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At least 325 records · Page 18

All sources NASA NTRS DOE OSTI

DOE OSTI2019

Use of Hygrothermal Models for Understanding Water Transport in Corrosion Under Insulation Applications

Thermal insulation is used in operating facilities to conserve heat and protect against freezing amongst others. A consequence of insulating the equipment is the necessity to manage the introduced threat of corrosion under insulation (CUI). For CUI to occur, water and oxygen must enter and migrate through the insulation to reach the external surface of the equipment. The water transport characteristics are dependent on several factors such as type of insulation, type of jacketing, equipment operating temperature, external weather, water entry/leakage rate and cyclic service. In hot piping, there are competing water transport characteristics, as in water vapor moves outwards away from the equipment as water enters insulation. Knowing the water transport and the parameters that influence the time of wetness at the metal surface helps in understanding conditions favoring CUI.The use of transient hygrothermal models for moisture control is well established in the building insulation design codes and standards. The building designs naturally shed the liquid water to minimize entry and facilitate vapor management so that moisture doesn’t accumulate within building. Several building industry hygrothermal models have been developed and are available for commercial use. One such commercial model has been used to understand water transport in a CUI application. The case study involves evaluation of piping and equipment installed with a closed cell polyurethane insulation. The hygrothermal model provided insights on the parameters influencing the time of wetness and the ease of water escaping the equipment-insulation-jacketing system.

Venkateswaran, Sai P.↗

DOE OSTI2019

ELECTRICAL BREAKDOWN STRENGTH AND AC WITHSTAND IN HARVESTED EPR INSULATIONS FOR NUCLEAR POWER PLANTS

While the operating voltages for some instrument and control (I&C) cables can be greater than 4 kV to operate pumps, controls, and provide auxiliary power, the operating voltage for most I&C cables is near 600 V. Although the electrical stress is not nearly as high in the insulation of these cables, an ac withstand two and one-half times greater than the operating voltage after a simulated design basis exposure (DBE) has been used in environmental qualification (EQ) to determine the ability of an insulation to meet a 40-year lifetime at an operating voltage. While multiple cable lengths greater than 10 feet are needed to replicate this EQ, systematic measurement of the electrical insulation strength in harvested cable insulations can be beneficial to better understand the remaining useful life of the insulation. This understanding can only be realized through systematic comparison to some level of DBE, and electrical insulation strength measurement can provide a baseline for comparison with other mechanical, chemical, and electrical characterizations that have been utilized. Accelerated aging of two types of ethylene propylene rubber (EPR) insulations from harvested cables was carried out, and the electrical breakdown strength and indenter modulus for both insulations were determined. Results showed that degradation of electrical breakdown strength occurred in only one type of BIW insulation and that this degradation did track with that measured by indenter modulus. The methodology for using Weibull statistics for electrical breakdown strength relative to time to failure is discussed.

Duckworth, Robert↗

DOE OSTI2013

Excavationless Exterior Foundation Insulation Exploratory Study

Building science research supports installing exterior (soil side) foundation insulation as the optimal method to enhance the hygrothermal performance of new homes. With exterior foundation insulation, water management strategies are maximized while insulating the basement space and ensuring a more even temperature at the foundation wall. Controlling for bulk water, vapor, and wall temperature differential reduces the risk of rot and mold formation to insulation and building materials, thereby improving opportunities for structural integrity, indoor air quality, comfort, and energy efficiency. The intent of this study by the NorthernSTAR Building America Partnership team is to search for combinations of existing technologies that could enable a minimally invasive, cost-competitive, easily deployable method of upgrading soil-side foundation insulation in existing buildings. Currently, insulating foundation walls on the exterior side involves exposing the foundation wall using an excavator. Following excavation, these walls can be waterproofed, and are typically insulated with board foam in a process similar to new construction. This process is expensive and highly disruptive to the landscape and the homeowner. Also, barriers such as porches and sidewalks prevent trenching. An ideal approach would involve excavating a very narrow trench directly next to the foundation wall. Full-height foundation wall insulation might be desired, so the trenching technology should be able to dig to a depth of 7 or 8 ft. Because houses often have hardscape obstructions that are expensive to demolish and remove, the ideal technology would be capable of digging under at least some obstructions that would remain in place.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DOE OSTI2022

High temperature ceramic thermal insulation material

Flexible and lightweight thermal insulation materials with hierarchical microstructures are ubiquitous in thermal management and protection systems. Ceramic aerogels promise high-temperature thermal insulation but lack mechanical robustness, while the fibrous materials with excellent mechanical elasticity display modest thermal insulation. Here we describe flexible hierarchical superhydrophobic ceramic insulation nanocomposites through the densified architectured hierarchical nanostructures, radiative insulation coating, and interfacial cross-linking among composites. The lightweight flexible ceramic nanocomposites exhibit a density of 0.13 g/cm 3 , high-temperature fire resistance with thermal conductivity of 0.024 W/(m·K), and super-hydrophobicity with the water contact angle of 152°. The mechanical robustness and high-temperature thermal insulation of ceramic nanocomposites, together with its soundproof performance, shed light on the low-cost flexible insulation materials manufacturing with scalability for high-temperature thermal insulation applications under high mechanical loading conditions.

36 MATERIALS SCIENCE↗

DOE OSTI2018

Evaluation of the Energy-Efficiency of an Aerated Slurry-Infiltrated Mesh Building System with Biomass-Based Insulation

Experimental investigations and numerical analyses were conducted on the thermal attributes of a building system made with locally available structural and insulation materials. The structural material, which also offers some insulation qualities, is referred to as aerated slurry-infiltrated mesh. The insulation materials used in this building are based on biomass; the alternatives considered here include ground wood, shredded straw, and cellulose. Thermal conductivity tests were performed on aerated slurries of different bulk densities, and on the biomass-based insulation materials, some of which were prepared with different bulk densities. The competitive merits of the biomass-based indigenous insulation materials were assessed. The correlations between bulk density and thermal conductivity were evaluated and rationalized based on the prevalent mechanisms of heat transfer in different materials. The effects of temperature on the thermal conductivity of different biomass-based indigenous insulation materials were investigated. For wall insulation, a cost analysis was conducted in order to select the optimum insulation level. As a result, the thermal mass of the aerated slurry-infiltrated mesh building system was found to favor its energy-efficiency when compared with a similar wood building.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DOE OSTI2015

Mechanism and influencing factors on critical pulse width of oil-immersed polymer insulators under short pulses

The critical pulse width (τ{sub c}) is a pulse width at which the surface flashover threshold (E{sub f}) is equal to the bulk breakdown threshold (E{sub BD}) for liquid-polymer composite insulation systems, which is discovered by Zhao et al. [Annual Report Conference on Electrical Insulation and Dielectric Phenomena (IEEE Dielectrics and Electrical Insulation Society, Shenzhen, China, 2013), Vol. 2, pp. 854–857]. In this paper, the mechanism of τ{sub c} is interpreted in perspective of the threshold and the time delay (t{sub d}) of surface flashover and bulk breakdown, respectively. It is found that two changes appear as the pulse width decreases which are responsible for the existence of τ{sub c}: (1) E{sub BD} is lower than E{sub f}; (2) t{sub d} of bulk breakdown is shorter than t{sub d} of surface flashover. In addition, factors which have influences on τ{sub c} are investigated, such as the dielectric type, the insulation length, the dielectric thickness, the dielectrics configuration, the pulse number, and the liquid purity. These influences of factors are generalized as three types if τ{sub c} is expected to increase: (1) factors causing E{sub BD} to decrease, such as increasing the pulse number or employing a dielectric of lower E{sub BD}; (2) factors causing E{sub f} to increase, such as complicating the insulator's configuration or increasing the liquid purity; (3) factors causing E{sub BD} and E{sub f} to increase together, but E{sub f} increases faster than E{sub BD}, such as decreasing the dielectric thickness or the insulation length. With the data in references, all the three cases are verified experimentally. In the end, a general method based on τ{sub c} for solid insulation design is presented and the significance of τ{sub c} on solid insulation design and on solid demolition are discussed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

Design, construction, and testing of no-insulation small subscale solenoids for compact tokamaks

Fusion energy systems studies (FESS) for next-step devices based on the most promising magnetic configurations indicate that high magnetic fields and high current density for magnet coil systems may reduce device size and lower the cost. High current density and radiation resistant fusion magnets are particularly beneficial for low cost, low aspect ratio compact reactor designs such as Fusion Nuclear Science Facility (FNSF), Fusion Pilot Plant (FPP) of low-aspect ratio spherical tokamak (ST) or compact stellarators. Unlike typical high field magnets for nuclear magnetic resonance (NMR), magnetic resonance imaging (MRI), or high energy physics research applications, neutron irradiation damage to organic insulations in the coil winding pack is a critical issue for next generation fusion reactors where orders of magnitude higher neutron fluence than those in present experimental reactors such as ITER are expected. Moreover, a high coil winding pack current density is needed for high field magnets in low cost, compact radial build next step fusion reactors. The slow current charging time, however, is an issue in fully non-insulated coils. In this work, we present the design, construction and testing of subscale Nb3Sn solenoids, up to half the diameter of the central solenoid (CS) for National Spherical Torus Experiment (NSTX), with and without inter-layer insulation for enhancing radiation resistance while improving the winding pack current density and coil performance. The major radius for the NSTX/NSTX-Upgrade (reference for compact ST) is 0.854/0.934 meter, and 4.8 meters for FNSF. The magnetic field for NSTX/NSTX-U at the plasma center is 0.6/1 Tesla and 9 Tesla for FNSF. The inner diameter of the central solenoid coil is 0.2/0.4 meter for NSTX/NSTX-U and 1.2 meters for FNSF. The current charging and discharging behavior of the prototype solenoids was investigated to quantify performance advantages of a simplified coil fabrication without error-prone vacuum pressure impregnation (VPI) for the removal of epoxy organic insulation. Scalability of the no insulation concept for fusion can be addressed via engineered coating for novel insulation on contact resistance or intra-layer no insulations. Radiation resistance and coil winding efficiency were significantly improved in the no insulation coils for next step compact fusion reactors.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2024

Impact of Insulation Strategies of Cross-Laminated Timber Assemblies on Energy Use, Peak Demand, and Carbon Emissions

Cross-Laminated Timber (CLT) panels have many structural benefits but do not have much thermal resistance. We have developed a solution to insulate CLT structures that uses high-performance insulation panels that provide R-values up to R40/inch. The CLT panels are made of layers of wood laminates (three, five, seven or more). The solution replaces some of the wood laminates in the CLT production with the insulation panels in a staggered fashion so that the wood laminates maintain contact throughout the panel, ensuring the CLT panel’s structural integrity. The insulated CLT panels have factory-installed water-resistive barriers reducing the installation time by eliminating installing insulation and water-resistive barriers on site. Per simulations, the CLT/insulation panel achieved code-required insulation levels with commonly available insulation materials. The significance of the thermal mass of CLT/insulation hybrid building envelopes was quantified by comparing the whole building energy performance and peak demand of traditional low mass and CLT wall assemblies resulting in up to 7% reduction in peak demand for cooling in Knoxville, TN, in a multifamily building. Buildings contribute over 40 percent of carbon emissions. The proposed CLT/insulation hybrid building envelope addresses both operational and embodied carbon by having high thermal resistances due to the embedded insulation sections and eliminating the use of high embodied carbon materials such as steel and concrete. The carbon benefit is estimated.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DOE OSTI2019

Evidence of a gate-tunable Mott insulator in a trilayer graphene moiré superlattice

The Mott insulator is a central concept in strongly correlated physics and manifests when the repulsive Coulomb interaction between electrons dominates over their kinetic energy. Doping additional carriers into a Mott insulator can give rise to other correlated phenomena such as unusual magnetism and even high-temperature superconductivity. A tunable Mott insulator, where the competition between the Coulomb interaction and the kinetic energy can be varied in situ, can provide an invaluable model system for the study of Mott physics. Here we report the possible realization of such a tunable Mott insulator in a trilayer graphene heterostructure with a moiré superlattice. The combination of the cubic energy dispersion in ABC-stacked trilayer graphene and the narrow electronic minibands induced by the moiré potential leads to the observation of insulating states at the predicted band fillings for the Mott insulator. Moreover, the insulating states in the heterostructure can be tuned: the bandgap can be modulated by a vertical electrical field, and at the same time the electron doping can be modified by a gate to fill the band from one insulating state to another. Here, this opens up exciting opportunities to explore strongly correlated phenomena in two-dimensional moiré superlattice heterostructures.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2018

Determination and Assessment of Optimum Internal Thermal Insulation for Masonry Walls in Historic Multifamily Buildings

A large portion of existing building stock is comprised of load-bearing masonry buildings, particularly in the Midwest and on the East Coast, though such buildings are distributed across the US. Most of them have uninsulated walls or suffer from insufficient thermal insulation materials. These buildings are inseparable parts of the cultural, social, and economic characteristics of their cities. Due to heritage and preservation concerns, zoning, and space restrictions, they cannot be retrofitted with exterior insulation. Interior insulation must therefore be considered as an alternative. Lack of insulation directly results in energy waste as well as heat loss and gain. Furthermore, it adversely affects heating, ventilation, and air conditioning (HVAC) loads, equipment sizing, indoor air quality, and thermal comfort for residents. The objective of this study is to simulate and evaluate the effects of various internal thermal insulation materials and strategies on mass masonry load-bearing walls in multifamily buildings with attention to various variables and parameters. It not only addresses the energy performance and cost savings associated with an interior insulation retrofit, but also outlines other variables and parameters that are factors in the selection of optimum insulation material, including installations costs, payback periods, useful internal space loss, and options for the depth of the interior insulation retrofit. In conclusion, the audience for this paper is diverse: homeowners, contractors and remodelers, architects and designers, engineers, housing and preservation authorities, and more can benefit from understanding the results outlined in this study.

42 ENGINEERING↗

DOE OSTI2015

Suppression of surface charge accumulation on Al{sub 2}O{sub 3}-filled epoxy resin insulator under dc voltage by direct fluorination

Surface charge accumulation on insulators under high dc voltage is a major factor that may lead to the reduction of insulation levels in gas insulated devices. In this paper, disc insulators made of Al{sub 2}O{sub 3}-filled epoxy resin were surface fluorinated using a F{sub 2}/N{sub 2} mixture (12.5% F{sub 2}) at 50 °C and 0.1 MPa for different durations of 15 min, 30 min and 60 min. A dc voltage was applied to the insulator for 30 min and the charge density on its surface was measured by an electrostatic probe. The results revealed significant lower surface charge densities on the fluorinated insulators in comparison with the original one. Surface conductivity measurements indicated a higher surface conductivity by over three orders of magnitude after fluorination, which would allow the charges to transfer along the surface and thus may suppress their accumulation. Further, attenuated total reflection infrared analysis and surface morphology observations of the samples revealed that the introduction of fluoride groups altered the surface physicochemical properties. These structure changes, especially the physical defects reduced the depth of charge traps in the surface layer, which was verified by the measurement of energy distributions of the electron and hole traps based on the isothermal current theory. The results in this paper demonstrate that fluorination can be a promising and effective method to suppress surface charge accumulation on epoxy insulators in gas insulated devices.

36 MATERIALS SCIENCE↗

DOE OSTI2018

Insulator-metal transitions in the T phase Cr-doped and M 1 phase undoped VO 2 thin films

${\mathrm{VO}}_{2}$ exhibits several insulating phases (monoclinic $M1,M2$, and triclinic $T)$, and the study of these phases is important for understanding the true nature of the insulator-to-metal transition (IMT) in ${\mathrm{VO}}_{2}$. These insulating phases have small but discernible crystallographic differences in the vanadium chains forming the dimers. Peculiarities of the electron localizations in the dimerized chains for many of the probes such as NMR make it difficult to characterize the true character of these phases [T. J. Huffman et al., Phys. Rev. B 95, 075125 (2017); J. Pouget et al., Phys. Rev. B 10, 1801 (1974)]. We present structural, electrical, ultrafast-reflectivity, and electronic structure studies of the $T$ phase Cr-doped ${\mathrm{VO}}_{2}$ and the $M1$ phase pure ${\mathrm{VO}}_{2}$ thin films, both grown by pulsed laser deposition under identical conditions. An intermediate $M2$ structure is observed in the Cr-doped ${\mathrm{VO}}_{2}$, while the pure ${\mathrm{VO}}_{2}$ directly goes from the insulating monoclinic $M1$ structure to a metallic rutile $R$ structure, manifested by temperature-dependent Raman spectroscopy. Temperature-dependent electronic structure studies utilizing x-ray near-edge absorption spectroscopy reveal that all these insulating phases (monoclinic $M1$ and $M2$ and triclinic $T)$ have similar electronic structures which place these insulating phases into the list of Mott-Hubbard insulators. This is a first combined experimental report on the electronic structure of all the three insulating phases, monoclinic $M1,M2$, and triclinic $T$.

36 MATERIALS SCIENCE↗

DOE OSTI2018

Signatures of long-range-correlated disorder in the magnetotransport of ultrathin topological insulators

In an ultrathin topological insulator (TI) film, a hybridization gap opens in the TI surface states, and the system is expected to become either a trivial insulator or a quantum spin Hall insulator when the chemical potential is within the hybridization gap. Here we show, however, that these insulating states are destroyed by the presence of a large and long-range-correlated disorder potential, which converts the expected insulator into a metal. We perform transport measurements in ultrathin dual-gated topological insulator films as a function of temperature, gate voltage, and magnetic field, and we observe a metalliclike nonquantized conductivity, which exhibits a weak antilocalizationlike cusp at low magnetic fields and gives way to a nonsaturating linear magnetoresistance at large fields. We explain these results by considering the disordered network of electron- and hole-type puddles induced by charged impurities. We argue theoretically that such disorder can produce an insulator-to-metal transition as a function of increasing disorder strength, and we derive a condition on the band gap and the impurity concentration necessary to observe the insulating state. Finally, we explain the linear magnetoresistance in terms of strong spatial fluctuations of the local conductivity using both numerical simulations and a theoretical scaling argument.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2018

Electronic structure of negative charge transfer CaFeO 3 across the metal-insulator transition

In this work, we investigated the metal-insulator transition for epitaxial thin films of the perovskite CaFeO 3 , a material with a significant oxygen ligand hole contribution to its electronic structure. We find that biaxial tensile and compressive strain suppress the metal-insulator transition temperature. By combining hard x-ray photoelectron spectroscopy, soft x-ray absorption spectroscopy, and density functional calculations, we resolve the element-specific changes to the electronic structure across the metal-insulator transition. We demonstrate that the Fe sites undergo no observable spectroscopic change between the metallic and insulating states, whereas the O electronic configuration undergoes significant changes. This strongly supports the bond-disproportionation model of the metal-insulator transition for CaFeO 3 and highlights the importance of ligand holes in its electronic structure. By sensitively measuring the ligand hole density, however, we find that it increases by ~5–10% in the insulating state, which we ascribe to a further localization of electron charge on the Fe sites. Finally, these results provide detailed insight into the metal-insulator transition of negative charge transfer compounds and should prove instructive for understanding metal-insulator transitions in other late transition metal compounds such as the nickelates.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2015

Innovative Retrofit Insulation Strategies for Concrete Masonry Foundations

This study was designed to test a new approach for foundation insulation retrofits, with the goal of demonstrating improved moisture control, improved occupant comfort, and reduced heat loss. Because conducting experimental research on existing below-grade assemblies is very difficult, most of the results are based on simulations. The retrofit approach consists of filling open concrete block cores with an insulating material and adding R-10 exterior insulation that extends 1 ft below grade. The core fill is designed to improve the R-value of the foundation wall and increase the interior wall surface temperature, but more importantly to block convection currents that could otherwise increase moisture loads on the foundation wall and interior space. The exterior insulation significantly reduces heat loss through the most exposed part of the foundation and further increases the interior wall surface temperature. This improves occupant comfort and decreases the risk of condensation. Such an insulation package avoids the full-depth excavation necessary for exterior insulation retrofits, reduces costs, and eliminates the moisture and indoor air quality risks associated with interior insulation retrofits. Retrofit costs for the proposed approach were estimated at roughly half those of a full-depth exterior insulation retrofit.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DOE OSTI2016

Field Testing of an Unvented Roof with Fibrous Insulation, Tiles, and Vapor Diffusion Venting

BSC TO5 Task 2.5 Field Testing of an Un-vented Roof with Fibrous Insulation and Tiles - Winter Park, FL 32789 Field test data available for wood moisture contents, temperature, and relative humidity. Un-vented roofs (aka cathedral-ized attics) are an established presence in Florida residential building markets. These roofs are built with a layer of spray polyurethane foam (SPF) on the underside of the roof deck. Such a roof configuration positions the heating, ventilating, and air-conditioning equipment and ductwork within the conditioned space and improves airtight-ness in practice (by shifting the air barrier from the ceiling to the roofline). However, SPF is more expensive than fibrous insulation. Some builders have also become wary of using SPF because of liability concerns about indoor air quality and off-gassing. Unfortunately, un-vented roofs that use only air-permeable fibrous insulation (cellulose or fiberglass) have been demonstrated to be at risk of moisture issues in climate zone 2A because condensation and moisture accumulation occur at the ridge. This report describes research about a test implementation of an un-vented tile roof assembly in a hot-humid climate (Orlando, Florida; climate zone 2A); the roof was insulated with air-permeable insulation (netted and blown fiberglass). Given the localized moisture accumulation and failures seen in previous work, the U.S. Department of Energy's Building America research team Building Science Corporation theorized that installation of diffusion vents might allow for the wintertime release of moisture to safe levels. Diffusion vents are open slots at the roof's highest points (the ridge and hips) that are covered with a water-resistant but vapor-open (500+ perm) air barrier membrane. The test home is a two-story slab-on-grade structure (3,600 ft2 ); the roof was insulated with a prototype insulation system (called boxed netting), which allows full depth insulation (i.e., it is not limited by the depth of the truss top chord). As a control comparison, one part of the roof was constructed as a typical un-vented roof (with a self-adhered membrane at the ridge). Ideally, failure would occur in the control roof and the experimental (diffusion vent) roofs would show sufficient drying to avoid failure. No intentional space conditioning was provided in the un-vented attic so worst-case humidity buildup conditions could be observed.

air leakage↗

NASA NTRS1973

Effects of insulator ablation on the operation of a quasi-steady MPD arc

Multimegawatt operation of quasi-steady MPD arcjets can involve serious ablation of the insulator surfaces within the arc discharge chamber. Various degrees of insulator ablation manifest themselves by significantly perturbing the voltage-current characteristics and the exhaust velocity profiles. Voltage-current characteristics for two different insulator materials, Plexiglas and boron nitride, are interpreted in terms of an empirical Ohm's law. Use of the refractory insulator material eliminates the ablation-dominated nature of the terminal voltage, but the exhaust stream is still disturbed by insulator material. An Alfven critical velocity model can be applied to this influence of insulator ablation on exhaust velocity. Appropriate changes in the propellant injection geometry eliminate this influence and result in arcjet operation which is independent of insulator material. A particular combination of propellant injection geometries reduces the terminal voltage for a given current and mass flow while maintaining insulator-independent operation, thus implying an improvement in the overall efficiency of the device.

Boyle, M. J.↗

NASA NTRS1976

Design and evaluation of thin metal surface insulation for hypersonic flight

An all-metal insulation was studied as a thermal protection system for hypersonic vehicles. Key program goals included fabricating the insulation in thin packages which are optimized for high temperature insulation of an actively cooled aluminum structure, and the use of state-of-the-art alloys. The insulation was fabricated from 300 series stainless steel in thicknesses of 0.8 to 12 mm. The outer, 0.127 mm thick, skin was textured to accommodate thermal expansion and oxidized to increase emittance. The thin insulating package was achieved using an insulation concept consisting of foil radiation shields spaced within the package, and conical foil supports to carry loads from the skin and maintain package dimensions. Samples of the metal-insulation were tested to evaluate thermal insulation capability, rain and sand erosion resistance, high temperature oxidation resistance, applied load capability, and high temperature emittance.

Miller, R. C.↗