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DOE OSTI2024

Size Dependence of the Tetragonal to Orthorhombic Phase Transition of Ammonia Borane in Nanoconfinement

We have investigated the thermodynamic property modification of ammonia borane via nanoconfinement. Two different mesoporous silica scaffolds, SBA-15 and MCM-41, were used to confine ammonia borane. Using in situ Raman spectroscopy, we examined how pore size influences the phase transition temperature from tetragonal (I4mm) to orthorhombic (Pmn21) for ammonia borane. In bulk ammonia borane, the phase transition occurs at around 217 K; however, confinement in SBA-15 (with ~8 nm pore sizes) reduces this temperature to approximately 195 K, while confinement in MCM-41 (with pore sizes of 2.1–2.7 nm) further lowers it to below 90 K. This suppression of the phase transition as a function of pore size has not been previously studied using Raman spectroscopy. The stability of the I4mm phase at a much lower temperature can be interpreted by incorporating the surface energy terms to the overall free energy of the system in a simple thermodynamic model, which leads to a significant increase in the surface energy when transitioning from the tetragonal phase to the orthorhombic phase.

Najiba, Shah↗

DOE OSTI2021

Coexisting Multiple Martensites in Ni 57-x Mn 21+x Ga 22 Ferromagnetic Shape Memory Alloys: Crystal Structure and Phase Transition

A comprehensive study of the crystal structure and phase transition as a function of temperature and composition in Ni 57–x Mn 21+x Ga 22 (x = 0, 2, 4, 5.5, 7, 8) (at. %) magnetic shape memory alloys was performed by a temperature-dependent synchrotron X-ray diffraction technique and transmission electron microscopy. A phase diagram of this Ni 57–x Mn 21+x Ga 22 alloy system was constructed. The transition between coexisting multiple martensites with monoclinic and tetragonal structures during cooling was observed in the Ni 51.5 Mn 26.5 Ga 22 (x = 5.5) alloy, and it was found that 5M + 7M multiple martensites coexist from 300 K to 160 K and that 5M + 7M + NM multiple martensites coexist between 150 K and 100 K. The magnetic-field-induced transformation from 7M martensite to NM martensite at 140 K where 5M + 7M + NM multiple martensites coexist before applying the magnetic field was observed by in situ neutron diffraction experiments. The present study is instructive for understanding the phase transition between coexisting multiple martensites under external fields and may shed light on the design of novel functional properties based on such phase transitions.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Effects of Plasma on Physical Properties of Water: Nanocrystalline-to-Amorphous Phase Transition and Improving Produce Washing

Washing fresh produce using Plasma-activated water recently became a promising eco-friendly alternative to using chemical additives such as Chlorine. We discuss the produce-washing experiments that illustrate that addition of plasma to washing water is a multi-faced phenomena. Not only it increases the sterilization ability of water by killing pathogens, but it also has improved washibility: the ability to remove pathogens from the cleaning surface. We propose an explanation of these features based on the recently discoveries that many physical and chemical properties of water change their temperature dependence between about 35 and 60 degrees Celsius. In particular, heat conductance, light absorption, and surface tension all change their temperature dependence. These drastic changes were associated with water gradually changing its mesoscopic structure: while at the higher temperatures water is a uniform media (amorphous state), at the temperatures below transition it consists of many nano-to-micro-scale clusters (crystalline state). This transition is similar to the second order phase transition. In the present paper we propose that treating water with non-thermal plasma (adding plasma-created active compounds) can lower the temperature of the transition and thus cause a significant change in such physical quantities as surface tension, viscosity, freezing rate, and wettability and washability.

He, Jinjie↗

DOE OSTI2020

KELT-9 b’s Asymmetric TESS Transit Caused by Rapid Stellar Rotation and Spin–Orbit Misalignment

KELT-9 b is an ultra-hot Jupiter transiting a rapidly rotating, oblate early-A-type star in a polar orbit. We model the effect of rapid stellar rotation on KELT-9 b’s transit light curve using photometry from the Transiting Exoplanet Survey Satellite to constrain the planet’s true spin–orbit angle and to explore how KELT-9 b may be influenced by stellar gravity darkening. We constrain the host star’s equatorial radius to be 1.089 ± 0.017 times as large as its polar radius and its local surface brightness to vary by ∼38% between its hot poles and cooler equator. We model the stellar oblateness and surface brightness gradient and find that it causes the transit light curve to lack the usual symmetry around the time of minimum light. We take advantage of the light-curve asymmetry to constrain KELT-9 b’s true spin–orbit angle (87{sup ∘}{sub −11{sup ∘+10{sup {sup ∘}}}}), agreeing with Gaudi et al. that KELT-9 b is in a nearly polar orbit. We also apply a gravity-darkening correction to the spectral energy distribution model from Gaudi et al. and find that accounting for rapid rotation gives a better fit to available spectroscopy and yields a more reliable estimate for the star’s polar effective temperature.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2020

Two Intermediate-mass Transiting Brown Dwarfs from the TESS Mission

We report the discovery of two intermediate-mass transiting brown dwarfs (BDs), TOI-569b and TOI-1406b, from NASA’s Transiting Exoplanet Survey Satellite mission. TOI-569b has an orbital period of P = 6.55604 ± 0.00016 days, a mass of M {sub b} = 64.1 ± 1.9 M{sub J}, and a radius of R {sub b} = 0.75 ± 0.02 R{sub J}. Its host star, TOI-569, has a mass of M {sub ⋆} = 1.21 ± 0.05 M{sub ⊙}, a radius of R {sub ⋆} = 1.47 ± 0.03 R{sub ⊙}, [Fe/H]=+0.29±0.09 dex, and an effective temperature of T {sub eff} = 5768 ± 110 K. TOI-1406b has an orbital period of P = 10.57415 ± 0.00063 days, a mass of M {sub b} = 46.0 ± 2.7 M{sub J}, and a radius of R {sub b} = 0.86 ± 0.03 R{sub J}. The host star for this BD has a mass of M {sub ⋆} = 1.18 ± 0.09 M{sub ⊙}, a radius of R {sub ⋆} = 1.35 ± 0.03 R{sub ⊙}, [Fe/H]=−0.08±0.09 dex, and an effective temperature of T {sub eff} = 6290 ± 100 K. Both BDs are in circular orbits around their host stars and are older than 3 Gyr based on stellar isochrone models of the stars. TOI-569 is one of two slightly evolved stars known to host a transiting BD (the other being KOI-415). TOI-1406b is one of three known transiting BDs to occupy the mass range of 40–50 M{sub J} and one of two to have a circular orbit at a period near 10 days (with the first being KOI-205b). Both BDs have reliable ages from stellar isochrones, in addition to their well-constrained masses and radii, making them particularly valuable as tests for substellar isochrones in the BD mass–radius diagram.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2020

KELT-25 b and KELT-26 b: A Hot Jupiter and a Substellar Companion Transiting Young A Stars Observed by TESS

We present the discoveries of KELT-25 b (TIC 65412605, TOI-626.01) and KELT-26 b (TIC 160708862, TOI-1337.01), two transiting companions orbiting relatively bright, early A stars. The transit signals were initially detected by the KELT survey and subsequently confirmed by Transiting Exoplanet Survey Satellite (TESS) photometry. KELT-25 b is on a 4.40 day orbit around the V = 9.66 star CD-24 5016 (T{sub eff}=8280{sub -180}{sup +440} K, M&lowast; = 2.18{sub -0.11}{sup +0.12} M{sub ⊙}), while KELT-26 b is on a 3.34 day orbit around the V = 9.95 star HD 134004 (T{sub eff} = 8640{sub -240}{sup +500} K, M&lowast; = 1.93{sub -0.16}{sup +0.14} M{sub ⊙}), which is likely an Am star. We have confirmed the substellar nature of both companions through detailed characterization of each system using ground-based and TESS photometry, radial velocity measurements, Doppler tomography, and high-resolution imaging. For KELT-25, we determine a companion radius of R{sub P} = 1.64{sub -0.043}{sup +0.039} R{sub J} and a 3σ upper limit on the companion’s mass of ~64 M{sub J}. For KELT-26 b, we infer a planetary mass and radius of M{sub P} = 1.41{sub -0.51}{sup +0.43} M{sub J} and R{sub P} = 1.94{sub -0.058}{sup +0.060} R{sub J}. From Doppler tomographic observations, we find KELT-26 b to reside in a highly misaligned orbit. This conclusion is weakly corroborated by a subtle asymmetry in the transit light curve from the TESS data. KELT-25 b appears to be in a well-aligned, prograde orbit, and the system is likely a member of the cluster Theia 449.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2020

HD 191939: Three Sub-Neptunes Transiting a Sun-like Star Only 54 pc Away

We present the discovery of three sub-Neptune-sized planets transiting the nearby and bright Sun-like star HD 191939 (TIC 269701147, TOI 1339), a K {sub s} = 7.18 mag G8 V dwarf at a distance of only 54 pc. We validate the planetary nature of the transit signals by combining 5 months of data from the Transiting Exoplanet Survey Satellite with follow-up ground-based photometry, archival optical images, radial velocities, and high angular resolution observations. The three sub-Neptunes have similar radii (R{sub b}=3.42{sub −0.11}{sup +0.11}, R{sub c}=3.23{sub −0.11}{sup +0.11}, and R{sub d}=3.16{sub −0.11}{sup +0.11} R{sub ⊕}), and their orbits are consistent with a stable, circular, and coplanar architecture near mean-motion resonances of 1:3 and 3:4 (P {sub b} = 8.88, P {sub c} = 28.58, and P {sub d} = 38.35 days). The HD 191939 system is an excellent candidate for precise mass determinations of the planets with high-resolution spectroscopy due to the host star’s brightness and low chromospheric activity. Moreover, the system’s compact and near-resonant nature can provide an independent way to measure planetary masses via transit timing variations while also enabling dynamical and evolutionary studies. Finally, as a promising target for multiwavelength transmission spectroscopy of all three planets’ atmospheres, HD 191939 can offer valuable insight into multiple sub-Neptunes born from a protoplanetary disk that may have resembled that of the early Sun.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2020

Transits of Known Planets Orbiting a Naked-eye Star

Some of the most scientifically valuable transiting planets are those that were already known from radial velocity (RV) surveys. This is primarily because their orbits are well characterized and they preferentially orbit bright stars that are the targets of RV surveys. The Transiting Exoplanet Survey Satellite (TESS) provides an opportunity to survey most of the known exoplanet systems in a systematic fashion to detect possible transits of their planets. HD 136352 (Nu{sup 2} Lupi) is a naked-eye (V = 5.78) G-type main-sequence star that was discovered to host three planets with orbital periods of 11.6, 27.6, and 108.1 days via RV monitoring with the High Accuracy Radial velocity Planet Searcher (HARPS) spectrograph. We present the detection and characterization of transits for the two inner planets of the HD 136352 system, revealing radii of 1.482{sub −0.056}{sup +0.058} R {sub ⊕} and 2.608{sub −0.077}{sup +0.078} R {sub ⊕} for planets b and c, respectively. We combine new HARPS observations with RV data from the Keck/High Resolution Echelle Spectrometer and the Anglo-Australian Telescope, along with TESS photometry from Sector 12, to perform a complete analysis of the system parameters. The combined data analysis results in extracted bulk density values of ρ{sub b}=7.8{sub −1.1}{sup +1.2} g cm{sup −3} and ρ{sub c}=3.50{sub −0.36}{sup +0.41} g cm{sup −3} for planets b and c, respectively, thus placing them on either side of the radius valley. The combination of the multitransiting planet system, the bright host star, and the diversity of planetary interiors and atmospheres means this will likely become a cornerstone system for atmospheric and orbital characterization of small worlds.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2020

Multiple Explanations for the Single Transit of KIC 5951458 Based on Radial Velocity Measurements Extracted with a Novel Matched-template Technique

Planetary systems that show single-transit events are a critical pathway to increasing the yield of long-period exoplanets from transit surveys. From the primary Kepler mission, KIC 5951458 b (Kepler-456b) was thought to be a single-transit giant planet with an orbital period of 1310 days. However, radial velocity (RV) observations of KIC 5951458 from the HIRES instrument on the Keck telescope suggest that the system is far more complicated. To extract precise RVs for this V≈13 star, we develop a novel matched-template technique that takes advantage of a broad library of template spectra acquired with HIRES. We validate this technique and measure its noise floor to be 4–8 m s{sup −1} (in addition to internal RV error) for most stars that would be targeted for precision RVs. For KIC 5951458, we detect a long-term RV trend that suggests the existence of a stellar companion with an orbital period greater than a few thousand days. We also detect an additional signal in the RVs that is possibly caused by a planetary or brown dwarf companion with mass in the range of 0.6–82 M {sub Jup} and orbital period below a few thousand days. Curiously, from just the data on hand, it is not possible to determine which object caused the single “transit” event. We demonstrate how a modest set of RVs allows us to update the properties of this unusual system and predict the optimal timing for future observations.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2020

A Fast, Two-dimensional Gaussian Process Method Based on Celerite: Applications to Transiting Exoplanet Discovery and Characterization

Gaussian processes (GPs) are commonly used as a model of stochastic variability in astrophysical time series. In particular, GPs are frequently employed to account for correlated stellar variability in planetary transit light curves. The efficient application of GPs to light curves containing thousands to tens of thousands of data points has been made possible by recent advances in GP methods, including the celerite method. Here we present an extension of the celerite method to two input dimensions where, typically, the second dimension is small. This method scales linearly with the total number of data points when the noise in each large dimension is proportional to the same celerite kernel and only the amplitude of the correlated noise varies in the second dimension. We demonstrate the application of this method to the problem of measuring precise transit parameters from multiwavelength light curves and show that it has the potential to improve transit parameters measurements by orders of magnitude. Applications of this method include transit spectroscopy and exomoon detection, as well a broader set of astronomical problems.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2021

HAT-P-68b: A Transiting Hot Jupiter around a K5 Dwarf Star

We report the discovery by the ground-based Hungarian-made Automated Telescope Network (HATNet) survey of the transiting exoplanet HAT-P-68b, which has a mass of 0.724 ± 0.043 M {sub J}, and radius of 1.072 ± 0.012 R {sub J}. The planet is in a circular P = 2.2984 day orbit around a moderately bright V = 13.937 ± 0.030 magnitude K-dwarf star of mass 0.673{sub −0.014}{sup +0.020} M {sub ⊙}, and radius 0.6726 ± 0.0069 R {sub ⊙}. The planetary nature of this system is confirmed through follow-up transit photometry obtained with the Fred L. Whipple Observatory (FLWO) 1.2 m telescope, high-precision radial velocities measured using Keck I/High Resolution Echelle Spectrometer (HIRES), FLWO 1.5 m/Tillinghast Reflector Echelle Spectrograph (TRES), and Observatoire de Haute-Provence (OHP) 1.9 m/Sophie, and high-spatial-resolution speckle imaging from WIYN 3.5 m/DSSI. HAT-P-68 is at an ecliptic latitude of +3° and outside the field of view of both the NASA Transiting Exoplanet Survey Satellite primary mission and the K2 mission. The large transit depth of 0.036 mag (r band) makes HAT-P-68b a promising target for atmospheric characterization via transmission spectroscopy.

47 OTHER INSTRUMENTATION↗

DOE OSTI2021

NEMESIS: Exoplanet Transit Survey of Nearby M-dwarfs in TESS FFIs. I

In this work, we present an analysis of 33,054 M-dwarf stars, located within 100 parsecs, via the Transiting Exoplanet Survey Satellite (TESS) full-frame images (FFIs) of observed sectors 1–5. We present a new pipeline called NEMESIS, developed to extract detrended photometry, and to perform transit searches of single-sector data in TESS FFIs. As many M-dwarfs are faint, and are not observed with a two-minute cadence by TESS, FFI transit surveys can provide an empirical validation of how many planets are missed, using the 30-minute cadence data. In this work, we detect 183 threshold crossing events, and present 29 candidate planets for sectors 1–5, 24 of which are new detections. Our sample contains orbital periods ranging from 1.25 to 6.84 days, and planetary radii from 1.26 to 5.31 R {sub ⊕}. With the addition of our new planet candidate detections, along with detections previously observed in sectors 1–5, we calculate an integrated occurrence rate of 2.49 ± 1.58 planets per star, for the period range ∈ [1, 9] days, and planet radius range ∈ [0.5,11] R {sub ⊕}. We project an estimated yield of 122 ± 11 transit detections of nearby M-dwarfs. Of our new candidates, 23 have signal-to-noise ratios >7, transmission spectroscopy metrics >38, and emission spectroscopy metrics >10. We present all of our data products for our planet candidates via the Filtergraph data visualization service, located at https://filtergraph.com/NEMESIS.

47 OTHER INSTRUMENTATION↗

DOE OSTI2021

The Hubble PanCET Program: Transit and Eclipse Spectroscopy of the Strongly Irradiated Giant Exoplanet WASP-76b

Ultra-hot Jupiters with equilibrium temperatures greater than 2000 K are uniquely interesting targets as they provide us crucial insights into how atmospheres behave under extreme conditions. This class of giant planets receives intense radiation from their host star and usually has strongly irradiated and highly inflated atmospheres. At such a high temperature, cloud formation is expected to be suppressed and thermal dissociation of water vapor could occur. We observed the ultra-hot Jupiter WASP-76b with seven transits and five eclipses using the Hubble Space Telescope and the Spitzer Space Telescope (Spitzer) for a comprehensive study of its atmospheric chemical and physical processes. We detected TiO and H{sub 2}O absorption in the optical and near-infrared transit spectrum. Additional absorption by a number of neutral and ionized heavy metals like Fe, Ni, Ti, and SiO help explain the short-wavelength transit spectrum. The secondary eclipse spectrum shows muted water feature but a strong CO emission feature in Spitzer’s 4.5 μm band indicating an inverted temperature pressure profile. We analyzed both the transit and eclipse spectra with a combination of self-consistent PHOENIX models and atmospheric retrieval. Both spectra were well fitted by the self-consistent PHOENIX forward atmosphere model in chemical and radiative equilibrium at solar metallicity, adding to the growing evidence that both TiO/VO and NUV heavy metals opacity are prominent NUV-optical opacity sources in the stratospheres of ultra-hot Jupiters.

47 OTHER INSTRUMENTATION↗

DOE OSTI2023

Bioverse: A Comprehensive Assessment of the Capabilities of Extremely Large Telescopes to Probe Earth-like O 2 Levels in Nearby Transiting Habitable-zone Exoplanets

Molecular oxygen is a strong indicator of life on Earth and may indicate biological processes on exoplanets too. Recent studies proposed that Earth-like O 2 levels might be detectable on nearby exoplanets using high-resolution spectrographs on future extremely large telescopes (ELTs). However, these studies did not consider constraints like relative velocities, planet occurrence rates, and target observability. We expanded on past studies by creating a homogeneous catalog of 286,391 main-sequence stars within 120 pc using Gaia DR3 and used the Bioverse framework to simulate the likelihood of finding nearby transiting Earth analogs. We also simulated a survey of M dwarfs within 20 pc accounting for η ⊕ estimates, transit probabilities, relative velocities, and target observability to determine how long ELTs and theoretical 50–100 m ground-based telescopes need to observe to probe for Earth-like O 2 levels with an R = 100,000 spectrograph. This would only be possible within 50 yr for up to ~21% of nearby M-dwarf systems if a suitable transiting habitable-zone Earth analog was discovered, assuming signals from every observable partial transit from each ELT can be combined. If so, Earth-like O 2 levels could be detectable on TRAPPIST-1 d–g within 16–55 yr, respectively, and about half that time with an R = 500,000 spectrograph. These results have important implications for whether ELTs can survey nearby habitable-zone Earth analogs for O 2 via transmission spectroscopy. Our work provides the most comprehensive assessment to date of the ground-based capabilities to search for life beyond the solar system.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2025

Laboratory Measurements of n >= 3 K-shell Transition Energies of Sulfur Ions from F-like S viii to Li-like S xiv

Inner-shell transitions are ubiquitous in nonequilibrium collisionally ionized plasmas, such as supernova remnants, and in photoionized plasmas, such as outflows from active galactic nuclei and X-ray binaries. Inner-shell X-ray emission can help determine key parameters of these systems, such as ionization time, τ, and ionization parameter, ξ. Despite their importance, only theoretical inner-shell transition energies are available for many ions. To provide experimental benchmarks, we have measured the dominant n → 1 K-shell transitions of sulfur ions where n ≥ 3 from Li-like S xiv to F-like S viii using LLNL’s SuperEBIT electron beam ion trap and the NASA/GSFC EBIT Calorimeter Spectrometer (ECS). We identify over 30 spectral features and measure their energies with uncertainties in the ∼0.1–1 eV range. We compare these results to Flexible Atomic Code (FAC) and multireference Møller–Plesset (MR-MP) calculations and find differences between theory and experiment of ∼1 eV for FAC and <0.5 eV for most MR-MP calculations. We also compare these results to two widely used atomic databases, AtomDB and CHIANTI, and find discrepancies as high as 7 eV. Furthermore, many transitions are missing from these databases despite being prominent in our data.

Atomic data benchmarking↗

DOE OSTI2025

Topological phase transition to a hidden charge density wave liquid

Charge density waves (CDWs), electronic crystals that form within a host solid, have long been speculated to melt into a spatially textured electronic liquid. Though they have not been previously detected, liquid CDWs may nonetheless be fundamental to the phase diagrams of many correlated electron systems, including high temperature superconductors and quantum Hall states. In one of the most promising candidate materials capable of hosting a liquid CDW, 1T-TaS2, a structural phase transition impedes its observation. Here, by irradiating the material with a femtosecond light pulse, we circumvent the structural phase transition to reveal how topological defect dynamics govern the otherwise invisible CDW correlations. Upon photoexcitation, the CDW diffraction peaks broaden azimuthally, initially revealing a hexatic state. At higher temperatures, photoexcitation completely destroys translational and orientational order and only a ring of diffuse scattering is observed, a key signature of a liquid CDW. Our work provides compelling evidence for a defect-unbinding transition to a CDW liquid and presents a protocol for uncovering states that are hidden by other transitions in thermal equilibrium.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2026

A robust aerosol impact on clouds along the subtropical to tropical transition

Marine clouds undergo a transition from subtropical stratocumulus (Sc) to shallow cumulus (Cu) and eventually to deep convective (DC) systems as air masses advect from the subtropics towards the deep tropics. How aerosols modulate this Lagrangian cloud evolution remains largely uncertain. Here we use both 5 years of satellite observations mapped along 8 d Lagrangian trajectories and complementary large-eddy simulations from 9 initiation locations across the Northeast Pacific, Southeast Pacific, and Southeast Atlantic. This Lagrangian framework allows us to quantify the aerosol effect and its co-variability with meteorological conditions on cloud microphysics, macrophysics, and top-of-atmosphere radiation through the full Sc-Cu-DC transition. We show that increasing aerosol concentrations leads to deeper and more reflective clouds throughout this cloud transition. Examining the thermodynamic evolution along the trajectory indicates a well-known trend: enhanced moistening near the boundary-layer top and lower free troposphere under polluted conditions, suggesting that part of the co-variability between aerosol and meteorological conditions may be internally driven. The agreement between model simulations and satellite data alongside the multi-basin coherence of the results indicates that aerosols systematically amplify cloud depth and reflectivity during the subtropical–to–tropical cloud transition.

54 ENVIRONMENTAL SCIENCES↗

NASA NTRS1971

Analysis of Free-Flight Laminar, Transitional, and Turbulent Heat-Transfer Results at Free-Stream Mach Numbers Near 20 (Reentry F)

Laminar, transitional, and turbulent heat-transfer data were measured during a reentry flight at a Mach number of 20 on a 5 deg half-angle cone 3.962 m (13 ft) long with an initial nose tip radius of 0.254 cm (0.1 in.). The free-stream Reynolds number increased during the prime data period from 7.0 x 10(exp 6) to 51.5 x 10(exp 6) per meter (2.1 x 10(exp 6) to 15.7 x 10(exp 6) per foot) and the ratio of wall to total temperature varied from 0.053 to 0.12. The angle of attack was less than 1deg for the prime data period. The experimental laminar and turbulent heating rates are compared with results from existing flat-plate prediction methods. At conditions of minimal tip blunting and angle of attack (above 26.8 km (88 000 ft)), values from a flat-plate laminar method agreed within 20 percent with the laminar data. The Schultz-Grunow skin-friction equation with reference enthalpy; conditions, with the Reynolds number based on distance from the transition location, and with the Colburn Reynolds analogy agreed within 10 percent with the experimental turbuleiit heating data. The Van Driest n skin-friction equation with Reynolds number greater than 10(exp 7) based on distance from the peak heating point and the Colburn Reynolds analogy was also within approximately 10 percent of the experimental turbulent heating data. A data correlation jbf the extent of transition and a simple empirical transition-zone heating correlation were also presented.

Zoby, Ernest V.↗