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A theoretical investigation is made of the development of a laminar boundary layer behind a suction slot that is assumed to cut off part of the boundary layer without exerting any sink effect. The development, which is approximate, is based on the heat conduction equation. The heat conduction equation enters the analysis through a linearization of the Prandtl-Mises form of the boundary-layer equation.
A solution is presented for the electromagnetic fields radiated by an arbitrarily oriented current filament over a conducting ground plane in the case where the current propagates along the filament at the speed of light, and this solution is interpreted in terms of radiation from lightning return strokes. The solution is exact in the fullest sense; no mathematical approximations are made, and the governing differential equations and boundary conditions are satisfied. The solution has the additional attribute of being specified in closed form in terms of elementary functions. This solution is discussed from the point of view of deducing lightning current wave forms from measurements of the electromagnetic fields and understanding the effects of channel tortuosity on the radiated fields. In addition, it is compared with two approximate solutions, the traditional moment approximation and the Fraunhofer approximation, and a set of criteria describing their applicability are presented and interpreted.
The energy spectra and anisotropies of protons and alpha particles are investigated at the plasmasheet boundary during the recovery phase of geomagnetic substorms using the Max Planck Institut/University of Maryland sensor system on the ISEE-1 satellite. The observations are found to reveal the presence of a thin nonthermal layer of approximately 60 keV/charge protons and alpha particles at the plasmasheet boundary, the particles streaming highly collimated in earthward direction. It is pointed out that the alpha particle layer is confined within the proton layer. It is thought that the principal features of the layers can be explained in terms of an acceleration model proposed by Speiser (1965) for the environment of a magnetic neutral line.
The theoretical problem posed by the buoyant escape of a magnetic field from the interior of a stably stratified body bears directly on the question of the present existence of primordial magnetic fields in stars. This paper treats the onset of the Rayleigh-Taylor instability of the upper boundary of a uniform horizontal magnetic field in a stably stratified atmosphere. The calculations are carried out in the Boussinesq approximation and show the rapid growth of the initial infinitesimal perturbation of the boundary. This result is in contrast to the extremely slow buoyant rise of a separate flux tube in the same atmosphere. Thus for instance, at a depth of 1/3 of a solar radius beneath the surface of the sun, a field of 100 G develops ripples over a scale of 1000 km in a characteristic time of 50 years, whereas the characteristic rise time of the same field in separate flux tubes with the same dimensions is 10 billion years. Thus, the development of irregularities proceeds quickly, soon slowing, however, to a very slow pace when the amplitude of the irregularities becomes significant. Altogether, the calculations show the complexity of the question of the existence of remnant primordial magnetic fields in stellar interiors.
A computational investigation of a pressure-gain combustor system for gas turbine applications is presented. The system consists of a valved pulse combustor and an ejector, housed within a shroud. The study focuses on two enhancements to previous models, related to the valve and ejector components. First, a new poppet inlet valve system is investigated, replacing the previously used reed valve configuration. Secondly, a new computational approach to approximating the effects of choked turbine inlet guide vanes present immediately downstream of the Ejector-Enhanced Resonant Pulse Combustor (EERPC) is investigated. Instead of specifying a back pressure at the EERPC exit boundary (as was done in previous studies) the new model adds a converging-diverging (CD) nozzle at the exit of the EERPC. The throat area of the CD nozzle can be adjusted to obtain the desired back pressure level and total mass flow rate. The results presented indicate that the new poppet valve configuration performs nearly as well as the original reed valve system, and that the addition of the CD nozzle is an effective method to approximate the exit boundary effects of a turbine present downstream of the EERPC. Furthermore, it is shown that the more acoustically reflective boundary imposed by a nozzle as compared to a constant pressure surface does not significantly affect operation or performance.
A new trigonometric approach to the finite difference calculus was applied to the problem of beam buckling as represented by virtual work and equilibrium equations. The trigonometric functions were varied by adjusting a wavelength parameter in the approximating Fourier series. Values of the critical force obtained from the modified approach for beams with a variety of boundary conditions were compared to results using the conventional finite difference method. The trigonometric approach produced significantly more accurate approximations for the critical force than the conventional approach for a relatively wide range in values of the wavelength parameter; and the optimizing value of the wavelength parameter corresponded to the half-wavelength of the buckled mode shape. It was found from a modal analysis that the most accurate solutions are obtained when the approximating function closely represents the actual displacement function and matches the actual boundary conditions.
A rapid, approximate method has been developed for calculating the heating rates on three-dimensional vehicles such as the Space Shuttle Orbiter and other advanced reentry configurations. The method is based on the axisymmetric analogue for three-dimensional boundary layers. It uses information obtained from a three-dimensional inviscid flowfield solution, such as HALIS, to calculate inviscid surface streamlines along which approximate heating rates are calculated independent of what happens along other streamlines. Three-dimensional effects are included through the metric coefficient that describes the divergence or convergence of streamlines. Boundary-layer edge properties are obtained from the inviscid flowfield solution by interpolating in the inviscid flowfield at a distance equal to the boundary-layer thickness away from the wall. This accounts, approximately, for the variable boundary-layer edge entropy. Using this method, heating calculations can be made along a typical streamline in a few seconds. This method has been used to accurately predict heating rates for simple shapes such as a spherically blunted cone and more complex shapes such as the Shuttle Orbiter for a variety of wind-tunnel and flight conditions. A unique feature of the method is its ability to accurately predict heating rates on the Shuttle Orbiter wing.
We have investigated the response of particles, in the energy range approximately 1-5000 MeV, to interplanetary shocks and coronal ejecta. Shocks can accelerate particles or cause decreases in particle densities. Ejecta cause decreases. Thus particle observations can provide information about solar wind disturbances. Of particular interest is that the boundaries of ejecta can often be more readily identified from approximately l GeV particle decrease observations than from most other phenomena associated with ejecta. We will discuss the properties of less energetic shocks and ejecta and compare them with those of the more energetic events which are normally discussed in the context of Forbush decreases, large proton events, etc. We use data from both Helios spacecraft and IMP 8 which allows some spatial variations to be studied.
The two-dimensional steady flow past an ellipse of arbitrary aspect ratio is investigated analytically, applying a linearized version of the Navier-Stokes equation based on the approximation of Burgers (1928). The resulting infinite system of linear equations is truncated to give reliable results for Reynolds numbers between zero and five, and separation, drag, and boundary-layer phenomena are characterized and illustrated with graphs. The Burgers approximation is found to provide good qualitative results near the ellipse, with reasonable quantitative accuracy for the special case of a circular cylinder.
The Weber-Davis model of the solar wind is generalized to include the effects of latitude. The principal assumptions of high electrical conductivity, rotational symmetry, the polytropic relation between pressure and density, and a flow-alined field in a system rotating with the sun, are retained. An approximate solution to the resulting equations for spherical boundary conditions at the base of the corona indicates a small component of latitudinal flow toward the solar poles at large distances from the sun as result of latitudinal magnetic forces.
A method for rapidly estimating the overall forces and moments at supercritical speeds, below drag divergence, of transport configurations with supercritical wings is presented. The method was also used for estimating the rolling moments due to the deflection of wing trailing-edge controls. This analysis was based on a vortex-lattice technique modified to approximate the effects of wing thickness and boundary-layer induced camber. Comparisons between the results of this method and experiment indicate reasonably good correlation of the lift, pitching moment, and rolling moment. The method required much less storage and run time to compute solutions over an angle-of-attack range than presently available transonic nonlinear methods require for a single angle-of-attack solution.
A 'cool' thermal model of the moon's early history is discussed in terms of lunar petrology. Heat from the totally molten outer half of the moon's volume was, according to the model, lost to space and to the lunar interior, so that, barring additions of heat from external sources, all petrogenesis operating exclusively on material of the initially totally molten zone must have occured in an environment of decreasing temperatures. Mare basalts would result from hybridization by migration, mixing, and reequilibration of a variety of intercumulus liquids. Evidence is considered for the layered structure and a significant structural boundary that should result from differentiation of the approximately 350-km-thick initially totally molten zone. Magnetization of lunar rocks is considered.
This paper reviews the development of generalized unsteady aerodynamic theory and presents a derivation of the generalized Possio integral equation. Numerical calculations resolve questions concerning subsonic indicial lift functions and demonstrate the generation of Kutta waves at high values of reduced frequency, subsonic Mach number, or both. The use of rational function approximations of unsteady aerodynamic loads in aeroelastic stability calculations is reviewed, and a reformulation of the matrix Pade approximation technique is given. Numerical examples of flutter boundary calculations for a wing which is to be flight tested are given. Finally, a simplified aerodynamic model of transonic flow is used to study the stability of an airfoil exposed to supersonic and subsonic flow regions.
A method for computing three-dimensional turbulent subsonic flow in curved ducts is being developed. A set of tube-like surface oriented coordinates is employed for a general class of geometries applicable to subsonic diffusers with offset bends. The geometric formulation is complex and no previous treatment of this class of viscous flow problems is known to the authors. The duct centerline is a space curve specified by piecewise polynomials. A Frenet frame is located on the centerline at each axial location. The cross sections are described by superellipses imbedded in the Frenet frame. Duct surfaces are also coordinate surfaces, which greatly simplifies the boundary conditions. The resulting coordinates are nonorthogonal. An approximate set of governing equations is employed for viscous flows having strong flow in a primary flow direction. The derivation is coordinate invariant and the resulting equations are expressed in tensor form. These equations are solved by an efficient alternating direction implicit (ADI) method. This numerical method is generally stable and permits solution in difficult geometries using the general tensor formulation.
A phenomenological model is presented which describes the emission processes occurring within the orificed, hollow cathode. The model defines a region of ion production inside the cathode and assumes that the cathode emission current can be accounted for by considering the ion and electron currents which cross the boundary of this region. Most of the current (approximately 72%) comes from electrons produced by field-enhanced, thermionic emission from a well-defined emission surface at the downstream end of the insert which circumscribes the ion product region. The electrons produced at the emission surface feed the ionization process in the region of ion production; the rest of the current (approximately 28%) is carried by the ions produced in the process. Moving at the Bohm velocity, these ions leave the production volume; they then complete the current path by being collected at various cathode potential surfaces, including the emission surface. The model establishes the ratio of ion to electron currents at the emission surface on the basis of the energy balance at that surface. Experimental results corroborating the principal assumptions of the model are presented and discussed.
Four upstream energetic proton events (30 keV-75 keV), which were simultaneously observed by the ISEE-1 and ISEE-3 satellites, are investigated. A comparison was made between the absolute flux values about 200 earth radii from the bow shock and the flux values several earth radii in front of the bow shock at two different energies. Close to the bow shock the particle distribution is more or less isotropic and indicates relatively strong scattering of these particles in the upstream wave field. At ISEE-3 between 100 and 200 earth radii upstream from the earth's bow shock, the particles move essentially scatter-free from the general bow shock direction. The proton differential intensity at ISEE-3 is a factor of about 4-15 less than at ISEE-1 at 30 keV. The spectra at ISEE-1 are steeper than the spectra at ISEE-3. Flux ratios and spectra are discussed in terms of a first order Fermi acceleration model with a diffusion coefficient increasing approximately linearly with energy and a free escape boundary at some distance upstream.
The development of accurate numerical model of the atmospheric general circulation experiment (AGCE) is discussed. The model will serve both as a design and diagnostic tool for the AGCE, as well as for conducting numerical experiments which otherwise cannot be performed by AGCE. The code in its final form will solve the complete three dimensional nonlinear Navier-Stokes energy equations with the Boussinesq approximation. The code will allow for any thermal boundary conditions and any external forcing in the form of rotation and body forces and will allow for variable thermodynamic coefficients.
One hundred ninety-three silicon sheet samples, approximately 880 square centimeters, were analyzed for twin boundary density, dislocation pit density, and grain boundary length. One hundred fifteen of these samples were manufactured by a heat exchanger method, thirty-eight by edge defined film fed growth, twenty-three by the silicon on ceramics process, and ten by the dendritic web process. Seven solar cells were also step-etched to determine the internal defect distribution on these samples. Procedures were developed or the quantitative characterization of structural defects such as dislocation pits, precipitates, twin & grain boundaries using a QTM 720 quantitative image analyzing system interfaced with a PDP 11/03 mini computer. Characterization of the grain boundary length per unit area for polycrystalline samples was done by using the intercept method on an Olympus HBM Microscope.