Results for “radius equation” — Page 18

NASA NTRS1986

A comparison of computed and experimental surface pressure and heating on 70 deg sphere cones at angles of attack to 20 deg

A method for handling the flow fields around 70 deg spherical cones at angles of attack up to 20 deg is described. Surface pressure and heating results are compared with existing wind tunnel data. Computed surface pressures are found to be in excellent agreement with experimental data, while the surface heating from approximate and finite difference forms of the boundary layer equations are in good agreement with the data. The effect of bluntness ratio on surface pressures and heating is very small. Body corner radius, while not having a significant impact on body aerodynamics, produced large changes in surface pressure and heating distribution.

Weilmuenster, K. J.↗

NASA NTRS1986

The temperature structure in accretion flows onto massive protostars

Radiation transfer problems involved in the infall of dust and gas during star formation are studied. Dust properties are discussed, and modifications of spherical radiative transfer equations are presented that permit forward scattering by dust to be treated for the small size of the star relative to the inner radius of the shell. A procedure for deriving the stellar radiation field incident on the inner edge of the shell is developed. The temperature correction procedure of Cassinelli and Hartmann (1975) for extended stellar atmospheres is modified so that the multitemperature nature of the grains in the cloud may be derived. Temperature distributions for three schematic models in which the density is prespecified are discussed. Radiative acceleration of grains is addressed, showing that the proper mean opacity differs by a large factor from the Rosseland mean opacity that is commonly used. Emergent fluxes for the models are given.

Wolfire, Mark G.↗

NASA NTRS1990

The position of the magnetotail neutral sheet in the near-earth region

The position of the near-earth neutral sheet throughout the nightside region between R = 5 R(E) and R = 8.8 R(E) is examined statistically using magnetic field data from AMPTE/CCE. As has been demonstrated previously, the latitudinal position of the neutral sheet is primarily controlled by the dipole tilt angle. The position also depends on local time, radial distance, and magnetic activity. These dependencis may be represented by the empirical formula MLAT = - (0.14 Kp + 0.69) /cos(Phi)/exp 1/3 (0.065 R exp 0.8 - 0.16) DTA, where MLAT is the position in degrees of the neutral sheet relative to the magnetic equator, Kp is the 3-hourly magnetic activity index, Phi is the magnetic local time in degrees (midnight = 0 deg), R is the radius in R(E), and DTA is the dipole tilt angle in degrees.

Lopez, Ramon E.↗

NASA NTRS1990

A GCM parameterization for the shortwave radiative properties of water clouds

A new parameterization was developed for predicting the shortwave radiative properties of water clouds, suitable for inclusion in general circulation models (GCMs). The parameterization makes use of the simple relationships found by Slingo and Schrecker, giving the three input parameters required to calculate the cloud radiative properties (the optical depth, single scatter albedo and asymmetry parameter) in terms of the liquid water path and equivalent radius of the drop size distribution. The input parameters are then used to derive the cloud radiative properties, using standard two-stream equations for a single layer. The relationships were originally derived for fairly narrow spectral bands but it was found that it is possible to average the coefficients so as to use a much smaller number of bands, without sacrificing accuracy in calculating the cloud radiative properties. This makes the parameterization fast enough to be included in GCMs. The parameterization was programmed into the radiation scheme used in the U.K. Meteorological Office GCM. This scheme and the 24 band Slingo/Schrecker scheme were compared with each other and with observations, using a variety of published datasets. There is good agreement between the two schemes for both cloud albedo and absorption, even when only four spectral bands are employed in the GCM.

Slingo, A.↗

NASA NTRS1992

Heat transfer in rotating serpentine passages with trips skewed to the flow

Experiments were conducted to determine the effects of buoyancy and Coriolis forces on heat transfer in turbine blade internal coolant passages. The experiments were conducted with a large scale, multi-pass, heat transfer model with both radially inward and outward flow. Trip strips, skewed at 45 deg to the flow direction, were machined on the leading and trailing surfaces of the radial coolant passages. An analysis of the governing flow equations showed that four parameters influence the heat transfer in rotating passages: coolant-to-wall temperature, rotation number, Reynolds number, and radius-to-passage hydraulic diameter ratio. The first three of these four parameters were varied over ranges which are typical of advanced gas turbine engine operating conditions. Results were correlated and compared to previous results from similar stationary and rotating models with smooth walls and with trip strips normal to the flow direction. The heat transfer coefficients on surfaces, where the heat transfer decreased with rotation and buoyancy, decreased to as low as 40 percent of the value without rotation. However, the maximum values of the heat transfer coefficients with high rotation were only slightly above the highest levels previously obtained with the smooth wall models. It was concluded that (1) both Coriolis and buoyancy effects must be considered in turbine blade cooling designs with trip strips, (2) the effects of rotation are markedly different depending upon the flow direction, and (3) the heat transfer with skewed trip strips is less sensitive to buoyancy than the heat transfer in models with either smooth or normal trips. Therefore, skewed trip strips rather than normal trip strips are recommended and geometry-specific tests are required for accurate design information.

Johnson, B. V.↗

NASA NTRS1992

Heat transfer in rotating serpentine passages with trips skewed to the flow

Experiments were conducted to determine the effects of buoyancy and Coriolis forces on heat transfer in turbine blade internal coolant passages. The experiments were conducted with a large scale, multi-pass heat transfer model with both radially inward and outward flow. An analysis of the governing flow equations showed that four parameters influence the heat transfer in rotating passages: coolant-to-wall temperature, rotation number, Reynolds number, and radius-to-passage hydraulic diameter ratio. Results were correlated and compared to previous results from similar stationary and rotating models with smooth walls and with trip strips normal to the flow direction. It was concluded that (1) both Coriolis and buoyancy must be considered in turbine blade cooling designs with trip strips, (2) the effects of rotation are markedly different depending upon the flow direction, and (3) the heat transfer with skewed trip strips is less sensitive to buoyancy than the heat transfer models with either smooth or normal trips. Therefore, skewed trip strips rather than normal trip strips are recommended and geometry-specific tests are required for accurate design.

Johnson, B. V.↗

NASA NTRS1994

Equilibrium structure of solar magnetic flux tubes: Energy transport with multistream radiative transfer

We examine the equilibrium structure of vertical intense magnetic flux tubes on the Sun. Assuming cylindrical geometry, we solve the magnetohydrostatic equations in the thin flux-tube approximation, allowing for energy transport by radiation and convection. The radiative transfer equation is solved in the six-stream approximation, assuming gray opacity and local thermodynamic equilibrium. This constitutes a significant improvement over a previous study, in which the transfer was solved using the multidimensional generalization of the Eddington approximation. Convection in the flux tube is treated using mixing-length theory, with an additional parameter alpha, characterizing the suppression of convective energy transport in the tube by the strong magnetic field. The equations are solved using the method of partial linearization. We present results for tubes with different values of the magnetic field strength and radius at a fixed depth in the atmosphere. In general, we find that, at equal geometric heights, the temperature on the tube axis, compared to the ambient medium, is higher in the photosphere and lower in the convection zone, with the difference becoming larger for thicker tubes. At equal optical depths the tubes are generally hotter than their surroundings. The results are comparatively insensitive to alpha but depend upon whether radiative and convective energy transport operate simultaneously or in separate layers. A comparison of our results with semiempirical models shows that the temperature and intensity contrast are in broad agreement. However, the field strengths of the flux-tube models are somewhat lower than the values inferred from observations.

Hasan, S. S.↗

NASA NTRS2022

Combined Bluntness and Roughness Effects on Cones at Hypersonic Speeds

This computational study investigates the effects of discrete roughness elements on a blunt cone at zero degrees angle of attack in a Mach 6 flow. Motivation was provided by experiments conducted in the Air Force Research Laboratory Mach 6 High Reynolds Number facility on a 7-degree half-angle cone with a roughness array located at 45 degrees from the apex on two nose tips of different blutness but equivalent roughness Reynolds number. Transition was only affected on the blunter cone, indicating that the transition onset is associated with the combined effects of bluntness and roughness. The present study investigates the 15.24 mm nose radius, 420 azimuthal wavenumber case via Navier-Stokes computations of the laminar base flow and instability analysis. Plane-marching parabolized stability equations (PSE) and inflow-resolvent analysis based on the three-dimensional, harmonic linearized Navier-Stokes equations (HLNSE) are used to calculate the amplification of disturbances along the roughness wake as well as over the roughness nearfield. Results show that the roughness shape can have a great impact on the characteristics of the most amplified wake instabilities. For the experimental configuration with cubic roughness elements of 15 μ m height, the flow is marginally unstable. For prismatic elements of 20 μ m height, the PSE predicts a logarithmic disturbance amplification ratio of N = 5.6 along its wake, but this ratio increases to N = 9.6 when the amplification over the roughness and separation regions is included in the inflow-resolvent analysis.

Boundary-layer transition↗

NASA NTRS2022

Combined Bluntness and Roughness Effects on Cones at Hypersonic Speeds

This computational study investigates the effects of discrete roughness elements on a blunt cone at zero degrees angle of attack in a Mach 6 flow. Motivation was provided by experiments conducted in the Air Force Research Laboratory Mach 6 High Reynolds Number facility on a 7-degree half-angle cone with a roughness array located at 45 degrees from the apex on two nose tips of different blutness but equivalent roughness Reynolds number. Transition was only affected on the blunter cone, indicating that the transition onset is associated with the combined effects of bluntness and roughness. The present study investigates the 15.24 mm nose radius, 420 azimuthal wavenumber case via Navier-Stokes computations of the laminar base flow and instability analysis. Plane-marching parabolized stability equations (PSE) and inflow-resolvent analysis based on the three-dimensional, harmonic linearized Navier-Stokes equations (HLNSE) are used to calculate the amplification of disturbances along the roughness wake as well as over the roughness nearfield. Results show that the roughness shape can have a great impact on the characteristics of the most amplified wake instabilities. For the experimental configuration with cubic roughness elements of 15 μ m height, the flow is marginally unstable. For prismatic elements of 20 μ m height, the PSE predicts a logarithmic disturbance amplification ratio of N = 5.6 along its wake, but this ratio increases to N = 9.6 when the amplification over the roughness and separation regions is included in the inflow-resolvent analysis.

Boundary-layer transition↗

DOE OSTI2023

Phase transition phenomenology with nonparametric representations of the neutron star equation of state

Astrophysical observations of neutron stars probe the structure of dense nuclear matter and have the potential to reveal phase transitions at high densities. Most recent analyses are based on parametrized models of the equation of state with a finite number of parameters and occasionally include extra parameters intended to capture phase-transition phenomenology. However, such models restrict the types of behavior allowed and may not match the true equation of state. We introduce a complementary approach that extracts phase transitions directly from the equation of state without relying on, and thus being restricted by, an underlying parametrization. We then constrain the presence of phase transitions in neutron stars with astrophysical data. Current pulsar mass, tidal deformability, and mass-radius measurements disfavor only the strongest of possible phase transitions (latent energy per particle ≳ 100 MeV). Weaker phase transitions are consistent with observations. Here we further investigate the prospects for measuring phase transitions with future gravitational-wave observations and find that catalogs of O (100) events will (at best) yield Bayes factors of ~ 10 : 1 in favor of phase transitions even when the true equation of state contains very strong phase transitions. Our results reinforce the idea that neutron star observations will primarily constrain trends in macroscopic properties rather than detailed microscopic behavior. Fine-tuned equation of state models will likely remain unconstrained in the near future.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2022

Neural network reconstruction of the dense matter equation of state from neutron star observables

The Equation of State (EoS) of strongly interacting cold and hot ultra-dense QCD matter remains a major challenge in the field of nuclear astrophysics. With the advancements in measurements of neutron star masses, radii, and tidal deformabilities, from electromagnetic and gravitational wave observations, neutron stars play an important role in constraining the ultra-dense QCD matter EoS. Here, in this work, we present a novel method that exploits deep learning techniques to reconstruct the neutron star EoS from mass-radius (M-R) observations. We employ neural networks (NNs) to represent the EoS in a model-independent way, within the range of ~1-7 times the nuclear saturation density. The unsupervised Automatic Differentiation (AD) framework is implemented to optimize the EoS, so as to yield through TOV equations, an M-R curve that best fits the observations. We demonstrate that this method works by rebuilding the EoS on mock data, i.e., mass-radius pairs derived from a randomly generated polytropic EoS. The reconstructed EoS fits the mock data with reasonable accuracy, using just 11 mock M-R pairs observations, close to the current number of actual observations.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2025

Bayesian quantification of observability and equation of state of twin stars

The possibility of discovering twin stars, two neutron stars (NSs) with the same mass but different radii, is usually studied in forward modelings by using a restricted number of NS matter equations of state (EOSs) encapsulating a first-order phase transition from hadronic to quark matter (QM). Informing our likelihood function with the NS radius data from GW170817 and using a metamodel with nine parameters capable of mimicking most NS EOSs available in the literature, we conduct a Bayesian quantification of the observability and underlying EOSs of twin stars. Of the accepted EOSs, between 12 and 18% yield twin stars, depending on the restrictions we place on the second branch. The possibility of twin stars remains robust even under recent observational constraints. Here, we show that many of these twin star scenarios are observable with currently available levels of accuracy in measuring NS radii. We also present the marginalized posterior probability density functions (PDFs) of every EOS parameter for each of four mass-radius correlation topologies. We find that the inferred EOS depends sensitively on not only whether twin stars are present, but also the category of twin stars, indicating that the observation of twin stars would provide a strong constraint on the underlying EOS. In particular, for two coexisting hybrid stars having QM cores at different densities, the PDF for QM speed of sound squared 𝑐$^2_{qm}$ has two peaks, one below and another above the conformal limit 𝑐$^2_{qm}$ = 1/3 predicted by perturbative QCD.

QCD in nuclear reactions↗

NASA NTRS1972

A study of the effect of selected material properties on the ablation performance of artificial graphite

Eighteen material properties were measured on 45 different, commercially available, artificial graphites. Ablation performance of these same graphites were also measured in a Mach 2 airstream at a stagnation pressure of 5.6 atm. Correlations were developed, where possible, between pairs of the material properties. Multiple regression equations were then formulated relating ablation performance to the various material properties, thus identifying those material properties having the strongest effect on ablation performance. These regression equations reveal that ablation performance in the present test environment depends primarily on maximum grain size, density, ash content, thermal conductivity, and mean pore radius. For optimization of ablation performance, grain size should be small, ash content low, density and thermal conductivity high, and mean pore radius large.

Maahs, H. G.↗

NASA NTRS1978

The accuracy of the narrow seal approximation in analyzing radial face seals

The accuracy of the narrow seal approximation which enables closed form analytical solutions for radial face seals is examined in this paper. Both hydrostatic and hydrodynamic effects in a flat, misaligned seal are considered. Analytical results obtained from a simplified Reynolds equation, based on the neglect of circumferential pressure gradient and seal curvature, are compared with accurate results from numerical solution of the complete Reynolds equation. The agreement between the approximate and accurate solutions is quite reasonable over a wide range of a seal's inner-to-outer radius ratio. For radius ratios greater than 0.8, the accuracy of the narrow seal approximation is better than 1 percent over most of the range of angular misalignment.

Etsion, I.↗

NASA NTRS1984

Predictions of occultations of stars by Comet Crommelin

Predictions of occultation of stars are presented on the basis of star and radio-source catalogs; these are: the AGK3 catalog, the SAO catalog south of the celestial equator, and Perth 70 catalog, as well as the Master List of Radio Sources. The predictions are formulated under the assumption of the coma radius of 22,500 km and a very large cometary radius of 675,000 km for cometary ion tails that may be involved in radio-source occultations. The predictions are expected to change with time.

Bowell, E.↗

NASA NTRS1986

Wave propagation in pulsar magnetospheres - Refraction of rays in the open flux zone

The propagation of waves through a relativistically outflowing electron-positron plasma in a very strong dipolar magnetic field, conditions expected in pulsar magnetospheres, is investigated. Halmilton's equations is derived for the propagation of rays through a plasma which is inhomogeneous in density, magnetic field directions, and Lorentz factor. These equations are solved for rays propagating through the plasmas outflowing along the 'open' dipolar field lines in which the density decreases inversely as the radius cubed and in the case where gradients transverse to the radial direction exist. In the radial case, the effects of refraction on pulse profiles, spectrum, and polarization are examined, and the effects of a transverse gradient are indicated. Attention is given to models in which the observed broad bandwidth in the radio emission has its origin in a radius to frequency map. Models with broad-band emission at a single radius are also studied. These are compared to observations of pulse width and pulse component separation as a function of frequency. The origin of 'orthogonal modes' is discussed.

Barnard, J. J.↗

NASA NTRS1986

Initiation of breakdown in slender compressible vortices

The initiation of the breakdown process for axially symmetric compressible flows is investigated using a numerical solution of the conservation equations for mass, momentum, and energy. The vortex is isolated, with its axis parallel to the direction of the main stream, and the core radius is small compared to the breakdown length. Computations for several flowfields indicate that the breakdown of the solution is shifted further downstream with increasing Mach number until breakdown is no longer observed. In the subsonic case, the influence of the initial temperature distribution on the breakdown length of the solution is more pronounced than in the supersonic case, with heating of the core enhancing breakdown, and cooling delaying it. The breakdown of the solution is seen to always occur for nonvanishing axial velocity components.

Krause, E.↗

NASA NTRS1986

Comptonization in supercritical winds. I - Spectral evolution. II - Dynamics and observational diagnostics

The physics governing spectral evolution in steady, fully ionized, radiatively driven winds from compact objects is examined. A largely analytic theory is developed to describe the effects of diffusion, adiabatic cooling, and repeated Compton scattering on the emergent radiation spectrum. Analytic forms for the wind temperature profile are derived, and spectral solutions obtained by considering a modified, time-independent Kompaneets equation are presented subject to a variety of initial conditions. A probabilistic formalism which describes the effect of diffusion photons travelling beyond the trapping radius is developed to allow the calculation of spectra observed at infinity. The second paper focuses on the dynamics of supercritical winds and on observational diagnostics which may be used to constrain model parameters in the contexts of specific astrophysical systems, including X-ray burst sources and mass-losing quasars.

Becker, Peter A.↗