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Results for “radius equation”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 217 records · Page 12
All sourcesNASA NTRSDOE OSTI
NASA NTRS1980

Vibration characteristics of a steadily rotating slender ring

Partial differential equations are derived to describe the structural vibrations of a uniform homogeneous ring which is very flexible because the radius is very large compared with the cross sectional dimensions. Elementary beam theory is used and small deflections are assumed in the derivation. Four sets of structural modes are examined: bending and compression modes in the plane of the ring; bending modes perpendicular to the plane of the ring; and twisting modes about the centroid of the ring cross section. Spatial and temporal characteristics of these modes, presented in terms of vibration frequencies and ratios between vibration amplitudes, are demonstrated in several figures. Given a sufficiently high rotational rate, the dynamics of the ring approach those of a vibrating string. In this case, the velocity of traveling wave in the material of the ring approaches in velocity of the material relative to inertial space, resulting in structural modes which are almost stationary in space.

Lallman, F. J.↗
NASA NTRS1992

Features of wavy vortices in a curved channel from experimental and numerical studies

Results are reported from an experimental study obtaining evidence of time-dependent, wavy vortex motions associated with undulating and twisting Dean vortices in a curved channel with 40-to-1 aspect ratio, and mild curvature (radius ratio = 0.979). The results are compared with direct numerical simulations of time-dependent 3D Navier-Stokes equations using boundary conditions in the spanwise and streamwise directions. When viewed in cross section, experimental visualizations of undulating and twisting vortex flows show rocking motion and changes in the direction of the flow between vortices that are like those observed in the simulations. Experimental spectra show that undulating vortices are replaced by the higher-frequency, shorter streamwise wavelength twisting vortices at higher Reynolds numbers. When undulating vortices are present, experimental power spectra and visualizations give frequencies that are somewhat lower than the most unstable frequencies predicted by linear stability analysis.

Ligrani, P. M.↗
NASA NTRS1994

On the maximum energy release in flux-rope models of eruptive flares

We determine the photospheric boundary conditions which maximize the magnetic energy released by a loss of ideal-magnetohydrodynamic (MHD) equilibrium in two-dimensional flux-rope models. In these models a loss of equilibrium causes a transition of the flux rope to a lower magnetic energy state at a higher altitude. During the transition a vertical current sheet forms below the flux rope, and reconnection in this current sheet releases additional energy. Here we compute how much energy is released by the loss of equilibrium relative to the total energy release. When the flux-rope radius is small compared to its height, it is possible to obtain general solutions of the Grad-Shafranov equation for a wide range of boundary conditions. Variational principles can then be used to find the particular boundary condition which maximizes the magnetic energy released for a given class of conditions. We apply this procedure to a class of models known as cusp-type catastrophes, and we find that the maximum energy released by the loss of equilibrium is 20.8% of the total energy release for any model in this class. If the additional restriction is imposed that the photospheric magnetic field forms a simple arcade in the absence of coronal currents, then the maximum energy release reduces to 8.6%

Forbes, T. G.↗
NASA NTRS1994

Effects of leading and trailing edge flaps on the aerodynamics of airfoil/vortex interactions

A numerical procedure has been developed for predicting the two-dimensional parallel interaction between a free convecting vortex and a NACA 0012 airfoil having leading and trailing edge integral-type flaps. Special emphasis is placed on the unsteady flap motion effects which result in alleviating the interaction at subcritical and supercritical onset flows. The numerical procedure described here is based on the implicit finite-difference solutions to the unsteady two-dimensional full potential equation. Vortex-induced effects are computed using the Biot-Savart Law with allowance for a finite core radius. The vortex-induced velocities at the surface of the airfoil are incorporated into the potential flow model via the use of the velocity transpiration approach. Flap motion effects are also modeled using the transpiration approach. For subcritical interactions, our results indicate that trailing edge flaps can be used to alleviate the impulsive loads experienced by the airfoil. For supercritical interactions, our results demonstrate the necessity of using a leading edge flap, rather than a trailing edge flap, to alleviate the interaction. Results for various time-dependent flap motions and their effect on the predicted temporal sectional loads, differential pressures, and the free vortex trajectories are presented

Hassan, Ahmed A.↗
NASA NTRS1997

Analysis of ripple formation in single crystal spot welds

Stationary spot welds have been made at the (001) surface of Fe-l5%Ni-15%Cr single crystals using a Gas Tungsten Arc (GTA). On the top surface of the spot welds, very regular and concentric ripples were observed after solidification by differential interference color microscopy. Their height (typically 1--5 micrometers and spacing, typically approximately 60 micrometers) decreased with the radius of the pool. These ripples were successfully accounted for in terms of capillary-wave theory using the fundamental mode frequency f(sub 0) given by the first zero of the zero-order Bessel function. The spacing d between the ripples was then equated to v(sub s)/f(sub 0), where v(sub s) is the solidification rate. From the measured ripple spacing, the velocity of the pool was deduced as a function of the radius, and this velocity was in good agreement with the results of a heat-flow simulation.

Rappaz, M.↗
NASA NTRS1990

Modeling the dust size distribution in comets with dust fragmentation

A hydrodynamic model was developed of a spherically symmetric dusty gas flow in a cometary atmosphere assuming a single fluid, inviscid, perfect gas. The hydrodynamics for gas and dust, which involves the gas drag force (momentum transfer), heat exchange between gas and dust, photodissociation energy for H2O gas, and radiative heating and cooling terms for dust particles, are solved using the Gear method for stiff, coupled differential equations. Calculations were done with a dust size distribution for radii alpha = 0.01 micron to 10 cm with densities variable with the size. A nucleus size of 4.0 km radius with a density of 0.5 g/cu cm and a total dust-to-gas mass ratio chi = 1 was adopted. There are indications from in situ observations that dust particle fragment into smaller ones. Fragmentation of dust particles was incorporated into the model. This is done by adding source and sink terms in the continuity equations for the dust. Lifetimes for the decay of dust particles were assumed as a function of particle size. It is also assumed that dust particles always fragment only into the next smaller size.

Konno, Ichishiro↗
NASA NTRS1990

Influence of airfoil nose radius on sound generated by gust interactions

The sound radiated by interaction of a short wavelength gust (k much greater than 1) with a symmetric thin airfoil is analyzed. The theory is based on a linearization of the Euler equations about the subsonic mean flow past the airfoil. The sound generation mechanism is found to be concentrated in a local region surrounding the parabolic nose of the airfoil; the size of this local region scales on the gust wavelength. Airfoil thickness produces terms of relative order O(sq rt S) in the far field sound, where S is a Strouhal number based on the airfoil nose radius. At low Mach numbers, entropy gusts generate much less sound than vorticity gusts. However, for O(1) Mach numbers and moderate values of S, entropy and vorticity gusts produce similar sound levels.

Tsai, C. T.↗
NASA NTRS1990

Heat transfer in rotating serpentine passages with smooth walls

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, smooth-wall 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 ratio, Rossby number, Reynolds number and radius-to-passage hydraulic diameter ratio). These four parameters were varied over ranges which are typical of advanced gas turbine engine operating conditions. It was found that both Coriolis and buoyancy effects must be considered in turbine blade cooling designs and that the effect of rotation on the heat transfer coefficients was markedly different depending on the flow direction. Local heat transfer coefficients were found to decrease by as much as 60 percent and increase by 250 percent from no rotation levels. Comparisons with a pioneering stationary vertical tube buoyancy experiment showed reasonably good agreement. Correlation of the data is achieved employing dimensionless parameters derived from the governing flow equations.

Wagner, J. H.↗
NASA NTRS1988

The field lines of an axisymmetric magnetic field

The equations of Willis and Young (1987) for the field lines of an arbitrary axisymmetric multipole are generalized to an arbitrary linear combination of multipoles, i.e., to an arbitrary axisymmetric magnetic field B outside a sphere of radius a, S(a), centered on the origin, and containing all the sources of B. For this field, axisymmetric Stokes stream function is expressed in terms of the Gauss coefficients. It is shown that if only one Gauss coefficient is nonzero, the field line equations are identical to those obtained by Willis and Young.

Backus, George E.↗
NASA NTRS1976

An experimental method to obtain the elastic strain energy function from torsion-tension tests

It is shown that by employing a torsion-tension test, it is possible to have a complete mapping near the origin of the two principal strain invariants associated with the rate of change of the strain energy function. However, the mathematical representation of the twist moment and normal forces vs strain and the strain energy function are complex. This problem is solved by using a set of solid cylindrical bars with different diameters such that the difference in diameter of two successive bars is small. The stress-strain equations can be grossly oversimplified by considering differences in twist moment and normal force as a function of difference in radius.

Peng, S. T. J.↗
NASA NTRS1978

Optimum satellite orbits for accurate measurement of the earth's radiation budget, summary

The optimum set of orbit inclinations for the measurement of the earth radiation budget from spacially integrating sensor systems was estimated for two and three satellite systems. The best set of the two were satellites at orbit inclinations of 80 deg and 50 deg; of three the inclinations were 80 deg, 60 deg and 50 deg. These were chosen on the basis of a simulation of flat plate and spherical detectors flying over a daily varying earth radiation field as measured by the Nimbus 3 medium resolution scanners. A diurnal oscillation was also included in the emitted flux and albedo to give a source field as realistic as possible. Twenty three satellites with different inclinations and equator crossings were simulated, allowing the results of thousand of multisatellite sets to be intercompared. All were circular orbits of radius 7178 kilometers.

Campbell, G. G.↗
NASA NTRS1987

Constraints on the mass-radius relation for the neutron star in the X-ray burst source 4U/MXB 1820-30 located in the globular cluster NGC 6624

From the spectral evolution of seven X-ray bursts observed from 4U/MXB 1820-30 (Haberl et al., 1986) during the phases of photospheric expansion and cooling, constraints are derived on the mass-radius relation of the neutron star in this system. Taking into account the uncertainty in the source distance and the possible anisotropy of the burst emission. If during bursts with radius expansion the outer layers of the neutron star are of a hydrogen-poor composition, none of the current equations of state of high-density matter is excluded. For a hydrogen-rich composition, only very soft equations of state are allowed.

Van Paradijs, J.↗
NASA NTRS1987

A multispacecraft study of the injection and transport of solar energetic particles

The November 22, 1977 and December 27, 1977 solar energetic particle (SEP) events observed simultaneously by the Helios and the Voyager space probes and the ISEE 1 satellite are described. The spacecraft instruments indicated flux increases for H, He, and (for November 22) for O and Fe, with the energy range of 0.5-20 MeV per nucleon. It was found that the data can be well fitted by a model based on the spherically symmetric Fokker-Planck equation including convection, diffusion, and adiabatic deceleration, assuming that the radial interplanetary diffusion coefficient increases in proportion to the heliocentric radius to the power of 0.6 and that there is an extended particle injection at the sun. This extended injection is of crucial importance for the event of November 22, where the injection functions are strongly dependent on times associated with a soft energy spectrum.

Beeck, J.↗
NASA NTRS1991

Heat transfer in rotating passages with smooth walls and radial outward flow

Experiments were conducted to determine the effects of rotation on heat transfer in turbine blade internal coolant passages. The experiments were conducted with a smooth wall, large-scale heat transfer model. The objective was to obtain the heat transfer data base required to develop heat transfer correlations and to assess computational fluid dynamic techniques for rotating coolant passages. An analysis of the governing equations showed that four parameters influence the heat transfer in rotating passages (coolant density ratio, Rossby number, Reynolds number, and radius ratio). These four parameters were varied over ranges that exceed the ranges of current open literature results, but that are typical of current and advanced gas turbine engine operating conditions. Rotation affected the heat transfer coefficients differently for different locations in the coolant passage. For example, heat transfer at some locations increased with rotation, but decreased and then increased again at other locations. Heat transfer coefficients varied by as much as a factor of five between the leading and trailing surfaces for the same test condition and streamwise location. Comparisons with previous results are presented.

Wagner, J. H.↗
NASA NTRS1974

Calculation of flow distribution in large radius ratio stages of axial flow turbines and comparison of theory and experiment

A method of calculating stage parameters and flow distribution of axial turbines is described. The governing equations apply to space between the blade rows and are based on the assumption of rotationally symmetrical, compressible, adiabatic flow conditions. Results are presented for stage design and flow analysis calculations. Theoretical results from the calculation system are compared with experimental data from low pressure steam turbine tests.

Herzog, J.↗
NASA NTRS1988

A simple, analytic 3-dimensional downburst model based on boundary layer stagnation flow

A simple downburst model is developed for use in batch and real-time piloted simulation studies of guidance strategies for terminal area transport aircraft operations in wind shear conditions. The model represents an axisymmetric stagnation point flow, based on velocity profiles from the Terminal Area Simulation System (TASS) model developed by Proctor and satisfies the mass continuity equation in cylindrical coordinates. Altitude dependence, including boundary layer effects near the ground, closely matches real-world measurements, as do the increase, peak, and decay of outflow and downflow with increasing distance from the downburst center. Equations for horizontal and vertical winds were derived, and found to be infinitely differentiable, with no singular points existent in the flow field. In addition, a simple relationship exists among the ratio of maximum horizontal to vertical velocities, the downdraft radius, depth of outflow, and altitude of maximum outflow. In use, a microburst can be modeled by specifying four characteristic parameters, velocity components in the x, y and z directions, and the corresponding nine partial derivatives are obtained easily from the velocity equations.

Oseguera, Rosa M.↗
NASA NTRS1971

Longitudinal impact of cylindrical shells.

The transient response due to longitudinal impact of three aluminum cylindrical shells of different thickness-to-radius ratios is studied both analytically and experimentally. The analyses were obtained from method of characteristics' solutions of two sets of equations: one which includes the transverse shear, radial inertia, and rotary inertial effects; and the other set is from a modified membrane theory. Experimentally, longitudinal and circumferential strains are monitored along the length of each of the shells; the velocity of the impacter ring is also measured. The experimental results of this study indicate that the wave front, after traveling three diameters from the impacted end, propagates at essentially the plate velocity, in agreement with the theory. In addition, the longitudinal and circumferential strain calculated from the two theories are in good agreement with the experimental results.

Mortimer, R. W.↗