SEARCH · Search NASA
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.
The optimal solution time that minimizes the sum of the two applied impulses necessary to rendezvous is obtained analytically for the Clohessy-Wiltshire equations with a linear gravity model assumption. A plume impingement inequality constraint on the solution is examined, and an optimal policy is developed. Numerical tests are conducted to verify the analysis and to illustrate the optimal solution algorithm.
The effect of solid-liquid interface shape on lateral solute segregation during steady-state unidirectional solidification of a binary mixture is calculated under the assumption of no convection in the liquid. A finite element technique is employed to compute the concentration field in the liquid and the lateral segregation in the solid with a curved boundary between the liquid and solid phases. The computational model is constructed assuming knowledge of the solid-liquid interface shape; no attempt is made to relate this shape to the thermal field. The influence of interface curvature on the lateral compositional variation is investigated over a range of system parameters including diffusivity, growth speed, distribution coefficient, and geometric factors of the system. In the limiting case of a slightly nonplanar interface, numerical results from the finite element technique are in good agreement with the analytical solutions of Coriell and Sekerka obtained by using linear theory. For the general case of highly non-planar interface shapes, the linear theory fails and the concentration field in the liquid as well as the lateral solute segregation in the solid can be calculated by using the finite element method.
The dynamic behavior of a spinning linear-elastic paraboloid subject to nonaxisymmetric deformation is investigated analytically, applying the Rayleigh-Ritz procedure described by Utku et al. (1983). Energy-density, strain-displacement, and velocity-displacement expressions are generated; expressions for the generalized strain and position vector are derived; and the discretized dynamic equations are obtained. Numerical results obtained with a computer-program implementation of the method are presented in extensive tables and graphs. The effects of spin rate and bending rigidity and results for the special case of a spinning disk are included.
A hyperbolic initial-boundary-value problem can be approximated by a system of ordinary differential equations (ODEs) by replacing the spatial derivatives by finite-difference approximations. The resulting system of ODEs is called a semidiscrete approximation. A complication is the fact that more boundary conditions are required for the spatially discrete approximation than are specified for the partial differential equation. Consequently, additional numerical boundary conditions are required and improper treatment of these additional conditions can lead to instability. For a linear initial-boundary-value problem (IBVP) with homogeneous analytical boundary conditions, the semidiscrete approximation results in a system of ODEs of the form du/dt = Au whose solution can be written as u(t) = exp(At)u(O). Lax-Richtmyer stability requires that the matrix norm of exp(At) be uniformly bounded for O less than or = t less than or = T independent of the spatial mesh size. Although the classical Lax-Richtmyer stability definition involves a conventional vector norm, there is no known algebraic test for the uniform boundedness of the matrix norm of exp(At) for hyperbolic IBVPs. An alternative but more complicated stability definition is used in the theory developed by Gustafsson, Kreiss, and Sundstrom (GKS). The two methods are compared.
A Perkin Elmer MGA-1200, turbomolecular-pumped, magnetic sector, multiple gas analyzer mass spectrometer with modified inlet for fast response was characterized for the analysis of hydrogen, helium, oxygen and argon in nitrogen and helium background gases. This instrument was specially modified for the Vanderberg AFB SLC-6 Hydrogen Disposal Test Program, as a part of the Hydrogen Sampling System (H2S2). Linearity, precision, drift, detection limits and accuracy among other analytical parameters for each of the background gas were studied to evaluate the performance of the instrument. The result demonstrates that H2S2 mass spectrometer is a stable instrument and can be utilized for the quantitative analytical determination of hydrogen, helium, oxygen and argon in nitrogen and helium background gases.
Rigorous analysis yields reliable criteria for "best-fit" functions. Improved "curve-fitting" method yields approximate solutions to differential equations of steady-state diffusion. Method applies to problems in which rates of diffusion depend linearly or nonlinearly on concentrations of diffusants, approximate solutions analytic or numerical, and boundary conditions of Dirichlet type, of Neumann type, or mixture of both types. Applied to equations for diffusion of charge carriers in semiconductors in which mobilities and lifetimes of charge carriers depend on concentrations.
A new analytical approach is presented for assessing the reflection of linear Alfven waves in smoothly nonuniform media. The general one-dimensional case in Cartesian coordinates is treated. It is shown that the wave equations, upon transformation into the form of the Klein-Gordon equation, display a local critical frequency for reflection. At any location in the medium, reflection becomes strong as the wave frequency descends past this characteristic frequency set by the local nonuniformity of the medium. This critical frequecy is given by the transformation as an explicit function of the Alfven velocity and its first and second derivatives, and hence as an explicit spatial function. The transformation thus directly yields, without solution of the wave equations, the location in the medium at which an Alfven wave of any given frequency becomes strongly reflected and has its propagation practically cut off.
It is shown analytically and numerically that in certain shear flows the linearized nondivergent barotropic vorticity equation has a limited number of neutral normal modes. The latitudinal structures of these shear flows can be expressed as polynomials of the sine of latitude. The first few such shear flows resemble the gross features of the zonal winds in the atmosphere of the earth at different times and altitudes. The spatial structures of the neutral normal modes in these shear flows are spherical harmonics, and, as a consequence, these modes are also the exact solutions of the fully nonlinear equation because the nonlinear interaction term vanishes identically. The spatial structures of the observed 5-, 4-, 2-, and 16-day free traveling waves in the atmosphere are often identified with the spherical harmonics with indices of (m, n) = ( 1, 2), (2, 3), (3, 3), and ( 1, 4), which are known previously as the neutral normal modes of the nondivergent barotropic vorticity equation in a motionless background state. Our results could explain why these free traveling waves can survive the shearing effects of zonal flows that are far different from rest because these spherical harmonics are also normal modes in certain shear flows that resemble the observations of the atmosphere.
This Letter reports on the results of numerical simulations which may provide a possible explanation for the strahl broadening during quiet solar conditions. The relevant processes involved in the broadening are due to kinetic quasi-linear wave-particle interaction. Making use of static analytical electron distribution in an inhomogeneous field, it is found that self-generated electrostatic waves at the plasma frequency, i.e., Langmuir waves, are capable of scattering the strahl component, resulting in energy and pitch-angle diffusion that broadens its velocity distribution significantly. The present theoretical results provide an alternative or complementary explanation to the usual whistler diffusion scenario, suggesting that self-induced electrostatic waves at the plasma frequency might play a key role in broadening the solar wind strahl during quiet solar conditions.
A linearized Euler solver for calculating unsteady flows in turbomachinery blade rows due to both incident gusts and blade motion is presented. The model accounts for blade loading, blade geometry, shock motion, and wake motion. Assuming that the unsteadiness in the flow is small relative to the nonlinear mean solution, the unsteady Euler equations can be linearized about the mean flow. This yields a set of linear variable coefficient equations that describe the small amplitude harmonic motion of the fluid. These linear equations are then discretized on a computational grid and solved using standard numerical techniques. For transonic flows, however, one must use a linear discretization which is a conservative linearization of the non-linear discretized Euler equations to ensure that shock impulse loads are accurately captured. Other important features of this analysis include a continuously deforming grid which eliminates extrapolation errors and hence, increases accuracy, and a new numerically exact, nonreflecting far-field boundary condition treatment based on an eigenanalysis of the discretized equations. Computational results are presented which demonstrate the computational accuracy and efficiency of the method and demonstrate the effectiveness of the deforming grid, far-field nonreflecting boundary conditions, and shock capturing techniques. A comparison of the present unsteady flow predictions to other numerical, semi-analytical, and experimental methods shows excellent agreement. In addition, the linearized Euler method presented requires one or two orders-of-magnitude less computational time than traditional time marching techniques making the present method a viable design tool for aeroelastic analyses.
Numerous analytical studies have been published for the nonlinear load-contact variations in clearance-fit bolted joints. In these studies, stress distributions have been obtained and failure predictions have been made. However, very little experimental work has been reported regarding the contact or the stresses. This paper describes a fiber-optic technique for measuring the angle of contact in a clearance-fit bolt-loaded hole. Measurements of the contact angle have been made in a quasi-isotropic graphite-epoxy laminate by the optical as well as an electrical technique, and the results have been compared with those obtained from a finite-element analysis. The results from the two experimental techniques show excellent agreement; the finite-element results show some discrepancy, probably due to the interfacial frictions.
The evaluation of sensitivity coefficients which are the changes in the eigencharacteristics with respect to changes in the structural parameters is important in the identification of structural systems. In such studies the commonly used linearized sensitivity coefficients for system identification have occasionally resulted in poor convergence or even divergence during the iteration process to update analytical models for better correlation with the test data. Nonlinear sensitivity coefficients and nonlinear correction terms, usually eliminated during the linearization process, have been developed to evaluate sensitivity coefficients of linear systems. Application to computer simulated example problems indicates a more rapid and stable convergence of the iteration processes to update the analytical model for the improvement of the correlation with test data. The successful application of combining the nonlinear sensitivity coefficients and nonlinear correction terms with the Multiple Boundary Condition Tests enhances the ability to validate large space structures by ground tests.
The relative motion problem is analyzed, as a linearized case, and as a numerically determined solution to provide a time history of the geometries representing the motion state. The displacement history and the hodographs for families of solutions are provided, analytically and graphically, to serve as an aid to understanding this problem area. Linearized solutions to relative motion problems of orbiting particles are presented for the impulsive and fixed thrust cases. Second order solutions are described to enhance the accuracy of prediction. A method was developed to obtain accurate, numerical solutions to the intercept and rendezvous problem; and, special situations are examined. A particular problem related to relative motions, where the motion traces develop a cusp, is examined in detail. This phenomenon is found to be dependent on a particular relationship between orbital eccentricity and the inclination between orbital planes. These conditions are determined, and, example situations are presented and discussed.
Theoretical models of planetary-atmosphere tidal fields are examined analytically, comparing models based on geometric-height coordinates with those employing log-pressure coordinates. The relationship between the linearized meteorological variables in the two systems is explored for classical tidal theory and its reduction to the Laplace tidal equation, and it is shown that identical horizontal and vertical equations are obtained. Also considered are the tidal zonal-mean bilinear flux convergences and their Eliassen-Palm formulations. Numerical results for problems involving the earth and Mars atmospheres are presented in graphs and discussed.
Investigation is made of the properties of low frequency transverse waves in a two-fluid solar wind having a radial magnetic field and radial streaming velocity. In order to examine what effects this streaming medium has on the waves, linearly polarized waves are decomposed into left and right circularly polarized waves. Computation is made of analytic expressions valid to first order for the radial amplitude and phase dependence of these constituent waves. It is shown that after travelling a given distance r, these waves have different amplitudes and phases. The former result causes their superposition to become elliptical rather than linear. The latter causes the axis of the ellipse of polarization to rotate through a well-defined angle. Analytic expressions are obtained for the eccentricity of the ellipse and for the angle of rotation. In analogy with regular Faraday rotation, in which the plane of polarization of a linear polarized wave rotates, the effect is denoted as generalized Faraday rotation.
Approximated maximal vibratory response of linear excited system to time modulated stationary random vibration
The paper proposes a reduced-order analytical model of a spur gear pair which consists of two identical spur gears, two identical flexible shafts, and four identical rolling element bearings of a given radial stiffness. The error associated with the undamped eigensolution is estimated by a comparison with a benchmark finite element model.
An analytical evaluation of the perturbations to mesoscale atmospheric flows induced by thermal inhomogeneities in the convective boundary layer is presented. The time evolution of these perturbations as a function of the intensity and of the horizontal and vertical scales of the diabatic forcing is studied. The problem is approached using Laplace transform theory for the time behavior and Green function theory for the spatial structure. Results show that the growth of the atmospheric perturbations closely follows the growth of the convective boundary layer; the transient being characterized by a number of inertia-gravity oscillations of decreasing intensity. The vertical scale is determined by the depth of the convective boundary layer; and the horizontal scale is determined by the local Rossby deformation radius. Sinusoidally periodic thermal forcing induce periodic atmospheric cells of the same horizontal scale. The intensity of mesoscale cells increases for increasing values of the wave number, reaches its maximum value when the wavelength of the forcing is of the order of the local Rossby radius, and then decreases as the wavelength of the forcing decreases.