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Spherical electrodes surrounding electrode-dielectric junctions eliminate high-voltage breakdown. The gap between the spherical electrode and the dielectric must be of an optimum size for proper operation. Modified, this electrode should be suitable as a high-voltage feedthrough between various liquid and gaseous media.
Interconnecting straight tube connects axially misaligned flanges in a duct assembly. It adjusts to accommodate variations in relative location of the flanges by pivoting. Adjustment is by spherical mating faces and a spherical-faced indexing swivel flange for bolting backup.
Solutions for the axially symmetric motion of an elastic spherical sandwich shell have been obtained from a theory of shells which includes the effects of transverse shear deformation and rotary inertia. Frequency equations and mode shapes are derived for the full vibrations of a closed spherical shell.
Computer program for determining geometric configuration view factors for spherical and conical surfaces of spherical radiating bodies
Heat transfer from inflatable spherical balloon shadow shield to spherical cryogen storage tank, noting several design factors and extensions of previous work
Optimization calculations to determine minimum 4 pi spherical-shell weights were performed at 200-, 375-, and 550-megawatt-thermal reactor power levels. Monte Carlo analyses were performed for a reactor power level corresponding to 375 megawatts. Power densities for the spherical reactor model used varied from 64.2 to 256 watts per cubic centimeter. The dose rate constraint in the optimization calculations was 0.25 mrem per hour at 9.14 meters from the reactor center. The resulting shield weights were correlated with the reactor power levels and power densities by a regression analysis. The optimum shield weight for a 375-megawatt, 160-watt-per-cubic-centimeter reactor was 202,000 kilograms.
The concept of the Lagrangian displacement of a balloon is introduced. It is shown that the general balloon response problem is extremely complicated because the wind-forcing functions in the balloon equations of motion are functions of the wind velocity vector and its Eulerian first derivatives evaluated at the location of the balloon. The linear perturbation equations for a spherical balloon are derived by perturbing the components of velocity of the balloon about a terminal velocity state which is in equilibrium with a space-time invariant mean horizontal flow. The atmospheric flow is also perturbed such that the resulting equations can be used to analyze the responses of spherical balloons to three-dimensional time-dependent flows. The wind field is represented in terms of a four-fold Fourier integral that involves three orthogonal wave numbers and a frequency, while the balloon components of velocity are represented as Fourier integrals involving a frequency which, in turn, is a function of the wind field wave numbers and frequency and the unperturbed flow components of velocity.
Numerical calculations of the generation and propagation of the two important fundamental symmetric tidal wave modes - the diurnal mode (1, 1, 1,) and the semidiurnal mode (2, 2, 2) - were performed applying a realistic model thermosphere and taking into account heat conduction and the temporally and spatially varying ion-neutral collision number. Both wave modes are predominantly generated by the solar EUV heat input. It is shown that the latitude structure of the (1, 1, 1)-mode which is identical with the Hough function(1, -1) within the lower non-dissipative atmosphere degenerates into the spherical function P sub 1, 1 at thermospheric heights. The pressure field of this mode constitutes the observed pressure bulge of the thermosphere, the diurnal component of which peaks at 15 h L. T. The electric polarization field of the geomagnetic Sq current generates a significant fraction of this wave mode at F layer heights. This wave component shifts the total horizontal wind system to earlier times by about 1 hour in agreement with ionospheric observations. The latitude structure of the (2, 2, 2) mode is identical with the Hough function (2, 2) within the lower non-dissipative atmosphere. It degenerates to the spherical function P sub 2, 2 at thermospheric heights.
Fluid mechanics experiments were performed in cylindrical and spherical chambers to evaluate the simulated-fuel containment resulting from various injection geometry and inlet flow conditions for application to the open-cycle GNR. A preliminary study in the cylindrical chamber was directed toward developing inlet flow conditions which minimize mixing between the simulated fuel and propellant. Gas concentration measurements were obtained at several outer-stream to inner-stream weight flow and density ratios for the best inlet configuration tested in the preliminary study. The spherical cavity flow study was conducted to evaluate techniques for injecting simulated-fuel and propellant into a cavity.
A new half-range differential approximation for radiative transfer with spherical symmetry is presented. The development is motivated by the various failures of existing differential approximations in determining emissive-power distributions and heat transfer for concentric-spheres problems. The new approach represents a modification of the four-moment double spherical-harmonics method, to which it reduces in the planar limit. The difference is effected by relocating the discontinuity of the assumed directional distribution of radiation intensity. The shift takes the discontinuity from precisely on the division between radially inward and radially outward, to just within the radially-outward directional half range. The method is tested on a variety of concentric spheres problems with and without internal heat sources, reproducing all the important features of the exact results.
A general theory of spherically symmetric boundary-value problems of the one-speed neutron transport theory is presented. The formulation is also applicable to the 'gray' problems of radiative transfer. The Green's function for the purely absorbing medium is utilized in obtaining the normal mode expansion of the angular densities for both interior and exterior problems. As the integral equations for unknown coefficients are regular, a general class of reduction operators is introduced to reduce such regular integral equations to singular ones with a Cauchy-type kernel. Such operators then permit one to solve the singular integral equations by the standard techniques due to Muskhelishvili. We discuss several spherically symmetric problems. However, the treatment is kept sufficiently general to deal with problems lacking azimuthal symmetry. In particular the procedure seems to work for regions whose boundary coincides with one of the coordinate surfaces for which the Helmholtz equation is separable.
Spherically blunted 0.44-radian (25 deg) half-angle conical models coated with elastomeric ablative materials were tested in supersonic arc-heated wind tunnels to evaluate performance of the ablators over a range of conditions typical of lifting entry. Four test conditions were combinations of stagnation point-heat transfer rates of 2.3 and 4.5 MW/m2 and stagnation pressures of 20 and 2kN/m2. Afterbody values of heat transfer rate and pressure were 0.05 to 0.20 of stagnation point values. Stagnation enthalpy varied from 4.4 to 25 MJ/kg (1900 to 11000 Btu/lbm) and free-stream Mach number was in a range from 3.5 to 4. Ablative materials retained the spherical nose shape throughout tests at the lower heat transfer level, but receded, assuming a flattened nose shape, during tests at the high heat transfer level. The residue layer that formed on the conical after-body was weak, friable, and extensively cracked. The reference ablative material, which contained phenolic microspheres, generally retained the conical shape on the model afterbody. However, a modified ablator, in which phenolic microspheres were replaced with silica microspheres, deformed and separated from the undegraded material, and thereby produced a very uneven surface. Substrate temperatures and ablator recession were in good agreement with values computed by a numerical analysis.
Design vessel with very low thickness-to-radius ratio to obtain low weight, and fabricate it with aid of precision tracer-lathe to limit and control imperfections in spherical shape. Vessel is thin-walled, spherical, monocoque shell constructed from hemispheres joined with sealed and bolted meridional flange.
An analysis is made of the flow within a three-dimensional explosion, or spark, created in a gas absorbing energy from a steady conical beam of radiation with nearly spherical symmetry. The radiation, typically from an array of lasers with a common focus, is assumed to be very intense and absorbed immediately behind an outwardly advancing strong shock. Departures of the laser power from spherical uniformity, which would result from practical problems of arrangement, are conveniently represented by an ascending series of Legendre polynomials in the polar angle. For nonuniformities of small amplitude, first-order perturbations of the flow field are analyzed in detail. Self-similarity is shown to be retained for zero counter-pressure and power constant with time. For the first five harmonics in power distortion, the resulting fourth-order system of equations is solved numerically for profiles of velocity components, density, pressure, and shock shape. Results are presented graphically.
The properties of finite-amplitude thermal convection for a Boussinesq fluid contained in a spherical shell are investigated. All nonlinear terms are retained in the equations, and both axisymmetric and nonaxisymmetric solutions are studied. The velocity is expanded in terms of poloidal and toroidal vectors. Spherical surface harmonics resolve the horizontal structure of the flow, but finite differences are used in the vertical. With a few modifications, the transform method developed by Orszag (1970) is used to calculate the nonlinear terms, while Green's function techniques are applied to the poloidal equation and diffusion terms.
Attention is given to electromagnetic induction in infinitesimally thin spherical cap current layers of arbitrary size and arbitrary axisymmetric integrated conductivity, taking into account a location at nonzero but otherwise arbitrary depth beneath the surface of observation. The description of a theoretical model is presented and the induced fields computed from the theoretical formulas for several different spherical cap models are discussed.
Standard plate or shell theories were used as a starting point to study the fracture problems in thin-walled cylindrical and spherical shells, assuming that the plane of the crack is perpendicular to the surface of the sheet. Since recent studies have shown that local shell curvatures may have a rather considerable effect on the stress intensity factor, the crack problem was considered in conjunction with a shell rather than a plate theory. The material was assumed to be isotropic and homogeneous, so that approximate solutions may be obtained by approximating the local shell crack geometry with an ideal shell which has a solution, namely a spherical shell with a meridional crack, a cylindrical shell with a circumferential crack, or a cylindrical shell with an axial crack. A method of solution for the specially orthotropic shells containing a crack was described; symmetric and skew-symmetric problems are considered in cylindrical shells with an axial crack.
The study investigates the acceleration of cosmic rays by superrelativistic plasma waves. The pulsar wave field imposed upon the particles is that of a magnetic dipole wave including azimuthal dependence and near field terms. The refractive index of the plasma is assumed to be constant everywhere. Two distinct zones appear: in the near zone spherical effects dominate, particles may be decelerated; in the far zone the results for the motion differ noticeably from the vacuum case. From a WBK-like treatment for a spherical S wave, it is concluded that for a wave solution to be valid even near the light cylinder, the wave can carry a sufficiently small particle flux.