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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 181 records · Page 10
All sourcesNASA NTRSDOE OSTI
NASA NTRS1958

Drag Minimization for Wings and Bodies in Supersonic Flow

The minimization of inviscid fluid drag is studied for aerodynamic shapes satisfying the conditions of linearized theory, and subject to imposed constraints on lift, pitching moment, base area, or volume. The problem is transformed to one of determining two-dimensional potential flows satisfying either Laplace's or Poisson's equations with boundary values fixed by the imposed conditions. A general method for determining integral relations between perturbation velocity components is developed. This analysis is not restricted in application to optimum cases; it may be used for any supersonic wing problem.

Heaslet, Max A↗
NASA NTRS2017

Growth Angle: A Microscopic View

A microscopic continuum mechanical model of the growth angle is proposed. It is based on the van der Waals type framework that is used for surface force phenomena. The obtained augmented Laplace type integro-differential equations are, in general, difficult to analyze. Here we focused primarily on the particular case of equal melt and crystal surface energies. We derived an approximate equation for the meniscus shape, and obtained an analytical relationship between the contact and the growth angle. Interestingly, the same result can be obtained using the macroscopic model of Herring. The case of a macroscopically sharp corner is also considered. For this case, the macroscopic angle is not defined and it can be any angle between the contact angles of both flat surfaces. The microscopic model yields the smooth shape for the meniscus that also is not unique, but depends on the initial position of the meniscus.

Mazuruk, Konstantin↗
NASA NTRS1983

Thermodynamic analysis of journal bearings operating under steady state loading in laminar regime

Thermohydrodynamic effects in journal bearings operating under steady load in laminar regime are investigated. An analytical model for the finite and infinitely long journal bearings is formulated. The model includes correction factors for the cavitation effects in the unloaded region of the bearing and the mixing of the recirculating oil and supply oil at the oil inlet. A finite difference computer program is developed to numerically solve the governing equations of the continuity, Reynolds, energy, Laplace heat conduction, and a viscosity-temperature relation simultaneously. The program includes a numerical technique for obtaining an isothermal shaft temperature. The numerical results of temperature distribution and the heat effects on the bearing load carrying capacity agree closely with those of experimental findings. Several different sets of simpler boundary conditions for the energy equation are studied.

Khonsari, M. M.↗
NASA NTRS1979

Off-axis impact of unidirectional composites with cracks: Dynamic stress intensification

The dynamic response of unidirectional composites under off axis (angle loading) impact is analyzed by assuming that the composite contains an initial flaw in the matrix material. The analytical method utilizes Fourier transform for the space variable and Laplace transform for the time variable. The off axis impact is separated into two parts, one being symmetric and the other skew-symmetric with reference to the crack plane. Transient boundary conditions of normal and shear tractions are applied to a crack embedded in the matrix of the unidirectional composite. The two boundary conditions are solved independently and the results superimposed. Mathematically, these conditions reduce the problem to a system of dual integral equations which are solved in the Laplace transform plane for the transformation of the dynamic stress intensity factor. The time inversion is carried out numerically for various combinations of the material properties of the composite and the results are displayed graphically.

Sih, G. C.↗
NASA NTRS1980

Steady, Oscillatory, and Unsteady Subsonic and Supersonic Aerodynamics, production version (SOUSSA-P 1.1). Volume 1: Theoretical manual

Recent developments of the Green's function method and the computer program SOUSSA (Steady, Oscillatory, and Unsteady Subsonic and Supersonic Aerodynamics) are reviewed and summarized. Applying the Green's function method to the fully unsteady (transient) potential equation yields an integro-differential-delay equation. With spatial discretization by the finite-element method, this equation is approximated by a set of differential-delay equations in time. Time solution by Laplace transform yields a matrix relating the velocity potential to the normal wash. Premultiplying and postmultiplying by the matrices relating generalized forces to the potential and the normal wash to the generalized coordinates one obtains the matrix of the generalized aerodynamic forces. The frequency and mode-shape dependence of this matrix makes the program SOUSSA useful for multiple frequency and repeated mode-shape evaluations.

Morino, L.↗
NASA NTRS1981

An analytic solution to the classical two-body problem with drag

The two body problem was analyzed with a specific drag model. The model treats drag as a force proportional to the vector velocity and inversely proportional to the distance to the center of attraction. The solution is expressed in terms of known functions and is of a simple and compact form. The time of flight is expressed as a quadrature in the true anomaly. The results are: (1) development of a vector differential equation which allows analysis of an infinite number of gravitational and drag models; and (2) obtaining the solution of a linear differential equation using the inverse method of laplace transforms.

Mittleman, D.↗
NASA NTRS1983

Time-dependent response of filamentary composite spherical pressure vessels

A filamentary composite spherical pressure vessel is modeled as a pseudoisotropic (or transversely isotropic) composite shell, with the effects of the liner and fill tubes omitted. Equations of elasticity, macromechanical and micromechanical formulations, and laminate properties are derived for the application of an internally pressured spherical composite vessel. Viscoelastic properties for the composite matrix are used to characterize time-dependent behavior. Using the maximum strain theory of failure, burst pressure and critical strain equations are formulated, solved in the Laplace domain with an associated elastic solution, and inverted back into the time domain using the method of collocation. Viscoelastic properties of HBFR-55 resin are experimentally determined and a Kevlar/HBFR-55 system is evaluated with a FORTRAN program. The computed reduction in burst pressure with respect to time indicates that the analysis employed may be used to predict the time-dependent response of a filamentary composite spherical pressure vessel.

Dozier, J. D.↗
NASA NTRS1988

Unsteady thermocapillary migration of bubbles

Upon the introduction of a gas bubble into a liquid possessing a uniform thermal gradient, an unsteady thermo-capillary flow begins. Ultimately, the bubble attains a constant velocity. This theoretical analysis focuses upon the transient period for a bubble in a microgravity environment and is restricted to situations wherein the flow is sufficiently slow such that inertial terms in the Navier-Stokes equation and convective terms in the energy equation may be safely neglected (i.e., both Reynolds and Marangoni numbers are small). The resulting linear equations were solved analytically in the Laplace domain with the Prandtl number of the liquid as a parameter; inversion was accomplished numerically using a standard IMSL routine. In the asymptotic long-time limit, the theory agrees with the steady-state theory of Young, Goldstein, and Block. The theory predicts that more than 90 percent of the terminal steady velocity is achieved when the smallest dimensionless time, i.e., the one based upon the largest time scale-viscous or thermal-equals unity.

Dill, Loren H.↗
NASA NTRS2000

Two-Dimensional Array Beam Scanning Via Externally and Mutually Injection Locked Coupled Oscillators

Some years ago, Stephan proposed an approach to one dimensional (linear) phased array beam steering which requires only a single phase shifter. This involves the use of a linear array of voltage-controlled electronic oscillators coupled to nearest neighbors. The oscillators are mutually injection locked by controlling their coupling and tuning appropriately. Stephan's approach consists of deriving two signals from a master oscillator, one signal phase shifted with respect to the other by means of a single phase shifter. These two signals are injected into the end oscillators of the array. The result is a linear phase progression across the oscillator array. Thus, if radiating elements are connected to each oscillator and spaced uniformly along a line, they will radiate a beam at an angle to that line determined by the phase gradient which is, in turn, determined by the phase difference between the injection signals.The beam direction is therefore controlled by adjusting this phase difference. Recently, Pogorzelski and York presented a formulation which facilitates theoretical analysis of the above beam steering technique. This was subsequently applied by Pogorzelski in analysis of two dimensional beam steering using perimeter detuning of a coupled oscillator array. The formulation is based on a continuum model in which the oscillator phases are represented by a continuous function satisfying a partial differential equation of diffusion type. This equation can be solved via the Laplace transform and the resulting solution exhibits the dynamic behavior of the array as the beam is steered. Stephan's beam steering technique can be similarly generalized to two-dimensional arrays in which the beam control signals are applied to the oscillators on the perimeter of the array. In this paper the continuum model for this two-dimensional case is developed and the dynamic solution for the corresponding aperture phase function is obtained. The corresponding behavior of the resulting far-zone radiation pattern is displayed as well.

Pogorzelski, Ronald J.↗
NASA NTRS1976

Test particle propagation in magnetostatic turbulence. 2: The local approximation method

An approximation method for statistical mechanics is presented and applied to a class of problems which contains a test particle propagation problem. All of the available basic equations used in statistical mechanics are cast in the form of a single equation which is integrodifferential in time and which is then used as the starting point for the construction of the local approximation method. Simplification of the integrodifferential equation is achieved through approximation to the Laplace transform of its kernel. The approximation is valid near the origin in the Laplace space and is based on the assumption of small Laplace variable. No other small parameter is necessary for the construction of this approximation method. The n'th level of approximation is constructed formally, and the first five levels of approximation are calculated explicitly. It is shown that each level of approximation is governed by an inhomogeneous partial differential equation in time with time independent operator coefficients. The order in time of these partial differential equations is found to increase as n does. At n = 0 the most local first order partial differential equation which governs the Markovian limit is regained.

Klimas, A. J.↗
NASA NTRS1981

Research on numerical algorithms for large space structures

Numerical algorithms for analysis and design of large space structures are investigated. The sign algorithm and its application to decoupling of differential equations are presented. The generalized sign algorithm is given and its application to several problems discussed. The Laplace transforms of matrix functions and the diagonalization procedure for a finite element equation are discussed. The diagonalization of matrix polynomials is considered. The quadrature method and Laplace transforms is discussed and the identification of linear systems by the quadrature method investigated.

Denman, E. D.↗
NASA NTRS1968

Vibration of semi-infinite cylindrical shells.

Semiinfinite Timoshenko-Love shell vibration, taking double Laplace transform of both Timoshenko and Vlasov equations of motion with respect to time and axial space variables

Berger, B. S.↗
NASA NTRS1999

Unsteady Aerodynamics - Subsonic Compressible Inviscid Case

This paper presents a new analytical treatment of Unsteady Aerodynamics - the linear theory covering the subsonic compressible (inviscid) case - drawing on some recent work in Operator Theory and Functional Analysis. The specific new results are: (a) An existence and uniqueness proof for the Laplace transform version of the Possio integral equation as well as a new closed form solution approximation thereof. (b) A new representation for the time-domain solution of the subsonic compressible aerodynamic equations emphasizing in particular the role of the initial conditions.

Balakrishnan, A. V.↗