Power-law bodies of maximum lift-to-drag ratio in hypersonic flow
Maximizing lift-drag ratio of slender, flat-top, hypersonic body assuming Newtonian pressure distribution and constant skin-friction coefficient
SKIN FRICTION↗
SEARCH · Search NASA
Results for “power-law distribution”
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.
Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.
Longitudinal aerodynamic performance of a series of power-law and minimum wave drag bodies at Mach 6 and several Reynolds numbers
Experimental data have been obtained for two series of bodies at Mach 6 and Reynolds numbers, based on model length, from 1.4 million to 9.5 million. One series consisted of axisymmetric power-law bodies geometrically constrained for constant length and base diameter with values of the exponent n of 0.25, 0.5, 0.6, 0.667, 0.75, and 1.0. The other series consisted of positively and negatively cambered bodies of polygonal cross section, each having a constant longitudinal area distribution conforming to that required for minimizing zero-lift wave drag at hypersonic speeds under the geometric constraints of given length and volume. At the highest Reynolds number, the power-law body for minimum drag is blunter (exponent n lower) than predicted by inviscid theory (n approximately 0.6 instead of n = 0.667); however, the peak value of lift-drag ratio occurs at n = 0.667. Viscous effects were present on the bodies of polygonal cross section but were less pronounced than those on the power-law bodies. The trapezoidal bodies with maximum width at the bottom were found to have the highest maximum lift-drag ratio and the lowest mimimum drag.
Ashby, G. C., Jr.↗
Impulsive 2-10 keV solar electron events not associated with flares
Data from the ISEE 3 satellite reveal a class of impulsive solar electron events with no measurable increase in flux above 10-20 keV. The flux histories and angular distributions indicate that the electrons propagate through interplanetary space with little or no scattering. The smooth extension of the power-law energy spectra down to the limit of the observations at 2 keV indicates that the electrons are accelerated at altitudes greater than 0.5 solar radii in the solar corona. Although these events occur more frequently than any other type of impulsive solar particle event observed, no correlation is found with flares or flare-related activity. However, there is a close correlation with low-frequency type III radio bursts.
Potter, D. W.↗
Boundary-layer transition and displacement thickness effects on zero-lift drag of a series of power-law bodies at Mach 6
Wave and skin-friction drag have been numerically calculated for a series of power-law bodies at a Mach number of 6 and Reynolds numbers, based on body length, from 1.5 million to 9.5 million. Pressure distributions were computed on the nose by the inverse method and on the body by the method of characteristics. These pressure distributions and the measured locations of boundary-layer transition were used in a nonsimilar-boundary-layer program to determine viscous effects. A coupled iterative approach between the boundary-layer and pressure-distribution programs was used to account for boundary-layer displacement-thickness effects. The calculated-drag coefficients compared well with previously obtained experimental data.
Ashby, G. C., Jr.↗
Approximate Turbulent Boundary-Layer Development in Plane Compressible Flow Along Thermally Insulated Surfaces with Application to Supersonic-Tunnel Contour Correction
Numerical solutions of the differential equation obtained from the momentum theorem for the development of a turbulent boundary layer along a thermally insulated surface in two-dimensional and in radial shock-free flow are presented in tabular form for a range of Mach numbers from 0.100 to 10. The solution can be used in a step-wise procedure with any given distribution of favorable pressure gradients and for zero pressure gradients. Solutions are also given for use with moderate adverse pressure gradients. The mean velocity in the boundary layer is approximated by a power-law profile. In view of the stepwise integration methods to be used, the exponent designated the profile shape can be varied along the surface between the integral fraction limits 1/5 and 1/11 through interpolation. Agreement obtained between theoretical and experimental boundary-layer development in a supersonic nozzle at a nominal Mach number of 2 indicates the general validity of the approximations used in the analysis - in particular, the method of extrapolating low-speed skin-friction relations to high Mach number flows. The extrapolation method used assumes that the skin-friction coefficient depend primarily on Reynolds number, provided that the density and the kinematic viscosity are evaluated at surface conditions.
BOUNDARY LAYER - WIND TUNNEL WALLS↗
BE Ursae Majoris /PG 1155 + 492/ - A unique cataclysmic-variable-like object
The variable spectrum of BE Ursae Majoris, which is similar to that of the cataclysmic variables (CVs), shows (1) an emission-line spectrum with the high-excitation CN 4650 A blend as the strongest optical feature, weaker H and He lines, and a strong Balmer jump, and (2) an absorption spectrum dominated by He. Although the object shows no evidence of photometric variability on either short or long time-scales, it has been shown by Kurochkin (1964, 1971) to have a 2.29-day, sinusoidal, 1.5-mag variation. The luminosity is dominated by a UV power-law component, though the 4000-10000 A continuum is flat. The hypothesis that this object is an active mass transfer binary is not supported by its photometric behavior, energy distribution and long period, despite the spectroscopic variability. Nevertheless, three components whose nature is not understood remain: (1) an ultraviolet source whose energy distribution is explainable neither by a uniform temperature primary star nor by an accretion disk; (2) a reprocessed component powered by the UV star; and (3) a component similar to a CV disk, producing the optically thick Balmer lines.
Ferguson, D. H.↗
Scaling laws and edge effects for polymer surface discharges
Specimens of Mylar sheet were exposed to a 20 kV electron beam. The resulting surface discharge arcs were photographed and the discharge current into a metal backing plate measured as a function of time. The area of the Mylar sheet was defined by a round aperture in a close-fitting metal mask, and the current pulse characteristics were plotted against area on log-log paper. The plots appear as straight lines (due to power-law behavior) with slopes of 0.50 for the peak current, 1.00 for the charge released, 1.49 for the energy and 0.55 for the pulse duration. Evidence is presented for the occurrence of banded charge distributions near grounded edges, on both Teflon and Mylar.
Balmain, K. G.↗
Observations of 1-30 MeV gamma rays from the galactic center
Preliminary results are reported for gamma ray observations of the galactic center region made during a 15-hour balloon flight from Alice Springs, Australia on April 18, 1979. The observations were carried out with the UGR double-scatter gamma-ray telescope at energies of 1 to 30 MeV. The observations are compatible with a galactic source of approximately equal brightness along the region of system II galactic longitudes between 300 and 60 deg. The energy distribution joins smoothly to previous spark chamber results at energies above 30 MeV and to scintillator results below 1 MeV. It appears to be a combination of nuclear gamma ray lines superimposed on a power-law bremsstrahlung spectrum. The metastable C-12 line at 4.4 MeV appears to be present with a significance of about 16 standard deviations. The flux in the line is 0.0006 + or - 0.0003 photons/sq cm per sec per rad. The oxygen line at 6.1 MeV does not seem to appear significantly above background.
Zanrosso, E.↗
A study of cosmic-ray positron and electron spectra in interplanetary and interstellar space and the solar modulation of cosmic rays
The differential energy spectra of cosmic-ray positrons and negatrons with energies between approximately 11 and 1500 MeV was measured during the period 1968-1971 using a balloon-borne magnetic spectrometer. These measurements fill a gap in the previously existing data and permit the determination of the interstellar spectra of cosmic-ray positrons and electrons. Knowledge of these spectra provides a crucial tool for studies of the distribution and density of matter and magnetic fields in the interstellar medium and the origin and dynamics of energetic particles contained in the fields. The differential energy spectrum of interstellar electrons may be represented as a power-law, j alpha T to the -1.8 power for 100 MeV approximately T approximately 2 GeV, but must flatten considerably at lower energies. From the measured electron charge composition, it is concluded that the majority of cosmic-ray electrons with energies above approximately 10 MeV originate in primary sources.
Cummings, A. C.↗
Energies of formation for ejecta blankets of giant impacts
Ejection energy-diameter scaling relations for impact craters are studied by assuming the energy is equal to a constant times the diameter raised to a (different) constant power. These scaling relations are derived from least-squares fits to calculated ejection energies over a range of crater diameters and vary according to ejection angle, ejecta blanket distribution, planetary radius, and the depth-diameter ratio. Extremely broad changes in ejection angle and ejecta blanket distribution result in relatively small changes in the total energy. The way in which the exponent in the scaling relation is dependent on the planetary radius of curvature as well as on the exponent of the power-law depth-diameter scaling relation is described. Two ejection energy-diameter scaling relations, one for simple craters with depth-diameter ratios of approximately 0.2 and the other for large complex craters, are presented. The scaling relations explicitly include target density, surface gravity, and planetary radius.
Croft, S. K.↗
Statistical study of precipitating electrons
Energy spectra of precipitating electrons are fitted to the sum of three distributions: a power law, a Maxwellian and a Gaussian. This fitting procedure determines seven parameters which characterize the essential features of each spectrum. These characteristic parameters are used to carry out various studies involving precipitating electrons. It is shown that the absence of the power-law population from a particular spectrum is related to the softness of the precipitating primary flux, that the Maxwellian temperature and the Gaussian peak energy have a positive correlation the strength of which varies with local time, that the upward moving Gaussian population has a loss cone distribution, and that the one dimensional velocity distribution parallel to the magnetic field occasionally displays a plateau or a hump on the tail.
Fontheim, E. G.↗
The correlation function for density perturbations in an expanding universe. IV - The evolution of the correlation function
The evolution of the two-point correlation function for the large-scale distribution of galaxies in an expanding universe is studied on the assumption that the perturbation densities lie in a Gaussian distribution centered on any given mass scale. The perturbations are evolved according to the Friedmann equation, and the correlation function for the resulting distribution of perturbations at the present epoch is calculated. It is found that: (1) the computed correlation function gives a satisfactory fit to the observed function in cosmological models with a density parameter (Omega) of approximately unity, provided that a certain free parameter is suitably adjusted; (2) the power-law slope in the nonlinear regime reflects the initial fluctuation spectrum, provided that the density profile of individual perturbations declines more rapidly than the -2.4 power of distance; and (3) both positive and negative contributions to the correlation function are predicted for cosmological models with Omega less than unity.
Mcclelland, J.↗
Three dimensional potential and current distributions in a Hall generator with assumed velocity profiles
Three-dimensional potential and current distributions in a Faraday segmented MHD generator operating in the Hall mode are computed. Constant conductivity and a Hall parameter of 1.0 is assumed. The electric fields and currents are assumed to be coperiodic with the electrode structure. The flow is assumed to be fully developed and a family of power-law velocity profiles, ranging from parabolic to turbulent, is used to show the effect of the fullness of the velocity profile. Calculation of the square of the current density shows that nonequilibrium heating is not likely to occur along the boundaries. This seems to discount the idea that the generator insulating walls are regions of high conductivity and are therefore responsible for boundary-layer shorting, unless the shorting is a surface phenomenon on the insulating material.
Stankiewicz, N.↗
No new limit on size distribution of gamma-ray bursts
It is argued that the results of Carter et al. (1976), who derived an upper limit to the balloon intensity of small gamma-ray bursts at about 100 below the extrapolated known size spectrum and therefore concluded that the gamma-ray bursts are of galactic origin, are entirely consistent with the -1.5 index power-law extrapolation, so that no conclusion regarding the origin of gamma-ray bursts can be drawn. A reply of Carter et al. is published. Points at issue include: (1) whether a selection criterion of three successive 0.6-sec increases in the gamma-ray count rate ignores a significant or only a small number of events, (2) whether the spectra of all bursts extend below 100 keV, the satellite energy threshold, and (3) the required correction for the distortion of a horizontal, flat detector.
Cline, T. L.↗
Characteristics of the lunar photoelectron layer in the geomagnetic tail.
The charged particle lunar environment experiment, a part of the Apollo 14 lunar surface package, is an ion-electron spectrometer capable of measuring ions and electrons with energies between 40 eV and 50 keV. The instrument, with apertures 26 cm above the surface, has detected a photoelectron gas layer above the sunlit lunar surface. No detectable flux above 200 eV has been observed. Experimental data for periods while the moon was in the earth's magnetotail for electrons with energies 40 eV less than or equal to 200 eV follow a power-law spectrum. In the absence of photoelectrons with E greater than 200, we assume that the surface potential is at least 200 V. The modulation of this potential in the presence of intense plasma-sheet fluxes has been observed. Also, a detailed history of the Feb. 10, 1971, total lunar eclipse, to determine the source distribution of high-energy solar photons, is presented.
Reasoner, D. L.↗
Second-order small-disturbance solutions for hypersonic flow over power-law bodies
Similarity solutions were found which give the adiabatic flow of an ideal gas about two-dimensional and axisymmetric power-law bodies at infinite Mach number to second order in the body slenderness parameter. The flow variables were expressed as a sum of zero-order and perturbation similarity functions for which the axial variations in the flow equations separated out. The resulting similarity equations were integrated numerically. The solutions, which are universal functions, are presented in graphic and tabular form. To avoid a singularity in the calculations, the results are limited to body power-law exponents greater than about 0.85 for the two-dimensional case and 0.75 for the axisymmetric case. Because of the entropy layer induced by the nose bluntness (for power-law bodies other than cones and wedges), only the pressure function is valid at the body surface. The similarity results give excellent agreement with the exact solutions for inviscid flow over wedges and cones having half-angles up to about 20 deg. They give good agreement with experimental shock-wave shapes and surface-pressure distributions for 3/4-power axisymmetric bodies, considering that Mach number and boundary-layer displacement effects are not included in the theory.
Townsend, J. C.↗
Production of hard X rays in a plasma focus
A model of a plasma focus is examined wherein large axial electric fields are produced by an imploding current sheet during the final nanoseconds of the collapse phase and where the fields provide a mechanism for creating a beam of electrons of highly suprathermal energies. The expected bremsstrahlung radiation above 100 keV is calculated for such a beam, which has a power-law spectrum, both from electron-deuteron collisions in the focused plasma and when the beam reaches the wall of the device. It is concluded that, since the experimental results indicate little or no radiation above 100 keV originating in the walls, that the electrons in the beam must be decelerated after leaving the plasma and before reaching the wall. Comparisons with the results and the total energy of the device yield qualitative agreement with the expected angular distribution of hard X-rays and reasonable agreement with the total energy in accelerated electrons required to produce the observed total energy in hard X-rays by this mechanism.
Newman, C. E.↗
Photoelectric spectrophotometry of radio galaxies
The absolute energy distributions from 3200 to 10,000 A of 26 3CR radio galaxies are determined on the basis of spectrophotometric observations with the multichannel spectrometer of the Hale 5-m telescope. It is found that there is a continuous range of emission-line characteristics and UV excess in the sample and that a strong correlation exists between the nonthermal component luminosity and hydrogen emission, which favors the hypothesis that direct photoionization by the nuclear radiation is responsible for the emission lines observed. Calculations are performed which show that in almost all cases the power-law component model provides sufficient UV photons to produce the observed H-beta line. Indications are obtained that the optical nuclear component is related to the radio emission in some complex manner and that strong radio galaxies tend to be accompanied by UV excess and emission lines.
Yee, H. K. C.↗