amount. Finally a sample calculation of the size of a potential TV interference zone around a hypothetical wind power station is presented.

Spera, David A.↗
NASA NTRS2003

Estimating Terrestrial Carbon Exchange from Space: How Often and How Well?

Data from a new space mission measuring integrated light-use efficiency could provide a breakthrough in understanding of global carbon, water, and energy dynamics, and greatly improve the accuracy of model predictions for terrestrial carbon cycles and climate. Over the past decade, Gamon and others have shown that changes in photo-protective pigments are sensitive indicators of declines in light-use efficiency of plants and plant canopies. The requirements for integrated diurnal measurements from space need to be defined, before a space mission can be formulated successfully using this concept. We used towerbased CO 2 flux data as idealized proxies for remote measurements, examining their sampling properties. Thousands of half-hourly CO 2 flux measurements are needed before their average begins to converge on an average annual net CO 2 exchange. Estimates of daily integrated fluxes (i.e., diurnal curves) are more statistically efficient, especially if the spacing between measured days is quasiregular, rather than random. Using a few measurements per day one can distinguish among days with different net CO 2 exchanges. Fluxes sampled between mid-morning to mid-afternoon are more diagnostic than early morning or late afternoon measurements. Similar results (correlation >0.935) were obtained using 2 measurements per day with high accuracy ([:plusmn:]5%), 3 measurements per day with medium accuracy ([:plusmn:] 10%), or 5 measurements per day at lower accuracy ([:plusmn:]20%). An observatory in a geosynchronous or near-geosynchronous orbit could provide appropriate observations, as could a multi-satellite constellation in polar orbits, but there is a potential trade-off between the required number of observations per day and quality of each observation.

Knox, Robert G.↗
NASA NTRS1981

Concept definition and aerodynamic technology studies for single-engine V/STOL fighter/attack aircraft

The results obtained in the early stages of a research program to develop aerodynamic technology for single-engine V/STOL fighter/attack aircraft projected for the post-1990 period are summarized. This program includes industry studies jointly sponsored by NASA and the Navy. Four contractors have identified promising concepts featuring a variety of approaches for providing propulsive lift. Vertical takeoff gross weights range from about 10,000 to 13,600 kg (22,000 to 30,000 lb). The aircraft have supersonic capability, are highly maneuverable, and have significant short takeoff overload capability. The contractors have estimated the aerodynamics and identified aerodynamic uncertainties associated with their concepts. Wind-tunnel research programs will be formulated to investigate these uncertainties. A description of the concepts is emphasized.

Nelms, W. P.↗
NASA NTRS2002

NASA 2nd Generation RLV Program Introduction, Status and Future Plans

The Space Launch Initiative (SLI), managed by the Second Generation Reusable Launch Vehicle (2ndGen RLV) Program, was established to examine the possibility of revolutionizing space launch capabilities, define conceptual architectures, and concurrently identify the advanced technologies required to support a next-generation system. Initial Program funds have been allocated to design, evaluate, and formulate realistic plans leading to a 2nd Gen RLV full-scale development (FSD) decision by 2006. Program goals are to reduce both risk and cost for accessing the limitless opportunities afforded outside Earth's atmosphere fo civil, defense, and commercial enterprises. A 2nd Gen RLV architecture includes a reusable Earth-to-orbit launch vehicle, an on-orbit transport and return vehicle, ground and flight operations, mission planning, and both on-orbit and on-the-ground support infrastructures All segments of the architecture must advance in step with development of the RLV if a next-generation system is to be fully operational early next decade. However, experience shows that propulsion is the single largest contributor to unreliability during ascent, requires the largest expenditure of time for maintenance, and takes a long time to develop; therefore, propulsion is the key to meeting safety, reliability, and cost goals. For these reasons, propulsion is SLI's top technology investment area.

Dumbacher, Dan L.↗
NASA NTRS2010

2010 JPC Abstract: Ares I First Stage Propulsion System Status

In November 2005, NASA created the Constellation Program to develop an entirely new fleet of spacecraft to include the Ares I Crew Launch Vehicle and Ares V Cargo Launch vehicles. This mission architecture included the Orion capsule (which would be used to transport astronauts to low-Earth orbit and beyond), the Altair lunar lander, and an Earth departure stage. The Ares First Stage Team has made significant progress on the design of a propulsion system to meet the objectives of the Constellation Program. Work on a first stage element propulsion system capable of lofting a new fleet of spacecraft is well underway. To minimize technical risks and development costs, the Solid Rocket Boosters (SRBs) of Shuttle served as a starting point in the design of a new motor that would meet the requirements of those new vehicles. This new propulsive element will provide greater total impulse utilizing a fifth segment to loft a safer, more powerful fleet of space flight vehicles. Performance requirements, basic architecture, and obsolescence issues were all factors in determining the new first stage element design and configuration. Early efforts focused on creating designs that would be capable of supporting the requisite loads and environments. While the motor casings are Shuttle legacy, because of Ares I s unique in-line configuration, the first stage will require entirely new forward structures (forward skirt, forward skirt extension, aeroshell, and frustum) and a modified systems tunnel. The use of composites facilitated a change in the geometry, which in turn afforded the ability to focus strength where it was needed without additional mass. The Ares First Stage rocket motor casting tooling was designed and built to achieve a propellant grain geometry that produces the specific required ballistic profile. The new propellant formulation is a polybutadiene acrylonitrile (PBAN) copolymer, which has been modified to attain the desired burn rate and retain adequate tailoring capability.

Priskos, Alex S.↗
NASA NTRS1982

Incompressible Navier-Stokes and parabolized Navier-Stokes solution procedures and computational techniques

Recent developments with finite-difference techniques are emphasized. The quotation marks reflect the fact that any finite discretization procedure can be included in this category. Many so-called finite element collocation and galerkin methods can be reproduced by appropriate forms of the differential equations and discretization formulas. Many of the difficulties encountered in early Navier-Stokes calculations were inherent not only in the choice of the different equations (accuracy), but also in the method of solution or choice of algorithm (convergence and stability, in the manner in which the dependent variables or discretized equations are related (coupling), in the manner that boundary conditions are applied, in the manner that the coordinate mesh is specified (grid generation), and finally, in recognizing that for many high Reynolds number flows not all contributions to the Navier-Stokes equations are necessarily of equal importance (parabolization, preferred direction, pressure interaction, asymptotic and mathematical character). It is these elements that are reviewed. Several Navier-Stokes and parabolized Navier-Stokes formulations are also presented.

Rubin, S. G.↗
NASA NTRS2000

Supplier's Status for Critical Solid Propellants, Explosive, and Pyrotechnic Ingredients

In the early 1970's a program was initiated at the Naval Surface Warfare Center/Indian Head Division (NSWC/IHDIV) to address the well-known problems associated with availability and suppliers of critical ingredients. These critical ingredients are necessary for preparation of solid propellants and explosives manufactured by the Navy. The objective of the program was to identify primary and secondary (or back-up) vendor information for these critical ingredients, and to develop suitable alternative materials if an ingredient is unavailable. In 1992 NSWC/IHDIV funded Chemical Propulsion Information Agency (CPIA) under a Technical Area Task (TAT) to expedite the task of creating a database listing critical ingredients used to manufacture Navy propellant and explosives based on known formulation quantities. Under this task CPIA provided employees that were 100 percent dedicated to the task of obtaining critical ingredient suppliers information, selecting the software and designing the interface between the computer program and the database users. TAT objectives included creating the Explosive Ingredients Source Database (EISD) for Propellant, Explosive and Pyrotechnic (PEP) critical elements. The goal was to create a readily accessible database, to provide users a quick-view summary of critical ingredient supplier's information and create a centralized archive that CPIA would update and distribute. EISD funding ended in 1996. At that time, the database entries included 53 formulations and 108 critical used to manufacture Navy propellant and explosives. CPIA turned the database tasking back over to NSWC/IHDIV to maintain and distribute at their discretion. Due to significant interest in propellant/explosives critical ingredients suppliers' status, the Propellant Development and Characterization Subcommittee (PDCS) approached the JANNAF Executive committee (EC) for authorization to continue the critical ingredient database work. In 1999, JANNAF EC approved the PDCS panel task. This paper is designed to emphasize the necessity of maintaining a JANNAF community supported database, which monitors PEP critical ingredient suppliers' status. The final product of this task is a user friendly, searchable database that provides a quick-view summary of critical ingredient supplier's information. This database must be designed to serve the needs of JANNAF and the propellant and energetic commercial manufacturing community as well. This paper provides a summary of the type of information to archive each critical ingredient.

Sims, B. L.↗
NASA NTRS2015

Solid State Ultracapacitor

NASA analyzes, tests, packages, and fabricates electrical, electronic, and electromechanical (EEE) parts used in space vehicles. One area that NASA wishes to advance is energy storage and delivery. Currently, space vehicles use rechargeable batteries that utilize silver zinc or lithium ion electrochemical processes. These current state-of-the-art rechargeable batteries cannot be rapidly charged, contain harmful chemicals, and suffer from early wear-out mechanisms. A solid state ultracapacitor is an EEE part that offers significant advantages over current electrochemical and electrolytic devices. The objective of this research is to develop an internal barrier layer ultracapacitor (IBLC) using novel dielectric materials as a battery replacement with a focus on these advantages: longer life, lower mass-toweight ratio, rapid charging, on-demand pulse power, improved on-pad standby time without maintenance, and environmental friendliness. The approach is unique in two areas. A deposition technique is used that has been shown to produce a more uniformly coated nanoparticle than sol-gel, which has resulted in colossal permittivities. These particles are then distributed in an ink formulation developed at NASA Marshall Space Flight Center (MSFC) and deposited utilizing a 3D aerosol jet technique. This additive manufacturing technique controls layer thickness, resulting in extremely large capacitance and energy density.

Rolin, Terry D.↗